Sensitivity Analysis, RR Parameters
The two catchments modelled with the NAM method are described with 7 parameters each. In order to determine which of the 14 parameters that are more sensitive and should be included in the calibration a sensitivity analysis is performed. The sensitivity is evaluated around the default parameter values and the influence of changing them one at a time is calculated.
Simulation specification
Model Parameters
Objective Functions
Sensitivity Analysis
Results
MIKE 11 produces results in res11 file whereas AutoCal evaluates objective functions by comparing dfs0 files. Hence, the .hd11 file specifies that time series output is to be generated additionally. See the .hd11 file.
As Model Parameter file, the RR11 file of the MIKE11 setup is specified since that is where the NAM parameters are specified. AutoCal automatically generates the template file Example2\Test2_Autocal.RR11. This file is edited and all the NAM parameters are marked as parameters by specifying their values as 1.01e-035 ...1.14e-035. Finally, Sensitivity analysis is chosen as the Simulation option.
The model parameter table is partly filled out automatically. AutoCal lists all the parameters recognised for the sensitivity analysis and allows the user to specify Name, Parameter type, Initial Value, Lower bound, Upper bound and Transformation. The specified parameters are listed in Table 2.1.
AutoCal calculates scaled sensitivity coefficients that are multiplied with the specified parameter interval. Hence, the specification of lower and upper bounds effects the result although these are derivatives evaluated around the initial value.
The objective function is the specification of the measure we want to use to quantify the quality of the calibration and hence use to measure parameter sensitivity. The measurements in this example are discharge timeseries at three locations.
We define an objective function as a weighted sum of the squared value of each output measure. We name the objective function Q_RMS. The output measures are defined as the root mean square of the residual between simulated and measured water level in the three measurement points. The three output measures are named RMS_Q_Branch1_39166, RMS_Q_Branch1_87827 and RMS_Q_Branch2_36933, respectively.
The sensitivity analysis parameters are left unaltered as the default values. This means that we will do a local sensitivity analysis (currently only available choice), use forward difference approximation with a 1% of the parameter interval as perturbation value. This means that AutoCal will evaluate the objective function, Q_RMS, at the initial parameter set and at 14 parameter sets where one parameter at a time has been increased with 1% of its parameter interval. The calculated value is used to make a two point forward finite difference approximation to the derivative of the initial parameter set.
The results of the sensitivity analysis can be found in the file Test2-Autocal_Sensitivity. The calculated Scaled sensitivity coefficients are listed in Table 2.2.
The most sensitive parameters are the overland flow runoff coefficient for both catchments (CQOF1 and CQOF2), followed by the thresholds for overland flow (TOF1 and TOF2) and time constant for overland flow routing for catchment 2 (CK2). Intermediate sensitive parameters are the maximum water content in surface and root zone storages (Umax1, Umax2, Lmax1, Lmax2). The least sensitive parameters are time constant for interflow (CKIF1 and CKIF2) and threshold value for interflow (TIF1 and TIF2).