Assimilation of Data Derived from Optimal-Member Products ...

atmosphere

Article

Assimilation of Data Derived from Optimal-MemberProducts of TREPS for Convection-Permitting TCForecasting over Southern China

Xubin Zhang 1,* and Meiling Chen 2

1 China Meteorological Administration/Guangdong Provincial Key Laboratory of Regional NumericalWeather Prediction, Institute of Tropical and Marine Meteorology, CMA, Guangzhou 510640, China

2 Guangdong Meteorological Public Service Center, China Meteorological Administration, Guangzhou 510640,China; [email protected]

* Correspondence: [email protected]

Received: 11 January 2019; Accepted: 15 February 2019; Published: 18 February 2019�����������������

Abstract: To improve the landfalling tropical cyclone (TC) forecasting, the pseudo inner-coreobservations derived from the optimal-member forecast (OPT) and its probability-matched mean(OPTPM) of a mesoscale ensemble prediction system, namely TREPS, were assimilated in a partial-cycledata assimilation (DA) system based on the three-dimensional variational method. The impact ofassimilating the derived data on the 12-h TC forecasting was evaluated over 17 TCs making landfall onSouthern China during 2014–2016, based on the convection-permitting Global/Regional Assimilationand Prediction System (GRAPES) model with the horizontal resolution of 0.03◦. The positive impactsof assimilating the OPT-derived data were found in predicting some variables, such as the TCintensity, lighter rainfall, and stronger surface wind, with statistically significant impacts at partiallead times. Compared with assimilation of the OPT-derived data, assimilation of the OPTPM-deriveddata generally brought improvements in the forecasts of TC track, intensity, lighter rainfall, andweaker surface wind. When the data with higher accuracy was assimilated, the positive impactsof assimilating the OPTPM-derived data on the forecasts of heavier rainfall and stronger surfacewind were more evident. The improved representation of initial TC circulation due to assimilatingthe derived data improved the TC forecasting, which was intuitively illustrated in the case studyof Mujigae.

Keywords: data assimilation; pseudo observations; convection permitting; tropical cyclone

1. Introduction

The operational forecasting of tropical cyclone (TC) tracks has been significantly improved inthe last two decades [1–3]. However, the progress in the TC intensity and structure forecasting isstill modest [4–6]. TCs can cause hazardous disasters, such as strong wind, heavy rainfall, and stormsurge, which are strongly related to the TC intensity and structure [7,8]. Thus, in order to reduce lossescaused by these disasters in terms of human life and economic interests, which are especially seriousin Southern China [9,10], it is very important and urgent to improve the forecasts of TC intensity andthe related rainfall and wind.

Developing high-resolution numerical weather prediction (NWP) models is an essential way tobetter predict the TC intensity and structure [2,11–13], because the TC intensity is primarily determinedby small-scale dynamics and moist processes. Besides, improving the representation of TC intensityand structure in the initial condition (IC) by assimilating inner-core observations, such as bogusvortex [14], dropsondes [15], and airborne Doppler radars [16], is an effective means for improving the

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TC intensity and structure forecasting [17]. Therefore, in order to improve the forecasting skill of TCintensity (as well as wind and rainfall), developing data assimilation (DA) techniques for inner-coreobservations in convection-permitting forecasts is necessary.

In the bogus DA (BDA; [14,18]), the synthetic vortex is generated based on an assumed idealizeddistribution of sea level pressure (SLP) and/or three dimensional (3D) wind structure. These idealizedor empirical distributions are not necessarily valid at convective scales [19], which may limit the use ofBDA in the convection-permitting DA. Although the assimilation of dropsondes or airborne radars hasdemonstrated some success in TC forecasting, the availability of dropsondes or airborne radars nearthe TC core is limited because the corresponding routine missions are only occasionally conducted fortargeted TCs especially in Atlantic basin.

Since TCs often spend most of their times over the ocean, assimilation of satellite observations,such as the Atmospheric Infrared Sounder (AIRS) [20] and Cross-track Infrared Sounder (CrIS) [21],can provide an important way to improve TC forecasting. Recently, assimilation of various satelliteobservations, such as microwave radiances and humidity sounders from polar-orbiting satellites [22–25],and atmospheric motion vectors and infrared radiances from geostationary satellites [26–30], has beendemonstrated to be useful to improve the TC intensity and structure forecasting in regional NWPmodels. Based on these encouraging results and the rapid development of satellite detection techniques,assimilation of satellite observations will undoubtedly play a crucial role in future TC forecasting.Currently, however, satellite data are still underutilized in convection-permitting NWP models, due tothe limitations in current model physics (especially for cloud and precipitation) and radiative transfermodels, as well as limited capabilities in effective quality control (QC), bias correction, and datathinning [28,31–34].

The Global/Regional Assimilation and Prediction System (GRAPES: [35,36]) has been used widelyin Southern China, especially for the forecasts of TC and heavy rainfall [37,38]. A convection-permittingregional NWP model based on GRAPES, which is named GRAPES-MARS3KM ([39]; hereafter [Z16]),was developed recently for short-term (12-h) forecasting over Southern China and has been used inoperation since July 2014. However, there is still no inner-core observations (especially satellite data)assimilated in ICs of GRAPES-MARS3KM currently, which greatly limits the forecasts of landfallingTCs, especially their intensity and related rainfall and wind.

Aiming to improve the deterministic/probabilistic short-range (12-h) TC forecasting, especiallyfor TCs making landfall on Southern China, a mesoscale ensemble prediction system (EPS), namelyTREPS, have been established recently and is quasi-operational at present ([40]; hereinafter [Z18]).One of the deterministic products from TREPS is the optimal-member forecast (OPT, hereafter),which is developed to estimate the true atmospheric state as accurately as possible. OPT is proposedto address the issue that some traditional deterministic products, i.e., ensemble-mean (EM) andprobability-matched-mean (PM) forecasts, tend to become physically unrealistic during modelintegration as a result of nonlinearity at both synoptic and convective scales [41,42]. In [Z18], OPTwas determined according to the closeness of the perturbed ensemble members’ forecasts to bothEM forecasts (for both track and intensity) and latest observations of the official real-time warninginformation (WARNING, hereafter) from the China Meteorological Administration (CMA). Based onthe verification of 19 TCs making landfall on mainland China during 2014–2016, OPT was demonstratedto be superior to PM for predicting rainfall and surface wind with smaller thresholds, which wereclosely related to the TC circulation [Z18]. Thus, OPT seems to have some capabilities in representingthe TC structure to some extent.

Can OPT be treated as the “pseudo observations”, which is similar to the “bogused observations”used in BDA, and then be assimilated by the three-dimensional variational (3D-Var) frameworkto improve ICs of the convection-permitting NWP models? This question is motivated by thepartial capabilities of OPT in representing the TC structure and explored in this study. Unlike thebogused observations in BDA, the pseudo observations derived from OPT can include not onlySLP and wind but also other 3D variables (e.g., temperature and specific humidity), and both 3D

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distributions of OPT-derived variables and interactive relationships between them are constrained bythe forecast models.

In this paper, the performance of assimilating OPT-derived observations for landfalling TCforecasting based on GRAPES-MARS3KM, was evaluated to examine the effectiveness. To this end,a batch experiment covering 17 TCs making landfall on Southern China during 2014–2016, as wellas a super typhoon case study, were carried out. Section 2 introduces the NWP model, DA system,and experimental design, along with an overview of the 17 TCs studied here. The OPT-derived dataand preprocessing procedures are described in Section 3. Results of the batch experiment and casestudy are presented in Sections 4 and 5, respectively. Section 6 concludes the paper and providesfurther discussion.

2. Design of Experiments

2.1. Forecast Model

The NWP model used in TREPS is TRAMS9KM [43], including 385 × 305 horizontal grid pointswith horizontal resolutions of 0.09◦ × 0.09◦. There are 55 vertical layers with an upper boundary of35 km. The center of the model domain is located at the position of the TC center, which is determinedin WARNING. TREPS issues 60-h forecasts twice per day at 0000/1200 UTC for 30 perturbed ensemblemembers. Both the high-resolution deterministic (HRES) and ensemble forecasts of the EuropeanCentre for Medium-range Forecasts (ECMWF) (http://apps.ecmwf.int/archive-catalogue) are used toconstruct TREPS. The control (deterministic or unperturbed) forecasts of TREPS (DETER, hereafter) arecold started, with the 0.125◦ × 0.125◦ HRES analyses and forecasts used as ICs and lateral boundaryconditions (LBCs), respectively. [Z18] can be referred to for more details of DETER.

The convection-permitting regional model used here is GRAPES-MARS3KM [Z16], which is anonhydrostatic model and adopts a semi-implicit, semi-Lagrangian scheme for temporal integration.The horizontal grid of the model is set on a longitude–latitude mesh with the Arakawa C-gridstaggering. The GRAPES-MARS3KM domain covers Southern China and the northern South ChinaSea (SCS) (Figure 1), comprising 634 × 434 horizontal grid points with horizontal resolutions of0.03◦ × 0.03◦ and 55 vertical layers up to 28 km. Its vertical coordinate is terrain-following withthe Charney–Phillips vertical layer skipping. The main forecast variables are zonal and meridionalvelocity (U, V), Exner pressure (Π), potential temperature (θ), and specific humidity (Q). The WRFSingle-Moment 6-class microphysics scheme [44], the five-layer thermal diffusion land surface model,the medium-range forecast PBL scheme [45], the rapid radiative transfer model longwave radiationscheme, and the Dudhia shortwave radiation scheme are used in the physics parameterization. 12-hforecasts are issued by GRAPES-MARS3KM based on ICs from the partial-cycle DA system (see below).

Both the Lateral Boundary Conditions (LBCs) for GRAPES-MARS3KM and the first backgroundfield for DA are determined from DETER. However, due to the limited range of TREPS, both theLBCs and the first background field provided by the DETER cannot adequately cover the domain ofGRAPES-MARS3KM for some TC cases. In such cases, the HRES forecasts are used.

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Figure 1. Tracks of the 17 tropical cyclones (TCs) examined in this study from the CMA best-track analysis. Here, the TC position at the first forecast initialization time is used as the beginning of the track. The sizes of the TC symbols represent the TC intensities, with larger sizes corresponding to stronger TCs; the number in parentheses is the first forecast initialization time (UTC) for the TC; the thin red solid rectangle indicates the domain for GRAPES-MARS3KM, with the thick red dashed lines outlining the “inner range” of GRAPES-MARS3KM; the dashed black rectangle indicates the verification area. ‘FJ’, ‘GD’, and ‘HN’ indicate the ‘Fujian’, ‘Guangdong’, and ‘Hainan’ provinces, respectively.

Both the Lateral Boundary Conditions (LBCs) for GRAPES-MARS3KM and the first background field for DA are determined from DETER. However, due to the limited range of TREPS, both the LBCs and the first background field provided by the DETER cannot adequately cover the domain of GRAPES-MARS3KM for some TC cases. In such cases, the HRES forecasts are used.

2.2. Partial-Cycle DA System

The DA system used here is GRAPES-CHAF3KM [Z16], which is based on the GRAPES 3D-Var framework [35,46] along with the multigrid technique [47] and the partial cycling strategy [48].

The GRAPES 3D-Var framework uses the incremental 3D-Var analysis scheme [49], which is similar to that used with the Weather Research and Forecasting model [50]. The cost function is as follows:

Figure 1. Tracks of the 17 tropical cyclones (TCs) examined in this study from the CMA best-trackanalysis. Here, the TC position at the first forecast initialization time is used as the beginning of the track.The sizes of the TC symbols represent the TC intensities, with larger sizes corresponding to strongerTCs; the number in parentheses is the first forecast initialization time (UTC) for the TC; the thin redsolid rectangle indicates the domain for GRAPES-MARS3KM, with the thick red dashed lines outliningthe “inner range” of GRAPES-MARS3KM; the dashed black rectangle indicates the verification area.‘FJ’, ‘GD’, and ‘HN’ indicate the ‘Fujian’, ‘Guangdong’, and ‘Hainan’ provinces, respectively.

2.2. Partial-Cycle DA System

The DA system used here is GRAPES-CHAF3KM [Z16], which is based on the GRAPES 3D-Varframework [35,46] along with the multigrid technique [47] and the partial cycling strategy [48].

The GRAPES 3D-Var framework uses the incremental 3D-Var analysis scheme [49], which issimilar to that used with the Weather Research and Forecasting model [50]. The cost function isas follows:

J =12

(xa − xb

)TB−1

(Xa − Xb

)+

12(H Xa − yo)TR−1(H Xa − yo) (1)

where Xa and Xb denote the analysis and background fields, respectively, and yo denotes theobservation vector; H denotes the observation operator; the background and observation errorcovariance matrices are denoted by B and R, respectively. Stream function, velocity potential,unbalanced Exner pressure, and pseudo–relative humidity are used as control variables in this system.In GRAPES 3D-Var, a linear balance equation which contains the curvature function is used to improvethe balance between the wind and pressure in TCs. The background error covariances are estimated

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by the innovation vector method [51] and then tuned to meet the needs of assimilation for theconvection-permitting model.

