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  • View in gallery

    The positions of (a) six radars with radar coverage and (b) the surface observation station in Taiwan.

  • View in gallery

    The best track of 15 typhoon cases.

  • View in gallery

    The experimental domain setting of WRF.

  • View in gallery

    The image of radar echo: (a),(d) observation at 0800 and 1000 UTC 19 Sep 2010. (b),(e) MAPLE forecast after 2 and 4 h from 0600 UTC. (c),(f) MAPLE and EC forecast after 2 and 4 h from 0600 UTC. Motion fields at 0600 UTC: (g) the VET, (h) the ECMWF reanalysis wind field at 400 hPa, (i) the blending VET obtained from (g) and (h).

  • View in gallery

    The rain map of (a) the observation, (b) MAPLE, and (c) MAPLE_EC after 4 h accumulated rainfall.

  • View in gallery

    The average SCC score of 4 typhoon cases on (a) the tests of different resolutions. 48 × 48 and 144 × 144 mean the resolution of the VET. 144d03 and 48d02 mean the combination of the VET (144 × 144, 7 km, and 48 × 48, 20 km) and the WRF wind in outputs (3 and 9 km); (b) the tests of different pressure levels; (c) the different experimental tests (Table 4).

  • View in gallery

    The radar echo and the rain map at 0600 UTC 19 Sep 2010 of the second and fourth hour accumulated precipitation of (a) the observation, (b) MAPLE, and (c) MAPLE_WRF.

  • View in gallery

    The ETS score at 0600 UTC 19 Sep 2010. (a) MAPLE; (b) MAPLE_WRF. The red represents the ETS score above 0.3.

  • View in gallery

    The ETS score of the accumulated rainfall of Typhoon Fanapi during entire period.

  • View in gallery

    The average SCC (solid) and RMSE (dashed) of all real cases.

  • View in gallery

    The performance diagram of 16 typhoon cases for the reflectivity threshold of (a) 15 and (b) 35 dBZ. The colors represent the forecast results of the different model in the legend, and the circles along a line are the scores of the echo forecast per 30 min.

  • View in gallery

    The average ETS in 4-h accumulated rainfall. In total, there were (a) 16 cases and (b) 11 cases that landed in Taiwan. (c) There were five cases that did not land in Taiwan.

  • View in gallery

    The average ETS of 11 cases landed Taiwan as in Fig. 12. (a) Stage T1, (b) stage T2, and (c) stage T3.

  • View in gallery

    The average FSS score of 16 typhoon cases during entire period. (a)–(c) 15 dBZ (~0.27 mm h−1), (d)–(f) 35 dBZ (~5.8 mm h−1), and (g)–(i) 45 dBZ (~27 mm h−1) during entire period of MAPLE (48 × 48), MAPLE (144 × 144), and MAPLE_WRF, respectively. The Z–R relationship in Eq. (1) is used to estimate the hourly rainfall rate.

  • View in gallery

    The average FSS of 11 cases landed in Taiwan as in Fig. 14. (a) Stage T1, (b) stage T2, and (c) stage T3.

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Improving Radar Echo Lagrangian Extrapolation Nowcasting by Blending Numerical Model Wind Information: Statistical Performance of 16 Typhoon Cases

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  • 1 Department of Atmospheric Sciences, National Central University, Taoyuan City, Taiwan
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Abstract

Severe weather nowcasting is a crucial mission of atmospheric science for the betterment of society to save life, limb, and property. In this study, composite radar data from the Central Weather Bureau of 16 typhoons are collected to examine the statistical performance of the McGill Algorithm for Precipitation nowcasting using Lagrangian Extrapolation (MAPLE) over Taiwan, an extrapolation algorithm that predicts future precipitation based on current radar echoes. In addition, instead of mixing the precipitation between radar extrapolation and numerical model forecast as in previous studies, a blending system is formed by synthesizing the wind information from model forecast with the echo extrapolation motion field via a variational algorithm to improve the nowcasting system. The statistical results of the radar echo extrapolation for 16 typhoon cases show that while the quantitative precipitation nowcasting skill can persist for up to 2 h, significant distortion for the rotational system is found after 2 h. On the other hand, the blending system helps to capture and maintain the rotation of typhoon rainband structures. The blending system extends the nowcasting skill by 1 h to a total of 3 h. Furthermore, the blending scheme performs especially well after the typhoon makes landfall in Taiwan. For disaster prevention and mitigation, this blending nowcasting technique may provide effective weather information immediately.

Denotes content that is immediately available upon publication as open access.

© 2020 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: Dr. Kao-Shen Chung, kschung@atm.ncu.edu.tw

Abstract

Severe weather nowcasting is a crucial mission of atmospheric science for the betterment of society to save life, limb, and property. In this study, composite radar data from the Central Weather Bureau of 16 typhoons are collected to examine the statistical performance of the McGill Algorithm for Precipitation nowcasting using Lagrangian Extrapolation (MAPLE) over Taiwan, an extrapolation algorithm that predicts future precipitation based on current radar echoes. In addition, instead of mixing the precipitation between radar extrapolation and numerical model forecast as in previous studies, a blending system is formed by synthesizing the wind information from model forecast with the echo extrapolation motion field via a variational algorithm to improve the nowcasting system. The statistical results of the radar echo extrapolation for 16 typhoon cases show that while the quantitative precipitation nowcasting skill can persist for up to 2 h, significant distortion for the rotational system is found after 2 h. On the other hand, the blending system helps to capture and maintain the rotation of typhoon rainband structures. The blending system extends the nowcasting skill by 1 h to a total of 3 h. Furthermore, the blending scheme performs especially well after the typhoon makes landfall in Taiwan. For disaster prevention and mitigation, this blending nowcasting technique may provide effective weather information immediately.

Denotes content that is immediately available upon publication as open access.

© 2020 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: Dr. Kao-Shen Chung, kschung@atm.ncu.edu.tw

1. Introduction

Heavy rain from typhoons is one of the most severe weather systems in Taiwan. Heavy rains and strong wind accompany typhoons, and these phenomena may last for several hours before and after landing in Taiwan, leading to disasters such as flooding and landslides. To mitigate the disastrous impacts of heavy rain from typhoons, quantitative precipitation forecasts (QPF) in the time scale of the very short term, known as “nowcasting” (less than 6 h), play an important role in disaster prevention in Taiwan.

