Improving the heavy rainfall forecasting using a weighted deep learning model

Weather forecasting has been playing an important role in socio-economics. However, operational numerical weather prediction (NWP) is insufficiently accurate in terms of precipitation forecasting, especially for heavy rainfalls. Previous works on NWP bias correction utilizing deep learning (DL) methods mostly focused on a local region, and the China-wide precipitation forecast correction had not been attempted. Meanwhile, earlier studies imposed no particular focus on strong rainfalls despite their severe catastrophic impacts. In this study, we propose a DL model called weighted U-Net (WU-Net) that incorporates sample weights for various precipitation events to improve the forecasts of intensive precipitation in China. It is found that WU-Net can further improve the forecasting skill of heaviest rainfall comparing with the ordinary U-Net and ECMWF-IFS. Further analysis shows that this improvement increases with growing lead time, and distributes mainly in the eastern parts of China. This study suggests that a DL model considering the imbalance of the meteorological data could further improve the precipitation forecasting generated by numerical weather prediction.

1 Introduction

Weather forecast has been playing an important role in socio-economics, covering many areas such as agriculture, transportation, business and energy management. Accurate weather forecast, especially rainfall prediction, is essential to the well-operation of society. Precipitation exerts significant impacts on socio-economics, for example, extreme precipitation events usually induce severe disasters such as floods and mudslides (Easterling et al., 2000; Changnon et al., 2000; Wang and Yuan, 2018; Tao et al., 2020; Wang et al., 2021). However, current operational weather forecast and seasonal prediction of precipitation is not satisfying yet (Wang and Yuan, 2018; Cloke and Pappenberger, 2009; Siddique et al., 2015; Kobold and Sušelj, 2005). There is intrinsic uncertainty in operational weather forecast based mainly on numerical weather prediction (NWP) models, due to the approximation in representing atmospheric dynamics and physics (Buizza et al., 1999; Palmer, 2000; Slingo and Palmer, 2011). Post-processing methods to correct NWP have been found to be effective in improving the forecast skill for decades (e.g., Glahn and Lowry, 1972; Wilks, 2009).

Model output statistics (MOS) method, as a traditional post-processing method, is highly utilized to promote forecast skills by establishing a linear relationship between model outputs and predictands (Glahn and Lowry, 1972; Wilks, 2009; Marzban et al., 2006). The Kalman filter approach is another bias correction method, which is able to update the real-time correction, while MOS is not (Homleid, 1995). Moreover, Robertson et al. (2013) utilized a Bayesian joint probability model approach, which joined the predictands and the model predictors into a joint probability distribution, to generate predicted probability distributions from the NWP of rainfall by Bayesian inference. However, most of these approaches are specific to individual observation stations.

Recently, deep learning (DL) techniques have been successfully applied in atmospheric and environmental research, owing to explosive computing resource and increasing amounts of meteorological datasets (Shen, 2018; Boukabara et al., 2019). DL is a kind of data-driven approaches that can extract features from big data on its own, for example, detecting spatial structures in grided data automatically, which is difficult to do with traditional methods. Furthermore, DL models are comprised of much more parameters than traditional ones, leading to more sophisticated results. Convolutional neural network (CNN) is widely used in meteorological and climatological applications for its capacity in processing images, which is a lot in common with processing grided data (e.g., Ham et al., 2019; Lagerquist et al., 2019; Wen et al., 2019; Weyn et al., 2020). Ham et al. (2019) constructed a statistical forecast model using CNN, which produced skillful ENSO forecast. Lagerquist et al. (2019) employed a CNN to identify Synoptic-Scale Fronts. Weyn et al. (2020) designed CNNs operating on cubed sphere to improve data-driven global weather prediction.

CNN-based architectures, together with other DL approaches, are also utilized in the post-processing of NWP (Rasp and Lerch, 2018; Han et al., 2021; Hu et al., 2021). U-Net is a CNN-based architecture first proposed for biomedical segmentation, and has acquired some achievements in the estimate of weather factors (Ronneberger et al., 2015; Larraondo et al., 2019). In this study, we will further explore its application in forecast correction of precipitation.

