Prediction Skill of GEFSv12 in Depicting Monthly Rainfall and Associated Extreme Events over Taiwan during the Summer Monsoon

M. M. Nageswararao aCPAESS, University Corporation for Atmospheric Research, NOAA/NWS/NCEP/EMC, College Park, Maryland

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Yuejian Zhu bNOAA/NWS/NCEP/EMC, College Park, Maryland

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Vijay Tallapragada bNOAA/NWS/NCEP/EMC, College Park, Maryland

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Meng-Shih Chen cCentral Weather Bureau, Taipei, Taiwan

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Abstract

The skillful prediction of monthly scale rainfall in small regions like Taiwan is one of the challenges of the meteorological scientific community. Taiwan is one of the subtropical islands in Asia. It experiences rainfall extremes regularly, leading to landslides and flash floods in/near the mountains and flooding over low-lying plains, particularly during the summer monsoon season [June–September (JJAS)]. In September 2020, NOAA/NCEP implemented Global Ensemble Forecast System, version 12 (GEFSv12), to support stakeholders for subseasonal forecasts and hydrological applications. In the present study, the performance evaluation of GEFSv12 for monthly rainfall and associated extreme rainfall (ER) events over Taiwan during JJAS against CMORPH has been done. There is a marginal improvement of GEFSv12 in depicting the East Asian summer monsoon index (EASMI) as compared to GEFS-SubX. The GEFSv12 rainfall raw products have been calibrated with a quantile–quantile (QQ) mapping technique for further prediction skill improvement. The results reveal that the spatial patterns of climatological features (mean, interannual variability, and coefficient of variation) of summer monsoon monthly rainfall over Taiwan from QQ-GEFSv12 are very similar to CMORPH than Raw-GEFSv12. Raw-GEFSv12 has an enormous wet bias and overforecast wet days, while QQ-GEFSv12 is close to reality. The prediction skill (correlation coefficient and index of agreement) of GEFSv12 in depicting the summer monsoon monthly rainfall over Taiwan is significantly high (>0.5) in most parts of Taiwan and particularly more during peak monsoon months, September, and August, followed by June and July. The calibration method significantly reduces the overestimation (underestimation) of wet (ER) events from the ensemble mean and probabilistic ensemble forecasts. The predictability of extreme rainfall events (>50 mm day−1) has also improved significantly.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yuejian Zhu, Yuejian.Zhu@noaa.gov

Abstract

The skillful prediction of monthly scale rainfall in small regions like Taiwan is one of the challenges of the meteorological scientific community. Taiwan is one of the subtropical islands in Asia. It experiences rainfall extremes regularly, leading to landslides and flash floods in/near the mountains and flooding over low-lying plains, particularly during the summer monsoon season [June–September (JJAS)]. In September 2020, NOAA/NCEP implemented Global Ensemble Forecast System, version 12 (GEFSv12), to support stakeholders for subseasonal forecasts and hydrological applications. In the present study, the performance evaluation of GEFSv12 for monthly rainfall and associated extreme rainfall (ER) events over Taiwan during JJAS against CMORPH has been done. There is a marginal improvement of GEFSv12 in depicting the East Asian summer monsoon index (EASMI) as compared to GEFS-SubX. The GEFSv12 rainfall raw products have been calibrated with a quantile–quantile (QQ) mapping technique for further prediction skill improvement. The results reveal that the spatial patterns of climatological features (mean, interannual variability, and coefficient of variation) of summer monsoon monthly rainfall over Taiwan from QQ-GEFSv12 are very similar to CMORPH than Raw-GEFSv12. Raw-GEFSv12 has an enormous wet bias and overforecast wet days, while QQ-GEFSv12 is close to reality. The prediction skill (correlation coefficient and index of agreement) of GEFSv12 in depicting the summer monsoon monthly rainfall over Taiwan is significantly high (>0.5) in most parts of Taiwan and particularly more during peak monsoon months, September, and August, followed by June and July. The calibration method significantly reduces the overestimation (underestimation) of wet (ER) events from the ensemble mean and probabilistic ensemble forecasts. The predictability of extreme rainfall events (>50 mm day−1) has also improved significantly.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yuejian Zhu, Yuejian.Zhu@noaa.gov

1. Introduction

Taiwan is a midsize island located in the subtropics off the southeastern coast of China. The area of Taiwan is only about 36 000 km2. It is dominated by the almost north–south-orientated Central Mountain Range (CMR) with six mountain peaks over 3500 m, an average height of about 2 km, and the highest peak, Yushan, is at 4 km (Chen and Chen 2003). The terrain and integrated monsoonal effects result in a unique rainfall pattern in Taiwan. Its climate variability is mainly influenced by East Asian and western North Pacific monsoons and complicated by the topographic effects. The surrounding ocean of Taiwan supplies plentiful moisture to this island. (Chen et al. 1999; Chen et al. 2010). The average annual total rainfall over Taiwan is about 2590 mm, and it is around 2.6 times the global average of 1000 mm. Due to steep topography in most parts of Taiwan, it is challenging to hold the rainwater, and only 20% of annual rainfall is available to utilize (Wang and Wang 2010; Yim et al. 2015; Lan and Hsu 2019).

In the last few decades, Earth’s surface temperature has been rising radically due to global warming, and its impact has been witnessed in the hydrological cycle and rainfall patterns throughout the world (IPCC 2014). There have been considerable changes in the amount, intensity, duration, and frequency of all types of precipitation, such as snow, fog, ice, rain, etc., over different parts of the globe in recent years (Trenberth 2011). With precipitous terrain and narrow basins over Taiwan, it regularly experiences rainfall extremes of hundreds of millimeters per day, especially during the summer monsoon season [June–September (JJAS)]. Henny et al. (2021) found a positive trend in the frequency of extreme rainfall (ER) events for the winter, spring, and typhoon seasons over Taiwan, and these trends are more significant over the northern part of Taiwan during winter and spring. During JJAS, ER has increased most over the southwestern mountain slopes, whereas the total seasonal rainfall significantly decreased in recent years (1955–2000) (Yu et al. 2006). The ER-positive trends in the recent period have caused an increase in flood situations, which causes widespread destruction of infrastructures, economic damages, and the loss of lives in this region (Chen et al. 2007; Rosenberg et al. 2010; Keller and Atzl 2014; Vogel et al. 2019). Shieh (1986) found that the annual weather-related economic losses due to typhoons and other extreme rainfall events in Taiwan from 1961 to 1982 were about $86 million (USD), with more than 100 casualties.

Most of the rainfall over Taiwan is influenced strongly by the low-level wind direction associated with the East Asian monsoon (Chen and Chen 2003; Chen et al. 1999). The year-to-year variation in seasonal rainfall in Taiwan depends on the low-level moisture availability and thermodynamic stratification. Kerns (2003) and Chen et al. (1999) have found diurnal variations in the rainfall characteristics over Taiwan. The diurnal variations in the rainfall during the mei-yu season (May–June) over Taiwan mainly depend on the surface airflow and the maximum rainfall that occurs on the windward slopes and mountainous areas during afternoon hours (Johnson and Bresch 1991; Chen and Li 1995; Yeh and Chen 1998). During the mei-yu season over Taiwan, the rainfall is associated mainly with mei-yu fronts (Yeh and Chen 1998). Several studies (Li et al. 1997; Yeh and Chen 1998, 2002; Teng et al. 2000) found the convective systems embedded within the southwesterly monsoon flow and mei-yu frontal systems from southern China frequently bring in heavy precipitation toward Taiwan. The rainfall was quite significant due to the orography of the CMR (Chen 2000). The maximum rainfall occurred over the western windward sloping areas in central and southern Taiwan (Yeh and Chen 1998).

