Dynamical systems-inspired machine learning methods for drought prediction

Drought is a naturally occurring phenomenon that affects millions of people and results in billions of dollars in damages each year, with impacts expected to worsen due to climate change. At the same time, definitions of drought are nebulous, and extant quantitative drought indicators suffer from short prediction horizons. One such indicator is the Normalized Vegetation Difference Index (NDVI), which measures photosynthetic activity, making it a strong proxy for vegetation density. Recent studies have identified chaotic attractors in satellite-derived NDVI time-series, suggesting a dynamical systems framework may be helpful for time-series prediction of NDVI. In this study, we compare the performance of a mechanistic model and two physics-informed machine learning methods (Sparse Identification of Nonlinear Dynamics [SINDy] and reservoir computing) on the prediction of NDVI time-series data in drought-prone regions of Kenya. We find that SINDy, a sparse polynomial modelling architecture, narrowly outperforms the other two methods with the use of precipitation data, while also retaining some of the interpretability of the mechanistic model. We also find that none of the methods perform as well in the regions in which the chaotic NDVI attractors were originally identified. We conclude by proposing more sophisticated extensions to the methods presented here, both with and without the availability of precipitation data, that draw on the existing dynamical systems and machine learning literature to enable better quantitative predictions of key drought indicators.