Evaluation of Operational Monsoon Moisture Surveillance and Severe Weather Prediction Utilizing COSMIC-2/FORMOSAT-7 Radio Occultation Observations

remote sensing

Article Evaluation of Operational Monsoon Moisture Surveillance and Severe Weather Prediction Utilizing COSMIC-2/FORMOSAT-7 Radio Occultation Observations

Yu-Chun Chen , Chih-Chien Tsai * , Yi-chao Wu , An-Hsiang Wang, Chieh-Ju Wang, Hsin-Hung Lin, Dan-Rong Chen and Yi-Chiang Yu

National Science and Technology Center for Disaster Reduction, New Taipei City 23143, Taiwan; [email protected] (Y.-C.C.); [email protected] (Y.-c.W.); [email protected] (A.-H.W.); [email protected] (C.-J.W.); [email protected] (H.-H.L.); [email protected] (D.-R.C.); [email protected] (Y.-C.Y.) * Correspondence: [email protected]; Tel.: +886-2-8195-8419

Abstract: Operational monsoon moisture surveillance and severe weather prediction is essential for timely water resource management and disaster risk reduction. For these purposes, this study

suggests a moisture indicator using the COSMIC-2/FORMOSAT-7 radio occultation (RO) observations and evaluates numerical model experiments with RO data assimilation. The RO data quality is

Citation: Chen, Y.-C.; Tsai, C.-C.; Wu, validated by a comparison between sampled RO profiles and nearby radiosonde profiles around Tai- Y.-c.; Wang, A.-H.; Wang, C.-J.; Lin, wan prior to the experiments. The suggested moisture indicator accurately monitors daily moisture H.-H.; Chen, D.-R.; Yu, Y.-C. variations in the South China Sea and the Bay of Bengal throughout the 2020 monsoon rainy season. Evaluation of Operational Monsoon For the numerical model experiments, the statistics of 152 moisture and rainfall forecasts for the 2020 Moisture Surveillance and Severe Meiyu season in Taiwan show a neutral to slightly positive impact brought by RO data assimilation. Weather Prediction Utilizing A forecast sample with the most significant improvement reveals that both thermodynamic and COSMIC-2/FORMOSAT-7 Radio dynamic fields are appropriately adjusted by model integration posterior to data assimilation. The Occultation Observations. Remote statistics of 17 track forecasts for typhoon Hagupit (2020) also show the positive effect of RO data Sens. 2021, 13, 2979. https:// assimilation. A forecast sample reveals that the member with RO data assimilation simulates better doi.org/10.3390/rs13152979 typhoon structure and intensity than the member without, and the effect can be larger and faster via multi-cycle RO data assimilation. Academic Editors: Michael E. Gorbunov, Xiaolei Zou, Vladimir Gubenko, Vinicius Ludwig Keywords: monsoon moisture surveillance; severe weather prediction; COSMIC-2/FORMOSAT-7; Barbosa, Xu Xu and Congliang Liu radio occultation; data assimilation; typhoon Hagupit; partial cycling

Received: 23 May 2021 Accepted: 26 July 2021 Published: 28 July 2021 1. Introduction Taiwan—as an island located in the East Asian monsoon region adjacent to the north- Publisher’s Note: MDPI stays neutral western Pacific Ocean—is subject to various severe weather systems, such as Meiyu fronts, with regard to jurisdictional claims in typhoons, and local thunderstorms [1]. Rainfall brought by these severe weather systems is published maps and institutional affil- the main source of water on the island, but excessive rainfall may cause massive landslides iations. or floods that threaten human life and property. For timely water resource management and disaster risk reduction, it is essential to enhance the surveillance of monsoon moisture and the prediction of severe weather systems. The enhancement relies greatly on utilizing more advanced and widespread remote sensing observations, especially meteorological Copyright: © 2021 by the authors. satellite observations over the ocean where in-situ measurements hardly exist. Most active Licensee MDPI, Basel, Switzerland. and passive meteorological satellites sense the radiation emitted and reflected by the Earth This article is an open access article and its atmosphere in the nadir direction using multiple channels of different wavelengths, distributed under the terms and which provide data at high horizontal resolution. However, with nadir sounding, the conditions of the Creative Commons vertical profiles of the atmospheric state are indirectly estimated by assuming weighting Attribution (CC BY) license (https:// functions as a function of altitude for all the channels. The vertical resolution of the esti- creativecommons.org/licenses/by/ mated profiles is limited, and the accuracy is vulnerable to the sensitivity of sensors and 4.0/).

Remote Sens. 2021, 13, 2979. https://doi.org/10.3390/rs13152979 https://www.mdpi.com/journal/remotesensing Remote Sens. 2021, 13, 2979 2 of 20

