Quantitative Precipitation Forecasting Using Multi-Model Blending with Supplemental Grid Points: Experiments and Prospects in China

基于相似网格点的多源定量降水预报融合算法

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  • Corresponding author: Kan DAI, daikan1998@163.com
  • Funds:

    Supported by the National Key Research and Development Program of China (2017YFC1502004), Special Project for Forecasters of China Meteorological Administration (CMAYBY2020-162), and Special Project for Forecasters of National Meteorological Center (Y202135)

  • doi: 10.1007/s13351-021-0172-5

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  • Quantitative Precipitation Forecast (QPF) is a challenging issue in seamless prediction. QPF faces the following difficulties: (i) single rather than multiple model products are still used; (ii) most QPF methods require long-term training samples not easily available, and (iii) local features are insufficiently reflected. In this work, a multi-model blending (MMB) algorithm with supplemental grid points (SGPs) is experimented to overcome these shortcomings.The MMB algorithm includes three steps: (1) single-model bias-correction, (2) dynamic weight MMB, and (3) light-precipitation elimination. In step 1, quantile mapping (QM) is used and SGPs are configured to expand the sample size. The SGPs are chosen based on similarity of topography, spatial distance, and climatic characteristics of local precipitation. In step 2, the dynamic weight MMB uses the idea of ensemble forecasting: a precipitation process can be forecast if more than 40% of the models predict such a case; moreover, threat score (TS) is used to update the weights of ensemble members. Finally, in step 3, the number of false alarms of light precipitation is reduced, thus alleviating unreasonable expansion of the precipitation area caused by the blending of multiple models.Verification results show that using the MMB algorithm has effectively improved the TS and bias score (BS) for blended 6-h QPF. The rate of increase in TS for heavy rainfall (25-mm threshold) reaches 20%−40%; in particular, the improvement has reached 47.6% for forecast lead time of 24 h, compared with the ECMWF model. Meanwhile, the BS is closer to 1, which is better than any single-model forecast. In sum, the QPF using MMB with SGPs shows great potential to further improve the present operational QPF in China.

    定量降水预报(QPF)是无缝隙精细化网格预报中最具挑战的部分,目前存在需要长时间序列的训练样本、大多基于单模式订正及局地偏差特征反应不足等问题。本文提出基于相似网格点的多源定量降水预报融合算法,以解决上述问题。该算法融合多家模式6小时降水预报产品生成最终预报产品。

    本文提出的融合算法分为模式偏差订正、动态权重融合和削空后处理三个步骤。其中模式偏差订正采用分位映射法,利用相似网格点(supplemental grid points)扩充用于建模的样本总量;相似网格点考虑了网格点之间地形、空间距离和降水气候特征之间的相似度。动态权重融合基于预报的Treat Score(TS)评分更新动态融合权重。融合后使用弱降水削空对融合结果进行后处理;弱降水削空采用概率预报的思想,当参与融合的模式中有超过40%的模式认为该网格点有降水时,才在该点预报降水。

    对2019年4–10月QPF的检验结果表明,多模式融合算法可有效改进各量级降水的TS和BiasScore (BS)评分。对暴雨量级(25mm阈值)的TS提升率可达20%–40%,其中24小时时效相较ECMWF模式提升47.6%;同时,融合方案BS评分更接近于1,优于单模式预报。


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  • Fig. 1.  Flowchart of the multi-model blending (MMB) algorithm.

    Fig. 2.  Locations of supplemental grid points (SGPs) for August 2019 over various sub-areas of the study region in China. The color shadings on the map denote the 95th percentile of the 6-h accumulated precipitation amounts for the month, determined from the data in 2017−2018. Hollow symbols denote the original points for which their SGPs were searched. Solid symbols indicate the SGPs. Darker symbols indicate a better match, and lighter symbols a poorer match. The original points (hollow) and SGPs (solid) are in various shapes for better viewing effect.

    Fig. 3.  (a) Threat scores (TSs) and (b) bias scores (BSs) for 6-h QPF derived from the raw models and the blended forecast (QMWM5), averaged from April to October 2019. The threshold is 0.1 mm.

    Fig. 4.  As in Fig. 3, but with the 25-mm threshold.

    Fig. 5.  Changes in the weight of each model during the blending process.

    Fig. 6.  Distributions of 6-h quantitative precipitation forecast (QPF). The start time of the forecast is 0000 UTC 5 June 2019, and the forecast lead time is 42 h. QMWM5 indicates the blended forecast and NMIC indicates the analyzed precipitation data provided by the National Meteorological Information Center (NMIC) of the China Meteorological Administration (CMA).

    Fig. 7.  As in Fig. 6, but with the forecast start time at 0000 UTC 2 September 2019, and the forecast lead time of 30 h.

    Fig. 8.  Distributions of 72-h precipitation amount associated with Tropical Cyclone Lichma during 9−11 August 2019. (a) The current best operational forecast in NMC of CMA, (b) our method, (c) forecast made by the Chief Forecaster of NMC, and (d) the analyzed precipitation data provided by NMIC.

    Table 1.  Models used in the multi-model blending (MMB) algorithm in this study

    Model nameTypeSpatial resolutionLead time/IntervalData source
    ECMWFGlobal deterministic model0.125°0–240 h/6 hourlyChina integrated meteorological information service system (CIMISS)
    NCEP0.5°0–240 h/6 hourly
    GRAPES-GFS0.5°0–240 h/6 hourly
    GRAPES-MesoRegional mesoscale model0.1°0–84 h/6 hourlyChina Meteorological Administration NWP cloud storage
    Shanghai-Meso9 km0–72 h/6 hourly
    Download: Download as CSV

    Table 2.  Verification thresholds (T)

    Product nameThreshold (mm)
    6-h QPF0.1, 4.0, 13.0, 25.0, and 60.0
    Download: Download as CSV

    Table 3.  Threat score (TS) and bias score (BS) for raw- and quantile-mapped ECMWF (Raw-EC, EC-QM1, and EC-QM2 ) 6-h quantitative precipitation forecasts (QPFs) from April to October 2019. The start time of the forecast is 0000 UTC and the forecast lead time is 18–72 h. The CMPAS-V2.1 dataset is used as the observation data

    Model nameTSBS
    0.1 mm4 mm13 mm25 mm60 mm0.1 mm4 mm13 mm25 mm60 mm
    Raw-EC0.3620.2530.1330.0650.0131.9411.2680.7740.6430.692
    EC-QM10.3880.2470.1440.0870.0170.9681.3421.3911.5931.284
    EC-QM20.3860.2470.1410.0790.0170.9991.3371.4241.5701.323


    Download: Download as CSV

    Table 4.  As in Table 3, but for quantile-mapped ECMWF, NCEP, GRAPES-GFS, GRAPES-Meso, Shanghai-Meso, and the MMB forecast of this study (QMWM5)

    Model nameTSBS
    0.1 mm4 mm13 mm25 mm60 mm0.1 mm4 mm13 mm25 mm60 mm
    ECMWF0.3880.2470.1440.0870.0170.9681.3421.3911.5931.284
    NCEP0.3610.2340.1490.0750.0200.9671.3560.9080.4680.433
    GRAPES-GFS0.3250.1860.1040.0570.0130.9641.0711.3701.9173.807
    GRAPES-Meso0.3250.1870.1050.0580.0150.9741.1281.4462.0253.917
    Shanghai-Meso0.3460.2060.1190.0680.0190.9151.0621.4112.0424.361
    QMWM50.3890.2780.1710.0990.0260.7971.2111.1230.9120.526
    Download: Download as CSV

