Spatiotemporal Convolutional Approach for the Short-Term Forecast of Hourly Heavy Rainfall Probability Integrating Numerical Weather Predictions and Surface Observations

Xi Liu aKey Laboratory of Transportation Meteorology of China Meteorological Administration, Nanjing Joint Institute for Atmospheric Sciences, Nanjing, China
bState Key Laboratory of Severe Weather and Institute of Artificial Intelligence for Meteorology, Chinese Academy of Meteorological Sciences, Beijing, China

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Yu Zheng aKey Laboratory of Transportation Meteorology of China Meteorological Administration, Nanjing Joint Institute for Atmospheric Sciences, Nanjing, China

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Xiaoran Zhuang cJiangsu Meteorological Observatory, Nanjing, China

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Yaqiang Wang bState Key Laboratory of Severe Weather and Institute of Artificial Intelligence for Meteorology, Chinese Academy of Meteorological Sciences, Beijing, China

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Xin Li aKey Laboratory of Transportation Meteorology of China Meteorological Administration, Nanjing Joint Institute for Atmospheric Sciences, Nanjing, China

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Zhang Bei aKey Laboratory of Transportation Meteorology of China Meteorological Administration, Nanjing Joint Institute for Atmospheric Sciences, Nanjing, China

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Wenhua Zhang bState Key Laboratory of Severe Weather and Institute of Artificial Intelligence for Meteorology, Chinese Academy of Meteorological Sciences, Beijing, China

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Abstract

The accurate prediction of short-term rainfall, and in particular the forecast of hourly heavy rainfall (HHR) probability, remains challenging for numerical weather prediction (NWP) models. Here, we introduce a deep learning (DL) model, PredRNNv2-AWS, a convolutional recurrent neural network designed for deterministic short-term rainfall forecasting. This model integrates surface rainfall observations and atmospheric variables simulated by the Precision Weather Analysis and Forecasting System (PWAFS). Our DL model produces realistic hourly rainfall forecasts for the next 13 h. Quantitative evaluations show that the use of surface rainfall observations as one of the predictors achieves higher performance (threat score) with 263% and 186% relative improvements over NWP simulations for the first 3 h and the entire forecast hours, respectively, at a threshold of 5 mm h−1. Noting that the optical-flow method also performs well in the initial hours, its predictions quickly worsen in the final hours compared to other experiments. The machine learning model, LightGBM, is then integrated to classify HHR from the predicted hourly rainfall of PredRNNv2-AWS. The results show that PredRNNv2-AWS can better reflect actual HHR conditions compared with PredRNNv2 and PWAFS. A representative case demonstrates the superiority of PredRNNv2-AWS in predicting the evolution of the rainy system, which substantially improves the accuracy of the HHR prediction. A test case involving the extreme flood event in Zhengzhou exemplifies the generalizability of our proposed model. Our model offers a reliable framework to predict target variables that can be obtained from numerical simulations and observations, e.g., visibility, wind power, solar energy, and air pollution.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yu Zheng, zhengyu@cma.gov.cn

Abstract

The accurate prediction of short-term rainfall, and in particular the forecast of hourly heavy rainfall (HHR) probability, remains challenging for numerical weather prediction (NWP) models. Here, we introduce a deep learning (DL) model, PredRNNv2-AWS, a convolutional recurrent neural network designed for deterministic short-term rainfall forecasting. This model integrates surface rainfall observations and atmospheric variables simulated by the Precision Weather Analysis and Forecasting System (PWAFS). Our DL model produces realistic hourly rainfall forecasts for the next 13 h. Quantitative evaluations show that the use of surface rainfall observations as one of the predictors achieves higher performance (threat score) with 263% and 186% relative improvements over NWP simulations for the first 3 h and the entire forecast hours, respectively, at a threshold of 5 mm h−1. Noting that the optical-flow method also performs well in the initial hours, its predictions quickly worsen in the final hours compared to other experiments. The machine learning model, LightGBM, is then integrated to classify HHR from the predicted hourly rainfall of PredRNNv2-AWS. The results show that PredRNNv2-AWS can better reflect actual HHR conditions compared with PredRNNv2 and PWAFS. A representative case demonstrates the superiority of PredRNNv2-AWS in predicting the evolution of the rainy system, which substantially improves the accuracy of the HHR prediction. A test case involving the extreme flood event in Zhengzhou exemplifies the generalizability of our proposed model. Our model offers a reliable framework to predict target variables that can be obtained from numerical simulations and observations, e.g., visibility, wind power, solar energy, and air pollution.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yu Zheng, zhengyu@cma.gov.cn

1. Introduction

Hourly heavy rainfall (HHR) exceeding 20 mm can quickly lead to catastrophic flash floods or landslides, resulting in significant loss of life and property in a short period (Li et al. 2017). For example, a recent record breaking extreme rainfall event took place in Zhengzhou, where more than 1500 automated weather stations (AWSs) observed HHR records (Yang et al. 2022), causing over 300 deaths and tremendous economic damage. The unpredictability of such extreme rainfall events, in terms of timing and location, presents a great challenge for operational numerical weather prediction (NWP) models and experienced forecasters. Therefore, it is imperative to emphasize short-term predictions of hourly rainfall and HHR events, which are crucial for early warnings of meteorological and hydrological disasters (e.g., Ganguly and Bras 2003; Liu et al. 2017; Zhu et al. 2017).