In recent years, numerical weather models have shown significant improvements in forecast skill due to the development and refinement of physical modeling and computational techniques. These models provide increasingly fine spatial and temporal resolution forecast fields for users in an ever-decreasing amount of time. However, model forecasts face spinup or spindown issues, whereby a certain amount of time (usually 1–3 h) is required after warm-start initialization to reach a stable model state (Shrestha et al. 2013; Chung et al. 2013; Jacques et al. 2017). On the other hand, by assimilating radar observations in different data assimilation systems, as previous studies have shown, the improvement of QPF sometimes could last up to 6 h (Kain et al. 2010; Sun et al. 2014), and sometimes the impact may remain confined to around 1–2 h (Aksoy et al. 2010; Chang et al. 2016; Chang et al. 2014; Chung et al. 2009). Therefore, to forecast precipitation of severe weather in the very short-term effectively, radar echo extrapolation remains a powerful and highly relevant method.

Because weather radar is capable of providing high temporal and spatial resolution over a certain area, it remains the most useful instrument to survey severe weather over land and near coasts where such radar systems are available. Radar extrapolation is a well-established technique to perform quantitative precipitation nowcasting (QPN). For instance, Thunderstorm Identification, Tracking, Analysis and Nowcasting (TITAN) tracked and extrapolated storms linearly by identifying the centroids of the weather system (Dixon and Wiener 1993). The Short-range Warnings of Intense Rainstorms in Localized System (SWIRLS) developed by the Hong Kong Observatory uses the technique named Tracking Radar Echoes by Correlations (TREC) (Rinehart and Garvey 1978; Tuttle and Foote 1990). TREC calculates the correlation coefficients between consecutive radar echo images and proceeds to compute an extrapolation forecast. When the information of SWIRLS is used to modify the hydrometeor variables of the numerical model, it can extend the forecast ability (Li and Lai 2004). Instead of finding the maximum correlation to get the motion vector, such as TREC, the McGill Algorithm for Precipitation nowcasting using Lagrangian Extrapolation (MAPLE; Germann and Zawadzki 2002, 2004) uses the variational method to minimize a cost function to define the motion field that then advects the radar echo images for nowcasting.

The major drawback of the extrapolation-based nowcasting based on extrapolation is that it is difficult to capture the growth and decay of the weather system and the uncertainty of the displacement. To overcome this issue, several studies have applied blending techniques to improve nowcasting systems. For instance, the Short-Term Ensemble Prediction System (STEPS; Seed 2003), developed by the Met Office and Bureau of Meteorology in Australia, utilized the Fourier filter to decompose precipitation information (radar echoes) into different spectral scales, and then combined the extrapolation nowcast and downscaled NWP forecast to produce a probabilistic precipitation forecast. Based on this algorithm, the forecasting skill can persist for up to 6 h in Australia (Bowler et al. 2006). The Rainstorm Analysis and Prediction Integrated Data-processing System (Li et al. 2005) merges the precipitation information from the Nonhydrostatic Model (NHM) with SWIRLS echo extrapolation. With a rainstorm case study, the results show an improvement of 3-h nowcasts. Similar to SWIRL, the Adjustment of Rain from Models with Radar (ARMOR; Lee et al. 2009) combines the Weather Research and Forecasting (WRF) Model with MAPLE. By estimating the phase error of precipitation between WRF and observations, the blending system modifies the rainfall rate of the model. It is able to improve the distribution of the precipitation and reduce the false alarm area from NWP, but echo extrapolation still outperforms the nowcast in the first few hours (DuFran et al. 2009). Instead of blending information between radar observations and NWP models, several studies focus on mixing model forecast winds with the nowcast system. By applying a fuzzy algorithm, Liang et al. (2010) proposed a composite approach by which model-predicted wind gradually replaces the motion field estimated by echo movement. In a summer case study, their results showed that a composite approach can perform effective nowcasts for up to a 3-h lead time. Sokol et al. (2017) included the information of tracking errors in the motion field. When focusing on strong convection in warm seasons, their results demonstrated that the forecast skill is useful up to 60 min. Ryu et al. (2019) introduced an advection-diffusion model to modify motion vectors, and concluded that when motion vectors are time dependent in the nowcast lead time, better nowcast performance can be achieved.

Recently, probabilistic nowcasting systems have also been used to improve the capability of nowcasting. Based on the stochastic perturbation of the Lagrangian extrapolation, Atencia and Zawadzki (2014) generated an ensemble to alleviate the errors of growth and decay. Their results have shown that this approach can better reproduce the spatial structure of the precipitation system and extend the nowcast lead time beyond 2–3 h statistically. Sokol et al. (2017) used random perturbations generated by the historic radar data from the warm season (May to September) of years 2009–12 to conduct an ensemble nowcast. Their results showed that the forecast skill in summertime (July 2012) can last approximately 30–40 min.

The purpose of this study is to examine and improve the performance of MAPLE for nowcasting heavy precipitation in the Taiwan area. Taiwan, a subtropical island, regularly experiences heavy precipitation exceeding 15 mm h−1 and 50 mm day−1 (Chen et al. 2007). Since the average mountain height in Taiwan is around 2 km with peaks up to 4 km, it is a natural environment for evaluating MAPLE’s performance over complex terrain. In previous studies, MAPLE has shown its capability for nowcasting up to 2–6 h depending on the regions being implemented (Germann and Zawadzki 2002, 2004; Turner et al. 2004; Bellon et al. 2010; Lee et al. 2010, Mandapaka et al. 2012). MAPLE was first applied and configured over Taiwan in 2018 (Pan et al. 2018). In their study, two typhoon cases and one frontal system case were selected to examine the performance of MAPLE. The results showed that MAPLE outperformed persistence and it produced reasonable skill for nowcasting up to 2 h. In this study, 16 typhoon cases are selected to examine the performance of MAPLE statistically over Taiwan’s complex terrain. In addition, to alleviate the distortion of the rotational weather system during extrapolation, wind information from a numerical model is included to improve the nowcasting system. Each typhoon is divided to three stages (before landing, after landing, and leaving Taiwan) to investigate the results of nowcasting in each stage.