    Table 5.  As in Table 3, but for MMB products generated by TS only (Blending-TS) and by TS and BS simultaneously (Blending-TSBS)

    Model nameTSBS
    0.1 mm4 mm13 mm25 mm60 mm0.1 mm4 mm13 mm25 mm60 mm
    Blending-TS0.3890.2780.1710.0990.0260.7971.2111.1230.9120.526
    Blending-TSBS0.3880.2620.1530.0850.0230.8631.2061.3031.4321.379
    Download: Download as CSV

    Table 6.  As in Table 3, but for multi-model blended product (Blended-TS) and probability-matched multi-model blended product (Blended-TSPM)

    Model nameTSBS
    0.1 mm4 mm13 mm25 mm60 mm 0.1 mm4 mm13 mm25 mm60 mm
    Blended-TS0.3890.2780.1710.0990.0260.7971.2111.1230.9120.526
    Blended-TSPM0.3700.2740.1700.1040.0270.9691.3421.3911.5931.284
    Download: Download as CSV

    Table 7.  TSs and BSs of 24-h QPF from April to October 2019. The start time of the forecast is 0000 UTC and the forecast lead time is 36 h. The result is relative to observations at 2193 national stations in central and eastern China

    Model nameTSBS
    0.1 mm10 mm25 mm50 mm100 mm0.1 mm10 mm25 mm50 mm100 mm
    Blended0.6160.4190.3140.2300.1321.0421.2471.0920.8360.405
    Operational0.6300.4270.3210.2370.1591.1171.1981.2051.2161.383
    Download: Download as CSV
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Quantitative Precipitation Forecasting Using Multi-Model Blending with Supplemental Grid Points: Experiments and Prospects in China

    Corresponding author: Kan DAI, daikan1998@163.com
  • 1. National Meteorological Center, China Meteorological Adminstration, Beijing 100081
  • 2. Dalian Meteorological Bureau, Dalian 116001
  • 3. China Meteorological Administration Training Center, Beijing 100081
Funds: Supported by the National Key Research and Development Program of China (2017YFC1502004), Special Project for Forecasters of China Meteorological Administration (CMAYBY2020-162), and Special Project for Forecasters of National Meteorological Center (Y202135)

Abstract: Quantitative Precipitation Forecast (QPF) is a challenging issue in seamless prediction. QPF faces the following difficulties: (i) single rather than multiple model products are still used; (ii) most QPF methods require long-term training samples not easily available, and (iii) local features are insufficiently reflected. In this work, a multi-model blending (MMB) algorithm with supplemental grid points (SGPs) is experimented to overcome these shortcomings.The MMB algorithm includes three steps: (1) single-model bias-correction, (2) dynamic weight MMB, and (3) light-precipitation elimination. In step 1, quantile mapping (QM) is used and SGPs are configured to expand the sample size. The SGPs are chosen based on similarity of topography, spatial distance, and climatic characteristics of local precipitation. In step 2, the dynamic weight MMB uses the idea of ensemble forecasting: a precipitation process can be forecast if more than 40% of the models predict such a case; moreover, threat score (TS) is used to update the weights of ensemble members. Finally, in step 3, the number of false alarms of light precipitation is reduced, thus alleviating unreasonable expansion of the precipitation area caused by the blending of multiple models.Verification results show that using the MMB algorithm has effectively improved the TS and bias score (BS) for blended 6-h QPF. The rate of increase in TS for heavy rainfall (25-mm threshold) reaches 20%−40%; in particular, the improvement has reached 47.6% for forecast lead time of 24 h, compared with the ECMWF model. Meanwhile, the BS is closer to 1, which is better than any single-model forecast. In sum, the QPF using MMB with SGPs shows great potential to further improve the present operational QPF in China.

基于相似网格点的多源定量降水预报融合算法

定量降水预报(QPF)是无缝隙精细化网格预报中最具挑战的部分,目前存在需要长时间序列的训练样本、大多基于单模式订正及局地偏差特征反应不足等问题。本文提出基于相似网格点的多源定量降水预报融合算法,以解决上述问题。该算法融合多家模式6小时降水预报产品生成最终预报产品。

本文提出的融合算法分为模式偏差订正、动态权重融合和削空后处理三个步骤。其中模式偏差订正采用分位映射法,利用相似网格点(supplemental grid points)扩充用于建模的样本总量;相似网格点考虑了网格点之间地形、空间距离和降水气候特征之间的相似度。动态权重融合基于预报的Treat Score(TS)评分更新动态融合权重。融合后使用弱降水削空对融合结果进行后处理;弱降水削空采用概率预报的思想,当参与融合的模式中有超过40%的模式认为该网格点有降水时,才在该点预报降水。

对2019年4–10月QPF的检验结果表明,多模式融合算法可有效改进各量级降水的TS和BiasScore (BS)评分。对暴雨量级(25mm阈值)的TS提升率可达20%–40%,其中24小时时效相较ECMWF模式提升47.6%;同时,融合方案BS评分更接近于1,优于单模式预报。


    • Quantitative precipitation forecasting (QPF) is an important part of seamless prediction. Seamless prediction has become one of the major development trends in weather forecasting (Rauser et al., 2017). For instance, a national digital forecast database was built in USA (Glahn and Ruth, 2003), which provides seamless gridded weather forecast products. Likewise, based on the ECMWF-Ensemble Prediction System (EPS), the Integrated Nowcasting through Comprehensive Analysis (INCA; Haiden et al., 2011), Application of Research to Operations at Mesoscale EPS (AROME-EPS; Seity et al., 2011), and Aire Limitee Adaptation Dynamique Developpement International-Limited-Area Ensemble Forecasting (ALADIN-LAEF; Wang et al. 2011), the European Union (EU) developed a seamless probability prediction system to serve the public (Wastl et al., 2018). China began developing its seamless prediction system in 2014 (Jin et al., 2019), including establishment of a merged subjective/objective grid forecasting platform (Gao et al., 2014; He et al., 2018; Tang et al., 2018; Wang et al., 2018), investigation of post-processing techniques for different forecast lead times and physical quantities (Cao et al., 2016; Xiong, 2017), and design of special verification algorithms for high-resolution gridded forecast products (Liu and Niu, 2013; Wei et al., 2019). Despite all these developments, the QPF in seamless prediction still faces considerable challenges. The mixed discrete/continuous characteristics of precipitation makes QPF more difficult than continuous variables such as temperature and humidity (Scheuerer and Hamill, 2015), although accurate QPF on high temporal and spatial resolutions is of great benefit for disaster prevention/mitigation and other public service applications.

      QPF is usually derived from post-processing of numerical weather prediction (NWP) model outputs. The statistical methods for such a post-processing include two categories: parametric methods that rely on certain prescribed statistical probability distribution and non-parametric methods with no prescribed statistical distribution but with requirement for large training samples (Dai et al., 2018). Bayesian Model Averaging (BMA; Raftery et al., 2005) is a common parametric method; while the commonly used non-parametric statistical methods include frequency matching (Zhu and Luo, 2015), probability matching (PM; Ebert, 2001), quantile mapping (QM; Maraun, 2013; Hamill et al., 2017), multi-model similarity integration (Chen et al., 2005; Liu and Niu, 2013; Dai et al., 2016), and the optimal percentile method (Dai et al., 2016).

      Zhang et al. (2016) used a logistic discriminant model to derive/forecast heavy precipitation. Two consecutive flood season tests in 2013 and 2014 showed that the threat score (TS) of their method was higher than that of the ECMWF’s. Wu et al. (2017) designed an OTS/OETS (optimal threat score/optimal equitable threat score) algorithm, and a test for 2014–2015 showed that the QPF using OTS/OETS performed better than that using the frequency match method, and the precipitation forecasts obtained with OTS/OETS were improved at all lead times. Despite these improvements, at present, there are still some major problems with the precipitation post-processing algorithms.

