User Manual for

Web Enabled Groundwater Recharge Estimation Model (WEGREM)

Ver. 1.0

Developed by:

Ms. Suman Gurjar, Dr. Narayan C. Ghosh, Mr. Sumant Kumar, Dr. Surjeet Singh, and Dr. Anupma Sharma

National Institute of Hydrology Roorkee, Uttarakhand India

Web:

http://nih.ernet.in

Contents

Section Content Page No. Foreword ........................................................................ i Disclaimer .................................................................... ii 1 Introduction .................................................................. 1 1.1 Motivation................................................................................ 1 2 The Mathematical Framework of the model...................... 2 3 Structure of the WE-GREM............................................ 3 3.1 Operating environment at user end.......................................... 3 4 Instructions to use WE-GREM......................................... 4 4.1 Front page................................................................................ 4 4.2 The WEGREM......................................................................... 5 4.2.1 Geometry of waterbody....................................................... 5 4.2.2 Aquifer parameters............................................................. 6 4.2.3 Observation time parameters.............................................. 7 4.2.4 Rainfall data....................................................................... 8 4.2.5 Inflow rate........................................................................... 10 4.2.6 Evaporation rate................................................................. 13 4.2.7 Outflow rate........................................................................ 16 4.2.8 Output.................................................................................. 17 5 Limitations.................................................................... 18 References........................................................................ 18 Annexure........................................................................ 19 Annexure I: Hantush’s (1967) solution............................................. 19 Annexure II: SCS-CN Rainfall-Runoff Model.................................. 19 Annexure III: Methods for calculation of evaporation rate............... 20

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FOREWORD

Accurate estimation of groundwater recharge is essential for effective management of surface and ground water resources. Recharge basin is one of the techniques of groundwater recharge for replenishing and re-pressurizing depleted aquifers, controlling saline intrusion or land subsidence and improving water quality through filtration and chemical and biological processes, etc. Groundwater recharge from a recharge basin is time varying because of influence of other hydrological variables. The “WE-GREM : Web Enabled Groundwater Recharge Estimation Model” developed by a group of scientists from the Groundwater Hydrology Division of the Institute is a step towards providing a computational platform to the groundwater professionals for accurately calculating the recharge and other hydrological components associated with a recharge basin.

This user manual provides the technical details of the “WE-GREM” and will help

users of this application in operation and execution of the facility. I complement the scientists for bringing out this application and expect that they will bring out more such applications in future.

Date: 27th May 2016 Place: Roorkee

[ Raj Deva Singh] Director

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DISCLAIMER The mathematical derivations and algorithms used in developing the application are already in public domain. The mathematical model is based on the water balance equation of a recharge basin, and the derivation of each hydrological component follows the process based mathematical equation. There is no mathematical ambiguity in the model description; all are based on published literature and well-accepted in hydrological research. The user manual contains the technical details of the web application including the mathematical bases based on which the model has been developed. The manual also provides help on each application and its detailed description.

If there is any ambiguity in the process and mathematical description, we will owe the responsibility. Copyright of this web application is belonged to the National Institute of Hydrology, Roorkee (India).

Ms. Suman Gurjar

Dr. Narayan C. Ghosh Mr. Sumant Kumar

Dr. Surjeet Singh Dr. Anupma Sharma

Date : 27th May, 2016 Place : Roorkee

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1. Introduction

The utility of this Web Enabled-Groundwater Recharge Estimation Model (WE-GREM) lies in its capability to compute groundwater recharge from a recharge basin in a simple way which may help water managers for sustainable management of groundwater. Groundwater recharge from a recharge basin plays an important role in management of surface and ground water of an area that faces water scarcity Presently all the analysis and modelling related with this crucial issue is done by proprietary and costly softwares. This poses a restriction on use of such softwares to many professionals . This has motivated the idea for developing this web enabled information system . The WE-GREM takes the requisite data as input for groundwater recharge estimation . The input data are acquired by user friendly interfaces and the outputs based on model results are presented in user friendly tabular and graphical formats. The source code is written in JavaScript and the interface is created using HTML. Groundwater professionals can use WE-GREM as a tool to analyse the groundwater recharge scenarios and can take decision for augmenting the groundwater recharge in field. It may also come in as an aid for resolving important issues related with groundwater management. The WE-GREM represents a process based time varying semi-analytical model that computes rate of groundwater recharge from a recharge basin and depth of water in that recharge basin. The recharge basin may be of varying size and shape. The model is based on the water balance of the recharge basin, and the physical processes considered are: runoff estimation from the basin catchment using SCS-CN model; water surface evaporation from the basin using option of three methods, PAN Evaporation, Mass Transfer, and combination of Pristely-Taylor and Penman method; and the groundwater recharge component by the Hantush’s (1967) approximate analytical equation for the rise of water table in a homogeneous and isotropic unconfined aquifer of infinite areal extent due to uniform percolation of water from a spreading basin in absence of a pumping well. The WE-GREM has both the options for assigning required input values of inflow (runoff), evaporation, and outflow rates i.e. using measured data in the field, or using the estimated values based on the method selected in the software. The other inputs required are: basin geometry, aquifer transmissivity, storage coefficient, vertical hydraulic conductivity, and initial groundwater table height. This user’s manual provides a guideline on use of the application, various screenshots of Input/ Output modules and also a detailed description of methods used in the software. 1.1 Motivation