the uncertainty of algorithms. To retrieve a more accurate atmospheric state at higher vertical resolution, the global navigation satellite system (GNSS [2,3]) radio occultation (RO) observations aboard low Earth orbit (LEO [4,5]) satellites have been regarded as the best solution thus far. From these limb-sounding observations, the Doppler shift of each refracted ray is used to derive the bending angle of the ray, and then the bending angle profile is used to derive refractivity that contains implicit information about atmospheric pressure, temperature, and humidity. The vertical resolution of GNSS RO profiles can reach up to dozens of meters in the lower troposphere via the high sampling rate of LEO receivers, and the accuracy is immune to the sensitivity of sensors because the phase information of electromagnetic waves is used instead of the amplitude. The first application of the GNSS RO technique to atmospheric sounding was made by the Microlab-1 microsatellite in the Global Positioning System/Meteorology (GPS/MET) experiment managed by the University Corporation for Atmospheric Research (UCAR) from 1995 to 1997, which confirmed the feasibility and potential of this technique [6]. Following the success of GPS/MET, more satellite missions with GNSS RO measurements have been launched, such as the Challenging Minisatellite Payload (CHAMP [7]) by Ger- many, the Satélite de Aplicaciones Científicas-C (SAC-C [8]) by Argentina, the Gravity Recovery and Climate Experiment (GRACE [9]) by the United States (US) and Germany, the Constellation Observing System for Meteorology, Ionosphere, and Climate/Formosa Satellite Mission 3 (COSMIC/FORMOSAT-3 [10]) and COSMIC-2/FORMOSAT-7 [11] by the US and Taiwan, the Meteorological Operational Satellite (MetOp [12]) by Europe, the Terra X-band Synthetic Aperture Radar (TerraSAR-X [13]) by Germany, the Lemur Cube- Sats [14] by the US, and the Sentinel-6 [15] by Europe and the US. Among these missions, COSMIC/FORMOSAT-3 was the first one dedicated to the needs of operational climate monitoring and weather forecasting by deploying a constellation of six LEO satellites in 2006, which was retired and succeeded by COSMIC-2/FORMOSAT-7 with another constellation of six in 2019. The major differences between the two constellations are the orbital inclination and the compatibility with GNSSs. The COSMIC/FORMOSAT-3 constellation had a 72◦ inclination, which led to a more uniform global distribution of observations, and only received signals from GPS. Instead, the COSMIC-2/FORMOSAT-7 constellation has a 24◦ inclination, which favors observations at low and middle latitudes, and receives signals from GPS and the Russian Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS [2,3]) with an average of 4000 profiles per day at present. This quantity is several times as large as that in COSMIC/FORMOSAT-3, and it can be larger when signals from the European Galileo system [2,3] are receivable as well. Therefore, evaluating the effects of COSMIC-2/FORMOSAT-7 RO observations on the essential monsoon moisture surveillance and severe weather prediction becomes the motivation of this study. For the purpose of monsoon moisture surveillance, information about atmospheric pressure, temperature, and humidity contained by RO refractivity data can be retrieved via a one-dimensional variational (1DVar) procedure and utilized. The 1DVar analyses were verified with radiosonde measurements and global weather analyses soon after the success of GPS/MET and proved reliable [16,17]. As for severe weather prediction, assimilating RO observations into numerical models is considered a key factor to improve forecast accuracy [18,19]. Regarding the assimilated variable, the retrieved pressure, temperature, and humidity may not be the best choice because of the uncertainty embedded in the 1DVar procedure. Therefore, the upstream variables, such as refractivity and the bending angle, have been more favorable for data assimilation with the necessity of corresponding observation operators [20,21]. The refractivity operator was derived as a function of the total pressure, the partial pressure of water vapor, and the absolute temperature [20], and the bending angle operator was derived as a function of the impact parameter and the Abel transform of a refractivity profile under a local spherical symmetry assumption [21]. It is also worth noting that some studies explored more sophisticated operators to alleviate the errors resulting from the local spherical symmetry assumption, such as ray-tracing operators [22–24]. Another advance was the proposal of a nonlocal linear observation operator Remote Sens. 2021, 13, 2979 3 of 20

for the modeled and observed excess phase paths, which integrate the modeled and Abel- derived refractivities, respectively, along the refracted ray trajectory below the top of the numerical model [25,26]. The excess phase path operator accurately accounts for horizontal along-track refractivity gradients, which are strong around severe weather systems, by canceling the linearization and discretization errors during the two integration processes, and it is faster than the ray-tracing operator and simple for practical implementation. There have been numerous studies employing the aforementioned operators to in- vestigate the effects of RO data assimilation on numerical model analyses and forecasts. The assimilation of refractivity from Microlab-1 was pioneered by a series of observing system simulation experiments using the fifth generation Penn State University/National Center for Atmospheric Research (NCAR) mesoscale model (MM5) three-dimensional variational (3DVar [27]) system for the scenario of an extratropical cyclone, which found that the analyses of temperature and humidity and the consequent forecast of the cyclone were improved [18]. The assimilation of the bending angle from Microlab-1 was pioneered using the Spectral Statistical Interpolation (SSI) 3DVar system of the National Centers for Environmental Prediction (NCEP), which found that the analysis increment of temperature was the largest in the middle and upper troposphere and stratosphere while that of humidity was the largest in the lower troposphere [19]. After these pioneering studies, multiple-run evaluations were performed by two studies using the NCEP SSI 3DVar system. One assimilated 837 bending angle profiles from Microlab-1 over 11 days and obtained more accurate analyses and forecasts of temperature and humidity between the 200- and 850-hPa levels, verified with 56 collocated radiosonde profiles [28]. The other assimilated 3030 bending angle profiles from CHAMP over 16 days and reduced the large cold bias of the NCEP analyses without CHAMP, verified with 264 collocated radiosonde and dropsonde profiles [29]. Both studies validated the positive effects of RO data assimilation, which were more pronounced in the Southern Hemisphere because more in-situ measurements were assimilated in the Northern Hemisphere. Hence, RO observations have been operationally assimilated worldwide at most numerical weather prediction centers, such as the European Centre for Medium-Range Weather Forecasts (ECMWF [30,31]), NCEP [32,33], Environment and Climate Change Canada (ECCC [34]), the Met Office [35], and the Deutscher Wetterdienst (DWD [36]). For further insight into severe weather prediction, several studies were devoted to optimizing RO data assimilation for tropical cyclone cases. It was found that the forecasts of tropical cyclone tracks, intensity, and induced rainfall could be improved by RO data assimilation [37–43], and more improvement could be made by increasing the number of assimilation cycles [38], using the nonlocal observation operator [39,41], using a flow-dependent assimilation scheme [38], or assimilating other kinds of observations in addition [37,38,40]. Similar conclusions were also drawn for rainfall forecasts in Meiyu cases [38,41,44]. Recent studies have started to assess the performance of the COSMIC-2/FORMOSAT-7 RO observations, which have the best coverage ever at low and middle latitudes as men- tioned earlier. Preliminary results revealed that the observations agreed well with inde- pendent radiosondes [11,45], LEO satellites [45,46], and model analyses [11], and their high signal-to-noise ratios benefited the accuracy of humidity retrieval [45]. Utilizing such high-resolution, high-quality RO observations—this study develops and evaluates operational products for monsoon moisture surveillance and severe weather prediction [47] at the National Science and Technology Center for Disaster Reduction (NCDR), which serves as a think tank on disaster risk reduction in Taiwan. The purpose is to understand the accuracy of these operational products and scrutinize the role played by the RO observations. Section2 describes the materials and methods, including the regional verification of the RO observations, a suggested RO moisture indicator, the design of numerical model experiments with RO data assimilation, and the statistical method of the paired t-test. Section3 presents the corresponding results. Section4 provides in-depth discussion on observational and modeling aspects. Section5 is devoted to conclusions. Remote Sens. 2021, 13, x FOR PEER REVIEW 4 of 21

