Decompositions of Taylor diagram and DISO performance criteria

Taylor diagram has been frequently used to evaluate climate or hydrology models or data. A Taylor diagram summarizes three frequently used metrics including correlation coefficient (CC), standard deviation (STD), and centred root mean square error (RMSEc). Although these three metrics are relevant metrics for some applications, in some cases, additional indicators are needed, which calls for a new method. This study firstly addressed the short comments about the distance between indices of simulation and observation (DISO) described in a previous study. Secondly, the number of statistical metrics of DISO is extended from 3 to more than 3. The statistical metrics of the expanded DISO are more flexible than the Taylor diagram which uses the three fixed metrics. Thirdly, the current work compares the Taylor diagram with the expanded DISO in terms of their theoretical bases, revealing the advantage of DISO in terms of its flexibility in the selection of different types of metrics, and its suitability as an effective single metric to express a model's or dataset's overall quality. The power and flexibility of the expanded DISO are discussed. Taylor diagram is decomposed including its limitations. DISO is decomposed from its definition to application comprehensively. The most important and best advantages of DISO are exibility and extensibility.