Rainfall is a key driver of terrestrial vegetation. Clarifying the response mechanism of vegetation to rainfall can advance the understanding of expected changes in ecosystems under projected rainfall scenarios. Besides the rainfall amount over a period of time, the frequency, duration and intensity are of importance in driving ecosystem processes. The pulsating nature of rainfall forcing and of vegetation response applies particularly to arid and semi – arid regions and led to conceptualize the “pulse-reserve” paradigm, which we used to explain the approach we propose in this study. We introduce the Transfer Function Analysis (TFA) method in the frequency domain to capture the response of vegetation to rainfall at multiple temporal scales. The TFA method determines coherence, gain, and phase to characterize the existence, strength, and time-lag, respectively, of the vegetation response to rainfall at different temporal scales. Specifically, the coherence measures the existence of the response and only with a significant response are the gain and phase values significant and valuable for further analysis. The gain measures the strength of the relationship between fluctuations in vegetation growth and fluctuations in rainfall, while the phase value (i.e. the time-lag) measures how fluctuations in vegetation growth lag (or lead) fluctuations in rainfall. The TFA method was applied to the 34-years (1982–2015) NDVI3g and CHIRPS precipitation dataset in the Sahel-Sudano-Guinean region (20°W ~ 60°E, 0–25°E). The Sahelian zone was characterized by a significant vegetation response to rainfall across all inter- and intra- annual time-scales, while the Sudano-Guinean zone was dominated by significant response at annual or 6-month scales. The negative phase lag indicated that rainfall variation normally led NDVI change for most areas and across timescales. However, a positive phase observed in part of the tropical rainforest area indicated that NDVI changes led rainfall variations, which may be caused by the strong vegetation-rainfall feedback through recycling of precipitation by evapotranspiration. In summary, these results suggested that the TFA method is a powerful tool to quantify the vegetation-rainfall response regime across a range of timescales, as conceptualized by the “pulse-reserve” paradigm. Unraveling the response of fluctuations in vegetation growth to separate components of the forcing by precipitation might improve our understanding of environmental change in the past decades in the Sahel - Sudan - Guinean region.

The time lag between anomalies in precipitation and vegetation activity plays a critical role in early drought detection as agricultural droughts are caused by precipitation shortages. The aim of this study is to explore a new approach to estimate the time lag between a forcing (precipitation) and a response (NDVI) signal in the frequency domain by applying cross-spectral analysis. We prepared anomaly time series of image data on TRMM3B42 precipitation (accumulated over antecedent durations of 10, 60, and 150 days) and NDVI, reconstructed and interpolated MOD13A2 and MYD13A2 to daily interval using a Fourier series method to model time series affected by gaps and outliers (iHANTS) for a dry and a wet year in a drought-prone area in the northeast region of China. Then, the cross-spectral analysis was applied pixel-wise and only the phase lag of the annual component of the forcing and response signal was extracted. The 10-day antecedent precipitation was retained as the best representation of forcing. The estimated phase lag was interpreted using maps of land cover and of available soil water-holding capacity and applied to investigate the difference in phenology responses between a wet and dry year. In both the wet and dry year, we measured consistent phase lags across land cover types. In the wet year with above-average precipitation, the phase lag was rather similar for all land cover types, i.e., 7.6 days for closed to open grassland and 14.5 days for open needle-leaved deciduous or evergreen forest. In the dry year, the phase lag increased by 7.0 days on average, but with specific response signals for the different land cover types. Interpreting the phase lag against the soil water-holding capacity, we observed a slightly higher phase lag in the dry year for soils with a higher water-holding capacity. The accuracy of the estimated phase lag was assessed through Monte Carlo simulations and presented reliable estimates for the annual component.