Managed Aquifer Recharge (MAR), popularly known as Artificial Recharge (AR) in

India, is promoted in many countries for replenishing and re-pressurizing depleted aquifers, controlling saline intrusion, improving groundwater quality, etc. MAR is generally used by conserving monsoon surface runoffs into a recharge scheme for augmentation of groundwater resources. A variety of recharge structures are used depending upon feasibility of the site; one such structure is a recharge basin/tank/pond. The size and shape of a recharge basin depends on the catchment area from which it receives inflow, field conditions, hydrological and hydrogeological factors/parameters, etc.

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The hydrological components associated with a recharge basin, viz. inflow to the basin,

rainfall over the basin, evaporation rate and outflow from the basin are time varying. Depth of water in the basin and the corresponding recharge rate, in such cases, are also vary with time. For constant depth of water in a basin, groundwater recharge rate also varies with time due to the change in potential head difference between the depth of water in the basin and the groundwater table underneath . Estimation of recharge rate by Darcy’s equation with constant potential head difference cannot give correct value of groundwater recharge. Thus, there is a need of an accurate computational tool that can provide correct estimate of time varying hydrological components associated with the recharge basin including the recharge component and depth of water in the basin. The WE-GREM is focused to fulfill the above requirements. 2. The Mathematical Framework of the Model

Ghosh et al, (2015) using the concept in Figure 1 developed a semi-analytical model for estimate of unsteady seepage from a large water body influenced by variable flows based on the following water balance equation:

[𝑄𝑄𝑖𝑖(𝑡𝑡) + 𝐴𝐴 𝑅𝑅(𝑡𝑡) ]∆𝑡𝑡 − �𝑄𝑄𝑜𝑜(𝑡𝑡) + 𝐴𝐴𝑖𝑖 (𝑡𝑡) 𝐸𝐸(𝑡𝑡) + 𝑄𝑄𝑔𝑔𝑔𝑔 (𝑡𝑡) � ∆𝑡𝑡 = ∆𝑉𝑉(𝑡𝑡) ..... (1)

in which, Qi(t) is the inflow rate to the recharge basin from its catchment at time t, ( L3 T-1); A is the gross surface area of the recharge basin, (L2) ; R(t) is the rainfall rate at time t, (LT-1); Q0(t) is the outflow rate from the basin at time t,(L3T-1); Ai(t) is the water surface area of the basin at time t; (L2); E(t) is the water surface evaporation rate at time t, ( LT-1); Qgw(t) is the groundwater recharge rate from the basin at time t, (L3T-1); ∆V(t) is the change in storage between time t and t +∆t , (L3); and ∆t is the time step size, (T).

After solving equation (1) (details in annexure-I), the expression for estimate of time varying groundwater recharge rate from the basin of variable cross-section is given by:

{ } )t,1),n(b),n(a(tkhH

)t,1n),(b),(a()(b)(a4

)t(Qh)tn(DHtk)n(b)n(a4

)tn(Qsv0

1n

1s

gw0v

gw ∆δ∆

∆γγγδγγ

∆γ∆∆

Αγ

+−

∑ +−−−+

=

−

= ....... (2)

The expression for time varying depth of water in the basin, D(n∆t), is given by (details in annexure-I):

( )( )

( ) ( ) ( ) ( ) ( )[ ]

( )

( ) ( )( ) ( )[ ] ( ) ( )[ ]

