An objective dynamic multivariable weighting method for reducing uncertainty in WRF parameterization scheme selection

Abstract. The selection of optimal physical parameterization schemes is a major source of uncertainty in WRF model simulations. A comprehensive evaluation of model performance requires simultaneous consideration of multiple output variables. However, existing multivariate approaches often rely on subjective or overly simplistic equal-weighting strategies and lack an objective mechanism to quantify variable importance. Such limitations can obscure significant biases in poorly simulated variables. To overcome this issue, this study proposes an objective dynamic weighting method for multivariate evaluation. The method employs a two-layer weighting framework based on two statistical metrics: the mean relative error, which measures the simulation accuracy of a variable, and the coefficient of variation of the absolute error, which reflects the sensitivity of a variable to the physical process under evaluation. The approach is applied and validated in assessing WRF parameterization schemes across two climatically distinct environments: the arid Northwest and the humid coastal Southeast of China. The results show that the method assigns greater weights to poorly simulated variables, such as precipitation and wind speed, thereby enabling the identification of more physically plausible and robust parameterization scheme combinations. Compared with the equal-weighting method, the scheme combinations obtained using this approach produce a lower Multivariate Integrated Evaluation Index (MIEI), a higher correlation coefficient (R), a lower Root Mean Square Error (RMSE), and exhibit superior performance in independent extreme-year validations. By dynamically incorporating both simulation performance and sensitivity specific to each variable, the method offers a more rigorous and objective framework for model evaluation and uncertainty reduction.