Recently, the multi-grid technique was proposed to assimilate the multi-scale information ofobservations on grids with different resolutions [47]. The cost function used in the multi-grid techniqueis as follows:

Jn =12

(xa

n − xbn

)TB−1

n

(xa

n − xbn

)+

12(Hnxa

n − yon)

TR−1n (Hnxa

n − yon) (2)

where n denotes the grid level with the total grid levels equaling N. The final analysis is the sum of theincremental analyses at all grid levels:

xa =N

∑n=1

xan (n = 1, 2, . . . , N) (3)

where xan denotes the solution of the minimization at the nth grid level. In the current GRAPES 3D-Var,

only two grid levels (i.e., N = 2) are used. Based on the multigrid technique, a two-step 3D-Varanalysis is conducted. First, the large-scale background fields are generated by projecting the modelgrid onto a coarse grid containing half the number of domain grid points, then the correspondinglarge-scale analyses are produced by 3D-Var analysis with the large-scale background error covarianceswith larger-scale length scales. Second, the large-scale analyses are interpolated onto the model gridto create the new small-scale background fields, then the corresponding small-scale analyses areproduced via 3D-Var analysis with the small-scale background error covariances with smaller-scalelength scales and adopted as the final analyses. Currently, this multi-grid GRAPES 3D-Var scheme hasbeen applied in both the heavy rainfall [39] and TC [52] forecasting in Southern China. The 6-h partialcycling strategy is implemented as follows. A cold start of multi-grid 3D-Var analysis is activated 6 hprior to the initial time of the 12-h forecasts, with the forecasts of DETER or ECMWF HRES as thebackground fields. Subsequent assimilation cycles are run at an interval of 3 h, with the 3-h forecastsof GRAPES-MARS3KM issued from the previous analysis as the background fields.

2.3. Experimental Design

Analysis-forecast cycles based on GRAPES-CHAF3KM and GRAPES-MARS3KM were carriedout, with the focus on the TCs making landfall on Southern China during 2014–2016. The configurationof these analysis-forecast cycles is shown in Figure 2. According to the TC track forecasting from TREPSEM, if the target TC is predicted to land in 24–36 h, the 6-h DA cycling with GRAPES-CHAF3KMand the subsequent 12-h forecasts with GRAPES-MARS3KM initiate per 12 h unless the target TChas made landfall before the initial time. Note that, if the target TC is predicted by TREPS EM to belocated outside the “inner range” of GRAPES-MARS3KM (Figure 1) at the time when the cold start ofGRAPES-CHAF3KM initiates, the corresponding analysis-forecast cycles are not conducted, becausethe TC circulation is not well covered by the domain of GRAPES-MARS3KM. Here, if the range fromthe target TC center to the half of the surface-wind radius of 17.2 m s−1 (gale_radius, hereafter), whichis reported in WARNING, is completely outside the inner range of GRAPES-MARS3KM, the TC isdefined outside the inner range. During the experimental period, 17 TC cases (Figure 1) with 28 12-hforecasts were collected.

Two experiments, namely control (CTL) and assimilation of OPT-derived observations (AOPT)respectively, were conducted to investigate the impacts of assimilating OPT-derived observations onTC forecasting of GRAPES-MARS3KM. Data from four types of observation (see Figure 1a of [Z16] forthe distributions), i.e., radiosonde, surface station, ship, and wind-profiling radar, were assimilatedin CTL. AOPT was identical to CTL except that OPT-derived observations were also assimilated.The impact of assimilating OPT-derived observations was thus evaluated by comparing the skill scores,which are introduced below, between CTL and AOPT.

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when the cold start of GRAPES-CHAF3KM initiates, the corresponding analysis-forecast cycles are not conducted, because the TC circulation is not well covered by the domain of GRAPES-MARS3KM. Here, if the range from the target TC center to the half of the surface-wind radius of 17.2 m s−1 (gale_radius, hereafter), which is reported in WARNING, is completely outside the inner range of GRAPES-MARS3KM, the TC is defined outside the inner range. During the experimental period, 17 TC cases (Figure 1) with 28 12-h forecasts were collected.

Figure 2. Schematic configuration of the analysis-forecasts cycles using GRAPES-CHAF3KM and GRAPES-MARS3KM. The analysis-forecasts cycles for TC Mujigae are shown as an example. ECMWF: European Centre for Medium-range Forecasts (HRES); DETER: control (deterministic or unperturbed) forecasts of TREPS; GRAPES: Global/Regional Assimilation and Prediction System.

Two experiments, namely control (CTL) and assimilation of OPT-derived observations (AOPT) respectively, were conducted to investigate the impacts of assimilating OPT-derived observations on TC forecasting of GRAPES-MARS3KM. Data from four types of observation (see Figure 1a of [Z16] for the distributions), i.e., radiosonde, surface station, ship, and wind-profiling radar, were assimilated in CTL. AOPT was identical to CTL except that OPT-derived observations were also assimilated. The impact of assimilating OPT-derived observations was thus evaluated by comparing the skill scores, which are introduced below, between CTL and AOPT.

2.4. Forecast Verification

Similar to [Z18], the TC center in this study is defined as the minimum of the geopotential height at 850 hPa (For all the TC cases examined in this study, the comparison between the TC center based on the minimum of the 850-hPa geopotential height and the center of the 850-hPa TC circulation showed small departures between each other), while the lowest SLP within 100 km of the TC center is used to define the minimum central pressure, viz. Pmin, and the highest 10-m wind speed within 250 km of the TC center is used to define the maximum sustained wind speed, viz. Vmax. The CMA best-track dataset ([53]; http://tcdata.typhoon.gov.cn) was used to calculate the absolute track, Pmin and Vmax error over the set of 28 forecasts. To ensure a fair comparison, a homogeneous sample of TC cases with observed or predicted Vmax larger than 10 m s−1 was used.

Forecasts of 1-h accumulated rainfall and 10-m wind were verified against hourly rainfall and 10-m wind observations respectively, from the automatic weather stations (AWSs) densely distributed over Southern China (see Figure 1b of [Z16] for the distributions). Both rainfall and 10-m wind observations were interpolated to the NWP model grids with Cressman interpolation to calculate skill scores. Fraction skill score (FSS; [54]) was computed for the 1-h accumulated rainfall and 10-m wind in consideration of the more significant “double penalties” due to the displacement error in the verification of high-resolution forecasts [55]. In calculating FSS, “neighborhood length” was defined as the length of area over which the fractions were computed. FSS was calculated for varying precipitation thresholds over different neighborhood lengths. However, only the 50-km-

Figure 2. Schematic configuration of the analysis-forecasts cycles using GRAPES-CHAF3KM andGRAPES-MARS3KM. The analysis-forecasts cycles for TC Mujigae are shown as an example. ECMWF:European Centre for Medium-range Forecasts (HRES); DETER: control (deterministic or unperturbed)forecasts of TREPS; GRAPES: Global/Regional Assimilation and Prediction System.

2.4. Forecast Verification

Similar to [Z18], the TC center in this study is defined as the minimum of the geopotential heightat 850 hPa (For all the TC cases examined in this study, the comparison between the TC center based onthe minimum of the 850-hPa geopotential height and the center of the 850-hPa TC circulation showedsmall departures between each other), while the lowest SLP within 100 km of the TC center is used todefine the minimum central pressure, viz. Pmin, and the highest 10-m wind speed within 250 km ofthe TC center is used to define the maximum sustained wind speed, viz. Vmax. The CMA best-trackdataset ([53]; http://tcdata.typhoon.gov.cn) was used to calculate the absolute track, Pmin and Vmax

error over the set of 28 forecasts. To ensure a fair comparison, a homogeneous sample of TC cases withobserved or predicted Vmax larger than 10 m s−1 was used.

Forecasts of 1-h accumulated rainfall and 10-m wind were verified against hourly rainfall and10-m wind observations respectively, from the automatic weather stations (AWSs) densely distributedover Southern China (see Figure 1b of [Z16] for the distributions). Both rainfall and 10-m windobservations were interpolated to the NWP model grids with Cressman interpolation to calculateskill scores. Fraction skill score (FSS; [54]) was computed for the 1-h accumulated rainfall and 10-mwind in consideration of the more significant “double penalties” due to the displacement error in theverification of high-resolution forecasts [55]. In calculating FSS, “neighborhood length” was defined asthe length of area over which the fractions were computed. FSS was calculated for varying precipitationthresholds over different neighborhood lengths. However, only the 50-km-length FSS was comparedbetween various forecasts here, as in [56], because the conclusions based on the comparison of FSSwith other neighborhood lengths are nearly the same. FSS ranges from 0 to 1, with higher valuescorresponding to higher skills.

The skill scores, i.e., absolute track/intensity error and FSS, were computed by averaging overthe 28 forecasts and the verification area (Figure 1). For the comparison of these skill scores, statisticalsignificances of the differences between different forecasts, e.g., CTL and AOPT, were assessed usinga bootstrap resampling procedure. Specifically, random samples of skill scores were generated withreplacement, and then the differences of skill scores were calculated. This procedure was repeated1000 times and bootstrapping was performed on the score differences between the paired samples.The rank at which the resampled score differences crossed zero was used as the significance level [11]to represent the probability that two skill scores were distinct. Here, a 90% significance level indicatesa 90% probability that two skill scores differ.

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2.5. Cases Overview

Most of the 17 TCs moved northwestward from the Western North Pacific or SCS to the southeastcoast of China and mainly made landfall on the Fujian (FJ), Guangdong (GD), and Hainan (HN)provinces. For TCs evolved around the northeast of the model domain, the description of steering flowsfrom the subtropical ridge in GRAPES-MARS3KM is generally insufficient, because the subtropicalridge only covers the limited area of the model domain. In order to quantitatively identify such TCs,the distances between the observed TC center, which is reported in WARNING, and the northernand eastern lateral boundaries are respectively calculated and averaged over all the analysis times.For a given TC case, if the sum of these two distances is smaller than 10.5◦, it is classified as “northeastTC”. Among the 17 TCs, northeast TCs include Matmo, Soudelor, Dujuan, Meranti, and Megi. For suchTC cases, the forecast performances of track based on OPT are overall poorer than those for the otherTC cases (not shown), which are classified as “non-northeast TCs”.

Mujigae, the strongest TC making landfall on GD in October since 1949, landed on GD at around0600 UTC 4 Oct 2015 with Pmin of 935 hPa and Vmax of 52 m s−1. Accompanied by several TC-spawnedtornadoes, Mujigae had caused great damage in GD [57,58]. Mujigae entered SCS at 0200 UTC2 October and strengthened rapidly with Vmax increasing from 28 (at 0600 UTC 3 Oct) to 50 (at 0600UTC 4 Oct) m s−1. In view of the serious nature of the resulting disaster and its rapid intensification(RI), which is difficult to be skillfully predicted currently [17], Mujigae was selected as the case study.

3. OPT-Derived Data and Preprocessing

3.1. Construction of OPT

TREPS comprises one unperturbed and 30 perturbed forecasts ranging up to 60 h at 0.09◦

horizontal resolution. The 30 60-h perturbed forecasts are used to construct OPT, which provide60-h deterministic forecasts. Specifically, a single member was selected to be OPT based on thecloseness of the perturbed ensemble members’ forecasts to both EM forecasts (for both track andintensity) and the latest observations of WARNING. OPT was determined by minimizing a costfunction as follows:

Ji =12

6

∑j=0

µj

2

(T j

iσT

)2

+

(Pj

iσP

)2

+

(W j

iσW

)2 +

1t

54

∑j=6

2

(T̃ j

iσT

)2

+1p

36

∑j=6

(P̃j

iσP

)2

+1w

60

∑j=6

(W̃ j

iσW

)2 (4)

The first term on the right-hand side of Equation (4) measures the closeness to the latestobservations, where T j

i , Pji , and W j

i denote absolute errors of the track, Pmin, and Vmax, respectively,

against WARNING observations for member i at lead time j; µj = 1000.0/Pjobs is the weighting factor

depending on the Pmin observation Pjobs at lead time j. The second term on the right-hand side measures

the closeness to EM forecasts, where T̃ ji , P̃j

i , and W̃ ji denote absolute differences of the track, Pmin, and

Vmax, respectively, compared with EM forecasts for member i at lead time j. σT , σP, and σW denote thestandard deviation of the TC track (15 km), Pmin (4 hPa), and Vmax (1 m s−1), respectively, which areused to normalize the various variables to maintain their mutual balance. If more than one memberhad a minimum cost function, OPT were produced by averaging over these members.

3.2. Data Derived from OPT

For each grid point in OPT, if its distance from the observed TC center reported in WARNINGwas smaller than the gale_radius, the corresponding variables located at this grid point were selectedto be derived. Considering that OPT is a type of forecast product, the variables derived from OPT areprobably characterized by spatial correlations in the forecast error. Thus, when OPT-derived data wereused as the pseudo observations, these observations may be horizontally correlated, implying thatthere are probably correlations in the “observation error”. In order to reduce the impacts of correlated

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observation errors on DA, data thinning has been widely used [59–61]. Consequently, the grid pointsof OPT were selected at an interval of 5. Because the horizontal resolution of TREPS is 0.09◦ × 0.09◦,the horizontal resolution of OPT-derived data is about 45 km (Figure 3a).

