Automated calibration applied to a GIS-based flood simulation model using PEST

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1 Floods, from Defence to Management Van Alphen, van Beek & Taal (eds) 2005 Taylor & Francis Group, London, ISBN Automated calibration applied to a GIS-based flood simulation model using PEST Y.B. Liu, O. Batelaan & F. De Smedt Department of Hydrology and Hydraulic Engineering, Vrije Universiteit Brussel, Brussels, Belgium J. Poórová & L. Velcická Slovak Hydrometeorological Institute, Bratislava, Slovakia ABSTRACT: This paper describes an automated calibration procedure applied to the GIS-based distributed WetSpa (Water and Energy Transfer between Soil, Plant and Atmosphere) model by incorporating a modelindependent parameter estimator PEST (Parameter ESTimation). This calibration approach is applied to estimate the most sensitive parameters of the model with observed flow hydrographs as the calibration target. The best set of parameters is selected from within reasonable ranges by adjusting the values until the discrepancies between observed and simulated hydrographs is reduced to a minimum in the weighted least squares sense. A case study is performed in the Margecany catchment, 1133 km 2, situated in the upstream part of the Hornad River basin, Slovakia. The parameter set obtained from the automated calibration procedure provides a good fit compared to observed flow hydrographs, indicating that the automated calibration scheme is a credible alternative to the manual approach. 1 INTRODUCTION Distributed hydrological models are usually parameterized by deriving estimates of parameters from the topography and physical properties of the soils, aquifers and land use of the basin. The reliability of model predictions depends on how well the model structure is defined and how well the model is parameterized. However, estimation of model parameters is often difficult due to the large uncertainties involved in determining parameter values, which can not be directly measured in the field. Therefore, model calibration is necessary to improve the model performance. The traditional procedure of model calibration is usually done manually by trial and error parameter adjustments. In this case, the goodness-of-fit of the calibrated model is evaluated based on a visual judgement by comparing simulated and observed data, and some selected statistical measures in order to support the judgement. The calibration is therefore time consuming and subjective. Because of the large number of spatial model parameters and the complexity in simulating hydrological processes, automated calibration techniques are becoming popular methods to account for parameter variability, while reducing the model calibration effort. Automated calibration is usually applied to models with conceptual components that do not represent the specific equations of the physical processes. This procedure is especially useful when a model has a large number of parameters that need calibration, when the link between these parameter values and physical processes is not straightforward, and when parameters are strongly interrelated (Al-Abed & Whiteley 2002). The use of automated calibration schemes applied to a complex, integrated and distributed hydrological modelling system has been an ongoing research area with limited experience in recent years (Madsen et al. 2002). For parameter estimation in groundwater modelling, gradient based local search techniques (e.g. McLaughlin & Townley 1996) and the populationevolution-based global optimization methods (e.g. Solomatine et al. 1999) have been widely applied. These optimization techniques are also applied to localize the global optimum on a response surface in distributed rainfall-runoff modelling, from which a general conclusion is obtained that the global optimization algorithms perform better than pure local search methods (Madsen et al. 2002, Yu & Schwartz 1999). In particular, the computer code PEST has been developed by Doherty et al. (1994, 2003) based on a Gauss-Marquardt-Levenberg optimization algorithm that locates the minima of a multidimensional function in model parameter calibration. In addition to the automated optimization techniques in distributed models, spatial patterns of 317

2 parameter values must be defined so that a given parameter mainly reflects the significant and systematic variation for a certain process, thus reducing significantly the number of free parameters that need to be adjusted subsequently. As pointed out by Refsgaard (1997), the important points considered in a parameterization procedure should include: (1) to select parameter classes (topography, soil type, land use, climatology, etc.) for easily associating parameter values, (2) to evaluate parameters explicitly which can be assessed from field data or need some kind of calibration, and (3) to keep a low number of real calibration parameters both from practical and methodological points of view. This paper describes the calibration process for the GIS-based WetSpa hydrological model using the PEST automated calibration routine. The procedures of integrating PEST with WetSpa, the methods of dealing with the calibration of spatial model parameters, and the steps in the estimation process, including model parameterization, choice of calibration parameters, and specification of calibration and evaluation criteria, are presented. The approach is illustrated for model calibration of the Margecany catchment, Slovakia, with 10 years observed daily flow hydrographs at the basin outlet as the calibration target. Calibration results show that this scheme has a good performance in estimation of model parameters, and can be a credible alternative to the manual approach. However, a further manual refinement is necessary to avoid the ill-posed problems associated with the direct inverse procedures. 