Partition of phase and magnitude contributions in residual variance analysis

Abstract

This paper presents a method that can decompose the total residual variance between the observations and numerical model predictions into two components: one due to the pure magnitude differences and the other due to the spatial and temporal mismatches, or the so‐called “phase errors.” Quantitative separation of these two components makes it possible to explicitly estimate their individual contributions to residual variabilities in numerical model predictions. The influence of random fluctuations in the data on residual variance between the observed and predicted fields has been simulated and discussed. It is found that random fluctuations on the average increase the residual variance through essentially the artificial phase errors which they create. The major impact of random fluctuations, however, occurs when the true observed and predicted fields are nearly in phase. Assuming the signal‐to‐noise ratio to be greater than 4.5, the simulation results suggest that for the proportion Q of the residual sum of squares attributable to spatial and temporal mismatches to exceed 0.71, it would strongly suggest that a real (spatial and/or temporal) phase error may exist. In numerical modeling, large Q coupled with large residual variance but small mean residual is often a reflection of compensating errors arising from physical discrepancies such as inaccurate simulation of dynamic transport or improper source allocations. Thus this method provides an additional tool to diagnose the underlying problems of model predictions.