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the weighting factor depending on the Pmin observation j

obsP at lead time j . The second term on the

right-hand side measures the closeness to EM forecasts, where j

iT , j

iP , and j

iW denote absolute

differences of the track, Pmin, and Vmax, respectively, compared with EM forecasts for member i at

lead time j . Tσ , Pσ , and Wσ denote the standard deviation of the TC track (15 km), Pmin (4 hPa), and Vmax (1 m s−1), respectively, which are used to normalize the various variables to maintain their mutual balance. If more than one member had a minimum cost function, OPT were produced by averaging over these members.

3.2. Data Derived from OPT

For each grid point in OPT, if its distance from the observed TC center reported in WARNING was smaller than the gale_radius, the corresponding variables located at this grid point were selected to be derived. Considering that OPT is a type of forecast product, the variables derived from OPT are probably characterized by spatial correlations in the forecast error. Thus, when OPT-derived data were used as the pseudo observations, these observations may be horizontally correlated, implying that there are probably correlations in the “observation error”. In order to reduce the impacts of correlated observation errors on DA, data thinning has been widely used [59–61]. Consequently, the grid points of OPT were selected at an interval of 5. Because the horizontal resolution of TREPS is 0.09° × 0.09°, the horizontal resolution of OPT-derived data is about 45 km (Figure 3a).

Figure 3. Horizontal distributions of 850-hPa geopotential height (contours with interval of 20 gpm) and 10-m wind speed (shaded, unit: m s-1) at 0600 UTC 3 Oct 2015 from OPT (a) and OPTPM (b). The dots indicate the grid points used to construct the OPT- and OPTPM-derived data, with different colors representing different ensemble spreads of 10-m wind speed (unit: m s−1), which are calculated as the square root of the sum of the squared 10-m-U and 10-m-V ensemble spreads. The green plus indicates the location of the TC center reported in WARNING.

U, V, geopotential height, temperature (T), and relative humidity (RH), which were derived from OPT at 1000, 925, 850, 700, 600, 500, 400, 300, 250, 200, 150, and 100 hPa, were used in a similar way to radiosonde observations. The surface variables from OPT, including SLP, 10-m U, 10-m V, 2-

Figure 3. Horizontal distributions of 850-hPa geopotential height (contours with interval of 20 gpm)and 10-m wind speed (shaded, unit: m s−1) at 0600 UTC 3 Oct 2015 from OPT (a) and OPTPM (b).The dots indicate the grid points used to construct the OPT- and OPTPM-derived data, with differentcolors representing different ensemble spreads of 10-m wind speed (unit: m s−1), which are calculatedas the square root of the sum of the squared 10-m-U and 10-m-V ensemble spreads. The green plusindicates the location of the TC center reported in WARNING.

U, V, geopotential height, temperature (T), and relative humidity (RH), which were derived fromOPT at 1000, 925, 850, 700, 600, 500, 400, 300, 250, 200, 150, and 100 hPa, were used in a similar way toradiosonde observations. The surface variables from OPT, including SLP, 10-m U, 10-m V, 2-m T, and2-m RH, were used to construct the OPT-derived data in a similar way to surface observations.

3.3. Data Derived from OPTPM

As illustrated in [Z18], when OPT was used, there were some mixed results with somedegradations in strong and extremely strong wind in TREPS forecasts. These degradations werecaused by the excessive smoothing in OPT fields, due to simple averaging over the ensemble memberswith nearly the same minimum cost function, which was used to determine the optimal members.Thus, underestimations were probably present in the OPT-derived data, especially for strong wind.For Mujigae, the observed Vmax at 0600 UTC 3 Oct 2015 was 33 m s−1. However, in OPT fields, whichwere produced by averaging two ensemble members, the area around predicted TC center with Vmax

exceeding 27 m s−1 was very limited (Figure 3a), indicating insufficient ability of OPT to describestrong TCs.

In order to cope with the issue of simply averaging all ensemble members, PM was proposedby [62] by blending the spatial pattern of EM fields with the frequency distribution of the whole EPS.Thus, it seems that the PM technique could be used to partially address the underestimations in OPT.In this study, a new TREPS product based on both the OPT and PM techniques, namely OPTPM, wasconstructed in three steps. First, the frequency distribution was formed by pooling predicted fields

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(e.g., 10-m U) from N ensemble members of TREPS, which were all selected to construct OPT, at eachgrid point in the domain of the OPT-derived data, ranking them from largest to smallest and keepingevery Nth value. Second, OPT fields in the domain of the OPT-derived data were also ranked fromlargest to smallest. Third, the grid point corresponding to the largest OPT fields was assigned thelargest value in the frequency distribution, and so on. An example of the OPTPM-derived data isshown in Figure 3b. Compared with OPT fields (Figure 3a), OPTPM fields described a stronger TCwith higher 10-m wind speed and lower SLP (Figure 3b). The differences in magnitude between OPTand OPTPM fields were more evident around the predicted TC center, where the excessive smoothingin OPT fields was more serious. Note that, because the patterns of OPT fields were the same as thoseof OPTPM fields, the locations of the TC center and thus the TC tracks did not differ between OPTand OPTPM.

The third experiment, namely AOPM, was thus conducted to investigate the impacts ofassimilating OPTPM-derived observations on TC forecasting. AOPM was identical to AOPT exceptthat the OPTPM-derived data instead of the OPT-derived data were assimilated.

3.4. Data Accuracy

In order to examine the accuracy of the derived data, the forecast errors of track and Vmax forboth the OPT- and OPTPM-derived data were calculated (Figure 4).Atmosphere 2019, 10, x FOR PEER REVIEW 10 of 27

Figure 4. Box-and-whisker plots for absolute errors of the TC track (a) and Vmax (b–d) with best-track data as the truth over all optimal-member forecast (OPT)- and its probability-matched mean (OPTPM)-derived data used in the analysis for forecasts of all TCs (a,b), non-northeast TCs (c), and northeast TCs (d). The red thick line in the box indicates the median value, the circle represents the mean value, the box shows the interquartile range (i.e., the 25th and 75th percentiles), the horizontal line outside the box (i.e., whiskers) marks the percentiles of 1.5 times the interquartile range, and points outside the whisker are outliers.

As illustrated above, the tracks were the same between OPT- and OPTPM-derived data, thus, the absolute track errors were the same between these two data (Figure 4a). Overall, the absolute track errors of the derived data were smaller than 100 km, with mean track errors around 50 km.

With a few exceptions, the absolute errors of Vmax for the OPT-derived data were generally below 20 m s−1 (Figure 4b). Actually, the larger Vmax errors, e.g., 30 m s−1, were attributed to the stronger TCs, e.g., Rammasun, whose peak maximum Vmax reached 72 m s−1 (Figure 12c of [Z18]). For the OPTPM-derived data, the absolute errors of Vmax were generally below 15 m s−1 (Figure 4b). Thus, compared with the OPT-derived data, the OPTPM-derived data showed some improvements in estimating the TC intensity, with the mean Vmax errors reduced from 8 m s−1 to 6 m s−1. Moreover, the improvements in estimating the TC intensity of the OPTPM-derived data over the OPT-derived data were more evident for northeast TCs (Figure 4d) than for non-northeast TCs (Figure 4c).

Compared with the track (Vmax) uncertainties of some TC best-track data [63], the track (Vmax) errors of the derived data were generally similar although a bit larger, especially for the OPTPM-derived data. Thus, the accuracy of the derived data should be generally acceptable, at least in terms of the TC track and intensity.

3.5. Observation Errors

Both OPT and OPTPM fields are the deterministic products of TREPS, which aim to estimate the true atmospheric state. Thus, the observation errors of the OPT- and OPTPM-derived data are closely related to the forecast uncertainties or errors of OPT and OPTPM fields. It is well known that the ensemble spread provided by EPSs can be used to estimate the forecast uncertainty or error [64]. Therefore, the ensemble spreads from TREPS for various variables, which have been used in the OPT- and OPTPM-derived data, were used to simply estimate their standard deviations of observation errors.

As an example, Figure 3 shows the horizontal distribution of the ensemble spreads from TREPS for 10-m wind speed. These ensemble spreads increased evidently when approaching the predicted TC center of OPT- or OPTPM-derived data, illustrating larger forecast errors around the predicted TC center. This result is not surprising, because divergence of predicted TC locations between ensemble members often leads to the most evident divergence of predicted surface wind

Figure 4. Box-and-whisker plots for absolute errors of the TC track (a) and Vmax (b–d) withbest-track data as the truth over all optimal-member forecast (OPT)- and its probability-matchedmean (OPTPM)-derived data used in the analysis for forecasts of all TCs (a,b), non-northeast TCs (c),and northeast TCs (d). The red thick line in the box indicates the median value, the circle represents themean value, the box shows the interquartile range (i.e., the 25th and 75th percentiles), the horizontalline outside the box (i.e., whiskers) marks the percentiles of 1.5 times the interquartile range, and pointsoutside the whisker are outliers.

As illustrated above, the tracks were the same between OPT- and OPTPM-derived data, thus, theabsolute track errors were the same between these two data (Figure 4a). Overall, the absolute trackerrors of the derived data were smaller than 100 km, with mean track errors around 50 km.

With a few exceptions, the absolute errors of Vmax for the OPT-derived data were generallybelow 20 m s−1 (Figure 4b). Actually, the larger Vmax errors, e.g., 30 m s−1, were attributed to thestronger TCs, e.g., Rammasun, whose peak maximum Vmax reached 72 m s−1 (Figure 12c of [Z18]).For the OPTPM-derived data, the absolute errors of Vmax were generally below 15 m s−1 (Figure 4b).Thus, compared with the OPT-derived data, the OPTPM-derived data showed some improvements inestimating the TC intensity, with the mean Vmax errors reduced from 8 m s−1 to 6 m s−1. Moreover,

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the improvements in estimating the TC intensity of the OPTPM-derived data over the OPT-deriveddata were more evident for northeast TCs (Figure 4d) than for non-northeast TCs (Figure 4c).

Compared with the track (Vmax) uncertainties of some TC best-track data [63], the track(Vmax) errors of the derived data were generally similar although a bit larger, especially for theOPTPM-derived data. Thus, the accuracy of the derived data should be generally acceptable, at leastin terms of the TC track and intensity.

3.5. Observation Errors

Both OPT and OPTPM fields are the deterministic products of TREPS, which aim to estimatethe true atmospheric state. Thus, the observation errors of the OPT- and OPTPM-derived data areclosely related to the forecast uncertainties or errors of OPT and OPTPM fields. It is well known thatthe ensemble spread provided by EPSs can be used to estimate the forecast uncertainty or error [64].Therefore, the ensemble spreads from TREPS for various variables, which have been used in the OPT-and OPTPM-derived data, were used to simply estimate their standard deviations of observation errors.

As an example, Figure 3 shows the horizontal distribution of the ensemble spreads from TREPSfor 10-m wind speed. These ensemble spreads increased evidently when approaching the predictedTC center of OPT- or OPTPM-derived data, illustrating larger forecast errors around the predicted TCcenter. This result is not surprising, because divergence of predicted TC locations between ensemblemembers often leads to the most evident divergence of predicted surface wind occurring aroundthe ensemble-mean TC center. Additionally, the regions with strong surface wind especially in thenortheast quadrant, which are often characterized by large forecast errors (e.g., [19,65]), correspondedwell with those with large ensemble spreads (Figure 3). This indicated that the ensemble spreadprovided by TREPS can estimate the observation error of the derived data to some extent.

However, as shown in Figure 3, the ensemble spread generally ranged from 2 to 6 m s−1,which was evidently larger than the standard deviation of observation errors for some conventionalobservations, e.g., radiosonde [66]. Consequently, the analysis increments due to assimilating thederived data would be evidently smaller than those due to assimilating conventional observations,if the ensemble spread was directly used as the estimation of observation errors. To increase theimpacts of assimilating the derived data on the analyses, 50% of the ensemble spread was used asthe standard deviation of observation errors for both the OPT- and OPTPM-derived data. Actually,some sensitivity experiments, in which the ensemble spread was scaled as 25%, 50%, 75%, and 100%of the original estimate, were conducted for two typical TC cases, which were Mujigae and Soudelor.Among these sensitivity experiments, those with 50% of the ensemble spread as the standard deviationof observation errors showed the best performance in both the TC track and TC intensity forecasting.Especially, 40% of the ensemble spread was used for the OPTPM-derived data in the northeast TCcases, considering the obvious improvements of OPTPM over OPT in estimating the TC intensityfor northeast TCs (Figure 4d). Note that, observation errors of the OPT- and OPTPM-derived datawere probably underestimated here. In order to avoid the excessive impacts of the derived data(especially those with poor qualities) on DA, the derived data must be further quality controlled (seethe below section).

3.6. Quality Control

The quality control (QC) is essential for the derived data, given that such data are in fact based onforecasts of NWP models and are thus characterized by inevitable forecast errors. QC applied herefollowed two steps.