2 METHODOLOGY 2.1 The WetSpa model The WetSpa model is a GIS-based distributed hydrological model for flood prediction and watershed management (Liu et al. 2003, Liu 2004). For each grid cell, four layers are considered including vegetation zone, root zone, transmission zone and saturated zone. The processes considered in the model include precipitation, interception, snowmelt, depression, surface runoff, infiltration, evapotranspiration, percolation, interflow, ground water flow, and water balance in the root zone and the saturated zone. The total water balance for a raster cell is composed of the water balance for the vegetated, bare-soil, open water and impervious parts of each cell. This allows accounting for the non-uniformity of the land use per cell, which depends on the resolution of the grid. Inputs to the model are digital maps of topography, soil type and land use, and time series of precipitation, potential evapotranspiration and temperature. Observed discharge data are used for model calibration. The model predicts peak discharges and flow hydrographs, which can be defined for any numbers and locations in the stream network, and simulates the distribution of hydrological variables in the catchment. The root zone water balance in the model is simulated continuously by equating inputs and outputs: (1) where D (m) is the root depth, (m 3 m 3 ) is the change in soil moisture, t (d) is the time interval, I (md 1 ) is the initial abstracts within time t, E (md 1 ) is the actual evapotranspiration from soil, R (md 1 ) is the percolation out of the root zone, and F (md 1 ) is the amount of interflow in depth over the time. The surface runoff or rainfall excess is calculated using a moisture-related modified rational method in relation with a potential runoff coefficient depending on cell characteristics, the magnitude of rainfall, and the antecedent soil moisture: (2) where s (m 3 m 3 ) is the soil porosity, C (-) is the potential runoff coefficient. The values of C are taken from literature and a lookup table is generated, linking values to slope, soil type and land-use classes (Liu 2004). The exponent (-) in the formula is a variable reflecting the effect of rainfall intensity on the rainfall excess coefficient. The value is higher for low rainfall intensities resulting less surface runoff, and approaches to 1 for high rainfall intensities. The threshold value can be defined during model calibration. If 1, a linear relationship is assumed between rainfall excess and soil moisture. The effect of rainfall duration is also accounted by the soil moisture content, in which more excess produces due to the increased soil moisture content. The difference between net precipitation and excess rainfall is the amount of infiltration into the soil. Other processes in the model are simulated using either conceptual or physical based equations. Interception loss is evaluated using a linear reservoir model, in which the rainfall rate is reduced until its storage capacity is achieved. Snowmelt is modelled using a degree-day coefficient method. Depression storage is estimated using the empirical equation of Linsley (1982) as a function of the rainfall intensity and the depression storage capacity for different slope, soil type and land use classes. Evapotranspiration from soil and vegetation is calculated as a function of potential evapotranspiration, vegetation type, stage of growth and soil moisture content. The total evapotranspiration 318

3 is calculated as the sum of evaporation from interception storage, depression storage, and the evapotranspiration from soil and groundwater storage. The percolation out of the root zone is equated as the hydraulic conductivity corresponding to the moisture content as a function of the soil pore size distribution index (Eagleson 1970). Interflow is assumed to occur in the root zone after percolation and becomes significant only when the soil moisture is higher than field capacity. Darcy s law and a kinematic wave approximation are used to estimate the amount of interflow generated from each cell, in function of hydraulic conductivity, the moisture content, slope angle, and the root depth. The routing of overland flow and channel flow is implemented by the method of the diffusive wave approximation (Liu et al. 2003). An approximate solution using a two-parameter response function, termed average flow time and the standard deviation of the flow time, is used to route water from each grid cell to the catchment outlet or a selected convergent point in the catchment. The flow time and its variance are determined by the local slope, surface roughness and the hydraulic radius for each grid cell. The flow path response function at the outlet of the catchment or any other downstream convergence point is calculated by convoluting the responses of all cells located within the drainage area in the form of the probability density function of the first passage time distribution. Groundwater flow in the model is simplified as a linear reservoir on small subcatchment scale. Finally, the total discharge is obtained by a convolution integral of the flow response from all distributed precipitation excess. 