Pulses of aboveground net primary productivity (ANPP) in response to discrete precipitation events are an integral feature of ecosystem functioning in arid and semi-arid lands. Yet, the usefulness of nonlinear, ecohydrological pulse response functions to predict regional-scale patterns of annual ANPP at decadal scales remains unclear. Here, we assessed how different pulse response (PR) models compete with simple linear statistical models to capture variability in yearly integrated values of Normalized Difference Vegetation Index (NDVIint), a remotely sensed proxy of annual ANPP. We examined 24-year-long time series of NDVIint calculated from Advanced Very High Resolution Radiometer (AVHRR) NDVI for 350,000 km2 of tropical grasslands in northern Australia. Based on goodness-of-fit statistics, PR models clearly outperformed statistical models when parameters were optimized for each site but all models showed the same error magnitude when all sites were combined in ensemble simulations or when the models were evaluated outside the calibration period. PR models were less biased and their performance did not deteriorate in the driest areas compared to linear models. Increasing the complexity of PR models to provide a better representation of soil water balance and its feedback with plant growth did not improve model performance in ensemble simulations. When error magnitude, bias, and sensitivity to parameter uncertainty were all considered, we concluded that a low-dimensional PR model was the most robust to capture NDVIint variability. This study shows the potential of long time series of AVHRR NDVI to benchmark process-oriented models of interannual variability of NDVIint in water-controlled ecosystems. This opens new avenues to examine at the global scale and over several decades the causal relationships between climate and leaf dynamics in the grassland biome.