This paper demonstrates a deep learning method to correct grided precipitation forecast data from NWP using U-Net models. We selected a domain covering the whole of China, which has not been studied on in existing work, as previous researches usually focused on local regions (Han et al., 2021; Han et al., 2022). NWP data from the European Center for Medium-range Weather Forecast Integrated Forecasting System (ECMWF-IFS) was adopted to be corrected, and the ECMWF Fifth-generation Reanalysis (ERA-5) was used as the ground truth. Notably, DL is essentially a statistical approach so that its performance is highly dependent on sample sizes. As precipitation is subject to skewed distribution with a long tail at the big end, the amount of large precipitation sample would be considerably smaller than that of tiny small precipitation, which could influence the performance of DL on extreme rainfalls (Tan et al., 2021; Yang et al., 2022; Fu et al., 2022). Therefore, we adopted a strategy of assigning heavier weights to larger precipitation grids, and investigated its improvement in forecasting heavy rainfalls.

The remainder of this paper is as follows. Section 2 introduces the employed dataset and methodology. Section 3 presents the experiment results, and finally, Section 4 concludes this work.

2 Data and methods

2.1 Dataset

In this study, we employed the NWP data from the ECMWF-IFS in the range of 2017–2022, at a resolution of 0.25° × 0.25°. The forecast issued twice a day at 0000 UTC and 1200 UTC, respectively, with a lead time from 6 to 72 h. The ground truth used in supervised learning is the ERA-5 dataset, which is often seen as the actual condition in bias correction. Additionally, elevation data from the ETOPO1 is also involved as correction factor. These data can be downloaded from https://www.ecmwf.int and https://www.ncei.noaa.gov/products/etopo-global-relief-model (Hersbach et al., 2020; Amante and Eakins, 2009). The study domain is located at 15°–54.75°N, 70°–134.75°E, which covers the whole of China.

This study used 16,000 instances from the ECMWF-IFS and the ERA-5, which were split into training (12000 instances) and testing datasets (4000 instances). The models are trained with data in all lead times to increase the sample size. Nevertheless, the sample size is somewhat small due to data incompleteness. The limited data size may affect our evaluation of models, but does not affect our cross-sectional comparison of WU-Net and U-Net performance. The inputs of the correction models include forecasted precipitation, 2 m-temperature, 10 m-wind, 500 hPa-geopotential height, sea-level pressure and relative humidity from the ECMWF-IFS, precipitation at the issue time, land-sea distribution, lake cover, high vegetation cover and low vegetation cover from the ERA-5 and elevation from the ETOPO1. The variables involved have been listed in Table 1. The original precipitation data has been converted to 6 h cumulative precipitation, and divided into five levels as shown in Table 2.

TABLE 1

TABLE 1. The input variables of the correction model.

TABLE 2

TABLE 2. The gradation of precipitation. Unit: mm.

2.2 Models

We applied U-Net (Figure 1) to realize the mapping from the input variables to the output correction field (Ronneberger et al., 2015). U-Net is a deep learning architecture consisting of a down-sampling encoder and a symmetrical up-sampling decoder. The encoder uses convolution and max-pooling layers to extract features at different levels, while the decoder is a reverse process using the same layers besides up-sampling layers to decode the features into correction fields. Recently, U-Net has been utilized in atmospheric science and proved to be effective and promising in weather prediction (Larraondo et al., 2019; Han et al., 2021; Hu et al., 2021).

FIGURE 1

FIGURE 1. The architecture of the U-Net using in this study.

Figure 1 illustrates the structure of the U-Net utilized in this investigation. The blue arrows depict the flow within the encoder and the decoder. The red arrows represent skip connections, which concatenate features from different levels of the encoder to the decoder counterpart, providing detailed information of different resolution. In this paper, the input is consisted of 13 2D-fields concatenated along channel, which are listed in Table 1, and the models would output a single-channel 2D-field of precipitation level. We blended all the lead time from 6 to 72 h together in the dataset, so there would not be the problem of cumulative errors generated from iteration.