Firstly, with the TC track and Vmax reported in WARNING as the truth, the Vmax bias, track error,and Vmax error of TC in OPT fields were calculated and averaged over all the analysis times during the6-h DA cycle. If one of the three situations occurred, that is, the Vmax bias, track error, and Vmax errorwere larger than 5 m s−1, 100 km, and 20 m s−1, respectively, both the OPT- and OPTPM-derived datawere treated as erroneous data and thus not used in DA. In this case, both AOPT and AOPM were the

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same as CTL. Actually, the 28 forecasts corresponding to the 17 TC cases (Figure 1) were determinedafter implementing such QC. Note that, the derived data with large overestimations of TC Vmax wereexcluded, because assimilation of such data tended to aggravate the intensity overestimation forweaker TCs in GRAPES-MARS3KM (not shown). After removing the above data, the distributions ofthe TC Vmax bias, track error, and Vmax error for the OPT-derived data used in this study are shown inFigure 5b–d.Atmosphere 2019, 10, x FOR PEER REVIEW 12 of 27

Figure 5. Box-and-whisker plots for the intensity index (a), which was calculated as the ratio of Vmax to Pmin, and then inflated 100 times and averaged over all the analysis times (unit: m s−1 hPa−1), and the Vmax bias (b), track error (c), and Vmax error (d) with official real-time warning information from CMA (WARNING) as the truth over all OPT-derived data used in the analysis for all the 28 forecasts. The red thick line in the box indicates the median value, the circle represents the mean value, the box shows the interquartile range (i.e., the 25th and 75th percentiles), the horizontal line outside the box (i.e., whiskers) marks the percentiles of 1.5 times the interquartile range, and points outside the whisker are outliers.

Secondly, observations of the derived data were further quality controlled by comparing the innovations, which were the differences between observations and background fields, with the standard deviation of observation errors. In GRAPES 3D-Var, if the innovations exceed qc times the standard deviation, the observations are assumed to be erroneous and thus not assimilated. Therefore, the value of qc determined how many observations can be assimilated. Considering that there were different characteristics in terms of forecast errors between different TCs for both OPT and OPTPM fields (Figure 4), different values of qc were set for different TCs as follows.

(1) Since TCs with different intensities show different characteristics of forecast or estimation errors [13,63], intensity index was defined here to divide all the 17 TCs into three groups. Specifically, intensity index was calculated as the ratio of Vmax to Pmin, which were both reported in WARNING, and then inflated 100 times and averaged over all analysis times. As shown in Figure 5a, intensity index for TCs investigated here ranged from 1 to 7 m s−1 hPa−1, with mean of roughly 4 m s−1 hPa−1. The TC cases with intensity index below 4 m s−1 hPa−1 were defined as “weak TCs”, those above 5 m s−1 hPa−1 were defined as “strong TCs”, while those ranging from 4 to 5 m s−1 hPa−1

were defined as “moderate TCs”. As illustrated in some literatures (e.g., [67–69]), lower horizontal resolutions of NWP models probably cannot well represent the intensity of stronger TCs. So, when the derived data, which were based on OPT and OPTPM fields with resolution of roughly 9 km, were used in the DA system with resolution of roughly 3 km, the representative error of the derived data should be larger for stronger TCs. For this reason, values of qc, namely qc1, were set to 5.0, 4.0, and 3.0 for weak, moderate, and strong TCs, respectively.

(2) The track error of OPT fields ranged from 10 to 90 km, with the mean around 50 km (Figure 5c). So, if such track error exceeded 50 km, the corresponding derived data was considered to be characterized by evident track errors. In this case, the value of qc, namely qc2, were set to qc1 − 1 to exclude observations with large innovations in a more rigorous way.

(3) For OPT fields, the ratio of the track error to the gale_radius, which was reported in WARNING, was also calculated and averaged over all the analysis times. If such ratio was larger, the risk that the TC circulation of OPT fields obviously deviated from the observed TC circulation was also larger. Thus, if such ratio exceeded 0.6, the corresponding derived data was thought to probably have detrimental impacts on DA and the value of qc, namely qc3, were set to qc2 − 1.

Figure 5. Box-and-whisker plots for the intensity index (a), which was calculated as the ratio of Vmax

to Pmin, and then inflated 100 times and averaged over all the analysis times (unit: m s−1 hPa−1), andthe Vmax bias (b), track error (c), and Vmax error (d) with official real-time warning information fromCMA (WARNING) as the truth over all OPT-derived data used in the analysis for all the 28 forecasts.The red thick line in the box indicates the median value, the circle represents the mean value, the boxshows the interquartile range (i.e., the 25th and 75th percentiles), the horizontal line outside the box(i.e., whiskers) marks the percentiles of 1.5 times the interquartile range, and points outside the whiskerare outliers.

Secondly, observations of the derived data were further quality controlled by comparing theinnovations, which were the differences between observations and background fields, with thestandard deviation of observation errors. In GRAPES 3D-Var, if the innovations exceed qc timesthe standard deviation, the observations are assumed to be erroneous and thus not assimilated.Therefore, the value of qc determined how many observations can be assimilated. Considering thatthere were different characteristics in terms of forecast errors between different TCs for both OPT andOPTPM fields (Figure 4), different values of qc were set for different TCs as follows.

(1) Since TCs with different intensities show different characteristics of forecast or estimationerrors [13,63], intensity index was defined here to divide all the 17 TCs into three groups. Specifically,intensity index was calculated as the ratio of Vmax to Pmin, which were both reported in WARNING,and then inflated 100 times and averaged over all analysis times. As shown in Figure 5a, intensityindex for TCs investigated here ranged from 1 to 7 m s−1 hPa−1, with mean of roughly 4 m s−1 hPa−1.The TC cases with intensity index below 4 m s−1 hPa−1 were defined as “weak TCs”, those above5 m s−1 hPa−1 were defined as “strong TCs”, while those ranging from 4 to 5 m s−1 hPa−1 were definedas “moderate TCs”. As illustrated in some literatures (e.g., [67–69]), lower horizontal resolutions ofNWP models probably cannot well represent the intensity of stronger TCs. So, when the deriveddata, which were based on OPT and OPTPM fields with resolution of roughly 9 km, were used in theDA system with resolution of roughly 3 km, the representative error of the derived data should belarger for stronger TCs. For this reason, values of qc, namely qc1, were set to 5.0, 4.0, and 3.0 for weak,moderate, and strong TCs, respectively.

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(2) The track error of OPT fields ranged from 10 to 90 km, with the mean around 50 km(Figure 5c). So, if such track error exceeded 50 km, the corresponding derived data was considered tobe characterized by evident track errors. In this case, the value of qc, namely qc2, were set to qc1 − 1 toexclude observations with large innovations in a more rigorous way.

(3) For OPT fields, the ratio of the track error to the gale_radius, which was reported in WARNING,was also calculated and averaged over all the analysis times. If such ratio was larger, the risk that theTC circulation of OPT fields obviously deviated from the observed TC circulation was also larger. Thus,if such ratio exceeded 0.6, the corresponding derived data was thought to probably have detrimentalimpacts on DA and the value of qc, namely qc3, were set to qc2 − 1.

(4) As illustrated in Section 2.5, OPT fields on average showed better performance in describingthe TC track for non-northeast TCs than for northeast TCs. Thus, the value of qc, namely qc4, were setto qc3 − 1 for northeast TCs.

After the above four-step QC, the value of qc can be finally determined. Additionally, theminimum value of qc was restricted to be 1.0. Note that, the above QC used the TC-dependentalthough somewhat ad hoc qc rather than the fixed or static qc, which is commonly used for realobservations. Actually, some sensitivity experiments were carried out for two TC cases, i.e., Mujigaeand Kujira, which were representative of TCs with different intensities. These sensitivity experimentsshowed the superiority of the TC-dependent qc over the fixed qc in TC forecasting (not shown).

4. Results of the Batch Experiment

4.1. Forecasts of TC Track and Intensity

For all the 28 forecasts, there were no statistically significant differences in TC track errors betweenAOPT or AOPM and CTL at 6-h and 12-h lead times (Figure 6a). However, in terms of the analyzedlocation of TC center, errors in both AOPT and AOPM were significantly larger than in CTL (Figure 6a).This degeneration of describing initial TC locations of both AOPT and AOPM relative to CTL limitedthe improvements by assimilating the derived data in the TC track forecasting. Compared with AOPT,AOPM showed some slight improvements in the TC track forecasting, with significant improvementsat the 12-h lead times.

On average, both AOPT and AOPM showed slightly smaller errors in analyzing and predictingthe TC intensity (i.e., Pmin and Vmax) than CTL, especially for Pmin in the later period of the 12-hforecasts (Figure 6b). The degeneration of TC Vmax forecasting of both AOPT and AOPM over CTL atthe 6-h lead times is likely the result of the poor spinup process due to assimilating the derived data.The TC intensity errors, with respect to both Pmin and Vmax, were generally similar between AOPTand AOPM, with smaller errors at the 12-h lead times in the latter than in the former (Figure 6b,c).

In summary, assimilating the derived data led to some degenerations (improvements) in analyzingand predicting the TC track (intensity). Recall from Figure 5c,d that there were a few evident deviationsof the derived data from WARNING in terms of both track and intensity, with track (Vmax) errorsexceeding 50 km (5 m s−1). Obviously, such derived data were characterized by larger errors or worsequalities relative to WARNING than other derived data. The differences in quality between differentderived data would potentially lead to differences in the contributions to forecast performance. Did theforecasts with these “large-error” derived data assimilated contribute to the degenerations due toassimilation of the derived data in the analysis and forecast of TC track? It is important to answerthis question for further revealing the deficiency of the proposed derived-data assimilation technique.For this purpose, the TC track and intensity errors were recalculated based on the 17 forecasts with the“small-error” derived data assimilated (Figure 6d–f). Here, for both the OPT- and OPTPM-deriveddata, if their track errors (Figure 5c) were below 50 km or Vmax errors (Figure 5d) were below 5 m s−1,the corresponding data were defined as “small-error” derived data; otherwise, “large-error” deriveddata were used to identify the corresponding data. The criterions (i.e., 50-km track errors and 5-ms−1

Vmax errors), used to separate the derived data between the “large-error” and the “small-error” ones,

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were nearly the mean or median values of errors for all TC cases (Figure 5c,d). Besides, there were17 (11) forecasts with the “small-error” (“large-error”) derived data assimilated, suggesting that thesamples were generally comparable between forecasts with “small-error” derived data assimilatedand those without. Thus, the comparison between forecasts with derived data of different qualitiesassimilated should be generally fair.

Atmosphere 2019, 10, x FOR PEER REVIEW 13 of 27

(4) As illustrated in Section 2.5, OPT fields on average showed better performance in describing the TC track for non-northeast TCs than for northeast TCs. Thus, the value of qc, namely qc4, were set to qc3 − 1 for northeast TCs.

After the above four-step QC, the value of qc can be finally determined. Additionally, the minimum value of qc was restricted to be 1.0. Note that, the above QC used the TC-dependent although somewhat ad hoc qc rather than the fixed or static qc, which is commonly used for real observations. Actually, some sensitivity experiments were carried out for two TC cases, i.e., Mujigae and Kujira, which were representative of TCs with different intensities. These sensitivity experiments showed the superiority of the TC-dependent qc over the fixed qc in TC forecasting (not shown).

4. Results of the Batch Experiment

4.1. Forecasts of TC Track and Intensity

For all the 28 forecasts, there were no statistically significant differences in TC track errors between AOPT or AOPM and CTL at 6-h and 12-h lead times (Figure 6a). However, in terms of the analyzed location of TC center, errors in both AOPT and AOPM were significantly larger than in CTL (Figure 6a). This degeneration of describing initial TC locations of both AOPT and AOPM relative to CTL limited the improvements by assimilating the derived data in the TC track forecasting. Compared with AOPT, AOPM showed some slight improvements in the TC track forecasting, with significant improvements at the 12-h lead times.

Figure 6. Absolute errors of the TC track (a), (d), Pmin (b), (e), and Vmax (c), (f) at different lead times, for all the 28 forecasts (a), (b), (c) and for the 17 forecasts with the “small-error” derived data assimilated (d), (e), (f). Black (gray) squares, diamonds and asterisks indicate the lead times for which the significance level of the absolute error differences is larger than 90% (85%) for the comparisons between assimilation of OPT-derived observations (AOPT) and control (CTL), between assimilation of OPTPM-derived observations (AOPM) and CTL, and between AOPT and AOPM, respectively. The legend in (d) identifies the three experiments shown in these panels.

Figure 6. Absolute errors of the TC track (a,d), Pmin (b,e), and Vmax (c,f) at different lead times, for allthe 28 forecasts (a–c) and for the 17 forecasts with the “small-error” derived data assimilated (d–f).Black (gray) squares, diamonds and asterisks indicate the lead times for which the significance levelof the absolute error differences is larger than 90% (85%) for the comparisons between assimilationof OPT-derived observations (AOPT) and control (CTL), between assimilation of OPTPM-derivedobservations (AOPM) and CTL, and between AOPT and AOPM, respectively. The legend in (d)identifies the three experiments shown in these panels.

As shown in Figure 6d, the TC track errors in both AOPT and AOPM became close to thosein CTL, after removing the forecasts with the “large-error” derived data assimilated. In this case,assimilating the derived data did not significantly influence the analysis and forecast of TC track.However, for the analysis and forecast of TC intensity, removing the forecasts with the “large-error”derived data assimilated did not further increase but even reduce the advantage of AOPT or AOPMover CTL (Figure 6e,f). The error of initial TC location in CTL was below 50 km over all the 28 forecasts(Figure 6a). Therefore, including the information of some “large-error” derived data would probablydegrade the analysis and thus the forecast performance of TC track. However, the case was different forTC intensity. Because the error of initial TC Vmax in CTL was evidently larger than 5 m s−1, additionallyassimilating some “large-error” derived data could still improve the analysis and thus the forecastperformance of TC intensity.