      (1) Most post-processing algorithms are still aimed at improving single NWP model products, with the integration and analysis of multi-source precipitation forecasts carried out manually by forecasters. With the rapid development of NWP models (Dee et al., 2011; Copernicus Climate Change Service, 2017; Shen et al., 2017), an increasingly large number of precipitation products become available, which need to be taken into consideration smartly by advanced QPF schemes.

      (2) Traditional non-parametric QPF algorithms require long time-series of historical data as the training data, but the rapid, iterative upgrading of NWP models makes it difficult to construct such long series of training data with inconsistent model bias, especially for multi-model blending (MMB) algorithms; therefore, it is necessary to design a non-parametric method with short-time series data.

      (3) Most post-processing algorithms use global correction, which means that all grid points in the domain are considered equally, which cannot reflect the local deviations caused by the geographical locations and climate characteristics of different grid points.

      For the first problem, MMB is widely adopted. Research based on TIGGE [The Observing System Research and Predictability Experiment (THORPEX; Bougeault et al., 2010) Interactive Grand Global Ensemble (TIGGE; Swinbank et al., 2016)] has shown that the forecasting accuracy of multi-model merged products is better than that of independent forecasts (Zhi et al., 2012; Zhang et al., 2015). As for blending, two fundamental approaches, either in the physical forecast space or in theprobability space (Vannitsem et al., 2020), are used.

      Blending in physical space generally corresponds to deterministic forecasts, with the most straightforward method being to assign different weights to products based on a specific score, and then calculating the weighted average. For example, in their blending of precipitation, Ji et al. (2020) used an object-based diagnos-tic evaluation method to generate the merging weights, and the results were found to be better than those obtained using traditional methods. In the field of nowcasting, a more widely used method is to combine model forecast and radar extrapolation products to generate the final forecasts (Yu et al., 2015; Nerini et al., 2019). Besides weighted blending, other commonly used blending algorithms include BMA (Raftery et al., 2005), ensem-ble model output statistics (EMOS; Scheuerer, 2014) and some deep learning-based algorithms (Yuan et al., 2007; Ahmed et al., 2020; Pakdaman et al., 2020).

      Blending in probability space corresponds to the probability forecast. To generate a reasonable probability forecast field (Kober et al., 2012; Bouttier and Marchal, 2020), the forecasting of neighbors is used to expand the total number of members (Theis et al., 2005; Schwartz and Sobash, 2017).

      The US National Weather Service (NWS) developed the National Blend of Models (NBM) system (Hamill et al., 2017; Hamill and Scheuerer, 2018; Craven et al., 2020), which is able to blend more than 30 kind of deterministic and ensemble forecasts, to generate the final products, while the EU’s PROFORCE (bridging of probabilistic forecasts and civil protection) forecasting system blends the forecast data of four EPSs (ECMWF, NCEP, UK Met Office, and French Meteorological Agency) to provide probabilistic forecasting products to the public (Wastl et al., 2018).

      In China, Cao et al. (2016) used subjective/objective blending, precipitation inversion, statistical downscaling, and time splitting, to build a national grid-based QPF system that was put it into operation at the National Meteorological Center (NMC) of China Meteorological Administration (CMA) in 2014, which can provide with 0–168-h, 10-km resolution, and 3-h gridded QPF. Verification showed that their method was able to improve the temporal and spatial refinement of precipitation forecasts significantly.

      For the second and third problems, the general solution is to expand the total number of samples based on similarity concepts, and then model each grid point independently. For example, in the NBM system, based on the similarity of precipitation characteristics, geographic information (including terrain and slope), and spatial distance, supplemental grid points (SGPs) are obtained (Hamill et al., 2017). The data at the SGPs are regarded as expanded data. For each grid point, the QM method is used to correct the bias of the model forecast. It should be noted that modeling each grid point separately is computationally expensive, so the algorithm cannot be too complicated.

      The NBM system provides a good solution to the three problems mentioned above. For the case of China, however, some regional mesoscale model forecasts need also to be integrated. On the one hand, the spatial resolution of global forecasts is coarser than that of regional mesoscale models such as GRAPES-Meso (a mesoscale NWP system developed by China) (Huang et al., 2017), and Shanghai-Meso (Lyu et al., 2019). On the other hand, current mainstream precipitation forecasts in China are still deterministic, as probabilistic forecasts are still in the development stage (Zong et al., 2012).

      Therefore, in this paper, with reference to the NBM system, SGPs are used to expand the total number of samples, and a weighting-based blending scheme is used to blend multiple deterministic QPFs to generate the final forecast in China. The paper is organized as follows. Section 2 introduces the data, the MMB algorithm, and the QPF verification formulae. Section 3 discusses the overall performance of the blending algorithm, as well as that in individual cases. Sections 4 and 5 provide further discussion and a summary, respectively.

    2.   Data and methods
    • The data used in this paper include two types: gridded forecast data and gridded observational data, on a spatial resolution of 0.05°. The study area covers central and eastern China (14.975°–55.025°N, 99.975°–130.025°E).

      The hourly gridded precipitation data generated by CMPAS-V2.1 (CMA multi-source merged precipitation analysis system) (Pan et al., 2018) are used as the gridded observational data. The spatial resolution of the data is 0.05°, and the time span is from April 2017 to October 2019. The hourly precipitation data of CMPAS-V2.1 need to be accumulated to obtain a gridded 6-h precipitation field. If there is a lack of observational data at a particular moment, the 6-h accumulated data containing this hour would be marked as missing.

      The forecast physical quantity is 6-h QPF. The NWP models include ECMWF-GFS, NCEP, GRAPES-GFS, GRAPES-Meso (9-km spatial resolution), and Shanghai-Meso. With the formal operation of the GRAPES-3km mesoscale model, once its QPF accumulates enough data, the blending scheme will use the GRAPES-3km QPF in place of GRAPES-Meso in the future.

      Due to the suspension of some automatic weather stations, and the insufficient ability to retrieve/estimate so-lid precipitation measured by satellite and radar, the quality of the CMPAS-V2.1 gridded precipitation product is not so reliable in winter and spring. Therefore, in this paper, only the April–October data are used. The data for April–October of 2017 and 2018 are selected as the data to train the bias-correction algorithm and to calculate the grid points’ SGPs. The data for April–October 2019 are selected as the verification data.

      The temporal and spatial resolutions and data sources of the NWP models involved in this study are shown in Table 1 (Tang et al., 2018). Since the Shanghai-Meso forecast is from 6 to 72 h, this paper only shows part of the verification results, for which the start time is 0000 UTC and the forecast lead time is 18–72 h.

      Model nameTypeSpatial resolutionLead time/IntervalData source
      ECMWFGlobal deterministic model0.125°0–240 h/6 hourlyChina integrated meteorological information service system (CIMISS)
      NCEP0.5°0–240 h/6 hourly
      GRAPES-GFS0.5°0–240 h/6 hourly
      GRAPES-MesoRegional mesoscale model0.1°0–84 h/6 hourlyChina Meteorological Administration NWP cloud storage
      Shanghai-Meso9 km0–72 h/6 hourly

      Table 1.  Models used in the multi-model blending (MMB) algorithm in this study

    • The flowchart of the MMB algorithm designed in this study is shown in Fig. 1. The algorithm can be divided into three major steps: single-model bias correction, MMB, and post-processing. Single-model bias correction involves selecting SGPs, calculating the cumulative distribution function (CDF) of precipitation, and QM. Post-processing involves light-precipitation elimination, and smoothing. The technical details of each step are as follows.

