5.5 Application of the ROPE Algorithm to Different Models and Different Catchments
Figure 5.9: Confidence band width of high depth Vs confidence band width of low depth
5.5 Application of the ROPE Algorithm to Different Models
Period Mean NS Max NS Min NS std 1961-1970 0.6944 0.7014 0.6921 0.00175 1971-1980 0.6241 0.6435 0.5860 0.00909 1981-1990 0.7465 0.7607 0.7251 0.00617 1991-2000 0.6777 0.6960 0.6493 0.00864
Table 5.8: Model performance for calibration time period 1961-1970 and validation for other time period for Rottweil
Catchments in England and Wales
The description of the catchments is given in Chapter 4. The HYMOD model was calibrated for the time period 1981-85 and validated for other time period. Table 5.9 shows the calibration and validation result for catchment 27. It can be seen from Table 5.9 that the ROPE algorithm can be used to calibrate HYMOD conceptual model on catchments other than those where it was developed. The parameters obtained by calibration are good for transferring to other time periods. The result form the other catchments shows a very similar trend.
Period Mean NS Max NS Min NS std 1981-1985 0.880 0.882 0.877 0.00089 1986-1990 0.843 0.848 0.8367 0.00229
Table 5.9: Model performance (NS) for calibration time period 1981-1985 and validation for the other time period for catchment 27 in the UK
5.5.2 Result from three reservoirs model Indian catchments
Some properties of Indian watersheds are quite different than their European counter-parts. Topographic slopes, particularly in headwater regions are steeper in India, rivers are much wider with uncontrolled widths, rainfall intensities are higher and so is the input solar radiation/temperature. Temporal distribution of rainfall is highly skewed in India. Some rivers, particularly on the Indian peninsular are non-perennial and due to this, stream gauging is usually limited to the monsoon season only. Typical catchment sizes that are considered for management of water and associated resources are larger in India than in Europe. Data measurement networks are comparatively weak in India;
typical lengths of time series data are shorter and data quality is poorer, also. The details of the Indian catchments is also given in Chapter4.
With the above background, the ROPE algorithm was tested on the data of Indian watersheds using a three reservoir conceptual model to test the performance of the ROPE algorithm under situations that are dramatically different than those for which it was developed.
5.5 Application of the ROPE Algorithm to Different Models and Different Catchments
Model calibration and validation
The data for the period 1983-86 was chosen for model calibration. The length of com-putational time step was one day. First, a few model runs were taken to have some idea about the range of the parameters. Maximum and minimum values of the model parameters are presented in Table 5.10. Next, a large number of uniformly distributed parameters sets were generated within the identified range and the model runs were taken with each set of parameters. The Nash-Sutcliffe coefficient (Nash and Sutcliffe, 1970) was used as the objective function for the model evaluation. Based on this index, the best 10 percent parameter sets were chosen and again the maximum and minimum values of the parameters were determined.
Parameters Maximum Minimum Unit
Smax 500 5 mm
Cmax 1500 15 mm
FC 0.90 0.1
-Finf 0.99 0.001
-Cint 0.99 0.001
-Table 5.10: Range of model parameters
After getting a proper range of parameters, the model was calibrated using the ROPE algorithm. Figure5.10shows the model and the observed hydrograph for the calibration period. It can be seen that during the calibration runs, the catchment dynamics has been captured well at low peaks but the model has not given good results for very high peaks. This could be due to data limitations.
1
0 500 1000 1500 2000 2500
1 51 101 151 201 251 301 351 401 451 501 551
Time(Days)
Discharge(m3/s)
Observed Model
Figure 5.10: Observed and model hydrograph for calibration run
During calibration, a very wide range of model parameters has been considered to avoid
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local minima. The ROPE algorithm has a feature that it does not give a single value of parameters after calibration; instead, it gives a vector of parameter set. After the calibration, the range of parameters has been considerably narrowed down and the final range is given in Table 5.11. It can be seen that some the parameters like Cmax have the maximum reduction in the range. The final range of the parameters is still very wide but they perform equally well. Please note that not all parameters in this range are good since it is not a uniform space.
Parameters Maximum Minimum Unit
Smax 95.093 95.093 mm
Cmax 921.545 167.429 mm
FC 0.888 0.481
-Finf 0.917 0.233
-Cint 0.931 0.104
-Table 5.11: Range of model parameters after calibration
It can be seen here that some parameters have a large range and some small. This happens because of different sensitivities of the parameters. The model was validated using the data for the period 1987-88. Robustness of the calibrated parameters can be seen in Table 5.12 in which the statistics of 1000 parameter sets is given. It is very clear from Table 5.12 that parameters obtained by the ROPE algorithm are well transferable to some other time period. The value of NS index is poor because of the quality of the data. Figure5.11 shows the observed and simulated hydrographs for the validation period. It may be noted that in the previous study by Jain (1993), on the same basin and using the same model, similar results were obtained. The result of the ROPE calibration was better as compared to the previous study due to its robustness in transferability of parameters in time. Further, instead of single value of each parameter, the ROPE calibration gives a space of good parameter sets.
Mean NS Max NS Min NS Std Calibration 0.612 0.622 0.609 0.00289 Validation 0.639 0.691 0.603 0.02875 Table 5.12: Performance for calibration and validation
The ROPE algorithm was tested on Indian watershed data using a conceptual model to examine its performance under situations that are diametrically different than those for which it was developed. It has been found that the algorithm is effective in estimating parameters of a conceptual model in a typical Indian watershed. There were limita-tions regarding spatial coverage of raingauge stalimita-tions as well as the quality of data, as mentioned earlier. Further, the potential evaporation data for the catchments was also not representative since the station was away from the basin. The performance of the model and the ROPE algorithm is encouraging in light of the above constraints on data availability.