Traditional short-term forecasting methods can usually be categorized into two approaches: 1) NWP models and 2) data-driven methods (e.g., Voyant et al. 2017; Akbari Asanjan et al. 2018; Pan et al. 2021). NWP models use the attributes of relevant dynamic and thermodynamic processes to simulate various meteorological variables, with precipitation being a critical one (Ritter and Geleyn 1992; Warner et al. 1997; Zahraei et al. 2012, 2013). To date, substantial advancements have been made in NWP models, such as higher spatiotemporal resolution, improved data assimilation methods, and various postprocessing methods (e.g., Ballard et al. 2016; Sun et al. 2014; Wang et al. 2016). However, NWP models still face considerable limitations, which are difficult to overcome simply by endlessly updating data assimilation techniques and enriched observation data (Sun et al. 2014; Wang et al. 2016). On the other hand, extrapolation-based methods are purely statistical and driven by data. Previous studies have shown that extrapolation methods produce better precipitation forecasts at short lead times of up to 2 h with lower computational costs than NWP models (Zahraei et al. 2012, 2013). In turn, NWP models perform better beyond initial hours (Gultepe et al. 2019). This suggests that relying solely on NWP models or data-driven methods may not yield optimal forecast results. Thus, the integration of massive observational data and high-resolution NWP simulations has been proposed as a viable solution (Akbari Asanjan et al. 2018; Voyant et al. 2017; Zahraei et al. 2012).

Deep learning (DL) can be a good solution to effectively extract high-quality features from massive meteorological data with superior nonlinear fitting and generalizability (LeCun et al. 2015; Liu et al. 2016; Zhao et al. 2017). For example, Geng et al. (2019) proposed a dual spatiotemporal encoder network model, called LightNet, to predict 6-h lightning. Based on LightNet, Lin et al. (2019) introduced a channelwise attention mechanism for the 12-h lightning forecast. More recently, a SegNet-based DL network named LightningNet-NWP (Zhou et al. 2021) has been implemented to merge multisource observation data with NWP simulations to improve lightning forecasts for 6 h. The results show that the longer the prediction period, the more advantageous the combinational use of observations and NWP data. However, due to the complex spatiotemporal evolution and intensity variation of heavy rainfall, DL-based short-term rainfall prediction integrating surface observations and NWP simulations as predictors has rarely been documented in the literature.

Most recently, Hess and Boers (2022) introduced a deep neural network for global rainfall modeling, using NWP ensemble simulations as input. The model provides 3-hourly rainfall predictions up to 12 h with a spatial resolution of 0.5°. However, a U-net based on convolutional neural networks (CNN) can struggle to capture long-term dependencies between distant frames due to its tendency to learn complicated state transitions as compositions of simpler ones through stacking convolutional layers (Wang et al. 2023). To address this issue, Shi et al. (2017) proposed a convolutional long short-term memory (ConvLSTM) network to improve the precipitation nowcasting by capturing spatiotemporal correlations. Additionally, Wang et al. (2017) proposed a predictive recurrent neural network (PredRNN), which enhances the ConvLSTM model by incorporating a spatiotemporal memory flow structure, providing a unified memory mechanism to handle both short-term deformations of spatial details and long-term dynamics. PredRNNv2 further improves PredRNN by decoupling the interlayer spatiotemporal memory and inner-layer temporal memory in latent space and proposes a new curriculum learning strategy (Wang et al. 2023). Consequently, PredRNNv2 is eminently suitable for conducting high spatial and temporal resolution precipitation forecasts by integrating observational data and regional NWP simulations as a sequence-to-sequence prediction model.

Unlike deterministic prediction, probabilistic forecasts can predict the most likely outcome, as well as the probability of rare events (Buizza 2008). For example, a probabilistic forecast derived from an ensemble prediction system can be used to assess the occurrence probability of events linked with the maximum acceptable losses, and can thus be more valuable than a deterministic forecast in weather-risk management (Fundel et al. 2019). Considering the problem of highly imbalanced HHR samples, it is challenging for DL models to fully extract the spatiotemporal information of HHR events. Therefore, we try to find a flexible, compatible, and fast approach to obtain the forecast of HHR probability from deterministic rainfall predictions. Several approaches are known to derive probabilistic guidance from deterministic forecast: the ensemble prediction system (e.g., Du et al. 1997); the neighborhood operator (e.g., Schwartz and Sobash 2017); and the analog ensemble technique (e.g., Sperati et al. 2017). Recent work has shown promising results using machine learning (ML) methods to derive probabilistic guidance of weather forecasts (Flora et al. 2021; Kirkwood et al. 2021). LightGBM is based on the gradient boosting decision tree (GBDT; Ke et al. 2017) and is widely used in classification tasks in all walks of life. Compared to other traditional GBDT frameworks, LightGBM has the advantages of high speed, memory saving, and better generalization ability (Liu et al. 2021). Using LightGBM, we can transform the complex sequence-to-sequence HHR prediction task into a simple HHR classification task based on deterministic rainfall forecasts.

In summary, we propose a two-step process to address the task of forecasting HHR probability. Initially, we use a PredRNNv2-based model to integrate observational rainfall data with regional NWP simulations, with the objective of forecasting hourly rainfall intensity and evolution up to 13 h ahead. Subsequently, we convert the deterministic rainfall prediction into the HHR probability forecast using LightGBM. Experiments using U-net and optical-flow as forecasting models are examined to ensure the superiority of our model. The importance of merging observational rainfall data is demonstrated in experiments that only use regional NWP simulations as input.