2.2 PEST description PEST is a nonlinear parameter estimation and optimization package, and is one of the most popular systems offering model independent optimization routines (Doherty & Johnston 2003). It applies a robust Gauss Marquardt Levenberg algorithm, which combines the advantages of the inverse Hessian method and the steep descent method and therefore provides faster and more efficient convergence towards the objective function minimum. The best set of parameters is selected from within reasonable ranges by adjusting the values until the discrepancies between the model generated values and those measured in the field is reduced to a minimum in the weighted least squares sense. The goodness-of-fit is apparent from the value of the optimized objective function and is also provided by computed correlation coefficient, which is independent from the number of observations. The level of uncertainty associated with those observations allows therefore for direct comparison of different parameter estimation runs (Baginska et al. 2003). One of the advantages of PEST is that it can account for prior information in the parameter estimation process. This is useful when some information concerning the parameters to be optimized is available, and is obtained independently of the current experiment. The inclusion of prior information into the objective function can change its structure in parameter space, often making the global minimum easier to find. It also enhances optimization stability and may reduce the number of iterations required to determine the optimal parameter set. The multiobjective calibration problem consists of a single weighted least-squares objective function, : (3) where B is a vector containing values of the parameters being estimated, m is the number of observations, n is the number of prior information values, x i is the ith observation, x i (B) is the simulated value corresponding to the ith observation, y j is the jth prior estimate, y j (B) is the jth simulated value, i is the weight for the ith observation, and j is the weight for the jth prior estimate. Due to its model-independent characteristic, PEST can be used easily to estimate parameters in an existing computational model, and can estimate parameters for one or a series of models simultaneously. Since its development, PEST has gained extensive use in many different fields, for instance, the automated model calibration and data interpretation in the groundwater model MODFLOW/MT3D (Doherty & Johnston 2003) and some other surface runoff and water quality models (Baginska et al. 2003, Syvoloski et al. 2003). 2.3 Combining PEST with WetSpa The process of combining PEST with WetSpa is illustrated in Figure 1. By combining a powerful inversion engine, PEST communicates with WetSpa through the Figure 1. Model inputs WetSpa model Model parameters Model simulation Model outputs PEST Optimization algorithm Objective function Observations Schematic of the WetSpa automatic calibration. 319

4 model s own input and output files. During automatic calibration, model parameters are adjusted automatically according to the PEST optimization objective functions. The process is repeated until the stopping criterion is satisfied, e.g. maximum number of iterations, convergence of the total objective function, or convergence of the parameter set. The specifications of the calibration algorithm include model parameterization, selection of calibration parameters, defining parameter variation range, assigning prior information to a parameter group, assigning weights to the observation group, etc. The WetSpa distributed model involves a large number of model parameters to be specified during the model setup. Most of these parameters can be assessed from field data, e.g. hydro-meteorological observations, maps of topography, soil types, and land use, etc. However, comprehensive field data are seldom available to fully support specification of all model parameters. In addition, some model parameters are of a more conceptual nature and cannot be directly assessed. In the process of WetSpa model parameterization, spatial patterns of the parameter values are defined using the available data to describe the most significant variations. This is done by defining appropriate parameter classes of topography, soil type, land use, etc. For each class, some parameters are assessed directly, and others are subjected to calibration. This approach enables the use of automated calibration procedures more efficiently when applied to a distributed model. The 11 major WetSpa model parameters