      Figure 1.  Flowchart of the multi-model blending (MMB) algorithm.

    • The purpose of calculating SGPs is to obtain a more reliable and smoother CDF of precipitation. The CDF is used in QM. For each grid point, the SGP selection algorithm is used to select the 150 most similar grid points (also named as SGPs). The SGPs need to be recalculated monthly. For the SGP selection algorithm, readers are referred to Hamill et al. (2017). It calculates the similarity between grid points based on the characteristics of precipitation, topographic features, and distance.

      For example, the SGPs used in the correction for the August 2019 forecast are calculated based on the observational data in July–September of 2017 and 2018. Along with the accumulation of CMPAS-V2.1 precipitation data, the accuracy of the SGPs will improve significantly. Figure 2 shows the SGP locations for August 2019 over various sub-areas of the study region in China.

      Figure 2.  Locations of supplemental grid points (SGPs) for August 2019 over various sub-areas of the study region in China. The color shadings on the map denote the 95th percentile of the 6-h accumulated precipitation amounts for the month, determined from the data in 2017−2018. Hollow symbols denote the original points for which their SGPs were searched. Solid symbols indicate the SGPs. Darker symbols indicate a better match, and lighter symbols a poorer match. The original points (hollow) and SGPs (solid) are in various shapes for better viewing effect.

      To numerically locate SGPs, we first define the similarity between points pi,j and pm,n as:

      $${\Delta _{i,j,m,n}}{\rm{ = }}\alpha \Delta {P_{i,j,m,n}} + \beta \Delta {Z_{i,j,m,n}} + \gamma \Delta {\rm{TF}}_{i,j,m,n} + \delta \Delta {D_{i,j,m,n}},$$ (1)

      where $\Delta {P_{i,j,m,n}}$ indicates the similarity of characteristics of precipitation, obtained by calculating the difference between the CDF of precipitation at pi,j and pm,n; $\Delta {Z_{i,j,m,n}}$ is the horizontal distance between pi,j and pm,n; $\Delta {\rm{TF}}_{i,j,m,n}$ indicates the difference in slope and aspect between point pi,j and pm,n; and $\Delta {D_{i,j,m,n}}$ is the vertical distance between pi,j and pm,n. The formulae for $\Delta {P_{i,j,m,n}}, \Delta {Z_{i,j,m,n}}, \Delta {\rm{TF}}_{i,j,m,n},$ and $\Delta {D_{i,j,m,n}} $ can be found in Hamill et al. (2017). The closer the value of ${\Delta _{i,j,m,n}}$ is to 0, the higher the similarity between the two points.

      A specific procedure to select the SGPs of point pi,j is given as follows. (1) Calculate the similarity between pi,j and all the remaining grid points pm,n (named as candidate points) with Eq. (1). (2) Sort all the candidate points by the value of ${\Delta _{i,j,m,n}}$, from smallest (tending toward 0) to largest, named as the candidate queue. (3) Take the first point from the candidate queue (this point is named pi,j,c), and add pi,j,c to the list of SGPs. (4) Take all the points in the candidate queue for which the horizontal distance to pi,j,c is less than 70 km (Hamill et al., 2017; the purpose of this step is to minimize the interference of resampling on the precipitation CDF). (5) Repeat steps 1–4 until there are 150 points in the list of SGP.

      During the retrieval of SGPs, it was found that even 150 SGPs is still too many for some regions, such as Yunnan, Guangdong, and Guangxi. Taking Yunnan as an example, the precipitation characteristics of this area are quite different from surrounding areas, which causes the SGPs (especially their tail part) to have insufficient similarity. The consequence of this is that some points with low similarity would be added into the list of SGPs. These points (in the list of SGPs, but with low similarity value) are named as “pseudo-similar points.” Pseudo-similar points might cause problems when calculating the precipitation CDF. Therefore, they need to be restricted (see Section 2.2.2).

    • QM requires the historical forecast CDF and observational CDF to implement the correction. This section briefly describes how to calculate the forecast/observational CDF. Since the calculation process for the two kinds of CDF is almost the same (the only difference being different data used), we only show how to calculate the observational CDF at one grid point.

      We need to first sort the 6-h accumulated precipitation amount of a grid point and its SGPs, from small to large, and then select specific precipitation values corresponding to the quantile values of 0.01%, 0.05%, 0.1%, 0.5%, 1%, 2%, 3%, …, 99%, 99.5%, 99.9%, 99.95%, and 99.99%. We then use these values to represent the CDF.

      For example, if we want to calculate the precipitation CDF at a grid point on 20 August 2019, we need to collect precipitation data from 21 July to 19 August in 2019, i.e., the precipitation data of the previous 30 days, and then sort the data of the point and its SGPs from small to large, and select specific quantile values (see above for required quantile value). These values constitute the precipitation CDF of the current grid point on 20 August 2019.

      Due to the significant regional characteristics of precipitation in some areas, adjustments will need to be made to the selection of SGPs [compared with the raw method in Hamill et al. (2017)]. Specifically, each time a similar point’s precipitation data are added, stop when the number of samples larger than 25 mm exceeds 40. The purpose of this is to reduce the interference of pseudo-similar points while ensuring that there are enough samples of large-value precipitation.

    • In this paper, QM is used to de-bias. Through matching the same quantile’s value of the forecast CDF and observational CDF, QM achieves bias correction.

      First, we denote the historical forecast and observational CDFs obtained in Section 2.2.2 as Ffst,t and Fobs,t, respectively. Also, we denote the raw forecast value as ${x_t}$, and the quantile value of ${x_t}$ in Ffst,t as ${\rm id}{x_t}$, which indicates ${x_t} = {F_{{\rm{fst}},t}}({\rm id}{x_t})$. Then the corrected forecast is ${\bar x_t} = {F_{{\rm{obs}},t}}({\rm id}{x_t})$. ${F_{{\rm{obs}},t}}(\bullet)$ indicates the value at the $ \bullet \times 100 \text%$ quantile of Fobs,t.

      Hamill and Scheuerer (2018) modified the basic QM method in the NBM system as follows:

      $$ \quad\quad {\bar x_t} = \left\{ {\begin{array}{*{20}{l}} { {F_{{\rm{obs}}}}[F_{{\rm{fst}},t}^{ - 1}({x_t})]}& \quad \quad \quad \quad {{x_t} \leqslant {F_{{\rm{fst}},t}}(0.90)}\\ {{F_{{\rm{obs}},t}}(0.90) + b[{x_t} - {F_{{\rm{fst}},t}}(0.90)]}& \quad \quad \quad \quad {{F_{{\rm{fst}},t}}(0.90) < {x_t} \leqslant {F_{{\rm{fst}},t}}(0.99).}\\ {{F_{{\rm{obs}},t}}(0.90) + b[{F_{{\rm{fst}},t}}(0.99) - {F_{{\rm{fst}},t}}(0.90)] + [{x_t} - {F_{{\rm{fst}},t}}(0.99)]} & \quad \quad \quad \quad {{F_{{\rm{fst}},t}}(0.99) < {x_t}} \end{array}} \right.$$ (2)

      Our study found that Eq. (2) cannot achieve a better result in China. Also, for different numerical models, the appropriate QM equations are inconsistent. Therefore, for the Chinese region, the following equations are used:

