Analysis of spatially coherent forecast error structures

Understanding error properties is an essential part in numerical weather prediction. Predictable relationship between errors of different regions due to some underlying systematic or random process can give rise to correlated errors. Estimation of error correlation is crucial for improvement of forecasts. However, the size of the corresponding correlation matrix is larger than what is possible to represent on geographical maps in order to diagnose its full spatial variation. Here, we propose a complex network-based approach to analyse forecast error correlations that enables us to estimate the spatially varying component of the error. A quantitative study of the spatio-temporal coherent structures of medium-range forecast errors of different climate variables using network measures can reveal common sources of errors. Such information is crucial, especially in cases such as the outgoing long-wave radiation, in which errors are correlated across very long distances, indicating an underlying climate mechanism as the source of the error. We show that the spatial patterns of forecast error co-variability may not be the same as that of the corresponding climate variable itself, thereby implying that the mechanisms behind the correlated errors may be different from the climate processes responsible for the spatio-temporal interactions of the climate variable. Our results highlight the importance of diagnosing the full spatial variation of error correlations to understand the origin and propagation of forecast errors, and demonstrate complex networks to be a promising diagnostic tool in this regard.