that need to be calibrated are listed in Table 1. Other spatial model parameters derived using GIS tools are not calibrated. Table 1. Parameterization of the different model components. Model Calibration Parameterizacomponent parameters tion Snowmelt Base temperature Melting Degree-day factor season Surface runoff Runoff coefficient Slope, soil Moisture exponent and land use classes Interflow/percolation Interflow scaling Soil classes factor Hydraulic conductivity Groundwater flow Recession constant Saturated Maximum storage zone Evapotranspiration Correction factor Land use classes Flow routing River bed resistance River system Hydraulic radius The choice of parameters to calibrate is based on earlier studies of the WetSpa model (Liu et al. 2003, Liu 2004). Six parameter groups are distinguished in the modelling approach: (1) base temperature and degreeday factor for modelling snowmelt, (2) potential runoff coefficient and moisture exponent for modelling surface runoff, (3) interflow scaling factor and soil hydraulic conductivity for modelling interflow and percolation out of the root zone, (4) groundwater flow recession constant and maximum active groundwater storage for modelling groundwater flow, (5) evapotranspiration correction factor for modelling actual evapotranspiration, and (6) river bed resistance and hydraulic radius for flow routing. Among the calibration parameters listed in the table, the two parameters controlling snowmelt affect flow hydrographs only in the melting season. The parameters controlling surface runoff, interflow, percolation and evapotranspiration affect model results mainly in the non-frozen period. The parameters controlling flow routing are required for the whole simulation period. These information statements are important for assigning parameter weights to the observations so as to reduce the computation efforts during model calibration. From the spatial point of view, the calibration parameters can be categorized into two classes: lumped parameters and distributed parameters. The lumped parameters include base temperature, degree-day factor, moisture exponent, interflow scaling factor, baseflow recession constant and maximum active groundwater storage. These parameters have more conceptual meaning, and are calibrated against their real values. The spatial model parameters include the potential runoff coefficient obtained from the combined maps of slope, soil type and land use, the hydraulic conductivity obtained from the soil type map, the evapotranspiration correction factor obtained from the land use map, and the river bed resistance and hydraulic radius derived from the stream network and land use maps. These parameters are location dependent, and have more physical meaning. Due to the large number of cell parameters, calibration for each class or the combination of different classes will be difficult to realize. Therefore, a simple approach by fixing the spatial pattern of the model parameters and multiplication by a correction factor is adopted in this study. This simplification highly reduces the optimization effort, and makes the calibration fast and feasible for a model with large number of cells and long calculation time series. In addition, an ill-posed problem may arise when the number of parameters is large, or when observation errors exist during parameter optimization. This will make the solution increasingly non-unique leading to poor results. Therefore, a manual refinement is necessary to check the reliability of the calibrated model parameters. 320

5 3 CASE STUDY 3.1 Catchment and data The automatic calibration procedure described above is applied for calibration of the WetSpa model on the Margecany catchment with cell size of m and daily time step. The Margecany catchment has an area of 1133 km 2 and is located in the upper Hornad River basin upstream of Ruzin reservoir in the eastern part of the Slovak Republic (Fig. 2). The topography varies from 333 m near Margecany station to 1556 m at the south-western ridge. The basin has a northern temperate mountainous climate with four distinct seasons. January is the coldest month and July is the warmest month of the year. The highest amount of precipitation occurs in the period from May to August and the least is in January and February. The mean annual precipitation ranges from about 640 mm in the valley to more than 1000 mm in the vicinity of the water divide. Three digital maps, DEM, soil type and land use, in raster format are used to derive spatial model parameters required in the WetSpa model. The elevation data for the river basin was digitized from an elevation map and interpolated to construct a 100 m grid size DEM, from which the drainage system was delineated. The original land cover information was reclassified into 14 categories and converted to a 100 m cell size grid for use in the WetSpa model, and re-grouped into 5 classes for deriving model parameters of potential runoff coefficient and depression storage capacity (Fig. 3). The land use consists of agriculture (23%), grass (25%), forest (50%), urban areas (1.9%), and open water (0.1%). The original soil map was reclassified into 12 USDA soil texture classes based on their textural