This paper is structured as follows. Section 2 describes the datasets and preprocessing methods, while section 3 outlines the model architecture. Sections 4 and 5 present the results for the hourly rainfall prediction and HHR classification, respectively. Conclusions and discussion are provided in section 6.

2. Data and methodology

a. Data sources

The hourly rainfall observations used in this paper are recorded from 5718 AWSs located over the Jiangsu region in eastern China (30°–35.95°N, 116.05°–122°N; red box in Fig. 1). Observations of hourly rainfall are under quality control (Ren et al. 2010). HHR records are defined as cumulative rainfall greater than 20 mm over a period of 1 h (Li et al. 2017).

Fig. 1.
Fig. 1.

(a) The experimental region of Jiangsu Province (red dashed box) and Henan Province (green dashed box). (b) Map of AWSs in Jiangsu region.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0068.1

The NWP results are derived from the Precision Weather Analysis and Forecasting System (PWAFS), which is the operational NWP model run by the Jiangsu Meteorological Bureau, China. It consists of the WRF-ARW model version 3.9.1 and a three-dimensional variational data assimilation system (Zhang et al. 2023). The PWAFS system employs a nested domain with a grid spacing of 15 km (481 × 361 grids, D01; Fig. S1 in the online supplemental material) and 3 km (841 × 841 grids, D02; Fig. 1a), respectively. This study uses 24 predicted variables from PWAFS D02 simulations, which are initialized every 3 h starting at 0000 UTC (coordinated universal time) every day, at 1-h intervals for the next 72 h. Specific predictors are listed in Table 1. More detailed information on PWAFS can be found in the supplemental material, including model configurations (Text S1 and Table S1), operational flowchart (Fig. S2), and data assimilation systems (Table S2).

Table 1.

Predictor variables.

Table 1.

b. Data preprocessing

In this study, we consider 24 predicted weather variables from PWAFS (hereafter PWAFS variables) and surface rainfall observations as input predictors for the deterministic rainfall prediction task (Table 1). At any time, 24 PWAFS variables, denoted as a tensor of PR841×841×24, encapsulate various meteorological information. Concurrently, surface rainfall observations are represented as RR5718. Considering the run-time requirement of PWAFS is 3–4 h, our DL model is initialized 5 h after each start-up of PWAFS. This delay is essential for acquiring comprehensive and reliable atmospheric conditions from PWAFS. This temporal alignment ensures the availability of predictions for the subsequent 13-h window, a period that includes operational forecast cycles such as 2000–0800 and 0800–2000 BST (Beijing standard time; BST = UTC + 8 h). Assuming the current time is 0700 BST, we need to achieve the hourly rainfall prediction for the next 13 h during 0800–2000 BST. Thus, we select PWAFS variables with a duration of 18 h from 0300 to 2000 BST initiated at 0200 BST, along with prior rainfall observations during 0200–0700 BST as input features. The preprocessing of input data involves a series of specific steps.

  1. Time matching: According to the 3-hourly initialization of PWAFS, eight sequences of surface rainfall observations and PWAFS variables can be matched every day. Each sequence contains 18 frames of PWAFS variables (PR841×841×24) and 6 frames of prior rainfall observations (RR5718) as input frames, with the subsequent 13 h of rainfall observations serving as ground truth (RR5718).

  2. Sequence screening. To facilitate the convergence of our DL models, we need to discard all nonrainy sequences from all the sequences matched in the previous step. If less than 5% of all 5718 AWSs observed a rain rate exceeding 0.1 mm h−1 at any time step in a sequence, we recognize it as a nonrainy sequence. Thus, 3994 rainy sequences remain in the dataset.

  3. Data interpolation. In the Jiangsu region, the AWSs are densely distributed with instances of 2–6 km. To minimize interpolation’s impact on surface rainfall observations and ensure spatial consistency with the existing operational DL forecast systems, we need to regrid surface rainfall observations and PWAFS variables at regular grid points. Therefore, we employ the inverse distance-weighted interpolation method to regrid surface rainfall observations and PWAFS variables to a spatial resolution of 0.05° (120 × 120 grids; Fig. 1b) with a radius of 20 km and a power of 2. After regridding, PWAFS variables can be denoted by PR120×120×18×3994×24, while rainfall observations can be expressed as RR120×120×18×3994.

3. Model architecture

As shown in the left column of Fig. 2, we achieve the goal of predicting the probability of HHR using two key modules: the rainfall forecast module and the HHR classification module. With t representing the current time, our PredRNNv2-AWS model processes surface rainfall observations from the preceding hours {Rt−5, Rt−4, …, Rt}, along with 24 PWAFS variables P covering an 18-h duration {Pt−4, Pt−3, …, Pt, Pt+1, …, Pt+13}, and output hourly rainfall predictions R^ for the next 13 h {R^t+1,R^t+2,,R^t+13}.

Fig. 2.
Fig. 2.

(left) General workflow. (right) The main architecture of PredRNNv2-AWS, where t represents the time step, Rt is the rainfall observation, and R^t is the rainfall prediction. PWAFS variables are denoted by Pt.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0068.1

To illustrate the advantage of the PredRNNv2 model in deterministic rainfall prediction and highlight the importance of including surface rainfall observation as a predictor, we adopt U-net (Ronneberger et al. 2015) as a baseline model and design four DL experiments with or without surface rainfall observations as input predictor:

  • PredRNNv2-AWS: This is the proposed model that uses rainfall observations and PWAFS variables as input. The architecture is shown in Fig. 2.