The organization of this study is as follows: the source of data and the selected cases are described in section 2; the methodology of MAPLE, the blending algorithm, and verification scores are illustrated in section 3; the results of echo extrapolation nowcasting with and without blending as well as a statistical analysis of the performance of nowcast skill are illustrated and discussed in section 4; section 5 presents the conclusion.

2. Data and cases overview

a. Radar network

Through a multiagency effort, Taiwan developed a QPE system called Quantitative Precipitation Estimation and Segregation Using Multiple Sensors (QPESUMS; Gourley et al. 2002; Zhang et al. 2009). QPESUMS integrates radar observations over Taiwan. The composite radar observations are from the Taiwanese Central Weather Bureau radars RCWF, RCCG, RCKT, and RCHL as well as the Taiwan Air Force radars RCCK and RCMK. RCCG, RCKT, and RCHL are S-band Doppler weather radars, and RCWF is an S-band dual-polarization radar. RCCK and RCMK are C-band dual-polarization radars. The positions of the six radars and the coverage of QPESUMS are shown in Fig. 1a.

Fig. 1.
Fig. 1.

The positions of (a) six radars with radar coverage and (b) the surface observation station in Taiwan.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

The composite reflectivity of the integrated radar network is selected to evaluate the performance of MAPLE. The horizontal grid resolution of the composite reflectivity is 0.0125° and the time interval is 10 min. Because of Taiwan’s complex terrain, quality control for the radar data is conducted to reduce the contamination from ground and sea clutter (Chang et al. 2009).

b. Rain gauge data

There are over 400 stations with rain gauges (Fig. 1b) over Taiwan Island, and the time resolution is once per hour. In this study, the nowcast performance is examined by comparing to surface observations. As the radars used by QPESUMS are not all dual-polarized radars, the Z–R relationship is applied to convert reflectivity (Z) to the rainfall rate (R). In this study, since Taiwan is subtropical, commonly used Z–R relationships such as the Marshall–Palmer formula of Z = 200R1.65 or Z = 300R1.4 derived in the midlatitudes may not be appropriate. Therefore, the following Z–R relationship developed using 7 years of precipitation data in Taiwan (Chen et al. 2017) is applied:
Z=223R1.51.

c. ECMWF ERA-Interim

The European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim) global reanalysis is used to examine the relationship between real wind and the motion vector through variational Echo tracking. The ERA-Interim is produced by a four-dimensional variational analysis (4D-Var) data assimilation system with a 6-h analysis window and a 0.125° resolution. In this study, only the wind fields on the vertical levels of 400, 500, 600, 700, and 850 hPa are used.

d. Cases description

A total of 16 events from 2008 to 2018, including 15 typhoons and 1 low pressure system, are selected for this study (Table 1). The MAPLE system is launched hourly to produce nowcasts up to 4-h lead time, amounting to a total of 650 times of nowcast. The best track of all typhoon cases is shown in Fig. 2. To better evaluate the performance of the typhoon nowcasts, various tracks that landed over all regions of Taiwan are included in these 16 typhoon cases. There are 11 typhoons that landed in Taiwan. Four of these landed in northern Taiwan, namely Marokot (2009), Soulik (2013), Dujuan (2015) and Nesat (2017); four typhoons landed in the middle of Taiwan, namely Typhoons Fung-Wong (2008), Matmo (2014), Soudelor (2015) and Megi (2016); and three landed in south Taiwan: Typhoons Fanapi (2010), Nepartak (2016) and Haitang (2017). The other five typhoons that did not make landfall are also examined. They are the following: Namtheun (2010) and Maria (2018), which passed the north of Taiwan; Fung-Wong (2014), which passed by the east coast of Taiwan; and Meranti (2016) and the low pressure system (2018), which passed the Bashi Channel southwest of Taiwan. These typhoons or tropical depression (TD) systems brought heavy rain in a short period of time over Taiwan.

Table 1.

List of 16 real cases, including the arrival and departure time according to the Central Weather Bureau (CWB). The number with parentheses indicates the total times of the nowcast.

Table 1.
Fig. 2.
Fig. 2.

The best track of 15 typhoon cases.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

3. Methodology

a. Description of MAPLE

The nowcasting system, MAPLE, is developed by the J. S. Marshall Radar Observatory of McGill University. By using the variational algorithm, the forecasting procedure of MAPLE uses Variational Echo Tracking (VET) to calculate the motion vector according to the previous observations and uses semi-Lagrangian advection to proceed with the extrapolation. These two components are introduced in the following section.

1) Variational echo tracking technique

The original VET technique, developed by Laroche and Zawadzki (1995), used Doppler data in a small region to generate a nowcast. The maximum reflectivity of the composite radar network is used to calculate the VET motion field. The cost function J of the VET technique can be expressed in terms of these two components as follows:
JVET(V)=JΨ+JV,
where V presents the two-dimensional motion vector that is evaluated by iteratively minimizing the cost function. The first term in Eq. (2) is the conservation of reflectivity constraint JΨ. It represents the sum of squares of the echo residuals in the domain. The equation of JΨ is
JΨ=β(x)[Ψ(t0,x)ΩΨ(t0Δt,xuΔt)]2dxdy,
where β(x) denotes the weight of the reflectivity constraint that is related to data quality. To comply with the conservation of the reflectivity means the echo does not decay or grow during the forecast, and therefore the integrated domain must be smaller than the actual composite map in order to ensure the offset displacement Ψ(t0 − Δt, xuΔt) remains within in the domain. The second term of Eq. (2) is a penalty function that smooths the motion field of the reflectivity by the second derivative in space. The function of JV can be expressed as
JV=γ[(2ux2)2+(2uy2)2+2(2uxy)2+(2υx2)2+(2υy2)2+2(2υxy)2]dxdy,
where γ is the weight of the smoothness constraint. To minimize the cost function efficiently, VET uses the conjugate-gradient algorithm described by Navon and Legler (1987) to locate the minimum. To avoid the probability of converging toward a secondary minimum, the scaling guess developed by Laroche and Zawadzki (1994) is used to determine the best motion field.

There are several user-selectable parameters that can affect the performance of MAPLE. The meaning of the parameters and the major settings used in this study are shown in Table 2.

Table 2.

The settings of MAPLE.

Table 2.