2.3 Metrics

We mainly adopted Threat Score (TS) to evaluate the model results, which can be calculated as follows:

$TS=\frac{Hits}{Hits+FalseAlarms+Misses}$

and False Alarm Rate (FAR) was also used, for comprehensive knowledge, which is defined as:

$FAR=\frac{FalseAlarms}{Hits+FalseAlarms}$

where $Hits$, $FalseAlarms$, and $Misses$ are determined by the confusion matrix (Table 3). To distinguish whether the observation and the prediction are True or not, we chose 0.1, 2.5, 10, and 20 mm as thresholds, according to the gradation in Table 2. Model with high TS and low FAR would be considered as well-performed.

TABLE 3

TABLE 3. Confusion matrix to calculate metrics. True or False is determined by the chosen thresholds of 0.1, 2.5, 10, and 20 mm.

2.4 The precipitation weights

Given the fact that precipitation quantity is not normally distributed, with severe rainfall comprising a small proportion of all sample points (Figure 2), ordinary models are unable to effectively distill signals about heavy rainfalls, which are of interest to us. Thus, we assigned a weight to each sample point according to its precipitation level when training the model. The weights were calculated by the formula:

$w_i=\frac{S}{n\times s_i}$

where $S$ is the number of all the sample points, $n$ is the number of levels and $s_i$ is the number of the sample points of level $i$. The loss function correspondingly turns into the following form:

$Loss\left(x\right)=-w_{\arg y_j=1}{\displaystyle \sum }_{j=1}^n{y}_j\log P_j\left(x\right)$

FIGURE 2

FIGURE 2. The occurrence of each precipitation level in the dataset.

Among which $j$ represents each component of probability vector, and $w_{\arg y_j=1}$ means the weight gets $w_j$ when the ground truth of the instance is in class $j$. The model is then referred as weighted U-Net (WU-Net).

3 Improving the heavy rain prediction

Figure 3 displays the relative quantile error (RQE) of the ECMWF-IFS relative to the ERA-5, using

$RQE={\displaystyle \sum }_{d=1}^D\frac{{\widehat{Q}}_d-Q_d}{Q_d}$

where ${\widehat{Q}}_d$ and $Q_d$ are the quantiles calculated on NWP and ground true, respectively, D = 25, corresponding to the percentiles from 75% to 99% with an interval of 1% (Pathak et al., 2022; Bi et al., 2022). It is evident that NWP’s ability to forecast heavy rainfall is still deficient, as it tends to underestimate the intensity of large precipitation. Similar limitations exist in the results of deep learning models, which are primarily attributable to the small number of extreme weather samples (e.g., Pathak et al., 2022). This section will demonstrate how the WU-Net could improve the heavy rainfall prediction.

FIGURE 3

FIGURE 3. Relative quantile error (RQE) of the ECMWF-IFS.

Figure 4A presents the TS of the ECMWF-IFS, U-Net and WU-Net, respectively. The TS rapidly decreases as the threshold increases for the ECMWF-IFS, from 0.65 to 0.18, indicating its limitation in heavy rainfall forecast. Compared to the NWP model, the two deep learning models outperform it at all precipitation levels. The U-Net model improves the forecast for each gradation by greater than 0.1, particularly for that with a threshold of 20 mm, whose TS increases from 0.18 to 0.34. By considering the sample weights, WU-Net further improves the heavy rainfall forecast relative to U-Net, with a TS of 0.53, which is a 194.4% improvement over the ECMWF-IFS and a 55.9% improvement over U-Net. Note that the TS of WU-Net model is marginally inferior to U-Net at forecasting light precipitation. This difference is mostly due to the reduced weight of light precipitation which has large sample sizes. FAR is similar to TS, as shown in Figure 4B. U-Net performs better than the ECMWF-IFS under all the four thresholds. WU-Net, though beaten by U-Net at the first three precipitation level, achieves a maximum improvement under threshold 20 mm, with a 62.5% reduction over ECMWF-IFS and a 41.3% reduction over U-Net. Overall, the results illustrate that adding a higher weight on the large precipitation events which seldom happen can make a great improvement on the forecast skill of them.

