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Vector quantities, e.g., vector winds, play an extremelyimportant role in climate systems. The energy and water exchanges betweendifferent regions are strongly dominated by wind, which in turn shapes theregional climate. Thus, how well climate models can simulate vector fieldsdirectly affects model performance in reproducing the nature of a regionalclimate. This paper devises a new diagram, termed the vector fieldevaluation (VFE) diagram, which is a generalized Taylor diagram and able toprovide a concise evaluation of model performance in simulating vectorfields. The diagram can measure how well two vector fields match each otherin terms of three statistical variables, i.e., the vector similaritycoefficient, root mean square length (RMSL), and root mean square vectordifference (RMSVD). Similar to the Taylor diagram, the VFE diagram isespecially useful for evaluating climate models. The pattern similarity oftwo vector fields is measured by a vector similarity coefficient (VSC) thatis defined by the arithmetic mean of the inner product of normalized vectorpairs. Examples are provided, showing that VSC can identify how close onevector field resembles another. Note that VSC can only describe the patternsimilarity, and it does not reflect the systematic difference in the meanvector length between two vector fields. To measure the vector length, RMSLis included in the diagram. The third variable, RMSVD, is used to identifythe magnitude of the overall difference between two vector fields. Examplesshow that the VFE diagram can clearly illustrate the extent to which theoverall RMSVD is attributed to the systematic difference in RMSL and howmuch is due to the poor pattern similarity

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