optimisation of streamgauge and raingauge network …

Optimization of Streamgauge and Raingauge Network for Upper Bhima Basin

CWPRS Report No: 4797 December 2010 1

OPTIMISATION OF STREAMGAUGE AND RAINGAUGE NETWORK F OR UPPER

BHIMA BASIN

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Report No.: 4797 Month: December 2010 ________________________________________________________________________________ 1. Introduction

1.1 General Hydrological and related meteorological data are collected through a network of specialized instruments to provide information on the quality and quantity of water moving through catchments and along rivers of a country. Water data, in its entire gamut, collected through the network, cater to the hydrological information needs of the region under purview; and constitute the Hydrological Information System (HIS) for the area. Ideally, the water data emanating from the network should enable accurate estimation of the hydrological regime of the region. HIS essentially provides the data required for planning, design and management of water resources of the regions; including operation and management of flood protection measures in inundation prone areas. Hydrological information system for a typical region comprises sub-systems for data collection & storage, data communication & transmission, data transformation for producing information and information-communication. Water data are collected, processed and stored by agencies such as the Central Water Commission (CWC), India Meteorological Department (IMD), State Irrigation Departments/ Water Resources Departments (WRDs), etc. Basically, the hydrological networks operating in different river basins of the country, and maintained by one or more of the agencies entrusted with the task, provide the data forming the core of HIS. The functions of hydrological services or equivalent agencies inter alia include: establishment and supervision of network; collection, processing and publication of basic data; preparation of reports on water resources; research & development; analysis/ design studies; and training. A national hydrological network will provide data that will be used for many types of decisions. Often, it is difficult to anticipate the uses to which water data will be put to use. Network design is a complex facet of hydrological engineering. What constitutes a hydrological network itself is open to debate, with many aspects such as hydrological phenomena/ processes under consideration, geographical scope, stage of water resources development in an area, and intended use of data coming into inter-play. In practice, hydrological network design is an evolutionary process, wherein a minimum network is established early in the development of a geographical area, and the network is reviewed and upgraded periodically until an optimum network is attained. Different types of hydrological and meteorological data that need to be a part of HIS for a region, depending on its geographical scope. Precipitation, gauge-discharge data for rivers/



lakes/ reservoirs, evaporation, sediment transport, water quality, water temperature, soil moisture, ground water, etc. are some of the major types of data that are relevant in this respect. Data on discharge and water level are basic to the solution of most design and operation problems. Information on precipitation is indispensable to water resources development and management. Establishment of networks on an integrated basis is very important, especially as regards streamflow and precipitation networks. In some cases, both precipitation and streamflow networks are operated by the same agency, though often in practice, such networks are managed independently. Obviously, good cooperation is required for operating and developing networks. For the purpose of this study, hydrometric network for streamflow related measurements, and raingauge networks for precipitation related data, is primarily considered. 1.2 Hydrology Project

Hydrology Project (HP) is currently being implemented by the Government of India (GoI), with external support from the World Bank. The primary objective of the project is improvement of the country’s institutional and technical capabilities to measure, collate, analyze and disseminate quality hydrometeorological data concerning all aspects of surface water and ground water resources. Hydrology Project I (HP I), the first phase of the project, was implemented during 1996-2003. In all, five central agencies and nine states participated in the project. The central Implementing Agencies (IAs) were: Central water Commission (CWC), Central Water and Power Research Station (CWPRS), Central Ground Water Board (CGWB), India Meteorological Department (IMD) and National Institute of Hydrology (NIH); and the State IAs: Andhra Pradesh, Chattisgarh, Gujarat, Karnataka, Kerala, Madhya Pradesh, Maharashtra, Orissa and Tamil Nadu. Within the overall framework of HP, CWPRS performed the role of a facilitator in R&D, training, activities involving special studies and technical support. Specific tasks undertaken by CWPRS included: activities related to institutional strengthening such as upgradation of Current Meter Rating Trolley (CMRT) and setting up of Hydrometric Instrumentation Services Facility (HISF); R&D studies and training. Three R&D studies, namely a) Reservoir Sedimentation Survey of Gangapur reservoir, b) Field Investigations and Development of Mathematical Model for Predicting Water Quality in the Panshet and Ujjani Reservoir Systems’ and c) Estimation of Irrigation Return Flows in the Kukadi Canal Command Area (in association with Maharashtra) were conducted earlier under HP I. Second phase of the project, namely Hydrology Project II (HP II) is currently under implementation as a six-year project. The project commenced in June 2006; and is scheduled to continue till June 2012. The IAs of HP II included, in addition to the IAs involved in HP I, the central agencies of Central Pollution Control Board (CPCB) and Bhakra-Beas Management Board (BBMB); and the states of Goa, Himachal Pradesh, Pudhucherry and Punjab.



The primary objective of HP II is to extend and promote the sustained and effective use of the Hydrological Information System (HIS) developed under HP I, by all potential users who are concerned with water resources planning and management. This is to be achieved by: i) strengthening the capacity of hydrology departments to develop and sustain the use of the HIS for hydrological designs and decision tools; ii) improving the capabilities of implementing agencies at state/ central level in using HIS for efficient water resources planning and management to meet the country’s poverty reduction objectives; iii) establishing and enhancing user-friendly, demand-responsive and easily-accessible HIS; and iv) improving access to the HIS by public agencies, civil society organizations and the private sector through supporting outreach services. Towards this end, HP II essentially consists of three main components: i) institutional strengthening, ii) horizontal expansion, and iii). vertical extension, CWPRS activities are restricted to the two categories afore-mentioned namely institutional strengthening and vertical extension. The vertical extension component involves a vertical shift from collection and processing HIS data towards the use of such data in the development of decision support system (DSS) for integrated planning and management of water resources in river basins/ sub-basins and including such activities as early flood warning, drought measurement, conjunctive use of surface and ground water and integrated operation of reservoirs. The specific activities planned under vertical extension include: development of hydrological design, decision support systems and purpose driven studies. Purpose driven studies under HP II are oriented to address issues that are relevant to the implementing agencies. Studies are expected to address surface/ ground water issues that are relevant to implementing agencies. Within the said provision under HP II for undertaking PDS, the present study of `Optimization of streamgauge network for Upper Bhima basin’ has been taken up. The ensuing Section 1.3 below details the rational for taking up the purpose driven study (PDS) as also scope of the proposed study. 1.3 Purpose Driven Study

A number of river basins constitute the geographical area of any state. Major rivers flowing wholly/ partly through Maharashtra include Krishna, Godavari, Tapi, Narmada, Mahanadi; and other west-flowing rivers originating from the Western Ghats. Amongst the major rivers, Narmada and Tapi flow to the west, and Godavari and Krishna to east. As is the practice elsewhere in the country, the hydrologic and meteorological stations in operation in different river basins in the state are controlled by the CWC; Water Resources Department (WRD), Government of Maharashtra (GoM); IMD and other agencies. WRD, GoM, is the primary agency entrusted with collection of hydrometeorological data relating to Maharashtra. The HIS for the state, in turn, is used to assess the quantum of water available in each basin/ sub-basin to facilitate optimum use of the water resources. The existing hydrometeorological network of Maharashtra includes 264 Gauge-Discharge (GD) stations, 641 Ordinary Rain Gauge (ORG) stations, 340 Self Recording Rain Gauge (SRRG) stations and 153 Full Climatic Stations (FCS). This network was developed over a period of time to meet the emerging needs from time-to-time for the basin.



GoM decided to review the hydrometric network in Maharashtra, in relation to such factors as overall objectives, minimum/ ideal/ optimal network, available budget and overall benefits of the water data. The review is oriented towards getting the network tuned to the present-day data needs essentially by proposing new stations wherever necessary, and deleting stations where not needed. Towards this, a purpose driven study (PDS) for optimization of streamgauge network was proposed by GoM jointly with CWPRS under existing provisions of Hydrology Project II (HP II). During discussions it was decided to conduct the detailed study for a pilot basin, namely Upper Bhima up to Ujjani reservoir. The study was approved by the Hydrological Information System Management Group (Technical) [HISMG-T]; and concurred by World Bank [vide MoWR letter No. 12/ 94/ 2005-B&B/ Vol. 5/ 1821-49 dated 20/5/2009]. Scope of the present study includes checking adequacy of the existing GD and raingauge network in the Upper Bhima basin, and detailed investigation on the preliminary review carried out by GoM. This report examines the methodology used in optimization of GD and associated raingauge networks under consideration; and arriving at the optimum networks for different regions, without compromising accuracy of the water data. While conducting the review, it is fully recognized that further changes in the network will definitely be needed in future. 1.4 Objectives

A monitoring network is based upon two considerations, namely the monitoring objectives and the physical characteristics of the system to be monitored. The identification of the monitoring objectives is the first step in the design and optimization of monitoring systems. A combination of analytical and practical approaches is adopted for optimizing the Upper Bhima GD network of WRD, Maharashtra. A Generalized Least Squares (GLS) approach is used to establish the empirical relationships between streamflow statistics of interest with basin characteristics such as Catchment Area (CA) and meteorological variables such as Mean Annual Precipitation (MAP), and to rank GD stations according to their influence on streamflow statistics under consideration. Monte Carlo studies by Stedinger & Tasker (1985, 1986) and Tasker & Stedinger (1987) document the GLS procedure to develop empirical relationships between streamflow statistics and basin characteristics. The GLS algorithm takes into account for differences in record length, variations of flows at different sites, and cross-correlation among concurrent streamflows. Spatial hydrologic regression is performed under GLS framework in the present study to review the network. Adequate number of rain gauges should be available, upstream of every streamgauging station, to estimate the areal rainfall with a specified accuracy. For a study of the nature, the raingauge network has to be considered in conjunction with surface water and groundwater networks. The former should have sufficient spatial coverage such that all GD stations in the hydrometric network are fully covered. This means that dependent on the objectives, rainfall-runoff computations can be made and/ or water balance quantification done. For the purpose of this study, the objective of the raingauge network in Upper Bhima basin is taken



to be reliable estimation of areal rainfall for the region, commensurate with the streamgauging network. Typically, rains in the Upper Bhima basin are almost entirely concentrated in the months June to September. The estimation error in the average monthly and annual rainfall, after computing spatial correlation structure of rainfall in the catchment, has been used as a measure of effectiveness for raingauge network optimization. Sections 2 and 3 of this report deal with the study area and the data availability for the study respectively; and Section 4 the methodology adopted for hydrologic network design. Sections 5-8 deal with review of streamgauge network and its optimization. Section 9 elaborates raingauge network optimization; and in Section 10 results of the study are summarized.



2. Study Area Bhima is a major tributary of Krishna river; and one of the two majors rivers of Maharashtra, with the other being Godavari. Bhima originates at Bhimashankar in the Sahyadri Ghats at the elevation of MSL 700m. The banks of Bhima are densely populated, and form fertile agricultural area. The river is prone to frequent flooding due to heavy rainfall during the monsoon season. Bhima flows southeast for a long journey of 725 km, before joining Krishna River at Krishna, Raichur district, Karnataka. The total catchment area of Bhima is 48,631 km²; comprising 219 sub-watersheds. For the present study, Upper Bhima basin up to Ujjani reservoir is considered. The Upper Bhima basin is located in the western part of Maharashtra between 170 53' N to 190 24' N latitude and 730 20' E to 750 18' E longitude. The basin covers a geographical area of 14,712 km2; comprising 68 sub-basins. Of the total geographical area under study, 25 % is hilly and/or highly dissected, 55 % plateau and the remaining plain area. Figure 2.1 gives a location map of Upper Bhima basin up to Ujjani.

Figure 2.1: Location of Upper Bhima basin up to Ujjani

About 25 % of the Upper Bhima basin, lying in the western zone, falls in good rainfall region. Remaining 75 % is rainfall deficit region; having annual rainfall less than 700 mm. In the Parner-Shirur region, rainfall is normally less than 600 mm. Of the total rainfall, 85 % comes from South-West monsoon during June-September, 11 % from North-East monsoon during September-December, and about 4 % after December. About 89 % of the basin is classified as drought-prone.



During the journey of Upper Bhima, many smaller rivers join it. The main tributaries of the river are: Ghod and Mula-Mutha rivers. Mula rises in Mulshi taluka, and Mutha in Velhe. River Ghod and its tributaries Kukadi and Meena also rise in the Sahyadri Ghats. The places of origins of the tributaries of Bhima fall in comparatively heavy rainfall region. Length of Bhima up to Ujjani is 275 km. The basin is spread over the three districts of Pune, Solapur and Ahmednagar in Maharashtra; and covers 13 talukas. Table 2.1 gives details relating to Bhima and its tributaries up to Ujjani reservoir.

Table 2.1: Details of Main River and Tributaries; Upper Bhima basin up to Ujjani reservoir

Origin Confluence No River/ Tributary

Streams Length (km) Place Altitude

(m) with Altitude

(m)

1 Bhima 275 Bhimashankar 700 Krishna in Raichur district, Karnataka 343

2 Indrayani 83 Aapti 900 Bhima --- 3 Kundalika --- --- --- Indrayani --- 4 Bhama --- --- --- Bhima --- 5

Bhima

Wel 60 --- --- Bhima --- 6 Pawana 55 Mula 900 Mula near Dapodi 439

7 Mula 50 Mazgaon --- 522

8

Mula-Mutha

Mutha 64 Davjhar 900

Mutha meet with Mula near Khadki. Mula-Mutha joins Bhima near Pargaon 564

9 Ghod 170 Gawadewadi 1,000 Bhima near Daund 498 10 Meena 53 Amboli --- Ghod --- 11 Kukadi 85 Ghatghar --- Ghod near Shirur 562 12 Pushpavat

i 35 Khireshwar --- Kukadi ---

13 Arr --- --- --- Kukadi --- 14 Hanga --- --- --- Ghod --- 15

Ghod

Palsi --- --- --- Ghod ---

The region, covering Upper Bhima basin, is highly industrialised and urbanised; resulting in substantial water quality problems in the region including Ujjani reservoir. Average annual water yield of the Upper Bhima basin up to Ujjani is 7,594 Mm3. There are 14 major and medium dams in the Upper Bhima basin. Major dams in the basin include: Pavana, Ghod, Mulshi (Tata), Khadakwasla, Chaskaman and Ujjani. The municipal corporations of Pune and Pimpri-Chinchwad, forming the Pune Metropolitan Region, constitute a part of this basin. Provisional population of the basin, as per 2001 census, is 73.72 lakh.

It is estimated that annually about 221 Mm3 water is utilized for domestic and 77 Mm3 for industrial uses. The present requirement of water for non-irrigation use is projected to be 298 Mm3; which is expected to increase to 844 Mm3 by 2030.

Hydrological challenges of the Upper Bhima basin are identified to be: drought management, flood management in Pandharpur (situated downstream of Ujjani dam) and Pune cities (due to releases from Panshet, Warasgaon, Temghar and Khadakwasala reservoirs), high evaporation from Ujjani reservoir; and river water pollution primarily resulting from industrial effluents and domestic waste.



3. Data Availability Figure 3.1 gives the map of Upper Bhima basin. The existing hydrometeorological network in the Upper Bhima basin, as of now includes 14 GD stations, 44 raingauge stations with 44 having ORG & 8 with SRRG facility; and 5 FCS. Daily streamflow data for 14 GD stations in the basin, namely Aamdabad, Askheda, Budhawadi, Chaskaman, Dattawadi, Kashti, Khamgaon, Nighoje, Pargaon, Paud, Pimpale-Gurav, Rakshewadi, Shirur and Wegre - having different record lengths for each station with a minimum 11 years for Pimpale-Gurav and a maximum 35 years for Chaskaman - are available. For optimization studies for raingauge network, historical rainfall data for 44 raingauge stations were used. Physiographic characteristics of the catchment/ sub-basins, used in the study, included drainage area, latitude and longitude and the meteorological variable - mean annual precipitation.

Figure 3.1: Existing GD and raingauge stations in Upper Bhima basin

3.1 Validation of Hydrometeorological data:

The procedure adopted by State Data Processing Center of WRD, Maharashtra for validation of the hydrometeorological data, which is used in the current PDS, is summarized below.



Two software were used for validation of hydrometeorological data namely SWDES (Surface Water Data Entry Software) and HYMOS (Hydrological Modeling System). SWDES is used for data entry and primary validation and HYMOS is used for secondary and hydrological validation.

3.1.1 Data Entry and Primary Validation:

Primary validation of rainfall data is carried out at the Sub-divisional level using primary module of dedicated data processing software SWDES and is concerned with data comparisons at a single station:

a. For a single data series, between individual observations and pre-set physical limits based on historical data. (Maximum, minimum, upper warning and lower warning limits)

b. Between two measurements of a variable at a single station, e.g. daily rainfall from a daily rain gauge (standard rain gauge) and an accumulated total from autographic rain gauge.

c. Multiple plot of rain gauge stations shows trend of the rainfall for selected stations having same topography.

d. Similarly trend of water level can be observed by plotting water levels of the river gauging stations, which are on the same river

3.1.2 Secondary validation:

Secondary validation is carried out at Division level. However since comparison with neighbouring stations is limited by Divisional boundaries, the validation of some stations near the Divisional boundaries is carried out at the State Data Processing Center, Nashik.

a. Secondary validation of rainfall data:

Following tests are carries out for secondary validation of rainfall data:

� Spatial correlation test � Screening of data series � Scrutiny by multiple time series graphs � Scrutiny by tabulations of daily rainfall series of multiple stations � Spatial homogeneity test of rainfall � Checking for systematic shifts using double mass analysis

b. Secondary validation of river gauging data:

For secondary validation of water level data, transformation from water level to discharge through the use of stage discharge relationships is done. Validation of this stage discharge curve called as rating curve is done by comparing rating curve of current year with the rating curves of previous years.

3.1.3 Hydrological Validation:



Hydrological validation is carried out at State Data Processing Center, Nashik. After secondary validation of the rainfall, climatic, water level and discharge data, hydrological validation is carried out on the same data. In hydrological validation the comparison of two different parameters such as rainfall and resulting runoff of a basin is done. Also isolines for rainfall and climatic parameters on ten-daily, fortnightly, monthly and yearly intervals are drawn to check the pattern in different months of the year or compared the pattern of current year with that of previous years.

3.1.4 Inter-agency validation

Inter-agency validation of meteorological data is carried out with Indian Meteorological Department (IMD) data and hydrological data with Central Water Commission (CWC) data.



4. Network Design 4.1 Hydrological Information System

A watershed can be viewed as a landmass wherein the water incident upon it flows overland to a common outlet. Hydrological Information System (HIS) for a region comprises sub-systems for water data collection and storage, data communication/ transmission, data transformation for producing information and information-communication. HIS provides reliable data for planning, design and management of water resources and for related research activities; and supports informed decision making. In India, primary data for HIS are collected, processed and stored by agencies such as CWC, IMD, State Irrigation Departments/ WRDs, etc. Basically, the hydrological networks operating in different river basins of the country, and maintained by one or more of the agencies entrusted with the task, provide the data forming the core of HIS.

HIS for a region, possibly covering a number of river systems/ subsystems, caters to the varied needs of water resources planning and management such as: assessment of regional/ national surface water resources; investigation of environmental, economic and social impacts of current and planned management practices on water resources and analysis and forecasting of extreme events of floods and droughts. Most problems arising from activities relating to planning and management of water resources are solved, and decisions made using the available information; namely facts, coupled with analysis and judgment. In this problem-solving process, if the relevancy of the information is higher, higher the quality of decision; and lower the uncertainty and element of risk.

A national hydrological network will provide water data to the HIS, which will be used for many types of decisions. Often, it is difficult to anticipate the uses to which water data will be put to use. Network design is a complex facet of hydrological engineering. What constitutes a hydrological network itself is open to debate, with many aspects such as hydrological phenomena/ processes under consideration, geographical scope, stage of water resources development in an area, and intended use of data coming into inter-play. In practice, hydrological network design is an evolutionary process, wherein a minimum network is established early in the development of a geographical area, and the network is reviewed and upgraded periodically until an optimum network is attained. Different types of hydrological and meteorological data need to be part of HIS for a region, depending on its geographical scope. Precipitation, gauge-discharge data for rivers/ lakes/ reservoirs, evaporation, sediment transport, water quality, water temperature, soil moisture, ground water, etc. are some of the major types of data that are relevant in this respect. Data on discharge and water level are basic to the solution of most design and operation problems. Information on precipitation is indispensable to water resources development and management. Establishment of networks on an integrated basis is very important, especially as regards streamflow and precipitation networks. In some cases, both precipitation and streamflow networks are operated by the same agency, though often in practice, such networks are managed independently. Obviously, good cooperation is required for operating and developing networks. For the purpose of this study, hydrometric network for streamflow



related measurements and rain gauge networks for precipitation related data are primarily considered. HIS output is having a wide variety of users, both in the public services domain and private sector. Users fall under the two broad clusters of: i) large scale and repeat users, and ii) occasional or one-time users. Large scale and repeat users of HIS generally belong to various policy/ operational level government departments, financial institutions, command area development authorities, irrigation/ water resources departments, Non-Government Organisations (NGOs), etc. Occasional users are of two types: i) those who need to find and use water in a micro-geographical area for their own use, and ii) those who need to find and use water for commercial or community activities.

4.2 Hydrological Measurements With increase in world human population and living standards, demand for water is rising faster today than at any time in the history of this planet. This needs to be seen in the context of diminishing water resources to support life in rivers, lakes, wetlands and similar habitats. Personnel with responsibilities for water resources need to be better equipped to deal with the issue. A hydrological network, the sum total of all the fixed hydrological instruments and stations providing hydrometric measurements in a basin or region, makes available the data used for assessing water resources for a variety of other purposes. The purpose can be many, say planning and management of natural resources, flood management, water quality control and environmental monitoring. There are many different kinds of hydrological and meteorological data that needs to be a part of the HIS for a region, depending on its geographical scope. Precipitation, gauge-discharge data for rivers/ lakes/ reservoirs, evaporation, sediment transport, water quality, water temperature, ice cover on rivers/ lakes/ reservoirs, soil moisture, ground water, etc. are some of the major types of data that are relevant in this respect. Discharge and water level data are basic to the solution of most design and operation problems. Information on precipitation is indispensable to water resources development and management. Establishment of various networks on an integrated basis is very important, especially as regards streamflow and precipitation networks. In some cases, both the networks are operated by the same agency. But often, each of these networks is managed independently. Obviously, good cooperation is required for operating and developing the networks. For the purpose of this study, hydrometric network for streamflow related measurements and rain gauge networks for precipitation related data are primarily considered. Hydrometric measurements are required to measure the variables of the hydrological cycle. Most of the instruments for such measurements need to be maintained in continuous operation, and many are exposed to the weather in harsh environment. These requirements impose a need for high standards of design and manufacture for hydrometric instruments. The main elements of the hydrologic cycle for which hydrometric instruments are required include precipitation, gauge (for open channels), flow velocity, groundwater characteristics, evaporation and soil moisture.