  • PredRNNv2: This model uses PWAFS variables only as input.

  • Unet-AWS: This model uses rainfall observations and PWAFS variables as input. The architecture is shown in Fig. S3.

  • Unet: This model uses PWAFS variables as input only.

Additionally, we benchmark these DL-based experiments against the original PWAFS rainfall forecasts and a combination of PWAFS forecasts with optical-flow extrapolations through weighted blending. During the evaluation, we shall designate these two experiments as PWAFS and Optical-flow.

For the deterministic rainfall prediction task, the preprocessed datasets are divided into training, validation, and testing datasets, as listed in Table 2. PredRNNv2-AWS and PredRNNv2 models encompass 53.1 million trainable parameters each, whereas Unet-AWS and Unet models contain 8.7 million trainable parameters each.

Table 2.

Training, validation, and testing periods for DL models.

Table 2.

Considering the pixel-based classification nature of LightGBM, training it with grid data introduces a substantial number of non-HHR samples, causing a severe sample imbalance issue. Therefore, we transform station-based observations at any time step into HHR hits HR5718, using the threshold of 20 mm h−1. This approach ensures the accuracy of the HHR target while alleviating sample imbalance in the dataset. Following that, we match the DL-based rainfall forecasts and 24 PWAFS variables located at the nearest grid point corresponding to each AWS. Among these, DL-based rainfall forecasts (R^R5718) and 24 PWAFS variables (PR5718×24) at any time step serve as inputs, with HHR observations HR5718 as ground truth. Unlike deterministic rainfall prediction, we did not include the rainfall observations from the preceding hours in the HHR classification task, because of LightGBM’s difficulties in capturing temporal relationships between consecutive time steps. Flood-producing storms usually exhibit substantial movement and development within a few hours. Including past precipitation observations as a predictor may cause LightGBM to learn information significantly different from the current moment. The final output will comprise the probability of HHR, assessed across all points on the 120 × 120 grid. Three experiments are designed:

  • PredRNNv2-AWS: This is the proposed model that uses PWAFS variables and rainfall predictions from the PredRNNv2-AWS model as input.

  • PredRNNv2: This experiment uses PWAFS variables and rainfall predictions from PredRNNv2 as input.

  • PWAFS: This experiment uses PWAFS variables as input only.

The datasets for HHR classification task are divided into training and testing datasets, as listed in Table 3. We set the fivefold cross-validation to train and validate the HHR classification results. In the widely used cross-validation method on a rolling basis, the training set is evenly divided into five groups. Four of the groups are used for training, and the remaining group serves as validation. This process is repeated five times to ensure that all samples are trained and validated.

Table 3.

Training and testing periods for LightGBM.

Table 3.

All experiments are implemented in Pytorch (Paszke et al. 2019) and performed on four NVIDIA RTX A6000 GPUs.

a. The PredRNNv2 model for rainfall prediction

The main schematic illustration of our model architecture is shown in Fig. 2. Here, we design a PredRNNv2 model with four spatiotemporal long short-term memory (ST-LSTM) layers, which are typically used in spatiotemporal predictions (e.g., Wu et al. 2022; Wang et al. 2023). This four-layer structure can strike a balance between prediction quality and training efficiency (Wang et al. 2023). Each ST-LSTM layer has 128 convolutional filters with a kernel size of 5 × 5 and a stride size of 1. For the convolution process, we employ the “same” padding method, which adds zero-padding around the input data to ensure the output maintains the same spatial dimensions as the input. We set the number of input and output channels to 25 and 1, respectively.

We align our core hyperparameter settings with those suggested in Wang et al. (2023). We adjusted the batch size and the learning rate. Since our model is trained on four NVIDIA A6000 GPUs, we chose a batch size of 8 to balance computational efficiency and predictive performance. Regarding the learning rate, we manually tuned it and tested different values ranging from 10−5 to 10−2, finding that 10−3 yielded relatively better results. Our primary objective is not to achieve a flawless prediction model, but to highlight the substantial enhancement in predictive performance achieved through the inclusion of prior observational data. Consequently, although further refinement of the hyperparameters might yield marginal improvements, it does not impact the conclusions drawn from our research.

As shown in Table 4, the frequencies of different rainfall levels are highly imbalanced. We propose to use the weighted mean absolute error as a loss function to solve this problem. The assignment of more weights to heavier rainfall is essential for DL models to achieve good performance at higher rain rate thresholds (Shi et al. 2017). Specifically, we assign a weight w(x) to each grid according to its rainfall intensity x:
w={1,0.1<x<12.5,1x<55,5x<1010,10x<2020,20x.
Table 4.

Rain-rate statistics.

Table 4.

b. The U-Net model for comparison

The U-net architecture has been established as the baseline model due to its adaptable design. The network architecture can be found in Fig. S3. It consists of two basic components: an encoder and a decoder. In this network, we use 64, 128, 256, and 512 filters for the convolutional layers in the encoder and 512, 256, 128, and 64 filters in the decoder. The encoder extracts the intermediate state from the input data by two 3 × 3 convolution operations, each followed by a group normalization (Wu and He 2018) and a leaky rectified linear unit (Leaky ReLU; Maas et al. 2013). After that, a 3 × 3 convolution operation with stride 2 is conducted for down-sampling. Each level in the decoder consists of an up-sampling of the feature map using a 2 × 2 transposed convolution with a stride of 2, followed by a concatenation with the intermediate state from the corresponding encoder level, and two 3 × 3 convolutions, each followed by a Leaky ReLU. In the final layer, a 1 × 1 convolution is used to map each 64-component feature vector to the desired rainfall forecasts in the next 13 h. In each convolutional operation, we use the “same” padding method to ensure the same spatial dimension between the input and output. The input data selection for the U-net experiments aligns with that of the PredRNN experiments. The only difference is that we concatenate all input data into a tensor with dimensions of 120 × 120 × (24 × 18 + 6) and 120 × 120 × (24 × 18) for U-net experiments with or without rainfall observation as predictor, respectively.

