Long‐Range Forecasting as a Past Value Problem: Untangling Correlations and Causality With Scaling
Lenin Del Rio Amador, S. Lovejoy
Abstract
Abstract Conventional long‐range weather prediction is an initial value problem that uses the current state of the atmosphere to produce ensemble forecasts. Purely stochastic predictions for long‐memory processes are “past value” problems that use historical data to provide conditional forecasts. Teleconnection patterns, defined from cross‐correlations, are important for identifying possible dynamical interactions, but they do not necessarily imply causation. Using the precise notion of Granger causality, we show that for long‐range stochastic temperature forecasts, the cross‐correlations are only relevant at the level of the innovations–not temperatures. This justifies the Stochastic Seasonal to Interannual Prediction System (StocSIPS) that is based on a (long memory) fractional Gaussian noise model. Extended here to the multivariate case (m‐StocSIPS) produces realistic space‐time temperature simulations. Although it has no Granger causality, emergent properties include realistic teleconnection networks and El Niño events and indices.