( ) ( )[ ][ ] tt,1,nb,natKhH

t,1n,b,aba4

tQhtnDHK

tnAA

ttnQAtnEAtnRtnQtnA

1tnA

ttnA)ttn(D)tn(D

sv0

s1n

1

gw0v

ws

rs

0wsvpsiws

wsws

∆∆δ∆

∆γγγδγγ

∆γ∆

∆

∆∆∆∆∆∆

∆∆∆

∆∆∆

γ

+−

+−∑−−+

−

−−++

−−=

−

=

................. (3)

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in which, ∆𝑉𝑉(𝑛𝑛∆𝑡𝑡) = [𝐴𝐴𝑔𝑔𝑤𝑤 (𝑛𝑛∆𝑡𝑡) 𝐷𝐷(𝑛𝑛∆𝑡𝑡) − 𝐴𝐴𝑔𝑔𝑤𝑤 (𝑛𝑛∆𝑡𝑡 − ∆𝑡𝑡)𝐷𝐷(𝑛𝑛∆𝑡𝑡 − ∆𝑡𝑡)] ; D(n∆𝑡𝑡) = depth of water at time t = n∆t; 𝐷𝐷(𝑛𝑛∆𝑡𝑡 − ∆𝑡𝑡) = depth of water at the preceding time step, i.e., (n-1)∆t; Aws(n-1)∆t = water surface area at the preceding time step, (n-1)∆t; Aws(n∆t) = water surface area at time step, (n∆t); As = the gross top surface area; �̅�𝐴𝑔𝑔𝑤𝑤 = (𝐴𝐴𝑔𝑔𝑤𝑤 (𝑛𝑛∆𝑡𝑡) + 𝐴𝐴𝑔𝑔𝑤𝑤 (𝑛𝑛 − 1)∆𝑡𝑡) 2⁄ ; �̅�𝐴𝑟𝑟𝑤𝑤 = 2 (𝑎𝑎(𝑛𝑛)𝑏𝑏(𝑛𝑛) + 𝑎𝑎(𝑛𝑛 − 1)𝑏𝑏(𝑛𝑛 − 1); δs(a(1),b(1),m), δs(a(2), b(2), m) ……δs(a(n), b(n) , m), m = 1, 2, ….n are the unit pulse response coefficients for (2a(1), 2b(1)), (2a(2), 2b(2)) ……. (2a(n), 2b(n)) of the length and width of the water spread area.

Figure 1: A schematic of the recharge basin water balance components including description of their hydrologic parameters.

3. Structure of the WE-GREM The structural framework of the WE-GREM comproses three modules (Figure 2): (i)

the mathematical model (the main engine) derived based on eqs(2) and (3) to estimate time varying recharge and depth water from/in the basin, (ii) user friendly data input module, and (iii) user friendly outputs module. The users have the option to navigate through the different modules and can see the inputs and outputs along with a brief help of each module.

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Figure 2 : Structural framework of the WEGREM. 3.1 Operating environment at user end

The WE-GREM can be used and accessed over Internet. It is totally independent of the

type of system being used. It is hoisted in such a way that user can access it with all operating systems like Windows, all flavours of Linux, OSX etc. It is accessible across all web-browsers like Internet Explorer, Firefox, Google Chrome, etc. The application has been developed using HTML and JavaScrip. The only pre-requirement for the system is the presence of browsers and internet connectivity. 4. Instructions to use the WE-GREM

This describes how to get started. It starts with a description of how to get access to the WE-GREM. The other sections focus on how the user can get familiarized with functionalities and use of the software. WE-GREM is available in public domain, anyone can access it with internet connectivity. It is simple to use and easy to access, no installation is required. 4.1 Front Page

After the website is accessed , the main front screen of the WE-GREM is displayed (Figure 3).

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Figure 3: Front main screen of the WE-GREM. This page contains five tabs in a menu bar. They are: Introduction: this tab provides the basic introduction of the WE-GREM. The methodology

used in designing the WE-GREM. WE-GREM : It is the main engine of the module, which performs all calculations and give

the results. Help Module : It provides the comprehensive help of the module in ‘pdf’ format. User can

download the ‘pdf’ and can use it as and when required. Feedback : This module is to receive feedback and suggestion from the users. Contact Us : This module gives the contact details of the person in case of any difficulty in

operation and technical query regarding the module. 4.2 The WE-GREM

The WE-GREM is the main engine of the application. All the calculations are done in this module. It is further divided into sub modules for ease of use and convenience of the user.

4.2.1 Geometry of the basin Recharge basin geometric data are essential inputs. In this module, user has to

provide the input data related to geometry of the basin. The screen for the ‘Geometry Parameters’ is shown in Figure 4.

