A Time–Frequency Analysis on the Impact of Climate Variability on Semi-Natural Mountain Meadows

This paper analyzes the impact of climate dynamics on vegetation growth for a rural mountainous region in northeastern Portugal. As a measure of vegetation growth, we use the normalized difference vegetation index (NDVI), which is based on the ten-day synthesis data set (S10) from Satellite Pour l´Observation de la Terre (SPOT-VEGETATION) imagery from 1998 to 2011. We test whether the dynamic growth pattern of the NDVI has changed due to climate variability, and we test the relationship of NDVI with temperature and available soil water (ASW). In order to do so, we use a time-frequency approach based on Kalman filter regressions in the time domain. The advantage of our approach is that it can be used even in the case where the sample size is relatively small. By estimating the important relationships in the time domain first and transferring them into the frequency domain, we are still able to derive a complete spectrum over all frequencies. In our example, we find a change of the cyclical pattern for the spring season and different changes if we take into account all seasons. In other words, we can distinguish between deterministic changes of the vegetation cycles and stochastic changes that only occur randomly. Deterministic changes imply that the data-generating process has changed (such as climate), whereas stochastic changes imply only temporary changes. We find that individual seasons undergo cyclical changes that are different from other seasons. Moreover, our analysis shows that temperature and ASW are the main drivers of vegetation growth. We can also recognize a shift of the relative importance away from temperature to soil water.