INTERCOMPARISON OF THE LUMPED VERSUS SEMI-DISTRIBUTED HEC - HMS HYDROLOGICAL MODEL IN THE KALAMAS RIVER BASIN

L. I. NTOANIDIS

Environmental Engineer - Hydrologist, 2 Tinou Str, 15562, Cholargos, Greece, E-mail: l.ntoanidis@gmail.com

ABSTRACT

This paper compares the lumped and semi-distributed structure of the HEC-HMS model, using daily data of the 1449.3 km2 Kalamas river basin in Greece. The hydrologic analysis of the study area is attempted for four storm events in two ways: a) with division of the area in two sub-basins (lumped model) and b) with division of the area in eight sub-basins (semi-distributed model). The model calibration procedure was conducted on two out of four flood events, and the model parameters were optimised using the trial and error technique for some parameters and the Univariate Algorithm for the rest. Results show that all applied individual mathematical models provide a reliable representation of the components of hydrological cycle; however, they provide better results when they are applied in small catchments. The results arising from both the lumped and the semi-distributed application of HEC-HMS lead to the conclusion that the semi-distributed form of the model has an advantage against the lumped form in the case of simulating complex flood hydrographs and when spatially detailed rainfall is available. With regard to the calibration of HEC-HMS, for both lumped and semi-distributed application scenarios, the resulting conclusion is that, for a more objective calibration of the model, which will support more reliable forecasts, a global multi-objective optimisation algorithm should be applied.

Keywords: hydrological modelling; semi-distributed models; calibration; HEC-HMS.

1. INTRODUCTION

Hydrological models can be classified into two major types: lumped and distributed. Lumped models were developed since the 1960s (e.g. the Stanford catchment model, Crawford and Lindsey, 1966). They consider the catchment as an undivided entity and use lumped values of input variables and parameters. For the most part (for a review, see Singh, 1995), they have a conceptual structure based on the interaction between storage elements representing the different processes with mathematical functions to describe the fluxes between the storage (e.g. HSPF, Donigian et al., 1995; GR, Perrin et al., 2003). In the last three decades, lumped models were challenged by distributed models whose spatial structure allows taking into account the spatial variability of processes within catchments and consequently the prediction of local hydrological responses for points within the catchment. In distributed models, parameters need to be defined for every spatial element and for each process representing equation. In principle, parameter adjustment should not be necessary for this type of models because parameters should be related to the physical characteristics of the surface, soil and land-use. However, in practical applications, calibration procedures are requested for both lumped and distributed models; consequently the models require effective or equivalent values for some parameters. A third smaller category is the so-called semi-distributed models. They represent a catchment by dividing it into smaller sub-catchments, with uniform as possible characteristics. They were initially developed to combine the advantages of both lumped

and distributed models. Semi-distributed models are commonly used in the operative hydrologic forecast services because of their well balanced ratio between the model spatial accuracy and duration of simulation and calibration effort. The scope of this paper is to investigate primarily the hydrological response of the Kalamas river basin in flood events and secondly to illustrate the comparative application of the model HEC-HMS in lumped and semi-distributed form.

2. STUDY AREA

The study area is part of the Kalamas river basin situated in western Greece. The basin covers a 1449.3 km2 area. The length of river from its springs up to the Kioteki streamflow gauge (outlet) is 108 km. The area is a combination of agricultural land and forests with mainly calcareous rocks and with mild slopes. Due to the calcareous geological background, groundwater flow is promoted and plays a decisive role in the maintenance of baseflow in the river. The mean annual precipitation volume amounts in 2770 x 106 m3, while the mean annual runoff is estimated around 1800 x 106 m3 of water. Climate ranks in the mild Mediterranean climate, with dry periods to coincide with warm. The average annual temperature varies between 13.5C and 14.5C for the period 1995-2004. Precipitation is abundant in the region, with an average annual rainfall of 1550 mm. The bedrock mainly consists of limestone (47%), loam (14%), flysch (24%) and silt (10%). The limestone rocks are mainly found in the northern part of the region upstream of the Soulopoulo while flysch and marl are found in the south-western part of the basin between Kioteki and Soulopoulo. The steeper slopes occur in the south-western part of the study area (maximum and mean are 71 and 16% respectively), while the northern part has more gentle slopes (maximum and mean of 58% and 12% respectively). Elevation ranging from sea level up to 2157m upstream of Soulopoulo, while the average altitude of the study area is 544m.

Fig.1: The Kalamas river basin with the flow and rain stations.

3. METHODOLOGY AND DATA AQUISITION

3.1 Methodology

As mentioned in the introduction, the aim of this paper is the analysis of the hydrological response of the Kalamas basin in flood events using the hydrological model HEC-HMS, in conjunction with Geographical Information System ArcView 3.2. The catchment analysis was undertaken for four flood events, in two ways: a) by dividing the study area into two sub-basins, and b) by dividing the study area into eight sub-basins. The connection between hydrology and spatial information is accomplished with the HEC-GeoHMS module of ArcView. The interaction between the HEC-GeoHMS and HEC-HMS, is shown in Figure 2. The final result of these processes is the production of two input files for HEC-HMS: the map file (background map file) and the basin file (basin model file) which as mentioned above can be lumped or distributed. The map file is a schematic representation of the sub-basins and watercourses of the basin and the relationships between them. The basin file contains the entire basins hydrological and geomorphological data as produced through the HEC-GeoHMS. The remaining data required for the operation of HEC-HMS is the creation of a meteorological file (meteorological component) containing the rainfall events and methods for spatial and temporal distribution and the determination of some specific parameters in mathematical models (hydrograph routing, rainfall losses, etc).