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Figure 4: The WE-GREM front screen describing geometric data requirement of the basin. . The required data are :.

• Geometrical shape of the basin • Length of the basin • Breadth of the basin • Groundwater table depth below the recharge basin • Height of the basin bed from the impervious stratum • Initial depth of water in the basin • Maximum depth of water in the basin upto the outflow level

Input Geometry Data I. Select the option ‘Select Geometry’ and from the dropdown list select the geometrical

shape of the basin. II. Enter the value of length in ‘Length’ input text in given unit

III. Similarly enter the value ‘Breadth1’ and ‘Breadth2’ in case of Trapezoidal geometry else ‘Breadth’ in case of rectangular geometry. Enter the values of ‘Groundwater Table Depth’ i.e, depth to groundwater table, ’Height of basin bed from the impervious stratum’, ‘Initial Depth of water in the basin’, ‘Maximum Depth upto Outflow point’.

IV. Proceed to next step.

4.2.2 Aquifer Parameters

Aquifer parameters: This tab takes the input parameters of the aquifer. The screen for the input aquifer parameters is shown in Figure 5.

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Figure 5: Input screen for assigning aquifer parameters of the WE-GREM. Required data To run the model user needs to assign the following parameters.

• Hydraulic conductivities ( m/day) • Storage Coefficient (Dimensionless) • Transmissivity (m2/day)

Input Aquifer Parameters I. Enter the value of ‘Hydraulic conductivity’ in input text in given unit.

II. Enter the value of ‘Storage Coefficient’ in input text in given unit. III. Enter the value of ‘Transmissivity’ in input text in given unit. IV. Proceed to next step.

4.2.3 Observation Time parameters

Figure 6: Input screen for observation time parameters.

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Observation parameters: In this tab, the user has to assign the time period or number of simulation days for which users wants to calculate the recharge. The screen for the observation parameter is shown in Figure 6. Required data

• Number of simulation days for which user wants to calculate recharge. Input simulation data

I. Enter the value of ‘Number of Simulation Days’ in input text in given unit . II. ‘Time step size’ is considered as 1 day for good results.

III. Proceed to next step.

4.2.4 Rainfall Data The input screen for assigning the rainfall data is in Figure 7.

Figure 7: Input screen for ‘Rainfall Data’. Rainfall Data : For assigning the rainfall data.. click on ‘Rainfall Data’ and its input screen will display as shown in Figure 7. This module has a provision to download the excel file in defined format and upload the excel file. ‘Steps to follow’ is a brief and quick help for the user to proceed in the module. Required Data:

• Daily rainfall data (m) along with dates. • Provide dates in defined format ‘DD/MM/YYYY’.

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Input Rainfall Data

I. Click the ‘Select Start Date’, it will create a sample empty excel file with Dates upto the number of simulation days given in ‘Observation Input parameters’.The preview of the empty table can be viewed in datagrid given below in ‘Preview Excel file’ section.

II. Click ‘Download Excel’ which will allow user to download the excel file. Save the created file in your system and use this file to prepare input file as shown in Figure 8.

Figure 8: Input screen for exporting Excel file of ‘Rainfall Data ‘.

III. Prepare the rainfall excel file with data.

Figure 9: Input screen for importing Excel file of ‘Rainfall Data’

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IV. Click ‘Import Rainfall Data’ an open file window will appear as shown in Figure 9,

add prepared rainfall data excel file. View the imported data in ‘Preview Excel file’. V. Proceed to next step.

4.2.5 Inflow Rate The screen for assigning ‘Inflow Rate’ is in Figure 10.

Figure 10: Input screen for ‘User Defined’ method of assigning ‘Inflow Data’.

Inflow Data For assigning inflow rate, Click on ‘Inflow Data’ and its input screen will display as shown in Figure 10. This module has a provision to download the excel file in defined format and upload the excel file. The options given in the module are: user can either directly input the Inflow Data or it can be calculated in the module itself by using SCS-CN model. “Steps to follow” is a brief and quick help for the user to proceed in the module. User Defined Method Required data:

• Daily ‘Inflow Data’ along with dates. • Provide Dates in defined format as ‘DD/MM/YYYY’.

Input Inflow Data using ‘User Defined method’ I. Click the ‘Select Start Date’, it will create a sample empty excel file with dates upto

the number of simulation days given in ‘Observation Input parameters’.The preview

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of the empty table can be viewed in datagrid given below in ‘Preview Excel file’ section.