c. Blending rainfall forecasts from optical-flow and PWAFS

This model employs a hybrid methodology by synergistically blending PWAFS-derived rainfall predictions with optical-flow extrapolations. First, we acquire rainfall extrapolations for the next 13 h using the dense model from the Rainymotion library (hereafter referred to as Rainymotion), which is based on the constant-vector advection scheme (Ayzel et al. 2019). Second, the weighted average rainfall predicted by PWAFS (Rp) and Rainymotion (Rr) is optimized against the rainfall observation (Ro) via mean squared error (MSE). The optimal weights w1 and w2 are derived by minimizing the MSE objective function at any time step t up to 13 h:
MSEt=1Ni=1N[(w1Rpi,t+w2Rri,t)Roi,t]2,
where N denotes the total number of rainy sequences in the training data. Constrained to w1 + w2 = 1, the weights are initialized at w1 = 0.5 and fine-tuned using quasi-Newton methods. Finally, the optimized w1 and w2 are applied to Rp and Rr in the testing data to achieve hourly rainfall forecasts with a lead time of up to 13 h. Specific values of optimized w1 and w2 can be found in Table S4.

d. The LightGBM model for HRR classification

LightGBM is a GBDT-based model that adopts an improved histogram-based algorithm to speed up the training process and reduce memory consumption (Ke et al. 2017). The schematic architecture is presented in Fig. S4. The histogram-based algorithm divides the continuous eigenvalues into k intervals and then constructs a histogram with a width of k (Qian et al. 2021). The application of this algorithm could speed up the training process and prevent overfitting (Ju et al. 2019). In addition, LightGBM model uses a leafwise generation strategy in the training process instead of the traditional levelwise strategy used by GBDT. This approach involves growing leaf nodes based on maximizing the information gain at each split, leading to faster convergence and potentially higher performance. Furthermore, LightGBM uses the exclusive feature bundling technique to bundle highly correlated features together, thereby reducing the number of features and simplifying the model complexity (Ke et al. 2017).

The open-source tool, “A Fast Library for Automated Machine Learning & Tuning” (hereafter FLAML), is used for hyperparameter tuning of our LightGBM model. FLAML is a lightweight open-source Python library for efficient automation of ML operations. It has been widely adopted in ML research for hyperparameter optimization (Schäfer et al. 2022; Alsharef et al. 2022; Balasus et al. 2023). The following command is used for hyperparameter tuning of our LightGBM model: automl = flaml.AutoML(); automl.fit(train_x, train_y, task=“classification”). The train_x means the tensor of input features, while train_y is the target tensor. More details about FLAML can be found at https://github.com/microsoft/FLAML. Detailed hyperparameters for LightGBM can be found in Table S3.

e. Evaluation metrics

Our evaluation metrics include four types of commonly used scores in meteorological forecasts (Dafis et al. 2018): the probability of detection (POD), false alarm ratio (FAR), threat score (TS) and frequency bias (FBIAS). The above metrics are calculated as follows:
TS=TPTP+FP+FN,
POD=TPTP+FN,
FAR=FPTP+FP,
FBIAS=TP+FPTP+FN,
where TP, FP, FN, and TN represent the number of true positive, false positive, false negative, and true negative grid cells, respectively.

For the forecast of HHR probability, results are evaluated using receiver operating characteristic (ROC; Jolliffe and Stephenson 2012) curves and Brier skill score (BSS; Murphy 1973). ROC curves represent the ability of the forecast to discriminate between events and nonevents by plotting the relationship between the true positive rate (same as POD) and false positive rate [FP/(FP+TN)].

The area under the ROC curve (AUC) is taken as an index of the overall accuracy of the model. AUC values vary between 0 and 1, with 1 representing a perfect model (Fielding and Bell 1997). The Brier score (BS) is the mean squared error adapted for binary (yes or no) classification problems, and thus can be used to validate the magnitude of probability forecast errors. The BS is calculated as follows:
BS=1Ni=1N(piai)2,
where N is the number of observed events. This equation verifies whether observed events, which were predicted with a probability of pi (with values between 0 and 1), have occurred or not in observations ai (1 = yes, 0 = no). BSS measures the improvement in BS of a probability forecast (BSV) relative to a reference forecast (BSR) that is PWAFS in the present study. BSS can be defined as
BSS=1BSVBSR.
The forecast is perfect when the BSS is equal to one. A zero BSS means no improvement compared to the PWAFS.

4. Deterministic forecast of hourly rainfall

In this study, the accurate prediction of hourly rainfall serves as the fundamental requirement for the HHR forecast. Figure 3 shows the forecast performance of six experiments on testing data during June–July 2020. In general, the forecast performance of the various experiments decreases as the rainfall threshold increases. Among these experiments, PredRNNv2-AWS shows the best performance at all thresholds (Fig. 3). Incorporation of AWS observations improves the forecast ability of both PredRNNv2-AWS and UNet-AWS, as reflected in their lower bias and higher POD, TS and success ratio. Furthermore, PredRNNv2-AWS provides a more accurate rainfall prediction compared to UNet-AWS. The six experiments exhibit unsatisfactory predictive skills at a threshold of 5.0 mm h−1. Nevertheless, in terms of the temporal variation of TS, surface observations can notably improve the predictive accuracy of DL models in the early hours (1–3 h; Fig. 4).