Furthermore, during the main rainy seasons (mei-yu and summer), the localized heavy rainfall over the mountainous regions of Taiwan frequently occurs and causes flooding and landslides (Lin et al. 2002; Chen and Chen 2003). Thermally driven circulations during the diurnal heating cycle and orographic blocking also result in the production of localized heavy precipitation when synoptic conditions are favorable. (Johnson and Bresch 1991; Akaeda et al. 1995; Chen and Li 1995; Li et al. 1997; Yeh and Chen 2002). The frequent nontyphoon extreme rainfall events during JJAS over Taiwan are mainly due to mountainous terrain, potential instability, and abundant moisture in the atmosphere. Chen et al. (2007) found that the maximum frequencies of the nontyphoon heavy rainfall events occur in August, followed by June and September. They also found that nontyphoon heavy rainfall events in northern Taiwan were slightly higher in June than in the other peak monsoon months. Apart from monsoon circulations during JJAS, tropical storms are frequent and bring in excessive rainfall with heavy property damage and losses over Taiwan. Therefore, the demand for accurate prediction of the amount of rain and associated extreme rainfall events on subseasonal-to-seasonal scales during the peak rainy season (JJAS) is high for disaster preparedness and risk management in various sectors such as agricultural, hydrology, water resource, and meteorological applications over Taiwan. Still, the precipitation forecast is one of the most challenging areas, especially for extreme events that have a high potential for hazards in steep and complex topography regions like Taiwan (Golding 2000; Fritsch and Carbone 2004; Cuo et al. 2011). It is particularly low rainfall prediction skill on a monthly/extended range scale at small regions like Taiwan and is one of the challenges of the meteorological scientific community.

The month-to-month variability during a year is tricky due to the considerable ambiguity associated with aberrant internal low-frequency fluctuations. The extended range/monthly scale is the bridge between medium-range and seasonal weather forecasts. It is a difficult time range for weather forecasting because much of the memory of the initial atmospheric conditions on this time scale is lost, affecting the forecast prediction skill. Furthermore, the atmospheric signal associated with the ocean anomalies is not significant enough to materialize over the atmospheric noise at extended and subseasonal time scales (Vitart and Robertson 2018).

In recent decades, there have been impressive advances in numerical modeling and prediction of weather and climate. In several studies (Houze 1997; Stevens and Feingold 2009; Krishnamurti et al. 2010; Stocker 2011; Bauer et al. 2015; Wheeler et al. 2016; Vitart et al. 2017) it is evident that there are remarkable improvements in the skill of short- and medium-range weather forecasts over extratropical regions, while the prediction skill is not up to mark particularly in tropical and monsoon regions. The low prediction skill over monsoon regions is due to innate complexities in numerical modeling of tropical processes influenced by interactions among atmospheric circulation, ocean–land–atmosphere feedback, organized convection, radiation, precipitation, moisture, aerosols, and clouds on different space and time scales. In addition, general circulation models (GCMs) still have considerable difficulties in faithful simulation on the monthly scale in a small region like Taiwan. These difficulties are due to the relatively coarse resolution of global models as well as not adequately representing land–sea contrast and topography (Xu 1999; Sperber et al. 2001; Kang et al. 2002).

NOAA/NCEP has implemented the Global Ensemble Forecast System, version 12 (GEFSv12), in September 2020 to support stakeholders for subseasonal forecasts, hydrological, and other meteorological applications (Zhou et al. 2022; Guan et al. 2022; Hamill et al. 2022; Nageswararao et al. 2022). NCEP GEFSv12 consistent reforecast data are available for 2000–19. In this study, the performance evaluation of GEFSv12 reforecast data depicts monthly scale rainfall and associated extreme events during JJAS over Taiwan for the period of 2000–19. The paper is organized as follows: a brief description of the data and analysis methodologies is given in section 2. The results are discussed in section 3 and the broad conclusions are presented in section 4.

2. Data and methodology

a. Data used

The NCEP GEFSv12 precipitation products over Taiwan for the reforecast period (2000–19) have been obtained from Amazon web services (AWS, https://registry.opendata.aws/noaa-gefs/), which are accessible by the broader community. The reforecast was integrated with daily 0000 UTC initial conditions with a forecast of up to 16 lead days except on Wednesday when the forecast lead time is extended to 35 days. In contrast to the current real-time forecast system, the reforecast system has a smaller ensemble size of 5 (11) members for the 16-day run (35-day run), while 31 members are used for the real-time forecasts. The GEFSv12 model configuration uses the Geophysical Fluid Dynamics Laboratory (GFDL) FV3 Cubed-Sphere dynamical core (Lin and Rood 1997; Lin 2004; Putman and Lin 2007; Harris and Lin 2013) with a horizontal resolution of ∼25 km (C384 grid) with 64 hybrid vertical levels. The top layer centered on the model is around 0.27 hPa (∼55 km). Physical parameterizations in the GEFSv12 include a modified scale-aware simplified Arakawa–Schubert (SAS) shallow and deep parameterization convection scheme (Han and Pan 2011; Han et al. 2017) to reduce excessive cloud-top cooling for the model stabilization, the hybrid eddy diffusivity mass flux (EDMF; Han et al. 2016) scheme is used for the vertical mixing process of the planetary boundary, GFDL cloud microphysics scheme with five predicted cloud species (cloud water, cloud ice, rain, snow, and graupel) (Zhou et al. 2019, 2022), the Rapid Radiative Transfer Model (RRTM) for the shortwave and longwave radiative fluxes (Clough et al. 2005), convective gravity wave drag (Chun and Baik 1998) and Alpert et al. (1988) orographic gravity wave drag, and mountain blocking schemes. A two-tiered sea surface temperature (SST) and near–sea surface temperature (NSST) approach (Zhu et al. 2017, 2018; Li et al. 2019) are used for estimating the SST boundary condition, and it accounts for the day-to-day variability and diurnal variation of SST, respectively. The stochastic kinetic energy backscatter (SKEB; Shutts and Palmer 2004; Shutts 2005) and stochastically perturbed parameterization tendencies (SPPTs; Buizza et al. 1999; Palmer et al. 2009) were used to improve the model’s uncertainty. More details of the GEFSv12 forecast system, including the impacts from the individual components, can be found in Zhou et al. (2019, 2022) and Guan et al. (2022).

In this study, the GEFSv12 rainfall reforecast products have been used, which are based on every Wednesday 0000 UTC forecast up to 35 lead days with 11 members. These products are available in grib2 format at 3-h intervals at 0.25° resolution for the first 10 days and 6-h intervals at 0.5° beyond 10 days of the forecast. For uniformity, day-1–10 forecasts are also considered at the same horizontal resolution as day-11–35 forecasts. NOAA CPC Morphing Technique (CMORPH) multi-satellite-based precipitation data for the same period (2000–19) were acquired from the official FTP server (https://www.ncei.noaa.gov/data/cmorph-high-resolution-global-precipitation-estimates/access/daily/0.25deg/) (Joyce et al. 2004) and used as a reference for the performance evaluation of GEFSv12 for monthly rainfall and associated extreme rainfall events over Taiwan during JJAS for the reforecast period (2000–19).