II. Click ‘Download Excel’ which will allow user to download the excel file. Save the created file in your system and use this file to prepare input file.

III. Prepare the Inflow excel file with data. IV. Click ‘Import Inflow Data’ an open file window will appear, add prepared inflow data

excel. View the imported data in ‘Preview Excel file’. V. Proceed to next step.

To be Calculated Method Required data:

• Total catchment area of the recharge basin. • Landuse and landcover classes falling into the basin area. • Soil group classfification of the basin area. • Rainfall data. • Provide dates in defined format ‘DD/MM/YYYY’.

Figure 11: Input screen for ’To be calculated’ method of ‘Inflow Data’. .

Input ‘Inflow Data’ using ‘To be calculated Method’ Click on ‘To be Calculated’ and it will give the screen to input the data for calculation of ‘Inflow data’ online using SCS-CN model as shown in Figure 11.

I. Enter the value of ‘Total Catchment area’ (in m2).

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II. Rainfall data are already provided, if the user has already uploaded rainfall data in the ‘Rainfall Data’ screen.

III. Click ‘Add Classes’ button, which will add a row in table . The user will need to select the type of Landuse and Landcover from dropdown ‘LULC Classes’ and also need to select, type of soil group from dropdown ‘Hydrological soil group’ and input the area of each class in the textbox ‘Area’. User can add more number of classes in similar way, if necessary.

IV. Click ‘Delete’ button to delete the added LULC Classes in case user added some additional classes by mistake.

V. Click ‘Save’ button, this will save the LULC Classes and other parameters. VI. Click ‘Calculate runoff’’ which will calculate the runoff or inflow rate and results will

be displayed in the datagrid. VII. Proceed to next step.

4.2.6 Evaporation Rate The snapshot of the input screen for assigning ‘Evaporation Rate’ is in Figure 12.

Figure 12: Input screen for User Defined’ method in Evaporation Data of WE-GREM.

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Evaporation Data : For assigning evaporation rate, Click on ‘Evaporation Data’ and its input screen will display as shown in Figure 12. This module has a provision to download the excel file in defined format and upload the excel file as well. User has option to directly input the ‘Evaporation Data’, if measured data are available or has the option to get the values calculated in the module itself using three methods i.e Pan Evaporation,Mass Transfer , and combination of Preistley-Taylor and Penman method, depending upon the data availability. “Steps to follow” is a brief and quick help for the user to proceed in the module.

User Defined Method Click ‘User Defined’ button that will will display the screen for direct input of Evaporation data. Required data:

• Daily ‘Evaporation Data’ (m/day) along with dates. • Provide Dates in defined format ‘DD/MM/YYYY’.

Input ‘Evaporation Data’ using ‘User Defined method’

I. Click the ‘Select Start Date’ button, it will create a sample empty excel file with dates upto the number of simulation days given in ‘Observation Input parameters’.The preview of the empty table can be viewed in datagrid given in ‘Preview Excel file’ section.

II. Click the ‘Select Evaporation method’, this will create the excel file with the parameters on the basis of selected method.

III. Click ‘Download Excel’ button, which will allow user to download the excel file. Save the created file in your system and use this file to prepare input file.

IV. Prepare the Evaporation excel file with data. V. Click ‘Import Evaporation Data’ an open file window will appear, add prepared

inflow data excel. View the imported data in ‘Preview Excel file’. VI. Proceed to next step.

To be Calculated Method

Required data:

• Daily evaporation data along with dates. • Pan coefficient • Water surface area • Elevation • Wind speed above 2 m from the ground • Air temperature • Relative humidity • Provide dates in defined format ‘DD/MM/YYYY’.

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Figure 13: Input screen for ‘To be calculated’ method of Evaporation Data.

Input ‘Evaporation Data’ using ‘To be Calculated Method’ Click on ‘To be calculated’ button and it will display the screen to input the data for calculation of evaporation data online using three different methods methods given in the screen i.e Pan Evaporation,Mass Transfer ,Preistley-Taylor and Penman Combination as shown in Figure 13.

I. Click on any one method based on the data availability to calculate the evaporation. II. After selection of a method, another window pops up as shown in Figure 14.

Figure 14: Input screen for ‘Mass Transfer Method’ in Evaporation Data of WE-GREM.

III. The brief description about the input data requirement by the chosen method will display on this window.

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IV. If User has data to calculate by all the methods ,click on button ‘Yes, if you want to proceed’ else user can click on button ‘Quit’ and select a specific method as per the data availability.