the accuracy of these operational products and scrutinize the role played by the RO observations. Section 2 describes the materials and methods, including the regional verification of the RO observations, a suggested RO moisture indicator, the design of numerical model experiments with RO data assimilation, and the statistical method of the paired t- Remote Sens. 2021, 13, 2979 4 of 20 test. Section 3 presents the corresponding results. Section 4 provides in-depth discussion on observational and modeling aspects. Section 5 is devoted to conclusions.

2.2. MaterialsMaterials andand MethodsMethods 2.1.2.1. SourceSource andand VerificationVerification ofof thethe COSMIC-2/FORMOSAT-7COSMIC-2/FORMOSAT-7 RO RO ObservationsObservations OnOn the the Taiwan Taiwan side, side, the the COSMIC-2/FORMOSAT-7 COSMIC-2/FORMOSAT-7 RO RO observations observations are are operationally operation- received,ally received, processed, processed, archived, archived, and and released released by by Taiwan Taiwan Analysis Analysis Center Center forfor COSMICCOSMIC (TACC(TACC [ 48[48]).]). TheThe firstfirst testtest datadata werewere releasedreleased onon 1010 DecemberDecember 2019,2019, andand real-timereal-time datadata havehave been been openopen toto thethe publicpublic sincesince 77 MarchMarch 2020.2020. TACCTACC providesprovides rawraw GNSSGNSS datadata asas wellwell asas retrieved retrieved atmosphericatmospheric andand ionosphericionospheric datadata atat variousvarious processingprocessing levels and formats, amongamong which which the the filesfiles namednamed atmPrfatmPrf andand wetPf2wetPf2 areare automatically downloadeddownloaded byby NCDR everyevery hour.hour. The The latency latency is isabout about 50 50min min from from the observation the observation time. time.The atmPrf The atmPrf files mainly files mainlycontain contain the profiles the profiles of the ofrefractivity, the refractivity, bending bending angle, angle, dry pressure, dry pressure, dry temperature, dry temperature, azi- azimuth,muth, and and impact impact parameter parameter at at the the heights heights of of the the refracted refracted rays. rays. The The wetPf2 wetPf2 files files mainly containcontain thethe profilesprofiles ofof thethe 1DVar-retrieved1DVar-retrieved pressure,pressure, temperature,temperature, andand humidity interpo- latedlated to to 50- 50- and and 100-m 100-m resolution resolution at at the the heights heights of of 0–20 0–20 and and 20–60 20–60 km, km, respectively. respectively.Figure Figure1 shows1 shows the the daily daily number number of the of the downloaded downloaded RO profilesRO profiles from from the start the start date, date, 1 October 1 October 2019, of2019, the firstof the test first data test to data a recent to a recent date, 26 date, April 26 2021.April The2021. average The average is 4114 is per 4114 day. per day.

FigureFigure 1. 1. TheThe dailydaily number of the COSMIC-2/FORMOSAT-7 COSMIC-2/FORMOSAT-7 RO RO profiles proﬁles from from 1 October 1 October 2019 2019 to to26 26April April 2021. 2021.