Fig. 3.
Fig. 3.

Performance diagram for the hourly rainfall predicted by diverse experiments at different rainfall thresholds (0.1, 0.5, 1, and 5 mm h−1). The evaluation is performed on the testing data during June–July 2020. The x axis shows the success ratio (SR), i.e., 1 − FAR. The y axis is the POD. The dashed lines indicate the FBIAS, while blue shadings show the TS.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0068.1

Fig. 4.
Fig. 4.

The TS of the hourly rainfall predicted by diverse experiments with respect to different forecast lead times at the thresholds of (a) 0.1, (b) 0.5, (c) 1.0, and (d) 5.0 mm h−1. The evaluation is performed on the testing data during June–July 2020. Shaded areas represent the 95% bootstrap confidence intervals for each experiment.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0068.1

At each threshold (Fig. 4), PredRNNv2-AWS and UNet-AWS show a TS enhancement over their respective models without AWS observations during the first 3 h. Specifically, PredRNNv2-AWS presents the highest TS of about 0.5 (0.35) at thresholds of 0.1–1 (5) mm h−1. Including surface rainfall observations significantly improves the average TS score over PWAFS by 263% and 186% at the 5 mm h−1 threshold for the first 3 forecast hours and the entire 13 forecast hours, respectively. This suggests that incorporating AWS observations can enhance the forecast accuracy of DL models, especially in the case of heavy rainfall.

It should be noted that while the TS rapidly declines in the initial hours, PredRNNv2-AWS still outperforms other models during the last several hours. It suggests that incorporation of observations also improves predictive accuracy in later hours. Although UNet-AWS and Optical-flow present forecast performance comparable to PredRNNv2-AWS over the first 3 forecast hours, their TS scores dramatically decline after the lead time of 4 h. Notably, Optical-flow records the lowest TS among all models in the final hours.

As shown in Fig. 4, the performance gain of PredRNNv2-AWS compared to optical-flow in a lead time shorter than 3 h is presented in the precipitation intensity of 0.1–1 mm h−1, but appears to diminish at the threshold of 5 mm h−1. This can be attributed to the following reasons. First, the Optical-flow assumes that pixel intensity remains largely unchanged between consecutive frames, and neighboring pixels exhibit similar motion. This makes its prediction less sensitive to rainfall intensity. Second, the loss function of the mean absolute error itself would minimize the variance in rainfall prediction, and the imbalance in heavy rainfall samples further contributes to the diminished predictive performance of DL models for rare events. Nevertheless, the forecasting performance of the Optical-flow in the final hours is still inferior to PredRNNv2-AWS, and this trend is consistent with the evaluations at thresholds of 0.1–1 mm h−1. Moreover, by examining specific cases in Figs. S5–S7, it becomes evident that the Optical-flow extrapolation occasionally displays noticeable deformations that deviate from the theoretical evolution of rainfall systems. Consequently, we designate PredRNNv2-AWS as the optimal model for rainfall prediction in this study.

5. The forecast of HHR probability

a. Quantitative performance evaluation

To transform the quantitative precipitation forecasts acquired in section 4 into the forecast of HHR probability, the LightGBM algorithm has been employed as a postprocessing module. Quantitative evaluations are made among PWAFS, PredRNNv2, and PredRNNv2-AWS models using ROC curves and BSS. Figures 5a and 5c indicate that PredRNNv2 and PWAFS exhibit very similar forecasting capabilities, with PredRNNv2 showing better performance. With the integration of rainfall observations, PredRNNv2-AWS exhibits better forecast accuracy compared to PredRNNv2, with relative improvements of 7% and 12% for the entire forecast and the initial hours (Fig. 5a), respectively. As the forecast lead time increases, the accuracy of PredRNNv2-AWS forecast gradually decreases during the final hours, yet remains comparable to the top-performing forecasts of PredRNNv2 and PWAFS (Fig. 5c). Therefore, the HHR or non-HHR event predicted by PredRNNv2-AWS can better reflect actual weather conditions than PredRNNv2 and PWAFS.

Fig. 5.
Fig. 5.

(a) ROC curves for the forecast of HHR probability from PredRNNv2-AWS, PredRNNv2, and PWAFS on testing dataset during June–July 2020. (b) BSS of PredRNNv2-AWS and PredRNNv2 relative to PWAFS. (c) AUC of each experiment with respect to different forecast lead times. Shaded areas in (a) and (c), and black error bars in (c) represent the 95% bootstrap confidence intervals.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0068.1

On the other hand, PredRNNv2 gives an average BSS of 0.17 relative to PWAFS. When AWS observations are included, PredRNNv2-AWS achieves the highest BSS of 0.35 (Fig. 5b). After the evident BSS decline, PredRNNv2-AWS presents a BSS increasing trend in the rest of the lead times. The results indicate that PredRNNv2-AWS can rectify the HHR prediction made by PWAFS during the last several hours, and notably improve the forecast skill during the initial hours.