FIGURE 4

FIGURE 4. (A) TS and (B) FAR of the ECMWF-IFS, U-Net and WU-Net, respectively, under the thresholds of 0.1, 2.5, 10, and 20 mm. The orange, green, and blue represent the ECMWF-IFS, U-Net and WU-Net, respectively.

This improvement can also be seen in different seasons (Figure 5). For TS, WU-Net and U-Net both do better than NWP model at all rainfall levels in all seasons. WU-Net gets even higher scores for stronger rainfall (under thresholds 10 and 20 mm), but a slightly lower score for light rain relative to U-Net. The biggest change happens in spring, with improvements of 25.9%, 54.1%, 87.0%, and 112.5% for U-Net and 19.0%, 51.4%, 130.4%, and 256.3% for WU-Net compared to the ECMWF-IFS under thresholds 0.1, 2.5, 10, and 20 mm, respectively. As to FAR, WU-Net makes the greatest improvement for the highest precipitation level in all seasons, reaching 37.0%, 68.6%, 67.6%, and 64.1% for winter, spring, summer, autumn, respectively.

FIGURE 5

FIGURE 5. (A) TS and (B) FAR as Figure 4, but for different seasons.

In addition to the improvement in different seasons throughout a year, the two deep learning models have significantly enhanced the forecasting skill on daily scale (Figure 6). For the maximum level of rainfall, the highest TS occurs at 0 and 6 o’clock, generated by WU-Net, 0.39 points higher than the ECMWF-IFS and 0.21 points higher than U-Net. The lowest FAR also occurs at 0 o’clock, achieving 0.22.

FIGURE 6

FIGURE 6. (A) TS and (B) FAR as Figure 4, but for different time.

Figure 7A shows the variation of TS over increasing lead time. The forecast skill of the ECMWF-IFS diminishes rapidly as lead time increases, due to the chaotic effect of the atmosphere. In contrast, the other two deep learning models exhibit a less pronounced decreasing trend and higher TS. Comparison of the two suggests that WU-Net outperforms U-Net for all lead time when the threshold is greater than 2.5 mm, but receives a slightly lower score when the threshold is less than 2.5 mm. The comparison is generally consistent with Figure 4, which suggests that WU-Net has a better forecast skill for heavier rainfall, but a slightly lower skill for lighter rainfall. Figure 7B shows the TS improvement of WU-Net and U-Net on the ECMWF-IFS. The enhancement in forecasting skill of the two deep learning models relative to the ECMWF-IFS does not diminish as lead time grows, but rather increases gradually, especially for WU-Net. This increase suggests that WU-Net and U-Net can not only enhance the overall forecast performance, but also the upper forecast limit.

FIGURE 7

FIGURE 7. (A) The variation of TS for the ECMWF-IFS, U-Net and WU-Net, from top to bottom: thresholds 0.1, 2.5, 10, and 20 mm. (B) The TS improvement of U-Net and WU-Net on the ECMWF-IFS as percentage, from top to bottom: thresholds 0.1, 2.5, 10, and 20 mm. The orange, green and blue represent the ECMWF-IFS, U-Net and WU-Net, respectively.

Figure 8 displays the horizontal distribution of TS. For small precipitation, all three models have better forecasts in East China, North China, and South China, and inferior forecasts for Northwest China, which may be related to the sparse observations there. For stronger precipitation, the forecast skill is higher in eastern China than in western China, which may be related to more observations in the East and more complex and large topography (e.g., Tibetan Plateau) in the West. Compared with the ECMWF-IFS, WU-Net and U-Net have a substantial improvement in overall light rain forecast. For stronger precipitation, the greater improvement of the deep learning models is distributed in the eastern parts of China. As the threshold rises, Northwest China gets great improvement under thresholds 0.1 and 2.5 mm, but misses value for heavier rainfall. It may be because that precipitation above 10 mm per 6 h rarely happens in these areas.

