DISO: A rethink of Taylor diagram

Climate models use quantitative methods to simulate the interactions of the important drivers of climate system, to reveal the corresponding physical mechanisms, and to project the future climate dynamics among atmosphere, oceans, land surface and ice, such as regional climate models and global climate models. A comprehensive assessment of these climate models is important to identify their different overall performances, such as the accuracy of the simulated temperature and precipitation against the observed field. However, until now, the comprehensive performances of these models have not been quantified by a comprehensive index except the existed single statistical index, such as correlation coefficient (r), absolute error (AE), and the root-mean-square error (RMSE). To address this issue, therefore, in this study, a new comprehensive index Distance between Indices of Simulation and Observation (DISO) is developed to describe the overall performances of different models against the observed field quantitatively. This new index DISO is a merge of different statistical metrics including r, AE, and RMSE according to the distance between the simulated model and observed field in a three-dimension space coordinate system. From the relationship between AE, RMSE, and RMS difference (RMSD) (i.e., standard deviation [SD] of bias time series), the new index also has the information of RMSD which is the statistical index in Taylor diagram. An example is applied objectively to display the applications of DISO and Taylor diagram in identifying the overall performances of different simulated models. Overall, with the strong physical characteristic of the distance in three dimensional space and the strict mathematical proof, the new comprehensive index DISO can convey the performances among different models. It can be applied in the comparison between different model data and in tracking changes in their performances.