Utilizing a 0.5 threshold, we categorize probabilities into HHR and non-HHR, conducting an analysis of temporal and spatial TS variations (Fig. 6). Although our model surpasses PWAFS in performance, its accuracy remains considerably influenced by PWAFS predictions. Examining Fig. 6, significant diurnal and spatial variations in model performance are presented. Specifically, lower TS values, observed in the afternoon hours (0400–0800 UTC; Fig. 6a) and over the southwestern region (Figs. 6c,d), may result from the poor predictability of local convective storms induced by solar heating and complex terrain (Luo and Chen 2015; Liu et al. 2020). It is crucial to emphasize that, despite consistently attaining low TS values (below 0.1) across all regions, our PredRNNv2-AWS model does not inherently imply a poor predictive capability. The prevalence of low TS values for rare events, like HHR in this study, stems from the fact that TS does not reward correct negatives (i.e., correct forecasts of non-HHR). Consequently, the model must accurately predict a substantial portion of events without generating excessive false alarms, which becomes more challenging as the frequency of events decreases.

Fig. 6.
Fig. 6.

(a) The TS results of the HHR probability forecasts at different hours (UTC) of a day from PredRNNv2-AWS, PredRNNv2, and PWAFS on testing dataset. (b) Accumulative occurrences of HHR observed in the testing dataset. (c)–(e) The spatial distribution of average TS of the HHR probability derived from diverse DL models on the testing dataset.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0068.1

Figure 7 underscores the poor reliability of our model, consistent with the findings of various studies that focus on the prediction or calibration of rare events (Gagne et al. 2017; Lagerquist et al. 2017; Burke et al. 2020). The rain rate statistics presented in Table 4 indicate that the HHR records constitute a mere 0.3% of the total dataset. Due to the highly imbalanced nature of the dataset, the model exhibits a tendency to predict the majority class (non-HHR) more frequently, leading to an uneven distribution of predicted probabilities in the reliability diagram (Figs. 7a–c). Nevertheless, operational forecasters generally incline toward assigning higher probabilities to extreme weather events. Underestimating the occurrence of extreme weather may lead to severe consequences, whereas the negative impacts of overestimation are comparatively minor. Consequently, the reliability diagram shows no resolution and a notable overestimation of our model (Fig. 7d). This phenomenon appears to be inevitable when evaluating rare events.

Fig. 7.
Fig. 7.

(a)–(c) The frequency of forecasts in each probability bin from diverse models. (d) Reliability diagram of HHR forecasts from diverse models.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0068.1

b. A representative case

To further illustrate the predictive skill of PredRNNv2-AWS, we examine the network performance on an extreme rainfall event that occurred over the Jiangsu region on 15 June 2020. In this case, more than 500 AWSs observed at least one HHR record during 0800–2000 BST. Compared to observations (Fig. 8), both PWAFS and PredRNNv2 approximately capture the spatial distribution of rainfall, but predict the HHR probability uniformly between 60% and 75%. For PredRNNv2-AWS, predicted HHR probabilities are greatly strengthened to 80%–95% over the most observed HHR area, resulting in higher AUC, CC, and POD than PWAFS and PredRNNv2 (Fig. 9). PredRNNv2-AWS also presents HHR evolutionary forecasts that closely resemble observations (Fig. 8). The superiority of PredRNNv2-AWS in forecasting rainy systems leads to a considerable improvement in HHR prediction against PWAFS and PredRNNv2.

Fig. 8.
Fig. 8.

Hourly precipitation observations (shading; mm h−1) and the forecast of HHR probability during 0800–2000 BST 15 Jun 2020 obtained from PredRNNv2-AWS, PredRNNv2, and PWAFS. The observational HHR records (blue crosses) are plotted in each panel. The boundaries of Nanjing and Jiangsu provinces are outlined.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0068.1

Fig. 9.
Fig. 9.

The (a) AUC, (b) correlation coefficient (CC), (c) POD, and (d) FAR of the HHR probability forecasts during 0800–2000 BST 15 Jun 2020 obtained from PredRNNv2-AWS, PredRNNv2, and PWAFS. Shaded areas represent the 95% bootstrap confidence intervals for each experiment.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0068.1

c. A test on the “21⋅7” Zhengzhou flood

Given that PredRNNv2-AWS works well over the Jiangsu region, we try to present the generalization of this model by testing it in a different geographical area. We choose an extreme rainfall event that occurred during 17–22 July 2021 in Henan Province, China (Fig. 10). During this event, more than 1500 AWSs observed at least one HHR record (Yang et al. 2022). However, both operational global NWP models (Shi et al. 2021) and convection-permitting resolution models (e.g., Wei et al. 2023; Zhu et al. 2022) predicted the general rain pattern well, but still had position errors of a few hundreds of kilometers.

Fig. 10.
Fig. 10.

As in Fig. 6, but using the testing data over the Henan region during 1100–2300 BST 20 Jul 2021. The observational HHR records (blue crosses) are plotted in each panel. The boundaries of Zhengzhou City and Henan Province are outlined.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0068.1

Similar to the results in the Jiangsu region, both PredRNNv2 and PWAFS substantially underestimate HHR probabilities, especially around Zhengzhou city (outlined in Fig. 10). Contrarily, PredRNNv2-AWS’s distribution and intensity of HHR probability closely align with the rainfall observations. The anticipated HHR areas identified by the PredRNNv2-AWS model exhibit a clustered distribution in the vicinity of Zhengzhou, with probabilities that basically exceed 85%. After a lead time of 4 h, PWAFS and PredRNNv2 give the predicted HHR biased to the west of Zhengzhou (Fig. 10), causing particularly low forecast accuracy (Fig. 11). In contrast, PredRNNv2-AWS effectively predicts most of the HHR records over Zhengzhou (Fig. 8), resulting in better performance than PWAFS and PredRNNv2 (Fig. 11).