properties and converted to a 100 m cell size grid. The main soil types are loam (42%), sandy loam (24%), and silt loam (23%). Besides, 10 years of daily precipitation data at 9 stations, temperature data at two stations, evapotranspiration data at Spisske Vlachy located at the downstream reach of the catchment, and discharge data at Margecany are available. These data are used for optimization of model parameters. Elevation (m) High : 1556 Low : 333 N Streams Reservoir Flow station Precipitation station Study catchment Hornad boundary Margecany km Ruzin Reservoir 3.2 Model calibration The WetSpa model was calibrated against the daily stream flow measurements at the Margecany station for the time period of 1991 to The automatic calibration module consists of 12 most important model parameters (Table 2), i.e. the base temperature Kt ( C), the degree-day factor Kd (mm C 1 d 1 ), the correction factor for potential runoff coefficient Kr (-), the moisture exponent Km (-) at a near zero rainfall intensity, the maximum rainfall intensity Kp (mm) over which Kr equals 1 and the actual runoff coefficient is equal to the potential runoff coefficient, the interflow scaling factor Ki (-), the correction Figure 2. Location, topography, streams and monitoring network of the study catchment. Land use Agriculture Grassland Needle leaf forest Broad leaf forest Urban area Open water Figure 3. N km Land use map of the study catchment. Table 2. Search space and parameter values before and after automated calibration. Auto Auto Manual Search Initial calibration calibration refine- Parameter space value 1 2 ment Kt Kd Kr Km Kp Ki Kc Kg Ks Ke Kn Kh

6 factor of hydraulic conductivity Kc (-), the groundwater flow recession constant Kg (d 1 ), the maximum active groundwater storage Ks (mm), the correction factor for potential evapotranspiration (-), and the correction factors for river bed resistance Kn (-) and hydraulic radius Kh (-). The parameters Km and Kp are combined to calculate the exponent variable in Equation 2, for which 1 when P Kp, Km when P approaches zero, and linear interpolation in between. Additionally, a limit is given in the program to ensure that the potential runoff coefficient is less than 1 after the correction of Kr. The parameter variation range or search space is defined by specifying a lower and an upper bound. These limits are chosen according to physical and mathematical constraints in the model and should reflect the prior knowledge of experienced values. The initial parameter values can be chosen arbitrarily within the search space. However, the mid-values within the variation range are selected for the first trial as listed in Table 2. More discussion about the setting of initial parameter values is given in the next section. By setting the initial soil moisture content to the field capacity and the initial active groundwater storage to the half of the maximum active groundwater storage, the model is run and the output is compared with the observed hydrographs at Margecany. To assess the model s performance in simulating stream flow variations, 4 evaluation criteria used by Hoffmann et al. (2004) are selected (Table 3). C1 evaluates the ability of the model to reproduce the water balance. The model s performance is evaluated as highest when the C1 criterion is close to 0, whereas the model performance is poorest with values close to 1. The accuracy of the model s representation of the observed hydrograph is evaluated through the Nash Sutcliffe criterion, C2. C3 and C4 are two adapted Nash Sutcliffe efficiencies to assess the model s performance for low flow and high flow. Criteria C2, C3 and C4 values close to 1 indicate a good model performance, whereas values close to 0 show a poor model performance. As can be seen in the table, the model gives a poor performance with initial parameter values. The flow volume is 13.2% over estimated, the Nash Sutcliffe efficiency is 0.453, and the other two adapted Nash Sutcliffe efficiencies for low flow and high flow evaluation are and 0.562, which indicate that further parameter optimizations are required. After the completion of the template file (identifying model parameters), the instruction file (identifying model output variables), and the input control file (supplying all necessary information for PEST) required for running PEST, the automated calibra-tion module is executed with equal weight for each calibration parameter and without prior information. The iteration process stops when the calibration parameters Table 3. Model evaluation results before and after calibration. Parameter sets C1 C2 C3 C4 Initial values Auto-calibration Auto-calibration Manual refinement have converged (maximum relative parameter change of in one iteration) or a maximum number of iterations of 30 is reached. The resulting parameter values are listed in the 4th column of Table 2. It can be seen that the parameter values differ considerably from the initial values. Specifically, the baseflow recession constant is reduced from 0.01 d 1 to d 1, the maximum active groundwater storage is reduced from 140 mm to 50 mm, and the potential evapotranspiration correction factor is increased from 1.10 to These changes result in a