2) Semi-Lagrangian advection

After the retrieval of the VET technique is applied, the VET motion field is obtained in the (m × m) subdomain, where (m × m) = (48 × 48) or (144 × 144) in this study, and is then interpolated to every grid point by bilinear interpolation. Therefore, the actual forecasts can be generated using the semi-Lagrangian scheme as proposed by Germann and Zawadzki (2002). The equation is
τ=NΔt,
α=Δtu(t0,xα2),
where τ is the entire time of the forecast, and α is the displacement vector. According to Eqs. (5) and (6), the entire time is divided into N steps of length Δt. The advantage of this method is that it allows for different motion velocities during the forecasting process and gives the ability to simulate the rotation of the system.

The choice of advection scheme is “backward in time and upstream in space,” which can also be interpreted to mean that the information at the current time is decided by the upstream information, as Germann and Zawadzki (2002) demonstrated. However, as Bellon et al. (2010) pointed out, as the center grid point (i, j) is in a divergent region, the neighboring grid points may have the same source as (i0, j0). Therefore, the grid point (i0, j0) may cause stretching or an increase in the area of the forecast precipitation. Conversely, if the grid point (i, j) is in a convergent region, the result may be compressing and decreasing in the area of the forecast precipitation. Due to these two effects, the results may generate distortions according to the magnitude of divergence/convergence of the VET motion field, which will be shown in section 4.

b. Model setup

The WRF (Powers et al. 2017; Skamarock et al. 2008) model version 3.7.1 is used in this study. The WRF domain of each case is displayed in Fig. 3. Three nested domains with 52 vertical layers and 27, 9, and 3 km horizontal grid spacings are used with 181 × 181, 301 × 301, 451 × 451 grid points, respectively. The physical parameterizations used are the Rapid Radiative Transfer Model (RRTM) longwave scheme (Mlawer et al. 1997), the Dudhia shortwave scheme (Dudhia 1989), the Yonsei University (YSU) planetary boundary scheme (Hong et al. 2006), the Grell–Freitas cumulus scheme (Grell and Dévényi 2002), and the Goddard Cumulus Ensemble (GCE) for the microphysics scheme (Tao et al. 2003). Note that the cumulus scheme is replaced by the microphysical scheme in domain 3.

Fig. 3.
Fig. 3.

The experimental domain setting of WRF.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

In this study, the initial conditions are taken from ERA-Interim (0.75° × 0.75°), and the simulation length for each case is 30 h. The first 6 h are not used to avoid the spinup issue.

c. Combination of VET with other sources

Since VET is estimated by the advection of radar echoes, the motion field outside of the echo area may not be reliable. Once the distortion of the nowcast becomes significant, the performance will degrade. To improve the performance of the VET motion field, we attempt to include the steering flow information using a blending technique. The formula of the blending system can be expressed as
Jcom=[w1(uuVET)2+w1(υυVET)2+w2(uuref)2+w2(υυref)2]dxdy,
where “ref” means the information from a source other than the VET, such as an analysis or numerical model, and w1 and w2 are the weighting coefficients for the VET and “ref”, respectively. In this study, in order to find the best set of weightings, a sensitivity test is conducted in section 4.

d. Verification scores

To examine the accuracy of the quantitative precipitation nowcasting (QPN) by MAPLE, the 0–4 h nowcasts of reflectivity are verified every hour. In this study, we evaluate the performance by continuous verification scores, namely the spatial correlation coefficient (SCC) and the root-mean-square error (RMSE), as well as categorical scores, namely the probability of detection (POD), the false-alarm rate (FAR), the bias, the critical success index (CSI), and the equitable threat score (ETS). When comparing the results with rain gauges, only the grid points at the positions of the rain gauge stations are verified with the ETS score. In addition, to alleviate the issue of double-penalty when examining the QPN at high resolution, the neighborhood method is also used to assess the performance of MAPLE.

1) Continuous verification

The SCC can evaluate the extent of the similarity between the echo distribution of the forecast and the observation. The SCC is defined as
SCC=(FF¯)(OO¯)(FF¯)2(OO¯)2,
where F and O are the accumulated rainfall of the prediction and the observation, and F¯andO¯ denote an area average over a two-dimensional plane of the field. The RMSE evaluates the rainfall difference between the forecast and the observation quantitatively. The equation of the RMSE is
RMSE=i=1N(FO)2N,
where F and O are the same definition as in Eq. (8), and N stands for the total number of grid points used for the calculation.

2) Categorical verification

The categorical verification scores are formulated as followed:
POD=aa+b,
FAR=ca+c,
CSI=aa+b+c,
Bias=a+ca+b,
where a, b, c, and d represent the hit, miss, false alarm, and correct negative, respectively, defined by the occurrence when the events are predicted and verified by the observation, the occurrence when the events are forecast but not verified by the observation, the occurrence when events are not predicted but verified by the observations, and the occurrence when the events are not predicted and verified by the observation.

The scores of these parameters are between 0 and 1 except BIAS. A POD or CSI equal to 1 represents a perfect forecast, and if POD or CSI equals 0 the model does not have the ability to forecast. CSI represents the probability of the successful forecast but does not account for correct negatives. FAR is the number of false hits per the total number of forecast points above a threshold, and a FAR of 1 means a perfect forecast. The bias is the ratio of the precipitation forecast to its observation. If the bias is greater than 1, it means the forecast overestimated the precipitation events and vice versa.

The ETS is similar to the CSI, but also considers the number of hits by chance. This index is defined as
ETS=aRa+b+cR,
R=(a+b)×(a+c)(a+b+c+d),
where R means a random forecast. The ETS can evaluate the capability of the model forecast beyond a random guess. If a is equal to R, the ETS shows a forecast skill score of zero; whereas ETS equal to 1 implies a perfect forecast. When the ETS is negative, it means the performance of the forecast is worse than the reference measure. In this study, following Kato et al. (2017), the predictability limit for ETS is defined as the forecast time when the ETS drops to the value of 0.3 or lower.

