Exploring relationships between phenological and weather data using smoothing.

Stepwise regression is often used to draw associations between phenological records and weather data. For example, the dates that a species first flowers each year might be regressed on monthly mean temperatures for a period preceding flowering. The months that 'best' explain the variation in first flowering dates would be selected by stepwise regression. However, daily records of weather are usually available. Stepwise regression on daily temperatures would not be appropriate because of high correlations between neighbouring days. Smoothing methods provide a way of avoiding such difficulties. Regression coefficients can be smoothed by penalising differences in slopes between neighbouring regressors. The resultant curve of regression gradients is intuitively attractive. Various possible approaches to smoothing regression coefficients are discussed. We illustrate the use of one method, P-spline signal regression, which is particularly appropriate when there are many more regressors than observations. Smoothing can be applied to more than one set of regressors. This results in a multi-dimensional surface of regression coefficients. We use this approach to investigate how the time of year that a plant species tends to flower affects its relationship with temperature records. Using this method, we found that later species tend to be affected by later temperatures.