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4.2. Forecasts of Precipitation

Similar to [56], rainfall with precipitation rates greater than 0.1, 10, 20, and 40 mm h−1 is definedas light, moderate, heavy, and extremely heavy rainfall, respectively, in this study.

Compared with CTL, both AOPT and AOPM significantly improved the forecasts of light rainfallduring the whole 12-h forecasts (Figure 7a). Moreover, AOPM outperformed AOPT in predicting lightrainfall, although the differences were not statistically significant (Figure 7a). However, the advantagesof AOPT or AOPM over CTL in predicting light rainfall were not significant for the forecasts with“small-error” derived data assimilated (Figure 7b), which implies that assimilation of “large-error”derived data still benefits the forecasts of rainfall with smaller threshold. As illustrated previously(Figure 6), assimilation of “large-error” derived data led to some improvements (degenerations) inpredicting the TC intensity (track). Probably, such degenerations in predicting the TC location do notnecessarily cause degenerations in predicting the whole TC circulation, which is closely related to thedistribution of light rainfall, because the differences of TC track errors between all the 28 forecasts andthe forecasts with “small-error” derived data assimilated were below 15 km (comparing Figure 6a,d),which are evidently smaller than the size of TC circulation. On the contrary, improvements in predictingthe TC intensity due to assimilation of “large-error” derived data can improve the forecasts of TCcirculation and thus light rainfall, especially for AOPM (comparing Figure 7a,b).

For the forecasts of moderate rainfall, AOPT showed significantly improvements over both AOPMand CTL in the first few hours (Figure 7c). However, for the performance during the whole 12-hforecasts, assimilating the OPT- or OPTPM-derived data did not bring significant improvements(Figure 7c). These conclusions are valid for all the forecasts, regardless of whether “large-error”or “small-error” derived data were assimilated (Figure 7c,d). Considering that the distribution ofmoderate rainfall should be closer to the TC center than that of light rainfall, degenerations causedby assimilating “large-error” derived data in the TC location forecasting are likely more evident forpredicting moderate rainfall than light rainfall. Consequently, such degenerations in predicting theTC location might compensate for the improvements in predicting the TC intensity and thus result inmarginal impacts of excluding “large-error” derived data on DA.

Comparison between AOPT and CTL showed that, assimilation of the OPT-derived dataresulted in consistent improvements in predicting heavy rainfall during the whole 12-h forecasts(Figure 7e). Assimilating the OPTPM-derived data seemed to degrade the forecasts of heavy rainfall,although the degradations were not statistically significant (Figure 7e). If only “small-error” OPT-or OPTPM-derived data were assimilated, the forecasts of heavy rainfall can be slightly improved,especially for the former (latter) during the first (last) few hours (Figure 7f). Obviously, improvementsin predicting the TC intensity due to assimilating “large-error” derived data were overwhelmed bydegenerations in predicting the TC location, which were highly related to the forecasts of heavy rainfall.

Due to limited observations or forecast samples for extremely heavy rainfall, the forecastdifferences among CTL, AOPT, and AOPM were not statistically significant; although the positiveimpacts of assimilating the derived data were still observed in some lead times (Figure 7g). Similar toheavy rainfall, excluding “large-error” derived data in DA increased the positive impacts of the deriveddata assimilation on the forecasts of extremely heavy rainfall, especially for AOPM (Figure 7h).

In summary, assimilation of the OPT-derived data was beneficial to the TC precipitationforecasting at some thresholds, with significant impacts on lighter rainfall. Significant positive impactsof assimilating the OPTPM-derived data were limited to the forecasts of light rainfall. The forecastdifferences of precipitation between AOPT and AOPM, especially for moderate and heavy rainfall,are attributed to the forecast differences of TC intensity, because both of the predicted precipitation(Figure 7a,c,e) and TC intensity (Figure 6b,c) were better (worse) during the last (first) few hours inAOPM than in AOPT. To improve the forecasts of heavier rainfall, it is better to assimilate “small-error”instead of “large-error” derived data, especially for the OPTPM-derived data.

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the whole TC circulation, which is closely related to the distribution of light rainfall, because the differences of TC track errors between all the 28 forecasts and the forecasts with “small-error” derived data assimilated were below 15 km (comparing Figure 6a,d), which are evidently smaller than the size of TC circulation. On the contrary, improvements in predicting the TC intensity due to assimilation of “large-error” derived data can improve the forecasts of TC circulation and thus light rainfall, especially for AOPM (comparing Figure 7a,b).

Figure 7. Fraction skill score (FSS) for forecasts of 1-h accumulated precipitation with thresholds of 0.1 (a), (b), 10 (c) (d), 20 (e), (f), and 40 (g), (h) mm and a neighborhood length of 50 km averaged over lead times from 1 to 3 h, 1 to 6 h, and 1 to 12 h, respectively, for all the 28 forecasts (left column) and for the 17 forecasts with the “small-error” derived data assimilated. Black numbers in the top of bars represent the numbers of FSS samples used to calculate the averaged FSS during different lead times. Black (gray) squares, diamonds and asterisks indicate the lead times for which the significance level of the absolute error differences is larger than 90% (85%) for the comparisons between AOPT and CTL, between AOPM and CTL, and between AOPT and AOPM, respectively. The legend in (e) identifies the three experiments shown in these panels.

Figure 7. Fraction skill score (FSS) for forecasts of 1-h accumulated precipitation with thresholds of0.1 (a,b), 10 (c,d), 20 (e,f), and 40 (g,h) mm and a neighborhood length of 50 km averaged over leadtimes from 1 to 3 h, 1 to 6 h, and 1 to 12 h, respectively, for all the 28 forecasts (left column) and forthe 17 forecasts with the “small-error” derived data assimilated. Black numbers in the top of barsrepresent the numbers of FSS samples used to calculate the averaged FSS during different lead times.Black (gray) squares, diamonds and asterisks indicate the lead times for which the significance level ofthe absolute error differences is larger than 90% (85%) for the comparisons between AOPT and CTL,between AOPM and CTL, and between AOPT and AOPM, respectively. The legend in (e) identifies thethree experiments shown in these panels.

In order to further investigate the impact of assimilating “small-error” derived data onheavy rainfall, the 25-km FSS was also compared between different experiments (Figure 8a).The improvements in predicting heavy rainfall of AOPM over AOPT and CTL progressed when

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the neighborhood length of FSS decreased, illustrating that the advantage of AOPM over AOPT andCTL was more evident for heavy rainfall with more local scales.Atmosphere 2019, 10, x FOR PEER REVIEW 17 of 27

Figure 8. FSS for forecasts of 1-h accumulated precipitation larger than 20 mm (a) and 10-m wind speed larger than 24.5 m s−1 (b), with neighborhood lengths of 50 (open bars with gray thick borders) and 25 (full bars with black thin borders) km averaged over lead times from 1 to 3 h, 1 to 6 h, and 1 to 12 h, respectively, for the 17 forecasts with the “small-error” derived data assimilated. Percentages in the top of bars represent the relative improvements in FSS of AOPT over CTL (red), AOPM over CTL (green), and AOPM over AOPT (black) during different lead times. The bold (italic) percentages corresponds to the comparison of FSS with neighborhood length of 25 (50) km. The legend in (a) identifies the three experiments shown in these panels.

4.3. Forecasts of Surface Wind

In this study, 10-m wind speed greater than 8.0, 17.2, 24.5, and 32.7 m s−1 is defined as weak, moderate, strong, and extremely strong wind, respectively.

During the whole 12-h forecasts, both AOPT and AOPM significantly underperformed CTL for predicting weak wind (Figure 9a). This result held even if only “small-error” derived data were assimilated (Figure 9b). However, the positive impacts of assimilating the OPTPM-derived data increased when only “small-error” derived data were assimilated, especially in the first few hours (Figure 9b). Furthermore, AOPM showed evident improvements over AOPT in predicting weak wind, especially in the forecasts with “small-error” derived data assimilated.

The conclusion for the comparison among AOPT, AOPM, and CTL in the forecasts of moderate wind was roughly similar to that for the forecasts of weak wind, except that the forecast differences among the three experiments were statistically insignificant (Figure 9c,d).

For the forecasts of strong wind during the whole 12-h forecasts, both AOPT and AOPM outperformed CTL, with significant improvements of AOPM over CTL during the last few hours (Figure 9e). Although AOPT showed better performance in predicting strong wind than AOPM, the differences between them were not statistically significant. The positive impacts of assimilating the derived data, especially the OPTPM-derived data, were more evident in the forecasts with “small-error” derived data assimilated than those with “large-error” one assimilated (Figure 9f).

There were no statistically significant differences among CTL, AOPT, and AOPM, because of limited observations or forecast samples for extremely strong wind (Figure 9g). Thus, the positive impacts of assimilating the derived data on the forecasts of extremely strong wind (Figure 9g) were the results based on some strong TC cases (e.g., Rammasun). Moreover, assimilation of the “small-error” OPTPM-derived data showed more positive impacts than that of the “large-error” one (Figure 9h).

In short, the forecast improvements due to assimilating the derived data were mainly limited to strong wind, especially with significant improvements based on the assimilation of the OPTPM-derived data. Again, similar to precipitation, the forecast differences of surface wind between AOPT and AOPM, especially for strong and extremely strong wind (Figure 9e,g), were closely related to the forecast differences of TC intensity (Figure 6b,c). Besides, the positive impacts of assimilating the “small-error” OPTPM-derived data increased with the predicted intensity of

Figure 8. FSS for forecasts of 1-h accumulated precipitation larger than 20 mm (a) and 10-m wind speedlarger than 24.5 m s−1 (b), with neighborhood lengths of 50 (open bars with gray thick borders) and 25(full bars with black thin borders) km averaged over lead times from 1 to 3 h, 1 to 6 h, and 1 to 12 h,respectively, for the 17 forecasts with the “small-error” derived data assimilated. Percentages in the topof bars represent the relative improvements in FSS of AOPT over CTL (red), AOPM over CTL (green),and AOPM over AOPT (black) during different lead times. The bold (italic) percentages corresponds tothe comparison of FSS with neighborhood length of 25 (50) km. The legend in (a) identifies the threeexperiments shown in these panels.

4.3. Forecasts of Surface Wind

In this study, 10-m wind speed greater than 8.0, 17.2, 24.5, and 32.7 m s−1 is defined as weak,moderate, strong, and extremely strong wind, respectively.

During the whole 12-h forecasts, both AOPT and AOPM significantly underperformed CTLfor predicting weak wind (Figure 9a). This result held even if only “small-error” derived data wereassimilated (Figure 9b). However, the positive impacts of assimilating the OPTPM-derived dataincreased when only “small-error” derived data were assimilated, especially in the first few hours(Figure 9b). Furthermore, AOPM showed evident improvements over AOPT in predicting weak wind,especially in the forecasts with “small-error” derived data assimilated.

The conclusion for the comparison among AOPT, AOPM, and CTL in the forecasts of moderatewind was roughly similar to that for the forecasts of weak wind, except that the forecast differencesamong the three experiments were statistically insignificant (Figure 9c,d).

For the forecasts of strong wind during the whole 12-h forecasts, both AOPT and AOPMoutperformed CTL, with significant improvements of AOPM over CTL during the last few hours(Figure 9e). Although AOPT showed better performance in predicting strong wind than AOPM, thedifferences between them were not statistically significant. The positive impacts of assimilating thederived data, especially the OPTPM-derived data, were more evident in the forecasts with “small-error”derived data assimilated than those with “large-error” one assimilated (Figure 9f).

There were no statistically significant differences among CTL, AOPT, and AOPM, because oflimited observations or forecast samples for extremely strong wind (Figure 9g). Thus, the positiveimpacts of assimilating the derived data on the forecasts of extremely strong wind (Figure 9g) were theresults based on some strong TC cases (e.g., Rammasun). Moreover, assimilation of the “small-error”OPTPM-derived data showed more positive impacts than that of the “large-error” one (Figure 9h).

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Atmosphere 2019, 10, x FOR PEER REVIEW 18 of 27

surface wind, which was also found in precipitation forecasting and probably attributed to similar reasons.

Figure 9. As in Figure 7, but for 10-m wind speed with thresholds of 8.0 (a), (b), 17.2 (c), (d), 24.5 (e), (f), and 32.7 (g), (h) m s−1. Figure 9. As in Figure 7, but for 10-m wind speed with thresholds of 8.0 (a,b), 17.2 (c,d), 24.5 (e,f), and32.7 (g,h) m s−1.

Atmosphere 2019, 10, 84 18 of 26

In short, the forecast improvements due to assimilating the derived data were mainly limited tostrong wind, especially with significant improvements based on the assimilation of the OPTPM-deriveddata. Again, similar to precipitation, the forecast differences of surface wind between AOPT andAOPM, especially for strong and extremely strong wind (Figure 9e,g), were closely related to theforecast differences of TC intensity (Figure 6b,c). Besides, the positive impacts of assimilating the“small-error” OPTPM-derived data increased with the predicted intensity of surface wind, which wasalso found in precipitation forecasting and probably attributed to similar reasons.