AlthoughAlthough thethe quality of of the the COSMIC-2/FOR COSMIC-2/FORMOSAT-7MOSAT-7 RO RO observations observations has been has been well wellrecognized recognized [11,45,46], [11,45, 46this], thisstudy study still stillbegins begins with with a comparison a comparison between between sampled sampled RO pro- RO profilesfiles and and nearby nearby radiosonde radiosonde profiles profiles around around Taiwan Taiwan so so as as to to understand their regional characteristicscharacteristics prior prior toto furtherfurther applications.applications. TheThe comparedcompared variablesvariables areare temperaturetemperature andand specificspecific humidity humidity ((s)) interpolated interpolated toto 10-hPa10-hPa resolutionresolution asas wellwell asas precipitableprecipitable waterwater ((Wx) aboveabove certain certain pressure pressure levels levels ((px),), calculatedcalculated asas [[49]:49]: 110 hPa =− Z (1) 1 W = − sdp (1) x g px where is gravity; the values of include 500, 600, 700, 850, 925, and 1000 hPa. The water vapor above the 10-hPa level is omitted. From 1 October 2019 to 23 June 2020, there where g is gravity; the values of p include 500, 600, 700, 850, 925, and 1000 hPa. The are 59 RO profiles sampled for beingx within 100 km and ±2 h from nearby radiosonde water vapor above the 10-hPa level is omitted. From 1 October 2019 to 23 June 2020, there profiles provided by six radiosonde stations, including Banqiao with 9 profiles, Hualien are 59 RO profiles sampled for being within 100 km and ±2 h from nearby radiosonde with 13, Tungsha with 13, Pingtung with 9, Magong with 11, and Green Island with 4 as profiles provided by six radiosonde stations, including Banqiao with 9 profiles, Hualien shown in Figure 2. The selection of the 100-km and ±2-h thresholds is a compromise be- with 13, Tungsha with 13, Pingtung with 9, Magong with 11, and Green Island with 4 tween sufficient samples and sufficient representativeness in space and time to ensure as shown in Figure2. The selection of the 100-km and ±2-h thresholds is a compromise statistical significance. Moreover, because the quality of RO observations in the tropical between sufficient samples and sufficient representativeness in space and time to ensure statisticallower troposphere significance. can Moreover,be influenced because by the the effect quality of multipath of RO observations propagation inresulting the tropical from lower troposphere can be influenced by the effect of multipath propagation resulting from the large vertical gradients of refractivity in precipitation systems [50,51], the 59 RO profiles

are divided into the sunny group and the cloudy/rainy group for separate statistics. An RO profile is classified into the sunny group if the majority of its surrounding area within a 30-km distance is cloudless, according to satellite images from Himawari-8; otherwise, it is classified into the cloudy/rainy group. Remote Sens. 2021, 13, x FOR PEER REVIEW 5 of 21

the large vertical gradients of refractivity in precipitation systems [50,51], the 59 RO profiles are divided into the sunny group and the cloudy/rainy group for separate statistics. Remote Sens. 2021, 13, 2979 An RO profile is classified into the sunny group if the majority of its surrounding5 area of 20 within a 30-km distance is cloudless, according to satellite images from Himawari-8; otherwise, it is classified into the cloudy/rainy group.

FigureFigure 2.2. TheThe distribution distribution of the of the59 sampled 59 sampled pairs pairsof COSMIC-2/FORMOSAT-7 of COSMIC-2/FORMOSAT-7 RO and ROradiosonde and ra- profiles. diosonde proﬁles.

2.2.2.2. ExperimentalExperimental DesignDesign forfor MonsoonMonsoon MoistureMoisture SurveillanceSurveillance TheThe rainyrainy seasonseason ofof thethe EastEast AsianAsian summersummer monsoonmonsoon consistsconsists ofof twotwo phasesphases [[52].52]. The firstfirstphase phasebegins begins withwith thethe onsetonset ofof thethe SouthSouth ChinaChina SeaSea summersummer monsoon,monsoon, characterized byby strongstrong southwesterly southwesterly flow flow that that penetrates penetrates the the South South China China Sea Sea and and transports transports abundant abun- moisturedant moisture to East to Asia. East ThisAsia. phase This phase is also is called also thecalled pre-flood the pre-flood period period [53], during [53], during which awhich large-scale a large-scale stationary stationary front with front heavy with rainheavy (called rain Meiyu)(called Meiyu) occurs overoccurs South over China,South Taiwan,China, Taiwan, and Okinawa. and Okinawa. The second The second phase isphase called is thecalled grand-onset the grand-onset phase, phase, characterized charac- byterized the stationary by the stationary front migrating front migrating to Central to Central and East and China, East China, the main the islands main islands of Japan of (calledJapan (called Baiu), andBaiu), the and Korean the Korean Peninsula Peninsula (called (called Changma). Changma). The moisture The moisture in this in phase this isphase mainly is mainly transported transported from the from Bay the of Bay Bengal of Bengal [54]. Therefore, [54]. Therefore, this study this study retrieves retrieves daily moisturedaily moisture variations variations in the Southin the ChinaSouth SeaChina during Sea during 26 April–10 26 April–10 June 2020, June and 2020, the and Bay the of BengalBay of duringBengal 1during May–30 1 May–30 July 2020, July using 2020, the using COSMIC-2/FORMOSAT-7 the COSMIC-2/FORMOSAT-7 RO observations, RO obser- anvations, observational an observational approach approach of monsoon of monsoon moisture moisture surveillance surveillance in addition in addition to the useto the of reanalysisuse of reanalysis data [52 data–54]. [52–54]. The indicator The indicator is total is precipitable total precipitable water (waterWT), calculated (), calculated as [49]: as [49]: 1 Z p20 WT = − 1 sdp (2) g p =− 0 (2) where p0 and p20 are the pressure at the heights of 0 and 20 km, respectively. Figure3 shows two separate surveillance domains in the South China Sea (110–120◦E, 5–15◦N) and the Bay of Bengal (80–97.5◦E, 0–22.5◦N). The RO observations in each domain are collected every 24 h from 12:00 to next 11:59 UTC (Coordinated Universal Time) and then averaged into a daily mean profile of pressure and specific humidity, from which the daily mean total precipitable water is derived via Equation (2). To evaluate this approach, the NCEP Climate Forecast System Reanalysis (CFSR [55]) data and the undermentioned regional Remote Sens. 2021, 13, x FOR PEER REVIEW 6 of 21

