Multiobjective sensitivity analysis and optimization of a distributed hydrologic model MOBIDIC

Calibration of distributed hydrologic models usually involves how to deal with the large number of distributed parameters and optimization problems with multiple but often conflicting objectives which arise in a natural fashion. This study presents a multiobjective sensitivity and optimization approach to handle these problems for a distributed hydrologic model MOBIDIC, which combines two sensitivity analysis techniques (Morris method and State Dependent Parameter method) with a multiobjective optimization (MOO) approach ϵ-NSGAII. This approach was implemented to calibrate MOBIDIC with its application to the Davidson watershed, North Carolina with three objective functions, i.e., standardized root mean square error of logarithmic transformed discharge, water balance index, and mean absolute error of logarithmic transformed flow duration curve, and its results were compared with those with a single objective optimization (SOO) with the traditional Nelder–Mead Simplex algorithm used in MOBIDIC by taking the objective function as the Euclidean norm of these three objectives. Results show: (1) the two sensitivity analysis techniques are effective and efficient to determine the sensitive processes and insensitive parameters: surface runoff and evaporation are very sensitive processes to all three objective functions, while groundwater recession and soil hydraulic conductivity are not sensitive and were excluded in the optimization; (2) both MOO and SOO lead to acceptable simulations, e.g., for MOO, average Nash–Sutcliffe is 0.75 in the calibration period and 0.70 in the validation period; (3) evaporation and surface runoff shows similar importance to watershed water balance while the contribution of baseflow can be ignored; (4) compared to SOO which was dependent of initial starting location, MOO provides more insight on parameter sensitivity and conflicting characteristics of these objective functions. Multiobjective sensitivity analysis and optimization provides an alternative way for future MOBIDIC modelling.

A modified variance-based importance measure and its solution by state dependent parameter

To overcome the disadvantage of traditional variance-based importance measures, i.e. the effects of different realizations of input variables on output response may mutually counteract each other, a modified variance-based importance measure is presented for importance analysis of the input variables. The proposed measure analyses the importance of the input variables comprehensively in terms of the expectation and variance of the output response. Compared with the traditional variance-based importance analysis method, the modified importance measure indices not only reflect the old one, but also provide a very useful supplement for it. Furthermore, combined with the advantages of the state dependent parameter model, a solution to the proposed measure indices is provided. Several examples are introduced to show that the modified importance measure is more comprehensive and reasonable, and the solution based on the state dependent parameter method can improve computational efficiency considerably with acceptable precision.