The positive impacts of assimilating the derived data (especially the OPT-derived data) on theforecasts of strong wind seemed to be weaker in the case of FSS with smaller neighborhood lengths(Figure 8b), illustrating the difficulties in further improving the forecasts of strong wind with more localscales by assimilating the derived data. This result is different from that of heavy rainfall, which maybe related to different predictabilities between strong wind and heavy rainfall. However, assimilationof the OPTPM-derived data was more effective in predicting strong wind with more local scales thanassimilation of the OPT-derived data.

5. Results of the Case Study

In the case study, two 12-h forecasts, which were respectively initialized at 1200 UTC 3 and 0000UTC 4 Oct 2015 (Figure 2), were discussed. Note that, the derived data assimilated in these twoforecasts were characterized by the “small-error” data.

5.1. Analyses

In the analyses at 1200 UTC 3 October, which served as IC of the 12-h forecasts, there were evidentdifferences for the TC intensity among CTL, AOPT, and AOPM, although the TC sizes were generallysimilar (Figure 10). Specifically, the analyzed TC was strongest in AOPM (Figure 10c), followed byAOPT (Figure 10b). Recall from Figure 3, where OPT and OPTPM fields derived 6 h earlier are shown,that stronger surface wind was present in OPTPM fields than in OPT fields, especially in the northeastquadrant. Additionally, at the analysis time 6 h earlier, the TC intensities in both OPT and OPTPMfields were larger than that in the analyses of CTL (not shown). Thus, compared with both CTL andAOPT, the stronger TC in IC of AOPM was attributed to the OPTPM-derived data assimilated duringthe 6-h DA cycle. Moreover, the area characterized by strong wind in AOPT and AOPM was evidentlylarger than that in CTL. Compared with AOPT, in AOPM, the TC shape was rounder and the strongwind was more widespread although with smaller area.

Atmosphere 2019, 10, x FOR PEER REVIEW 19 of 27

The positive impacts of assimilating the derived data (especially the OPT-derived data) on the forecasts of strong wind seemed to be weaker in the case of FSS with smaller neighborhood lengths (Figure 8b), illustrating the difficulties in further improving the forecasts of strong wind with more local scales by assimilating the derived data. This result is different from that of heavy rainfall, which may be related to different predictabilities between strong wind and heavy rainfall. However, assimilation of the OPTPM-derived data was more effective in predicting strong wind with more local scales than assimilation of the OPT-derived data.

5. Results of the Case Study

In the case study, two 12-h forecasts, which were respectively initialized at 1200 UTC 3 and 0000 UTC 4 Oct 2015 (Figure 2), were discussed. Note that, the derived data assimilated in these two forecasts were characterized by the “small-error” data.

5.1. Analyses

In the analyses at 1200 UTC 3 October, which served as IC of the 12-h forecasts, there were evident differences for the TC intensity among CTL, AOPT, and AOPM, although the TC sizes were generally similar (Figure 10). Specifically, the analyzed TC was strongest in AOPM (Figure 10c), followed by AOPT (Figure 10b). Recall from Figure 3, where OPT and OPTPM fields derived 6 h earlier are shown, that stronger surface wind was present in OPTPM fields than in OPT fields, especially in the northeast quadrant. Additionally, at the analysis time 6 h earlier, the TC intensities in both OPT and OPTPM fields were larger than that in the analyses of CTL (not shown). Thus, compared with both CTL and AOPT, the stronger TC in IC of AOPM was attributed to the OPTPM-derived data assimilated during the 6-h DA cycle. Moreover, the area characterized by strong wind in AOPT and AOPM was evidently larger than that in CTL. Compared with AOPT, in AOPM, the TC shape was rounder and the strong wind was more widespread although with smaller area.

Figure 10. Analyses for 10-m wind speed (shaded, unit: m s−1) and wind vector (arrows), and geopotential heights at 850 (>1440 gpm; black contours with interval of 40 gpm) and 500 (white contours for values equal to 5880 gpm) hPa at 1200 UTC 3 Oct 2015 from CTL (a), AOPT (b), and AOPM (c).

The initial TC location was also changed, when AOPT or AOPM was compared with CTL. The subtropical ridge, which is indicated by the 5880-gpm contour in Figure 10, located more north in both AOPT and AOPM (Figure 10b,c) than in CTL (Figure 10a). As a result, the TC tracks in both AOPT and AOPM were generally more north than that in CTL during the first 6 h of forecasts (Figure 11).

Figure 10. Analyses for 10-m wind speed (shaded, unit: m s−1) and wind vector (arrows), andgeopotential heights at 850 (>1440 gpm; black contours with interval of 40 gpm) and 500 (whitecontours for values equal to 5880 gpm) hPa at 1200 UTC 3 Oct 2015 from CTL (a), AOPT (b), andAOPM (c).

Atmosphere 2019, 10, 84 19 of 26

The initial TC location was also changed, when AOPT or AOPM was compared with CTL.The subtropical ridge, which is indicated by the 5880-gpm contour in Figure 10, located more north inboth AOPT and AOPM (Figure 10b,c) than in CTL (Figure 10a). As a result, the TC tracks in both AOPTand AOPM were generally more north than that in CTL during the first 6 h of forecasts (Figure 11).Atmosphere 2019, 10, x FOR PEER REVIEW 20 of 27

Figure 11. Observations (black) and forecasts (red, blue, and green) of track (lines), Pmin (dots), and Vmax (circles) for Mujigae from 1200 UTC 3 to 1200 UTC 4 October 2015. The sizes of the dots (circles) represent the TC intensities, with smaller (larger) sizes corresponding to stronger TCs. ‘OBS’ represents the observations from CMA best-track dataset. The start TC location at the lower right corner of the panel indicates the analyses at 1200 UTC 3 October 2015, while the other TC locations indicate the forecasts.

Thus, assimilation of the derived data during the DA cycle can modify not only the TC intensity and structure but also the TC location and steering flow.

5.2. Forecasts

Both AOPT and AOPM did not show consistent advantages over CTL in predicting the TC track, actually with evident advantages mainly in the first 12-h forecasts (Figure 11). Compared with CTL, the underestimation of TC intensity in both AOPT and AOPM was evidently reduced, especially in terms of Vmax (Figure 11). Obviously, these improvements of AOPT or AOPM over CTL in the TC intensity forecasting were closely related to the improved descriptions of TC intensity in the analyses (Figures 10 and 11).

At 1600 UTC 3 October when Mujigae approached HN, moderate wind was observed near the coasts of southwest GD and northeast HN (Figure 12a). Apparently, moderate wind was underestimated in both CTL and AOPT, especially in CTL (Figure 12b,c). Overall, AOPM showed the best performance in predicting moderate wind (Figure 12d), followed by AOPT (Figure 12c). Moreover, strong and even extremely strong wind was observed to occur in the northwest and southwest quadrants of the TC circulation (Figure 12a). Again, AOPM outperformed both AOPT and CTL in predicting the intensity and structure of (extremely) strong wind, although the location error was indeed present (Figure 12d).

Figure 11. Observations (black) and forecasts (red, blue, and green) of track (lines), Pmin (dots), andVmax (circles) for Mujigae from 1200 UTC 3 to 1200 UTC 4 October 2015. The sizes of the dots (circles)represent the TC intensities, with smaller (larger) sizes corresponding to stronger TCs. ‘OBS’ representsthe observations from CMA best-track dataset. The start TC location at the lower right corner ofthe panel indicates the analyses at 1200 UTC 3 October 2015, while the other TC locations indicatethe forecasts.

Thus, assimilation of the derived data during the DA cycle can modify not only the TC intensityand structure but also the TC location and steering flow.

5.2. Forecasts

Both AOPT and AOPM did not show consistent advantages over CTL in predicting the TC track,actually with evident advantages mainly in the first 12-h forecasts (Figure 11). Compared with CTL,the underestimation of TC intensity in both AOPT and AOPM was evidently reduced, especially interms of Vmax (Figure 11). Obviously, these improvements of AOPT or AOPM over CTL in the TCintensity forecasting were closely related to the improved descriptions of TC intensity in the analyses(Figures 10 and 11).

At 1600 UTC 3 October when Mujigae approached HN, moderate wind was observed nearthe coasts of southwest GD and northeast HN (Figure 12a). Apparently, moderate wind wasunderestimated in both CTL and AOPT, especially in CTL (Figure 12b,c). Overall, AOPM showed the

Atmosphere 2019, 10, 84 20 of 26

best performance in predicting moderate wind (Figure 12d), followed by AOPT (Figure 12c). Moreover,strong and even extremely strong wind was observed to occur in the northwest and southwestquadrants of the TC circulation (Figure 12a). Again, AOPM outperformed both AOPT and CTL inpredicting the intensity and structure of (extremely) strong wind, although the location error wasindeed present (Figure 12d).Atmosphere 2019, 10, x FOR PEER REVIEW 21 of 27

Figure 12. 10-m wind speed (shaded, unit: m s−1) of AWS observation (a) and 4-h forecasts from CTL (b), AOPT (c), and AOPM (d) at 1600 UTC 3 October 2015. The outlines of the observed wind speed are contoured at the 17.2 m s−1 threshold in magenta lines in (b)–(d).

At 0000 UTC 4 October, i.e., 6 h ahead of the landfall of Mujigae, several rainbands characterized by moderate rainfall occurred in the southwest GD, with heavy and extremely heavy rainfall in some areas (Figure 13a). Among the three experiments, AOPM generally performed best in predicting the observed rainbands in terms of both magnitude and location (Figure 13d). The advantages of AOPT over CTL were limited to predicting the outer rainbands; while for inner rainbands, AOPT behaved worse than CTL (Figure 13b,c).

The improvements of AOPM over AOPT and CTL in predicting both the inner and outer rainbands (Figure 13d) were relevant to those in predicting the structure of TC circulation, i.e., wind fields (Figure 12d), because the pattern of TC rainbands was generally similar to that of TC surface wind, especially around the TC inner core. However, the stronger predicted surface wind in AOPM/AOPT than in CTL did not necessarily lead to heavier predicted rainfall. Thus, the underestimation of heavy and extremely heavy rainfall in CTL was not well alleviated in both AOPM and AOPT.

Figure 12. 10-m wind speed (shaded, unit: m s−1) of AWS observation (a) and 4-h forecasts from CTL(b), AOPT (c), and AOPM (d) at 1600 UTC 3 October 2015. The outlines of the observed wind speed arecontoured at the 17.2 m s−1 threshold in magenta lines in (b–d).

At 0000 UTC 4 October, i.e., 6 h ahead of the landfall of Mujigae, several rainbands characterizedby moderate rainfall occurred in the southwest GD, with heavy and extremely heavy rainfall in someareas (Figure 13a). Among the three experiments, AOPM generally performed best in predicting theobserved rainbands in terms of both magnitude and location (Figure 13d). The advantages of AOPTover CTL were limited to predicting the outer rainbands; while for inner rainbands, AOPT behavedworse than CTL (Figure 13b,c).

The improvements of AOPM over AOPT and CTL in predicting both the inner and outer rainbands(Figure 13d) were relevant to those in predicting the structure of TC circulation, i.e., wind fields(Figure 12d), because the pattern of TC rainbands was generally similar to that of TC surface wind,especially around the TC inner core. However, the stronger predicted surface wind in AOPM/AOPTthan in CTL did not necessarily lead to heavier predicted rainfall. Thus, the underestimation of heavyand extremely heavy rainfall in CTL was not well alleviated in both AOPM and AOPT.

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Figure 13. 1-h accumulated rainfall (shaded, unit: mm) of automatic weather station (AWS) observation (a) and 12-h forecasts from CTL (b), AOPT (c), and AOPM (d) at 0000 UTC 4 October 2015. The outlines of the observed rainfall are contoured at the 10 mm threshold in magenta lines in (b)–(d).

6. Conclusions and Discussion

In order to partially address the difficulty that insufficient inner-core observations have been assimilated in the current convection-permitting NWP model in Southern China, which has severely limited the operational forecast skill of landfalling TCs, assimilation of the pseudo observations derived from some deterministic products of TREPS was implemented in this study.

Both OPT and OPTPM fields from TREPS were used to derive pseudo observations with the horizontal resolution of roughly 45 km. The derived data generally showed acceptable accuracy, compared with the TC track and Vmax uncertainties of some best-track data. And the estimation of TC intensity was more accurate in the OPTPM-derived data than in the OPT-derived data, because the excessive smoothing in OPT fields can be avoided in OPTPM fields. The ensemble spreads from TREPS after some scaling processes were used to simply estimate the standard deviations of observation errors for the derived data. A series of QC steps were carried out to reduce the impacts of inevitable forecast errors present in the derived data on DA.

The impact of assimilating the derived data on the 12-h forecasts of TC track, intensity, precipitation and surface wind was examined by conducting a batch experiment covering 17 TCs making landfall in Southern China during 2014–2016. This batch experiment included 28 analysis-forecast cycles based on the GRAPES-CHAF3KM DA system and GRAPES-MARS3KM model whose horizontal resolution is about 3 km. The control experiment (CTL) without the derived data assimilated was compared with the experiments, namely AOPT and AOPM, with the OPT- and OPTPM-derived data assimilated respectively.