reduction of the simulated groundwater flow and an increase of simulated evapotranspiration from the groundwater storage. The evaluation results of model performance after the first trial of automated calibration are presented in Table 3. One can see that the model performance is improved significantly. The model bias is reduced to 0.043, and the three Nash Sutcliffe efficiencies are increased to 0.675, 0.594, and respectively. However, the simulation result is still not satisfactory as can be seen by plotting and comparing the observed and simulated hydrographs. Therefore, additional adjustment of the calibration parameters is necessary by setting different weights and including prior information for some of the parameters in the PEST control file. The correlation coefficient matrix of the calibration parameters after the first trial of the automated calibration is presented in Figure 4. High positive correlation between calibrated parameters is clearly illustrated by dark grey cells and high negative correlation by bright grey cells in the displayed image. Especially, parameters Kr, Km and Kp are highly correlated as they jointly control the volume of surface runoff. There is also a high correlation between Ks and Ke, both controlling the amount of evapotranspiration from the groundwater storage. Similar correlation is found between Kn and Kh, both controlling the process of flow simulation. A highly negative correlation is found between Kp and Ki, Ki and Kc as they jointly control the volume of interflow out of each grid cell, and between Ks and Kg both controlling the rate of groundwater flow. These excessive parameter correlations may result in a high level of parameter uncertainty. As pointed out by Doherty et al. (1994), increasing the number of parameters, sooner or later, 322

7 Kh Kn Ke Ks Kg Kc Ki Q(m 3 /s) Precipitation Q Observed Q Calculated P(mm/d) Kp Km Kr Kd Kt Kt Kd Kr Km Kp Ki Kc Kg Ks Ke Kn Kh Figure Model calibration at Margecany for the year Figure 4. Correlation matrix of the calibration parameters. will result in some parameters to become highly correlated. This results from the fact that the measurement set upon which the parameter estimation process is based may not have the ability to discriminate between different combinations of parameter values, each combination giving rise to an equally low objective function. In addition to the non-uniqueness problem, the optimization process becomes very slow if there are many parameters in need of adjustment, particularly when some parameters are highly correlated. Therefore, rearrangement of the PEST control file by setting different weights and by incorporating prior information is required in order to reduce parameter uncertainty and to ensure better process representation. Since one of the main purposes of the model is to predict floods at the basin outlet, it is expected that the high flow observations are more important than the low flow values in the model calibration process. This is simply achieved in this study by giving a double weight to the flow observations with values higher than 20 m 3 /s in the PEST control file, while the weights for the rest flow observations are maintained as they are. In addition, some prior information is included in the re-optimization process: (1) parameter Kr has a preferred value of 1.0, (2) the ratio between the estimated values of parameters Kp and Km should be about 25 based on the analysis of model test for different parameter combinations, (3) parameter Ke has a preferred value of 1.15 based on the water balance analysis for the whole simulation period, (4) parameters Kc, Kh and Kn have a preferred value of 1.0, corresponding the default parameter set predetermined in the model, (5) parameter Kg has a preferred value of d 1 based on the analysis of the baseflow recession curves at the Margecany station, and (6) parameter Kt is less sensitive and can be fixed at 0 C. The prior information is included in the estimation process by simply defining a linear equation in the PEST control file and giving a higher weight for each of them. Specifically, the parameters Km and Kp are log-transformed in order to define the relationship between the logs of the two parameters in the prior information equation. After the above modifications in the PEST control file, the automated calibration is performed again using PEST in the regularization mode. The resulting parameter values are listed in the 5th column of Table 2. It can be seen that the parameter values are changed noticeably from the values obtained from the first trial of automated calibration with equal weight and without prior information. Moreover, the optimization time is highly reduced (about 8 minutes for a 10-year calibration period with a daily time step on a PEN- TIUM 4 CPU 3.00 GHz, 1.00 GB RAM), which is about 2/3 of the first automated calibration trial. This is due to the inclusion of prior information into the objective function, which changes its structure in parameter space and makes the global minimum easier to find. This enhances optimisation stability and reduces the number of iterations required to determine the optimal parameter set (Doherty et al. 1994). The plot of simulated and observed flow hydrographs for the year 1997 is presented in Figure 5, for which a good fit is achieved for both summer and spring floods. This is also illustrated by the model evaluation results listed in Table 3, where model bias is reduced from to 0.023, and the three Nash-Sutcliffe efficiencies are increased significantly. The adapted Nash-Sutcliffe efficiency for high flows is 0.846, which indicates that floods are well predicted. 3.3 Sensitivity analysis Sensitivity analysis is useful in the initial model parameterization process to investigate which parameters are sensitive with respect to the available observations, 323

