A general probabilistic framework for uncertainty and sensitivity analysis of deterministic models

Uncertainty and sensitivity analysis are valuable tools for the assessment of model applications and several methods were developed in the last decades. However, the applicability of these methods is limited to scalar parameters and in many cases the analysis is still made by One-A-Time methods. These severely constrain the ability of a general assessment of the model in practical applications. In this study a general probabilistic framework for uncertainty and sensitivity analysis of deterministic models is presented. The approach is able to consider all the sources of uncertainty i.e., input, distributed parameters and model structure. In this context a global uncertainty analysis is used as a tool to evaluate the performance of the model. A global sensitivity analysis based on Sobol's method is then used as complementary tool to find the most important sources of uncertainty. The framework is used in a loop to optimize the further activities and improve the performance of the model in a goal-oriented approach. The effectiveness of the framework is demonstrated with an example with SWAP model, a 1D physicalbased hydrological model. The procedure is applied in a cropped field in Northern Germany for the year 2011. The simulation results are compared with the soil moisture detected in the root zone and considering the variance of evapotranspiration and bottom fluxes below the root zone simulated by the model. The results show that the errors in the estimation of evapotranspiration and bottom fluxes are negatively correlated. In this way the evaluation of the soil moisture alone can not be seen as a good assessment of the model performance. Finally, the sources of uncertainty are different for each process and improvement of the performance of the model strictly depends on the output considered.