Long-Range Forecasting as a Past Value Problem: Untangling Correlations and Causality With Scaling

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 Nino events and indices. Plain Language Summary For forecasts less than about 10 days, Numerical Weather Prediction (NWP) and General Circulation Models (GCMs) have been highly successful, yet for longer ranges, their skill is disappointing. This has motivated the development of alternatives that are based on either the strong spatial correlations-teleconnection patterns such El Nino events-or on the long memories whereby the atmospheric state at any moment is strongly influenced by its own past. In particular, a model only using the long memory already rivals GCM monthly and seasonal temperature forecasts: The Stochastic Seasonal to Interannual Prediction System (StocSIPS). In this paper, we answer the question of whether StocSIPS skill can be further improved by using teleconnections. We do this by developing the space-time m-StocSIPS model that is optimally forecast by StocSIPS. In m-StocSIPS, spatial co-predictors do not improve the skill: There is no causal relation between different locations useful for long-range predictions. Although m-StocSIPS has strong spatial correlations and reproduces teleconnection patterns including El Nino events, they cannot be used to improve the long-memory StocSIPS forecasts. The teleconnections were already used to build the history at every location, which is enough to produce the optimal forecast. Key Points Granger causality shows that spatial correlations in temperature cannot be used to improve on memory-based predictions of infinitely long series Scaling-based long-range stochastic forecasting is a past value problem not an initial value problem Real-world statistics and teleconnection patterns can be reproduced with stochastic simulations with a total lack of causal relationships

Automated summary

Granger causality analysis demonstrates that spatial correlations in temperature are not useful for improving predictions based on long memory, indicating that long-term stochastic temperature forecasting is a past value problem. The m-StocSIPS model, despite reproducing teleconnection patterns and El Nino events, does not have causal relationships between different locations useful for long-range predictions. Real-world statistics and teleconnection patterns can be accurately represented through stochastic simulations without causal relationships.