After parameter sensitivity analysis, a small number of the most sensitive parameters can be selected for auto-calibration. The value ranges of parameters may be the same with those defined in the parameter sensitivity analysis, or they may be narrowed by excluding values that result in an unacceptable model performance, such as in cases where NSE is less than zero.
In the current version of SEIMS, the NSGA-II algorithm (Non-dominated Sorting Genetic Algorithm II) was used for auto-calibration. During NSGA-II execution, the Latin-hypercube sampling method (Iman and Shortencarier, 1984) was used to generate initial samples of calibrated parameters. The crossover and mutation operations were similar to the original implementations in NSGA-II by Deb et al. (2002).
For simple usage, open a CMD window, enter the following commands to execute the auto-calibration of the streamflow modeling of the Youwuzhen watershed model.
The runtime logs of auto-calibration including commands of each model run, the average model performance indicators of each generation, and the time-consuming were showed in Figure 1.
Like the parameter sensitivity analysis, the calibration values of selected parameters will be generated and imported as CALI_VALUES field into the PARAMETERS collection of the main spatial database for each generation during the optimization of auto-calibration (Figure 2).
The results of the auto-calibration can be found in SEIMS\data\youwuzhen\demo_youwuzhen30m_longterm_model\CALI_NSGA2_Gen_2_Pop_4. The near-optimal Pareto solutions plotted as a scatter plot can give a simple and direct interpretation of the calibration optimization processes. For example, Figure 3 showed the near optimal Pareto solutions of the first and second generations with the objectives of maximize the NSE and minimize the RSR of the simulated streamflow at the watershed outlet, which indicated an evolutionary directory to maximum NSE and minimum RSR.
In the meantime, to have a better aware of the calibration results, one best solution with the maximum NSE of the calibration period was plotted for each generation (red dash line in Figure 4) together with the 2.5% and 97.5% levels of the cumulative distribution of the output variables (gray band in Figure 4), i.e., streamflow at the watershed outlet in this demo.
The configuration file of auto-calibration, such as that of the Youwuzhen watershed model shown in the following code block, includes four sections, i.e., SEIMS_Model, CALI_Settings, NSGA2, and OPTIONAL_MATPLOT_SETTING. Among them, OPTIONAL_MATPLOT_SETTING is optional. The names of sections and options should not be changed.
SEIMS_Model: Basic settings of the SEIMS-based watershed model, see Section 2:4.3.2 for details. Note that the OpenMP version of SEIMS main program is used by default. However, the options of version, MPI_BIN, and processNum are supported if the MPI&OpenMP version is wanted.CALI_Settings: Basic settings for auto-calibration.paramRngDef: Filename of the definition of parameters’ range for calibration. The format is the same with paramRngDef of parameter sensitivity analysis (Section 2:6.2).Cali_Time_start: Starting date time of the calibration period for model calibration with the format of YYYY-MM-DD HH:MM:SS.Cali_Time_end: Ending date time of the calibration period for model calibration with the format of YYYY-MM-DD HH:MM:SS.Vali_Time_start: (Optional) Starting date time of the validation period with the format of YYYY-MM-DD HH:MM:SS for visualization only to explore the effective of the calibrated parameters, e.g., Figure 2:7 4.Vali_Time_end: (Optional) Ending date time of the validation period with the format of YYYY-MM-DD HH:MM:SS. The Vali_Time_start and Vali_Time_end should be specified simultaneously.NSGA2: Parameter settings of NSGA-II algorithm.GenerationsNum: Maximum number of generations.PopulationSize: Initial population size, i.e., the number of individuals.CrossoverRate: Crossover probability, ranges from 0 to 1. A larger crossover rate indicates a higher possibility to take place the crossover operation between two parent individuals.MutateRate: Mutate probability.MaxMutatePerc: Maximum percent of genes to be mutated.SelectRate: Selection rate of the evaluated and sorted individuals for each generation which is known as near-optimal Pareto solutions.OPTIONAL_MATPLOT_SETTINGS: Plot settings for matplotlib, see Section 2:5.2.The Python scripts of auto-calibration are in SEIMS/seims/calibration. The main_nsga2.py is the entrance for the auto-calibration based on NSGA-II algorithm, which can be executed though the unified format of running SEIMS Python scripts, e.g.,
Also see introduction of the Python package seims.calibration package