Most spatial models assume that distant locations do not influence each other. But climate breaks this rule: tropical Pacific sea surface temperatures affect precipitation in the Rocky Mountains months later. Such long-range links are called teleconnections, and they are usually described by preselected indices like El Niño. The problem is that the appropriate index depends on the region and may not be known before analysis. This work sits alongside studies that predict El Niño, separate weather noise from climate signal, or improve hurricane forecasts, but here the focus is on directly incorporating remote data into a statistical model.
The authors developed the RESP (remote effects spatial process) model, which extends standard geostatistics. Instead of a single teleconnection index, the model integrates the influence of remote covariates, such as sea surface temperature, across the entire remote region. To handle multicollinearity and computational complexity, the remote influence coefficients are approximated via predictive processes with knots placed across the ocean. The coefficients are then transformed using empirical orthogonal functions (EOFs), which extract the dominant patterns of ocean temperature variability. Parameter estimation is performed in a hierarchical Bayesian framework using Markov chain Monte Carlo methods.
The model was applied to winter precipitation in Colorado from 1981 to 2013. The local covariate was the average air temperature over Colorado, and the remote covariate was the Pacific sea surface temperature. Leave-one-year-out cross-validation showed that RESP yields better probabilistic forecasts than models without remote covariates, models with preselected El Niño indices, and canonical correlation analysis. For example, the ranked probability score for RESP was lower than that for the model with fixed indices in most years. The estimated teleconnection effects align with the known pattern: during El Niño, northern and western Colorado receive less precipitation, while the east receives more.
This work differs from neighboring studies in that it does not require preselecting teleconnection indices; instead, it directly uses the spatial structure of remote data. Neighboring works often predict the indices themselves or apply ready-made patterns, whereas here the model itself identifies significant remote influences. This adds physically meaningful structure to statistical climate models and may improve downscaling, where global climate model forecasts are translated into local precipitation.
The model can be extended to multiple remote regions, such as adding the Atlantic Ocean, or to multivariate remote covariates. Temporal dependence has not yet been considered, but it could be introduced for seasonal or decadal forecasts. It is also promising to adapt the model to non-Gaussian data, such as the number of heavy rainfall events, and to large spatial domains using sparse geostatistical methods.
The method will be useful in climatology for precipitation downscaling, in hydrology for water supply forecasting, and also in ecology and human geography where teleconnections exist.
Apply the model to global climate model outputs to forecast future precipitation. Investigate how teleconnections vary by season and decade.
In spatial statistics, an open question remains how to model dependencies at multiple scales simultaneously. This work shows that one can directly include long-range correlations without disrupting local structure, which relates to the screening effect and uncertainty quantification for entire regions.
The empirical orthogonal function extracted from Pacific sea surface temperatures explains 30% of the total variability and closely mirrors the El Niño pattern: warm water in the central and eastern Pacific, cool water in the west.