The advent of abundant Earth observation data enables the development of novel predictive methods for forecasting climate impacts on the state and health of terrestrial ecosystems. Here, we target the spatial and temporal variations of land surface reflectance and vegetation greenness, measuring the density of green vegetation and active foliage area, conditioned on current and past climate and the local topography. We train two alternative recurrent deep learning models that rely on convolutional layers for forecasting the spatially resolved deviation of surface reflectance across a heterogeneous landscape from a specified initial state (Baseline Framework). We demonstrate efficiency of the Baseline Framework with respect to training convergence speed. Using data from diverse ecosystems and land cover types across Europe and following a standardized model evaluation framework (EarthNet2021 Challenge), results indicate increased performance in predicting surface greenness during drought events of the models presented here, compared to currently published benchmarks. Our results demonstrate how deep learning methods enable early-warning of vegetation responses to the impacts of climatic extreme events, such as the drought-related loss of green foliage.