V. User has to assign the required values using excel, and the excel file is already downloaded in step II in User defined method.

VI. Click ‘Browse’ button, and browse the excel with input values and this can be seen in datagrid as shown in Figure 15. The user can also verify whether all the values have come properly.

Figure 15: Input screen after importing data in ‘Mass Transfer Method’.

VII. Click ‘Calculate Evaporation’ button which will calculate the evaporation using

selected method. The results will be shown in the datagrid. VIII. Proceed to next step.

4.2.7 Outflow Rate

The snapshot of the input screen for assigning ‘Outflow Rate’ is shown in Figure 16.

Outflow Data :

To assign the outflow rate (if any), Click on ‘Outflow Data’ button, the input screen for assigning data will be displayed as shown in Figure 16. This module has a provision to download the excel file in defined format and upload the excel file. I.‘Steps to follow’ is a brief and quick help for the user to proceed in the module.

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Figure 16: Input screen for assigning ’ Outflow Data ‘.

Required data:

• Daily ‘Outflow Data’ (m3/day) along with dates. • Provide dates in defined format ‘DD/MM/YYYY’.

Input ‘Rainfall Data’

I. Click the ‘Select Start Date’ button, it will create a sample empty excel file with dates upto the number of simulation days given in ‘Observation Input parameters’.The preview of the empty table can be viewed in datagrid in ‘Preview Excel file’ section.

II. Click ‘Download Excel’ button, which will allow user to download the excel file. Save the created file in your system and use this file to prepare input file.

III. Prepare the Outflow excel file with data. IV. Click ‘Import Rainfall Data’ button, an open file window will appear, add prepared

rainfall data excel. View the imported data in ‘Preview Excel file’. V. Proceed to next step.

4.2.8 Output

The snapshot of the output screen is shown in Figure 17.

To run the model with assign databases for computing the recharge and depth of water in the basin and to view the results, follow the following steps:

I. Click ‘Calculate Recharge’ button to calculate the recharge. II. Click ‘Show chart’ button, for creating graphs of day wise time-varying recharge along

with the change in depth. III. Click ‘Select Chart type’ button, to view cumulative charts for all the other parameters. IV. The generated chart has option to export the chart in the form of JPEG,PNG and PDF.

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V. The results are also available in tabular format in datagrid for convenience of the user. VI. Click ‘Export Data in Excel’ button to export the data in excel forma,t which user can

save on his desktop.

Figure 17: Screen for visualizing ‘Output Data”..

Results

The snapshot of the results screen is shown in Figure 18. Results are shown in an interactive charts and animations as shown in Figure 18.

Figure 18: Screen showing results of time varying depth of water in the basin and groundwater recharge.

In case of any difficulty in operation of the WE-GREM, please contact us through the address given in “Contact Us” toolbar.

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5. Limitations • The time step size is one day because runoff calculated by SCS-CN method

is on daily basis. • The model will not work if there is no water in the recharge basin. • The sub-surface formation below the recharge basin is assumed to be

homogeneous and isotropic and the concept of equivalent hydraulic conductivity is considered.

• It is also assumed that there is no lateral flow of infiltrated water from the basin, the flow will only take place along vertical direction.

• The start time of the recharge is assumed from the onset of infiltration i.e from time t=0.

• The model will hold good for porous medium.

References Abtew, W., (2001). Evaporation estimation for Lake Okeechobee in south Florida. Jour. Irri.

and Drain. Engg., Am. Soc. Civil Engr., 127(3): 140-146. Allen, R., L.S. Pereira, D. Raes, and M. Smith. 1998. Crop evapotranspiration –Guidelines

for computing crop water requirements. FAO Irrigation and Drainage Paper N° 56. Rome, Italy.

De-Bruin, H. A. R. (1982). Temperature and energy balance of a water reservoir determined from standard weather data of a land station. J. Hydrol. 59, 261-274.

Ghosh, N. C., Sumant Kumar, Gesche Grützmacher, Shakeel Ahmed, Surjeet Singh, Christoph Sprenger, Raj Pal Singh, Biswajit Das, and Tanvi Arora, (2015). Semi-analytical model for estimation of unsteady seepage from a large water body influenced by variable flows. Jour. Water Resources Management, Springer, 29(9): 3111-3129.

Hantush, M. S., (1967). Growth and decay of groundwater mounds in response to uniform percolation. Water Resour. Res. 3, 227-234.