3) Neighborhood method

The fractions skill score (FSS) is used to verify the adjacent grid points between the ratio of the echo exceeding the given threshold in the various search distances. The FSS is defined as
FSS(L)=11Nij[O(L)(i,j)F(L)(i,j)]21NijO(L)(i,j)2+1NijF(L)(i,j)2,
where N is the total number of grid points over the verified domain, and the double sum indicates the total number of the grid points in the verified domain. O(L)(i, j) and F(L)(i, j) are the observation and the forecast fractions at the grid point (i, j), where the fractions are the ratio of the number of grid points exceeding the given threshold within the radius of search L. Thus, we can understand the spatial distribution of the model skill by the FSS under various radii and thresholds. The value of the FSS ranges from 0 to 1, where FSS equal to 1 represents a perfect forecast. Roberts and Lean (2008) provided the reference value of the FSS, which is named FSSref in this study. It defined as FSSref = 0.5 + fo/2, where fo is the fraction of the number of grid points exceeding the threshold in the verified domain. Thus, when the FSS less than FSSref, the model does not have the skill to provide a useful forecast. To examine the sensitivity of the search radius (L) to the FSS, L = 1, 3, 5, 7, 10, 17, and 21 grid points, according to the distances of 1, 4, 7, 10, 14, 23, and 29 km, respectively, are used and the threshold of the reflectivity is 15, 35, and 45 dBZ.

4. Results and discussion

In this section, we first examined the correlation between the motion field of the VET and the reanalysis wind field of ECMWF in section 4a. We then demonstrate with one typhoon case that blending the VET wind with reanalysis wind has the potential to mitigate the distortion problem in MAPLE nowcasts. In section 4b, we further show the feasibility of blending the VET wind with wind derived from a WRF forecast. In addition, a series of sensitivity tests are done to obtain the optimal settings of the blending system. The results of nowcasts for Typhoon Fanapi (2010) and all cases are shown in sections 4c and 4d, respectively.

a. Comparing VET with the reanalysis wind field of ECMWF

Chan and Gray (1982) showed that the relationship between the steering flow wind field and the track of the typhoon is, to a first order, quite instructive. When the skill of nowcasting by echo extrapolation could last for a couple of hours, the question naturally arises whether there is any correlation between the motion field of VET and steering flow. We begin by examining the wind field from ECMWF reanalysis in comparison to the VET wind. The latitude and longitude of the domain are from 20°N, 118°E to 27°N, 123.5°E. Table 3 shows the correlation of the u and υ components for 16 typhoon cases. Results show that for the selected pressure levels, moderate to high correlation coefficients are found between the VET wind and the reanalysis wind. It can be inferred that since the typhoon is an equivalent barotropic system, there exist fairly good correlations as long as the rotation circulation continues.

Table 3.

The correlation of u and υ component with the reanalysis wind (at 400, 500, 600, 700, and 850 hPa) of ECMWF and the VET field for 16 typhoon cases.

Table 3.

Figures 4a–f compare the radar echoes between observation (Figs. 4a,d) and nowcast at different lead times for Typhoon Fanapi. It is found that the radar extrapolation of MAPLE begins to exhibit shape distortions from the 2nd hour nowcast (Fig. 4b), and the distortion becomes significant at the 4 h lead time (Fig. 4e). This is because the motion field from VET can represent the circulation of typhoon well in the echo region, but it cannot capture the rotation structure outside of the rainband area (Fig. 4g versus Fig. 4h). Therefore, the advection by VET cannot accurately maintain the rotation structure and causes shape distortion. However, as the wind field of ECMWF is based on a full dynamical model along with a reanalysis of all available observations, the wind field of ECMWF can accurately reflect this phenomenon (Fig. 4g). Moreover, since there are high correlations between the VET wind and the analysis wind, we investigate if combining the reanalysis wind field with the VET could improve the nowcasting system. This may be useful, for example, if a forecast system is reliable after a given amount of spinup or spindown time in order to merge in the nowcast. Furthermore, during spinup, the wind field of a forecast model may be reliable even if the precipitation is not. Therefore, this type of investigation allows the “best of both worlds” by combining the strengths of MAPLE and a full numerical weather prediction model. By incorporating the reanalysis wind field of ECMWF (Fig. 4g), with equal weighting coefficients for VET and reanalysis, the blended motion field indeed has less distortion and more accurately reproduces the circulation in the nonecho region (Figs. 4c,f,i). When further examining the 4-h accumulated rainfall on the surface in Fig. 5, results show that, compared to the observations in Fig. 5a, nowcasts from the blending motion field (Fig. 5c) can capture the heavy rainfall pattern better than the nowcast from echo extrapolation alone (Fig. 5b). This indicates that the modification of the motion field outside of the rainband region can potentially improve the capability of QPN.

Fig. 4.
Fig. 4.

The image of radar echo: (a),(d) observation at 0800 and 1000 UTC 19 Sep 2010. (b),(e) MAPLE forecast after 2 and 4 h from 0600 UTC. (c),(f) MAPLE and EC forecast after 2 and 4 h from 0600 UTC. Motion fields at 0600 UTC: (g) the VET, (h) the ECMWF reanalysis wind field at 400 hPa, (i) the blending VET obtained from (g) and (h).

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

Fig. 5.
Fig. 5.

The rain map of (a) the observation, (b) MAPLE, and (c) MAPLE_EC after 4 h accumulated rainfall.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

The results of the blending system demonstrate the improvement of the nowcast. However, of course, the utility of blending the VET wind with the reanalysis wind is limited for nowcasting due to the lack of reanalysis data at operational times. On the other hand, tropical cyclone track prediction by numerical models has recently shown significant improvement (Halperin et al. 2016; Wu et al. 2007). Therefore, we investigate blending the VET with the wind from a forecast WRF model in this study. The following section will evaluate if combining VET with the wind field of WRF output has the same beneficial effect as combining VET with the wind field of ECMWF.

b. Sensitivity test of the combination of VET and WRF wind fields

To obtain higher temporal resolution of the steering flow around the typhoon system, a forecast wind field is used. The variational method in Eq. (7) is applied to combine the VET with the wind field of WRF. According to the studies by Bellon et al. (2010) and Pan et al. (2018), there is little improvement to be found in modifying the resolution of VET. However, different resolutions of the VET and numerical model outputs are investigated here to find the optimal blending ratios. For the resolution of VET, vector densities of 144 × 144 (approximately 7-km resolution) and 48 × 48 (approximately 20-km resolution) are selected. For the WRF model, resolutions of 9- and 3-km are chosen. In addition, to determine the weighting of w1 and w2 in Eq. (7), and to decide which vertical level is used for blending, a series of sensitivity tests are conducted. In addition, four typhoon cases are selected to evaluate the tests, and they are as follows: Fung-Wong (2008), Soulik (2013), Nepartak (2016), and Meranti (2016). The four typhoon cases passed the Taiwan area via Bashi Channel, the south of Taiwan, the middle of Taiwan and the north of Taiwan, respectively. The averaged SCC score of 4 typhoon cases is used to verify the results.

