Multivariable integrated evaluation of model performance with the vector field evaluation diagram

Abstract. This paper develops a multivariable integrated evaluation (MVIE) method to measure the overall performance of climate model in simulating multiple fields. The general idea of MVIE is to group various scalar fields into a vector field and compare the constructed vector field against the observed one using the vector field evaluation (VFE) diagram. The VFE diagram was devised based on the cosine relationship between three statistical quantities: root mean square length (RMSL) of a vector field, vector field similarity coefficient, and root mean square vector deviation (RMSVD). The three statistical quantities can reasonably represent the corresponding statistics between two multidimensional vector fields. Therefore, one can summarize the three statistics of multiple scalar fields using the VFE diagram and facilitate the intercomparison of model performance. The VFE diagram can illustrate how much the overall root mean square deviation of various fields is attributable to the differences in the root mean square value and how much is due to the poor pattern similarity. The MVIE method can be flexibly applied to full fields (including both the mean and anomaly) or anomaly fields depending on the application. We also propose a multivariable integrated evaluation index (MIEI) which takes the amplitude and pattern similarity of multiple scalar fields into account. The MIEI is expected to provide a more accurate evaluation of model performance in simulating multiple fields. The MIEI, VFE diagram, and commonly used statistical metrics for individual variables constitute a hierarchical evaluation methodology, which can provide a more comprehensive evaluation of model performance.