## 1 Introduction
Paper [7] introduced the concept of regional synchronization characteristics of small hydropower generation for the modeling of small hydropower output based on the differences in climatic conditions in different regions. Paper [8] analyzed the influencing factors and characteristics of small hydropower generation and found that small hydropower output has a strong correlation with long-term precipitation, but the correlation with temperature and wind is very weak. When there is plenty of rainfall in summer, the output of small hydropower fluctuates greatly, and the change has a lag effect. Paper [9] inputted different combinations of rainfall and power generation for \(t\) days before the forecast day into the echo state network (ESN), obtained the prediction results of each combination, and used the comparison method to obtain the optimal result of the model. Papers [10,11] found that there are similar hydrological and meteorological conditions between large and small hydropower stations in the same basin. Therefore, the power generation of small hydropower stations can be predicted by using the predicted inflow of large- and medium-sized hydropower stations. In summary, the key to improving the forecast accuracy of the power generation capacity of small hydropower stations lies in obtaining more abundant precipitation and historical operating data and adopting appropriate methods to fully extract the potential characteristic information. Considering the scattered distribution of small hydropowerstations, the wide area of rain collection, and the extremely uneven spatial distribution of precipitation, it is necessary to consider the difference in the temporal and spatial distribution of precipitation in forecasting the short-term power generation of small hydropower stations. However, no scholars have conducted relevant research on the abovementioned problems. Therefore, with the help of the precipitation distribution field obtained by meteorological satellite remote sensing observations and the partial mutual information method, the difference in the temporal and spatial distribution of precipitation is included in a forecast of the short-term power generation of small hydropower stations for the first time in this paper. First, the spatial distribution of precipitation observed by satellite remote sensing and the actual precipitation observed at ground meteorological stations are used to generate the precipitation grid covering the region of the group of small hydropower stations. Then, the partial mutual information method is used to select the precipitation time scale that has the most significant impact on changes in short-term power generation. Finally, combined with the recent major trends in historical power generation data, a model is built to forecast the short-term power generation of the group of small hydropower stations. To fully explore the characteristic information contained in the temporal and spatial distribution of precipitation data and the general trend of recent and historical power generation, this paper proposes a multimodal deep learning network based on a convolutional neural network and multilayer perceptron (CM-MDLN). The convolutional neural network (CNN) is good at processing data in the form of multiple arrays and can deeply express the effective spatial feature information contained in the grid data of precipitation. Multilayer perceptron (MLP) has a simple structure and strong adaptive ability. It can theoretically approximate any non-linear function and can learn representative trend characteristics of recent changes from historical power generation data. In this paper, the effectiveness of the proposed method is verified by using real data from a group of small hydropower stations in southern China for approximately 3 years, and the results are compared with the results of other forecasting models.