 2005 Royal Statistical Society 0035–9254/05/54555 Appl. Statist. (2005) 54, Part 3, pp. 555–573 Modelling association between two irregularly observed spatiotemporal processes by using maximum covariance analysis A. Salim, Australian National University, Canberra, Australia Y. Pawitan Karolinska Institutet, Stockholm, Sweden and K. Bond University College Cork, Republic of Ireland [Received March 2003. Revised June 2004] Summary. Climatic phenomena such as the El-Ni ˜ no–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 associ- ated 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 like- lihood 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-Ni ˜ no–southern oscillation and the north Atlantic oscillation phenomena. Keywords: Canonical covariance; Climate changes; Incomplete data; Mixed models; Partial least squares; Smoothing 1. Introduction Climate studies have shown that many climatic phenomena are results of interaction between two or more meteorological variables. For example, the relationship between sea surface tem- perature anomalies (SSTAs) in the equatorial Pacific and the southern oscillation (SO) has been well studied (Barnston, 1994). The SO is a seesaw pattern of sea-level pressure (SLP) between the eastern and western Pacific. The standard SO index (SOI) measures the SLP anomalies difference between Tahiti and Darwin, Australia. Sometimes, the SLP tends to be lower in the Address for correspondence: A. Salim, National Centre for Epidemiology and Population Health, Australian National University, Canberra, ACT 0200, Australia. E-mail: agus.salim@anu.edu.au