## 1 Introduction
Currently, research on data-driven and knowledge-guided floods mostly relies on deterministic point prediction to output prediction results. This method may not eliminate absolute prediction errors and lacks effective evaluation methods [16]. Interval prediction can effectively quantify the uncertainty of flood forecasting, thereby more reasonably estimating potential uncertainties and risks. At present, the representative interval prediction method is upper- and lower-bound estimation (LUBE) [17]. Research on this mainly focuses on the construction of interval prediction functions and the optimization of the training process. However, the above methods may still require multiple iterations to use the PI evaluation index as the objective function, resulting in high computational resource consumption. In addition, the above method performs interval prediction without losing the original input data. When the input data are partially missing, the output accuracy of the above model may be affected to a certain extent. The phenomenon of missing original input data is common in the field of flood forecasting [18]. With the lack of input data in flood forecasting, the current solutions mainly include two types. One method is to directly delete the missing data in the entire section [19]. Another method is to use algorithms to convert incomplete data into complete data, which is the data interpolation method [20]. At present, the more popular technology in the field of flood time-series data preprocessing is tensor-based decomposition and interpolation technology [21]. [PERSON] et al. [22] completed data interpolation work based on the Tucker decomposition three-process framework by discovering spatiotemporal patterns and underlying structures from incomplete data. [PERSON] et al. [23] proposed a new incremental algorithm, while [PERSON] et al. [24] introduced the idea of adaptive randomization to handle it. [PERSON] et al. [25] completed tensor processing using the low-rank structure of the TR potential space, which is robust to model selection. In addition, we note that in the face of time-varying massive hydrological heterogeneous and complex data, the above incremental methods do not deeply consider the sparsity of data decomposition. This will affect the accuracy of model predictions and the overall computational resource consumption of the prediction model. The main limitations of flood time-series prediction based on data-driven models are as follows. Intelligent data-driven flood prediction models are easily affected by data noise in practical engineering. Then, the presence of missing data makes the model prone to unreasonable or unrealistic predictions, and existing tensor preprocessing methods cannot effectively solve the sparsity problem of flood data. In addition, data-driven models only consider flood prediction from the perspective of data, lacking consideration and research on the spatiotemporal characteristics of the flood process itself, and cannot avoid prediction errors caused by a lack of physical knowledge. For this reason, we propose data-driven and knowledge-guided heterogeneous graphs and temporal convolution networks for flood forecasting. The main contributions of this article are summarized as follows. 1. This article proposes a data-driven and knowledge-based dual-drive flood prediction model, which optimizes the initial conditions of the model through heterogeneous graph modules and introduces prior knowledge of the watershed. TCN with integrated attention is used to fit the model, significantly reducing data noise and enhancing the robustness of the model. 2. The proposed model effectively integrates the guiding framework technology of flood physics theory into data-driven models, and introduces physical constraints that comply with the physical laws of flood flow prediction principles, solving the problem of errors in common data-driven model predictions that do not conform to physical knowledge. 3.