Countrywide networks have usually developed over a period of time in order to meet the emerging national/ international needs from time to time. Examples of stages of evolvement of a national network can be: flood prevention, development of hydropower, control of water pollution, water resources management, contribution towards global environmental monitoring, etc. The above scenario is in contrast to the networks set up by scientific design, which have been employed particularly in the establishment of representative and experimental basins and in specific projects and studies. Such networks are normally single-purpose in their objective. They have often been designed to provide spatially distributed random samples of the hydrological variable concerned. Alternatively, they produce systematic samples, or stratified random samples or samples of other types across the basin or region. In short, for hydrological design and water resources assessment purposes proper estimates of river flow and river stages are required. Their measurement is the domain of hydrometry. The majority of streamflow measurement techniques are based on velocity area method. Though the use of float measurements is sometimes inescapable, current meter gauging is the most widely favoured velocity-area method technique. A recommended set of guidelines for streamflow measurement techniques are available in the Design Manual on Hydrometry, Vol. 4, prepared under Phase I of the Hydrology Project. The types of streamflow measurement techniques for which details are available include: current meter gauging sites, float measurement, discharge monitoring by Acoustic Doppler Current Profiler (ADCP), slope-area method, selection of natural control (rated section) station site, and selection of artificial control sites. 4.3 Network Design - General Requirements A hydrometric network, essentially forming a subsystem of the full-fledged hydrologic network, is a collection of stream gauging stations in a river basin, wherein essential data such as river stage, discharge, sediment characteristics, etc. are measured as per design of the specific station. Ideally, the water data emanating from a hydrometric network should enable accurate estimation of the hydrological regime of the region. The network provides water data needed for planning, design and management of the natural resources of the region. In flood prone areas, the hydrologic network inter alia provides data for planning, design, operation and management of flood protection measures. A national hydrological network will provide data that will be used for many types of decisions. Often, it is difficult to anticipate the uses to which water data will be put to use. What constitutes a hydrological network itself is open to debate, with many aspects such as hydrological phenomena/ processes under consideration, geographical scope, stage of water resources development in an area, and intended use of data coming into inter-play. In practice, hydrological network design is an evolutionary process wherein a minimum network is established early in the development of a geographical area, and the network is reviewed, and upgraded periodically until an optimum network is attained.



There are many different kinds of hydrological and meteorological data that needs to be a part of the HIS for a region, depending on its geographical scope. Precipitation, gauge-discharge data for rivers/ lakes/ reservoirs, evaporation, sediment transport, water quality, water temperature, ice cover on rivers/ lakes/ reservoirs, soil moisture, ground water, etc. are some of the major types of data that are relevant in this respect. Discharge and water level data are basic to the solution of most design and operation problems. Information on precipitation is indispensable to water resources development and management. Establishment of various networks on an integrated basis is very important, especially as regards streamflow and precipitation networks. In some cases, both the networks are operated by the same agency. But often, each of these networks is managed independently. Obviously, good cooperation is required for operating and developing the networks. For the purpose of this study, however, hydrometric network for streamflow related measurements and rain gauge networks for precipitation related data are primarily considered. 4.4 Hydrometric Network Design

4.4.1 General Considerations Aspects involved in hydrometric network design for a region include inter alia the following basic components.

i) Classification of stations ii) Minimum networks iii) Networks for large river basins iv) Networks for small river basins v) Networks for deltas and coastal flood plains vi) Representative basins vii) Sustainability viii) Duplication avoidance, and ix) Periodic re-evaluation

i) Classification of stations All stations in the network need to be classified according to type of use of the station; which may range from stations for: management and other decisions, regional and long-term analysis of water resources, design and planning purposes, etc. A network can be national, regional, representative or experimental. Measurements at individual stations might be carried out during one year up to several years. Primary stations are maintained as key/ principal/ benchmark stations; with measurements continued for a long period of time to generate representative flow series of the river system, and provide general coverage of a region. Secondary stations are essentially short duration stations, intended to be operated only for such a length of period that is sufficient to establish the flow characteristics of the river or stream, relative to those of a basin gauged by the primary station.



Special purpose stations are usually required for the planning and design of projects or special investigations; and are discontinued when their purpose is served. The purpose could vary from design, management and operation of a project to monitoring and fulfillment of legal agreements between states in respect of interstate basins. Primary and secondary stations may also at times serve as special purpose stations. ii) Minimum networks A minimum network should include at least one primary streamflow station in each of the climatologic and/ or physiographic areas in a state. A river that flows through more than one state should invariably be gauged at the state boundary. At least one primary gauging station should be established in those basins having potential for future development. A minimum network should also include special stations, as required. Where a project is of particular socio-economic importance to a state/ region, it is essential that a gauging station is established for planning, design and operational purposes. At times, special stations are required to fulfill a legal requirement, say quantification of the compensation releases or abstraction controls. Benefit-cost ratios for special stations are usually the highest, and can often help support the remainder of the hydrometric network.

iii) Networks for large river basins

A primary station might be planned at a point on the main river where the mean discharge attains its maximum value. For rivers flowing across the plains, this site is usually at the downstream region of the river; but immediately upstream of the point where the river normally divides itself into branches before joining the sea or a lake or crosses a State boundary. In the case of mountainous rivers, it is the point where water leaves the mountainous reach and enters the plain land. Subsequent stations are established at sites where significant changes in the volume of flow are noticed, namely below the confluence of a major tributary or at the outflow point of a lake etc. If a suitable location is not available below a confluence, the sites can be located above the confluence, preferably on the tributary.

While establishing sites, care should be taken to ensure that no other small stream joins the main river so as to avoid erroneous assessment of the contribution of the tributary to the main river. In the case of a large river originating in mountains, though the major contribution is from the upper regions of the basin, several stations may need to be located in the downstream stretch of the river. Such stations are intended to provide an inventory of water loss from the channel by way of evaporation, infiltration; and by way of utilization for irrigation, power generation, industrial and other domestic needs.

The distance between two stations on the same river may vary from 30 km to several hundred kilometers; depending on the volume of flow. The drainage areas, computed from the origin up to consecutive observation sites on a large river, should preferably differ by more than 10 percent, such that the difference in quantities of flow is significant. The uncertainties in discharge values, especially for high flows, are unlikely to be less than ±10 percent. However, every reasonable attempt should be made to minimize such



uncertainties. When tributary inflows are to be known, it is generally better to gauge the river directly, rather than deriving the flow from the difference of a downstream and an upstream station along the main. A more accurate discharge record for a main stream is obtained from monitoring the feeder-rivers, than by a station on the main stream alone, though at an additional cost.

iv) Network for small river basin

There are a large number of independent rivers, which flow directly into the sea, as is the case of west flowing rivers of Maharashtra. In such cases, the first hydrological observation station might be established on a stream that is typical of the region. Further stations can be added to the network so as to widely cover the area. Streams in a particular area having meager yields should not be avoided from inclusion in the network. Absence of a station on a low flow stream can lead to wrong conclusions on the water potential of the area as a whole, evaluated on the basis of the flow in the high flow streams. Care needs to be exercised in designing the network so as to ensure that all distinct hydrologic areas are adequately covered. However, in practice, it may not be possible to operate and maintain gauging stations on all the smaller watercourses. Hence, representative basins may need to be selected, and the data from those used to develop techniques for estimating flows for similar un-gauged sites.

v) Network for deltas and coastal flood plains

Deltaic areas where gradients are usually low and channels bifurcate are often important as water use is productive. Such areas need monitoring. This is particularly important since deltas are dynamic systems, which often continually change. However, the type of network required may differ from more conventional river basins. On account of the low gradients, it is often not possible to locate stations with stable stage-discharge relationships; and variable backwater effects can occur due to tidal influences and/ or changes in aquatic vegetation growth. Stage readings should be made at all principal off-takes/ bifurcations/ nodes in the system; which can be supplemented by current meter gauging wherever required. At some sites, consideration may need to be given to installing a slope-area method station.

vi) Representative Basin

When gauging stations are included in a network to obtain representative data from a particular physiographic zone, it is better if the chosen basins are those with water resource relatively underutilized wherein the basins can be considered to be close to their natural state.

vii) Sustainability

As regards hydrometric networks, sustainability is of paramount importance. It is a relatively straightforward task to design a dense network of streamflow stations. However, the implementation and operation of a network is lot more difficult. Experience shows that there is a tendency to adopt an idealistic approach and attempt to have as many stations as



possible. There are many examples of networks throughout the world that are no longer functioning well due to issues that can be attributed to financial support, skilled manpower and logistic support such as vehicles. It is far better to operate and maintain 10 gauging stations well, than to operate and maintain double the stations badly. Higher quality data from fewer stations is preferable to lower quality of data from a greater number of stations.

viii) Duplication avoidance Since more than one organization such as State WRDs, CWC, local bodies, etc. is generally responsible for establishment of gauging stations, it is essential that the activities are coordinated such that they complement each other, with duplication of efforts avoided. ix) Periodic Re-evaluation Gauging station networks require periodic re-evaluation. Developments, which take place in the basin such as construction of new irrigation/ hydroelectric projects and industrialization of the area, can warrant addition/ closure/ re-location of stations. For example, a river reach can become increasingly polluted due to discharge of effluents from a newly set up industry. Hence, a need may arise to establish station(s) to assist with water quality monitoring and pollution assessments. Since hydrometric network normally exist for any region, the network design process tends to be a matter of evaluation, reviewing and updating of an existing network. The historic evolution of a large many hydrometric networks tends to be of reactive in nature; rather than strategically planned. Often gauging stations continue to be operated, with the original objectives remaining unclear. Hence, it is necessary to regularly undertake a detailed review of the existing networks to achieve the following.

� Define and/ or re-define the purpose of each gauging station � Identify gaps in the existing network � Identify stations which are no longer required � Establish a framework for the continual evaluation and updating of the network

There is a tendency for hydrologists and water resources planners to be reluctant to discontinue gauging stations, even though the stations might have fulfilled their intended objectives. In design and evaluation of networks, it is essential that a hard-nosed approach is adopted, and stations that are no longer providing significant benefits discontinued. 4.4.2 Main Steps in Network Design Keeping in view the above-mentioned general principles, the main steps in the network design process can be summarized as follows:

i) Review mandates, roles and aims of the organizations involved in the operation of HIS in the particular area and evaluate communication links.

ii) Collect maps and other background information



iii) Define the purposes of the network; who are the data users, and what will the data be used for? Define the objectives of the network; what data are required, and with what frequency?

iv) Evaluate the existing network; How well does the existing network meet the overall objectives?

v) Review existing data to identify gaps, ascertain catchment behaviour and variability

vi) Identify gaps and over-design in the existing network; Propose new stations and delete existing stations wherever necessary

vii) Prioritize gauging stations

viii) Estimate average capital and recurrent costs of installing and maintaining different categories of hydrometric stations. Estimate overall cost of operating and maintaining the network.

ix) Review revised network in relation to overall objectives, ideal network, available budget and the overall benefits of the data. Investigate sustainability of the proposed network

x) Prepare a phased implementation plan; which needs to be prioritized, realistic and achievable

xi) Decide on approximate locations of sites, and commence site surveys. If site is not feasible, review the location and see if another strategy can be adopted, say gauge a tributary to estimate total flow at required spot, rather than trying to measure total flow in the main stem river

xii) Establish framework for regular periodic network reviews. As hydrometric network design is a dynamic process, networks have to be continually reviewed and updated such that they react to new priorities, changes in policies and fiscal changes. Regular formalized network reviews are recommended to take place after three years, or at a shorter interval, if new data needs to be developed.

4.4.3 Design Considerations

i) Designers and planners of water resources projects increasingly utilize the statistical characteristics of streamflow rather than flow at specific times. The probability that the historical sequence of flow observed at a given site will occur again is remote, and the prediction of future flows needed for design and planning must consider all probable flow sequences. The information on long streamflow records enables prediction of future streamflow, not in terms of specific events, but in terms of probability of occurrence over a span of years. It is not feasible to collect a long continuous record at every site where it will be needed. A number of such stations are required to provide information which can be transferred to un-gauged sites or to sites where a small amount of streamflow data is available.

ii) Network should have at least one primary streamflow station in each climatologic and/ or physiographic area in a state

iii) A river or stream which flows through more than one state needs to be gauged at the state boundary



iv) A primary station might be planned at a point on the main river where the mean discharge attains its maximum value. For rivers flowing across the plains, this site is usually in the downstream part of the river, immediately upstream of the point where the river normally divides itself into branches before joining the sea or a lake or crosses a State boundary. In the case of mountainous rivers, it is the point where water leaves the mountainous reach and enters the plain land. Subsequent stations are established at sites where significant changes in the volume of flow are noticed, say below the confluence of a major tributary or at the outflow point of a lake, etc.

v) Several stations may need to be located at downstream stretch of a river. Such stations are intended to provide inventory of water loss from the channel by way of evaporation, infiltration and by way of utilisation for irrigation, power generation, industrial and domestic needs.

vi) The distance between two stations on the same river may vary from 30 km to several hundred kilometers, depending on the volume of flow. The drainage areas computed from origin up to consecutive observation sites on a large river should preferably differ by more than 10 percent so that the difference in quantities of flow is significant.

vii) A different approach is to be adopted in dealing with small independent rivers that flow directly into the sea, as in the case of west flowing rivers of Kerala and Maharashtra and some east flowing rivers of Tamil Nadu.

viii) In such cases, the first hydrological observation station might be established on a stream that is typical of the region. Further stations could be added to the network so as to widely cover the area. For example, it may not be possible to operate and maintain gauging stations on all smaller watercourses in the Western Ghats. Hence, representative basins have to be selected and the data from those are used to develop techniques for estimating flows for similar un-gauged sites.

ix) For trans-boundary water balance studies, it is indispensable to have for each international river a gauge at the entrance and/ or the outlet of the country

x) Confluence between a major and a minor tributary: It is useful to have a gauge in order to appreciate the discharge variation for the main river, downstream of the confluence

xi) Along a river, installation of a gauge should consider the other stations available on the river. If the difference between the flows at two stations is inferior to the margin of error of flow measurement, it is useless to intercalate a supplementary station

4.5 Network Density The World Meteorological Organization (WMO) has issued guidelines on the density of minimum hydrometric network, and is given in Table 4.1 (a) and (b).

It is not possible to provide specific, general guidelines on an appropriate network density. WMO recommendations are general guidelines, which if adopted literally for some of India’s larger river basins could result in an excessively dense network. Even though the WMO guidelines might be used as rough rule of thumb as part of an initial network appraisal, their use in the final design of the network can possibly be avoided. Network density must



ultimately be based on the network objectives, the temporal and spatial variability of river stages and flow and on the availability of finance, manpower and other resources.

Table 4.1 (a): Minimum density of hydrometric network (WMO)

[Area in km2 per station] No Type of region Range of norms for

minimum network Range of provisional norms

tolerated in difficult1 conditions

I Flat regions of temperate and tropical zones

1,000 - 2,000 3,000 - 10,000

II Mountainous regions of temperate and tropical regions

300 - 1,0002 1,000 - 5,0003

III Arid zones 5,000 - 20,0004 ------------------

Source: Design Manual, Hydrological Information System, Hydrometry, Hydrometeorology Vol. 1, Hydrology Project Technical Assistance, Government of India & Government of the Netherlands, 2001

Table 4.1 (b): Recommended minimum densities of streamflow stations [Area in km2 per station]

Physiographic unit Minimum density per station

Coastal

2,750 Mountainous

1,000 Interior plains

1,875 Hilly/ undulating

1,875 Small islands

300 Polar/arid

20,000 Source: WMO No.168, Guide to Hydrological practices, Fifth edition, 1994

4.6 Optimization of Network

4.6.1 Criteria for network optimization Identification of a set of criteria for hydrological network adequacy assessment is a complex task. The criteria to be applied should depend on the network type but also on the climatic conditions and on the territory characteristics and vulnerability. Figure 4.1 gives a schematic showing different methods/ criteria used for network optimization. As depicted therein, streamgauge network optimization can be broadly tackled through knowledge, empirical criteria and analytical methods. Knowledge:

The characteristics of the existing network, along with the territory and climate properties, have to be considered to address the problem of optimization of streamgauge network. The

1 Last figure in the range should be tolerated only for exceptionally difficult conditions 2Under very difficult conditions, this may be extended up to 10,000 km2 3 Under very difficult conditions, this may be extended up to 10,000 km2 4 Great deserts not included



knowledge of territory - say, orography, geo-morphological properties, urban and rural locations, etc. - is fundamental to the process. For instance, the local orography governs spatial distribution of precipitation over complex terrain. Moreover, information on historical flooding events could be a basic tool to optimize location of stations for flood mitigation purposes. Appropriate spatial distribution of the measurement stations should also consider location of urban and industrial areas adjacent to rivers and flood plains, where a continuous water level monitoring should be carried out. Knowledge of climate characteristics is also useful since the precipitation type influences the spatial resolution of the rain gauge network. Clearly, optimization criteria based on knowledge statement have to be integrated with a more in-depth analysis based on empirical approaches, or more sophisticated statistics and/ or geostatistical methodologies. Empirical rules:

The problem of streamgauge location can be mainly addressed through empirical considerations. Obviously a stream gauge has to be located at accessible sites, and should monitor water level at appropriate sites upstream of historical flooding prone regions; particularly when urbanized areas are involved. For man-made reservoirs, stream gauging upstream and downstream of the structure for monitoring inflows and outflows from the facility.

Figure 4.1: Overview of the Criteria for Streamgauge Network Optimization

Streamgauge Network Optimization for Water Resources Assessment and Planning

Knowledge Analytical criteria Direct/ empirical Criteria

Existing streamgauge Network

Territory characteristics • Orography • Geomorphological

characteristics • Historical flooding

events • Urban/ rural area

location

Climate Characteristics • Precipitation type

Statistical approach

Geostatistical methods

Coverage models

• Each main tributary be gauged

• Reservoirs • Location of urban

areas, industrialization

•



Analytical Methods:

Streamgauge network assessment and optimization can be based also on statistical approaches using clustering technique to identify groups of similar gauging stations, and on entropy-based methods; which allow quantify the relative information content. Geostatistical methods (Moss, 1982; Tasker, 1986), most commonly based on the standard error in estimating regional discharge at un-gauged sites, or coverage models that deal with the network design as a facility location problem, can also be employed (Barbetta et al, 2009). Methodology of spatial hydrologic regression under generalized least squares framework, adopted in optimizing Upper Bhima streamflow network is introduced in section 4.6.2 and detailed in section 6.

4.6.2 Statistical Approach

Identification of monitoring objectives is the first step in the design and optimisation of monitoring systems. The second variable to be considered is the dynamics of river flow and stages in time and space. This requires a critical analysis of historical data. To enable optimal design of the monitoring system, a measure that quantifies the effectiveness level is required. This measure depends on the monitoring objectives, and can be related to an admissible error in say the mean flow during a certain period, monthly flow values for water balances, extreme flows and/ or river stages, etc. This error is a function of the sampling locations, sampling frequency and sampling accuracy, i.e. where, when and with what river/ reservoir are stages and flows to be measured. Network design approaches have traditionally been relied largely on statistical methods, with the most commonly used method based on the standard error in estimating regional discharge at ungauged sites. During the 1970s and 1980s, USGS developed and applied statistical regression techniques to locate gauges (Moss, 1982; Stedinger & Tasker 1985 & 1986). A regional optimization model for a hydrological region can be developed using regression. Dependent variable is often taken to be annual average flow, annual maximum flow, 50-year (yr) flood or 100-yr flood, 7-day 10-yr low flow, etc. Basin characteristics such as catchment area, length of the major stream, elevation, population, annual average rainfall, total annual monsoon discharge, location-parameter of the station, length of data or forest cover percentage, etc. can be used as explanatory variable in multivariate regression equation. A planning horizon of say, 5-yr, 10-yr or 25-yr can be considered.

In each region, the analysis begins with all candidate stations included, and then stepped backwards, eliminating the least informative station at each step. There are both strengths and limitations of the statistical approach to network design. The method is rigorous and reproducible, yielding quantitative results about the degree of uncertainty of particular quantiles for a given gauge network. The gauge sites can thereby be arranged in an unambiguous rank ordering from highest to lowest information content. Although statistical methods can quantify trade-offs between information and cost, these trade-offs (and the value of any particular gauge network) change with different design objectives. For example, the optimal network to support regional estimation of annual average flow and the 50-year



flood may differ substantially from the optimal network supporting regionalized estimation of 7-day 10-yr low flow.

Thus, statistical methods for stream network design should be used to justify incremental decisions to add or eliminate individual gauges within a local gauge network serving narrow, well-defined goals (such as hydrologic regionalization). However, one important limitation of statistical methods is the decoupling of performance metrics used to evaluate network performance from the possibly unrelated purposes for which the gauges were installed in the first place. For example, a gauge may serve a critical purpose for water management or flood forecasting even if it is not one of the gauges most useful for estimating regional hydrologic information at ungauged sites. Although statistical procedures offer numerical precision for network design, supporting regional hydrologic estimation, these approaches do not support the many other goals and uses of site-specific streamflow data.