where and are the pressure at the heights of 0 and 20 km, respectively. Figure 3 shows two separate surveillance domains in the South China Sea (110–120°E, 5–15°N) and the Bay of Bengal (80–97.5°E, 0–22.5°N). The RO observations in each domain are collected every 24 h from 12:00 to next 11:59 UTC (Coordinated Universal Time) and then Remote Sens. 2021, 13, 2979 averaged into a daily mean profile of pressure and specific humidity, from which the daily6 of 20 mean total precipitable water is derived via Equation (2). To evaluate this approach, the NCEP Climate Forecast System Reanalysis (CFSR [55]) data and the undermentioned regional model analyses with RO data assimilation are also used to calculate domain-aver- modelaged total analyses precipitable with RO water data assimilationevery 00:00 areUTC also during used tothe calculate surveillance domain-averaged periods for inter- total precipitablecomparison. water every 00:00 UTC during the surveillance periods for intercomparison.

FigureFigure 3.3. TwoTwo monsoonmonsoon moisturemoisture surveillancesurveillance domainsdomains inin the South China Sea (110–120(110–120°E,◦E, 5–15°N) 5–15◦N) and the Bay of Bengal (80–97.5°E, 0–22.5°N). and the Bay of Bengal (80–97.5◦E, 0–22.5◦N).

2.3.2.3. ExperimentalExperimental DesignDesign forfor Severe Weather Prediction ToTo examineexamine thethe effectseffects ofof COSMIC-2/FORMOSAT-7COSMIC-2/FORMOSAT-7 RO data assimilation on severe weatherweather predictionprediction aroundaround Taiwan,Taiwan, thisthis studystudy employs the version 3.8.1 of the Weather ResearchResearch andand ForecastingForecasting (WRF)(WRF) modelmodel andand WRF data assimilation (WRFDA) system [56] [56] withwith one-way,one-way, triple-nested domains, domains, as as shown shown in in Figure Figure 4.4 Domains. Domains 1, 1,2, and 2, and 3 span 3 span 221 221× 127,× 127 183, 183× 195,× 195, and and150 150× 180× 180horizontal horizontal grid grid points points at at45-, 45-, 15-, 15-, and and 5-km 5-km resolution, resolution, respectively.respectively. There There are are 45 45 vertical vertical eta levelseta levels with with a model a model top of 30top hPa. of 30 The hPa. physics The schemesphysics includeschemes the include Goddard the Goddard Cumulus Cumulus Ensemble Ensemble (GCE) microphysics (GCE) microphysics [57], Kain–Fritsch [57], Kain–Fritsch cumulus parameterizationcumulus parameteri [58zation], revised [58], MM5revised surface MM5 surface layer [ 59layer], Noah [59], Noah land surfaceland surface model model [60], Yonsei[60], Yonsei University University planetary planetary boundary boundary layer [layer61], and [61], the and Rapid the Rapid Radiative Radiative Transfer Transfer Model forModel GCMs for (RRTMG)GCMs (RRTMG) longwave longwave and shortwave and shortwave radiation radiation [62]. [62]. For dataFor data assimilation, assimilation, the 3DVarthe 3DVar component component of WRFDA of WRFDA is used is used with with the backgroundthe background error error covariance covariance option option of five of controlfive control variables variables (CV5), (CV5), which which contain contain the stream the stream function, function, unbalanced unbalanced velocity velocity potential, po- unbalancedtential, unbalanced surface surface pressure, pressure, unbalanced unbala temperature,nced temperature, and pseudo and pseudo relative relative humidity. hu- Threemidity. outer Three loops outer are loops applied are applied to the minimization to the minimization of the cost of the function. cost function. The background The back- errorground variance error variance and length and scaling length variables scaling variables refer to empirical refer to empirical values in avalues previous in a study previous [43]. Implementingstudy [43]. Implementing this configuration, this configuration, two operational two operational 84-h forecast 84-h members forecast are members initialized are withinitialized the NCEP with Globalthe NCEP Forecast Global System Forecast (GFS) System 0.5◦ forecast(GFS) 0.5 every° forecast 00:00, every 06:00, 00:00, 12:00, 06:00, and 18:0012:00, UTC. and 18:00 Member UTC. 1 Member assimilates 1 assimilates the Global the Telecommunication Global Telecommunication System System (GTS) in-situ(GTS) observationsin-situ observations at the initial at the time initial for alltime the for three all domains.the three Memberdomains. 2 Member additionally 2 additionally assimilates theassimilates RO refractivity the RO refractivity profiles within profiles±3 hwithin from the±3 h initial from the time, initial which time, are which thinned are to thinned 200-m verticalto 200-m resolution vertical resolution to approach to approach the model th resolution.e model resolution. For each WRFFor each member, WRF member, 152 moisture 152 andmoisture rainfall and forecasts rainfall initializedforecasts initialize duringd 00:00 during UTC 00:00 26 May–18:00 UTC 26 May–18:00 UTC 2 July UTC 2020, 2 July are verified2020, are with verified the water with the vapor wa mixingter vapor ratio mixing data ratio of the data NCEP of the GFS NCEP analyses GFS and analyses the radar- and derived quantitative precipitation estimation (QPE [63]) data around Taiwan from the Central Weather Bureau (CWB); 17 track forecasts for Typhoon Hagupit (2020) initialized during 12:00 UTC 1 August–12:00 UTC 5 August 2020 are verified with the best track data

from CWB. Moreover, the forecast samples initialized at 12:00 UTC 6 June and 12:00 UTC 1 August 2020, for the cases of Meiyu and typhoon Hagupit, respectively, are spatially scrutinized, and the latter is additionally compared with two sensitivity experiments that perform three 6-h assimilation cycles prior to the forecast. Remote Sens. 2021, 13, x FOR PEER REVIEW 7 of 21

the radar-derived quantitative precipitation estimation (QPE [63]) data around Taiwan from the Central Weather Bureau (CWB); 17 track forecasts for Typhoon Hagupit (2020) initialized during 12:00 UTC 1 August–12:00 UTC 5 August 2020 are verified with the best track data from CWB. Moreover, the forecast samples initialized at 12:00 UTC 6 June and Remote Sens. 2021, 13, 2979 12:00 UTC 1 August 2020, for the cases of Meiyu and typhoon Hagupit, respectively,7 of are 20 spatially scrutinized, and the latter is additionally compared with two sensitivity experiments that perform three 6-h assimilation cycles prior to the forecast.