Fig.2: Flood event simulation process flowchart using HEC-HMS and HEC-GeoHMS (reproduced from M.R. Knebl et al, 2005)

3.2 Data aquisition

HEC-GeoHMS uses as inputs the digital elevation model (DEM), digital maps of soil types and land uses and some auxiliary files for spatial data in vector format such as the file with the meteorological and river-stage stations in the basin and the river network for a more complete and accurate representation of the basin.

Elevation data The DEM of Kalamas basin produced by digitizing maps of Hellenic Military Geographical Service (HMGS) in the laboratory of Hydrology and Water Resources, National Technical

University of Athens and has a resolution of 50m, which is good enough for the scale of the basin.

Land use (LU) and geology data The digital land use map produced by the Organization of Land and Mapping of Greece (OLMG) and contains the polygons of land use in the basin of Kalamas, according to the European coding (program Corrine Land Cover). From the LU map can be estimated the Manning friction coefficient for the river channel and flood plains, which is necessary in some routing models. The soil type map of the region contains respectively the polygons with the different rock types present in the study area. In combination with the land use map and with the help of tables from the literature, the runoff curve numbers can be identified for each sub-basin, needed to calculate the runoff loss volume with the SCS method.

Rainfall data In this study the rainfall data for the study basin come from four stations under the authority of Public Power Corporation of Greece (PPC) with temporal step of 1hour. The raw data of the four rainfall stations were given as cumulative rainfall recorded in tapes of the rainfall recorders. From the reading of the tapes derived the hourly rainfall in digital form for input to the model. For the control of rainfall measurements of each station, comparison of the daily cumulative rainfall was conducted with rainfall measurements of an adjacent station. The rainfall stations, while providing a good temporal resolution of rainfall, it is though punctual. In this study, the method used for the derivation of areal rainfall is the method of Thiessen polygons. Weighting coefficients for each sub-basin were calculated taking into account all four stations in the region and also for the three out of four because for two flood events station Polylofo was not functioning.

River discharge data The river discharge data are necessary for two main reasons: a) the calibration of the model and b) the determination of certain parameters required by the model. In this study, these data are available in river station Kioteki, which coincides with the outlet point of the whole basin. There is another hydrometric station at Soulopoulo, but the data was not available for the simulations periods. In these positions are established river-stage recorders functioning under the PPC authority that record the stage of the river with a time step of one hour. The locations of the stations are shown in Figure 1. To calculate the river discharge from the river-stage records requires the stage-discharge curve at specific locations. For the period 1995 - 2004 which involves the simulations periods, the stage-discharge curve at station Kioteki has a polynomial form as follow:

Q = 2.7688h2 + 11.448h + 2.3206, R2=0.963

where Q is the discharge in m3/s and h the rivers stage in m.

4. MODEL SELECTION AND APPLICATION

The HEC-HMS model provides the option of a variety of mathematical models to represent different components of the hydrological cycle, depending on the needs of the simulation and the quantity and quality of input data. In the present study concerning the time scale was chosen the event simulation and for the spatial scale was chosen the lumped simulation, since the study area was divided in two sub-basins in the first scenario and in eight sub-basins in the second. Figure 3 present the HEC-HMS map file of the study area for the two scenarios. For both scenarios of spatial distribution, the same mathematical models and the same calibration procedure was applied.

Fig.3 Schematic of the study area in the lumped and semi-distributed form of HEC-HMS

Rainfall loss model In this study the curve number CN loss model of the Soil Conservation Service (SCS, 1972) was applied. It is easy to apply and consists of only one parameter (CN), which is a function of soil type, land use and soil moisture status. For this study CN values were taken from tables in greek bibliography (Koutsogiannis, 1993). The calculation of the composite curve number for each sub-basin using the above equation was done with the help of HEC-GeoHMS and digital maps of land use and soil types of the study area.

Baseflow model For the representation of the baseflow in this study was chosen to implement the exponential recession model described by the equation:

tt kQQ = 0

where Q0 is the initial value of the base flow at time 0, Qt is the value of the base flow at any time t and k is a constant of exponential decline.

Direct runoff model In this study was chosen to implement the Snyders synthetic unit hydrograph. The equations that determine the parameters of the UH are:

2433

75.2

)(75.0 3.0

p

p

pp

Cmtp

tT

t

ACQ

LLCt

+=

=

=

where Ct = basin coefficient, Lm = length of the main stream from the outlet to the divide, Lc = length along the main stream from the outlet to a point nearest the watershed centroid, Qp = peak of UH, A = watershed drainage area, Cp = UH peaking coefficient, T = duration of UH and tp = basin lag.