FIGURE 8

FIGURE 8. (A) TS distribution, from top to bottom: the ECMWF-IFS, U-Net and WU-Net, and from left to right: thresholds 0.1, 2.5, 10, and 20 mm. (B) Spatial improvement of TS as percentage, from top to bottom: U-Net on the ECMWF-IFS, WU-Net on the ECMWF-IFS and WU-Net on U-Net, and from left to right: thresholds 0.1, 2.5, 10, and 20 mm. The blank areas derive from the denominator of zero when calculating the TS, due to all the samples on the grids are True Negative (to see in Table 3). The areas out of China have been masked out.

Figure 9 provides three cases from the validation dataset, and case 1 occurred during the process of the severe rainstorm disaster in Henan province on July 21, 2021. The ERA-5 precipitation field, the ECMWF-IFS output, the U-Net and WU-Net correction are presented sequentially. In these cases, the distribution and intensity accuracy are enhanced after correction. More specifically, for light rainfall, both the U-Net and the WU-Net correction fields are more related to the ERA-5 than the ECMWF-IFS, but WU-Net tends to extend the precipitation areas, which is consistent with the relatively high FAR on light rainfall for WU-Net. For heavy rainfall, WU-Net outperforms other models, as the distribution of “heavy rain” and “rainstorm” is very close to those in ERA-5.

FIGURE 9

FIGURE 9. Examples of precipitation forecasts by different models. (A) 21/07/2021 0000 UTC, lead time 48 h. (B) 13/08/2018 0600 UTC, lead time 42 h. (C) 27/07/2021 1200 UTC, lead time 36 h.

4 Conclusion

In this paper, we used U-Net based models to correct the ECMWF-IFS forecast for 6 h cumulative precipitation, and evaluated their performance. Via assigning larger weights to heavier rainfall events, we partly solved the problem of imbalanced data distribution.

The results present that both U-Net and WU-Net can improve the ECMWF-IFS forecast significantly, while WU-Net outperforms U-Net with regarding to intensive precipitation, by considering the sample weights. Specifically, U-Net improves the forecast for each gradation by greater than 0.1 in TS, particularly for heavy rainfall. The WU-Net model does even better on the heaviest precipitation level, as is triple the ECMWF-IF and 55.9% higher than the ordinary U-Net. Moreover, the improvement increases with growing lead time, indicating an extended upper forecast limit.

The quantitative results in the article should be treated with caution due to sample limitations, but this does not prevent the conclusion that WU-Net has the potential to enhance heavy rainfall forecasting skills. The capacity of WU-Net should be further validated in the future using a more complete and larger dataset.

Considering the normalcy, integrity, and accessibility of the data, the study uses the reanalysis dataset as the ground truth which is common in previous studies (e.g., Larraondo et al., 2019; Han et al., 2021; Hu et al., 2021). Given that there are still discrepancies between the reanalyzed precipitation data and observations, we will employ the observed data for additional testing and modeling in the future. Moreover, it is worthwhile to investigate how to integrate two deep learning models (U-Net and WU-Net) to further improve forecasting skill.

Data availability statement

Publicly available datasets were analyzed in this study. ECMWF-IFS is on the page: https://www.ecmwf.int/en/forecasts/dataset/thorpex-interactive-grand-global-ensemble. ERA-5 can be found here: https://www.ecmwf.int/en/forecasts/dataset/ecmwf-reanalysis-v5. And EPOTO1 can be downloaded from: https://www.ncei.noaa.gov/products/etopo-global-relief-model.

Author contributions

YC: Conceptualization, methodology, data curation, investigation, formal analysis, visualization, writing—original draft; GH: Funding acquisition, resources, supervision; YW: Conceptualization, methodology, funding acquisition, resources, supervision, writing—review and editing; WT: Supervision; QT: Resources; KY: Supervision; JZ: Supervision; HH: Supervision.

Funding

This work was supported by the Second Tibetan Plateau Scientific Expedition and Research (STEP) program (grant no. 2019QZKK0102) and the National Natural Science Foundation of China (42141019, 41831175, 91937302 and 41721004) and the Strategic Priority Research Program of Chinese Academy of Sciences (XDA20060501).

Conflict of interest

Author QT was employed by the company CMA; Author JZ was employed by the company Shanghai Investigation, Design and Research Institute Co., Ltd.; Author HH was employed by the company Zhejiang Institute of Communications Co., Ltd.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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