Keywords: Spatial basis functions, Hierarchical, Bayesian, Climate, Empirical orthogonal functions 

## 1 Introduction 

While most spatial data can be modeled with the assumption that distant points are uncor- related, some problems require dependence at both far and short distances. Spatial climate data is an example of the latter, as it is influenced by local (i.e., short distance) factors, as well as by remote (i.e., far distance) phenomena called teleconnections. Teleconnections refer to changes in patterns of large-scale atmospheric circulation that can drive changes in temperature and precipitation in distant regions (e.g., Tsonis & Swanson, 2008; Ward et al., 2014). Most teleconnection modeling approaches in the statistical literature do not explicitly estimate dependence within remote phenomena. The statistical literature includes spatially varying coefficient models, analogs, and covariance matrix estimation (Calder, Craigmile, & Mosley-Thompson, 2008; Choi, Li, Zhang, & Li, 2015; McDermott & Wikle, 2016; Wikle & Anderson, 2003). Explicitly modeling dependence in remote phenomena can add phys- ically sensible structure that improves prediction accuracy and addresses some modeling challenges. We propose a geostatistical model that addresses this unmet modeling need for teleconnection. 

Teleconnections can be forced by changes in sea surface temperature (SST), and there have been many observational and modeling studies studying the link between SSTs, circu- lation patterns, and impacts on global and regional climate. Several seminal studies connect U.S. precipitation with SST anomalies in the tropical Pacific due to the El Ni˜ no–Southern Oscillation teleconnection (ENSO) (Montroy, 1997; Montroy, Richman, & Lamb, 1998), as well as with SST anomalies in the Pacific (e.g., Dong & Dai, 2015). The ENSO telecon- nection has been critical in seasonal climate forecasting (Goddard et al., 2001), and decadal variability of sea surface temperature anomalies have been identified as a source of potential 