Fig. 11.
Fig. 11.

As in Fig. 7, but using the testing data over the Henan region during 1100–2300 BST 20 Jul 2021. Shaded areas represent the 95% bootstrap confidence intervals for each experiment.

Citation: Weather and Forecasting 39, 3; 10.1175/WAF-D-23-0068.1

In short, PredRNNv2-AWS can enhance the probability intensity of predicted HHR and greatly revise position bias. Although we tested the PredRNNv2-AWS model directly over the Henan region without retraining, it still produced reliable HHR forecasts that are not inferior to those over the Jiangsu region. This demonstrates the model’s exceptional ability to generalize well.

6. Conclusions and discussion

A DL model, PredRNNv2-AWS, is proposed for short-term rainfall prediction. The present model employs PredRNNv2 as a backbone and has been specially crafted to leverage the spatial-temporal information obtained from multiple input variables. The dataset containing multiple atmospheric variables from PWAFS simulations and hourly rainfall observations from AWSs during 2018–20 is presented for hourly rainfall forecast. Twenty-four PWAFS variables and surface rainfall observations are used to provide 3D dynamic and thermodynamic information on rainy systems. Quantitative evaluation shows that surface rainfall observations significantly improve predictive accuracy (TS score) over PWAFS by 263% and 186% at the threshold of 5 mm h−1 for lead times of 1–3 and 1–13 h, respectively.

Subsequently, the machine learning model, LightGBM, is employed to forecast the HHR probability. Large AUC and BSS values demonstrate that the HHR or non-HHR event predicted by PredRNNv2-AWS can better reflect the actual conditions than PredRNNv2 and PWAFS. A representative case shows that PredRNNv2-AWS can effectively intensify predicted HHR probabilities. Surface rainfall observations facilitate the DL model to better forecast HHR evolution that closely resembles observations. The superiority of PredRNNv2-AWS in forecasting the development of the rainy system leads to a considerable improvement in HHR prediction over PWAFS and PredRNNv2 during the entire forecast. The experiment of directly testing over the Henan area, a completely different spatial domain from the training data, demonstrates the generalization of our DL model.

Many studies utilize DL or ML algorithms to rectify NWP results, with the aim of achieving more accurate predictions with higher resolution. For example, Yoshikane and Yoshimura (2022) employed support vector machines to correct precipitation forecasts with a spatial scale ranging from 2500 to 40 000 km in NWP models. However, they also noted that the forecast performance in the longer forecast lead time did not improve. On the other hand, Rojas-Campos et al. (2023) indicated that one of the primary limitations of past numerical forecasting correction methods is the insufficient utilization of atmospheric information. Thus, they used the complete low-resolution NWP as an informed prior for training a generative adversarial network that produces high-resolution precipitation maps. Nevertheless, it is undeniable that previous studies on NWP correction still demonstrate the potential for improvement in the longer forecast time. Our fundamental idea is to combine precipitation extrapolation with NWP correction. Without considering surface rainfall observations as input, the PredRNNv2 experiment establishes a connection between thermodynamic information from PWAFS and rainfall observations, including spatial and temporal constraints. Integrating surface rainfall observations and NWP forecast as input is equivalent to imposing atmospheric thermodynamic constraints for the task of sequential rainfall prediction. Compared to the PredRNNv2 experiment (without AWS), the incorporation of AWS in PredRNNv2-AWS serves to amplify the propagation of temporal information related to surface rainfall evolution, resulting in improvements in spatial distribution of predicted hourly rainfall and better performance in the longer forecast time.

In summation, the proposed architecture is versatile and can be utilized to predict various target variables obtained from numerical simulations and observations, such as visibility, wind power, solar energy, and air pollution. This model provides a robust framework for the prediction of these variables. Despite its high temporal resolution of 1 h, the forecast lead time of up to 13 h remains relatively limited. However, short-term forecasts can suffer from cumulative forecast errors when the model is recurrently called too many temporal steps. To alleviate cumulative forecast errors, Bi et al. (2023) exploit a straightforward yet effective strategy named hierarchical temporal aggregation in their Pangu-Weather model. They train four individual models for 1-, 3-, 6-, and 24-h prediction, respectively. For example, for a 23-h forecast, they execute a 6-h forecast 3 times, followed by a 3-h forecast 1 time and a 1-h forecast 2 times. We are also contemplating the incorporation of hierarchical temporal aggregation strategy in the future improvement of our PredRNN-AWS model, with the objective of achieving longer forecast lead times and better forecast performance.

Acknowledgments.

This work was supported by the National Key R&D Program of China (2022YFC3003904), the Open Research Program of the State Key Laboratory of Severe Weather (2023LASW-B16), Natural Science Foundation of Jiangsu Province (BK20231107), the Basic Research Fund of CAMS (2020Z011, 2021Z003, and 2023Z017), and the Key Innovation Team of China Meteorological Administration (CMA2022ZD07). The authors thank anonymous reviewers for providing insightful comments that greatly improved the quality of the article. The authors thank Jiangsu Meteorological Observatory and Jiangsu Meteorological Information Center for providing the data and computing resources used in this paper.

Data availability statement.

The datasets are available at https://doi.org/10.7910/DVN/7EQVQT.

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