Vector Field Evaluation Research Articles

An improved multivariable integrated evaluation method and tool (MVIETool) v1.0 for multimodel intercomparison

Abstract. An evaluation of a model's overall performance in simulating multiple fields is fundamental to model intercomparison and development. A multivariable integrated evaluation (MVIE) method was proposed previously based on a vector field evaluation (VFE) diagram, which can provide quantitative and comprehensive evaluation on multiple fields. In this study, we make further improvements to this method from the following aspects. (1) We take area weighting into account in the definition of statistics in the VFE diagram and MVIE method, which is particularly important for a global evaluation. (2) We consider the combination of multiple scalar fields and vector fields against multiple scalar fields alone in the previous MVIE method. (3) A multivariable integrated skill score (MISS) is proposed as a flexible index to measure a model's ability to simulate multiple fields. Compared with the multivariable integrated evaluation index (MIEI) proposed in the previous study, MISS is a normalized index that can adjust the relative importance of different aspects of model performance. (4) A simple-to-use and straightforward tool, the Multivariable Integrated Evaluation Tool (MVIETool version 1.0), is developed to facilitate an intercomparison of the performance of various models. Users can use the tool coded either with the open-source NCAR Command Language (NCL) or Python3 to calculate the MVIE statistics and plotting. With the support of this tool, one can easily evaluate model performance in terms of each individual variable and/or multiple variables.

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.

A diagram for evaluating multiple aspects of model performance in simulating vector fields

Abstract. Vector quantities, e.g., vector winds, play an extremely important role in climate systems. The energy and water exchanges between different regions are strongly dominated by wind, which in turn shapes the regional climate. Thus, how well climate models can simulate vector fields directly affects model performance in reproducing the nature of a regional climate. This paper devises a new diagram, termed the vector field evaluation (VFE) diagram, which is a generalized Taylor diagram and able to provide a concise evaluation of model performance in simulating vector fields. The diagram can measure how well two vector fields match each other in terms of three statistical variables, i.e., the vector similarity coefficient, root mean square length (RMSL), and root mean square vector difference (RMSVD). Similar to the Taylor diagram, the VFE diagram is especially useful for evaluating climate models. The pattern similarity of two vector fields is measured by a vector similarity coefficient (VSC) that is defined by the arithmetic mean of the inner product of normalized vector pairs. Examples are provided, showing that VSC can identify how close one vector field resembles another. Note that VSC can only describe the pattern similarity, and it does not reflect the systematic difference in the mean vector length between two vector fields. To measure the vector length, RMSL is included in the diagram. The third variable, RMSVD, is used to identify the magnitude of the overall difference between two vector fields. Examples show that the VFE diagram can clearly illustrate the extent to which the overall RMSVD is attributed to the systematic difference in RMSL and how much is due to the poor pattern similarity.