Spatial Correlation in Weather Forecast Accuracy: A Functional Time Series Approach

TL;DR

This paper introduces a functional time series method to analyze and improve spatial correlation modeling in weather forecast errors across U.S. cities, especially for longer forecast horizons, by capturing regional effects and temporal dependencies.

Contribution

It develops a novel functional approach that models spatial and temporal dependencies in forecast errors, improving bias correction and uncertainty quantification in weather forecasts.

Findings

Effective modeling of spatial correlation for 6-day forecasts.

Captures regional variance differences, e.g., inland vs. coastal.

Enhances forecast accuracy and reduces error variance.

Abstract

A functional time series approach is proposed for investigating spatial correlation in daily maximum temperature forecast errors for 111 cities spread across the U.S. The modelling of spatial correlation is most fruitful for longer forecast horizons, and becomes less relevant as the forecast horizon shrinks towards zero. For 6-day-ahead forecasts, the functional approach uncovers interpretable regional spatial effects, and captures the higher variance observed in inland cities versus coastal cities, as well as the higher variance observed in mountain and midwest states. The functional approach also naturally handles missing data through modelling a continuum, and can be implemented efficiently by exploiting the sparsity induced by a B-spline basis. The temporal dependence in the data is modeled through temporal dependence in functional basis coefficients. Independent first order autoregressions with generalized autoregressive conditional heteroskedasticity [AR(1)+GARCH(1,1)] and Student-t innovations work well to capture the persistence of basis coefficients over time and the seasonal heteroskedasticity reflecting higher variance in winter. Through exploiting autocorrelation in the basis coefficients, the functional time series approach also yields a method for improving weather forecasts and uncertainty quantification. The resulting method corrects for bias in the weather forecasts, while reducing the error variance.