Modelling association between two irregularly observed spatiotemporal processes by using maximum covariance analysis

Summary.  Climatic phenomena such as the El-Niño–southern oscillation and the north Atlantic oscillation are results of complex interactions between atmospheric and oceanic processes. Understanding the interactions has enabled scientists to give early warning of the forthcoming phenomena, thereby reducing damage caused by them. Statistical methods have played an important role in revealing effects of these phenomena on different regions of the world. One such method is maximum covariance analysis (MCA). Two apparent weaknesses are associated with MCA. Firstly, it tends to produce estimates with a low signal-to-noise ratio, especially when the sample size is small. Secondly, there has been no objective way of incorporating incomplete records, which are frequently encountered in climatology and oceanographic data-bases. We introduce an MCA which incorporates a smoothing procedure on the estimates. The introduction of the smoothing procedure is shown to improve the signal-to-noise ratio on the estimates. The estimation of smoothing parameters is carried out by using a penalized likelihood approach, which makes the inclusion of incomplete records quite straightforward. The methodology is applied to investigate the association between Irish winter precipitation and sea surface temperature anomalies around the world. The results show relationships between Irish precipitation anomalies and the El-Niño–southern oscillation and the north Atlantic oscillation phenomena.