Harbeck, G.E.,(1962). A practical field technique for measuring reservoir evaporation utilizing mass-transfer theory. US Geological Survey Professional Paper.

Mishra S K and Singh V P. 1999. Another look at SCS-CN method, J. Hydrol. Eng. ASCE, 4(3), 257-264. Priestley, C.H.B. and R. J. Taylor,(1972). On the assessment of surface heat flux and

evaporation using large scale parameters. Monthly Weather Review, 100: 81-92. Reis, R.J.D. ,and N. L. Dias, (1998). Multi-season lake evaporation: energy budget estimates

and CRLE model assessment with limited meteorological observations. Jour. of Hydrology, 208: 135-147.

SCS, (1993). Hydrology-National Engineering Handbook, Supplement A, Section 4, Chapter 10, Soil Conservation Service. United State Department of Agriculture (USDA), Washington, DC.

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Annexure :

Annexure-I : Hantush’s (1967) solution The Hantush’s expression for rise of water table in absence of pumping well is given by:

)t,y,x(fS4tw)t,y,x(h

= ........................... ( AI:1)

in which, )t,y,x(h is the rise in groundwater table below the rectangular spreading basin at location x, y, ( L); w is the constant rate of percolation per unit area, (LT-1); S is the storage coefficient of the aquifer (dimensionless); t is the time since the percolated water joins the water table, (T); and f(x,y,t) is the analytical expression derived by Hantush (1967), which is given by:

2):(AI ...... )S/tT(2

)yb(,)S/tT(2

)xa(F)S/tT(2

)yb(,)S/tT(2

)xa(F

)S/tT(2)yb(,

)S/tT(2)xa(F

)S/tT(2)yb(,

)S/tT(2)xa(F t)y,f(x,

−−+

+−+

−++

++=

where T is the transmissivity = KH; H is the weighted mean of the depth of saturation during the period of flow; K is the coefficient of permeability (i.e., hydraulic conductivity) of the aquifer material; a is the half of the length and b is the half of the width of the rectangular basin; x, and y are the coordinates at which response is to be determined;

dz)z/q(erf).z/p(erf q) (p, F1

0∫= ; and due2 (x) erf

X

0

2u∫= −π

.

The unit step response function, Us(t) for rise in water table height due to unit recharge per unit area per unit time, i.e., w = 1 (L3 L-2 T-1), from eq (A1:1) is given by:

)t,y,x(fS4t)t(U s

= ..................................... ( AI:3)

The unit pulse response function coefficients, δs (n∆t), in discrete time steps of size, ∆t, (t = n ∆t), which takes place during the first time period, ∆t, and no recharge afterwards, is given by:

{ }

t

t)1n(U)tn(U)tn( ss

s ∆∆∆

∆δ−−

= .................................... ( AI:4)

Annexure-II: SCS-CN Rainfall-Runoff Model

The runoff yield by the SCS-CN model is given (SCS, 1993; Mishra & Singh, 1999) by:

20

( )( )S1P

SPQ2

λλ−+

−= SPfor λ> ................................ (AII:1)

0Q = SPfor λ≤

254CN

25400S −= ................................. (AII:2)

where, S is the maximum potential retention (mm); λ is the i). nitial abstraction weight as a fraction of S, normally 0 ≤ λ ≤0.3, but conventionally 0.2; 25400 and 254 in eq. (AI:2) are arbitrary constants in units of S; and CN is the Curve Number, dimensionless. Substituting S and λ =0.2, eq. (AII:1), yields to:

2P 20025.4 225.4 CNQ ; valid for P 0.2SP 800 8

25.4 CN

− + = ≥ + −

.......................... (AII:3)

The watershed specific-CNs relating to the antecedent moisture condition (AMC) (SCS, 1985) is:

III

II

4.2 CNCN

10 0.058 CN=

− ................................. (AII:4)

IIIII

II

23 CNCN

10 0.13 CN=

− ...................................... (AII :5)

where, subscripts indicate the AMC, I being dry, II normal, and III wet.

Annexure-III : Methods for calculation of evaporation rate 1. Pan evaporation (PE) method

panpEKE = .......................... (AIII:1)

E : evaporation rate estimated by pan evaporimeter, mm/day. Kp : pan coefficient (dimensionless) Epan : pan evaporation , mm/day.

2. Mass transfer (MT) method

( )as eeUE −= 2µ .....................................(AIII:2)

E : evaporation rate, mm/day.