To decide on the number of sites to be sampled, accuracy goals need to be set, which in turn need streams to be classified as principal streams and minor streams. More costly developments on large streams justify a higher accuracy goal for principal streams than for minor streams. The proposed goal for principal streams is an accuracy equivalent to that obtained from 25-yr record. For remaining streams, accuracy equivalent to that obtained from 10-yr of record is proposed as the goal. Besides the regional regression analysis, Slade et al. (2001) analyzed the correlation among paired stations upstream and downstream of one another on the same river. They found the expected strong correlations in flows for upstream and downstream stations on the same river, especially for the annual average flow. As a result, stations for a core network can be selected which were not highly correlated with other selected stations. 4.6.3 Periodic review using survey techniques/ multi-criteria analysis:

Tools like survey techniques/ multi-criteria analysis can be used in the periodic review and optimisation of hydrometric stations network. This will enable judging density of network and comparing it with WMO norms. It will also help in analyzing the network according to population density. The existing problems with GD stations such as construction of structures upstream or downstream, site(s) affected by backwater effect, sufficient discharge data being collected for the stable channel and only gauge need to be measured, need for upgradation of the methods of measurements, station becoming obsolete, new data requirement for design/ planning purpose, etc. can be answered using tools like survey techniques and/ or multi-criteria analysis. 4.6.4 Coverage sub-watershed model approach:

In contrast, coverage models are based on articulating a goal, defining a measure of success (“metric”) or procedure that identifies locations supporting that goal, and applying this procedure using geographic information system (GIS) analysis to yield a set of potential sites (e.g., for gauges). The design of a streamgauge network has much in common with a rich family of facility location problems. These include the siting of facilities for fire protection, ambulances and hospitals, vehicle emission test stations, hazardous facilities, oil-spill response centers, and “hubs” for air passengers and cargo transport.



As a consequence of defining a coverage model, sampling at discrete locations subdivides a spatial domain into sub-regions; each sub-region is explicitly associated with its respective measurement point. When streamgauges are located in a stream network, the watershed draining to that streamgauge can analogously be delineated; a unique subarea associated with each gauge defines the land area whose drainage flows past that gauge before it reaches any other gauge (Figure 4.2a). This sub-watershed is the coverage area associated with that streamgauge. Any set of points on a stream network can be used to subdivide a watershed into sub-watersheds. In contrast to network designs used to monitor continuous surfaces, fluxes, or fields (e.g., air quality, solar radiation, contaminated groundwater), streamgauge locations are confined to the stream network (Figure 4.2a), suggesting analogues with facility location in transportation and communication networks. For example, facilities may be optimally sited in a transportation network to intercept traffic flows for vehicle safety inspections or to detect the transportation of hazardous substances. The flow interception location problem engenders subtle trade-offs between maximizing capture by locating facilities at the “outlet” of directed networks through which all traffic must flow and “protecting” the network which favors siting more facilities in the “upstream” reaches of the network for early detection.

Figure 4.2a: Spatial subdivision of a region using sub-watersheds of streamgauges

Figure 4.2b:Spatial subdivision of a region using Thiessen polygons.

Rainfall varies continuously over space, but it can be directly measured only at discrete points. This is typically the case for computing mean areal rainfall from point measurements at raingauges, in which Thiessen polygons drawn around the raingauge locations are used to estimate watershed average rainfall using an areally weighted average of the raingauge values (Figure 4.2b).



5. Review of Streamgauge Network 5.1 Existing Network:

The existing hydrometeorological network for the Upper Bhima basin was finalised by the WRD, GoM, in consultation with the IMD and CWC. Table 5.1 gives the details of the 14 GD stations in the basin.

Table 5.1: GD Stations in Upper Bhima Basin

No. Station Year of

establishment District Tributary

Catchment Area (km2)

1 Aamdabad 1996 Pune Ghod 1522.528

2 Askheda 1983 Pune Bhama 239.470

3 Budhawadi 1981 Pune Kundalika 151.920

4 Chaskaman 1973 Pune Bhima 389.050

5 Dattawadi 1982 Pune Mutha 741.290

6 Kashti 1984 Ahmednagar Ghod 4392.000

7 Khamgaon 1985 Pune Mula-Mutha 2832.970

8 Nighoje 1991 Pune Indrayani 832.300

9 Pargaon 1982 Pune Bhima 6251.000

10 Paud 1984 Pune Mula 473.640

11 Pimple Gurav

1997 Pune Pawana 506.700

12 Rakshewadi 1984 Pune Bhima 3279.844

13 Shirur 1984 Pune Ghod 3204.180

14 Wegre 1994 Pune Mutha 91.150

5.2 Objective of Streamgauge Network:

The prime objective of the hydrometric network in Upper Bhima basin maintained by WRD, Maharashtra is adjudged to be the collection of hydrometeorological data, which will be used to assess the quantum of water available in each basin/sub basin for water resources development and management, and simultaneously for flood management purpose. 5.3 Classification of Stations:

The stations in the GD network of Upper Bhima basin is classified into the following three categories.



I. Primary Stations (maintained as benchmark stations with measurements continued for a longer period of time to generate representative flow series of the river system, and provide general coverage of a region):

Pargaon and Chaskaman

II. Secondary Stations (essentially short duration stations, intended to be operated only for such a length of period that is sufficient to establish the flow characteristics of the stream, relative to those of a basin gauged by the primary station):

Aamdabad, Askheda, Budhawadi, Dattawadi, Kashti, Khamgaon, Nighoje, Paud, Pimpale Gurav, Rakshewadi, Shirur and Wegre

III. Special purpose Stations (for planning and design of projects or special investigations monitoring and fulfillment of legal agreements between states in respect of interstate basins, special studies or research; discontinued when their purpose is served):

None identified in the Upper Bhima basin

According to WMO, minimum density of stream gauge network for mountainous region is recommended as 1,000 km2/ station and for interior plains or hilly/ undulating regions, it is 1,875 km2/ station (in terms of ranges, for flat region, the range is 1,000-2,000 km2/ station and for Mountainous regions, it is 300-1,000 km2/station). Maharashtra is considered as semi-hilly area. Upper Bhima basin consists of 14 GD stations for geographical area 14,712 km2. Thus, the network density for existing network works out approximately to 1,050 km2/ station; which agrees with the minimum density norms provided by WMO. 5.4 Summary of Preliminary Review:

A preliminary review of existing GD network in the basin was performed by WRD by surveying all the 14 GD stations under the network. The procedure adopted by GoM for preliminary review inter alia included: review of existing GD network to see whether the station is affected by backwater on account of Kolhapur Type (KT) weirs, other hydraulic structures or unsteady flow conditions; whether sufficient discharge data has been collected for the stable channel and only gauge can be measured; need for upgradation of the methods of measurements, station becoming obsolete; and identifying new locations on basins/ sub-basins where gauging needs to be done (for reasons to be explicitly established). Detailed proposals are also being made for closing/ establishing new stations, preparing maps showing location-details of the network, etc. This has helped in judging the density of network and to compare it with WMO norms. Findings of the review conducted have been analyzed in the following paragraphs. Table-5.2 gives the summary of survey findings by WRD, GoM. In the table, reasons for establishment of the particular GD station are included, as also recommendations on the basis of the review.



Table 5.2: Results of preliminary review of GD stations in the Upper Bhima

No GD Station Purpose/ objectives Method of measurement

Priority1 (A/B/C)

Decision2 (N/R/D)

Data length

(yr)

Sites affected by Hydraulic structures

Remarks

1 Aamdabad Measure gauge and discharge

Current meter

A R 12

2 Askheda Measure gauge and discharge & rainfall

Cableway A R 25

Discharge measured during rainy season only; Bhama-Askheda dam located 5 km u/s

Proposed for closure, Bhama-Askheda dam will act as GD

3 Budhawadi Measure gauge and discharge & rainfall

Current meter

A R 27 NA

4 Chaskaman Measure gauge and discharge and climatic parameters

Cableway A R 35

Discharge measured during rainy season only; Chaskaman dam 10 km u/s

Proposed for closure, ChaskmanDam will act as GD

5 Dattawadi Measure discharge of Mutha river Bridge C D 26

Discharge is measured during rainy season only; Khadakwasla dam located 25km u/s

Proposed for closure, Khadakwasla Dam will act as GD

6 Kashti Measure gauge and discharge and climatic parameters

Current meter A R 21 Ghod dam 25 km u/s

7 Khamgaon Measure gauge and discharge & rainfall

Current meter A R 23 NA

8 Nighoje Measure gauge and discharge & rainfall


9 Pargaon Measure gauge and discharge and climatic parameters


10 Paud Measure gauge and discharge & rainfall


11 PimpleGurav NA Current meter C D 11 NA

12 Rakshewadi

Bhima discharge measurement before confluence with Mula-Mutha river

Cableway C D 20

Velocity affected due to backwater of Bhima; Mula-Mutha confluence 0.5 km d/s of site; Pargaon KT weir located 4.92 km d/s; Discharge is measured during rainy season only; Nearby station on the same stream, Pargaon 5 km d/s

Proposed for closure, and Gauges and discharges will be measured at Pargaon GD

13 Shirur

Discharge measurement of Ghod river before Ghod dam

Cableway C D 17

Discharge measured during rainy season only; Affected by backwater effect of KT weir located d/s; Dimbhe dam 105 km u/s and Ghod dam 25 km d/s; Ghod dam 25 km d/s and Kashti station 50 km d/s

Proposed for closure, AWS is proposed under ongoing RTDAS project

14 Wegre Discharge measurement of Mutha river

Cableway C D 13

Discharge is measured during rainy season only; Temghar dam 9 km u/s; Discharge can be measured at Temghar dam site.

Proposed for closure, Temghar dam will act as GD

Note: 1. Priorities: A – High, B – Medium, C – Low 2. Decision: N – Establish new station, R – retain existing station, D – discontinue station

On the basis of the preliminary review, GoM has proposed closure of six GD stations due to backwater effect arising from construction of structures downstream or flow affected due to



construction of structures upstream of the existing site (Table 5.2). In case, this is considered, there will remain only eight GD stations in the basin and the network density will reduce to 1,839 km2/ station. Out of these above mentioned six GD sites, streamflow has affected due to construction of structures upstream for four sites, namely, Askheda, Chaskaman, Dattawadi and Wegre. For these four sites, the required discharge data can be continued to be measured at spillways of the upstream dams, namely, Bhama-Askheda, Chaskaman, Khadakwasala and Temghar respectively. Due to the budget constraint for future maintenance, two GD stations out of existing fourteen may be required to be closed, for which case data collection at 12 GD stations will be continued and the network density will reduce to 1,226 km2/ station.

By looking at the hydrological problems in the basin such as flooding and importance of the basin for the whole region, it is not considered advisable to close all the six GD stations proposed for closure, unless alternative arrangements are made for collection of hydrometeorological data relating to these stations.

Common improvements required in the infrastructure, as reported in review, included the following.

i) All GD sites should be converted to a common benchmark, say GTS.

ii) Use of current meter on GD sites wherever feasible.

iii) Adequate staff to be posted at each GD site.

iv) Shifting of GD sites affected by backwater effect; else provision of auxiliary site downstream of the present GD site.

v) When rating curves are consistent for a GD station, stages can be recorded; and discharge worked out using stage-discharge curve.

vi) Installation of DWLR/ AWLR on the sites which represents the sub-basin.

vii) Stages should be recorded at least for five years after closure of the site.

viii) Provision of raingauge station proposed in the catchment having GD site, but with no raingauge station at present.

ix) Establishment of new GD sites as per need.



6. Spatial Hydrologic Regression for Regional Info rmation

6.1 Spatial Hydrologic Regression in GLS framework

One of the important uses of GD-station network is the estimation of flood quantities and other parameters such as annual flood peaks, monthly and annual/ seasonal flow volumes, low-flow d-day averages at ungauged locations, etc. Such statistics can be estimated by employing spatial/ regional models by use of physiographic characteristics of a catchment such as catchment area, main channel slope, land use and land cover statistics and meteorological variables such as mean annual precipitation. Ordinary least squares (OLS) procedure, often used to calibrate the fit of empirical hydrologic models is not the most efficient or statistically appropriate estimation procedure. OLS ignores the actual length of the gauged records employed in the parameter estimation step, the differences in the variations of flows at different sites, and possible cross-correlation among concurrent streamflows at the various gauged sites. Inclusion of short-record sites often decreases the precision of estimated model parameters while using OLS (Moss & Karlinger, 1974).

Monte Carlo studies by Stedinger & Tasker (1985, 1986) and Tasker & Stedinger (1987) have documented the value of generalized least squares (GLS) procedure to estimate empirical relationships between streamflow statistics and basin physiographic characteristics. The GLS algorithm takes into account for differences in record length, the variations of flows at different sites, and cross-correlation among concurrent streamflows.

Model description and assumptions:

Let the hydrological region under consideration have ‘n’ GD (stream gauging) stations. We estimate, at each gauging site, a streamflow characteristic, say ‘monsoon average daily flow’ or ‘50 year flood’. Let us assume that the streamflow statistics of interest, after suitable transformation of the response and the explanatory variables can be written in a linear multivariate regression model as follows.

Yi = β0 + β1X1i + β2X 2 i+ εi (two explanatory variables ‘catchment area’ and ‘mean monsoon precipitation’)

In matrix notation, εβ += XY

where ‘Y’ is an n x 1 vector of streamflow statistics at n sites, X is an n x (k+1) matrix of k basin characteristics augmented by a column of 1’s. β is a (k+1) x 1 vector of regression parameters and ε is an n x 1 vector of random errors. Error term ε has two

components, ηγε += , where γ is model error and η is sampling error. βX is the true but

unknown value of streamflow statistics. The dependent variable ‘Y’ is a flow characteristic, such as logarithm of ‘monsoon average daily flow’ or ‘50 year flood’. The natural logarithm of basin characteristics may also be taken. It is assumed that

Λ=== )()(;0)( 'εεεε EVarE i.e. errors have zero means. The unknown variance-



covariance matrix can be estimated using the relation ∧∧∧Σ+=Λ I2γ where

∧2γ is an estimate

of the model error variance due to an imperfect model and∧Σ , an n x n matrix of sampling

covariance with elements

≠

==Σ

jifornn

m

jiforn

ji

jiij

ij

i

i

ij

,

,2

σσρ

σ

∧σ is an estimate of the standard deviation of the observed transformed flows at site i, in is

the record length at site i, ijm is the concurrent record length of sites i and j, and ijρ is an

estimate of correlation of flows between sites i and j.

A more appropriate estimate of parameter vector β is the GLS estimator given by

YXXX 1'11' )( −−−∧

ΛΛ=β

In the Estimated Generalized Least Squares (EGLS) model, β and 2γ are determined by a

numerical search method so that

knXYXY −−=−Λ−∧∧

−∧

)1()()( 1' ββ

The variance–covariance matrix of ∧β is

11' )()( −−∧

Λ= XXVar β

Residuals are calculated using

∧∧−=−= βXYYYe

A measure of the capacity of the regression model to explain streamflow statistics through physiographic basin characteristics is R2; which is also called as coefficient of determination and is calculated using the following formula

2'

'2 )()(

1ynYY

XYXYR

−

−−−=∧∧ββ



This is actually the multiple correlation coefficient. For comparing two subsets of regressors, R2 and R2

adj statistics have been used. The advantage of R2adj is that it does not

automatically increase as new regressors are inserted into the model. R2adj is calculated

using the following relation

)1(1

11 22 R

kn

nRadj −

−−−−=

The standard error of estimate or sample standard deviation of regression is computed as the expected value of the squares of the observed values of Y from the expected

(estimated) values ∧Y using the following formula

1

)()()(

'2

−−−−=−=

∧∧∧

kn

XYXYYYESE

ββ

Influence/ Diagnostics statistics:

The leverage of site i is the ith diagonal element of matrix 1'11' )( −−− ΛΛ= XXXXH .

The leverage statistics identifies points that are potentially influential due to their location in

the regression variable space. 11

+=∑=

khn

iii , on an average hii will have value

n

k 1+, so that

observations with values of hii in excess of n

k 12

+ can be considered as high leverage

observations.

In deciding how to extend an existing streamflow data collection network by adding new stations, generally, the best new stations to include in a network are those new stations that

have leverage at least as large asn

k 1+.

One of the most important influence statistics in regression is Cook’s D. This statistic is a natural measure of how the fit of the model at site i is changed by deletion of the observation at site i. The generalized version of Cook’s D is

2'

2'

))(1( iiii

iiii hk

hD

−+=

∧

λε

where 'iih are the diagonal elements of matrix Λ= HH ' and iiλ are the ith diagonal elements

of matrix Λ . If Di is large, say in excess of n

4, then the site i observation has more

influence on model fit and can be singled out for close examination for possible data errors.

The precision with which the regression estimate at the site approximates the true streamflow statistic at a site can be described by the sampling mean squared error (MSE) .



xXXxxMSESampling 11'')()( −−Λ=

The regional information contained in the regression model for the site is proportional to the reciprocal of sampling MSE.

Because of the cost and limited availability of resources for regional data collection, it is important to develop efficient data collection plans. The GLS technique provides a means by which a data collection network can be evaluated and future gauging strategies and plans ranked in terms of their efficiency in collecting regional statistical information. To objectively evaluate the merits of each of the GD stations operating within the network, GLS method is useful.

6.2 Algorithm

Steps for carrying out spatial hydrologic regression of streamflow statistics of interest, say, monsoon average daily flow on basin characteristics, say, catchment area & mean monsoon precipitation, using GLS procedure as discussed above, are summarized below.

Steps:

i. Calculate monsoon average daily flow series for each station from historical records a. Consider historical daily streamflow series for each GD station in the network

for monsoon period June-October b. Perform initial validation checks; treat missing values, outliers, etc c. Calculate basic annual series for each station for deriving station’s streamflow

statistics d. Calculate single value of streamflow statistics for all existing GD station

ii. Compile catchment area & mean monsoon precipitation for all stations

iii. Transform the series using natural logarithm to take care of positively skewed nature of probability distribution of streamflow statistics

iv. Calculate data lengths (in years) and standard deviation for each GD station for series in finalized in step-i

v. Calculate concurrent record length matrix (14X14) for network’s stations series of step-i

vi. Calculate cross-correlation matrix (14X14) for series in step-i

vii. Construct matrices Y (dependent variable) and X (regressors or independent variables).

viii. In GLS spatial hydrologic regression set-up, estimate regression coefficients β, variance-covariance matrix, model error using numerical search technique. Computer program will take care of computations involved in iterations.



ix. Calculate R2, predicted values of monsoon average daily flow and standard error of estimate.

x. Calculate leverage statistics, Generalized Cook's D statistic, sampling MSE which will help in ranking GD stations according to their influence for computing monsoon average daily flow at ungauged locations.

xi. Use of fitted model for prediction

xii. Make an estimate of the costs involved in development and operation of the network.

6.3 Data Analysis and Results

Homogeneity of the region:

Substantial database is a pre-requisite for carrying out network optimization studies. Upper Bhima basin is a geographically contiguous region, and assumed to be statistically/ hydrologically homogeneous. The rational behind this assumption is that geographically adjacent catchments could have similarities in hydrological response since; in general, climate and watershed conditions vary gradually in space. Regional homogeneity of the region is also checked using simple regression approach wherein the overall goodness of fit of the regression was seen. A plot of the data-based estimates of monsoon average daily flow against those derived from the regression shows no unusual outliers. Data Collection Status:

The Upper Bhima GD network consists of 14 stations, established during 1973-1997. Daily discharge data are being collected at each of the 14 GD stations. Historical data lengths of different stations in this network vary between 12 years to 35 years. In majority of the cases, streamflow is recorded during monsoon season; with the non-monsoon flows being recorded nil. Moreover, it is noticed that some stations report nil flow for the entire year. For example, in the case of Dattawadi station, for 1985, 1989, 2001 and 2003, daily discharges have been reported as nil for the entire part. Table 6.1 shows the detailed annual data collection status of daily streamflow for Upper Bhima basin.



Table 6.1: Annual Data Collection Status of Daily Streamflow in Upper Bhima GD Network

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Yr A

amda

bad

Ask

heda

Bud

haw

adi

Cha

skm

an

Dat

taw

adi

Kas

hti

Kha

mga

on

Nig

hoje

Par

gaon

Pau

d

Pim

pale

Gur

av

Rak

shew

adi

Shi

rur

Weg

re

1973 70

1974 0

1975 12

1976 118

1977 126

1978 133

1979 127

1980 130

1981 111 117

1982 129 117 101 92

1983 105 123 125 93 210

1984 94 138 112 30 43 301 111 93 102

1985 70 123 128 0 50 153 161 130 66 87

1986 72 153 108 153 61 153 362 123 105 113

1987 68 83 87 153 28 153 210 112 71 110

1988 95 111 100 61 73 153 366 76 93 56

1989 103 115 121 0 76 153 365 35 90 40

1990 135 130 107 152 83 153 279 97 125 115

1991 97 112 104 153 98 153 127 214 131 126 118

1992 66 101 66 92 51 183 101 274 75 74 40

1993 116 69 95 135 58 183 145 331 108 126 84

1994 110 119 92 106 67 153 116 230 92 83 71 101

1995 27 57 93 10 15 105 96 104 47 87 17 87

1996 96 40 74 96 32 73 153 122 148 52 107 88 89

1997 68 40 62 15 54 18 153 153 115 68 64 88 48 50

1998 95 0 115 83 19 84 183 86 197 116 118 110 74 88

1999 93 127 135 59 30 66 168 132 158 105 140 92 42 128

2000 34 66 75 58 2 14 147 101 140 65 135 62 6 86

2001 40 92 39 46 0 12 164 135 140 92 101 95 102

2002 9 66 77 81 1 8 147 128 0 91 54 95 102

2003 0 89 105 46 0 0 130 110 105 72 87 84 134

2004 82 54 82 56 15 39 139 133 127 123 47 129

2005 122 90 152 89 153 33 150 123 153 153 153

2006 109 83 131 88 123 122 124 125 149 124 124

2007 107 82 87 73 11 111 121 124 38 86



Streamflow statistics of interest:

Three streamflow characteristics, namely `Mean of Monsoon Average Daily Flow (µMADQ)’, ‘Mean of Annual Maximum Flow (µAMQ)’ and ’50 Year Flood (Q50)’ have been considered in the analysis for regional information. GD station-wise series of µMADQ has been derived as per the procedure described in Sec 6.2. ’50-Year Flood (Q50)’ at 14 GD sites were obtained by fitting Pearson Type-III probability distribution to the annual maximum series of respective GD station. The probability distribution function of Pearson Type-III probability distribution is given below:

( ) ( )

−−

−

−Γ

= βαγ

βα

γβ

x

ex

xf1

1; where -∞< x < ∞, γ>0, -∞ < β < ∞

where α, β and γ are location, scale and shape and position parameters of the distribution. Floods corresponding 50-year return period (Q50) were estimated using computer programme. The GD station-wise series for µAMQ has been derived in the similar fashion as for µMADQ. The spatial regression model which will be developed for µMADQ will give an idea about water availability at any ungauged locations on stream in the basin. The other two streamflow statistics µAMQ and Q50 will give information on peak flows in the basin. Table 6.2 gives the computed values of these three streamflow statistics based on available historical data.

