Spatially coherent structure of forecast errors – A complex network approach

The quality of weather forecasts has improved considerably in recent decades as models can better represent the complexity of the Earth’s climate system, benefitting from assimilation of comprehensive Earth observation data and increased computational resources. Analysis of errors is an integral part of numerical weather prediction to produce better quality forecasts. The Earth’s climate, being a highly complex interacting system, often gives rise to significant statistical relationships between the states of the climate at distant geographical locations. Likewise, correlated errors in forecasting the state of the system can arise from predictable relationships between forecast errors at various regions resulting from an underlying systematic or random process. Estimation of error correlations is very important for producing quality forecasts and is a key issue for data assimilation. 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. In this work, we propose an approach based on complex network theory to quantitatively study the spatiotemporal coherent structures of medium-range forecast errors of different climate variables. We demonstrate that the spatial variation of the network measures computed from the error correlation matrix can provide insights into the origin of forecast errors in a climate variable by identifying spatially coherent patterns of regions having common sources of error. Notably, the network topology of forecast errors of a climate variable is significantly different from those of random networks corresponding to a deterministic phenomenon which the model fails to simulate adequately. This is especially important to reveal the spatial heterogeneity of the errors – for example, the forecast errors of outgoing long-wave radiation in tropical regions can be correlated across very long distances, indicating an underlying climate mechanism as the source of the error. Additionally, we highlight that these structures of forecast errors may not always be directly derivable from the spatiotemporal co-variability pattern of the corresponding climate variable, contrary to the expectations that the patterns should resemble each other. We further employ other common statistical tools such as, empirical orthogonal functions, to support these findings. Our results underline the potential of complex networks as a very promising diagnostic tool to gain better understanding of the spatial variation, origin, and propagation of forecast errors.