Different resolutions of VET and WRF outputs are first examined. Figure 6a shows the tests of different resolutions of VET and blending with WRF outputs. The experiments include: low resolution VET (48 × 48), high resolution VET (144 × 144), low resolution blending between VET and WRF (48d02), and high-resolution blending (144d03). The weightings of VET and WRF outputs are equal and set to 0.5. Results show that: 1) the SCC score is almost overlapping in different resolutions of VET. As Lee et al. 2010 and Pan et al. 2018 point out, improvement from increasing the resolution of VET is insignificant; and 2) the blending motion field has a certain improvement after a 2-h nowcast lead time. The reason is as shown in Fig. 4i that the blending motion field can capture the rotation of the typhoon structure better than the motion field from echo tracking alone, especially in the nonecho area. Therefore, the SCC reveals some improvement after approximately a 2-h nowcast lead time. Overall, the combination of both high resolution of VET and WRF output (144d03) demonstrates the best performance for nowcasting.

Fig. 6.
Fig. 6.

The average SCC score of 4 typhoon cases on (a) the tests of different resolutions. 48 × 48 and 144 × 144 mean the resolution of the VET. 144d03 and 48d02 mean the combination of the VET (144 × 144, 7 km, and 48 × 48, 20 km) and the WRF wind in outputs (3 and 9 km); (b) the tests of different pressure levels; (c) the different experimental tests (Table 4).

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

Second, different vertical levels (850, 700, 600, 500, and 400 hPa) of WRF horizontal wind are examined (Fig. 6b), and the weightings of VET (echo tracking only) and WRF outputs are still set to have equal weight. In general, there is no significant difference between extracting wind from different levels.

Third, echo tracking only (w1 = 1) and WRF output only (w2 = 1) are tested. In addition, since the result in Fig. 4h indicates that echo and nonecho regions may have different accuracy and performance, the weighting is further differentiated in these two regions (i.e., the echo area and nonecho area). Therefore, the echo area and the nonecho area are separated by the threshold of 15 dBZ. Table 4 displays the experimental design of different weightings in Eq. (7). Results of Fig. 6c show that in the first 1–2 h, the purely MAPLE weighting of Exp1 has the best SCC score compared to Exp2 and Exp3. When differentiating the weightings between the echo and nonecho area, Exp4 illustrates a better performance than Exp5 of the blending system after the 2-h nowcast lead time. From the results above, it is confirmed that the motion field estimated by echo tracking is superior in the echo regions, but it is beneficial to combine the model forecasting wind field to modify the motion field in the nonecho regions.

Table 4.

The experimental tests of different weightings on Eq. (7).

Table 4.

According to a series of sensitivity tests illustrated in this section, the optimal setting of the blending model is established, which is called MAPLE_WRF. Before examining the statistical result of 16 typhoon cases, one typhoon case is first examined to demonstrate the improvement under the optimal settings.

c. An example of the typhoon cases

Before examining the results statistically, Typhoon Fanapi is selected to demonstrate the performance of MAPLE and MAPLE_WRF. Fanapi had an extremely heavy rainfall event occur at 0600 UTC 19 September 2010 in southwest Taiwan. Strong reflectivity was observed in southern Taiwan, and the rainband was almost stationary (Fig. 7). The maximum value of the 4-h accumulated precipitation was over 100 mm h−1 (Fig. 7a), which caused heavy flooding and numerous downed trees in Tainan, Kaohsiung, and Pingtung in southern Taiwan.

Fig. 7.
Fig. 7.

The radar echo and the rain map at 0600 UTC 19 Sep 2010 of the second and fourth hour accumulated precipitation of (a) the observation, (b) MAPLE, and (c) MAPLE_WRF.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

From the results of the nowcasts in Figs. 7b and 7c, both MAPLE and MAPLE_WRF are able to reproduce the strong reflectivity in southern Taiwan. However, as mentioned in section 3a(2), severe shape distortion of reflectivity occurred on the MAPLE system after 2 h of nowcast. When blending WRF horizontal wind with the nowcasting system, the shape distortion is alleviated and the rotation structure of the typhoon is well maintained (Fig. 7c). This result shows that the motion field of MAPLE_WRF can improve the circulation of the typhoon. Furthermore, comparing total accumulated rainfall estimated by radar echo with surface observations in Fig. 7a, the nowcasting results of MAPLE and MAPLE_WRF have a similar precipitation pattern as the observations in south Taiwan, but the total rainfall from both results are underestimated in the nowcast lead time in general. However, MAPLE_WRF (Fig. 7c) represents better accumulated rainfall pattern after a 2-h nowcast lead time compared to MAPLE (Fig. 7b). Overall, blending WRF horizontal winds produces similar effects and features as seen when combining the wind of the reanalysis ECMWF with the echo extrapolation system.

Figure 8 shows the ETS score of MAPLE and MAPLE_WRF at 0600 UTC 19 September 2010. An ETS score above 0.3 is marked in red and considered as good performance. Results of accumulated rainfall in Fig. 8a show that MAPLE performs relatively well at nowcasting, especially at capturing the heavy rainfall (a precipitation threshold above 30 mm h−1). On the other hand, Fig. 8b illustrates that MAPLE_WRF has further improved the nowcasting system. The ETS of MAPLE_WRF is generally higher than the ETS of MAPLE in all different categories of precipitation. Moreover, the ETS of MAPLE_WRF is around 0.5 after a 4-h nowcast lead time for the threshold above 40 mm.

Fig. 8.
Fig. 8.