Table 6.2: Streamflow statistics of Upper Bhima basin

No GD Station Data length

Mean of Annual Average Flow µAAQ (m3/ s)

Mean of Monsoon Average Daily Flow

µMADQ (m3/ s)

Mean of Annual Maximum Flow

µAMQ (m3/ s)

50 Year Flood

Q50 (m3/ s)

1 Aamdabad 12 13.588 32.301 405.805 2108.883 2 Askheda 25 6.041 14.411 291.177 1042.098 3 Budhawadi 27 5.387 12.851 142.442 353.472

4 Chaskaman 35 9.787 23.348 405.341 1475.460 5 Dattawadi 26 14.675 35.010 552.756 2215.217 6 Kashti 21 17.188 40.717 759.044 3639.079 7 Khamgaon 23 51.980 123.153 1407.431 5729.631 8 Nighoje 17 22.741 54.221 632.099 2213.190 9 Pargaon 26 102.625 244.437 2591.806 9485.638 10 Paud 24 8.675 20.694 256.648 1187.302 11 PimpleGurav 11 12.260 29.247 417.568 2149.049 12 Rakshewadi 20 41.439 98.858 1408.020 5516.113 13 Shirur 17 23.909 57.039 732.217 3388.668 14 Wegre 13 6.554 15.634 152.894 429.043

Basin physiographic characteristics:

The physiographic characteristics of the Upper Bhima basin such as catchment area (CA) and meteorological variable – mean monsoon precipitation (MMP) or mean annual



precipitation (MAP), used as independent variables in the regression model are shown in Table-6.3.

Table 6.3: Catchment Area & Mean Monsoon/ Annual Precipitation at GD Network of Upper Bhima basin

Sr No GD Station Year of

Establishment Taluka Tributary Catchment

Area (km2)

Mean Monsoon Precipitation

(mm)

Mean Annual Precipitation

(mm)

1 Aamdabad 1996 Shirur Ghod 1522.5 1012.8 1061.7 2 Askheda 1983 Khed Bhama 239.4 1703.4 1745.8 3 Budhawadi 1981 Maval Kundalika 151.9 2907.4 2954.9 4 Chaskaman 1973 Khed Bhima 389.0 1581.2 1633.8 5 Dattawadi 1982 Haveli Mutha 741.2 2056.3 2105.6 6 Kashti 1984 Shrigonda Ghod 4392.0 700.0 747.4 7 Khamgaon 1985 Daund Mula-Mutha 2832.9 1713.1 1756.6 8 Nighoje 1991 Khed Indrayani 832.3 2271.6 2319.8 9 Pargaon 1982 Daund Bhima 6251.0 1376.0 1420.5 10 Paud 1984 Mulshi Mula 473.6 2731.2 2749.6 11 PimpleGurav 1997 Haveli Pawana 506.7 2127.8 2179.6 12 Rakshewadi 1984 Shirur Bhima 3279.8 1167.9 1215.4 13 Shirur 1984 Shirur Ghod 3204.1 798.6 845.5 14 Wegre 1994 Mulshi Mutha 91.1 1898.3 1923.8 For performing the spatial hydrologic regression of streamflow statistics on selected physiographic/ meteorological basin characteristics using GLS procedure, computer-oriented models in FORTRAN have been developed. The computer program and output of GLS Regression of ‘Monsoon Average Daily Flow’ on Catchment Area and Mean Monsoon Precipitation is enclosed in Appendixes 1 to 3. Spatial GLS Regression results:

The summary of regression results is presented in Table 6.4. Regression standard errors of estimate are less when the two basin characteristics catchment area and mean monsoon/ or annual precipitation are used. The coefficients of determination (R2) for three regression models for µMADQ, µAMQ and Q50 on two basin characteristics are computed as 78.2 %, 84.7 % and 89.6 % respectively. When the information on MMP/ MAP is not available, then streamflow statistics at any location on stream in the basin can be estimated using catchment area only, but with somewhat less accuracy.



Table 6.4: Spatial GLS Regression results for Upper Bhima Basin

Standard Error Sr No

Fitted model

R2

(%) R2

adj

(%) ( log units) (original units)

1 µAAQ=0.293 CA0.617 70.2 45.1 0.490 40.1

2 µAAQ=0.012 CA0.679 MMP0.367 78.2 54.0 0.438 34.9

3 µAMQ=7.933 CA0.626 81.4 63.5 0.374 364.2

4 µAMQ=0.974 CA0.670 MAP0.240 84.7 66.6 0.355 312.3

5 Q50=14.339 CA0.730 87.9 75.4 0.339 1147.2

6 Q50=2.008 CA0.771 MAP0.226 89.6 76.7 0.328 896.8

Abbreviations: Mean of Annual Average Flow (m3/Sec) - µMADQ ; Mean of Annual Maximum Flow - µAMQ; 50 Year Peak Flow – Q50; Catchment Area (km2) – CA; Mean Monsoon Precipitation (mm) – MMP; Mean Annual Precipitation (mm) – MAP

Table 6.5 gives the Observed & Estimated values of Mean of Monsoon Average Daily Flow using only one regressor CA and two regressors CA and MMP, after carrying out the spatial GLS regression for Upper Bhima basin GD network.

Table 6.5: Observed & Estimated Mean of Monsoon Average Daily Flow (m3/ sec) using GLS Spatial Regression for Upper Bhima Basin

Estimated Sr No GD Station Observed

µMADQ µMADQ=0.7 CA0.617 µMADQ=0.043 CA0.672 MMP0.322

1 Aamdabad 32.301 64.336 54.683

2 Askheda 14.411 20.550 18.633

3 Budhawadi 12.851 15.521 16.302

4 Chaskaman 23.348 27.735 25.228

5 Dattawadi 35.010 41.263 42.339

6 Kashti 40.717 123.720 99.043

7 Khamgaon 123.153 94.368 98.354

8 Nighoje 54.221 44.324 47.257

9 Pargaon 244.437 153.725 156.019

10 Paud 20.694 31.299 34.315

11 PimpleGurav 29.247 32.640 33.153

12 Rakshewadi 98.858 103.326 95.974

13 Shirur 57.039 101.807 83.559

14 Wegre 15.634 11.331 10.086



A plot of observed mean of monsoon average daily flow (in log transformation) against those derived from the spatial GLS regression in Figures 6.1 (a) & 6.1 (b) below shows no unusal outliers.

Figure 6.1: Observed versus predicted mean of annual average flow in log units (µAAQ in m3/ s)

Tables 6.6 and 6.7 details the corresponding observed and estimated values of ‘Mean of Annual Maximum Flow’ and ’50 Year Flood’ using only one regressor CA and two regressors CA and MAP, using GLS Spatial Regression for Upper Bhima basin GD network.



Table 6.6: Observed & Estimated Mean of Annual Maximum Flow (m3/ s) using GLS Spatial Regression for Upper Bhima Basin

Estimated No GD Station Observed

µAMQ µAMQ=7.933 CA0.626 µAMQ=0.974 CA0.670 MAP0.240

1 Aamdabad 405.805 781.246 704.713

2 Askheda 291.177 245.231 229.800

3 Budhawadi 142.442 184.421 192.197

4 Chaskaman 405.341 332.483 313.278

5 Dattawadi 552.756 497.671 512.561

6 Kashti 759.044 1517.455 1318.118

7 Khamgaon 1407.431 1152.674 1205.573

8 Nighoje 632.099 535.173 567.046

9 Pargaon 2591.806 1891.755 1946.815

10 Paud 256.648 375.910 404.742

11 PimpleGurav 417.568 392.266 400.671

12 Rakshewadi 1408.020 1263.840 1217.920

13 Shirur 732.217 1244.974 1098.488

14 Wegre 152.894 133.995 123.194 Table 6.7: Observed & Estimated Fifty Year Flood (m3/ s) using Spatial GLS Regression for

Upper Bhima Basin

Estimated No GD Station Observed

Q50 Q50=14.339 CA0.730 Q50=2.008 CA0.771 MAP0.226

1 Aamdabad 2108.883 3021.716 2746.191

2 Askheda 1042.098 782.646 738.108

3 Budhawadi 353.472 561.398 585.274

4 Chaskaman 1475.460 1116.060 1057.666

5 Dattawadi 2215.217 1786.154 1839.686

6 Kashti 3639.079 6552.618 5743.534

7 Khamgaon 5729.631 4755.466 4965.106

8 Nighoje 2213.190 1944.053 2056.293

9 Pargaon 9485.638 8473.085 8708.632

10 Paud 1187.302 1287.799 1383.359

11 PimpleGurav 2149.049 1353.352 1383.442

12 Rakshewadi 5516.113 5294.321 5117.596

13 Shirur 3388.668 5202.372 4628.601

14 Wegre 429.043 386.840 358.572



The plots of observed and predicted values of ‘Monsoon Average Daily Flow’ and ‘50-Year Flood’ after the application of GLS spatial regression using only one regressor-catchment area for Upper Bhima basin are shown in Figure 6.2. With the help of existing GD network of the basin, this process will assist in estimating water availability at any ungauged locations/ sub-basins of Upper Bhima in terms of average monsoon flow. The only information needed for the purpose is catchment area of that sub-basin. Accuracy of the prediction can be improved by incorporating more and more informative basin characteristics into the spatial regression model. Similarly, for any ungauged location in the basin, the 50-year flood, or flood magnitude of desired return period can be estimated based on information on some basin physiographic characteristics, as demonstrated in Figure 6.2.

Figure 6.2: Observed & Estimated streamflow statistics using GLS Spatial Regression for Upper Bhima



GLS spatial hydrologic regression has been used to correlate streamflow statistics of interest with basin characteristics by using existing network of hydrologic stations of a basin. Due to cost constraints for future maintenance of network, data collection agencies may think of reducing the size of the network. In such situations, the stations in a network which adds less information on streamflow statistics can be separated out for termination. The diagnostic statistics discussed in Sec. 6.1, can be used for ranking the stations in terms of their influence on streamflow statistics of interest. The determination of final optimal network can be done by considering the outcomes of analytical methods and empirical rules. This has been worked out for Upper Bhima basin network in the next section.



7. Streamgauge Network Optimization 7.1 Basic Principles

Water Resources Department, Maharashtra provides streamflow data and other related information needed to protect life and property from floods, to plan and manage water resources, and to protect water quality. Streamflow statistics computed using GD network data such as the monsoon average daily flow, 50-year flood, 7-day 10-year low flow (7Q10), etc have been frequently used by engineers, land managers, biologists, and others to help guide decisions in their everyday work. Streamflow statistics also are used for design of dams, bridges, culverts; water-supply planning and management, and water-use appropriations and permitting; wastewater and industrial discharge permitting; hydropower facility design and regulation; and habitat preservation for protection of endangered species. In addition, researchers, planners, regulators, and the like often need to know the physical and climatic characteristics of the drainage basins upstream from locations of interest to help them understand the mechanisms that control water availability and water quality at these locations.

Streamflow statistics can be needed at any location along a stream. Commonly, the statistics are computed from available data when they are needed at the locations of data-collection stations, which include GD stations, where streamflow data are collected continuously; partial-record stations, where streamflow measurements are collected systematically over a period of years to estimate peak-flow or low-flow statistics; and miscellaneous-measurement stations, where streamflow measurements usually are collected for specific hydrologic studies with various objectives. More often, however, the statistics are needed at ungauged sites, where no observed data are available to compute the statistics.

The knowledge of the main hydrological quantities is fundamental and depends on accurate data acquisition. The development of complex hydrological models requires data with high spatiotemporal resolution. Moreover, new technologies such as Radar and remote sensing are able to provide spatially distributed information, which needs to be validated with ground observations. Thus, a reliable hydrometeorological network is fundamental for water resources planning, development and management.

Sampling data in hydrology is essentially a way of communicating with the natural system which is uncertain prior to the making of any observation. Each collected sample represents a signal from the natural system. Redundant information does not help to reduce the uncertainty further; it only increases the costs of obtaining data as huge funding is required for establishing and continuously operating any hydrometric network. Thus, there is a need for evaluating existing GD network and optimize it so that continuous data collection is ensured, and it can be performed in a cost effective manner.

Reliable procedures for hydrometeorological network optimization in general and streamgauge network optimization in particular, have been investigated for addressing the adequacy of the network operating on the territory of Upper Bhima basin. The problem of location of streamgauges was mainly addressed through empirical considerations.



7.2 GD Network analysis and optimization

7.2.1 Goals - GD Network for Upper Bhima Basin

Figure 7.1 delineates the GD network operated by WRD, Maharashtra in Upper Bhima basin. The network is primarily responsible for the following goals.

� Obtain flow rates and volumes in major tributaries of Bhima � Estimating monsoon water availability and other flow characteristics at un-gauged

basins � Estimating peak flows at un-gauged basins � Benchmark stations with measurements continued for a longer period of time to

generate representative flow series of the river system, and provide general coverage of a region (E.g. Pargaon/ Chaskaman stations)

Figure 7.1: WRD, Maharashtra’s GD network in Upper Bhima basin

7.2.2 Stations affected by backwater effects and recommended for closure by GoM

In its preliminary review carried out by field Engineers of WRD, GoM has proposed closure of six GD stations namely, Askheda (data length – 25 yrs), Chaskaman (35 yrs), Dattawadi (26 yrs), Rakshewadi (20 yrs), Shirur (17 yrs) and Wegre (13 yrs)]; due to backwater effect arising from construction of structures downstream or flow affected due to construction of structures upstream of the existing site. In case, this is considered, there will remain only eight GD stations for the whole basin and the network density will reduce to 1,839 km2/



station. Out of the above mentioned six GD sites, for the four stations, streamflow has affected due to construction of structures upstream namely, Askheda, Chaskaman, Dattawadi and Wegre. GoM officers suggested that these four sites can be shifted upstream and the requisite discharge data can be continued to be measured at spillways of the upstream dams, namely, Bhama-Askheda, Chaskaman, Khadakwasala and Temghar respectively. Due to the budget constraint for future maintenance, two GD stations out of existing fourteen may be required to be closed, for which case data collection at 12 GD stations will be continued and the network density will reduce to 1,226 km2/ station. Shirur and Dattawadi can be separated out for termination.

7.2.3 Cross-Correlation among paired stations in the network

Cross-correlation matrix for Upper Bhima GD network has been computed by considering monsoon average daily flow series. Table-7.1 gives the relevant cross-correlation matrix. There are [(n-1)xn]/2=91 possible GD stations pairs in the network of 14 stations. Out of these, the lag-zero cross-correlations among concurrent flows between paired stations upstream and downstream of one another on the same river have been considered for redundancy analysis. As expected, strong correlations are found between paired stations. Amongst these, four station-pairs have reported high values of correlation coefficients. Station pair Aamdabad and Kashti had correlation of 0.969, Station pair Aamdabad and Shirur had correlation of 0.986, Station pair Kashti and Shirur had correlation of 0.944, and station pair Khamgaon and Rakshewadi had correlation of 0.883. This indicates that out of the three GD stations of Aamdabad, Shirur and Kashti on the Ghod River, two are relatively redundant, and does not provide additional substantial information for the core network for estimation of monsoon average daily flow at ungauged locations. Similarly, out of the two GD stations of Khamgaon and Rakshewadi on Bhima, one is redundant. Thus, there is a scope for considering discontinuation of three GD stations, while considering core network for estimation of monsoon average daily flow. Shirur and Rakshewadi can be separated out for termination.

Table 7.1: Cross-correlation Matrix for Upper Bhima GD Network for ‘Monsoon Average Daily Flow’

Station Aamda

bad Askhed

a Budhawadi

Chaskaman

Dattawadi Kashti

Khamgaon Nighoje

Pargaon Paud

PimpleGurav

Rakshewadi Shirur Wegre

Aamdabad 1 -0.029 0.572 0.489 0.794 0.969 0.418 0.609 0.11 0.511 0.614 0.666 0.986 0.454

Askheda 1 0.18 0.141 0.042 -0.082 0.31 0.444 0.011 0.141 0.071 0.055 0.127 0.536

Budhawadi 1 0.434 0.402 0.632 0.537 0.709 0.272 0.557 0.79 0.539 0.49 0.616

Chaskaman 1 0.419 0.539 0.589 0.652 0.179 0.433 0.669 0.784 0.649 0.662

Dattawadi 1 0.589 0.37 0.645 0.231 0.61 0.699 0.34 0.232 0.45

Kashti 1 0.459 0.669 0.247 0.426 0.695 0.539 0.944 0.392

Khamgaon 1 0.752 0.414 0.569 0.66 0.883 0.708 0.728

Nighoje 1 0.221 0.761 0.806 0.775 0.825 0.843

Pargaon 1 0.234 0.595 0.217 0.698 0.472

Paud 1 0.847 0.466 0.516 0.687

PimpleGurav 1 0.522 0.899 0.832

Rakshewadi 1 0.581 0.586

Shirur 1 0.497

Wegre 1



7.2.4 Influential stations in GLS Spatial Regression Model

The stations in the GD network have been arranged in descending order of importance for the purpose of estimation of monsoon average daily flow by using the measures- generalized version of Cook’s D and sampling mean squared error, as mentioned in Section 6.1. Generalized Cook’s D statistics (which is a natural measure of how the fit of the model at site i is changed by deletion of the observation at site i) and sampling MSE (regional information contained in the regression model for the site is proportional to the reciprocal of sampling MSE) have been calculated for the GD network in the computer-oriented model developed in FORTRAN for GLS spatial hydrologic regression of ‘Monsoon Average Daily Flow’ on catchment area and mean monsoon precipitation. The formulas used for computing these statistics are reproduced here.

The generalized version of Cook’s D is 2'

2'

))(1( iiii

iiii hk

hD

−+=

∧

λε

where 'iih are the diagonal

elements of matrix Λ= HH ' and iiλ are the ith diagonal elements of matrix Λ . If Di is large,

say in excess of n

4, then the site i observation has more influence on model fit.

The precision with which the regression estimate at the site approximates the true streamflow statistic at a site can be described by the sampling mean squared error (MSE).

xXXxxMSESampling 11'')()( −−Λ=

Table 7.2: Stations ranked according to their influence on GLS Spatial Regression for estimation of ‘Monsoon Average Daily Flow’ for Upper Bhima

Station Sampling

MSE Station

Generalized Cook's D statistics

PimpleGurav 0.019 Wegre 4.050 Dattawadi 0.019 Shirur 1.312 Nighoje 0.023 Paud 0.848 Paud 0.028 Kashti 0.413

Chaskaman 0.029 Khamgaon 0.308 Budhawadi 0.032 Budhawadi 0.279 Askheda 0.034 Pargaon 0.073

Khamgaon 0.035 Nighoje 0.060 Rakshewadi 0.041 Askheda 0.028

Pargaon 0.051 PimpleGurav 0.016 Aamdabad 0.053 Aamdabad 0.011

Wegre 0.055 Rakshewadi 0.008 Shirur 0.078 Chaskaman 0.005 Kashti 0.097 Dattawadi 0.001

Note: influence statistics taken from Appendix 2



Table 7.2 shows the stations in GD network arranged in descending order of importance for the purpose of estimation of monsoon average daily flow. Although Dattawadi is least influential, it has not been recommended for closure since the site is falling in highly urbanized and industrialized Pune Metropolitan region. Hence, in conjunction with the results obtained in sections 7.2.2 and 7.2.3, two stations Shirur and Rakshewadi can be separated out from the core network of WRD Maharashtra serving multi-objectives at a time. 7.3 Finalization of Optimum Network

The network adequacy was assessed through different criteria. Basically, a need exists to gauge each major tributary of the main Bhima river, with a significant amount of discharge. Further, locations of streamgauges need to be well distributed along with the main tributaries. Areas affected by floods need to be gauged at appropriate points. Streams flowing through highly populated urban areas and industrialized zones also need to be gauged. The redundancy of data acquisition and gauging stations is verified using analytical tools. Monitoring of inflows and outflows at Ujjani reservoir needs to be ensured, considering their significant role within real time flood warning system. Thus, a combination of analytical and practical approaches is considered as a robust procedure for optimizing Upper Bhima GD network.

By looking at the hydrological issues in the basin such as flooding and the importance of the basin for the state, it may not be advisable to close forthwith all the six GD stations which are backwater affected/ or flow affected due to construction structures at upstream, unless proper alternative arrangements are made for the collection of hydrometeorological data under the jurisdiction of these stations. For the four stations for which streamflow has affected due to construction of structures upstream namely, Askheda, Chaskaman, Dattawadi and Wegre, GoM officers suggested that these four affected sites can be shifted upstream and the requisite discharge data can be continued to be measured at spillways of the upstream dams, namely, Bhama-Askheda, Chaskaman, Khadakwasala and Temghar respectively. At the outset, by combining the outcomes of the statistical methods and empirical rules, data collections at 2 GD stations out of 14, namely, Rakshewadi and Shirur can possibly be terminated, if it is essential for WRD the reduction in the network due to cost constraint for future maintenance. Thus, the suggested final optimum network can possibly consist of 12 GD stations, namely, Aamdabad, Askheda, Budhawadi, Chaskaman, Dattawadi, Kashti, Khamgaon, Nighoje, Pargaon, Paud, PimpaleGurav and Wegre; with a network density 1,226 km2 per one GD station.