FigureFigure 4.4. TheThe employedemployed triple-nestedtriple-nested WRFWRF modelmodel domains.domains.

2.4.2.4. StatisticalStatistical MethodMethod ofof thethe PairedPaired t-testt-test ToTo properlyproperly assess assess the the statistical statistical signiﬁcance significance for for the the comparisons comparisons between between the sampledthe sam- ROpled and RO radiosonde and radiosonde proﬁles profiles and between and betw theeen rainfall the rainfall forecasts forecasts made made by WRF by WRFMembers Mem- 1 andbers 2,1 and the paired2, the paired t-test ist-test carried is carried out [ 64out]. [64]. Suppose Suppose there there are naresampled sampled pairs pairs with with an averagean average pair pair difference difference of d of. The . Thet value t value forthe for pairedthe pairedt-test t-test is calculated is calculated as: as:

d − −µ t == √0 (3)(3) sd/⁄n√ wherewhere µ0is is the the expected expected value value of ofthe the population;population; sdis is the the sample sample standard standard deviation deviation of of thethe pairpair differences.differences. In In this this study, study,µ0 is set is set to 0 to and 0 and then then the calculatedthe calculatedt value t value is compared is com- againstpared against the critical the critical value with value a 95%with conﬁdence a 95% conf interval.idence interval. If the absolute If the absolutet valueis t smallervalue is thansmaller the than critical the value, critical it meansvalue, it there means is no there statistically is no statistically signiﬁcant significant difference difference between thebe- twotween groups. the two groups.

3.3. ResultsResults 3.1. Comparison between the Sampled RO and Radiosonde Profiles 3.1. ComparisonFigure5a–f between calculate the the Sampled average RO temperature, and Radiosonde specific Profiles humidity, and precipitable waterFigure differences 5a–f calculate of the sampled the average COSMIC-2/FORMOSAT-7 temperature, specific humidity, RO profiles and minus precipitable nearby radiosondewater differences profiles of the for sampled the sunny COSMIC-2/FORMOSAT-7 and cloudy/rainy groups RO separately. profiles minus The nearby standard ra- deviationsdiosonde profiles of the temperature for the sunny and and specific cloudy/r humidityainy groups differences separately. are also The shown. standard All sample devia- numbertions of curvesthe temperature reveal a decreasingand specific trend humidity below differences the 700-hPa are level also becauseshown. theAll lowestsample observablenumber curves altitudes reveal of a the decreasing RO profiles trend near be Banqiao,low the 700-hPa Hualien, level and because Pingtung the radiosonde lowest ob- stations,servable locatedaltitudes on of the the mountainousRO profiles near main Banqiao, island Hualien, of Taiwan, and are Pingtung mostly higher radiosonde than thesta- othertions, samples.located on The the temperature mountainous difference main island for the of Taiwan, sunny group are mostly is small higher at most than levels the other with asamples. standard The deviation temperature of approximately difference 1for K (Figurethe sunny5a), whereasgroup is the small one at for most the cloudy/rainy levels with a group is notably negative below the 850-hPa level, reaching −2.7 K (Figure5b) . The specific humidity difference for the sunny group is positive above the 450-hPa level but negative below, and the absolute value and standard deviation decrease with altitude owing to rare water vapor at high levels (Figure5c). The vertical distribution of the specific humidity difference for the cloudy/rainy group is analogous to the sunny group, except for a larger absolute value and a positive difference instead between the 550- and 700-hPa levels (Figure5d). It is to be noticed that the point-to-point temperature and specific humidity comparison between the RO and radiosonde profiles within a certain spatial and temporal Remote Sens. 2021, 13, x FOR PEER REVIEW 8 of 21

