Influenced by global climate change, the frequency and scale of extreme weather events have been on the rise in recent years, and urban flooding disasters caused by extreme weather events such as typhoons and short-lived heavy rainstorms have been increasing (Ferreira et al., 2015; Zhang et al., 2017). The intensity of extreme precipitation in most regions of the world shows a trend towards intensification and a concentration of rainfall events (Yin et al., 2022). Yin used simulations from a large climate–hydrology model ensemble of 111 members, their results provide crucial insights towards assessing and mitigating adverse effects of compound hazards on ecosystems and human wellbeing (Yin et al., 2023). Urbanization increases hardened area, reduces infiltration, increases runoff and triggers higher and faster peak water flow (Nayeb Yazdi et al., 2019; Sofia et al., 2019). It has reduced groundwater recharge from natural infiltration and has contributed to the high runoff (Nath et al., 2021). A large number of low-lying areas prone to flooding are incorporated into urban development plans, and the lack of drainage capacity further exacerbates the risk of flooding (Du et al., 2012). With increasing impervious cover in urban areas driving dramatic changes in rainfall infiltration and storage capacity, which lead that urban flood appear sudden and frequent (Mu et al., 2020).

Waterlogging events on a global scale may have a serious and direct impact on the economy and humanitarianism, as well as continue to adversely affect economic development (Arshad et al., 2019). Globally, the occurrence of urban floods has been unprecedented resulting in huge economic and social losses (Sundaram et al., 2021). In July 2021, the rainstorm in Zhengzhou, China caused 380 deaths and a direct economic loss of 120.06 billion yuan. Urban flood disaster has become a crucial problem restricting the healthy development of China’s economy and society (Duan et al., 2022; Li et al., 2022). Urban floods can cause huge economic losses and casualties, and countries all over the world attach great importance to urban flood warning and mitigation. Therefore, obtaining timely and highly accurate waterlogging depth information with wide coverage is urgently needed for emergency response and risk mitigation, especially using an affordable, accurate, and widespread approach (Deo and Wen, 2016). Nowadays, more and more researchers have started to pay attention to urban waterlogging (Yin et al., 2015). Among them, accurate prediction of inland flooding is a hot research problem in the field. For accurate prediction and warning of the extent and depth of internal flooding, there are mainly numerical simulation methods, hydrological methods, and data-driven methods.

Numerical simulation method. Based on the principles of hydrodynamics, the model uses the underlying surface and elevation factors comprehensively in waterlogging process; it performs the whole process of city waterlogging formation in detail. Its simulation results are waterlogging distribution and waterlogging depth maps of a certain time step (Xue et al., 2016). Numerical simulation methods allow easy estimation of waterlogging under each recurrence period rainfall. It is interesting to note that under different urbanization and rainfall scenarios, the urban waterlogging susceptibility has a considerable variation (Explicit the urban waterlogging spatial variation and its driving factors: The stepwise cluster analysis model and hierarchical partitioning analysis approach). The hydrological and hydrodynamic model couples the distributed hydrological model and two-dimensional hydrodynamic model, which not only ensures the accuracy of the model but also has good calculation efficiency. It is a promising research direction for the flood model (Liu et al., 2022a). On the other hand, it also shortens waterlogging simulation time, and finally improves the applicability of waterlogging simulation (Zounemat-Kermani et al., 2020). But the disadvantage is that small number of data mining model parameters, such as the obscure physical implications of model parameters and the insufficient amount of simulation training, the simulation is prone to the problem of different arguments (Tang et al., 2021). Furthermore, the computational efficiency of numerical models is too low to meet the requirements of urban emergency management. Thus, many coupled methods of numerical simulation and other methods such as machine learning have emerged. A new method was established by combining a long short-term memory neural network model with a numerical model, which can quickly predict the waterlogging depth. The principle is to train the long and short-term memory neural network to predict and simulate the internal flooding process by using the numerical simulation results as training samples (Liu et al., 2022a). However, the disadvantage of this method is that the accuracy of LSTM results is extremely dependent on the results of previous numerical simulation. If the error of numerical simulation results is large, the results are difficult to guarantee.

In recent years, with the application of water sensor, many cities have established urban waterlogging monitoring and early warning system. But water level sensors are expensive and cannot be deployed all over the city (Loftis et al., 2018). Moreover, the simple monitoring data can only reflect the real-time depth of water accumulation, which does not have robust forecasting function (Liu et al., 2022b). As more and more water level sensors acquire large amounts of historical waterlogging data, some studies are beginning to train models based on historical real waterlogging data, or to use coupled models to improve the performance of prediction methods. The most representative of these is the data-driven method based on time series. Ding et al. proposed an explicable spatiotemporal attention long—short memory model (STA-LSTM) based on LSTM and attention mechanism, and established the model using dynamic attention mechanism and LSTM method to make explicable analysis of flood prediction (Ding et al., 2020). Yan et al. proposed a prediction model of the maximum water depth in time and space employing a neural network-numerical simulation model on the basis of coupling a two-dimensional hydrological and hydrodynamic model and a statistical analysis model. But due to data limitations, the actual rainfall and waterlogging data were not added to the database for training. Therefore, although the performance of the prediction model is satisfactory, its accuracy can be improved further after collecting enough data (Yan et al., 2021). Wu et al. established a real-time prediction model of flood depth based on waterlogging point by using GBDT algorithm based on multi-factor analysis and verified the validity and applicability of the model for real-time prediction of waterlogging process. However, the model that Wu used only be predicted when rainfall occurs, and cannot predict the flood depth after rainfall (Wu et al., 2020a).