The ETS score at 0600 UTC 19 Sep 2010. (a) MAPLE; (b) MAPLE_WRF. The red represents the ETS score above 0.3.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

The entire period of Typhoon Fanapi over the Taiwan area (~50 h) is validated by categorical verification and the neighborhood method. Figure 9 displays the ETS score of accumulated rainfall for Typhoon Fanapi. Results show no significant difference of changing the density of VET (48 × 48 versus 144 × 144). In addition, the results of echo extrapolation from MAPLE (48 × 48, 144 × 144) and blending with MAPLE_WRF are in general better than the result for WRF, and the ETS scores for different thresholds of rainfall accumulation are all above or near 0.3 for 4-h nowcast lead time. MAPLE_WRF performs especially well during the heavy rainfall accumulation up to the second hour. These results indicate that blending system (MAPLE_WRF) is an improvement for Typhoon Fanapi.

Fig. 9.
Fig. 9.

The ETS score of the accumulated rainfall of Typhoon Fanapi during entire period.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

d. Statistical performance

As the results of Typhoon Fanapi in section 4c show, the blending system (MAPLE_WRF) quantitatively improves and extends nowcasting skill after 2 h. In addition, significant improvement is demonstrated when Typhoon Fanapi is inland over Taiwan. In this section, 16 real typhoon cases are examined in order to evaluate the performance of the nowcasting system statistically.

First, verification of the echo is performed. Figure 10 presents the SCC and RMSE of MAPLE48 × 48, MAPLE144 × 144 and MAPLE_WRF (the blending system). The SCC score demonstrates that MAPLE has the best performance in the 0–2 h nowcast, and MAPLE_WRF outperforms the echo extrapolation in the 2–4 h nowcast. As mentioned above, this is because the nowcast of the MAPLE system presents severe shape distortion after 2 h of nowcast lead time. By blending the information from the WRF model, this issue can be alleviated. The results of RMSE also show that MAPLE has smaller errors in the 0–2 h nowcast, and MAPLE_WRF performs better in the 2–4 h nowcast. Figure 11 demonstrates multiple verification measures of forecast accuracy on the performance diagram (Roebber 2009). The best forecast quality means POD, the successive ratio (1-FAR), BIAS, and CSI all approach 1, and lie in the upper-right corner of the diagram. The warm color area represents CSI > 0.6. The dashed line represents BIAS, and the results along the diagonal are equals to 1, meaning the forecast is unbiased. Figures 11a and 11b display thresholds of 15 and 35 dBZ, respectively. Again, MAPLE with different densities of VET (blue and green dots) shows no significant difference in skill, while in contrast MAPLE_WRF (red dots) moves the scores toward the upper-right corner consistently for all the cases, indicating improvements over the two MAPLE runs without blending. This indicates some improvement by using multiple verifications in the performance diagram.

Fig. 10.
Fig. 10.

The average SCC (solid) and RMSE (dashed) of all real cases.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

Fig. 11.
Fig. 11.

The performance diagram of 16 typhoon cases for the reflectivity threshold of (a) 15 and (b) 35 dBZ. The colors represent the forecast results of the different model in the legend, and the circles along a line are the scores of the echo forecast per 30 min.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

Figure 12 compares the ETS scores of WRF, MAPLE48, MAPLE144, and MAPLE_WRF verified against surface rain gauges. When examining a total of 16 typhoon cases in Fig. 12a, results show that the nowcasting systems outperform complex model forecasts in the 0–4 h nowcast in general. In addition, MAPLE_WRF has very good performance (ETS > 0.3) for the heavy rainfall condition (a threshold of 100 mm accumulation) in the 2-h nowcast lead time (Fig. 12a). When differentiating the types of typhoons by landfall (Fig. 12b) and without landfall (Fig. 12c) over Taiwan, nowcasts by MAPLE and MAPLE_WRF are better than WRF in general given this particular experimental setup. In addition, Fig. 12b illustrates that when typhoons land over Taiwan and bring large amount of accumulated rainfall (threshold > 90 mm), MAPLE_WRF can perform better than WRF with our experimental setup.

Fig. 12.
Fig. 12.

The average ETS in 4-h accumulated rainfall. In total, there were (a) 16 cases and (b) 11 cases that landed in Taiwan. (c) There were five cases that did not land in Taiwan.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

On the other hand, according to the arrival and departure time of typhoon issued by Central Weather Bureau (CWB), 16 typhoon cases are further divided into three stages: T1 is the stage when a typhoon approached but its center did not land on Taiwan; T2 is the stage after the typhoon center landed and before it left the island; and T3 is the stage after the typhoon left Taiwan. When evaluating the nowcasting system in different stages in Fig. 13, the ETS score at stage T1 illustrates that nowcasts from the WRF model perform better than the others. However, MAPLE and MAPLE_WRF perform better than WRF at stages T2 and T3. The ETS scores of both MAPLE and MAPLE_WRF at stage T2 are near 0.3 in the 0–2 h nowcast lead time (Fig. 13b), much higher than those of WRF. For the threshold >90 mm when typhoons are away from Taiwan, MAPLE_WRF in Fig. 13c shows that the blending system can still capture the heavy rainfall situation that the other systems could not achieve (with no data for computing ETS).

Fig. 13.
Fig. 13.

The average ETS of 11 cases landed Taiwan as in Fig. 12. (a) Stage T1, (b) stage T2, and (c) stage T3.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

Figure 14 presents the FSS score for 16 typhoons in the entire period over Taiwan area. MAPLE and MAPLE_WRF perform well for light rain (Figs. 14a–c). For the moderate rainfall (35 dBZ) with search distance L = 14 km (purple line), the nowcast ability of MAPLE is less than 3 h, while MAPLE_WRF can improve and extend the nowcast capability beyond 3 h statistically (Figs. 14d–f). For heavy rainfall events (45 dBZ) with L = 29 km (Figs. 14g–i), there is no significant difference among the three nowcasting systems. MAPLE_WRF only demonstrates improvement when a very large distance is examined (L = 41, not shown). The FSS score is further computed in two groups: one group in which all typhoons landed over Taiwan, and another in which typhoons passed by but did not land in Taiwan. Results of FSS are similar to Fig. 14 (not shown), and they indicate that the capability of nowcasting is not affected by whether or not the typhoon has landed in Taiwan.

Fig. 14.
Fig. 14.