      ECMWF:

      $$\quad\quad {\bar x_{{\rm{ECMWF}},t}} = \left\{ {\begin{array}{*{20}{l}} {{F_{{\rm{obs}}}}[F_{{\rm{fst}},t}^{ - 1}({x_t})]}&{{x_t} \leqslant {F_{{\rm{fst}},t}}(0.90)}\\ {{F_{{\rm{obs}},t}}(0.90) + {b_3}[{x_t} - {F_{{\rm{obs}},t}}(0.90)]}&{{F_{{\rm{fst}},t}}(0.90) < {x_t} \leqslant {F_{{\rm{fst}},t}}(0.99).}\\ {{F_{{\rm{obs}},t}}(0.90) + {b_4}[{F_{{\rm{obs}},t}}(0.99) - {F_{{\rm{obs}},t}}(0.90)] + [{x_t} - {F_{{\rm{obs}},t}}(0.99)]}&{{F_{{\rm{fst}},t}}(0.99) < {x_t}} \end{array}} \right.$$ (3)

      GRAPES-GFS and GRAPES-Meso:

      $$ \quad\quad{\bar x_{{\rm{model}},t}} = {F_{{\rm{obs}}}}[F_{{\rm{fst}},t}^{ - 1}({x_t})].$$ (4)

      NCEP:

      $$\quad\quad {\bar x_{{\rm{NCEP}},t}} = \left\{ {\begin{array}{*{20}{l}} {{F_{{\rm{obs}}}}[F_{{\rm{fst}},t}^{ - 1}({x_t})]}& \quad \quad \quad \quad \quad \quad \quad\quad \quad \quad \quad \quad\!\!\!\!\! {{x_t} \leqslant {F_{{\rm{fst}},t}}(0.90)}\\ {{a_0}{F_{{\rm{obs}},t}}(0.95) + {b_0}[{x_t} - {F_{{\rm{obs}},t}}(0.90)]}& \quad \quad \quad \quad \quad \quad \quad\quad \quad \quad \quad \quad\!\!\!\!\! {{F_{{\rm{fst}},t}}(0.90) < {x_t} \leqslant {F_{{\rm{fst}},t}}(0.99).}\\ {{a_1}{F_{{\rm{obs}},t}}(0.90) + {b_1}[{x_t} - {F_{{\rm{obs}},t}}(0.90)]}& \quad \quad \quad \quad \quad \quad \quad\quad \quad \quad \quad \quad\!\!\!\!\! {{F_{{\rm{fst}},t}}(0.99) < {x_t}} \end{array}} \right.$$ (5)

      Shanghai-Meso:

      $$\quad\quad {\bar x_{{\rm{Shanghai}} - {\rm{Meso}},t}} = \left\{ {\begin{array}{*{20}{l}} {{F_{{\rm{obs}}}}[F_{{\rm{fst}},t}^{ - 1}({x_t})]}& \quad \quad \quad \quad \quad \quad \quad \quad \quad\!\!\!\!\! {{x_t} \leqslant {F_{{\rm{fst}},t}}(0.90)}\\ {{a_2}{F_{{\rm{obs}},t}}(0.95) + {b_2}[{x_t} - {F_{{\rm{obs}},t}}(0.90)]}& \quad \quad \quad \quad \quad \quad \quad \quad \quad\!\!\!\!\!{{F_{{\rm{fst}},t}}(0.90) < {x_t}} \end{array}}\right. \!\!\!\!\!.$$ (6)

      Only GRAPES-GFS and GRAPES-Meso can use the raw QM formula to obtain better correction results. Other models require hyper-parameters for manual intervention.

    • According to Fig. 1, the weighted average method is adopted to blend the de-biased forecasts. The following formula is used to update the blending weights:

      $${w_{{\rm{model}},t}} = \alpha {w_{{\rm{model}},t - 1}} + (1 - \alpha){w_{{\rm{model}},14}},$$ (7)

      where ${w_{{\rm{model}},14}}$ is based on the TS in the past 14 days,

      $${w_{{\rm{model}},14}}{\rm{ = }}\sum\limits_{\rm{level}} {\rm T{\rm S_{{\rm{model}},{\rm{level}},14}}} /\sum\limits_{\rm{level}} {(\sum\limits_{\rm{model}} {\rm T{\rm S_{{\rm{model}},{\rm{level}},14}}})} .\!\!\!\!\!\!$$ (8)

      Here, the subscript level indicates different thresholds of 0.1, 4, 13, 25, and 60 mm, which correspond to light rain, moderate rain, heavy rain, rainstorms, and extraordinary rainstorms, respectively. The term ${w_{{\rm{model}},t - 1}}$ in Eq. (7) represents the blending weight for day t − 1, and $\alpha $ is a hyper-parameter (0.85 in this paper). The formula for the TS can be found in Section 2.3.

      The blended forecast is:

      $${x_{{\rm{blend}},t}} = \sum\limits_{\rm{model}} {({w_{{\rm{model}},t}} \times {{\bar x}_{{\rm{model}},t}})},$$ (9)

      where the subscript model denotes one of the models mentioned above.

      The influence of adding BS into the weight blending process is discussed in Section 4.2.

    • For the blended QPF field, the following judgements are made for each grid point: count the number of models in which the precipitation is greater than 0, recorded as x; mark the grid point as “empty point” if x < 0.4n, in which n is the total number of models involved in the blending; and set the precipitation amount to 0 for all “empty points.”

      The purpose of doing this is to reduce the number of false alarms of light rain as reasonably as possible. Light-precipitation elimination adopts the idea of probabilistic forecasting: grid points with a precipitation probability higher than 40% are regarded as the effective precipitation area.

    • In order to obtain a forecast field that is acceptable to the forecasters, it is necessary to smooth the precipitation field obtained in Section 2.2.5. The Savitzky–Golay smoothing algorithm (Savitzky and Golay, 1964; Gorry, 1990) is used for this purpose. This smoothing algorithm is a weighted average algorithm with a sliding window. Its weights are obtained by the least-squares fitting of a given high-order polynomial in the sliding window. Compared with traditional smoothing algorithms, the Savitzky–Golay algorithm retains more edge details and improves the filtering effect at the same time (Li and Yang, 2010). The polynomial used in this paper is a 3-order polynomial and the sliding window size is 15 × 15.

    • TS and BS are calculated as follows:

      $$\begin{array}{l} {\rm{T}}{{\rm{S}}_T} = {\rm{N}}{{\rm{A}}_T}/({\rm{N}}{{\rm{A}}_T} + {\rm{N}}{{\rm{B}}_T} + {\rm{NC}}_T^{})\\ {\rm{B}}{{\rm{S}}_T} = ({\rm{N}}{{\rm{A}}_T} + {\rm{N}}{{\rm{B}}_T})/({\rm{N}}{{\rm{A}}_T} + {\rm{N}}{{\rm{C}}_T}) \end{array},$$ (10)

      where NAT is the total number of grid points that are correctly forecasted, i.e., both the forecast and observation are larger than thresholds (T); NBT is the total number of grid points that are false alarmed, meaning that the forecast is larger than T but the observation is lower than T; and NCT is the total number of grid points that are missed, i.e., the forecast is lower than T but the observation is larger than T.

      The threshold T is shown in Table 2. The observational data are the 6-h accumulated precipitation amount (obtained from CMAPS-V2.1).

      Product nameThreshold (mm)
      6-h QPF0.1, 4.0, 13.0, 25.0, and 60.0

      Table 2.  Verification thresholds (T)

    3.   Results
    • The SGP retrieval algorithm used 2-yr precipitation data to calculate the SGPs. However, it is a question as to whether 2-yr data can represent the characteristics of precipitation. To be more specific, which of the following two situations is more advantageous: calculating the SGPs based on topographic data and 2-yr historical precipitation data, or calculating the SGPs based on the topographic data only.

