The predictability of New Zealand's climate: the failure of some statistical methods and a new physical approach

Abstract

Some moderately strong contemporary covariations exist between time series of New Zealand climate anomalies, (of sunshine hours, rainfall total, and monthly mean daily maximum, mean, and minimum temperatures) and various indices of atmospheric flow in the Australian-New Zealand region. These indices include the empirical orthogonal functions of Trenberth, based on monthly mean sea level pressures, and new empirical orthogonal function series based on upper air temperatures in a meridional cross-section extending from Nandi, Fiji to Campbell Island. Only very weak lag 1 month relations exist, in general, using these predictor series. Averaged over all the data, the strongest lag 1 month relations are with temperature; both rainfall and sunshine are only very weakly predictable, in a linear sense. This conclusion has been tested using a variety of approaches with differing aggregations of stations in spatial smoothings of the predictand time series (county, response area, eigenfield). In the regressive sense, the eigenfields are shown to be more conservative quantities for rainfall and sunshine, than the regional averaging approach and the reverse is true for temperature. A study of mean values, variability, and correlation structure of the upper air temperatures is presented. Several large scale regimes of highly persistent temperatures are demonstrated. Variations across time and space are considered showing strong gradients. The temperature empirical orthogonal function series perform comparably to the pressure empirical orthogonal function series, as predictors, but demonstrate considerably stronger contemporary relations with surface temperatures. Apart from the upper air time series, a number of new physically motivated time series have been tested. These include sea surface temperatures, Antarctic sea ice extent, land sea heating contrasts, and an Australian Monsoon index. While some demonstrate statistically significant covariations, suggesting real physical relationships, no useful predictive power emerges on lag 1 month scales. Preliminary exploration with simple adaptive filtering techniques is made, and interesting, large differences to the Buys-Ballot method shown to be possible, but on the limited data set studied, no large change in predictability resulted. Based on this and earlier work some possible future directions are considered. On the assumption that the inertial speed relation expresses a mixing length relationship, a simple momentum transport model is shown to give reasonable answers. The Taylor vorticity transfer idea can be similarly developed. Consideration of the basic fluid flow equations of Navier-Stokes, together with the inertial relation, for the eddy flux terms, allows derivation of Rossby type relationships. Preliminary examination of a simple diffusion hypothesis for the zonal velocity is made, and some interesting deductions follow.