The karst NDVI correlation with climate and its BAS-BP prediction based on multiple factors

•The responses of the NDVI to climatic factors were spatiotemporal heterogeneous.•Karst NDVI in southwest China was predicted based on multiple factors.•The model performance regarding NDVI at the spatial scales was relatively good.•The 1 km resolution NDVI data were suitable for predicting karst vegetation. Karst vegetation (KV) is one of the most important indicators for maintaining the surface energy balance in southwestern China. The spatial pattern of KV is mainly affected by climate, human activities, and environmental factors. The relationships between the KV and these factors are complex and nonlinear. Most previous studies on the nonlinear relationship characteristics and regional regularity were not comprehensive. In this study, the correlation and the time-lagged response of KV to climatic factors were investigated using Pearson correlation analysis, and a nonlinear model of the relationships between the karst normalized difference vegetation index (NDVI) and multiple factors was built based on a back propagation neural network optimized using the beetle antennae search algorithm (BAS-BP), and then, the karst NDVI was predicted. The results showed that (1) in most karst regions, the seasonal NDVI was mainly influenced by temperature, but the autumn NDVI was mainly affected by precipitation. The correlation between the interannual variation in the NDVI and the interannual variation in the precipitation was higher than the correlation between the interannual variation in the NDVI and the interannual variation in temperature. The NDVI and the other climatic factors were not strongly correlated. The NDVI responded to the climatic factors with different time-lagged intervals in different spatiotemporal scales. (2) At multiple spatial scales, the mean correlation coefficient (R) and means squared error (MSE) values of the vegetation prediction in the different geomorphic areas were 0.6565 and 0.0072, respectively. The maximum R was up to 0.9059. In different lithology areas, the mean values of R and MSE were 0.6898 and 0.0072, respectively. The maximum R value was 0.9142. (3) The prediction model of the interannual variation in the NDVI was trained, and it was then tested for the validation period. The R values ranged from 0.5299 to 0.7744, with an average of 0.6606. In contrast to the prediction results on different spatial scales, the model’s performance regarding the interannual variation in the NDVI was relatively poor. (4) The mean R values were