      To answer this question, during the process of constructing the historical CDFs, we use the following two schemes, respectively: (1) set the value of α in Eq. (1) to 0.1, which means using the 2-yr precipitation data to calculate the SGPs, and using these SGPs to construct the CDFs; and (2) set the value of α in Eq. (1) to 0, which means using only the topographic data to calculate the SGPs, and using these SGPs to construct the CDFs. The CDFs generated from the above two schemes are then used in the QM. The results are shown in Table 3.

      Model nameTSBS
      0.1 mm4 mm13 mm25 mm60 mm0.1 mm4 mm13 mm25 mm60 mm
      Raw-EC0.3620.2530.1330.0650.0131.9411.2680.7740.6430.692
      EC-QM10.3880.2470.1440.0870.0170.9681.3421.3911.5931.284
      EC-QM20.3860.2470.1410.0790.0170.9991.3371.4241.5701.323


      Table 3.  Threat score (TS) and bias score (BS) for raw- and quantile-mapped ECMWF (Raw-EC, EC-QM1, and EC-QM2 ) 6-h quantitative precipitation forecasts (QPFs) from April to October 2019. The start time of the forecast is 0000 UTC and the forecast lead time is 18–72 h. The CMPAS-V2.1 dataset is used as the observation data

      The TS of the quantile mapped forecast is significantly improved compared to that of the raw ECMWF forecast. The BS is greatly improved at the 0-mm threshold. However, at higher thresholds (13 mm and larger), TS tends to increase at the cost of losing BS (because TS is more important in actual service, owing to the disastrous effects of heavy precipitation).

      In addition, compared with only using topographic data to calculate the SGPs (EC-QM2 in Table 3), using 2-yr precipitation data and topographic data simultaneously (EC-QM1 in Table 3) shows a slight improvement in TS, but little change in BS.

      Therefore, using the precipitation data of the last two years as the climatic characteristics of precipitation can play a certain role in the correction. Also, with the accumulation of historical data, this effect will continue to increase. Thus, the precipitation term is retained in Eq. (1).

    • Table 4 shows the TS and BS of raw NWP forecasts corrected by QM along with the MMB forecast (named as QMWM5). Although the quantile-mapped ECMWF forecasts show a better performance than the other four models, the blending still achieves a better improvement.

      Model nameTSBS
      0.1 mm4 mm13 mm25 mm60 mm0.1 mm4 mm13 mm25 mm60 mm
      ECMWF0.3880.2470.1440.0870.0170.9681.3421.3911.5931.284
      NCEP0.3610.2340.1490.0750.0200.9671.3560.9080.4680.433
      GRAPES-GFS0.3250.1860.1040.0570.0130.9641.0711.3701.9173.807
      GRAPES-Meso0.3250.1870.1050.0580.0150.9741.1281.4462.0253.917
      Shanghai-Meso0.3460.2060.1190.0680.0190.9151.0621.4112.0424.361
      QMWM50.3890.2780.1710.0990.0260.7971.2111.1230.9120.526

      Table 4.  As in Table 3, but for quantile-mapped ECMWF, NCEP, GRAPES-GFS, GRAPES-Meso, Shanghai-Meso, and the MMB forecast of this study (QMWM5)

      In terms of BS, five models show a good performance at the 0.1-mm threshold, and then a rapid increase as the threshold increases. Also, the blending shows a better performance in term of BS, especially when the threshold is larger than 13 mm (heavy rain threshold).

      Therefore, compared with single-model forecasts, the blended forecast can effectively improve the TS and performs better in terms of BS. This is because models tend to forecast large-value precipitation even if the probability is not high and the large-value precipitation might cause more severe disaster, which will cause a high BS. Blending can adjust the large-value precipitation to a more reasonable value through the weighting, which can reduce the BS. Section 4.3 demonstrates another advantage of controlling the BS to less than 1.

    • Figures 3 and 4 show the TS and BS of the blended forecasts and those of the raw forecasts. Only the scores for the 0.1- and 25-mm thresholds are shown since the performance of 4- and 13-mm thresholds are similar to that of the 25-mm threshold.

      Figure 3.  (a) Threat scores (TSs) and (b) bias scores (BSs) for 6-h QPF derived from the raw models and the blended forecast (QMWM5), averaged from April to October 2019. The threshold is 0.1 mm.

      Figure 4.  As in Fig. 3, but with the 25-mm threshold.

      For the 0.1-mm threshold, the blended forecast (blue line in Fig. 3a) shows a significant improvement in terms of TS when the forecast lead time is less than 60 h. Also, the TS presents a ladder shape: 18–36 h is the first level, 42–60 h is the second level, and 66–72 h is the third level. Moreover, as the forecast lead time increases, the TS of the blended forecast drops rapidly. When the forecast lead time is 66–72 h, TS of the blended forecast is even lower than that of the raw ECMWF model (yellow line).

      Figure 3b shows the BS at the 0.1-mm threshold. The BS of the raw model forecast is significantly higher than 1. Meanwhile, the BS of the global models (NCEP, ECMWF, and GRAPES-GFS) is significantly higher than that of the regional mesoscale models (GRAPES-Meso and Shanghai-Meso), which indicates that global models produce a significant false alarm for precipitation. In contrast, the BS of the blended forecast is much closer to 1, indicating that the QM and light-precipitation elimination play an important role in optimizing the forecast results.

      Figures 4a and 4b shows the TS and BS of rainstorms (25-mm threshold). TS in general shows an oscillating downward trend as the forecast lead time extends, with a period of 24 h. The local maximum appears at 24, 48, and 72 h, and the local minimum at 18, 42, and 66 h. The TS of the blended forecast is significantly better than that of the raw model forecast. For example, when the forecast lead time is 24 h, TS of the raw ECMWF and the blended forecast is 0.0952 and 0.1405, respectively, which indicates a 47.6% improvement.

      The start time of the forecast is 0000 UTC (0800 BT). Forecasts with a lead time of 24, 48, and 72 h correspond to precipitation during 0200–0800 BT (night to early morning). The precipitation during this period is mostly large-scale precipitation. It looks that models perform better for large-scale than for mesoscale processes. Thus, the TS during these periods is higher than that in other periods. For the afternoon and evening, the model’s ability is relatively poor, resulting in a relatively low TS.

      For rainstorms, the BSs of the global models are lower than those of the regional mesoscale models (Fig. 4b), indicating that global models are relatively conservative, which manifests as insufficient rainstorm forecasting; whereas regional models are more aggressive, showing a tendency to over-forecast rainstorms to obtain a higher TS.

      For the blended forecast, the BS decreases with the prolongation of the forecast lead time and oscillates around 1, which is significantly better than for both the global and regional mesoscale models. From the TS point of view, when the threshold is 4 or 13 mm, the performances of the blended forecast and raw model forecast are almost the same as at the 25-mm threshold (data not shown here). From the BS point of view, for the 13-mm threshold, the blended forecast’s BS is closer to 1 than most of the models, albeit with some insufficiencies still existing compared to the GRAPES-GFS model.

      Based on the above analysis, the TS presents a periodic characteristic relative to the forecast lead time for both the raw model forecast and the blended forecast. The local maximum of TS appears at around 24, 48, and 72 h. This is because the forecasted precipitation during this period is dominated by large-scale precipitation processes, and models perform well for this type of process.

      Compared with single-model forecasts, blended forecast shows a significant improvement in both TS and BS. For the forecast of large-value precipitation in particular, the blended forecast not only improves the TS, but also maintains the BS at around 1, which shows advantages over single-model forecasts.