GEFS-SubX is a real-time ensemble system to support the NOAA Subseasonal Experiment (SubX) project that provided a 17-yr reforecast (hindcast; once per week; 11 members; out to 35 days) for model calibration. The details of GEFS-SubX can be found in Pegion et al. (2019), Zhu et al. (2018), and Li et al. (2019). The GEFS-SubX (Zhu et al. 2018) reforecast data at TL574L64 (days 0–8; ∼34-km horizontal resolution) and TL382L64 (days 8–35; ∼52-km horizontal resolution) is considered a benchmark dataset to measure the ability of the GEFSv12 forecast to predict the summer monsoon (JJAS) daily rainfall over Taiwan with different forecast lead times days 1–35 based on every Wednesday initial conditions. The major differences between GEFS-SubX and GEFSv12 can be found in Table 1.

Table 1

The major differences between GEFS-SubX and GEFSv12.

Table 1

b. East Asian summer monsoon index

Various East Asian summer monsoon (EASM) indices are defined based on different variables at different levels to study the EASM and its variability (Wu and Ni 1997; Huang and Yan 1999; Wang and Fan 1999; Lau et al. 2000; Dai et al. 2000; Zhu et al. 2000; Wang et al. 2001; Zhang et al. 2003; Wang et al. 2008; Zhao and Zhou 2009; Xie et al. 2009). These indices are mainly classified into five categories such as (i) the north–south thermal contrast index (Zhu et al. 2000), (ii) the east–west thermal contrast index (Zhao and Zhou 2009), (iii) the South China Sea monsoon index (Dai et al. 2000), (vi) the southwest monsoon index (Wu and Ni 1997; Wang et al. 2001), and (v) the shear vorticity index (Huang and Yan 1999; Wang and Fan 1999; Lau et al. 2000; Zhang et al. 2003; Xie et al. 2009). Wang et al. (2008) used these indices for understanding the characteristics of the EASM and the associated climate and found that some problems exist.

The East Asian jet stream (EAJ) at 200 hPa is an important part of the EASM system and greatly influences weather and climate around East Asia (Tao and Wei 2006; Huang et al. 2012; Qu and Huang 2012). Many studies (Lau and Li 1984; Liang and Wang 1998; Kwon et al. 2007) evidently show the association of the East Asian upper-level jet with EASM. Dai et al. (2013) found that summer thermal structure and winds over Asia show a larger land–ocean thermal gradient in the upper than in the lower troposphere. This implies a bigger role of the upper troposphere in driving the EASM circulation. Zhao et al. (2015) recently proposed a new EASM index (EASMI) based on 200-hPa zonal wind, which considers wind anomalies in the southern (about 5°N), middle (about 20°N), and northern areas (about 35°N) of East Asia. The EASMI is defined as follows:
EASMI=Nor{[u(2.5°10°N,105°140°E)u(17.5°22.5°N,105°140°E)+u(30°37.5°N,105°140°E)]},
where “Nor” represents standardization and u is the JJA-mean 200-hPa zonal wind. During a stronger EASM, the EASMI is positive, and the easterly anomalies appear around 20°N and westerly anomalies appear around 5° and 35°N (Zhao et al. 2015).

The EASMI can capture the interannual and interdecadal variations in EASM-related climate anomalies and it is good at describing precipitation and air temperature variations over East Asia (Zhao et al. 2015). The EASMI is closely associated with the East Asian–Pacific or the Pacific–Japan teleconnection and there is a possible role of internal dynamics in the EASM variability. It is also significantly linked to ENSO and tropical Indian Ocean Sea surface temperature anomalies. There is a need to evaluate the predictability of EASMI from GEFS-SubX and GEFSv12 to understand the prediction skill of EASM rainfall over Taiwan. In this study, the performance evaluation of GEFS-SubX and GEFSv12 day-1–35 forecast lead times for EASMI against the NOAA NCEP GEFSv12 Reanalysis for the period 2000–19 has been done by using standard skill metrics. The NOAA NCEP GEFSv12 Reanalysis assimilates most of the observations that were assimilated into the operational data assimilation system used for initializing global predictions (Hamill et al. 2022). These include a variety of conventional data, infrared and microwave radiances, global positioning system radio occultations, and more. The reanalysis quality is generally superior to that of NOAA’s previous-generation Climate Forecast System Reanalysis (CFSR) and more details can be found in Hamill et al. (2022).

c. Calibration method

It is well known that the raw products of any GCMs are not directly useful, and suitable statistical postprocessing is highly required for skillful forecast guidance and increase its usability. In the previous studies, various ensemble-based statistical postprocessing techniques have been used, e.g., frequency match method (FMM; Zhu and Luo 2015), quantile mapping method (Nageswararao et al. 2022; Guan et al. 2022), “poor man’s ensemble” (Ebert 2001), and analog method (Hamill and Whitaker 2006). This study uses the quantile mapping postprocessing technique to calibrate GEFSv12 rainfall reforecast data to improve prediction skills. The main advantage of this calibration method is to transform rainfall simulated by GEFSv12 to bias-corrected data statistically and make it applicable for use in the impact assessment of the GEFSv12 model. The technique is also called “histogram equalization” and/or “rank matching” (Wood et al. 2004; Hamlet et al. 2002; Piani et al. 2010).

The statistics of daily rainfall for CMORPH and GEFSv12 reforecasts were determined independently for each lead time (day-1–35 forecast lead times) and grid point over Taiwan during JJAS. This calibration method is applied separately to each individual and the mean of its 11 ensemble members at the grid point. For example, in the June month analysis, the GEFSv12 reforecast data for the period of 20 years (2000–19) is based on forecasts initialized at 0000 UTC every Wednesday between 16 May and 15 June. The corresponding sample size at each grid point for each lead time and each member is about 89 forecasts. The July, August, and September analyses have been practiced like the June analysis for implementing the calibration method. The rainfall intensity distributions from CMORPH and GEFSv12 reforecasts are well approximated by the gamma distribution. The empirical probability distributions of CMORPH and GEFSv12 rainfall values have been used in this technique. The calibrated output is the inverse of the cumulative distribution function (CDF) of CMORPH values at the probability corresponding to the GEFSv12 model output CDF at the particular value. Suppose CDFs, FCMORPH for CMORPH, and FGEFSv12 for an ensemble member rainfall forecast of the GEFSv12 model. For Ft the bias-corrected value Q will then be as follows:
Q=FCMORPH1[FGEFSv12(Ft)].
Here, F−1 is an inverse of the CDF. Thus, the technique of the quantile mapping is a transformation between two CDFs of the CMORPH and GEFSv12 model. The leave-one-out cross-validation procedure has been practiced in the entire process. Hereafter, the raw and calibrated outputs of GEFSv12 are mentioned as Raw-GEFSv12 and QQ-GEFSv12, respectively. In a similar way, the quantile mapping method is applied for all individual 11 members for ensemble probabilistic precipitation forecasts.

