Norway spruce (Picea abies): Bayesian analysis of the relationship between temperature and bud burst

Climate change has already affected the phenology of several species. To be able to assess the impacts of climate change under various climate scenarios, we need superior models of the phenology of different species. Linear regression methods alone are of limited value for the analyses of natural indicators or phenological data because most time series of naturally occurring events in ecosystems do change in a nonlinear way. In this paper, we applied a Bayesian probability approach to investigate time series of the phenological phase of bud burst in Norway spruce (Picea abies (L.) Karst.) and mean monthly/weekly temperatures of corresponding climate stations in Germany. In these temperature and Norway spruce bud burst time series we detected years with the highest probability for discontinuities. We analysed rates of change and the relationship between temperature changes and bud burst of Norway spruce in the 51-year period 1953-2003. We used a Bayesian method for a coherence analysis between phenological onset dates and an effective temperature generated as a weighted average of monthly and weekly means from January to May. Weight coefficients were obtained from an optimization of the coherence factor by simulated annealing. In all investigated cases we found coherence factors that suggested a relationship between temperature and phenological time series. Norway spruce bud burst and mean temperature times series of April and May exhibited abrupt changes, particularly at the beginning of the 1980s. April and May temperature time series revealed an increased warming until 2003, and bud burst events advanced. Norway spruce bud burst, in particular, exhibited responses to temperatures of the previous (April) and current month (May). We suggest that besides commonly used sums of daily mean temperatures, forcing temperatures in phenology models should also include solutions where weighted effective temperatures in a sensitive time span are considered.