8. Rating Curves 8.1 Basic premises

The gauge-discharge (G-Q) data recorded at the existing gauging stations of upper Bhima basin up to Ujjani were analyzed with the objective of developing functional relationships between G and Q. Phenomenological reasons suggest gauge to be dependent on discharge. The functional relationship can be written as )Q(fG = . Under the assumption of

single control, the gauge-discharge relation can generally be expressed as a power curve of the form βα−= )G(CQ , where Q is the discharge (m3/s), G is the gauge (m), C & β are the coefficients and α is the correction factor. 8.2 Data Used

Daily streamflow data for 14 GD stations in the upper Bhima basin, namely Aamdabad, Askheda, Budhawadi, Chaskaman, Dattawadi, Kashti, Khamgaon, Nighoje, Pargaon, Paud, Pimpale-Gurav, Rakshewadi, Shirur and Wegre were used to develop rating curves. Table 8.1 summarizes the results. The rating curves were developed at different gauge elevation wherever shifting of curve is applicable. A computer program, named RCURV was used to establish the single-valued functional relationship. 8.3 Results

From Table 8.1 it may be noted that there is a good correlation between the observed and estimated discharge using rating curve developed for the respective gauging stations except Dattawadi and Kashti. The R2 varied from 0.280 to 0.996.

From Table 8.1, it may be noted that the rating curves for seven GD stations Askheda, Budhawadi, Dattawadi, Khamgaon, Nighoje, Pargaon and Wegre were developed at different gauge elevations, possibly due to the changes in gauge level. Graphical representation of rating curves for few selected GD sites is given in Figures 8.1a and 8.1b. From figures, it may be seen that, at Wegre GD station, two different ranges of stages were found namely 98.560-100.780 for Jun1994 – Sep1994 period and 591.880-594.180 for Jul1995 - Oct2006 period; possible due to shifting of zero-of-gauge level. Exact reason(s) for such shift(s) may need to be explored, and identified.



Table 8.1: Rating curves of 14 GD stations in Upper Bhima basin

No. Gauging station Period NOBS ZGR (m) Rating curve SE R2

1 Aamdabad Jul 1996-Oct 2007

855 561.830-577.150

Q=37.720(G-556.961)2.385 24.767 0.947

Jul 1983-Sep 1984

243 94.590-95.650

Q=30.810(G-94.440)1.938 34.472 0.914

Jun 1985-Oct 1990

1,509 598.400-603.290

Q=17.694(G-598.065)1.992 28.224 0.935 2 Askheda

Jun 1991-Oct 2007 215

96.010-98.590 Q=39.220(G-95.738)1.880 126.945 0.803

Jun 1981-Oct 1983

363 88.380-91.340

Q=4.179(G-87.660)2.746 30.707 0.929

Jun 1984-Oct 1994

1,254 95.050-98.800

Q=0.982(G-94.050)3.432 120.240 0.774 3 Budhawadi

Jul 1995-Sep 2007

1,113 605.060-609.530

Q=0.030(G-603.125)5.054 41.593 0.885

4 Chaskaman Aug 1973- Oct 2007

3,077 593.130-599.170

Q=0.368(G-592.250)3.945 219.968 0.466

Jul 1982-Oct 1993

461 88.820-90.000

Q=0.027(G-85.958)5.824 66.530 0.323 5 Dattawadi

Jun 1994-Sep 2007 379

542.700-547.020 Q=0.013(G-538.952)5.708 39.465 0.891

6 Kashti Jul 1984-Oct 2004

1,017 502.800-510.990

Q=3.009(G-501.157)2.473 179.900 0.280

Jun 1985-Oct 1990

918 91.030-99.050

Q=0.594(G-89.901)3.658 111.460 0.667 7 Khamgaon

Jun 1991-Oct 2007

2,427 509.900-518.660

Q=36.629(G-509.580)1.881 52.127 0.721

Jun 1991-Oct 1994

489 95.700-99.960

Q=4.337(G-94.884)3.553 23.851 0.962 8 Nighoje

Jul 1995-Oct 2007 1,563

561.880-566.200 Q=5.537(G-561.200)3.465 50.203 0.882

Oct 1982-Apr 1984

423 91.010-96.580

Q=54.161(G-90.970)0.877 115.079 0.709 9 Pargaon

Jun 1984-Oct 2007

4,578 506.650-517.350

Q=0.010(G-503.951)5.713 102.063 0.687

Jul 1984-Sep 1994

572 91.640-97.500

Q=30.034(G-91.408)0.902 75.335 0.486 10 Paud

Jul 1995-Sep 2007

1,091 564.340-570.750

Q=0.061(G-561.952)4.555 62.975 0.724

11 PimpaleGurav Jun 1997-Sep 2007

1,078 548.120-557.700

Q=0.616(G-546.758)3.359 59.436 0.734

12 Rakshewadi Jun 1984-Sep 2003 1,017

509.670-519.980 Q=31.052(G-509.350)1.648 66.278 0.643

13 Shirur Jun 1984-Aug 2000

1,211 548.520-554.450

Q=0.109(G-546.960)5.616 43.478 0.823

Jun-Sep 1994

101 98.560-100.780

Q=20.563(G-98.312)2.295 7.458 0.996 14 Wegre

Jul 1995-Oct 2006

866 591.880-594.180

Q=21.884(G-591.685)2.294 34.611 0.910

NOBS: Number of observations; ZGR: Zero Gauge Range; SE: Standard Error; R2: Multiple Correlation Coefficient



Figure 8.1a: Rating Curve for Wegre GD Station (Jun-Sep 1994)

Figure 8.1b: Rating Curve for Wegre GD Station (Jul 1995-Oct 2006)



9. Evaluation of Raingauge Network 9.1 Significance

For hydrological design and water resources assessment purposes, proper estimates of rainfall and evapotranspiration is pre-requisite. In HIS, interest is often focused on the temporal and spatial variation of rainfall and evaporation/ evapotranspiration, both important water balance components. Areal rainfall amounts are estimated from point rainfall data, generally measured by a network of recording and non-recording rain-gauges. 9.2 Methodology for Raingauge Network Optimization

General considerations:

Any monitoring network is based upon two considerations, namely the monitoring objectives and physical characteristics of the systems to be monitored. The identification of the monitoring objectives is the first step in design and optimization of monitoring systems. Related to this is the identification of the potential data users and their future needs. In a multi-objective scenario, priorities need, however to be set. Identification of monitoring objectives is important since they determine the scale of changes to be detected in the data, the kind of information to be extracted, and hence the way the data is analyzed. The analysis of the data emanating from the network is also determined by the dynamics of the measured processes. The physical basis of the relevant processes must be known in order to be able to make preliminary guesses of the scale of the variability with respect to space and time. To enable an optimal design of a monitoring network, a measure is required, which quantifies the effectiveness level. Which measure is adequate depends on the monitoring objectives. Often, this measure is related to statistical concepts like errors in areal estimates, interpolation error, trend detectability, etc; and can be formulated as a function of sampling variables (what), sampling locations (where), sampling frequencies (when) and sampling accuracy (with what) (i.e. technique/ equipment)). These aspects also determine the cost of establishing and running of the network, like the costs related to land acquisition, station construction, equipment procurement and installation, station operation, maintenance, data processing and storage and staffing of field stations and data centres. Once the relationship between the chosen effectiveness measure and costs has been established, the optimal network can be found, in principle, by weighing the two in a cost–benefit analysis. It is stressed that once the network is operational, it has to be evaluated regularly to see whether the revised objectives still match with the produced output in a cost-effective manner. A network, therefore, is to be seen as a dynamic system and should not be considered as a static entity. This requires some flexibility in establishing new stations and closing down others.



Integration of networks: In the HIS for a region, the following networks are normally operational: hydrometeorological network of rainfall and full climatic stations, hydrometric network, surface water quality network, geo-hydrological network, and groundwater quality network. As already noted earlier, these networks are operated by various State and Central agencies. To avoid duplication of work and to reduce cost, the networks operated by various agencies have to be integrated, technically and organizationally. The hydro-meteorological network has to be considered in conjunction with surface water and groundwater networks. The former should have sufficient spatial coverage so that all discharge stations in the hydrometric network are fully covered. This means that dependent on the objectives, rainfall-runoff computations can be made or water balances established. Similar water balance and resource assessment considerations apply also for the hydro-meteorological network in relation to the groundwater network. Organizational integration of the networks implies that the networks are complimentary and that regular exchange of field data takes place to produce authenticated data of high quality. Review of the networks is also to be done in close collaboration. Raingauge Network: The major uses of rainfall data are generally for water resources planning, design, management, and research.

Water resources planning require generally long historical series of areal monthly, seasonal or annual data. Often, one is only interested in the long-term mean value of areal rainfall. For assessment of dependable amounts of rainfall, its variability is also required, either for a particular month or season in the year or for sequential months/seasons. For network design, it is of importance to know which statistical parameters have to be estimated and with what accuracy. Given the variability in space and time, this determines the number of stations required in the network and the duration of the measurements.

For design of structures generally statistics of short duration rainfall (e.g. quarterly, hourly or daily) have to be estimated. Rather than focusing on the average amounts, here the interest is particularly on the extremes and on the areal extent of extreme rainfall. The spatial correlation structure of short duration rainfall (minutes, hours or days) differs generally much from the same of long duration rainfall data as discussed for planning. This feature has important consequences not only for the required network density but also for the type of equipment to be used for rainfall measurement. Management requires less historical data. Here the interest is particularly in data on a real time basis for operational purposes like reservoir operation and flood forecasting. Historical data are here required for the design of rule curves and operational strategies and for model development.



Research needs intensive data to improve the understanding of certain processes or phenomena. The type of data required for research varies from study to study, but is often comparable with the requirements for design. From the discussion above, it is self evident that different objectives lead to different information needs and given the variation of the spatial correlation structure of rainfall with duration, different network densities will be required unless concessions are made towards the required accuracy. Measure of effectiveness: Based on the discussions in the above paragraphs, the objective of the raingauge network in Upper Bhima basin is conjectured to be to give reliable estimates of areal rainfall for areas commensurate with the hydrometric network. The latter condition stems from the need of integration of the networks. The streamgauge density in the plains is approximately one gauge per 2,000 km2; and one per 1,000 km2 in the hilly areas. Upstream of every streamgauging station, sufficient rain gauges should be available to estimate the areal rainfall with a specified accuracy. With respect to areal rainfall, the interest is in individual areal estimates, and/ or long term mean values. Due to the presence of spatial correlation among the point rainfall stations and near absence of serial correlation, (see Figure 9.1) these objectives will lead to different networks and durations of operation. If spatial correlation is absent, then each point rainfall data in time or in space would equally contribute to the improvement of the long term mean areal rainfall estimate, provided the rainfall field is homogeneous. However, correlation reduces the effective number of data, since information in one is to some extent already included in others. Hence, due to the spatial correlation, data points in time are more effective than data points in space to improve the long term areal mean. In other words, a less dense network operated for a longer period of time is more cost-effective than a denser network providing the same number of point rainfall data points. A reduction in the density of the network, however, adversely affects the quality of the individual areal estimates possibly to an unacceptable level. The latter is better served with a higher density, though this in turn may be sub-optimal for estimating the long term mean but is certainly not harmful.

(data hi,1 to hi,N spatially correlated)

(data h1,j to hn,j serially not correlated)

Figure 9.1: Data matrix n X N of n years of data at N stations



For most hydrological purposes, the objective of the raingauge network should be to provide reliable estimates of individual events of areal rainfall of a particular duration, like say duration of one hour, day, month, or season. It implies that the uncertainty in each element of the areal rainfall series, estimated from point rainfall data, should not exceed a certain value. This is particularly so for the network in use for HIS, where various users need to be served with different objectives. A measure for the quality of the areal rainfall data is the mean square error of the estimate. Hence, the root mean square error in estimating the areal rainfall of a particular duration, expressed as a percentage of the average rainfall in an area is an appropriate measure for the effectiveness of the network. Spatial correlation of rainfall: The required network density depends on the spatial correlation between point rainfall data. The spatial correlation structure of rainfall data in spatially homogeneous areas is well described by an exponential relation of the following type:

r (d) = r0 exp(-d/d0) where r(d) = correlation coefficient as a function of distance d = distance r0 = correlation coefficient at d = 0 d0 = characteristic correlation distance: if d = d0, r(d0) = r0e

-1 = 0.368 r0 The parameters r0 and d0 are determined from the correlation coefficients between the point rainfall series available in the basin for that particular duration or interval (e.g. series of August rainfall of sequential years). The correlation coefficients are presented as a function of the distance between the various sites. Hence, the above equation represents the average correlation structure of the rainfall for the considered duration over the number of years considered and the structure for an individual event (hourly, daily or monthly totals, etc.) may deviate from this. The parameter r0 is generally less than 1 due to random errors in the point rainfall data and microclimatic irregularities in the region. Some practical aspects in estimating the spatial correlation function are mentioned below. The individual correlation coefficients, plotted as a function of distance, generally show a large scatter. To create some order in the scatter, average correlation coefficients for distance intervals are determined. To estimate the parameters r0 and d0 either a manual approach is used by plotting the entries on semi-log paper, drawing a straight line through the points and read r0 and d0 from the plot at d=0 and r(d)=0.37, respectively, or a least squares approach is applied on ln(r(d)) versus distance d. In estimating the parameters r0 and d0, often entries have to be discarded from the data set, particularly when the least squares approach is used, as outliers may disturb the estimation too much. Spatial homogeneity in the rainfall field has been assumed. Orographical effects or other types of non-homogeneity have first to be eliminated from the point rainfall data series. Standard error of areal rainfall estimate:

Let the true areal rainfall in a basin be denoted by h*A and its estimate, based on N point

rainfall values, by hA then the error R in estimating h*A is given by



*AA hhR −=

If hA is an unbiased estimate of h*A then the mean square error is the error variance σ2

R. Further, let the (time) average rainfall be denoted by hav then the root mean square error Zareal in estimating the areal rainfall, expressed as a fraction of hav , is defined by

av

Rareal h

Zσ

=

This relative root mean square error is equivalent to the relative standard error. As will be elaborated below, the relative root mean square error is a function of the coefficient of variation of the point rainfall time series, the spatial correlation structure of the rainfall field, the size of the basin for which an areal estimate has to be made and the number of point rainfall data considered in estimating the areal rainfall. Let there be N raingauge stations in a basin with catchment area S km2, equally distributed over the basin. The rainfall in the basin is statistically homogeneous. The areal rainfall over S, hA is estimated as the arithmetic average of the observations at the N point rainfall stations

∑=

=N

iiA h

Nh

1

1

where hi = point rainfall observed at raingauge station i. Kagan (1972) showed that the error variance σ2

R in the areal rainfall estimate for the entire area S, when hA is estimated by above equation follows from

∑=

+−==

N

j

hRjR N

S

dr

NN1 00

22

22 23.0

11 σσσ

If the coefficient of variation of a rainfall series at any fixed point in S is denoted by CV= σh / hav then by substituting σ2

R from above equation in Zareal, the standard error in the areal rainfall over S, expressed as a fraction of the (time) average rainfall, finally becomes

+−==

N

S

dr

NCV

hZ

av

Rareal

00

23.01

1σ

By stating the permissible value of Zareal one obtains an estimate for the required minimum number of stations N in a basin with area S. Typical values for Zareal given as a percentage, are 5% or 10%. Note that when conducting water balance studies, the errors in the various components have to be judged. Errors of the order of about 5% to 10% for rainfall are considered widely acceptable. It should be recalled that Zareal is the root of the mean square error and, in specific cases; errors twice and even three times as high as Z are possible. In the above derivation a uniformly spaced raingauge network was assumed. If the distribution is less even, the error variance will be somewhat larger, and so will Z.



9.3 Computational Procedure

Steps for optimizing raingauge network, as detailed in Section 9.2 are summarized below. Steps:

i. Based on the topography, movement of weather systems and computed statistics; divide the region under study into homogeneous areas.

ii. Select the smallest duration or time interval (say, month) for which areal rainfall estimates have to be made and define the maximum acceptable value for Zareal for a particular season in the year (say, 5% or 10%).

iii. Collect the rainfall data of all the stations (N=44 for Upper Bhima) in the region under study with a time interval of the data equal to month (for monsoon months: June-September) and year for annual series.

iv. Validate the data thoroughly but do not fill in missing data as this will generally affect the variability of the point processes and increase the correlation between the series and will lead to an inadequate network.

v. Collect distance [d] between all the station-pairs. Distance matrix (44X44) can also be computed using Great Circle Distance Formula, using decimal degrees as

= 6378.7 * arc cos [sin (lat 1/57.2958) * sin (lat 2/57.2958) + cos (lat 1/57.2958) * cos (lat 2/57.2958) * cos (lon 2/57.2958 – lon 1/57.2958)] (Appendix 4)

vi. Consider rainfall data for the month of June.

vii. Compute areal rainfall (using simple arithmetic average over 44 stations).

viii. Derive the basic statistics of the point monthly rainfall time series i.e. mean, standard deviation and coefficient of variation.

ix. For deriving the spatial correlation structure, compute correlation coefficient between the point rainfall time series of all the stations [r(d)]. i.e. compute spatial correlation matrix (44X44) for June rainfall.

x. To reduce the scatter, compute average correlation coefficient and average distance for distance intervals of 10 km. Plot the average correlation coefficient against average distance on linear or semi-log paper.

xi. Eliminate outliers from the plot, fit a straight line through the data points using a semi-log scale and estimate the parameters r0 and d0 or alternatively, by least squares approach applied on ln (r(d)) versus distance d.

xii. Determine the relative root mean square error as a function of the number of gauging sites N for a design area S (to be derived from the hydrometric network) and compute for each period the required gauge density for a series of values for Zareal.

xiii. Repeat above steps for July, August, September and annual point rainfall series.

xiv. Make an estimate of the costs involved in development and operation of the network.

xv. Analyze the consequences of not meeting the Zareal -target.



9.4 Optimization of Upper Bhima Raingauge Network

The Upper Bhima basin covers a geographical area of 14,712 km2. Of the total geographical area, 25 % is hilly & highly dissected, 55 % plateau and about 20 % plain & valley filled. About 25 % of the Bhima basin lying in the western zone falls in good rainfall region. Remaining 75 % is rainfall deficit region having annual areal rainfall less than 700 mm. In the Parner/ Shirur region, rainfall is normally less than 600 mm. In tropical countries like India, orographic effects are considered substantial above an elevation of 800m, and hence this influence can be considered insignificant in the Upper Bhima basin.

Figure 9.1: Map showing locations of raingauge stations in Upper Bhima basin

A raingauge network should be able to provide actual monthly rainfall values for monsoon period, and as an alternative seasonal or annual areal rainfall with a relative root mean square of not more than 5% on the average. Monthly and annual point rainfall series, derived from daily observations in the period 1971-2007 for all the available 44 raingauge stations of WRD, Maharashtra in the Upper Bhima basin were used in the analysis. The historical data were carefully screened using data processing techniques. For the period 1971-2007, average data length is found to be 32 years, minimum of 7 years for PimpleGurav station and concurrent data length is found just as 5 years, wherein records for all the 44 stations were available simultaneously. Figure 9.1 gives a map showing locations of raingauge stations in the catchment areas of GD stations. Table 9.1 gives details of raingauge network in Upper Bhima basin.



Table 9.1: Network of raingauge stations in the Upper Bhima Basin

ORG stn No

Station Name Catchment Latitude Longitude Altitude Start date End Date Remark

r1 Alandi Indrayani 18:40:35N 073:54:00E 561.59 6/1/1980 12/1/2007 ORG r2 Askheda Bhama 18:49:22N 073:46:18E 626.02 1/1/1971 12/1/2007 ORG GD r3 Aundhe Bhama 18:57:20N 073:37:50E 716.46 1/1/1971 12/1/2007 ORG r4 Budhawadi Kundalika 18:47:09N 073:31:40E 612.61 1/1/1972 12/1/2007 ORG GD r5 Chaskman Bhima 18:55:15N 073:50:06E 602.51 1/1/1971 12/1/2007 ORG SRRG FCS GD r6 Hingangaon Bhima 18:04:00N 075:06:00E 487.8 1/1/1984 12/2/2007 ORG r7 Holkarpul Mula 18:33:15N 073:51:50E 565 1/1/1971 12/1/2007 ORG r8 Kashti Ghod 18:33:00N 074:35:00E 511.15 1/1/1971 12/4/2007 ORG SRRG FCS GD r9 KatrajTunnel Mula_Mutha 18:23:50N 073:51:30E 674.5 1/1/1971 12/5/2007 ORG

r10 Khamgaon Mula-Mutha 18:33:00N 074:13:00E 522.19 6/1/1984 12/6/2007 ORG GD r11 Khandala Indrayani 18:45:20N 073:22:30E 646 1/1/1971 12/7/2007 ORG SRRG r12 Kiwale Pawana 18:39:20N 073:43:10E 590 1/1/1971 12/1/2007 ORG r13 Kolgaon Palsi 18:47:38N 074:40:08E 647.87 1/1/1971 12/9/2007 ORG r14 Koliye Bhama 18:53:45N 073:38:15E 701.22 1/1/1971 12/10/2007 ORG r15 Kumbheri Mula 18:35:45N 073:24:35E 778 1/1/1971 12/11/2007 ORG r16 Kurwandi Vel 18:58:45N 073:52:08E 854.27 1/1/1971 12/12/2007 ORG r17 Lonikand Bhima 18:37:15N 074:01:30E 584 1/1/1971 12/1/2007 ORG r18 Malavali Indrayani 18:44:30N 073:29:00E 610 1/1/1972 12/1/2007 ORG r19 Malshiras Bhima 18:24:45N 074:14:45E 704 1/1/1979 12/15/2007 ORG r20 Mulshi Mula 18:31:05N 073:31:09E 685 6/1/1984 12/1/2005 ORG r21 Nighoje Indrayani 18:42:31N 073:47:38E 567.2 6/1/1995 12/17/2007 ORG GD r22 Pargaon Bhima 18:33:30N 074:22:30E 519.82 6/1/1971 12/18/2007 ORG SRRG FCS GD r23 Paud Mula 18:32:00N 073:37:00E 572 1/1/1977 12/19/2007 ORG GD r24 PimpaleGurav Pawana 18:36:10N 073:49:15E 554.7 6/1/1999 12/20/2005 ORG SRRG FCS GD r25 PimpalgaonJoga Arr 19:18:15N 073:53:45E 686.52 6/1/1971 12/21/2007 ORG r26 Pimpalwandi Kukadi 19:10:15N 074:04:00E 629.47 6/1/1971 12/22/2007 ORG SRRG r27 Rakshewadi Bhima 18:34:15N 074:20:45E 530.1 6/1/1983 12/23/2007 ORG GD r28 RanjangaonGanpati Bhima 18:45:05N 074:14:45E 609.76 6/1/1971 12/24/2007 ORG r29 Shikrapur Vel 18:41:30N 074:08:20E 574.7 6/1/1971 12/25/2007 ORG r30 Shirur Ghod 18:50:30N 074:21:30E 571.69 6/1/1972 12/26/2007 ORG GD r31 Shive Bhama 18:51:30N 073:41:00E 689.33 1/1/1971 12/1/2007 ORG r32 Supa Hanga 18:57:40N 074:32:19E 725.61 6/1/1971 12/1/2007 ORG r33 Tembhurni Bhima 18:01:30N 075:11:30E 495.43 1/1/1971 12/1/2007 ORG r34 Thitewadi Vel 18:48:00N 074:02:55E 685.98 6/1/1985 12/1/2007 ORG r35 Wagholi Mula-Mutha 18:35:00N 073:59:00E 580 1/1/1971 12/1/2007 ORG SRRG r36 Wegre(Muthe) Mutha 18:27:00N 073:37:00E 594.49 6/1/1994 12/1/2007 ORG SRRG FCS GD r37 Whiram Bhama 18:57:30N 073:35:40E 702.13 6/1/1971 12/1/2007 ORG r38 Amboli Bhima 18:56:30N 073:36:10E 688.11 1/1/1971 31/1/2007 ORG r39 Chandoh Ghod 18:57:48N 074:10:15E 594.815 1/1/1971 31/1/2007 ORG r40 Kadus Bhama 18:53:45N 073:49:08E 640.55 1/1/1971 31/1/2007 ORG r41 Kathapur Ghod 18:57:36N 074:09:15E 601.52 1/1/1971 31/1/2007 ORG r42 Pabal Vel 18:49:50N 074:03:20E 670.73 1/1/1971 31/1/2007 ORG r43 Sarola-Kasar Sina 18:56:45N 074:39:30E 685.975 1/1/1971 31/1/2007 ORG r44 Savale Indrayani 18:57:15N 073:29:25E 658 1/1/1984 31/1/2007 ORG

Note: In addition to the above, Aamdabad and Dattawadi GD sites exist in the basin. Basic statistics:

The characteristics of the monthly point rainfall series are displayed in Figure 9.2. Typically, the rainfall in Upper Bhima basin is concentrated in the monsoon season, with July and August being the wettest months, both with a long-term average rainfall of 355.5 mm and



291.4 mm respectively. The long term average annual rainfall of this region is 1141 mm (areal). In the same figure, the coefficient of variation of the monthly rainfall series is also displayed. It is observed that the CV-values for the monsoon months are lowest, and are approximately 0.4. The CV-values in the non-monsoon season range from 0.79 to 2.01. The CV-value for the areal annual rainfall series is 0.22. It shows that the variation for the annual series is about half the value of the monthly series.