21

µ : mass transfer coefficient (mm s m-1 kPa-1); U2 : wind speed at 2m above the water surface, m/s. es : saturated vapour pressure at water temperature (kPa); ea : actual vapour pressure at air temperature (kPa).

2.1 Equation for calculation of µ ,

05.0909.2 −= Aµ .................................. (AIII:2.1)

A : surface area of water body in km2.

2.2 Equation for calculation of 2U ,

( )

−

=42.58.67ln

87.42 z

UU Z

................................. (AIII:2.2)

Uz : wind speed at z m above the ground surface, (ms-1) ; z : height of measurement of wind above ground surface.

2.3 Equation for calculation of se :

+

=3.237

269.17exp6108.0w

ws T

Te ...................... (AIII:2.3)

2.4 Equation for calculation of ae :

( ) ( )2

100100min

max0max

min0 RHTe

RHTe

ea

+=

........................ (AIII: 2.4)

Tw: water temperature at the water surface of waterbody, (0C) e0(Tmax) : saturated vapour pressure at maximum air temperature, (kpa); e0(Tmix) : saturated vapour pressure at minimum air temperature, (kpa); RHmax : maximum relative humidity (%); RHmin : minimum relative humidity (%).

3. De-Bruin Model (Combination of Priestly-Taylor and Penman Method)

𝑬𝑬 = 𝜶𝜶𝜶𝜶−𝟏𝟏

� 𝜸𝜸∆+𝜸𝜸

�𝑭𝑭(𝒖𝒖)(𝒆𝒆𝒔𝒔 − 𝒆𝒆𝒂𝒂) .............................. (AIII:3.1)

E : Evaporation in watt/m2

22

Emegajoules=E*0.0864 (Megajoules) E= Emegajoules *2.45 (mm/day)

𝜶𝜶 : Priestley and Taylor coefficient : Psychrometric constant

Δ : slope of saturation vapour pressure-temperature curve ea, es: vapour pressures in milibars F(u) : wind function in W/m2/mb

3.1 𝜶𝜶 : PT Coefficient (1.26) 3.2 Equation for Calculation of γ :

λγ

××=

1000622.0PCpa

............................. (AIII: 3.2)

Cpa : specific heat capacity, generally taken as 1.013 x 10 -3MJ/kg/0 C; Numerical value,0.622(=18.016/28.996) represents the ratio of molecular weights of water to dry air. P : atmospheric pressure, (kpa).

3.3 Equation for calculation of P :

The atmospheric pressure at elevation, z, is calculated as (Allen, et al.,1998):

26.5

2930065.02933.101

−

=zP

............................. (AIII: 3.3)

Z : Elevation in meter

3.4 Equation for calculation of Δ:

( )230.237

3.23727.17exp6108.04098

+

+

=∆a

a

a

T

TT

............................... (AIII:3.4)

Ta : air temperature, (0C)

3.5 Wind function :

𝑭𝑭(𝒖𝒖) = 𝟐𝟐.𝟗𝟗 + 𝟐𝟐.𝟏𝟏𝒖𝒖 ..................................... (AIII:3.5)

F(u) : wind function in W/m2/mb u: wind speed measured at 2m height (m/s)

γ

23

3.6 ea : actual vapour pressure (milibars) 𝒆𝒆𝒂𝒂 = 𝟑𝟑𝟑𝟑.𝟖𝟖𝟖𝟖𝟑𝟑𝟗𝟗 [(𝟎𝟎.𝟎𝟎𝟎𝟎𝟎𝟎𝟑𝟑𝟖𝟖 ∗ 𝑻𝑻𝒂𝒂 + 𝟎𝟎.𝟖𝟖𝟎𝟎𝟎𝟎𝟐𝟐 )𝟖𝟖 – 𝟎𝟎.𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟏𝟏𝟗𝟗𝟏𝟏|𝟏𝟏.𝟖𝟖 ∗ 𝑻𝑻𝒂𝒂 + 𝟒𝟒𝟖𝟖| +

𝟎𝟎.𝟎𝟎𝟎𝟎𝟏𝟏𝟑𝟑𝟏𝟏𝟖𝟖] .......................................................... (AIII:3.6)

Ta : air temperature, (0C)

3.7 es : saturated vapour pressure (milibars) 𝒆𝒆𝒔𝒔 = 𝒆𝒆𝒂𝒂 /𝑹𝑹𝑹𝑹 ................................................ (AIII:3.7)

ea : actual vapour pressure RH: relative humidity

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