    • Figure 5 shows the blending weight when the forecast lead time is 24 h. The weights of the ECMWF and NCEP models increase with the lead time, which is consistent with the higher TS of these two models. Since the hyper-parameter α is set to 0.85, the variation trend of the weight is relatively gentle.

      Figure 5.  Changes in the weight of each model during the blending process.

      Figure 5 shows the weights’ variation only for the lead time of 24 h. In fact, for any forecast lead time between 18 and 72 h, the trend is almost the same: the weights of the ECMWF and NCEP models are at a relatively high level, within which the weight of the NCEP model is slightly higher than that of the ECMWF model. Moreover, with increased forecast lead time, the values of the ECMWF and NCEP models’ weights are on the rise. Therefore, GRAPES-GFS and GRAPES-Meso still have more room for improvement than the ECMWF and NCEP models.

      On the other hand, for some precipitation processes, when the ECMWF and NCEP models show large deviations in their forecasted rainband’s location, GRAPES-GFS/GRAPES-Meso can sometimes show a higher degree of accuracy. In this case, the blending algorithm can blend the GRAPES-GFS/GRAPES-Meso forecasts into the final product, thereby improving the forecast accuracy. A related example is shown in Section 3.5.

    • A rainfall process that occurred on 6 June 2019 is taken as an example to demonstrate the blending algorithm’s ability in correcting the rainband’s location. The forecast start time in this case is 0000 UTC 5 June 2019, and the forecast lead time is 42 h. Figure 6 shows the forecasts of the blending algorithm (QMWM5), the ECMWF, NCEP, GRAPES-GFS, GRAPES-Meso, and Shanghai-Meso models, and the observed precipitation field.

      Figure 6.  Distributions of 6-h quantitative precipitation forecast (QPF). The start time of the forecast is 0000 UTC 5 June 2019, and the forecast lead time is 42 h. QMWM5 indicates the blended forecast and NMIC indicates the analyzed precipitation data provided by the National Meteorological Information Center (NMIC) of the China Meteorological Administration (CMA).

      In this rainfall process, the forecasts of ECMWF and NCEP are relatively weak, with the location of the rainband significantly further north than the actual location. The forecast of GRAPES-GFS is relatively weak in strength, and the heavy rainfall center at the border of Jiangxi and Zhejiang provinces is not captured. GRAPES-Meso shows a relatively accurate forecast of the rainband’s location, but the intensity of the strong rainfall center is also weak. Shanghai-Meso gives a southerly rainband forecast. The blending algorithm (QMWM5) produces a more accurate forecast: the main rainband resembles that in the forecast of GRAPES-Meso, while the rain pattern in the northwestern part of Jiangxi mimics the ECMWF forecast.

      However, the blending algorithm shows some defects when dealing with maximum values. For instance, the heavy-rain area at the border of Jiangxi and Zhejiang does not show up. This is because, in the process of blending, the algorithm adopts a grid-weighted average scheme. Since the locations of the maximum in different models are not consistent, the maximum value is weakened during the weighted average process. Taking this rainfall process as an example, the maximum rainfall location in Shanghai-Meso’s forecast is in southern Jiangxi, but the rain is reduced to light rain after the weighted average, since the other four models’ forecasts have no large-value precipitation here. Therefore, a possible direction for improving the blending algorithm would be to investigate how to reasonably accommodate maximum and large-precipitation regions from different models.

    • The blending algorithm can not only adjust the location of the rainband, but also eliminate the light rain produced by the blending process. Figure 7 shows an example of a rainfall case, of which the forecast start time is 0000 UTC 2 September 2019 and forecast lead time is 30 h.

      Figure 7.  As in Fig. 6, but with the forecast start time at 0000 UTC 2 September 2019, and the forecast lead time of 30 h.

      As Fig. 7 shows, in the southeast coastal area of China, the southwestern region of China, and Henan Province, the raw model forecasts present different degrees of large-area light rain (false alarms), while the blended forecast (QMWM5) eliminates these false alarms whilst retaining the major precipitation region. This result may be mainly because that 1) the QM used in the bias correction process might have corrected the systematic bias of the model, leading to elimination of some of the false alarms; and 2) the light-rain elimination (Section 2.2.5) process has effectively controlled the single model’s influence on the blended forecast.

    4.   Discussion
    • In addition to TS, BS is another commonly used index when evaluating forecast performance. In this section, BS is added into the weight calculation formula [Eq. (8)], to assess the impact of BS on the blending algorithm.

      By inserting the bias term into Eq. (8), we obtain the following formula:

      $${w_{{\rm{model}},14}}{\rm{ = }}\frac{{\sum\limits_{\rm{level}} {{\rm{0}}{\rm{.9}} \times {{\rm{TS}}_{{\rm{model}},{\rm{level}},14}} + 0.1 \times {{[{\rm{abs}}(1 - {{\rm{BS}}_{{\rm{model}},{\rm{level}},14}})]}^{ - 0.5}}} }}{{\sum\limits_{\rm{model}} {{\rm{\{ }}\sum\limits_{\rm{level}} {{\rm{0}}{\rm{.9}} \times {{\rm{TS}}_{{\rm{model}},{\rm{level}},14}} + 0.1 \times {{[{\rm{abs}}(1 - {{\rm{BS}}_{{\rm{model}},{\rm{level}},14}})]}^{ - 0.5}}} {\rm{\} }}} }},$$ (11)

      where BS’s power exponent is set to −0.5 to prevent the bias term from taking too much weight when the BS is very close to 1.

      The statistical results are shown in Table 5, in which Blending-TS and Blending-TSBS indicate the blended forecasts generated with Eqs. (8) and (11), respectively. After adding the BS into the blending weight calculation formula, for moderate rain (4-mm threshold) and below, the BS is close to 1 at a cost of losing the TS. However, for heavy rain (13-mm threshold) and above, while the TS decreases, BS increases significantly.

      Model nameTSBS
      0.1 mm4 mm13 mm25 mm60 mm0.1 mm4 mm13 mm25 mm60 mm
      Blending-TS0.3890.2780.1710.0990.0260.7971.2111.1230.9120.526
      Blending-TSBS0.3880.2620.1530.0850.0230.8631.2061.3031.4321.379

      Table 5.  As in Table 3, but for MMB products generated by TS only (Blending-TS) and by TS and BS simultaneously (Blending-TSBS)

      The reason for the above results might be that, for small thresholds, BS tends towards 1, which leads to a significant increase in the weight of small thresholds due to the influence of the BS term in Eq. (11). Also, this will lead to a more significant improvement in small-value precipitation in the blending result.

    • The blending algorithm adopts a weighted average based on dynamic weights, but this kind of method may weaken the extreme value of precipitation. This section attempts to use the PM method (Ebert, 2001) to correct the intensity of the blended forecast.

      The PM method is mainly used to blend data sources with different temporal and spatial distributions: suppose there are a data source (like NCEP) with a better spatial distribution (hereafter named as the spatial source), and another data source (like ECMWF) with a better intensity distribution (hereafter named as the intensity source); PM is used to combine the two data sources to obtain a better forecast. Specific steps of PM are as follows: (1) sort all precipitation values in the intensity source, from large to small, to obtain sequence A, wherein the elements in sequence A are named as a1, a2, … an, and a1a2 ≥ … ≥ an, where n is the total number of grid points; (2) sort all precipitation values in the spatial source, from large to small, to obtain sequence B, wherein the elements in sequence B are named as b1, b2, … bn, and b1b2 ≥ … ≥ bn; and (3) for element bi (1 ≤ in) in sequence B, obtain the spatial location of bi in the spatial distribution field, then replace the precipitation value at that location with value ai, and traverse each element in sequence B to obtain the combined precipitation field.