d. Analysis procedure

Foremost, gridpoint-wise patterns of climatological mean, interannual variability (IAV), and coefficient of variation (CV) of monthly rainfall over Taiwan from CMORPH, Raw-GEFSv12, and QQ-GEFSv12 during JJAS for the reforecast period have been analyzed. The IAV is the standard deviation, and it measures the amount of variation or dispersion of monthly rainfall from CMORPH, Raw-GEFSv12, and QQ-GEFSv12. A low IAV indicates that the values tend to be close to the climatological monthly mean rainfall, while a high IAV indicates the aberrant behavior of monthly rainfall. The CV is also known as the relative standard deviation, and it is defined as the ratio between the IAV and climatological mean of monthly rainfall. The performance of Raw-GEFSv12 and QQ-GEFSv12 in depicting summer monsoon monthly scale rainfall over Taiwan has been evaluated by using various skill metrics such as correlation coefficient (CC), index of agreement (IOA), mean bias, and root-mean-square error (RMSE). The CC measures the strength of the relationship between the relative movements of observed and model monthly scale rainfall. The CC ranges between −1 and 1. Here “−1” indicates model monthly rainfall having a strong inverse relationship with observed monthly rainfall, while “1” indicates model monthly rainfall is in the phase with observed monthly rainfall. The RMSE is used to measure the differences between model and observed monthly rainfall. The IOA is a standardized measure of the degree of model (GEFSv12) error with observation (CMORPH), and it ranges from 0 to 1 (Willmott 1981). Here “1” indicates good agreement between model and observation, while “0” represents no agreement. It is the ratio between the mean square error and the potential error of the model. The potential error is the sum of the squared absolute values of the distances from the estimated values to the mean of actual observed values. The IOA detects additive and proportional differences in the observed and estimated means and variances. It computed as
d=1[i=1N(PiOi)2i=1N(|PiO¯|+|OiO¯|)2],
where Oi and Pi represent observed and predicted monthly rainfall at the ith time, respectively. The O¯ indicates observed monthly climatological mean rainfall.

For a better understanding of GEFSv12 performance in depicting various intense rainfall events, daily rainfall probability distributions from Raw-GEFSv12 and QQ-GEFSv12 during June, July, August, and September over the entire Taiwan island (pooling all grid points) for the reforecast period have been calculated and compared with CMORPH.

Further, the analysis has been extended for wet days (≥2.5 mm day−1) and extreme rainfall events (ER ≥ 50 mm day−1). The spatial distribution of wet and ER events on a monthly scale over Taiwan during JJAS from CMORPH, Raw-GEFSv12, and QQ-GEFSv12 (frequency of ensemble mean forecast and average frequency of all 11 individual members’ forecasts) have been analyzed. The statistical categorical skill metrics, such as accuracy (ACC), frequency bias (BIAS), probability of detection (POD), false alarm rate (FAR), success ratio (SR), threat score (TS), equitable threat score (ETS), etc. by using a contingency table (https://www.cawcr.gov.au/projects/verification/) for Raw-GEFSv12 and QQ-GEFSv12 against CMORPH in depicting wet days and ER events have been computed (Wilks 2011). Further, statistical categorical skill scores for wet and ER events have been summarized using a performance diagram, which measures the geometric relationship between POD, SR, frequency bias, and threat scores of wet and ER events (Roebber 2009; Huang and Luo 2017).

The deterministic methods cannot represent the inherent uncertainty in forecasts if the uncertainty estimated for the particular category forecast is more helpful, especially for the climate risk management in various sectors. Nowadays, probabilistic forecasts are vital to using monthly and seasonal scale prediction (Mason et al. 1999; Palmer et al. 2004; Mason 2004). To assess the skill of GEFSv12 for probabilistic forecasts of wet and ER events, Brier score (BS), and Brier skill score (BSS) have been used (Brier 1950; Epstein 1969; Murphy 1993; Toth et al. 2003; Mason 2004; Kulkarni et al. 2012). The BS is a quadratic measure of the error in probabilistic forecasts and can also be used in multievent situations (Brier 1950). The BS is used in a dichotomous situation where an event of interest either happened or did not happen (Toth et al. 2003). It ranges from 0 to 1, and the perfect score is 0. BSS measures the BS improvement of the probabilistic forecast relative to a reference forecast. If BSS equals 1, the forecast is perfect, while BSS equals 0 indicates no improvement over the reference forecast/climatological probability forecast. The negative values of BSS indicate the forecast is worse than the reference forecast (Wilks 1995; Toth et al. 2003).

3. Results and discussion

To understand the prediction skill of EASM rainfall over Taiwan, first, the performance of GEFS-SubX and GEFSv12 against NOAA NCEP GEFSv12 Reanalysis is evaluated using standard skill metrics (Fig. 1) that depict the EASMI, which describe the interannual and interdecadal variations in EASM-related climate anomalies over East Asia. Both models are good in capturing the EASMI for all forecast lead times (Fig. 1). However, the RMSE of both the models in depicting EASMI increases with lead time and the RMSE of GEFSv12 is relatively less than the GEFS-SubX (Fig. 1a).

Fig. 1.
Fig. 1.

(a) RMSE, (b) correlation coefficient, and (c) index of agreement of GEFS-SubX and GEFSv12 in depicting the East Asian summer monsoon index (EASMI) against the GEFSv12 reanalysis based on every Wednesday initial conditions for forecast lead time day 1–35 for the period 2000–19.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

The prediction skill (CC and IOA) of both models in representing the EASMI is considerably high for all lead time forecasts (CC > 0.65 and IOA > 0.8) and it is particularly more up to lead Day 23 (CC > 0.7 and IOA > 0.85). However, the CC and IOA of both models for EASMI decreases with lead time. The prediction skill of EASMI from GEFSv12 is relatively higher for all forecast lead times than the GEFS-SubX (Figs. 1b,c).

Furthermore, the performance of GEFS-SubX and GEFSv12 in depicting JJAS daily rainfall over Taiwan is evaluated for all forecast lead times from day 1–35 against CMORPH by using standard skill metrics (figure not provided). There is a strong wet bias over Taiwan from both models, while both models underestimate the IAV and CV. As expected, the ensemble spread from both models increases with lead time. The GEFSv12’s ensemble spread is relatively smaller up to 2 weeks compared to GEFS-SubX while after 2 weeks it is relatively higher. The RMSE from both models depicting JJAS daily rainfall over Taiwan increases with lead time while the prediction skill (correlation coefficient and Index of agreement) decreases with lead time. However, the RMSE (prediction skill) from GEFSv12 is lesser (better) than the GEFS-SubX.

The probabilistic forecast biases over Taiwan from both models against CMORPH were measured for wet (>2.5 mm day−1) and ER (>50 mm day−1) (Fig. 2). Both models are overforecasting the wet and ER events over Taiwan during all monsoon months. Overall, the GEFSv12 has relatively better reliability than the GEFS-SubX for all four summer monsoon months over Taiwan for both Wet and ER days. The relative operating characteristic (ROC) curve for the Taiwan probabilistic rainfall forecast from both models has been computed and illustrated in Fig. 3. The graph of the ROC curve from both models is above the diagonal line for wet and ER days for all the summer monsoon months. The GEFSv12 has relatively outperformed the GEFS-SubX for both categorical rainfall events during all the months and it is notably more for ER days. The area under the curve (AUC) is more than 0.6 in both models. Moreover, the AUC value of GEFSv12 is higher than the GEFS-SubX for both wet and ER days during all the months (Fig. 3).

Fig. 2.
Fig. 2.

The reliability diagram for Taiwan probabilistic quantitative precipitation forecast (PQPF) from 2000 to 2019 for wet (>2.5 mm day−1) and ER (>50 mm day−1) days. The red and green indicate GEFS-SubX and GEFSv12, respectively.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

Fig. 3.
Fig. 3.