Figure 9.2: Average Monthly Rainfall (1971-2007) and its Coefficient of Variation in Upper

Bhima Basin

Measure of effectiveness: From analysis of the rainfall data, it is noted that the rainfall in Upper Bhima basin is almost entirely concentrated in the months of June to September. Hence, for water resources assessment, it is sufficient to concentrate on these months and on the annual total. It was assumed that the network should be able to provide monthly and as an alternative seasonal or annual areal rainfall. Consequently, we will use as a measure of effectiveness the estimation error in the areal average monthly and annual rainfall, whose value should not be more than 5% on an average. Spatial correlation coefficients have therefore been computed for all the monsoon months individually and for the annual series. Analysis for the month of October (which is having more CV than monsoon months), having average rainfall of 70.4 mm has also been appended.

Spatial Correlation of Rainfall: Spatial correlation coefficients have been computed for all the possible pairs of raingauge stations, for each monsoon month June-September separately, for annual series and also for October month. For N=44 stations, this leads to N(N+1)/2 = 946 pairs. Spatial correlation



matrices of the order 44X44 has been formed for each case and given in Appendixes 5-10. Subsequently the distance ‘d’ between all station pairs has also been derived from the latitude/ longitude coordinates of the sites (vide Appendix 4). Computed values of rij(d) and d have been plotted in Figure 9.3 (a)-(f). A large scatter is observed.

Figure 9.3: Spatial Correlation Structure of Rainfall in Upper Bhima

To estimate the parameters r0 and d0 of spatial correlation functions for June-September and Annual series, exponential curve is plotted on the scatters of each of the above plot. The fitted spatial correlation structures and respective estimates for r0 and d0 for each monsoon



month and year are listed in Table 9.2. Months of September and June gave low values for r0. The low value of r0 for June can possibly be attributed to June measurements being less accurate than rest of the monsoon period and/ or more microclimatic disturbances. The CV value of June rainfall is also reported higher than other three months in the monsoon period.

Table 9.2: Spatial correlation function and estimates of r0 and d0

Duration / Series

Spatial Correlation Function r0 d0

Jun r(d)=0.6733e-0.0063d 0.67 159 Jul r(d)=0.7623e-0.0096d 0.76 104 Aug r(d)=0.8821e-0.0095d 0.88 105 Sep r(d)=0.5282e-0.0032d 0.52 313 Oct r(d)=0.6076e-0.0017d 0.60 588

Annual r(d)=0.6447e-0.0071d 0.64 141 Estimation of Optimum Raingauge Network Density:

Minimization of error in estimation of the areal rainfall of individual months in the monsoon period and of the annual total was taken as the measure of effectiveness of the rainfall observation network, as the criterion for optimization of WRD’s raingauge network in Upper Bhima basin. Since monthly and annual rainfall data together with flow data are usually considered in water balance studies, the estimation error in both types of data should be of the same order of magnitude. The root mean square error in the areal rainfall estimate relative to the point (time) average value Zareal is computed. The estimation error and hence the optimum number of stations required, is seen to depend strongly on the point rainfall characteristic CV, the measuring error (1-r0) and the characteristic correlation distance d0. The design surface area S of Upper Bhima basin is given as S=14,712 km2. For 5% value of admissible estimation error (Zareal) for each month and for annual data, estimated number of stations (N) actually required is presented in Table 9.3. Density requirement for September rainfall has been computed as 35, the highest amongst other monsoon months and year as a whole. This is because of high value of CV and low value of r0. From Table 9.3, it is observed that the area per gauge ranges from 420 km2 to 1,794 km2. A high density is required for estimating the September/June areal rainfall with the desired accuracy, mainly because of the low r0/ high CV values for these months. To reach for all months the required accuracy, the network density is estimated to be one gauge per 420 km2. Thus, 35 stations, which will satisfy network requirements as regards other monsoon months and annual total, can be taken as the optimal value of network requirement for Upper Bhima basin.



Table 9.3: Raingauge Network requirement for WRD in Upper Bhima with 5% admissible error in estimation of average areal rainfall

Statistics Jun Jul Aug Sep Oct Annual

Average rainfall (hav) (mm) 201.75 355.52 291.41 170.49 70.36 1141.09

Standard deviation (σh) 95.40 127.76 113.68 72.73 55.56 250.94

CV 0.47 0.36 0.39 0.43 0.79 0.22

r0 0.6733 0.7623 0.8821 0.5282 0.6076 0.6447

d0 159 104.2 105.3 312.5 588.2 140.8

Required network density N 32 16 12 35 100 8.2

Area to be covered by one

raingauge NS (km2) 460 920 1,226 420 147 1,794

For establishing a relationship between estimation error and network density, required network densities have been calculated for a range of values of admissible error in estimation, say, 2% to 16%. The estimated relationship between estimation error and network requirement is given in Figure 9.4. One of the main features of June and September rainfall observed from Figure 9.4 is that the required network density for these months would be four times as less, if the acceptable estimation error is increased from 5% to 10%. There is a need to improve accuracy of measurements in June rainfall. Although the figures for October are presented, they are not taken into account for finalizing the optimum network, since the average rainfall in October is only 71 mm; which is very less when compared with monsoon months. Apparently, highly accurate areal rainfall estimates can only be obtained with a disproportionate increase in network density. This observation stresses the need for a careful assessment of the acceptable estimation error.



Figure 9.4: Raingauge Network requirement in Upper Bhima basin

The objective used in the study is to arrive at a raingauge network that is capable in estimating the areal rainfall for a catchment area of 14,712 km2 with an error less than 5 % of the long term average rainfall for monsoon months/ year. From Table 9.3, it is observed that the area per gauge ranges from 420 km2 to 1,794 km2. A high density is required for estimating the September/June areal rainfall with the desired accuracy, mainly because of the low r0/ high CV values for these months. To get the required accuracy for all months the network density is estimated to be one gauge per 420 km2. To get a proper estimate of the annual value, the demands on the network density is highly reduced. WMO minimum ORG density for 'Upper Bhima basin up to Ujani', which is considered as semi-hilly region, is 500 km2/ gauge. Thus, for estimating areal rainfall over the Upper Bhima basin for monsoon months with 5% admissible error, 35 raingauges are considered sufficient, out of the existing 44 ORG stations.

Finalization of Raingauge Network for Future:

Establishment of raingauges, their maintenance and possible termination is a dynamic process. The network should be periodically reviewed so as take care of changes took place in the basin over the time and future needs. Spatial correlation analyses carried out in previous paragraphs have estimated the optimum number of raingauges required to estimate areal rainfall as 35, with scope for discontinuing few ORG stations. It may be noted from Figure 9.1 that existing raingauge stations are not evenly distributed over the entire basin. Thus, while optimizing the existing network, care needs to be taken to ensure that final network is evenly distributed over the entire basin, over each of the six zones formed based on isohyetal lines. In addition to this, as discussed in section 9.2, hydrometeorological



network of WRD, Maharashtra must also be evaluated in conjunction with the surface water networks, namely GD network. The raingauge network should have sufficient spatial coverage so that all GD stations in the hydrometric network are fully covered. If WRD has decided to delete some stations due to budget constraints for future maintenance, while deleting the existing station, adding new station or shifting the station, combinations of evaluations as done below in tables 9.4 and 9.6 can be utilized so that the individual raingauge requirements of each of the ‘catchment area of GD station’ and ‘Rainfall Zone based on isohyetal lines’ can be simultaneously taken care of.

Rainfall Zone-wise Distribution:

For evaluation of distribution of raingauges over the entire Upper Bhima basin, six zones have been formed by drawing isohyetal lines of 500 mm, 1000 mm, 1500 mm, 2000 mm, and 2500 mm, as shown in Figure 9.5. The optimum raingauges of 35 required have been distributed among six zones in proportion with catchment area and standard deviation of annual rainfall of each zone, and is presented in Table 9.4. Thus, appropriate redistribution i.e. addition, deletion or shifting of raingauges may be required.

Figure 9.5: Rainfall Zones of Upper Bhima Basin and Distribution of Existing

Hydrometeorological Network



Table 9.4: Rainfall Zone-wise Distribution of Existing and Optimum Raingauges in Upper

Bhima Basin

Annual Rainfall Raingauge Stations Zone Catchment

Area (km2) Average (mm)

Standard Deviation Existing Required* To Be

Deleted To Be Added

I 469 3866.0 947.3 3 4 0 1 II 855 2465.5 700.6 5 5 0 0 III 1147 1874.6 596.3 4 5 0 1 IV 1961 1083.0 323.3 2 5 0 3 V 10270 626.3 157.2 26 14 12 0 VI 928 448.0 131.4 4 2 2 0

Upper Bhima Basin

15630 1141.0 250.9 44 35 14 5

*Note: Optimum raingauges required (35) have been distributed among six zones in proportion with catchment area and variation

GD Station-wise Distribution:

WRD, Maharashtra’s raingauge network is also required for assessing the rainfall-runoff with respect to each GD station. In Table 9.5, existing and optimum raingauge network requirement for Upper Bhima basin, in conjunction with each GD stationwise requirement, is presented. Network density according to WMO standards is also given. It can be seen from Table 9.5 and Figure 9.1 that, existing raingauge stations are not evenly distributed over the basin, and also with respect to the catchment area of each GD station. Thus, enough number of raingauges needed for the catchment area of every GD station.

For estimating the areal rainfall over the Upper Bhima basin, with 5% admissible error in the estimation, for monsoon months and also for the purpose of independent estimation of areal rainfall for each GD station separately, the re-distribution of raingauge network as given in Table 9.6 is proposed. The whole basin is divided into 15 mutually exclusive regions based on the catchment areas of the existing 14 GD stations. The ideal network will have raingauges evenly distributed over the entire basin satisfying, the raingauge requirement of these 15 divisions based on GD catchments as well as simultaneously satisfying the rainfall-zone requirement as given in Table 9.4. In Table 9.6, optimum raingauges needed for each of the 15 regions is given and the figures are rounded to the next integer. The estimated number of optimum raingauges of 35 has thus increased to 42 for simultaneously taking care of two objectives at a time. In the last two columns of table 9.6, it is shown that 15 rainauges can possibly be deleted, while 13 new ones may need to be added. Thus, the final re-distribution may lead to the deletion of two raingauge stations. While making readjustment of the raingauge network, the general principles of network design needs to be followed. WRD can take into account the local needs in the respect too.



Table 9.5: GD station-wise assessment of raingauge network in Upper Bhima basin

Existing raingauges Raingauges after optimization

GD Stn No

GD Station name

Catchment Catchment Area (km 2)

stations No of stns (N)

area covered by one

raingauge (S/N) km2

N

N (rounded to next integer)

S/N km2

1 Aamdabad Ghod 1523 Chandoh, Kathapur 2 761.5 3.6 4 420

2 Askheda Bhama 239 Askheda, Aundhe, Kadus, Koliye, Shive, Whiram

6 39.8 0.6 1 420

3 Budhawadi Kundalika 152 Budhawadi 1 152.0 0.4 1 420

4 Chaskaman Bhima 389 Amboli, Chaskaman 2 194.5 0.9 1 420

5 Dattawadi Mutha 741 Wegre 1 741.0 1.8 2 420

6 Kashti Ghod 4392 Chandoh, Kathapur, PimpalgaonJoga, Pimpalwandi, Shirur, Kashti, Kolgaon, Supa, Sarola-Kasar

9 488.0 10.5 11 420

7 Khamgaon Mula-Mutha 2833

Wegre, Kumbheri, Mulshi, Paud, Kiwale, PimpleGurav, KatrajTunnel, Holkarpul, Wagholi, Malshiras, Khamgaon

11 257.5 6.7 7 420

8 Nighoje Indrayani 832 Budhawadi, Khandala, Malavali, Nighoje, Savale

5 166.4 2.0 2 420

9 Pargaon Bhima 6251

Wegre, Kumbheri, Mulshi, Paud, Kiwale, PimpleGurav, KatrajTunnel, Holkarpul, Wagholi, Malshiras, Khamgaon, Budhawadi, Khandala, Malavali, Savale, Nighoje, Askheda, Aundhe, Kadus, Koliye, Shive, RanjangaoGanpati, Shikrapur, Lonikand, Thitewadi, Aalandi, Kurwandi, Rakshewadi,Whiram, Amboli, Chaskaman, Pabal, Pargaon

33 189.4 14.9 15 420

10 Paud Mula 474 Kumbheri, Mulshi, Paud 3 158.0 1.1 2 420

11 PimpleGurav Pawana 507 Kiwale, PimpleGurav 2 253.5 1.2 2 420

12 Rakshewadi Bhima 3280

Budhawadi, Khandala, Malavali, Savale, Nighoje, Askheda, Aundhe, Kadus, Koliye, Shive, RanjangaoGanpati, Shikrapur, Lonikand, Thitewadi, Aalandi, Kurwandi, Rakshewadi,Whiram, Amboli, Chaskaman, Pabal

21 156.2 7.8 8 420

13 Shirur Ghod 3204 Chandoh, Kathapur, PimpalgaonJoga, Pimpalwandi, Shirur

3 1068.0 7.6 8 420

14 Wegre Mutha 91 Wegre 1 91.0 0.2 1 420

Upper Bhima basin Bhima 14712

Wegre, Kumbheri, Mulshi, Paud, Kiwale, PimpleGurav, KatrajTunnel, Holkarpul, Wagholi, Malshiras, Khamgaon, Budhawadi, Khandala, Malavali, Savale, Nighoje, Askheda, Aundhe, Kadus, Koliye, Shive, RanjangaoGanpati, Shikrapur, Lonikand, Thitewadi, Aalandi, Kurwandi, Rakshewadi,Whiram, Amboli, Chaskaman, Pabal, Pargaon, Chandoh, Kathapur, PimpalgaonJoga, Pimpalwandi, Shirur, Kashti, Kolgaon, Supa, Sarola-Kasar, Hingangaon, Tembhurni

44 334.4 35.0 42

420

*Upper Bhima basin is considered as semi-hilly region, for which WMO minimum ORG density is 500 km2/ gauge



Table 9.6: Proposed redistribution of raingauge network for Upper Bhima basin

Name of the region Main stream

Geographical area (km2)

existing raingauges

Optimum raingauges

Optimum raingauges (rounded to next

interger)

Raingauges to be added

Raingauges to be

deleted

1 Aamdabad GD catchment Ghod 1523 2 3.6 4 2 -- 2 Shirur GD catchment Ghod 1681 3 4.0 4 1 --

3 Shirur GD site to Kashti GD site

Ghod 1188 4 2.8 3 -- 1

4 Chaskaman GD catchment Bhima 389 2 0.9 1 -- 1 5 Askheda GD catchment Bhama 239 6 0.6 1 -- 5 6 Budhawadi GD catchment Kundalika 152 1 0.4 1 0 0

7 Budhawadi GD site to Nighoje GD site

Indrayani 680 4 1.6 2 -- 2

8

Rakshewadi GD catchment excluding Chaskaman+ Askheda+ Nighoj GDs catchment area

Bhima 1820 8 4.3 5 -- 3

9 PimpleGurav GD catchment Pawana 507 2 1.2 2 0 0 10 Paud GD catchment Mula 474 3 1.1 2 -- 1 11 Wegre GD catchment Mutha 91 1 0.2 1 0 0

12 Weghre GD site to Dattawadi GD site Mutha 650 0 1.5 2 2

13

Khamgaon GD catchment excluding PimplrGurav+ Paud+ Dattawadi GDs catchment area

Mula-Mutha 1111 5 2.6 3 -- 2

14

Pargaon GD catchment excluding Rakshewadi+ Khamgaon GDs catchment area

Bhima 138 1 0.3 1 0 0

15

Upper Bhima catchment area excluding Kashti+ Pargaon GDs catchment area Bhima

4069 2 9.7 10 8 --

Total Upper Bhima basin upto Ujjani reservior Bhima 14712 44 35.0 42 13 15



10. Results and discussions

10.1 Findings

Evaluation and optimization studies have been carried out on GD and raingauge networks for the selected pilot basin, namely, Upper Bhima basin up to Ujjani reservoir. Findings of the studies have been summarized below.

i. Catchment area of Upper Bhima basin is 14,712 km2. Western zone falls in good rainfall region, and about 75% of the basin comes under rainfall deficit region. About 85% of the rains receive from south-west monsoon.

ii. The existing GD network consists of 14 stations, which were established during the period starting from 1971. Existing raingauge network consists of 44 raingauge stations; established for the purpose of collection of hydrometeorological data in conjunction with GD network for water resources planning in the basin. Amongst these 8 are SRRG and 5 FCS.

iii. No single method of network optimization can be claimed as the best for the case of streamgauge network optimization; since such networks serves multiple objectives at a time. A combination of statistical methods and empirical rules was adopted for optimizing the GD network of Maharashtra. Statistical methods used were GLS Spatial Regression for regional information and Cross-Correlation analysis.

iv. The hydrometric (GD/ WQ) and hydrometeorological (raingauge/ FCS) network of WRD, Maharashtra was set up to provide inputs to water resources planning with goals of: i) Obtain flow rates and volumes in major tributaries of Bhima, ii) Estimating water availability and other flow characteristics at ungauged basins, and iii) Estimating peak flows at ungauged basins.

v. Two GD stations, namely Pargaon and Chaskaman can be considered as primary stations maintained as benchmark stations with measurements continued for a longer period of time to generate representative flow series of the river system, and provide general coverage of the region. Remaining 12 stations are classified as secondary stations, which are essentially short duration stations, intended to be operated only for such a length of period that is sufficient to establish the flow characteristics of the stream, relative to those of a basin gauged by the primary station. No special purpose station observed in the basin.

vi. Network density of existing GD network is 1,050 km2 per one GD station; which agrees with the minimum density norms provided by WMO (for semi-hilly area WMO norm is 1,875 km2). In its preliminary review carried out by field Engineers of WRD, GoM has proposed closure of six GD stations namely, Askheda (data length – 25 yrs), Chaskaman (35 yrs), Dattawadi (26 yrs), Rakshewadi (20 yrs), Shirur (17 yrs) and Wegre (13 yrs)]; due to backwater effect arising from construction of structures downstream or flow affected due to construction of structures upstream of the existing site. If the proposal is implemented, there will remain only 8 GD stations for the basin; and the network density will reduce to 1,839 km2/ station. By looking at the hydrological problems in the basin such as flooding and importance of the basin in



general, it is not advisable to close all the 6 backwater affected GD stations, unless alternative arrangements are made for collection of data. Out of these 6 GD sites, streamflow at 4 stations, namely, Askheda, Chaskaman, Dattawadi and Wegre has found to be affected due to construction of structures upstream. GoM officers suggested that these four sites can be shifted upstream and the flows can be continued to be measured at spillways of the upstream dams, namely, Bhama-Askheda, Chaskaman, Khadakwasala and Temghar respectively.

vii. Spatial hydrologic regression for regional information under GLS framework is performed to estimate empirical relationships between streamflow statistics of interest and basin physiographic characteristics. Influence measures - Generalized Cook's D and sampling Mean Squared Error have been computed for ranking GD stations according to their influence on the objective function, i.e. for computing monsoon average daily flow at ungauged locations.

viii. Cross-correlation matrix has been derived for possible GD station pairs upstream and downstream of one another on the same river in Upper Bhima. Four pairs Aamdabad-Kashti, Aamdabad-Shirur, Kashti-Shirur and Khamgaon-Rakshewadi have reported high cross-correlations. This points to the possible indication that out of the three GD stations of Aamdabad, Shirur and Kashti on the Ghod River, two are redundant and does not provide additional information for core network for estimation of monsoon average daily flow in the basin. Out of Khamgaon and Rakshewadi on Bhima, one is station redundant. Thus, there is a scope for discontinuing redundant GD stations.