      The quantile-mapped ECMWF forecast is selected as the intensity source, the blended forecast is selected as the spatial source, and the combined results are shown in Table 6. For rainstorms ( ≥ 25 mm), the TS is slightly improved (about 5%), with a significant increase in BS (from 0.912 to 1.593). Possible reasons for the results are: 1) even the smoothed extreme value still exceeds the maximum threshold of TS (60 mm here); therefore, the improved algorithm cannot show its advantage; 2) in the process of QM, in order to obtain a better result, hyper-parameters are used [see Eqs. (2)–(6)]—this manual adjustment increases the TS, but it may also affect the distribution characteristics of precipitation, which in turn might influence the effect of PM; and 3) only the past 2-yr precipitation data are used in the QM process, which might cause the inaccurate CDF.

      Model nameTSBS
      0.1 mm4 mm13 mm25 mm60 mm 0.1 mm4 mm13 mm25 mm60 mm
      Blended-TS0.3890.2780.1710.0990.0260.7971.2111.1230.9120.526
      Blended-TSPM0.3700.2740.1700.1040.0270.9691.3421.3911.5931.284

      Table 6.  As in Table 3, but for multi-model blended product (Blended-TS) and probability-matched multi-model blended product (Blended-TSPM)

      Operationally, it is inappropriate to sacrifice a huge amount of BS in exchange for a 5% increase in TS. Therefore, in the blending algorithm described in Section 2, the PM blending method is not included.

    • The data used in operational verification are obtained from 2408 standard observation stations in China. Meanwhile, the hyper-parameters used in this paper are obtained based on CMPAS-V2.1 gridded observational data. Different observational data sources might affect the verification results.

      The operational product of the NMC/CMA is a 24-h QPF (named NMC-24QPF). In order to compare the difference between the blended forecast and NMC-24QPF, every four consecutive 6-h QPF are accumulated to generate a 24-h QPF. Then, the blended forecast is interpolated onto 2193 standard observation stations (there are 2193 such stations in the current study domain). The verification results (Table 7) reveal that in terms of TS, the 24-h QPF generated from blended forecast still has some gaps compared with the NMC operational product (especially for 100-mm threshold). However, from the perspective of BS, the blending algorithm reduces the false alarm efficiency for large-value precipitation, which makes the blended forecast more reliable.

      Model nameTSBS
      0.1 mm10 mm25 mm50 mm100 mm0.1 mm10 mm25 mm50 mm100 mm
      Blended0.6160.4190.3140.2300.1321.0421.2471.0920.8360.405
      Operational0.6300.4270.3210.2370.1591.1171.1981.2051.2161.383

      Table 7.  TSs and BSs of 24-h QPF from April to October 2019. The start time of the forecast is 0000 UTC and the forecast lead time is 36 h. The result is relative to observations at 2193 national stations in central and eastern China

      One special benefit of keeping the BS at a low level is that when the accumulated precipitation is required (for example, the accumulated precipitation amount for the last 72 h), a better result can be obtained based on a forecast with lower BS.

      Taking the precipitation process of Typhoon Lichma in 2019 as an example, Fig. 8 shows the accumulated 72-h (9–12 August 2019) precipitation amount. The 72-h precipitation amount obtained based on the blended forecast is closer to the real observation than the NMC operational forecast. Furthermore, the false alarms are better controlled, implying that the service needs of early warning can be better met for major weather processes.

      Figure 8.  Distributions of 72-h precipitation amount associated with Tropical Cyclone Lichma during 9−11 August 2019. (a) The current best operational forecast in NMC of CMA, (b) our method, (c) forecast made by the Chief Forecaster of NMC, and (d) the analyzed precipitation data provided by NMIC.

      In addition, the current NMC 3-h QPF is obtained through time-splitting based on 24-h QPF. If the 6-h QPF is integrated into the operational process, the time splitting can be directly based on the 6-h QPF, which can improve the reliability of the operational forecast.

      Therefore, in the next step for this study, it will be of significance to increase the TS of the 6-h QPF on the premise of a good control of BS. One possible approach is to improve the blending algorithm over heavy rainfall centers/large-value rainfall area. Since the current MMB forecast only blends five deterministic models, with no ensemble forecast in the blending process, we plan to add ensemble forecasts into the blending process. To obtain better results, we could restrict the area of large-value precipitation based on the probability forecast generated from ensemble forecasts.

    5.   Conclusions
    • In this paper, a multi-model blending (MMB) algorithm with supplemental grid points (SGPs) was designed and reported. The algorithm can blend deterministic forecasts from the ECMWF, NCEP, GRAPES-GFS, GRAPES-Meso, and Shanghai-Meso models, to generate blended quantitative precipitation forecasts (QPFs). The algorithm uses the quantile mapping (QM) method to correct the bias, dynamic weight averaging to blend the multi-source quantile-mapped forecast, and light-precipitation elimination and Savitzky–Golay smoothing to generate the final forecast.

      QM is used to correct the bias of raw forecasts. During the correction process, the SGPs are used to extend the number of samples, so as to minimize the negative effect of lacking sufficient historical data. The topographic similarity, spatial distance, height difference and climatic characteristics of precipitation processes are considered when generating the SGPs.

      Dynamic weight blending is based on the TS of the quantile-mapped forecast. Studies have shown that simply adding the BS term into the weight’s calculation formula could improve the BS for small-value precipitation, but has a negative effect on large-value precipitation. Therefore, there is still room for further research on this topic.

      Light-precipitation elimination uses the idea of probabilistic forecasting. It assumes that, if the precipitation probability is higher than 40%, a precipitation event can be forecast at that grid point.

      Verification of the QPF using the MMB with SGPs in China shows that (1) The SGPs obtained based on 2-yr historical precipitation data and geographic information have some effect on the improvement in forecast accuracy. (2) The MMB algorithm can effectively improve the precipitation forecast, with single-model bias-correction using the QM, dynamic weight blending based on the TS in past 14 days, and light-precipitation elimination. For large-area light rain, the MMB algorithm has a good ability in eliminating false alarms. For the forecasting of heavy rainfall, while the TS is improved, the BS is maintained at around 1. (3) Using the TS to compute blending weights can effectively improve the blended forecast. Adding the BS into the weight calculation formula shows a slight improvement for small-threshold BS but a negative effect for large-threshold BS, which needs further study. (4) For the problem of large-value precipitation being smoothed during blending, second blending using probability matching (PM) is unable to play a positive role in the correction. This may be because in this case, the maximum precipitation is greater than 60 mm even after smoothing, and thus the improvement cannot be reflected by the TS and BS. (5) Compared with the current operational products released by the NMC/CMA, the 6-h QPFs generated in this study have better control over the BS, which is conducive to the accumulation process of rainfall. In general, the QPF using MMB with SGPs experimented in this study shows great potential to further improve the present operational QPF in China.

      Based on the above conclusions, our future work might include: (1) incorporate ensemble forecasts into the blending process; (2) generate probabilistic and deterministic forecasts simultaneously; (3) unify the spatial distributions of probabilistic and deterministic forecasts; and (4) further improve the blending algorithm to alleviate the maximum value smoothing problem.

      Acknowledgments. The authors thank National Meteorological Information Center of the China Meteorological Administration (NMIC/CMA) for providing the CMPAS-V2.1 data. The authors appreciate the anonymous reviewers for their constructive comments that have significantly improved the quality of this paper.

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