Verification of the TC track forecasting indicated the statistically insignificant impacts of assimilating the derived data, which was due to the degeneration of describing initial TC location caused by the assimilation of derived data. Furthermore, compared with the OPT-derived data, assimilating the OPTPM-derived data slightly improved the TC track forecasting at later lead times. Overall, both the analysis and forecast of TC intensity were slightly improved by assimilating the

Figure 13. 1-h accumulated rainfall (shaded, unit: mm) of automatic weather station (AWS) observation(a) and 12-h forecasts from CTL (b), AOPT (c), and AOPM (d) at 0000 UTC 4 October 2015. The outlinesof the observed rainfall are contoured at the 10 mm threshold in magenta lines in (b–d).

6. Conclusions and Discussion

In order to partially address the difficulty that insufficient inner-core observations have beenassimilated in the current convection-permitting NWP model in Southern China, which has severelylimited the operational forecast skill of landfalling TCs, assimilation of the pseudo observations derivedfrom some deterministic products of TREPS was implemented in this study.

Both OPT and OPTPM fields from TREPS were used to derive pseudo observations with thehorizontal resolution of roughly 45 km. The derived data generally showed acceptable accuracy,compared with the TC track and Vmax uncertainties of some best-track data. And the estimation of TCintensity was more accurate in the OPTPM-derived data than in the OPT-derived data, because theexcessive smoothing in OPT fields can be avoided in OPTPM fields. The ensemble spreads from TREPSafter some scaling processes were used to simply estimate the standard deviations of observationerrors for the derived data. A series of QC steps were carried out to reduce the impacts of inevitableforecast errors present in the derived data on DA.

The impact of assimilating the derived data on the 12-h forecasts of TC track, intensity,precipitation and surface wind was examined by conducting a batch experiment covering17 TCs making landfall in Southern China during 2014–2016. This batch experiment included28 analysis-forecast cycles based on the GRAPES-CHAF3KM DA system and GRAPES-MARS3KMmodel whose horizontal resolution is about 3 km. The control experiment (CTL) without the deriveddata assimilated was compared with the experiments, namely AOPT and AOPM, with the OPT- andOPTPM-derived data assimilated respectively.

Verification of the TC track forecasting indicated the statistically insignificant impacts ofassimilating the derived data, which was due to the degeneration of describing initial TC locationcaused by the assimilation of derived data. Furthermore, compared with the OPT-derived data,

Atmosphere 2019, 10, 84 22 of 26

assimilating the OPTPM-derived data slightly improved the TC track forecasting at later lead times.Overall, both the analysis and forecast of TC intensity were slightly improved by assimilating thederived data, especially in the later period of the 12-h forecasts. Similar performances of TC intensityforecasting were found between AOPT and AOPM, although AOPM outperformed AOPT at later leadtimes. Assimilating the “large-error” derived data, which were characterized by track (Vmax) errorsexceeding 50 km (5 m s−1) compared with WARNING, degraded both the analysis and forecast of TCtrack, but it could still improve the analysis and forecast of TC intensity.

Assimilating the OPT-derived data brought improvements in predicting the TC precipitation atsome thresholds, especially the lighter rainfall. Limited benefits of assimilating the OPTPM-deriveddata were found in the forecasts of light rainfall, besides, the negative impacts, albeit statisticallyinsignificant, on TC Vmax forecasting in the first few hours probably limited the positive impactson the forecasts of heavier rainfall. Assimilation of the “small-error” derived data, especially theOPTPM-derived data, which were characterized by track errors below 50 km or Vmax errors below5 m s−1 compared with WARNING, improved the forecasts of heavier rainfall. And this positiveimpact was more evident for heavy rainfall with more local scales.

The forecasts of strong wind were improved by assimilating the derived data, especially theOPTPM-derived data. Moreover, assimilation of the “small-error” OPTPM-derived data can furtherimprove the forecasts of stronger wind. Although the further improvement in the forecasts ofstrong wind with more local scales by assimilating the derived data was limited, assimilationof the OPTPM-derived data was more effective to address this difficulty than assimilation of theOPT-derived data.

A case study focused on the TC Mujigae, with the corresponding derived data identified as the“small-error” one, was used to intuitively demonstrate the impacts of assimilating the derived data.For this case, assimilation of the derived data (especially the OPTPM-derived data) during the 6-hDA cycle improved the representation of initial TC circulation by improving the description of TCintensity and structure in the analyses, which thus led to the improvements in the forecasts of TCintensity, surface wind, and precipitation. The initial TC location and steering flow were also modifiedby assimilating the derived data; however, the TC track forecasting did not be improved consistently.

The above conclusions highlight some values of assimilating the derived data from TREPS inlandfalling TC forecasting for some variables, e.g., intensity, heavier rainfall, and stronger wind.However, neutral or negative impacts have been also observed for some variables, e.g., track andweaker wind, which strongly calls for further improvements in the technique of assimilating thederived data. Obviously, the accuracy of derived data highly depends on the forecast performanceof deterministic products of EPSs, which definitely benefits from the improvements in EPSs. Thus,developments of EPSs, especially their deterministic guidance, are essential for further improvementsin the derived data assimilation. Moreover, there are some ad hoc setups in the preprocessing of deriveddata, e.g., selecting the grid points, determining the observation errors, and QC, which are of relevanceto the information derived from EPSs. Therefore, improvements of these setups in future works willfurther improve the effectiveness of the derived data assimilation. However, the current ad hoc setupsare still excessive and would probably limit the broader applicability of the derived data assimilation.Most of these setups are used to address the deficiency due to the poor quality of the derived data inDA. Hence, improving the quality of the derived data will reduce the requirement of ad hoc setupsand thereby widen the applicability of the derived data assimilation. More ground-based observations,especially those located around the coast, such as Doppler radar, should also be assimilated alongwith the derived data, because both the coverage and accuracy of derived data are still insufficientto fully describe the TC circulation. Consequently, the experiments incorporating the derived dataand more observations will be conducted in a future study. Considering less observations and forecastsamples (especially for extremely heavy rainfall and extremely strong wind) used in this study, moreexperiments covering more TC cases are needed to draw general conclusions about the performance of

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assimilating the derived data in TC forecasting, which is very necessary for prompting the assimilationof EPS-derived data in operation.

Author Contributions: X.Z. developed the methods, designed and performed the experiments, and wrote themanuscript; M.C. provided thorough reviews of the earlier version of the manuscript and revised some ofthe figures.

Funding: This work was supported by the National Basic Research and Development Project (973 program) ofChina (2015CB452802), Meteorology Public Welfare Scientific Research Projects (GYHY201506022), NationalKey R&D Program of China (2017YFC1501603), and Natural Science Foundation of Guangdong Province(2017A030313225, 2016A03031000).

Conflicts of Interest: The authors declare no conflict of interest.

References

1. Rappaport, E.N.; Franklin, J.L.; Avila, L.A.; Baig, S.R.; Beven, J.L., II; Blake, E.S.; Burr, C.A.; Jing, J.G.;Juckins, C.A.; Knabb, R.D.; et al. Advances and challenges at the National Hurricane Center. Weather Forecast.2009, 24, 395–419. [CrossRef]

2. Goldenberg, S.B.; Gopalakrishnan, S.G.; Tallapragada, V.; Quirino, T.; Marks, F.; Trahan, S.; Zhang, X.;Atlas, R. The 2012 Triply-Nested, High-Resolution Operational Version of the Hurricane Weather Researchand Forecasting System (HWRF): Track and Intensity Forecast Verifications. Weather Forecast. 2015, 30,710–729. [CrossRef]

3. Gopalakrishnan, S.; Toepfer, F.; Gall, R.; Marks, F.; Rappaport, E.N.; Tallapragada, V.; Forsythe-Newell, S.;Aksoy, A.; Bao, J.W.; Bender, M.; et al. 2015 HFIP R&D Activities Summary: Recent Results and OperationalImplementation; HFIP Technical Report: HFIP2016-1; NOAA: Washington, DC, USA, 2016.

4. Yu, H.; Chen, P.; Li, Q.; Tang, B. Current Capability of Operational Numerical Models in Predicting TropicalCyclone Intensity in the Western North Pacific. Weather Forecast. 2013, 28, 353–367. [CrossRef]

5. DeMaria, M.; Sampson, C.R.; Knaff, J.A.; Musgrave, K.D. Is Tropical Cyclone Intensity Guidance Improving?Bull. Am. Meteorol. Soc. 2014, 95, 387–398. [CrossRef]

6. Cangialosi, J.P.; Franklin, J.L. National Hurricane Center Forecast Verification Report. 2015 Hurricane Season;Presented at NWS; NOAA: Washington, DC, USA, 2016.

7. Nishijima, K.; Maruyama, T.; Graf, M. A preliminary impact assessment of typhoon wind risk of residentialbuildings in Japan under future climate change. Hydrol. Res. Lett. 2012, 6, 23–28. [CrossRef]

8. Chen, S.S.; Zhao, W.; Donelan, M.A.; Tolman, H.L. Directional Wind–Wave Coupling in Fully CoupledAtmosphere–Wave–Ocean Models: Results from CBLAST-Hurricane. J. Atmos. Sci. 2013, 70, 3198–3215.[CrossRef]

9. Shi, X.; Liu, S.; Yang, S.; Liu, Q.; Tan, J.; Guo, Z. Spatial–temporal distribution of storm surge damage in thecoastal areas of China. Nat. Hazards 2015, 79, 237–247. [CrossRef]

10. Wang, Y.; Wen, S.; Li, X.; Thomas, F.; Su, B.; Jiang, T.; Wang, R. Spatiotemporal distributions of influentialtropical cyclones and associated economic losses in China in 1984–2015. Nat. Hazards 2016, 84, 2009–2030.[CrossRef]

11. Davis, C.; Wang, W.; Dudhia, J.; Torn, R. Does Increased Horizontal Resolution Improve Hurricane WindForecasts? Weather Forecast. 2010, 25, 1826–1841. [CrossRef]

12. Gopalakrishnan, S.G.; Goldenberg, S.; Quirino, T.; Zhang, X.; Marks, F.; Yeh, K.-S.; Atlas, R.; Tallapragada, V.Toward Improving High-Resolution Numerical Hurricane Forecasting: Influence of Model Horizontal GridResolution, Initialization, and Physics. Weather Forecast. 2012, 27, 647–666. [CrossRef]

13. Xue, M.; Schleif, J.; Kong, F.; Thomas, K.W.; Wang, Y.; Zhu, K. Track and Intensity Forecasting of Hurricanes:Impact of Convection-Permitting Resolution and Global Ensemble Kalman Filter Analysis on 2010 AtlanticSeason Forecasts. Weather Forecast. 2013, 28, 1366–1384. [CrossRef]

14. Zou, X.; Xiao, Q. Studies on the Initialization and Simulation of a Mature Hurricane Using a VariationalBogus Data Assimilation Scheme. J. Atmos. Sci. 2000, 57, 836–860. [CrossRef]

15. Torn, R.D.; Hakim, G.J. Ensemble Data Assimilation Applied to RAINEX Observations of Hurricane Katrina(2005). Mon. Weather Rev. 2009, 137, 2817–2829. [CrossRef]

Atmosphere 2019, 10, 84 24 of 26

16. Zhang, F.; Weng, Y.; Gamache, J.F.; Marks, F.D. Performance of convection-permitting hurricane initializationand prediction during 2008-2010 with ensemble data assimilation of inner-core airborne Doppler radarobservations. Geophys. Res. Lett. 2011, 38, 15810. [CrossRef]

17. Rogers, R.; Aberson, S.; Aksoy, A.; Annane, B.; Black, M.; Cione, J.; Dorst, N.; Dunion, J.; Gamache, J.;Goldenberg, S.; et al. NOAA’S Hurricane Intensity Forecasting Experiment: A Progress Report. Bull. Am.Meteorol. Soc. 2013, 94, 859–882. [CrossRef]

18. Xiao, Q.; Zou, X.; Wang, B. Initialization and Simulation of a Landfalling Hurricane Using a VariationalBogus Data Assimilation Scheme. Mon. Weather Rev. 2000, 128, 2252–2269. [CrossRef]

19. Weng, Y.; Zhang, F. Assimilating Airborne Doppler Radar Observations with an Ensemble Kalman Filter forConvection-Permitting Hurricane Initialization and Prediction: Katrina (2005). Mon. Weather Rev. 2012, 140,841–859. [CrossRef]

20. Lau, W.K.; Susskind, J.; Brin, E.; Riishojgaard, L.P.; Reale, O.; Liu, E.; Fuentes, M.; Rosenberg, R. AIRS impacton the analysis and forecast track of tropical cyclone Nargis in a global data assimilation and forecastingsystem. Geophys. Res. Lett. 2009, 36. [CrossRef]

21. Wang, P.; Li, J.; Li, Z.; Lim, A.H.N.; Li, J.; Schmit, T.J.; Goldberg, M.D. The Impact of Cross-track InfraredSounder (CrIS) Cloud-Cleared Radiances on Hurricane Joaquin (2015) and Matthew (2016) Forecasts.J. Geophys. Res. Atmos. 2017, 122, 13–201. [CrossRef]

22. Schwartz, C.S.; Liu, Z.; Chen, Y.; Huang, X.-Y. Impact of Assimilating Microwave Radiances with aLimited-Area Ensemble Data Assimilation System on Forecasts of Typhoon Morakot. Weather Forecast.2012, 27, 424–437. [CrossRef]