ix. By combining outcomes of the statistical methods and empirical rules, data collections at 2 GD stations out of 14, namely Rakshewadi and Shirur can possibly be terminated, if it is essential for WRD the reduction in the network due to cost constraint for future maintenance. The suggested optimum network can possibly consists of 12 GD stations, namely, Aamdabad, Askheda, Budhawadi, Chaskaman, Dattawadi, Kashti, Khamgaon, Nighoje, Pargaon, Paud, Pimpale-Gurav and Wegre; with network density 1,226 km2 per one GD station.

x. Final fitted models using GLS Spatial Regression for regional information for three selected streamflow characteristics, namely Monsoon Average Daily Flow (µMADQ), Annual Maximum Flow (µAMQ) and 50-Year Flood (Q50) (m

3/s) are mentioned below.

a. µAAQ = 0.043 CA0.672 MMP0.322

b. µAMQ = 0.974 CA0.670 MAP0.240

c. Q50 = 2.008 CA0.771 MAP0.226

where CA=Catchment Area (km2), MMP=Mean Monsoon Precipitation (mm) and MAP=Mean Annual Precipitation (mm)

Above models can be used to predict streamflow statistics at any ungauged location in the basin.

xi. Rating curves have been developed for all the 14 GD stations in Upper Bhima using daily gauge-discharge series. It is observed that the rating curves for 7 GD stations namely, Askheda, Budhawadi, Dattawadi, Khamgaon, Nighoje, Pargaon and Wegre



are at different gauge elevations, possibly due to changes in the gauge level. The reason(s) for such shift(s) may need to be explored, and identified. Zero of Gauge for all the GD sites may be reviewed to ensure that all historical data at different stations are comparable.

xii. Common improvements recommended in the infrastructure of GD network are mentioned below.

a. All GD sites should be converted to a common benchmark, say GTS.

b. Use of current meter on GD sites wherever feasible.

c. Adequate staff to be posted at each GD site.

d. Shifting of GD sites affected by backwater effect; else provision of auxiliary site downstream of the present GD site.

e. When rating curves are consistent for a GD station, stages can be recorded; and discharge worked out using stage-discharge curve.

f. Installation of DWLR/ AWLR on the sites which represents the sub-basin.

g. Stages should be recorded at least for five years after closure of the site.

h. Provision of raingauge station proposed in the catchment having GD site, but with no raingauge station at present.

i. Establishment of new GD sites as per need.

xiii. Raingauge network in the basin under study has been reviewed using Spatial Correlation Analysis approach. The network is also evaluated in conjunction with the GD network of the basin.

xiv. It is observed that existing raingauge network is not evenly distributed over the basin and also with respect to catchment area of each GD station.

xv. From the analysis of basic statistics, it is revealed that the rainfall in the Upper Bhima basin is almost entirely concentrated in the months of June to September. Hence, for water resources assessment, monsoon months and annual total was analyzed. Consequently, the estimation error in the areal average monthly and annual rainfall is selected as a measure of effectiveness of the network.

xvi. Optimum number of raingauges needed for the sole estimation of areal rainfall in monsoon months, and year as a whole, has been arrived at as 35 by considering 5% admissible estimation error. This is equivalent to one raingauge station per 420 km2 area. WMO minimum ORG density for 'Upper Bhima basin’ is one station per 500 km2 area. Somewhat dense network is needed for Upper Bhima basin as compared with WMO norms. This may be because of higher spatial and temporal variability in the rainfall of this region.

xvii. The ideal raingauge network of WRD Maharashtra will have raingauges evenly distributed over the entire basin as well as over different rainfall zones, estimating areal rainfall with the given accuracy, satisfying the raingauge requirement of the catchment areas of every GD station. For simultaneously taking care of two objectives of estimating areal rainfall over the entire basin and for the requirement of the existing GD stations, 42 raingauges will be needed. While re-distributing the



raingauge network, the general principles of network design and local needs of WRD in the respect would need to be taken into account.

xviii. If WRD decides to delete some raingauge stations due to budget constraints for future maintenance of the network; while deleting the existing station, adding new station or shifting the station, individual raingauge requirements of each of the ‘catchment area of GD station’ and ‘Rainfall Zone based on isohyetal lines’ may be simultaneously met with so that final network would be as evenly distributed as possible over the entire basin.

xix. For the historical period 1971-2007 of Upper Bhima raingauge network of WRD, average data length of raingauge station is found to be 32 years, minimum 7 years for Pimple-Gurav station and concurrent data length is found as 5 years wherein records for all the 44 stations were available simultaneously.

xx. The characteristics of the monthly point rainfall series in Upper Bhima basin have been studied in detail. Rainfall is concentrated in the monsoon season, with July and August being the wettest months, both with a long-term average rainfall of 355.5 mm and 291.4 mm respectively. The long term average annual rainfall of this region is 1141 mm (areal). It is observed that coefficients of variation during monsoon months are lowest, and are approximately 0.4. In the non-monsoon season, it ranges from 0.79 to 2.01 and for areal annual rainfall series, variation is 0.22. It shows that the variation for the annual series is about half the value of the monthly series.

xxi. Spatial correlation structures have been determined for each monsoon month separately, and for annual series; based on computed spatial correlation and distance matrixes. The low value of characteristic correlation for June can possibly be attributed to June measurements being less accurate than rest of the monsoon period and/ or more microclimatic disturbances.

10.2 Suggestions

i. Since hydrometric network design is a dynamic process, networks need to be regularly reviewed and updated such that they react to new priorities, changes in policies and fiscal changes. Regular, formalized network reviews are recommended at least once in five years.

ii. Of late, there is a growing concern on effect of global/ regional climate change on river systems in any region. Such changes affect rainfall variability and intensity. Due to urbanization and development in agriculture, abstraction of water from rivers is increasing day-by-day. As such, in future more and more hydrometeorological data with long record lengths may be required to study such changes. This aspect may need to be taken into consideration, while deciding to terminate any station in an existing network.

iii. Many hydrological studies require data converted into naturalized flows, whose calculation requires inflow/outflow from reservoirs. Therefore, it is recommended that data collection agencies may maintain data on naturalized flows in addition to actually observed discharges.



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23) WMO [1982], ‘Concepts and techniques in hydrological network design’ by Moss M.E.; Operational Hydrology Report No.19, WMO No.580, Geneva



Acknowledgements

We express our sincere thanks to Shri H T Mendhegiri, Chief Engineer, Hydrology Project, Water Resources Department, Govt of Maharashtra, Nashik for technical discussions, timely provision of hydrometeorological data for the study, extending hospitality during our visits to Nashik. We are also thankful to Shri M K Pokale, Superintending Engineer, Hydrology Project Circle (Collection); Shri S R Tejale, Superintending Engineer, Hydrology Project Circle (Analysis); Dr P K Pawar, Executive Engineer, Hydrometeorological Data Processing Division (HDPD); Shri D A Bagade, ex. Executive Engineer, HDPD; Shri Mhetre, Executive Engineer, Hydrology Project, (Pune office); Miss C P Deshpande, Assistant Engineer-II for their excellent support during the course of this PDS.

Technical discussions especially with Dr P K Pawar, Executive Engineer, Miss C P Deshpande, Assistant Engineer-II and Dr M M Kshirsagar, Senior Research Officer, CWPRS improved the quality of the report. Thanks are due to Dr J S Tomar, a Trainee Research Officer, for his assistance during rainfall data processing.

Our sincere thanks are due to Mr Stephen Parsons, Team Leader (Hydrology Project-II), Technical Assistance (Implementation Support) and Management Consultancy (TAMC), who extended all support to this purpose driven study, and encouraged us. We are also thankful to Mr Frank A K Farquharson, and Ms Helen A Houghton, Senior Hydrologist of TAMC for having technical discussions during their visit to CWPRS on 29.4.2009.



Appendix 1

Computer Program in FORTRAN for GLS Spatial Hydrolo gic Regression of streamflow statistics: ‘Monsoon Average Daily Flow’ on ‘catchment area’ and ‘mean monsoon precipitation’ and deriving influence statistics & Cross-Correlation for streamgauge network optimization fo r Upper Bhima Basin PROGRAM SPATIAL HYDROLOGIC REGRESSION FOR REGIONAL INFORMATION Use MSFLIB USE MSIMSL USE MSIMSLMD USE MSIMSLMS USE MSIMSLSD USE MSIMSLSS Character * 20 ipfnm, opfnm CHARACTER * 80 DUMMY Integer S(14), YR(35), DL(14),M(14,14) Real DIS(35,14), SD(14), DISBAR(14), LN_AVGMADQ(14),LNCA(14) Real LNMMP(14) REAL CC(14,14),AB(14,14),A(14), B(14), SSA(14), SSB(14) REAL Y(14,1) REAL BT(3,1) REAL SIG(14,14), ME(14,14), ID(14,14), L(14,14) REAL LI(14,14) REAL X(14,3),B3(3,14), B4(3,3), B4I(3,3), B5(3,1) REAL B11(105,1),B12(6,1) INTEGER B21(14,1),B22(3,1) REAL ST3(14,1), ST1(1,14), ST4(1,14), DF(1,1), H(14,14), S_LE REAL YT(1,14), Rsqr(1,1),HD(14,14), COOK_D(14), XROWT(3,1) REAL MSE(1), AVG_MSE(1), Yhat(14,1) REAL N,K, Rsqr_adj(1,1), SE_ORG(1,1) Write(*,*) 'Enter Input Data File Name (20chars)' Read (*,1001) ipfnm Write(*,*) 'Enter Output File Name (20chars)' Read (*,1001) opfnm Open (5,file=ipfnm) Open (6,file=opfnm) Write (6,*) "SPATIAL HYDROLOGIC REGRESSION FOR REGIONAL INFORMATIO 1N" Read (5,1002) DUMMY Read (5,*) n Read (5,1002) DUMMY Read (5,*) k Write (6,*) "number of sites n=" write (6,*) n Write (6,*) "number of basin physiographic characteristics k=" write (6,*) k



Read (5,1002) DUMMY Read (5,*) (S(i), i=1,14) write(6,*)"******************************************************" Write (6,*) "STATION NUMBERS ARE" write(6,1003) (S(i), i=1,14) write(6,*)"******************************************************" Read (5,1002) DUMMY Read (5,*) (YR(i), i=1,35) Write (6,*) "DATA PERIOD" write(6,1003) (YR(i), i=1,35) write(6,*)"******************************************************" Read (5,1002) DUMMY Read (5,*) ((DIS(YR(i),S(j)), j=1,14), i=1,35) Read (5,1002) DUMMY Read (5,*) (LN_AVGMADQ(i), i=1,14) Write (6,*) "LN(AVG MADQ) FOR STN NUMBERS 1 TO 14" write(6,1005) (LN_AVGMADQ(i), i=1,14) write(6,*)"******************************************************" Read (5,1002) DUMMY Read (5,*) (LNCA(i), i=1,14) Write (6,*) "LN(CATCHMENT AREA) FOR STN NUMBERS 1 TO 14" write(6,1005) (LNCA(i), i=1,14) write(6,*)"******************************************************" Read (5,1002) DUMMY Read (5,*) (LNMMP(i), i=1,14) Write (6,*) "LN(MEAN ANNUAL PRECIPITATION)FOR STN NUMBERS 1 TO 14" write(6,1005) (LNMMP(i), i=1,14) write(6,*)"******************************************************" Write (6,*) "DATA LENGTH FOR STATIONS 1 TO 14 IS" do j = 1,14 COUNT=0 do i = 1973,2007 IF (DIS(i,j) > -10.000) THEN COUNT=1 DL(J) = DL(J)+ COUNT END IF end do end do COUNT=0 write(6,1003) (DL(J), j=1,14) write(6,*)"******************************************************" Write (6,*) "ESTIMATED SD (of LN transformed DIS ANNUAL SERIES)FOR 1 STATIONS 1 TO 14 IS" do J=1,14 do I=1973,2007 IF (DIS(i,j) > -10.000) THEN DISBAR(J)=DISBAR(J)+ DIS(i,j)/DL(J) END IF end do end do do J=1,14



do I=1973,2007 IF (DIS(i,j) > -10.000) THEN SD(J)=SD(J)+ (DIS(i,j)-DISBAR(J))**2 END IF end do SD(J)=SQRT(SD(J)/(DL(J)-1)) end do write(6,1005) (SD(J), j=1,14) write(6,*)"******************************************************" Write (6,*) "CONCURRENT RECORD LENGTHS" do I = 1,14 DO J= 1,14 COUNT=0 do P = 1973,2007 IF ((DIS(P,I) > -10.000).AND.(DIS(P,J) > -10.000)) THEN COUNT=1 M(I,J) = M(I,J)+ COUNT END IF end do END DO end do COUNT=0 write(6,1003) ((M(I,J), I=1,14), J=1,14) write(6,*)"******************************************************" Write (6,*) "CROSS CORRELATION BETWEEN STATIONS (LN TRANSFORMED AN 1NUAL DIS SERIES)" do I = 1,14 DO J= 1,14 A(I)=0 B(J)=0 SSA(I)=0 SSB(J)=0 do P = 1973,2007 IF ((DIS(P,I) > -10.000).AND.(DIS(P,J) > -10.000)) THEN A(I)=A(I)+ DIS(P,I)/M(I,J) B(J)=B(J)+ DIS(P,J)/M(I,J) END IF END DO do P = 1973,2007 IF ((DIS(P,I) > -10.000).AND.(DIS(P,J) > -10.000)) THEN SSA(I)=SSA(I)+ (DIS(P,I)-A(I))**2 SSB(J)=SSB(J)+ (DIS(P,J)-B(J))**2 AB(I,J) = AB(I,J)+(DIS(P,I)-A(I))*(DIS(P,J)-B(J)) END IF end do CC(I,J)= AB(I,J)/SQRT(SSA(I)*SSB(J)) END DO end do write(6,1005) ((CC(I,J), I=1,14), J=1,14) write(6,*)"******************************************************"



Write (6,*) "ESTIMATE OF MATRIX SIGMA" DO I = 1,14 DO J= 1,14 SIG(I,J) = (CC(I,J)*SD(I)*SD(J)*M(I,J))/(M(I,I)*M(J,J)) END DO END DO SIG = RESHAPE((/((SIG(I,J), I=1,14), J=1,14)/), (/14, 14/)) WRITE(6,1005) SIG write(6,*)"******************************************************" Write (6,*) "MATRIX Y" Y = RESHAPE((/(LN_AVGMADQ(i), i=1,14)/), (/14, 1/)) WRITE(6,1005) Y write(6,*)"******************************************************" Write (6,*) "MATRIX X" DO I=1,14 X(I,1)=1 X(I,2)=LNCA(I) X(I,3)=LNMMP(I) END DO WRITE(6,1009) X write(6,*)"******************************************************" do i = 1,14 do j = 1,14 ID(I,J) = 0.0 end do end do do I = 1,14 DO J= 1,14 IF (I .EQ. J) THEN ID(I,J) = 1 END IF END DO end do G=0.001 100 ME= G*G*ID L=ME+SIG CALL L2NRG (14, L, 14, LI,14,B11,B21) CALL MXTYF(14,3,X,14,14,14,LI,14,3,14,B3,3) B4=MATMUL(B3,X) CALL L2NRG (3, B4, 3, B4I,3,B12,B22) B5=MATMUL(B3,Y) BT=MATMUL(B4I,B5) ST3=Y-MATMUL(X,BT) CALL TRNRR (14,1,ST3,14,1,14,ST1,1) ST4=MATMUL(ST1,LI) DF=MATMUL(ST4,ST3) IF (ABS(DF(1,1)-(N-K-1)) .GT. 0.001) THEN G=G+.00001 GOTO 100 END IF



write(6,*)"******************************************************" Write(6,*) "OUTPUT USING NUMERICAL SEARCH METHOD" WRITE(6,*) "DF=n-k-1" WRITE(6,*) "ACTUAL DF is" write(6,*) n-k-1 WRITE(6,*) "taken value of DF in NUMERICAL SEARCH is" WRITE(6,1006) DF write(6,*)"******************************************************" WRITE(6,*) "Final value of gamma is" WRITE(6,1006) G write(6,*)"******************************************************" WRITE(6,*) "Final value of model error " WRITE(6,1006) G*G write(6,*)"******************************************************" WRITE(6,*) "Final estimate of MATRIX lambda is" WRITE(6,1009) L write(6,*)"******************************************************" Write(6,*) "GLS estimate of Beta is" WRITE(6,1008) BT write(6,*)"******************************************************" Write(6,*) "Variance-Covariance Matrix of BetaHat" WRITE(6,1008) B4I write(6,*)"******************************************************" Write(6,*) "Estimated values of Y i.e.Y^" Yhat= MATMUL(X,BT) WRITE(6,1006) Yhat write(6,*)"******************************************************" Write(6,*) "Residual values i.e. Y-Y^" WRITE(6,1006) ST3 write(6,*)"******************************************************" write(6,*) "R^2 i.e. Explained Variation is" Ybar=0.0 DO I=1,14 DO J=1,1 Ybar=Ybar+Y(I,J)/14 end do end do CALL TRNRR (14,1,Y,14,1,14,YT,1) Rsqr=1-(MATMUL(ST1,ST3)/(MATMUL(YT,Y)-(14*Ybar*Ybar))) WRITE(6,1006) Rsqr write(6,*)"******************************************************" write(6,*) "R^2 adj. is" Rsqr_adj=1-((n-1)/(n-k-1))*(1-(Rsqr*Rsqr)) WRITE(6,1006) Rsqr_adj write(6,*)"******************************************************" write(6,*) "STANDARD ERROR OF ESTIMATE (SAMPLE STANDARD DEVIATION 1OF REGRESSION)" DO I=1,14 SE=SE+ST3(I,1)**2 END DO



SE=SE/(N-K-1) SE=SQRT(SE) WRITE(6,1006) SE write(6,*)"******************************************************" Write(6,*) "LEVERAGE OF SITES" H=MATMUL(MATMUL(X,B4I),B3) do I = 1,14 WRITE (6,1012) I,I,H(I,I) end do Write(6,*)"Sum of LEVERAGES" do I = 1,14 S_LE=S_LE + H(I,I) end do WRITE(6,1006) S_LE Write(6,*)"SITES WITH LEVERAGE AT LEAST (k+1)/n" do I = 1,14 IF (H(I,I).GE. (K+1)/N) THEN WRITE (6,1012) I,I,H(I,I) END IF end do Write(6,*)"HIGH LEVERAGE SITES Hii >= 2(k+1)/n" do I = 1,14 IF (H(I,I).GE. (2*(K+1)/N)) THEN WRITE (6,1012) I,I,H(I,I) END IF end do write(6,*)"******************************************************" WRITE(6,*) "Generalized Cook's D statistic" WRITE(6,*) "measure of the influence of site i on the fit" HD= MATMUL(H,L) DO I=1,14 COOK_D(I)= (HD(I,I)*ST3(I,1)**2)/(2*(L(I,I)-HD(I,I))**2) WRITE(6,1013) I, COOK_D(I) END DO WRITE(6,*) "Cook's Di >= 4/n" do I = 1,14 IF (COOK_D(I).GE. (4/N)) THEN WRITE (6,1013) I, COOK_D(I) END IF end do write(6,*)"******************************************************" WRITE(6,*) "sampling MSE" AVG_MSE=0.0 DO I=1,14 CALL TRNRR (1,3,X(I,1:3),1,3,1,XROWT,3) MSE=MATMUL(MATMUL(X(I,1:3),B4I),XROWT) AVG_MSE=AVG_MSE+MSE/14 WRITE (6,1014) I,MSE END DO WRITE(6,*) "AVERAGE SAMPLING MSE =" WRITE(6,1006) AVG_MSE



write(6,*)"******************************************************" WRITE(6,*) "OUTPUT IN ORIGINAL SCALE i.e. m3/sec" write(6,*)"******************************************************" WRITE(6,*) " Y Y^ resiuduals" write(6,*)"******************************************************" DO I=1,14 WRITE(6,1008) EXP(Y(I,1)),EXP(Yhat(I,1)),EXP(Y(I,1))-EXP(Yhat(I,1) 1) END DO write(6,*)"******************************************************" write(6,*) "STANDARD ERROR OF ESTIMATE (in original scale)" DO I=1,14 SE_ORG=SE_ORG+ (EXP(Y(I,1))- EXP(Yhat(I,1)))**2 END DO SE_ORG=SE_ORG/(N-K-1) SE_ORG=SQRT(SE_ORG) WRITE(6,1006) SE_ORG write(6,*)"******************************************************" 1001 Format(A20) 1002 format(A80) 1003 format(14I8) 1004 format(14f6.3) 1005 format(14F8.3) 1006 format(1F8.5) 1007 format(2F10.3) 1008 format(3F10.3) 1009 format(14F8.3) 1012 FORMAT("H(", I2, ",", I2, ") = ",F8.5) 1013 FORMAT("SITE = ", I2, ",", "COOK_D = ",F8.5) 1014 FORMAT("SITE = ", I2, ",", "MSE = ",F8.5) Close (6) Close (5) END



Appendix 2a

FORTRAN Output for GLS Spatial Hydrologic Regressio n of streamflow statistics: ‘Monsoon Average Daily Flow’ on ‘catchm ent area’ and ‘mean monsoon precipitation’ and deriving influence stati stics & Cross-Correlation for streamgauge network optimization for Upper Bhim a Basin SPATIAL HYDROLOGIC REGRESSION FOR REGIONAL INFORMATION number of sites n= 14.000000 number of basin physiographic characteristics k= 2.000000 ****************************************************** STATION NUMBERS ARE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ****************************************************** DATA PERIOD 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

****************************************************** LN(AVG MADQ) FOR STN NUMBERS 1 TO 14 3.475 2.668 2.553 3.150 3.556 3.707 4.813 3.993 5.499 3.030 3.376 4.594 4.044 2.749

****************************************************** LN(CATCHMENT AREA) FOR STN NUMBERS 1 TO 14 7.328 5.478 5.023 5.964 6.608 8.388 7.949 6.724 8.740 6.160 6.228 8.096 8.072 4.513

****************************************************** LN(MEAN ANNUAL PRECIPITATION)FOR STN NUMBERS 1 TO 14 6.920 7.440 7.975 7.366 7.629 6.551 7.446 7.728 7.227 7.912 7.663 7.063 6.683 7.549