Relative operating characteristic (ROC) curve for verification of Taiwan probabilistic quantitative precipitation forecast (PQPF) from 2000 to 2019 for wet (>2.5 mm day−1) and ER (>50 mm day−1) days. The red and blue indicate GEFS-SubX and GEFSv12, respectively.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

The above analysis concluded that there is a marginal improvement in the prediction skill of GEFSv12 in representing the East Asian summer monsoon circulation dynamics and its influence on summer monsoon rainfall over Taiwan as compared to GEFS-SubX, and these improvements may be attributed to the combined influence of advanced data assimilation to provide better initial conditions including initial perturbations, new dynamic core (FV3), advanced microphysics schemes, updated stochastic schemes, and finer resolution (Zhou et al. 2022; Guan et al. 2022).

Further, the Raw-GEFSv12 rainfall products over Taiwan are calibrated with quantile–quantile mapping technique to improve the model rainfall intensity distribution to CMORPH rainfall intensity distribution for all individual ensemble members and its ensemble mean. The performance evaluation of Raw-GEFSv12 and QQ-GEFSv12 against CMORPH for rainfall reforecast products over Taiwan during June, July, August, and September months have been done. The summer monsoon monthly rainfall spatial patterns over Taiwan during June, July, August, and September from Raw-GEFSv12 more or less similar to CMORPH and there is a limitation in capturing the magnitude and it is particularly more for September (Fig. 4). However, the spatial patterns of climatological mean, of summer monsoon monthly rainfall over Taiwan from QQ-GEFSv12 are more similar to CMORPH than Raw-GEFSv12. The monthly rainfall is more prominent over the western windward sloping areas in central and southern Taiwan (300–500 mm), decreasing north and west. During June, July, and August, the maximum rainfall is mainly due to the convective systems embedded within the southwesterly monsoon flow. In addition, the mei-yu frontal systems from southern China also frequently bring heavy precipitation toward Taiwan (Yeh and Chen 1998; Chen 2000). Furthermore, the rainfall is quite substantial along the CMR. During June, the pronounced monsoon rainfall covers most parts of Taiwan and reduces west to east as the season progresses. Among the months, the maximum observed (CMORPH) monthly rainfall occurred during August (271 mm), followed by June (246 mm), July (211 mm), and September (200 mm). After August, the maximum rainfall zone shifted toward the north with seasonal progress, and similar patterns can be seen for Raw-GEFSv12 (Fig. 4). However, the Raw-GEFSv12 has a large wet bias in most parts of Taiwan, and it is notably more during July (115 mm) followed by June (81 mm), August (56 mm), and September (41 mm). After calibration, the monthly rainfall patterns over Taiwan are very similar to CMORPH, the wet bias is significantly reduced for all the months, and the magnitude of the monthly rainfall from QQ-GEFSv12 is relatively closer to CMORPH than Raw-GEFSv12.

Fig. 4.
Fig. 4.

Spatial distribution of monthly rainfall (mm) during summer monsoon from CMORPH, Raw-GEFSv12, and QQ-GEFSv12 (ensemble mean of 11 ensembles) based on weekly once initial conditions for the period 2000–19. The value at the bottom-right corner of each panel indicates the average climatological mean of monthly rainfall in Taiwan.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

Furthermore, the interannual variability (IAV) of monthly rainfall analysis reveals that the spatial patterns of IAV of monthly rainfall over Taiwan in most of the months from Raw-GEFSv12 more or less similar to CMORPH but it is unable to capturing the magnitude (Fig. 5). The maximum IAV of monthly rainfall from Raw-GEFSv12 can be seen over prominent monsoon rainfall regions, particularly Taiwan’s southern and eastern parts (>180 mm). In contrast, CMORPH shows maximum IAV, but Raw-GEFSv12 does not capture the exact magnitude. The maximum IAV of monthly rainfall over Taiwan from CMORPH is seen during the peak monsoon month, August (167 mm) followed by September (166 mm), June (146 mm), and July (126). Nevertheless, the Raw-GEFSv12 overestimated monthly rainfall in most parts of Taiwan during JJAS. The IAV of monthly rainfall from Raw-GEFSv12 during July (137 mm), followed by August (128 mm), June (118 mm), and September (109 mm) is lesser than the CMORPH (Fig. 5). After calibration, spatial patterns of IAV of monthly rainfall over Taiwan from QQ-GEFSv12 during all the months are like CMORPH. The underestimation of IAV of monthly rainfall of June, August, and September and overestimation of July over Taiwan from Raw-GEFSv12 decreased for all the months, and it has some similarities to CMORPH (Fig. 5).

Fig. 5.
Fig. 5.

Interannual variability (IAV) of monthly rainfall (mm) during summer monsoon from CMORPH, Raw-GEFSv12, and QQ-GEFSv12 (ensemble mean of 11 ensembles) based on weekly initial conditions for the period 2000–19. The value at the bottom-right corner of each panel indicates the average IAV of monthly rainfall in Taiwan.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

For the monthly rainfall, patterns in the CV from CMORPH reverse the patterns in the IAV and climatological mean from Raw-GEFSv12 (figure not provided). For example, the CV of monthly rainfall is low over prominent rainfall regions from CMORPH and Raw-GEFSv12. However, the Raw-GEFSv12 has underestimated the CV of monthly rainfall in most parts of Taiwan during all the months while overestimating the climatological mean and IAV of monthly rainfall in the same regions. It has also been observed that the CV from Raw-GEFSv12 and CMORPH is smaller during the peak monsoon months of August and June, while the CV of monthly rainfall is relatively higher in the low rainfall month of September. After calibration, the CV patterns of monthly rainfall over Taiwan improved for all the months. However, still, there is a slight overestimation of the CV of monthly rainfall in most parts of the country in most months.

The RMSE of Raw-GEFSv12 for monthly rainfall is high over prominent rainfall regions, particularly in the south and eastern part of Taiwan (>200 mm), and it decreases from south to north and east to west during all the months (Fig. 6a). The RMSE of Raw-GEFSv12 for monthly rainfall over Taiwan is high for July (211 mm), followed by August (189 mm), June (185 mm), and September (169 mm). The Raw-GEFSv12 has a low prediction skill in depicting monthly rainfall during July compared to other months in which rainfall and its variability are less than in August and June. After calibration, the RMSE of monthly rainfall over Taiwan decreased for June and July months while it increased for August and September (Fig. 6a). The calibration method improves the in IAV for all the months but it is slightly overestimated. Sometimes, the increased IAV may lead to an increase in the RMSE, and it is clearly reflected in August and September. The mean-bias analysis reveals that the Raw-GEFSv12 has a large wet bias in most parts of Taiwan for all the months and is more during July (114 mm) followed by June (87 mm), August (57 mm), and September (42 mm) (Fig. 6b). The mean bias of Raw-GEFSv12 for monthly rainfall is more in the south and eastern parts of Taiwan, and this analysis supports the findings from Fig. 4. The overestimation of monthly rainfall in most parts of Taiwan is also relatively more for July than the other months where the RMSE is also more. The Raw-GEFSv12 has a dry bias over some parts of northern Taiwan during September (Fig. 6b). After calibration, the mean bias error for monthly rainfall decreased significantly for all the months. However, a slight overestimation (1–3 mm) in most parts of Taiwan for all the months still exists.