standard deviation of approximately 1 K (Figure 5a), whereas the one for the cloudy/rainy group is notably negative below the 850-hPa level, reaching −2.7 K (Figure 5b). The specific humidity difference for the sunny group is positive above the 450-hPa level but negative below, and the absolute value and standard deviation decrease with altitude owing to rare water vapor at high levels (Figure 5c). The vertical distribution of the specific humidity difference for the cloudy/rainy group is analogous to the sunny group, except for a larger absolute value and a positive difference instead between the 550- and 700-hPa Remote Sens. 2021, 13, 2979 8 of 20 levels (Figure 5d). It is to be noticed that the point-to-point temperature and specific humidity comparison between the RO and radiosonde profiles within a certain spatial and temporal distance is very rigorous, especially for moisture that can have larger spatial and temporaldistanceis gradients. very rigorous, Therefore, especially the forprecipitable moisture thatwater can vertically have larger integrating spatial and the temporal specific humiditygradients. above Therefore, the 500-, the 600-, precipitable 700-, 850-, water 925-, vertically and 1000-hPa integrating levels is the also specific compared. humidity The precipitableabove the 500-, water 600-, difference 700-, 850-, for 925-, the andsunny 1000-hPa group levelsis near is zero also above compared. all the The six precipitablelevels (Fig- urewater 5e), difference whereas forthe theone sunny for the group cloudy/rainy is near zero group above is notably all the six negative levels (Figure above 5thee), whereas925- and 1000-hPathe one for levels, the cloudy/rainy reaching −5.5 group kg m is2 notably(Figure negative5f). Paired above t-tests the are 925- carried and 1000-hPa out with levels, the wholereaching 59 −sampled5.5 kg m pairs2 (Figure of RO5f). and Paired radiosonde t-tests are profiles. carried For out withtemperature, the whole the 59 absolute sampled t valuespairs of are RO smaller and radiosonde than the critical profiles. values For at temperature, almost all levels the absolute (Figure 5g). t values For specific are smaller humidity,than the the critical absolute values t values at almost exceed all levelsthe crit (Figureical values5g). Forbelow specific the 900-hPa humidity, level the and absolute above thet values 400-hPa exceed level the (Figure critical 5h). values As a belowconcludi theng 900-hPa remark, level the sunny and above group the exhibits 400-hPa greater level consistency(Figure5h). Asthan a concluding the cloudy/rainy remark, group, the sunny and groupthe overall exhibits consistency greater consistency is great except than thefor specificcloudy/rainy humidity group, at very and low the overalllevels (where consistency sample is greatnumbers except are for small) specific and humidity high levels at (wherevery low moisture levels (where is rare). sample numbers are small) and high levels (where moisture is rare).

(a) (b) (c) (d)

Figure 5. Cont.

Remote Sens. 2021, 13, x FOR PEER REVIEW 9 of 21 Remote Sens. 2021, 13, 2979 9 of 20

(e) (f) (g) (h)

Figure 5.5. The average (a,,b)) temperaturetemperature difference, (c,d) specificspecific humidity difference, and ( e,f) precipitable water differ- enceence ofof thethe sampledsampled COSMIC-2/FORMOSAT-7COSMIC-2/FORMOSAT-7 RO prof profilesiles minus nearby radios radiosondeonde profiles profiles for the (a,,c,,e)) sunnysunny andand ((bb,,dd,,ff)) cloudy/rainycloudy/rainy groups. groups. The The bl blueue and and green green curves curves in in(a– (af)– fdenote) denote the the average average differences differences and and sample sample numbers, numbers, respectively. The red curves in (a–d) denote the standard deviations of the temperature and specific humidity differences. respectively. The red curves in (a–d) denote the standard deviations of the temperature and specific humidity differences. The profiles of the paired t-tests for (g) temperature and (h) specific humidity are also shown, where the blue and red The profiles of the paired t-tests for (g) temperature and (h) specific humidity are also shown, where the blue and red curves curves denote the t values and critical values, respectively. denote the t values and critical values, respectively.

3.2. Monsoon Moisture Surveillance Figure 66 calculates calculates thethe dailydaily totaltotal precipitableprecipitable waterwater inin thethe SouthSouth ChinaChina SeaSea during during 26 April–10 April–10 June June 2020, 2020, retrieved retrieved with with the the COSMIC-2/FORMOSAT-7 COSMIC-2/FORMOSAT-7 RO ROobservations, observations, the theCFSR CFSR data, data, and andthe analyses the analyses of the of aforem the aforementionedentioned WRF WRFMember Member 2. The 2. 41-year The 41-year (1979– (1979–2019)2019) climatological climatological average average with the with CFSR the CFSR data datais also is shown. also shown. It is Itobvious is obvious that thatthe theRO ROobservation observation curve curve corresponds corresponds well wellwith with the CFSR the CFSR and andWRF WRF analysis analysis curves, curves, which which look looksmoother smoother with larger with larger data size data though. size though. This confirms This confirms that the that direct the use direct of the use RO of humid- the RO humidityity retrieval retrieval is sufficient is sufficient for an foraccurate an accurate moisture moisture indicator indicator in a monsoon in a monsoon region. region. In com- In comparisonparison with with the theclimatological climatological average, average, the the total total precipitable precipitable water water in in the the South South China Sea was significantlysignificantly higher during 3–7 May and 20–24 May 2020, with southeasterly and southwesterly prevailingprevailing winds winds (not (not shown), shown), respectively, respectively, according according to the to CFSRthe CFSR data. data. The valueThe value during during 20–24 20–24 May May 2020 2020 that that reached reached 60 60 kg kg m −m2−2led led to to pronounced pronounced northeastwardnortheastward moisture fluxflux and,and, consequently,consequently, the the heaviest heaviest daily daily rainfall rainfall (668.5 (668.5 mm) mm) of theof the year year in Taiwan in Tai- onwan 22 on May 22 May 2020. 2020. Therefore, Therefore, for a for more a more comprehensive comprehensive outlook outlook on monsoon on monsoon rainfall, rainfall, it is necessaryit is necessary to supplement to supplement the moisture the moisture indicator indicator with thewith information the information of wind, of wind, which which is not containedis not contained in the in RO the observations. RO observations. Likewise, Figure7 calculates the daily total precipitable water in the Bay of Bengal during 1 May–30 July 2020, retrieved with the RO observations and CFSR data. The RO observation curve still corresponds well with the smoother CFSR analysis curve, reconfirming the usability of the RO humidity retrieval. The comparison with the climatological average reveals tremendous moisture in the Bay of Bengal throughout the 2020 monsoon rainy season. The first peak that exceeded 60 kg m−2 on 19 May 2020, was due to cyclone Amphan, which was the first and strongest tropical cyclone in the 2020 North Indian Ocean cyclone season. Since mid-June 2020, the total precipitable water had kept around 60 kg m−2 for a couple of months, with a southwesterly prevailing wind (not shown) according to the CFSR data. This led to extreme northeastward moisture flux toward southern China and, consequently, the most devastating floods in the Yangtze basin since 1998.

