Assessing the relative importance of two lump hydrological models parameters using Morris, Sobol and Entropy index methods

In recent decades following the massive increase in computational power, considerable progress has been made in hydrological models. As the complexity of the model increases, model parameters increases and this lead to increasing the chances of overfitting and difficulty in identifying both model parameter values and model structure. One possible way to mitigate over-parameterization/non-identifiability is reducing the number of parameters to a small number that can be sufficiently calibrated with limited data. Sensitivity analysis (SA) is a commonly used approach for identifying important parameters that dominate model behaviors. Overall, they can be categorized into two groups: local SA and global SA. The local SA explores the changes of model response by varying one parameter while keeping other parameters constant . On the other hand, the global SA examines the changes of model response by varying all parameters at the same time. No general rule has yet been defined for verifying the convergence of the General SA methods. In order to fill this gap this paper presents a convergence analysis of three widely used SA methods (Morris screening, Sobol and Entropy index) for two rainfall-runoff models, TOPMODEL and HBV. The simulations are carried out over ChehlChay watershed within Gorganrood River Basin.
The sensitivity and interaction analysis based onSobol, Morris screen and Entropy methods were applied. The Morris method has been proposed as a screening method to identify a subset of inputs that have the greatest influence on the outputs.Sobol SA is a global, variance-based method that attributes variance in the model output to individual parameters and their interactions.Mutual entropy analysis is a sensitivity analysis method in which the mutual entropy of two variables is regarded as the correlative extent between these two variables. The distribution character of data (X, Y) can be expressed by contingency tables. The HBV model and TOPMODEL are used as a test problem. There are thirteen and nine parameters in the HBV model and TOPMODEL models, respectively. In each model, samples of the model parameter space are obtained using a latin-hypercube. The convergence analysis has been performed by increasing the number of simulations until there was no significant change of the sensitivity measure. In addition, the three SA methods are evaluated and compared in terms of convergence, the related evolution of the parameter ranking results and required computation cost.
Results of the quantitative convergence analysis for Morris screen was achieved at 700 and 1000 number of simulations for HBV and TOPMODEL models, respectively. Results for the Sobol method deviated considerably from the other methods by 22000 and 28000 for the TOPMODEL and HBV models, respectively. In Entropy method need about 6000 samples for the same purpose in both hydrological models. The ranking of parameters sensitivity indices in TOPMODEL for the first two most sensitive parameters for the three methods are similar. In general, the ranks of sensitive parameters are the same for all methods. Meanwhile for Entropy method, M and Srmax as the third and fourth ranking are vice versa than other two methods. In HBV model, Sobol and Morris screen methods provide similar results for those model parameters having the highest influence. For the parameter P, the sensitivity obtained from Entropy method was 3rd rank but in two other methods the parameter ranking varies from 3rd to sixth. In Entropy parameter FC becomes the most important parameter but in Morris screen and Sobol methods, the model parameter BETA selected as the parameter with the highest importance.
There is no single best strategy for all problems. Therefore in general use of two or more methods, preferably with dissimilar theoretical foundations, may be needed to increase confidence in the ranking of the key inputs.This study conducted a comprehensive evaluation of the effectiveness and efficiency of three SA methods by using the HBV and TOPMODEL models as test problem. The strengths and limitations of qualitative and quantitative SA methods are explored.For the Sobol method, a comparatively large number of simulations (>20 000) were required to sufficiently cover the parameter space. Hence, performing Sobol method for complex models is often becoming problematic. The Morris method, instead, is computationally cheap and needed only