Fig. 6.
Fig. 6.

(a) Root-mean-squared error and (b) mean bias of Raw-GEFSv12 and QQ-GFSv12 against CMORPH in depicting monthly rainfall (mm) during summer monsoon for the period 2000–19. The value at the bottom-right corner of each panel indicates the average RMSE/mean bias of monthly rainfall in Taiwan.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

The correlation coefficient (CC) analysis reveals that the Raw-GEFSv12 is good in capturing the year-to-year variations in the monthly summer monsoon rainfall over Taiwan against CMORPH for most of the summer monsoon months except July (CC < 0.2) (Fig. 7a). The Raw-GEFSv12 and QQ-GEFSv12 have a significant correlation coefficient in most parts of Taiwan (CC > 0.4 at 90% confidence level) in predicting monthly rainfall over Taiwan. The prediction skill of Raw-GEFSv12 is notably greater during September (0.43), followed by August (0.41) and June (0.36). The Raw-GEFSv12 and QQ-GEFSv12 had correlation coefficient values >0.4 (significant at 90% confidence level) over prominent rainfall regions (Fig. 7a). After calibration, there is a similar correlation coefficient pattern over Taiwan from QQ-GEFSv12 for all the months. However, there is a slight decrease in the correlation coefficient values. The reason is that the quantile–quantile mapping method matches the forecast probability distributions to observations, but the temporal structure is lost in this method. Furthermore, the Index of Agreement (IOA) analysis indicates the Raw-GEFSv12 agrees well with CMORPH in predicting monthly rainfall over Taiwan for all the months (Fig. 7b). The IOA values from Raw-GEFSv12 in most parts of Taiwan are good (IOA > 0.5) for most of the summer monsoon months except July (IOA < 0.2) and are notably higher for the peak monsoon of August (IOA > 0.6). After calibration, there has been a marginal improvement in the IOA of QQ-GEFSv12 in most parts of Taiwan. The average IOA values for Taiwan for June, July, August, and September are 0.58, 0.49, 0.62, and 0.62, respectively. The analysis concluded that the calibration method improves the prediction skill of GEFSv12 in depicting the monthly rainfall over Taiwan for all the monsoon months.

Fig. 7.
Fig. 7.

(a) Correlation coefficient and (b) index of agreement of Raw-GEFSv12 and QQ-GFSv12 against CMORPH in depicting monthly rainfall during summer monsoon for the period 2000–19. The value at the bottom-right corner of each panel indicates the average CC/IOA of monthly rainfall in Taiwan.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

The Raw-GEFSv12 forecast tends to underestimate the probability of daily (24 h accumulated) rainfall (full domain of Taiwan) less than ∼30 mm day−1 for all the monsoon months, while it has been overestimating the probability for more than 30 mm day−1 (Fig. 8). The CDF curve of Raw-GEFSv12 is relatively farther from the CMORPH’s CDF curve for July daily rainfall than the other months, and the low skill for July is evident in the previous analysis (Fig. 8). The CDF curve from Raw-GEFSv12 during the low rainfall month of September is relatively closer to the CMORPH’s CDF curves than during the peak monsoon months. After calibration, the CDF curves from QQ-GEFSv12 are relatively closer to CMORPH’s CDF curves for all the months except July. Therefore, the calibration method has well-adjusted the probability distribution of various intensity rainfall events over Taiwan for all the months to CMORPH (Wood et al. 2004; Hamlet et al. 2002; Piani et al. 2010). After calibration, the predictability of high-intensity rainfall events (>30 mm days−1) during all the months, while the predictability of these events from Raw-GEFSv12 is very low. The Raw-GEFSv12 has an overestimation of less than (30 mm day−1) rainfall events over Taiwan during June, July, August, and September, while it has been underestimated for greater than 30 mm day−1. After calibration, the probability distribution of various intensity rainfall events is adjusted well from QQ-GEFSv12 to the CMORPH for all months (figure not provided). The improvement in adjusting the probability of various rainfall events is particularly more for September while it is low for July.

Fig. 8.
Fig. 8.

Cumulative distribution function (CDF) of 24-h accumulated precipitation from CMORPH (black lines), Raw-GEFSv12 (purple lines), and QQ-GEFSv12 (green lines) (calibration on the ensemble mean of 11 members) over Taiwan during June, July, August, and September for reforecast period 2000–19.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

By using the contingency table, various statistical categorical skill scores such as POD, frequency bias, FAR, ACC, SR, TS, and ETS have been computed for wet (≥2.5 mm day−1) and ER (≥50 mm day−1) events over Taiwan for the reforecast period (2000–19). The frequency bias analysis of wet days reveals that the ensemble mean (Raw-GEFSv12-ENSM) has a large overestimation of wet days in most parts of Taiwan for all the months than the Average of all induvial members frequency (Raw-GEFSv12-All-Members-Avg) (figure not provided). After calibration, the probability distribution of Wet days over Taiwan is well adjusted from Raw-GEFSv12-ENSM and Raw-GEFSv12-All-Members-Avg to CMORPH for all the months and the overestimation reduced. The improvement is more from QQ-GEFSv12-ENSM in most parts of Taiwan for all the months while the QQ-GEFSv12-All-Members-Avg still has a considerable overestimation of wet days in most parts of Taiwan. In the case of ER events analysis, the Raw-GEFSv12-ENSM has a large underestimation of ER events in most parts of Taiwan for all the months (figure not provided), while the Raw-GEFSv12-All-Members-Avg is relatively closer to CMORPH. After calibration, both QQ-GEFSv12-ENSM and QQ-GEFSv12-All-Members-Avg have captured the ER events in most parts of the country.

From Fig. 9, the ETS of Raw-GEFSv12-ENSM in depicting wet days over Taiwan is relatively low during all the months than Raw-GERFSv12-All-Members-Avg. The ETS of Raw-GEFSv12-ENSM and Raw-GEFSv12-All-Members-Avg for wet days is relatively high in the west and northern parts of Taiwan and decreases toward the south and east in most of the months.

Fig. 9.
Fig. 9.

Equitable threat score (ETS) of Raw-GEFSv12 and QQ-GEFSv12-ENSM and mean skill of all individual members for wet Days (≥2.5 mm days−1) on a monthly scale over Taiwan against CMORPH for the period 2000–19.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

The ETS of Raw-GEFSv12-ENSM and Raw-GEFSv12-All-Members-Avg for wet days is somewhat lower in the south and eastern part of Taiwan during all the months, where wet days and associated rainfall prominently occur (Fig. 9). After calibration, the ETS score (>0.5) of QQ-GEFSv12-ENSM and QQ-GEFSv12-All-Members-Avg for wet days has marginally improved in most parts of Taiwan for all the months. Both Raw-GEFSv12-ENSM and Raw-GEFSv12-All-Members-Avg are having similar patterns of ETS for ER events over Taiwan for all the months (Fig. 10). The ETS score of ER events from both Raw-GEFSv12-ENSM and Raw-GEFSv12-All-Members-Avg is decreasing from south to north and east to west. However, the ETS of ER events from QQ-GEFSv12-ENSM is less in most parts of Taiwan than Raw-GEFSv12-All-Members-Avg for all the months. It is observed that the ER events’ ETS score from both Raw-GEFSv12-ENSM and Raw-GEFSv12-All-Members-Avg is less in most parts of Taiwan than on wet days during all months (Fig. 10). The calibration method marginally improved the ETS of QQ-GEFSv12-ENSM and QQ-GEFSv12-All-Members-Avg for ER events in most parts of Taiwan for all months. The ETS improvement for ER events is relatively more in most parts of Taiwan for all the months from QQ-GEFSv12-ENSM than QQ-GEFSv12-All-Members-Avg.