****************************************************** DATA LENGTH FOR STATIONS 1 TO 14 IS 12 25 27 35 26 21 23 17 26 24 11 20 17 13 ****************************************************** ESTIMATED SD (of LN transformed DIS ANNUAL SERIES)FOR STATIONS 1 TO 14 IS 3.081 1.977 .617 1.804 3.922 2.615 .535 .382 2.508 .649 .650 .524 1.080 .444

****************************************************** CONCURRENT RECORD LENGTHS 12 12 12 12 12 9 12 12 12 12 11 8 5 11 12 25 25 25 25 21 23 17 25 24 11 20 17 13 12 25 27 27 26 21 23 17 26 24 11 20 17 13 12 25 27 35 26 21 23 17 26 24 11 20 17 13 12 25 26 26 26 21 23 17 26 24 11 20 17 13 9 21 21 21 21 21 20 14 21 21 8 20 17 11 12 23 23 23 23 20 23 17 23 23 11 19 16 13 12 17 17 17 17 14 17 17 17 17 11 13 10 13 12 25 26 26 26 21 23 17 26 24 11 20 17 13 12 24 24 24 24 21 23 17 24 24 11 20 17 13 11 11 11 11 11 8 11 11 11 11 11 7 4 10



8 20 20 20 20 20 19 13 20 20 7 20 17 10 5 17 17 17 17 17 16 10 17 17 4 17 17 7 11 13 13 13 13 11 13 13 13 13 10 10 7 13 ****************************************************** CROSS CORRELATION BETWEEN STATIONS (LN TRANSFORMED ANNUAL DIS SERIES) 1.000 -.029 .572 .489 .794 .969 .418 .609 .110 .511 .614 .666 .986 .454 -.029 1.000 .180 .141 .042 -.082 .310 .444 .011 .141 .071 .055 .127 .536 .572 .180 1.000 .434 .402 .632 .537 .709 .272 .557 .790 .539 .490 .616 .489 .141 .434 1.000 .419 .539 .589 .652 .179 .433 .669 .784 .649 .662 .794 .042 .402 .419 1.000 .589 .370 .645 .231 .610 .699 .340 .232 .450 .969 -.082 .632 .539 .589 1.000 .459 .669 .247 .426 .695 .539 .944 .392 .418 .310 .537 .589 .370 .459 1.000 .752 .414 .569 .660 .883 .708 .728 .609 .444 .709 .652 .645 .669 .752 1.000 .221 .761 .806 .775 .825 .843 .110 .011 .272 .179 .231 .247 .414 .221 1.000 .234 .595 .217 .698 .472 .511 .141 .557 .433 .610 .426 .569 .761 .234 1.000 .847 .466 .516 .687 .614 .071 .790 .669 .699 .695 .660 .806 .595 .847 1.000 .522 .899 .832 .666 .055 .539 .784 .340 .539 .883 .775 .217 .466 .522 1.000 .581 .586 .986 .127 .490 .649 .232 .944 .708 .825 .698 .516 .899 .581 1.000 .497 .454 .536 .616 .662 .450 .392 .728 .843 .472 .687 .832 .586 .497 1.000 ****************************************************** ESTIMATE OF MATRIX SIGMA .791 -.007 .040 .078 .369 .279 .030 .042 .033 .043 .102 .036 .080 .044 -.007 .156 .008 .014 .013 -.017 .013 .013 .002 .007 .004 .002 .011 .019 .040 .008 .014 .014 .036 .038 .007 .006 .016 .008 .012 .006 .012 .006 .078 .014 .014 .093 .085 .073 .016 .013 .023 .014 .022 .021 .036 .015 .369 .013 .036 .085 .591 .232 .030 .037 .087 .060 .068 .027 .038 .030 .279 -.017 .038 .073 .232 .326 .027 .026 .062 .030 .041 .035 .127 .018 .030 .013 .007 .016 .030 .027 .012 .007 .021 .008 .010 .010 .017 .008 .042 .013 .006 .013 .037 .026 .007 .009 .008 .008 .012 .006 .012 .008 .033 .002 .016 .023 .087 .062 .021 .008 .242 .015 .037 .011 .073 .020 .043 .007 .008 .014 .060 .030 .008 .008 .015 .018 .015 .007 .015 .008 .102 .004 .012 .022 .068 .041 .010 .012 .037 .015 .038 .006 .013 .017 .036 .002 .006 .021 .027 .035 .010 .006 .011 .007 .006 .014 .016 .005 .080 .011 .012 .036 .038 .127 .017 .012 .073 .015 .013 .016 .069 .008 .044 .019 .006 .015 .030 .018 .008 .008 .020 .008 .017 .005 .008 .015 ****************************************************** MATRIX Y 3.475 2.668 2.553 3.150 3.556 3.707 4.813 3.993 5.499 3.030 3.376 4.594 4.044 2.749

****************************************************** MATRIX X 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 7.328 5.478 5.023 5.964 6.608 8.388 7.949 6.724 8.740 6.160 6.228 8.096 8.072 4.513 6.920 7.440 7.975 7.366 7.629 6.551 7.446 7.728 7.227 7.912 7.663 7.063 6.683 7.549

****************************************************** OUTPUT USING NUMERICAL SEARCH METHOD DF=n-k-1 ACTUAL DF is 11.000000 taken value of DF in NUMERICAL SEARCH is 11.00048 ******************************************************



Final value of gamma is .27451 ****************************************************** Final value of model error .07536 ****************************************************** Final estimate of MATRIX lambda is .867 -.007 .040 .078 .369 .279 .030 .042 .033 .043 .102 .036 .080 .044 -.007 .232 .008 .014 .013 -.017 .013 .013 .002 .007 .004 .002 .011 .019 .040 .008 .089 .014 .036 .038 .007 .006 .016 .008 .012 .006 .012 .006 .078 .014 .014 .168 .085 .073 .016 .013 .023 .014 .022 .021 .036 .015 .369 .013 .036 .085 .667 .232 .030 .037 .087 .060 .068 .027 .038 .030 .279 -.017 .038 .073 .232 .401 .027 .026 .062 .030 .041 .035 .127 .018 .030 .013 .007 .016 .030 .027 .088 .007 .021 .008 .010 .010 .017 .008 .042 .013 .006 .013 .037 .026 .007 .084 .008 .008 .012 .006 .012 .008 .033 .002 .016 .023 .087 .062 .021 .008 .317 .015 .037 .011 .073 .020 .043 .007 .008 .014 .060 .030 .008 .008 .015 .093 .015 .007 .015 .008 .102 .004 .012 .022 .068 .041 .010 .012 .037 .015 .114 .006 .013 .017 .036 .002 .006 .021 .027 .035 .010 .006 .011 .007 .006 .089 .016 .005 .080 .011 .012 .036 .038 .127 .017 .012 .073 .015 .013 .016 .144 .008 .044 .019 .006 .015 .030 .018 .008 .008 .020 .008 .017 .005 .008 .091 ****************************************************** GLS estimate of Beta is -3.155 .672 .322 ****************************************************** Variance-Covariance Matrix of BetaHat 9.014 -.213 -1.007 -.213 .010 .020 -1.007 .020 .116 ****************************************************** Estimated values of Y i.e.Y^ 4.00156 2.92495 2.79127 3.22794 3.74572 4.59555 4.58858 3.85561 5.04998 3.53559 3.50113 4.56408 4.42556 2.31111 ****************************************************** Residual values i.e. Y-Y^ -.52656 -.25695



-.23827 -.07794 -.18972 -.88855 .22442 .13739 .44902 -.50559 -.12513 .02992 -.38156 .43789 ****************************************************** R^2 i.e. Explained Variation is .78151 ****************************************************** R^2 adj. is .53998 ****************************************************** STANDARD ERROR OF ESTIMATE (SAMPLE STANDARD DEVIATION OF REGRESSION) .43818 ****************************************************** LEVERAGE OF SITES H( 1, 1) = .00145 H( 2, 2) = .09181 H( 3, 3) = .34271 H( 4, 4) = .07565 H( 5, 5) = -.01310 H( 6, 6) = .08850 H( 7, 7) = .32392 H( 8, 8) = .23715 H( 9, 9) = .10435 H(10,10) = .26192 H(11,11) = .10253 H(12,12) = .38497 H(13,13) = .42824 H(14,14) = .56982 Sum of LEVERAGES 2.99992 SITES WITH LEVERAGE AT LEAST (k+1)/n H( 3, 3) = .34271 H( 7, 7) = .32392 H( 8, 8) = .23715 H(10,10) = .26192 H(12,12) = .38497 H(13,13) = .42824 H(14,14) = .56982



HIGH LEVERAGE SITES Hii >= 2(k+1)/n H(14,14) = .56982 ****************************************************** Generalized Cook's D statistic measure of the influence of site i on the fit SITE = 1,COOK_D = .01099 SITE = 2,COOK_D = .02847 SITE = 3,COOK_D = .27897 SITE = 4,COOK_D = .00456 SITE = 5,COOK_D = .00082 SITE = 6,COOK_D = .41314 SITE = 7,COOK_D = .30790 SITE = 8,COOK_D = .06024 SITE = 9,COOK_D = .07340 SITE = 10,COOK_D = .84814 SITE = 11,COOK_D = .01601 SITE = 12,COOK_D = .00816 SITE = 13,COOK_D = 1.31160 SITE = 14,COOK_D = 4.04972 Cook's Di >= 4/n SITE = 6,COOK_D = .41314 SITE = 7,COOK_D = .30790 SITE = 10,COOK_D = .84814 SITE = 13,COOK_D = 1.31160 SITE = 14,COOK_D = 4.04972 ****************************************************** sampling MSE SITE = 1,MSE = .05252 SITE = 2,MSE = .03379 SITE = 3,MSE = .03221 SITE = 4,MSE = .02912 SITE = 5,MSE = .01912 SITE = 6,MSE = .09678 SITE = 7,MSE = .03459 SITE = 8,MSE = .02340 SITE = 9,MSE = .05148 SITE = 10,MSE = .02798 SITE = 11,MSE = .01854 SITE = 12,MSE = .04142 SITE = 13,MSE = .07817 SITE = 14,MSE = .05460 AVERAGE SAMPLING MSE = .04241



****************************************************** OUTPUT IN ORIGINAL SCALE i.e. m3/sec ****************************************************** Y Y^ resiuduals ****************************************************** 32.298 54.683 -22.386 14.411 18.633 -4.222 12.846 16.302 -3.456 23.336 25.228 -1.892 35.023 42.339 -7.317 40.731 99.043 -58.311 123.100 98.354 24.746 54.217 47.257 6.960 244.447 156.019 88.429 20.697 34.315 -13.618 29.254 33.153 -3.899 98.889 95.974 2.915 57.054 83.559 -26.505 15.627 10.086 5.541 ****************************************************** STANDARD ERROR OF ESTIMATE (in original scale) 34.91679 ******************************************************



Appendix 2b

FORTRAN Output for GLS Spatial Hydrologic Regressio n of streamflow statistics: ‘50 Year Flood’ on ‘catchment area’ and ‘mean annual precipitation’ and deriving influence statistics & Cross-Correlati on for streamgauge network optimization for Upper Bhima Basin SPATIAL HYDROLOGIC REGRESSION FOR REGIONAL INFORMATION Number of sites n = 14 Number of basin physiographic characteristics k = 2 ****************************************************** STATION NUMBERS ARE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ****************************************************** DATA PERIOD 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 ****************************************************** LN (50 YEAR FLOOD) FOR STN NUMBERS 1 TO 14 7.654 6.949 5.868 7.297 7.703 8.199 8.653 7.702 9.158 7.079 7.673 8.615 8.128 6.062 ****************************************************** LN (CATCHMENT AREA) FOR STN NUMBERS 1 TO 14 7.328 5.478 5.023 5.964 6.608 8.388 7.949 6.724 8.740 6.160 6.228 8.096 8.072 4.513 ****************************************************** LN (MEAN ANNUAL PRECIPITATION)FOR STN NUMBERS 1 TO 14 6.968 7.465 7.991 7.399 7.652 6.617 7.471 7.749 7.259 7.919 7.687 7.103 6.740 7.562 ****************************************************** DATA LENGTH FOR STATIONS 1 TO 14 IS 12 25 27 35 26 21 23 17 26 24 11 20 17 13 ****************************************************** ESTIMATED SD (of LN transformed DIS ANNUAL SERIES)FOR STATIONS 1 TO 14 IS 1.965 1.306 .421 1.245 2.419 1.768 .749 .541 1.677 .704 .807 .651 .867 .479 ****************************************************** CONCURRENT RECORD LENGTHS 12 12 12 12 12 9 12 12 12 12 11 8 5 11 12 25 25 25 25 21 23 17 25 24 11 20 17 13 12 25 27 27 26 21 23 17 26 24 11 20 17 13 12 25 27 35 26 21 23 17 26 24 11 20 17 13 12 25 26 26 26 21 23 17 26 24 11 20 17 13 9 21 21 21 21 21 20 14 21 21 8 20 17 11 12 23 23 23 23 20 23 17 23 23 11 19 16 13 12 17 17 17 17 14 17 17 17 17 11 13 10 13 12 25 26 26 26 21 23 17 26 24 11 20 17 13 12 24 24 24 24 21 23 17 24 24 11 20 17 13 11 11 11 11 11 8 11 11 11 11 11 7 4 10



8 20 20 20 20 20 19 13 20 20 7 20 17 10 5 17 17 17 17 17 16 10 17 17 4 17 17 7 11 13 13 13 13 11 13 13 13 13 10 10 7 13 ****************************************************** CROSS CORRELATION BETWEEN STATIONS (LN TRANSFORMED ANNUAL DIS SERIES) 1.000 .181 .562 .278 .840 .959 .669 .731 .092 .584 .807 -.189 .991 .806 .181 1.000 .530 .628 .270 .040 .344 .611 .129 .409 .373 .212 .339 .555 .562 .530 1.000 .603 .226 .421 .777 .775 .477 .568 .818 .486 .543 .844 .278 .628 .603 1.000 .497 .204 .607 .623 .242 .771 .709 .436 .679 .614 .840 .270 .226 .497 1.000 .570 .476 .658 .195 .692 .682 .032 .122 .692 .959 .040 .421 .204 .570 1.000 .645 .658 .260 .436 .734 .293 .824 .718 .669 .344 .777 .607 .476 .645 1.000 .715 .651 .695 .846 .618 .747 .726 .731 .611 .775 .623 .658 .658 .715 1.000 .297 .724 .862 .299 .718 .834 .092 .129 .477 .242 .195 .260 .651 .297 1.000 .392 .297 .337 .645 .438 .584 .409 .568 .771 .692 .436 .695 .724 .392 1.000 .914 .303 .647 .720 .807 .373 .818 .709 .682 .734 .846 .862 .297 .914 1.000 .179 .999 .857 -.189 .212 .486 .436 .032 .293 .618 .299 .337 .303 .179 1.000 .483 .097 .991 .339 .543 .679 .122 .824 .747 .718 .645 .647 .999 .483 1.000 .711 .806 .555 .844 .614 .692 .718 .726 .834 .438 .720 .857 .097 .711 1.000 ****************************************************** ESTIMATE OF MATRIX SIGMA .322 .019 .017 .019 .154 .119 .043 .046 .012 .034 .107 -.008 .041 .053 .019 .068 .011 .029 .033 .004 .013 .017 .011 .015 .016 .007 .015 .014 .017 .011 .007 .009 .009 .012 .009 .007 .012 .006 .010 .005 .007 .006 .019 .029 .009 .044 .043 .013 .016 .012 .014 .019 .020 .010 .021 .010 .154 .033 .009 .043 .225 .094 .033 .033 .030 .045 .051 .002 .010 .031 .119 .004 .012 .013 .094 .149 .035 .025 .030 .023 .036 .016 .060 .024 .043 .013 .009 .016 .033 .035 .024 .013 .031 .015 .022 .012 .020 .011 .046 .017 .007 .012 .033 .025 .013 .017 .010 .011 .022 .004 .012 .013 .012 .011 .012 .014 .030 .030 .031 .010 .108 .018 .015 .014 .036 .014 .034 .015 .006 .019 .045 .023 .015 .011 .018 .021 .022 .006 .016 .010 .107 .016 .010 .020 .051 .036 .022 .022 .015 .022 .059 .003 .015 .023 -.008 .007 .005 .010 .002 .016 .012 .004 .014 .006 .003 .021 .014 .001 .041 .015 .007 .021 .010 .060 .020 .012 .036 .016 .015 .014 .044 .009 .053 .014 .006 .010 .031 .024 .011 .013 .014 .010 .023 .001 .009 .018 ****************************************************** MATRIX Y 7.654 6.949 5.868 7.297 7.703 8.199 8.653 7.702 9.158 7.079 7.673 8.615 8.128 6.062 ****************************************************** MATRIX X 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 7.328 5.478 5.023 5.964 6.608 8.388 7.949 6.724 8.740 6.160 6.228 8.096 8.072 4.513 6.968 7.465 7.991 7.399 7.652 6.617 7.471 7.749 7.259 7.919 7.687 7.103 6.740 7.562 ****************************************************** OUTPUT USING NUMERICAL SEARCH METHOD DF=n-k-1 ACTUAL DF is 11.000000 Taken value of DF in NUMERICAL SEARCH is 11.00059 ******************************************************



Final value of gamma is 0.26369 ****************************************************** Final value of model error 0.06953 ****************************************************** Final estimate of MATRIX lambda is .391 .019 .017 .019 .154 .119 .043 .046 .012 .034 .107 -.008 .041 .053 .019 .138 .011 .029 .033 .004 .013 .017 .011 .015 .016 .007 .015 .014 .017 .011 .076 .009 .009 .012 .009 .007 .012 .006 .010 .005 .007 .006 .019 .029 .009 .114 .043 .013 .016 .012 .014 .019 .020 .010 .021 .010 .154 .033 .009 .043 .295 .094 .033 .033 .030 .045 .051 .002 .010 .031 .119 .004 .012 .013 .094 .218 .035 .025 .030 .023 .036 .016 .060 .024 .043 .013 .009 .016 .033 .035 .094 .013 .031 .015 .022 .012 .020 .011 .046 .017 .007 .012 .033 .025 .013 .087 .010 .011 .022 .004 .012 .013 .012 .011 .012 .014 .030 .030 .031 .010 .178 .018 .015 .014 .036 .014 .034 .015 .006 .019 .045 .023 .015 .011 .018 .090 .022 .006 .016 .010 .107 .016 .010 .020 .051 .036 .022 .022 .015 .022 .129 .003 .015 .023 -.008 .007 .005 .010 .002 .016 .012 .004 .014 .006 .003 .091 .014 .001 .041 .015 .007 .021 .010 .060 .020 .012 .036 .016 .015 .014 .114 .009 .053 .014 .006 .010 .031 .024 .011 .013 .014 .010 .023 .001 .009 .087 ****************************************************** GLS estimate of Beta is .697 .771 .226 ****************************************************** Variance-Covariance Matrix of BetaHat 7.324 -0.185 -0.809 -0.185 0.008 0.017 -0.809 0.017 0.092 ****************************************************** Estimated values of Y i.e.Y^ 7.91797 6.60409 6.37208 6.96382 7.51735 8.65583 8.51019 7.62866 9.07207 7.23227 7.23233 8.54044 8.44001 5.88213 ****************************************************** Residual values i.e. Y-Y^ -.26397 .34491 -.50408



.33318 .18565 -.45683 .14281 .07334 .08593 -.15327 .44067 .07456 -.31201 .17987 ****************************************************** R^2 i.e. Explained Variation is 0.89602 ****************************************************** R^2 adj. is 0.76701 ****************************************************** STANDARD ERROR OF ESTIMATE (SAMPLE STANDARD DEVIATION OF REGRESSION) 0.32794 ****************************************************** LEVERAGE OF SITES H (1, 1) = .04450 H (2, 2) = .12711 H (3, 3) = .35675 H (4, 4) = .12208 H (5, 5) = .00767 H (6, 6) = .18618 H (7, 7) = .25670 H (8, 8) = .23161 H (9, 9) = .17850 H (10, 10) = .23770 H (11, 11) = .07219 H (12, 12) = .32477 H (13, 13) = .32705 H (14, 14) = .52714 Sum of LEVERAGES 2.99995 SITES WITH LEVERAGE AT LEAST (k+1)/n H (3, 3) = .35675 H (7, 7) = .25670 H (8, 8) = .23161 H (10, 10) = .23770 H (12, 12) = .32477 H (13, 13) = .32705 H (14, 14) = .52714 HIGH LEVERAGE SITES Hii >= 2(k+1)/n H (14, 14) = .52714 ****************************************************** Generalized Cook's D statistics - Measure of the influence of site i on the fit SITE = 1, COOK_D = .01166 SITE = 2, COOK_D = .15161 SITE = 3, COOK_D = 1.85036



SITE = 4, COOK_D = .18162 SITE = 5, COOK_D = .00486 SITE = 6, COOK_D = .35227 SITE = 7, COOK_D = .11477 SITE = 8, COOK_D = .01842 SITE = 9, COOK_D = .01201 SITE = 10, COOK_D = .08560 SITE = 11, COOK_D = .16370 SITE = 12, COOK_D = .03735 SITE = 13, COOK_D = .98213 SITE = 14, COOK_D = .50410 Cook's Di >= 4/n SITE = 3, COOK_D = 1.85036 SITE = 6, COOK_D = .35227 SITE = 13, COOK_D = .98213 SITE = 14, COOK_D = .50410 ****************************************************** OUTPUT IN ORIGINAL SCALE i.e. m3/ sec ****************************************************** Y Y^ residuals ****************************************************** 2109.065 2746.182 -637.117 1042.107 738.109 303.998 353.541 585.274 -231.733 1475.866 1057.669 418.197 2214.983 1839.677 375.306 3637.313 5743.547 -2106.235 5727.302 4965.087 762.215 2212.770 2056.285 156.484 9490.058 8708.633 781.425 1186.781 1383.363 -196.582 2149.520 1383.437 766.083 5513.748 5117.599 396.149 3388.018 4628.597 -1240.580 429.233 358.571 70.662 ****************************************************** STANDARD ERROR OF ESTIMATE (in original scale) 896.79110 ******************************************************

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