Spatio-temporal modelling of forest monitoring data: modelling German tree defoliation data collected between 1989 and 2015 for trend estimation and survey grid examination using GAMMs

Spatio-temporal modelling of tree defoliation data from the German forest condition survey is statistically challenging, particularly due to irregular grids. In the present study, generalized additive mixed models (GAMMs) were used to estimate the spatio-temporal trends in defoliation of the main tree species spruce, pine, beech and oak from 1989 to 2015 and to examine the suitability of different monitoring grid resolutions (standard 16 × 16 km grid and denser grids). Although data has been collected since 1989, this is the first time spatio- temporal modelling for all of Germany has been carried out. GAMMs proved to be a statistically sound and highly flexible choice for spatio-temporal modelling of defoliation data. In addition to the space-time component, stand age showed a significant effect on defoliation. The mean age and the species-specific relation between defoliation and age determined the general level of defoliation. However, further investigations are necessary in order to understand what is behind the age effect. Adjustment for stand age was carried out for identifying hotspots of high defoliation that are not merely the result of the age effect. Fluctuations in defoliation were most likely related to weather conditions. South-western Germany has emerged as the region with the highest defoliation since the drought year 2003. This region was characterized by the strongest water deficits in 2003 compared to the long-term reference period (1961-1990). Furthermore, the spatio-temporal model was used to carry out a simulation study to compare different survey grid resolutions in terms of prediction error. The model-based approach for grid analysis turned out to be appropriate for the given data and sample design. The grid analysis indicated that an 8 × 8 km grid instead of the standard 16 × 16 km grid is necessary for spatio-temporal trend estimation and for detecting hotspots in defoliation in space and time, especially regarding oaks.