Fig. 10.
Fig. 10.

Equitable threat score (ETS) of Raw-GEFSv12 and QQ-GEFSv12-ENSM and mean skill of all individual members for extreme rainfall days (≥50 mm days−1) on a monthly scale over Taiwan against CMORPH for the period 2000–19.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

The performance diagram is a suitable method for summarizing several categorical skill scores such as POD, frequency bias, TS, and SR (1 − FAR) in a single graph (Roebber 2009; Huang and Luo 2017). The solid contour lines in the performance diagram (Fig. 11) show the TS, while the dash lines indicate the frequency bias with extended labels on the x and y top and right axes, respectively. From Fig. 11a, the Raw-GEFSv12-ENSM has a considerable overestimation (frequency bias is > 2) of wet days (>2.5 mm day−1) over Taiwan for all months, whereas the POD is remarkably high (POD > 0.9). After calibration, a substantial reduction of overestimated wet days over Taiwan from QQ-GEFSv12-ENSM has been detected for all months. In contrast, the POD of wet days over Taiwan decreased for all months. After calibration, the TS and SR skill scores for wet days over Taiwan from QQ-GEFSv12-ENSM (TS > 0.5 and SR > 0.8) are extraordinarily higher than Raw-GEFSv12-ENSM (TS < 0.5 and SR < 0.5) for all the months (Fig. 11a). The Raw-GEFSv12-ENSM has a considerable underestimation of ER events over Taiwan for all the months (frequency bias < 0.4), and the POD in most of the months also is low (POD < 0.3) (Fig. 11b). After calibration, the POD and TS of ER events over Taiwan from QQ-GEFSv12-ENSM marginally improved for all the months. The frequency of ER events over Taiwan from QQ-GEFSv12-ENSM has risen notably for all months. It is mainly due to adjusting the probability distribution of various intensity rainfall events from GEFSv12-ENSM to the CMORPH.

Fig. 11.
Fig. 11.

Performance diagram summarizing the SR, POD, frequency bias, and TS statistical categorical skill scores of Raw-GEFSv12 and QQ-GEFSv12 against CMORPH for (a) wet days and (b) extreme rainfall events on the monthly scale over Taiwan during June, July, August, and September for the period 2000–19. The solid and dashed lines represent TS and frequency bias scores, respectively.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

The analysis of the performance diagram for Raw and QQ-GEFSv12-All-Members have also been done (figure not provided). Most of the statistical categorical skill scores of wet and ER events are higher for the average of all individual members (Raw-GEFSv12-All-Members) than the ensemble mean forecast (Raw-GEFSv12-ENSM). There is a larger overestimation (underestimation) of wet days (ER events) from Raw-GEFSv12-ENSM than the mean of All individual members (Raw-GEFSv12-All-Members). The overestimation of wet days from Raw-GEFSv12 is due to the ensemble’s mean most days shows some rainfall. The underestimation of ER events is mainly because the ensemble mean is to smooth out the peaks in rainfall.

The higher (lower) POD of wet days (extreme events) from the Raw-GEFSv12-ENSM is mainly due to the overestimation (underestimation) of wet days (ER events). The overestimation (underestimation) of wet days (Extreme events) can cause a higher (lower) false alarm rate. The calibration method notably decreases (increases) the frequency of wet days (ER events) and leads to a decrease (increase) in the POD. The calibration method improved the statistical categorical skill scores of frequency bias, success rate, threat score, and equitable threat score for both the wet days and extreme events, while the POD is improved only for extreme events.

The above analysis concluded that the Raw-GEFSv12-ENSM for wet and ER events is not of much use without calibration. But the calibration method marginally improved most of the statistical categorical skill scores of QQ-GEFSv12-ENSM for wet and ER events than QQ-GEFSv12-All-Members-Mean. The calibrated ensemble mean deterministic forecast of wet and ER events is very much more helpful than the calibrated individual ensemble members’ mean. However, the calibrated individual members may be helpful in generating better probabilistic forecasts of wet and ER events.

Further, the probabilistic forecasts of wet and ER events from Raw-GEFSv12 and QQ-GEFSv12 have been evaluated by using standard skill metrics such as the BS and BSS (Brier 1950; Toth et al. 2003; Mason 2004; Kulkarni et al. 2012). The BS is a special case of a rank probabilistic score (RPS) with two categories (Brier 1950). The BS for probabilistic wet and ER events forecasts from Raw-GEFSv12 and QQ-GEFSv12 indicate that the BS of wet days from Raw-GEFSv12 in most regions of Taiwan is good (BS < 0.5) except over some parts of the eastern (BS > 0.5) (Fig. 12a). After calibration, the BS (<0.3) of QQ-GEFSv12 for wet days in most parts of Taiwan improved significantly during all the months. The BS is considerably lower for ER events (BS > 0.05) from Raw-GEFSv12 and QQ-GEFSv12 in most parts of Taiwan than wet days for all the months. After calibration, the BS for ER events from QQ-GEFSv12 has marginally improved in most of Taiwan for all months (Fig. 12b).

Fig. 12.
Fig. 12.

Brier score of Raw-GEFSv12 and QQ-GEFSv12 against CMORPH for (a) wet days (>2.5 mm day−1) and (b) extreme rainfall events (>50 mm day−1). Ensemble probabilistic forecasts over Taiwan during June, July, August, and September for the period 2000–19.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

Further, the BSS and RPSS skill scores are extensively used to evaluate categorical probabilistic forecasts compared to reference forecasts. The BSS can describe the special case of an RPSS with two forecast categories (Weigel et al. 2007). From Fig. 13a, the Raw-GEFSv12 probabilistic forecast of wet days for all the monsoon months in most parts of Taiwan is worse than the reference forecast (BSS < 0). In contrast, the Raw-GEFSv12 probabilistic forecast of wet days in northwest Taiwan is better than the reference forecast for all the months. After calibration, the spatial coverage of a better probabilistic forecast of wet days than the reference forecast from QQ-GEFSv12 increased marginally for all the months (Fig. 13a). Interestingly, the BSS of Raw-GEFSv12 is relatively more for ER events than the wet days for most parts of the country during all the months (Figs. 13a,b). The better BSS skill of Raw-GEFSv12 is particularly more during August, which month ER events frequently occurred in most parts of Taiwan. After calibration, the spatial coverage of better BSS skill (>0) of QQ-GEFSv12 for ER events increased marginally for all the months. The above performance analysis concluded that the calibration method marginally improved the prediction skill of GEFSv12 for probabilistic forecasts of wet and ER events for all the months, and their spatial extent of better skill is notably increased.

Fig. 13.
Fig. 13.