23. Zou, X.; Weng, F.; Zhang, B.; Lin, L.; Qin, Z.; Tallapragada, V. Impacts of assimilation of ATMS data in HWRFon track and intensity forecasts of 2012 four landfall hurricanes. J. Geophys. Res. Atmos. 2013, 118, 11–558.[CrossRef]

24. Zhang, M.; Zupanski, M.; Kim, M.-J.; Knaff, J.A. Assimilating AMSU-A Radiances in the TC Core Area withNOAA Operational HWRF (2011) and a Hybrid Data Assimilation System: Danielle (2010). Mon. Weather Rev.2013, 141, 3889–3907. [CrossRef]

25. Xu, D.; Min, J.; Shen, F.; Ban, J.; Chen, P. Assimilation of MWHS radiance data from the FY-3B satellite withthe WRF Hybrid-3DVAR system for the forecasting of binary typhoons. J. Adv. Model. Earth Syst. 2016, 8,1014–1028. [CrossRef]

26. Wu, T.-C.; Liu, H.; Majumdar, S.J.; Velden, C.S.; Anderson, J.L. Influence of Assimilating Satellite-DerivedAtmospheric Motion Vector Observations on Numerical Analyses and Forecasts of Tropical Cyclone Trackand Intensity. Mon. Weather Rev. 2014, 142, 49–71. [CrossRef]

27. Zou, X.; Qin, Z.; Zheng, Y. Improved Tropical Storm Forecasts withGOES-13/15Imager Radiance Assimilationand Asymmetric Vortex Initialization in HWRF. Mon. Weather Rev. 2015, 143, 2485–2505. [CrossRef]

28. Zhang, F.; Minamide, M.; Clothiaux, E.E. Potential impacts of assimilating all-sky infrared satellite radiancesfrom GOES-R on convection-permitting analysis and prediction of tropical cyclones. Geophys. Res. Lett. 2016,43, 2954–2963. [CrossRef]

29. Honda, T.; Miyoshi, T.; Lien, G.-Y.; Nishizawa, S.; Yoshida, R.; Adachi, S.A.; Terasaki, K.; Okamoto, K.;Tomita, H.; Bessho, K. Assimilating All-Sky Himawari-8 Satellite Infrared Radiances: A Case of TyphoonSoudelor (2015). Mon. Weather Rev. 2018, 146, 213–229. [CrossRef]

30. Minamide, M.; Zhang, F. Assimilation of All-Sky Infrared Radiances from Himawari-8 and Impacts of Moistureand Hydrometer Initialization on Convection-Permitting Tropical Cyclone Prediction. Mon. Weather Rev. 2018,146, 3241–3258. [CrossRef]

31. Han, H.; Li, J.; Sohn, B.-J.; Goldberg, M.; Wang, P.; Li, J.; Li, Z.; Li, J. Microwave sounder cloud detection usinga collocated high resolution imager and its impact on radiance assimilation in tropical cyclone forecasts.Mon. Weather Rev. 2016, 144, 3937–3959. [CrossRef]

32. Sieron, S.B.; Clothiaux, E.E.; Zhang, F.; Lu, Y.; Otkin, J.A. Comparison of using distribution-specific versuseffective radius methods for hydrometeor single-scattering properties for all-sky microwave satellite radiancesimulations with different microphysics parameterization schemes. J. Geophys. Res. Atmos. 2017, 122,7027–7046. [CrossRef]

33. Lin, H.; Weygandt, S.S.; Benjamin, S.G.; Hu, M. Satellite Radiance Data Assimilation within the HourlyUpdated Rapid Refresh. Weather Forecast. 2017, 32, 1273–1287. [CrossRef]

Atmosphere 2019, 10, 84 25 of 26

34. Okamoto, K. Evaluation of IR radiance simulation for all-sky assimilation of Himawari-8/AHI in a mesoscaleNWP system. Q. J. R. Meteorol. Soc. 2017, 143, 1517–1527. [CrossRef]

35. Xue, J.; Liu, Y. Numerical weather prediction in China in the new century—Progress, problems and prospects.Adv. Atmos. Sci. 2007, 24, 1099–1108. [CrossRef]

36. Chen, D.H.; Xue, J.S.; Yang, X.S.; Zhang, H.L.; Shen, X.S.; Hu, J.L.; Wang, Y.; Ji, L.R.; Chen, J.B. New generationof multiscale NWP system (GRAPES): General scientific design. Chin. Sci. Bull. 2008, 53, 3433–3445.

37. Su, W.; Corbett, J.; Eitzen, Z.; Liang, L. Next-generation angular distribution models for top-of-atmosphereradiative flux calculation from CERES instruments: methodology. Atmos. Meas. Tech. 2015, 8, 611–632.[CrossRef]

38. Li, H.; Ding, W.; Xue, J.; Chen, Z.; Gao, Y. A study on the application of FY-2E cloud drift wind heightreassignment in numerical forecast of typhoon CHANTHU (1003) track. J. Trop. Meteorol. 2015, 21, 34–42.

39. Zhang, X.; Luo, Y.; Wan, Q.; Ding, W.; Sun, J. Impact of Assimilating Wind Profiling Radar Observationson Convection-permitting Quantitative Precipitation Forecasts during SCMREX. Weather Forecast. 2016, 31,1271–1292. [CrossRef]

40. Zhang, X. A GRAPES-based mesoscale ensemble prediction system for tropical cyclone forecasting:Configuration and performance. Q. J. R. Meteorol. Soc. 2018, 144, 478–498. [CrossRef]

41. Ancell, B.C. Nonlinear Characteristics of Ensemble Perturbation Evolution and Their Application toForecasting High-Impact Events. Weather Forecast. 2013, 28, 1353–1365. [CrossRef]

42. Hollan, M.A.; Ancell, B.C. Ensemble Mean Storm-Scale Performance in the Presence of Nonlinearity.Mon. Weather Rev. 2015, 143, 5115–5133. [CrossRef]

43. Zhang, C.; Zhong, S.; Dai, G.; Xu, D.; Yang, Z.; Chen, Z.; Huang, Y.; Feng, Y. Track of Super Typhoon Haiyanpredicted by a typhoon model for the South China Sea. J. Meteorol. Res. 2014, 28, 510–523.

44. Hong, S.-Y.; Noh, Y.; Dudhia, J. A New Vertical Diffusion Package with an Explicit Treatment of EntrainmentProcesses. Mon. Weather Rev. 2006, 134, 2318–2341. [CrossRef]

45. Hong, S.-Y.; Pan, H.-L. Nonlocal Boundary Layer Vertical Diffusion in a Medium-Range Forecast Model.Mon. Weather Rev. 1996, 124, 2322–2339. [CrossRef]

46. Xue, J.; Zhuang, S.; Zhu, G.; Zhang, H.; Liu, Z.; Liu, Y.; Zhuang, Z. Scientific design and preliminary resultsof three-dimensional variational data assimilation system of GRAPES. Chin. Sci. Bull. 2008, 53, 3446–3457.[CrossRef]

47. Xie, Y.; Koch, S.; McGinley, J.; Albers, S.; Bieringer, P.E.; Wolfson, M.; Chan, M. A Space–Time MultiscaleAnalysis System: A Sequential Variational Analysis Approach. Mon. Weather Rev. 2011, 139, 1224–1240.[CrossRef]

48. Hsiao, L.-F.; Chen, D.-S.; Kuo, Y.-H.; Guo, Y.-R.; Yeh, T.-C.; Hong, J.-S.; Fong, C.-T.; Lee, C.-S. Applicationof WRF 3DVAR to Operational Typhoon Prediction in Taiwan: Impact of Outer Loop and Partial CyclingApproaches. Weather Forecast. 2012, 27, 1249–1263. [CrossRef]

49. Courtier, P.; Thepaut, J.; Hollingsworth, A. A strategy for operational implementation of 4D-Var, using anincremental approach. Q. J. R. Meteorol. Soc. 1994, 120, 1367–1387. [CrossRef]

50. Barker, D.M.; Huang, W.; Guo, Y.-R.; Bourgeois, A.J.; Xiao, Q.N. A Three-Dimensional Variational DataAssimilation System for MM5: Implementation and Initial Results. Mon. Weather Rev. 2004, 132, 897–914.[CrossRef]

51. Hollingsworth, A.; Lönnberg, P. The statistical structure of short-range forecast errors as determined fromradiosonde data. Part I: The wind field. Tellus A 1986, 38A, 111–136. [CrossRef]

52. Gao, Y.; Xiao, H.; Chan, P.W.; Hon, K.K.; Wan, Q.; Ding, W. Application of the multigrid 3D variation methodto a combination of aircraft observations and bogus data for Typhoon Nida (2016). Meteorol. Appl. 2019.[CrossRef]

53. Ying, M.; Zhang, W.; Yu, H.; Lu, X.; Feng, J.; Fan, Y.; Zhu, Y.; Chen, D. An Overview of the China MeteorologicalAdministration Tropical Cyclone Database. J. Atmos. Ocean. Technol. 2014, 31, 287–301. [CrossRef]

54. Roberts, N.M.; Lean, H.W. Scale-Selective Verification of Rainfall Accumulations from High-ResolutionForecasts of Convective Events. Mon. Weather Rev. 2008, 136, 78–97. [CrossRef]

55. Ebert, E.E. Fuzzy verification of high-resolution gridded forecasts: A review and proposed framework.Meteorol. Appl. 2008, 15, 51–64. [CrossRef]

Atmosphere 2019, 10, 84 26 of 26

56. Zhang, X. Application of a convection-permitting ensemble prediction system to quantitative precipitationforecasts over southern China: Preliminary results during SCMREX. Q. J. R. Meteorol. Soc. 2018, 144,2842–2862. [CrossRef]

57. Zhao, K.; Wang, M.; Xue, M.; Fu, P.; Yang, Z.; Chen, X.; Zhang, Y.; Lee, W.-C.; Zhang, F.; Lin, Q.; et al. DopplerRadar Analysis of a Tornadic Miniature Supercell during the Landfall of Typhoon Mujigae (2015) in SouthChina. Bull. Am. Meteorol. Soc. 2017, 98, 1821–1831. [CrossRef]

58. Bai, L.; Meng, Z.; Huang, L.; Yan, L.; Li, Z.; Mai, X.; Huang, Y.; Yao, D.; Wang, X. An Integrated Damage,Visual, and Radar Analysis of the 2015 Foshan, Guangdong EF3 Tornado in China Produced by theLandfalling Typhoon Mujigae (2015). Bull. Am. Meteorol. Soc. 2017, 98, 2619–2640. [CrossRef]

59. Järvinen, H.; Undén, P. Observation screening and first guess quality control in the ECMWF 3D-VAR dataassimilation system. Presented at Reading: ECMWF. 1997. Available online: https://www.ecmwf.int/en/elibrary/ (accessed on 11 January 2019).

60. Buehner, M. Error Statistics in Data Assimilation: Estimation and Modelling; Springer Nature: Berlin, Germany,2010; pp. 93–112.

61. Simonin, D.; Ballard, S.P.; Li, Z. Doppler radar radial wind assimilation using an hourly cycling 3D-Var witha 1.5 km resolution version of the Met Office Unified Model for nowcasting. Q. J. R. Meteorol. Soc. 2014, 140,2298–2314. [CrossRef]

62. Smith, D.H.; Sulaiman, A.; Naughton, M. Multiscale verification calculations for regional ensemble forecasts.ANZIAM J. 2011, 52, 882. [CrossRef]

63. Torn, R.D.; Snyder, C. Uncertainty of Tropical Cyclone Best-Track Information. Weather Forecast. 2012, 27,715–729. [CrossRef]

64. Tracton, M.S.; Kalnay, E. Operational Ensemble Prediction at the National Meteorological Center: PracticalAspects. Weather Forecast. 1993, 8, 379–398. [CrossRef]

65. Zhang, F.; Weng, Y.; Sippel, J.A.; Meng, Z.; Bishop, C.H. Cloud-Resolving Hurricane Initializationand Prediction through Assimilation of Doppler Radar Observations with an Ensemble Kalman Filter.Mon. Weather Rev. 2009, 137, 2105–2125. [CrossRef]

66. Wang, X.; Barker, D.M.; Snyder, C.; Hamill, T.M. A hybrid ETKF–3DVARdata assimilation scheme for theWRF model. Part I: Observing system simulation experiment. Mon. Weather Rev. 2008, 136, 5116–5131.[CrossRef]

67. Gentry, M.S.; Lackmann, G.M. Sensitivity of Simulated Tropical Cyclone Structure and Intensity to HorizontalResolution. Mon. Weather Rev. 2010, 138, 688–704. [CrossRef]

68. Jin, H.; Peng, M.S.; Jin, Y.; Doyle, J.D. An Evaluation of the Impact of Horizontal Resolution on TropicalCyclone Predictions Using COAMPS-TC. Weather Forecast. 2014, 29, 252–270. [CrossRef]

69. Short, C.J.; Petch, J. How Well Can the Met Office Unified Model Forecast Tropical Cyclones in the WesternNorth Pacific? Weather Forecast. 2018, 33, 185–201. [CrossRef]

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