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.

Abstract. Vector quantities, e.g. vector winds, play an extremely important role in climate system. Energy and water exchanges between different regions are strongly dominated by wind, which in turn shapes regional climate. Thus, how well climate models can simulate vector fields directly affect model performance in reproducing the nature of regional climate. The paper devises a new diagram, termed vector field evaluation (VFE) diagram, which is very similar to Taylor diagram but to provide a concise evaluation of model performance in simulating vector fields. The diagram can measure how well of two vector fields match each other in terms of three statistical variables, i.e. vector similarity coefficient, root-mean-square (RMS) length (RMSL), and RMS vector difference (RMSVD). As the Taylor diagram, the VFE diagram is especially useful in 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 inner product of normalized vector pairs. Examples are given showing that VSC can well identify how close one vector field resemble another. Note that VSC can only describe the pattern similarity and do 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 overall difference between two vector fields. Examples show that the new diagram can clearly illustrate how much the overall RMSVD is attributed to the systematic difference in RMSL and how much is due to the poor pattern similarity.

Here, we explored in depth the relationship among the deterministic prediction skill, the probabilistic prediction skill and the potential predictability. This was achieved by theoretical analyses and, in particular, by an analysis of long-term ensemble ENSO hindcast over 161 years from 1856 to 2016. First, a nonlinear monotonic relationship between the deterministic prediction skill and the probabilistic prediction skill, derived by theoretical analysis, was examined and validated using the ensemble hindcast. Further, the co-variability between the potential predictability and the deterministic prediction skill was explored in both perfect model assumption and actual model scenario. On these bases, we investigated the relationship between the potential predictability and probabilistic prediction skill from both the practice of ENSO forecast and theoretical perspective. The results of the study indicate that there are nonlinear monotonic relationships among these three kinds of measures. The potential predictability is considered to be a good indicator for the actual prediction skill in terms of both the deterministic measures and the probabilistic framework. The relationships identified here exhibit considerable significant practical sense to conduct predictability researches, which provide an inexpensive and moderate approach for inquiring prediction uncertainties without the requirement of costly ensemble experiments.

Variations in the sea surface temperature (SST) field in both the North Pacific (represented by the Victoria mode [VM]) and the South Pacific (represented by the South Pacific quadrapole [SPQ] mode) are related to the state of the El Niño–Southern Oscillation (ENSO) three seasons later. Here with the aid of observational data and numerical experiments, we demonstrate that both VM and SPQ SST forcing can influence the development of ENSO events through a similar air‐sea coupling mechanism. By comparing ENSO amplitudes induced by the VM and SPQ, as well as the percentages of strong ENSO events followed by the VM and SPQ events, we find that the VM and SPQ make comparable contributions and therefore have similar levels of importance to ENSO. Additional analysis indicates that although VM or SPQ SST forcing alone may serve as a good predictor for ENSO events, it is more effective to consider their combined influence. A prediction model based on both VM and SPQ indices is developed, which is capable of yielding skillful forecasts for ENSO at lead times of three seasons.