Geographically Weighted Convolutional Long Short-Term Memory Neural Networks: A Geospatial Deep Learning Model for Monthly NDVI Prediction

Vegetation is a key component of biodiversity and ecosystem stability. The normalized difference vegetation index (NDVI) is widely used to monitor the vegetation growth status. Timely spatiotemporal prediction of NDVI is of great significance to agriculture and the ecological environment. Traditional deep learning models neglect the local spatial relationships and the effect of spatial autocorrelation in vegetation, failing to capture the neighboring contributions to the forecast target. In this study, a geographically weighted convolutional long short-term memory (GWConvLSTM) model is coupled with the spatial weight and the convolutional long short-term memory (ConvLSTM) model by the Hadamard product is proposed to predict NDVI. In the GWConvLSTM model, a spatiotemporal memory flow with the ConvLSTM unit is designed to calculate the spatial weight of each step, which is iteratively updated with the training of the model. We use the proposed GWConvLSTM model to forecast the monthly NDVI of Huangpi District and the experiment results indicate that the developed GWConvLSTM model outperforms five other baseline models. The predictive coefficient of determination ( $R^{2}$ ) reached up to 0.8427, 0.8209, and 0.8149 for one-, three-, and five-month lead times, respectively. The mean absolute error (MAE) decreased by 14.26%, 10.04%, and 16.75% for GWConvLSTM versus the baseline ConvLSTM model in one-, three-, and five-month NDVI predictions, respectively. Therefore, the developed GWConvLSTM model could be an effective geospatial deep learning model for spatiotemporal NDVI prediction at region scales.