8 and which are insensitive and can be set to fixed values. PEST provides an independent sensitivity analysis module by adjusting model inputs, running the model, reading the outputs of interest, recording their values, and re-commencing the computing cycle. However, the results of such an analysis should be carefully interpreted. The dimensionless, scaled sensitivities depends on the parameter values, and hence sensitivity statistics evaluated at some initial parameter values may be very different from the statistics obtained using other parameter sets (Hill 1998). In addition, sensitivity statistics do not properly account for parameter correlations, implying that parameters that seem to be insensitive may have important correlations with other parameters that are essential for the model behaviour (Madsen 2002). The result of parameter sensitivity analysis after PEST implementation with equal weight and prior information is presented in Figure 6. The parameter sensitivity value is expressed by the relative composite sensitivity, which is obtained by multiplying its composite sensitivity by the magnitude of the value of the parameter. The use of relative sensitivities in addition to normal sensitivities assists in comparing the effects that different parameters have on the parameter estimation process when these parameters are of different type, and possibly of very different magnitudes (Doherty et al. 1994). As can be seen in the figure, the relative sensitivity of the 12 calibration parameters varies within the range 0.02 to Parameter Ke has the highest relative sensitivity, which controls the actual evapotranspiration from soil and the groundwater storage. Parameters Km and Kr are second and third in sensitivity both controlling the volume of surface runoff in the model. Parameter Kt has the least relative sensitivity, and therefore can be fixed in the parameter estimation process. To test the parameter sensitivities around the optimised parameter set, a manual refinement is performed by adjusting parameter values in the WetSpa input file. A trial parameter set is listed in the 6th column of Relative sensitivity Figure 6. Kt Kd Kr Km Kp Ki Kc Kg Ks Ke Kn Kh Parameters Relative sensitivity of the calibration parameters. Table 2, and the evaluation result of the model performance is given in Table 3. It is seen that the evaluation results change slightly. Model bias is more or less the same as for the previous value, while the Nash Sutcliffe coefficient and its adapted value for high flow assessment increase slightly, and the adapted value for low flow assessment decreases noticeably. However, these changes are difficult to identify from the visually comparison of the flow hydrographs. Usually, a manual adjustment of the model parameters is necessary after the automated calibration to test if the global minimum in the objective function is achieved, or if an ill-pose problem exists, which is commonly associated with the direct inverse procedures. 4 DISCUSSION To test the effect of initial parameter values on the results of automated calibration in this study, a number of different parameter set was employed to start the automated calibration process. It is found that the calibrated parameter set resulting from different initial values may differ considerably, and so does the evaluation results of the model performance. This is due to model nonlinearity, model uncertainty and high correlations between some model parameters, which makes the global minimum in the objective function difficult to find. Nonlinearity is one of the major problems in the application of distributed modelling concepts in hydrology, particularly in modelling of large scale catchments. In the WetSpa model, the surface runoff is estimated by a modified rational method, the routing of flow is characterized by the linear transfer functions of the diffusive flood wave, and the groundwater flow is simplified by the linear reservoir method. This apparent linearity does not apply to the relationship between rainfall inputs and river discharge that is known to be a nonlinear function of antecedent conditions, rainfall volume, and the interacting surface and subsurface processes of runoff generation. As pointed out by Beven (2001), the use of pedotransfer functions to estimate a set of average model parameters at the element scale of a distributed hydrological model should not be expected to give accurate results. The problem of uncertainty arising from the modelling process is associated with the input data (temporal and spatial variability of parameters, initial and boundary conditions), the model assumptions and algorithms for describing the processes, and the measurements for model calibration and validation. The high uncertainty and correlations of the model parameters usually result in the non-uniqueness of parameter estimates and model predictions, making optimization difficult by the fact that the objective function may possess local minima distinct from the global minimum. 324