Brier skill score of Raw-GEFSv12 and QQ-GEFSv12 against CMORPH for (a) wet days (>2.5 mm day−1) and (b) extreme rainfall events (>50 mm day−1). Ensemble probabilistic forecasts over Taiwan during June, July, August, and September for the period 2000–19.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

The probabilistic forecast biases for the wet and ER days over Taiwan from Raw-GEFSv12 and QQ-GEFSv12 against CMORPH were measured by reliability diagrams (figure not provided). The closer the reliability curve is to the diagonal line, the better the reliability. Overall, the QQ-GEFSv12 slightly outperforms the Raw-GEFSv12 for all four summer monsoon months June, July, August, and September over Taiwan. The improvement in the QQ-GEFSv12 is more detectable for ER days (>50 mm day−1) during the peak monsoon month of August, which is the month when ER events frequently occurred. The reliability closer to zero indicates a better forecast. The reliability of QQ-GEFSv12 for wet and ER days is relatively better than Raw-GEFSv12 for all forecast lead times (day 1–35) during all the months, while the improvement is notably greater for wet days (Fig. 14).

Fig. 14.
Fig. 14.

Reliability of (left) wet and (right) ER events probabilistic forecast over Taiwan during June, July, August, and September from Raw-GEFSv12 and QQ-GEFSv12 against CMORPH based on every Wednesday initial conditions with increasing forecast lead time for days 1–35 for the period 2000–19.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0025.1

The above performance analysis concluded that the calibration method notably improved the prediction skill of GEFSv12 for probabilistic forecasts of wet and ER events for all the months, and their spatial extent of better skill has also increased.

4. Summary and conclusions

In September 2020, NOAA/NCEP implemented the Global Ensemble Forecast System, version 12 (GEFSv12), to support subseasonal forecast guidance tools for various meteorological and hydrological applications. They generated a consistent reforecast product of this model based on daily 0000 UTC initial conditions out to 16 days with 5 ensemble members except on Wednesdays when the integration extended to 35 days with 11 members for the period 2000–19. In the present study, the performance evaluation of the GEFSv12 reforecasts for monthly rainfall and associated extreme events over Taiwan during JJAS compared against CMORPH. Furthermore, the quantile-quantile mapping calibration technique is incorporated to enhance the prediction skill of GEFSv12 rainfall reforecast products.

The performance evaluation reveals that there is a remarkable improvement in the prediction skill of GEFSv12 in representing the East Asian summer monsoon circulation dynamics and its influence on summer monsoon rainfall over Taiwan compared to GEFS-SubX. These improvements may be attributed to the combined influence of better initial conditions, more advanced microphysics schemes, updated stochastic schemes, finer resolution, and a new FV3 dynamic core. The GEFSv12 can represent the climatological features mean, IAV, and CV of monthly rainfall over Taiwan during the summer monsoon season. The mean and IAV of monthly rainfall are greater during August (271, 167 mm), followed by June (246, 146 mm), July (211, 126 mm), and September (200, 166 mm). After August, the maximum rainfall zone shifted toward the north with seasonal progress and similar patterns can be found from GEFSv12. However, GEFSv12 has a significant overestimation for monthly rainfall and associated wet days (>2.5 mm day−1) in Taiwan for all summer monsoon months. It is particularly more during the peak monsoon months of August, June, and July. The spatial patterns of the CV of monthly rainfall over Taiwan from CMORPH in most months are the opposite of the climatological mean and IAV. The same features have been noticed from Raw-GEFSv12. However, Raw-GEFSv12 has a large underestimation of CV in most parts of Taiwan for all the months. After calibration, the overestimation in the mean and underestimation in the IAV and CV of monthly rainfall over Taiwan from QQ-GEFSv12 is notably reduced.

The RMSE and mean bias errors of monthly rainfall from Raw-GEFSv12 are high in the south and eastern part of Taiwan, whereas prominent monthly rain and its IAV are significantly high. The errors of RMSE and mean bias decrease from south to north and east to west during all the months. After calibration, both errors notably decreased for all the months in most parts of the country. The prediction skill (CC and IOA) of GEFSv12 in depicting monthly rainfall over Taiwan is significantly high (CC and IOA > 0.5) in most parts of Taiwan and particularly more during the peak monsoon months. The correlation coefficient (CC) of the Raw-GEFSv12 monthly rainfall forecast is high for September (0.43), followed by August (0.41), June (0.36), and September (0.19), while the IOA of Raw-GEFS is higher for September (0.6), followed by August (0.59), June (0.55), and July (0.44). After calibration, the IOA values marginally improved from QQ-GEFSv12 for September (0.62), August (0.62), June (0.58), and July (0.49).

There is a considerable overestimation of wet days in most parts of Taiwan from Raw-GEFSv12 during all months, despite an underestimation of ER events. After calibration, the probability distribution of various intensity rainfall events is well adjusted to the CMORPH in most parts of the country. The QQ-GEFSv12 can depict ER events (>50 mm days−1), in which rainfall events lead to floods and landslides over Taiwan. The statistical categorical skill score analysis reveals that the accuracy of Raw-GEFSv12 for wet and ER events over Taiwan is remarkably high, while the POD (∼1) is only for wet days. The calibration method significantly improved most of the statistical categorical skill scores (BIAS, ACC, SR, FAR, TS, and ETS) for wet and ER events. The POD also significantly improved for ER events in most parts of the country for all the months. The assessment of probabilistic forecasts reveals that the skill of wet and ER events over prominent rainfall zones such as the south and eastern part of Taiwan from Raw-GEFSv12 is worse (BSS < 0) than the climatological forecast during all the months. However, better skill (BSS > 0) for the probabilistic forecast of wet and ER events from Raw-GEFSv12 has been found over the northwestern part of Taiwan. The calibration method marginally improved the prediction skill of GEFSv12 for probabilistic forecasts of wet and ER events for all the months, and their spatial extent over Taiwan is also increased.

Therefore, the calibration of GEFSv12 rainfall raw products using the quantile mapping postprocessing technique is a useful tool to provide rainfall forecast guidance over Taiwan on a monthly scale, along with short- and medium-range forecasts. It can be helpful for tactical adjustments to the strategic decisions made based on the long-lead seasonal forecast outlooks for managing the risk in various sectors due to floods and droughts over Taiwan.

Acknowledgments.

This work is carried out with generous funding support from the NCEP Visiting Scientist Program managed by the University Corporation for Atmospheric Research (UCAR) Cooperative Programs for the Advancement of Earth System Science (CPAESS). The authors are grateful to the Ensemble Team members at the NCEP Environmental Modeling Center (EMC) for providing access to the datasets used in this study. Drs. Partha Bhattacharjee, Eric Sinsky, and Mary Hart are thanked for their careful reviews of the manuscript. The authors are also very appreciative of the anonymous reviewers for providing valuable suggestions and comments that helped improve the quality of the manuscript.

Data availability statement.

The GEFSv12 reforecast products over Taiwan island for the period (2000–19) have been obtained from Amazon web services (AWS), which are accessible by the broader community. The products are available at https://noaa-gefs-retrospective.s3.amazonaws.com/index.html), NOAA CPC Morphing Technique (CMORPH) multi-satellite-based precipitation data for the same period (2000–19) were acquired from the official FTP server (https://www.ncei.noaa.gov/data/cmorph-high-resolution-global-precipitation-estimates/access/daily/0.25deg/) of the Climate Prediction Center of the National Oceanic and Atmospheric Administration. The GEFS-SubX reforecast products over Taiwan island have been obtained from the Data library of the International Research Institute (IRI) for Climate Society. They are available at https://iridl.ldeo.columbia.edu/SOURCES/.Models/.SubX/.EMC/.GEFS/.hindcast/.pr/.

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