The average FSS score of 16 typhoon cases during entire period. (a)–(c) 15 dBZ (~0.27 mm h−1), (d)–(f) 35 dBZ (~5.8 mm h−1), and (g)–(i) 45 dBZ (~27 mm h−1) during entire period of MAPLE (48 × 48), MAPLE (144 × 144), and MAPLE_WRF, respectively. The Z–R relationship in Eq. (1) is used to estimate the hourly rainfall rate.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

The FSS score for typhoons landed in Taiwan is computed at stages T1 (Fig. 15a), T2 (Fig. 15b), and T3 (Fig. 15c). The threshold of light rain (15 dBZ) is quite good for all the systems. Considering the moderate rainfall (35 dBZ) with search distance L = 14 km (purple line), while the performance of MAPLE48 and MAPLE144 can last between 2 and 3 h of nowcast lead time, MAPLE_WRF shows some improvement and extends the capability of nowcasting for more than 3 h statistically at stages T1 and T2. For heavy rainfall events (45 dBZ), MAPLE_WRF only demonstrates slight improvement when very large distances are examined (L = 41, not shown). Overall, the results of MAPLE and MAPLE_WRF at stage T2 are better than the other stages statistically. This demonstrates that MAPLE_WRF can provide beneficial information to mitigate the disastrous events after a typhoon makes landfall in Taiwan.

Fig. 15.
Fig. 15.

The average FSS of 11 cases landed in Taiwan as in Fig. 14. (a) Stage T1, (b) stage T2, and (c) stage T3.

Citation: Monthly Weather Review 148, 3; 10.1175/MWR-D-19-0193.1

In summary, the blending of WRF wind information with echo tracking motion field is found to be a feasible method for precipitation nowcasting. Examining the performance of nowcasting for typhoon cases over Taiwan, we demonstrated that MAPLE is able to improve nowcast skill over WRF for at least 2 h. After solving the issue of severe shape distortion by blending wind information from WRF, significant improvement is seen in the 2–4 h nowcast, even for extremely heavy rainfall. In addition, when differentiating typhoons in three stages, the forecast of WRF performs better before typhoons land over Taiwan. Both MAPLE and MAPLE_WRF have good performance when typhoons stay inland of Taiwan. The results indicate that the nowcasting system based on the extrapolation method can nowcast (0–3 h) relatively well even when typhoons have made landfall and are affected by complex terrain.

5. Conclusions

In this study, we investigate the capability of echo extrapolation over the Taiwan for severe precipitation nowcasting area with 16 typhoon cases. By providing additional information from reanalysis or a NWP forecast, the blending system (MAPLE_WRF) is formed and its performance is assessed. Through the statistical results of 16 typhoon cases, feasibility assessments of MAPLE and MAPLE_WRF are presented. The verification is examined by using continuous verification with SCC and RMSE, categorical verification with POD, FAR, CSI, BIAS, and ETS and the neighborhood method with FSS. The results of this study are summarized as follows:

  1. When examining the relationship of the motion field (VET) and horizontal wind, it is found that VET and the reanalysis wind field of ECMWF are highly correlated, and the high correlation coefficient between VET and the reanalysis wind field can be extended from the low levels to high levels as mature typhoons are, to a first order, essentially barotropic systems. Furthermore, the “best-case” results of combining the reanalysis wind field (which is not generally available at runtime) and the VET illustrate the potential improvement of the nowcasting for maintaining the rotation structure and presenting a better precipitation pattern of the accumulated rainfall.
  2. The severe distortion of the typhoon circulation is illustrated after 2 h of the nowcasting during the process of the echo extrapolation. To improve the nowcasting system, a series of sensitivity tests are conducted to test how to properly combine the NWP model and MAPLE. The result shows that blending the resolution of VET ~10 km with WRF horizontal wind at 3-km resolution provides the best performance. For the weightings between VET and the wind of the numerical model, results show that VET is quite reliable and it should be given more weight in the echo region. On the other hand, adopting the wind of the numerical model in the areas without radar echo improves the nowcasting from the second hour of nowcast onward.
  3. Through the statistical performance of 16 real cases, the capability of MAPLE nowcasting is shown to last around 2 h. For the heavy rain event of 45 dBZ, the system can last for approximately 1 h. Overall, in typhoon cases, echo extrapolation can provide beneficial information for up to 2 h in both categorical and neighborhood verifications.
  4. The results of MAPLE_WRF show the blending system helps to capture and maintain the rotation of the typhoon rainband structures. Compared to MAPLE, ETS and FSS scores both show that the significant improvement is found after the 2-h nowcasting lead time, especially for moderate and heavy rain events (with threshold of 35 and 45 dBZ, respectively). The performance of MAPLE_WRF illustrates that it improves the nowcasting system for another hour, which extends the nowcast skill up to 3 h.
  5. Before landing in Taiwan, the radar network could not effectively capture the entire typhoon structure and the corresponding rapid growth and/or decay of rainbands when propagating from ocean to land. Therefore, the performance of nowcasting needs improvement during stage T1. When the entire typhoon structure is covered by the radar network, the performance of nowcasting could be adequate for at least 3 h at the stage of T2 and T3, even though the structure of typhoon is affected by the complex terrain over Taiwan.

Overall, the above results show the nowcasting system by using echo extrapolation can provide useful nowcasting information in the very short-term forecast in typhoon cases. By combining the VET motion with the wind field from other sources, such as data from a numerical weather model, the nowcast can better capture the rotational structure of the typhoon, especially in the nonecho areas. This blending scheme is feasible for application to other radar-based nowcasting systems in general. Although the growth and decay of the weather system is still an unresolved issue in the current system, the blending nowcasting system extends the ability of very short-term forecasts, and it can be used to help reduce the devastation caused by severe weather systems.

Acknowledgments

This work was supported by Ministry of Science and Technology of Taiwan under Research Grant 107-2625-M-008-003. Discussions with Dr. Isztar Zawadzki on the MAPLE system have been of great inspiration. The authors thank the Central Weather Bureau for providing QPESUMS data. The authors are grateful to Dr. Jeffrey Lawrence Steward, who provided review and proofreading of the manuscript.

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  • Zhang, J., and et al. , 2009: High-resolution QPE system for Taiwan. Data Assimilation for Atmospheric, Oceanic and Hydrologic applications, S. K. Park and L. Xu, Eds., Springer, 147–162.

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