However, some recent studies have shown that the prediction performance of a single method or model is always limited. Accounting for model structure, parameter and input forcing uncertainty in flood inundation modeling using Bayesian model averaging. The combination of multiple models can effectively improve the prediction performance. Multi-model combination methods to deal with model uncertainty and improve model performance (Yan and Hamid, 2016). Zhou et al. proposed an extreme flood information estimation method considering the uncertainty of distribution and model structure using the BMA method. They construct a comprehensive prediction model by BMA and three machine learning methods (support vector machines (SVM), Back Propagation Neural Network (BPNN) and Adaptive Boosting (AdaBoost)) use rainfall forecast data to drive BMA model for fine early warning of urban flood. The analysis of early warning in two different urban flood events indicates that BMA is more suitable for the prediction of severe waterlogging and illustrates the great potential and prospects of BMA in urban flood early warning (Zhou et al., 2022). Naive Bayes (NB) and Random Forest (RF) algorithm were used to forecast the waterlogging point and the waterlogging process at the waterlogging point respectively to achieve the goal of predicting the whole process of urban waterlogging (Wang et al., 2021). Historical flooding events and the value of flood contributing factors are used as inputs for the model. These input data are converted to raster layers with help of GIS tools. Our dependent variable would be a one-hot encoded vector stating whether or not it was flooded with those conditions (Khatri et al., 2022). The stochastic forest (RF), Logistic model tree (LMT) and other bivariate models combined with data mining tools can be used to simulate flood susceptibility. The study found that the LMT has good predictive power, so the model can be used for future flood mitigation in specific areas (Shahabi et al., 2020). Data warehouse and deep learning algorithm were used to assess urban flood risk. The GBDT model shows 88.48% accuracy in the depth of water accumulation prediction (Wu et al., 2020b). An application of data-driven models using artificial neural network was presented, support vector regression and long-short term memory approaches and distributed forcing data for runoff predictions. The results showed that the long-short term memory and support vector regression models outperforms artificial neural network model for hourly runoff forecasting, and the predictive performance of the models was greater during the wet seasons compared to the dry seasons (Han and Morrison, 2021). Puttinaovarat and Horkaew proposed a novel flood forecasting system based on fusing meteorological, hydrological, geospatial, and crowdsource big data in an adaptive machine learning framework (Puttinaovarat and Horkaew, 2020).

Existing studies have not sufficiently analyzed rainfall time series. Combined with waterlogging sensor data, more accurate predictions of waterlogging depths can be obtained with an accuracy of centimeters or even millimeters. The input condition used in this paper is rainfall data, which is free from the limitation of waterlogging sensors. The transfer of the model prediction capability can be achieved at locations where the features are similar to the sensor points.

The paper conducted experiments on four monitoring stations. As shown in Table 3, in the comparison of the three algorithms, Random Forest (RF) has the smallest MSE except at station D, where RF has a slightly larger MSE than Gradient Boosting Decision Tree (GBDT), indicating that RF is better adapted to this prediction task.

Compared to direct prediction using the original time series, the method of adding extracted features achieves a larger improvement at all four stations (Table 4). It indicates that using features for training can improve the prediction ability of the model to a greater extent.

As shown in Figure 4, the constructed and extracted features possess different weights, and with the algorithmic feature visualization function, we conclude. The R m e a n , C w and R s t d of rainfall are the three most important features. In fact, these three features correspond to the magnitude, variability and temporal characteristics of rainfall, respectively.

After the configuration combination experiments, the configuration with the best results was finally selected as follows: when selecting the original rainfall data, it is better to use the 1-h sliding rainfall, which can enhance the fine waterlogging prediction. Of the total number of features constructed and extracted, 9 feature combinations were determined to balance computational efficiency and prediction accuracy (rain dry, rain month, rain min, rain AUC and rain cum were removed). Nine features did not overfit on 4 stations, proving that our feature construction makes sense. The experimental results of the three algorithms were compared, and the RF algorithm had superior robustness.

In Figure 5, the blue curve is the rainfall and the orange curve is the waterlogging depth, and it can be seen that there is a strong correlation between the two. Figure 6 shows the predicted and true values of the waterlogging depth, and it can be seen that the model can predict the change trend well, with an average error within 2 cm. Prediction model evaluation for four stations can be seen in Table 5.

1) The method in this paper has a smaller MSE and more accurate prediction results than the results obtained by directly using the original rainfall event series. The model enhances the performance and robustness by time series feature extraction. Better prediction results are achieved by adjusting the feature parameters when the model is not over-fitted.

Short-term prediction of waterlogging has been a hot issue for research, because earlier warning can reduce casualties and property damage from disasters. Due to the Markovian character of itself, future waterlogging can be predicted using the waterlogging of previous periods. However, how to use rainfall data to predict waterlogging where there are no sensors becomes an urgent problem. In this study, a time-series machine learning model using feature extraction for rainfall events significantly improves the prediction with an average error of less than 2 cm. The nine features extracted are validated and proved to be really beneficial and reasonable for model capability improvement. Combined with future rainfall forecast information, it is possible to calculate whether waterlogging will form at a point in the short-term future time period. Based on the prediction results, the government can dispatch rescue forces or block the relevant roads in advance. It provides a reliable basis for government emergency decision-making and risk analysis.