9 To tackle this problem, it is necessary to supply an initial parameter set close to the optimum parameter set. This makes PEST optimization more efficient, especially for highly nonlinear models or models with local objective function minima in the parameter space. Moreover, a suitable choice for the initial parameter set can also reduce the number of iterations necessary to minimize the objective function. For modelling of large catchments or modelling with a high spatial and temporal resolution, this can mean considerable savings in computer time (Doherty et al. 1994). However, specifying a proper initial parameter set is not an easy task. It needs a fully understanding of both the hydrological model and the physical characteristics of the study area. A trial with a number of different initial parameter set in PEST to find a more reliable parameter estimates is sometimes necessary. From the experiences of this study, it is illustrated that PEST can be incorporated with a distributed hydrological model to estimate efficiently the model parameters. Division of model parameters into different classes (topography, soil type, land use, climate, etc.) makes it easy to specify parameter values in an objective way. Moreover, the number of real calibration parameters should be kept low in the automated calibration process. This can be done by fixing the insensitive parameter values based on the PEST sensitivity analysis, and by fixing the spatial pattern of a parameter but allowing its absolute value to be modified through model calibration. The use of prior information in PEST provides the system with the ability to supply a unique set of parameter estimates. This technique should be used carefully, because specifying prior information usually results in parameter estimates that are close to the values specified in the prior information. Also, assigning different weights to the observations depending upon the data accuracy or the main target of the model may highly increase the efficiency of model calibration and the reliability of the parameter set. In addition to the application of PEST described in this paper, PEST also has many other capabilities, such as defect data interpretation, estimation of the system properties from the measurement set, various predictive analyses to maximize or minimize a specified prediction while maintaining the model in a calibrated state, and model parameter estimations for multi-site measurements and multiple response modes. These functions need to be studied further when incorporating with a distributed hydrological model. 5 CONCLUSION In this paper, a strategy is presented for automatic calibration of the GIS-based WetSpa hydrological model by incorporating a model-independent parameter estimator PEST. The WetSpa model is capable of simulating hydrological processes in a watershed including surface runoff, interflow, groundwater flow and other water balance variables. The flow hydrograph at the basin outlet is used in the PEST optimization approach as calibration targets. The application of this approach is demonstrated for the Margecany catchment, Slovakia. Seven lumped parameters and five distributed parameters are estimated using the PEST automated calibration scheme. The distributed parameters are calibrated by multiplication by an overall correction coefficient while keeping the spatial pattern derived from the GIS maps fixed. The results of this study demonstrate that the use of combining a GIS-based hydrological model with PEST can produce calibrated parameters that are physically sensible. Without the use of such techniques, calibration of parameters takes much longer and the obtained results may be unrealistic in terms of the calibrated parameter values. The incorporation of different weights and prior information into the estimation process can add stability to an over-parameterized system. Likewise, removing a number of parameters from the process by holding them fixed at strategic values may yield considerable improvements in the calibration performance. This scheme is faster and less subjective than trial and error method, and may serve as an optimization algorithm to estimate the WetSpa model parameters. Furthermore, the calibration results from this study show the great potential and the possibility of PEST to be used in the calibration process of spatially distributed hydrological models. REFERENCES Al-Abed, N.A. & Whiteley, H.R Calibration of the Hydrological Simulation Program Fortran (HSPF) model using automatic calibration and geographical information systems. Hydrological Processes 16: Baginska, B., Milne-Home, W. & Cornish, P Modelling nutrient transport in Currency Creek, NSW with AnnAGNPS and PEST. 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