Channel routing model The flood routing model applied in this study is the Muskingum model. This method was chosen because it does not require knowledge of the river sections and the Manning roughness coefficient and because the two parameters (K, X) it contains can be determined either by measured flood hydrographs or even through calibration. The parameter X is called storage coefficient and is a dimensionless parameter that expresses the attenuation of the flood wave. The parameter K represents the travel time of the flood wave through the reach.

Model calibration In this study we applied both calibration techniques: trial and error and automated by applying an optimization algorithm offered in HEC-HMS. In both cases, the calibration of the model was based on the measured flows at Kioteki station, using two out of the four floods events that simulated, with peaks on 12/2/99 and 27/12/96. The trial and error technique was applied to the parameters Cp and Ct of Snyders unit hydrograph, the parameters K and X of Muskingum routing model and the SCS CN losses model. The choice of this technique was to obtain the best parameter values for the model, which would be constant for each sub-basin and storm event. For the rest of the models parameters, such as the flow at the inflection point of the hydrograph and the exponential recession constant in the baseflow model and initial runoff losses in the SCS CN model, applied the automatic calibration for each hydrograph separately, using the Univariate Gradient optimization algorithm and as an objective function the Sum of Squared Differences. The equations of performance indices are shown in Table 1, where qs is the estimated flow, qo is the observed flow for the same time, qm is the mean observed flow, VS is the total estimated volume and VO is the total observed volume. For indices PE, b and RMSE the perfect calibration occurs when they are equal to zero, while for the index R2 occurs when it is equal to unity. The RMSE and R2 indices are a measure of error of the volume and peak flow between the observed and estimated hydrographs while the PE index is a measure of error only to peak flows and the index b only to the total volume.

Table 1. Models calibration performance indices Performance index Equation

Root Mean Square Error ( ) = 21

oS qqNRMSE

Nash Sutcliffe coefficient ( )( )

= 2

22 1

mo

oS

qq

qqR

Total volume absolute error 100=O

OS

VVVb

Peak flow absolute error 100)()()(

=

peakqpeakqpeakq

PEo

oS

5. SIMULATION RESULTS

Figures 4a to 4d present the estimated flood hydrographs at Kioteki station for the four simulated storm events, after the calibration of the model for both scenarios (lumped and semi-distributed). Table 2 presents the results of the statistical performance indices as derived from the application of HEC-HMS under lumped and semi-distributed form for the four floods.

Table 2. Values of the performance indices after calibration of HEC-HMS under lumped and semi-distributed form

PERFORM. INDICES

FLOOD WITH PEAK ON 12/2/99

FLOOD WITH PEAK ON 27/12/96

Semi-distributed Lumped Semi-distributed Lumped R2 0.907 0.855 0.909 0.905

RMSE 0.515 0.644 0.392 0.401 PE 12.585 7.294 8.376 7.777 b 1.208 2.817 0.586 1.029

PERFORM. INDICES

FLOOD WITH PEAK ON 22/12/99

FLOOD WITH PEAK ON 30/3/95

Semi-distributed Lumped Semi-distributed Lumped R2 0.788 0.618 0.893 0.893

RMSE 0.918 1.234 0.456 0.456 PE 9.468 6.816 3.664 2.039 b 0.195 0.991 0.179 0.304

a) b)

c) d) Fig. 4 Results after calibration of HEC-HMS under lumped and semi-distributed form for flood

events with peak flows on a) 30/3/95 b) 22/12/99 c) 27/12/96 and d) 12/2/99

6. CONCLUSIONS

The conclusions from the conducted simulations, referred to the application and comparison of a lumped and semi-distributed form of the model, are presented below: A model performance improvement based on the volume absolute error is observed

when using the semi-distributed version of the HEC-HMS in comparison to its lumped

counterpart. Moreover, the same conclusion applies prior to calibration of the model. The best simulation of the total volume with the semi-distributed version of HEC-HMS, also leads to the conclusion that the modules for calculating the volume of direct runoff and base flow volume, are best applicable in small basins.

Referring to the floods on 27/12/96 and 30/3/95, it appears that differences in values of performance indices between lumped and semi-distributed form of HEC-HMS is very small. This is partially because the flood hydrographs on 27/12/96 and 30/3/95 show only one peak and partly because of the fact that rainfall data for that flood events were from three out of four stations in the area. This observation leads to the conclusion that the application of the semi-distributed form is preferred against the lumped, only if it is to simulate complex hydrographs and detailed data of spatial distribution of rainfall is available.

The results of the simulations indicate for both scenarios that while for the three out of four indices, their value was improved after calibration, for the index absolute error in peak PE, the value became worse or improved a little. These results may be due to merits in the calibration procedure. The Univariate Gradient algorithm finds a local minimum of the objective function, while it depends on the initial values of the parameters. Moreover the objective function of sum of squared differences emphasises on improving the indices R2 and RMSE. We therefore suggest using a multiobjective optimisation algorithm able to identify the global minimum for a better calibration and performance of the model.

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