Remote Sens. 2021, 13, x FOR PEER REVIEW 10 of 21

Remote Sens. 2021, 13, x FOR PEER REVIEW 10 of 21 Remote Sens. 2021, 13, 2979 10 of 20

Figure 6. The daily total precipitable water in the South China Sea during 26 April–10 June 2020, retrieved with the COSMIC-2/FORMOSAT-7 RO observations (black curve), the CFSR data (blue solid curve), and the analyses of WRF Member 2 (red curve). The blue dotted curve denotes the 41- year (1979–2019) climatological average with the CFSR data.

Likewise, Figure 7 calculates the daily total precipitable water in the Bay of Bengal during 1 May–30 July 2020, retrieved with the RO observations and CFSR data. The RO observation curve still corresponds well with the smoother CFSR analysis curve, reconfirming the usability of the RO humidity retrieval. The comparison with the climatological average reveals tremendous moisture in the Bay of Bengal throughout the 2020 monsoon rainy season. The first peak that exceeded 60 kg m−2 on 19 May 2020, was due to cyclone Amphan, which was the first and strongest tropical cyclone in the 2020 North Indian Ocean cyclone season. Since mid-June 2020, the total precipitable water had kept around Figure 6. 60Figure kg m 6.− 2The Thefor dailya daily couple total total ofprecipitable precipitable months, withwater water a in insouthw the the South Southesterly China China prevailing Sea Sea during during wind 26 26 April–10 April–10 (not shown) June June 2020, 2020,ac- cordingretrievedretrieved to with with the theCFSR the COSMIC-2/FORMOSAT-7 COSMIC-2/FORMOSAT-7 data. This led to extrem RO ROe northeastwardobse observationsrvations (black (black moisture curve), curve), fluxthe the CFSRtoward CFSR data data south- (blue (blue ernsolidsolid China curve), curve), and, and and consequently, the the analyses analyses ofof theWRF WRF most Member Member devastat 2 (r 2ed (reding curve). floods curve). The in The blue the blue Yangtzedotted dotted curve basin curve denotes since denotes the 1998. 41- the year41-year (1979–2019) (1979–2019) climatological climatological average average with with the theCFSR CFSR data. data.

FigureFigure 7. 7. TheThe daily daily total total precipitable precipitable water water in in the the Bay Bay of of Bengal Bengal during during 1 1May–30 May–30 July July 2020, 2020, retrieved retrieved withwith the the COSMIC-2/FORMOSAT-7 COSMIC-2/FORMOSAT-7 RO RO observations observations (b (blacklack curve) curve) and and CFSR CFSR data data (blue (blue solid solid curve). curve). TheThe blue blue dotted dotted curve curve denotes denotes the the 41-year 41-year (1979–2019) (1979–2019) climatological climatological average average with with the the CFSR CFSR data. data.

3.3.3.3. Severe Severe Weather Weather Prediction Prediction TheThe 152 152 moisture moisture and and rainfall rainfall forecasts forecasts made made by by each each WRF WRF member member are are verified verified with with thethe NCEP NCEP GFS GFS analysis analysis and and radar-derived radar-derived QPE QPE data, data, respectively. respectively. For For the the moisture moisture fore- fore- casts,casts, Figure Figure 88 calculatescalculates the the root-mean-squa root-mean-squarere error error of of the the predicted predicted 850-hPa 850-hPa water water vapor vapor mixing ratio at 24 h in Domain 2 for both members. Although the COSMIC-2/FORMOSAT-7 RO observations contain implicit information about humidity, the two similar curves indicate that the impact of RO data assimilation tends to become neutral on the moisture field after 24-h model integration posterior to data assimilation. Nevertheless, a slightly positive impact exists in the predicted 24–48-h rainfall. Figure9 calculates the correlation coeffi- Figurecient, 7. root-mean-square The daily total precipitable error, and water threat in the score Bay of above Bengal a 40-mmduring 1 threshold May–30 July of 2020, the predicted retrieved with24–48-h the COSMIC-2/FORMOSAT-7 rainfall for both members. RO observations It is found (b thatlack Member curve) and 2 CFSR mostly data has (blue higher solidcorrela- curve). Thetion blue coefficients, dotted curve lower denotes root-mean-square the 41-year (1979–2019) errors, climatological and higher threat average scores with thanthe CFSR Member data. 1 despite limited differences. The average correlation coefficient, root-mean-square error, 3.3.and Severe threat Weather score values Prediction for Members 1 and 2 are 0.163 and 0.171, 14.5 and 14.3 mm, and 0.0562The and 152 0.0633, moisture respectively. and rainfall Paired forecasts t-tests made are by carried each WRF out with member the whole are verified 152 pairs with of therainfall NCEP forecasts GFS analysis made byand Members radar-derived 1 and 2.QPE The data, absolute respectively. t valuesare For 1.67 the andmoisture 1.14 for fore- the casts,correlation Figure coefficient8 calculates and the root-mean-squareroot-mean-square error,error of respectively. the predicted Both 850-hPa values water are smaller vapor than 1.97, which is the critical value with a 95% confidence interval. This infers that the additional assimilation of the RO observations at the initial time has a neutral to slightly

Remote Sens. 2021, 13, x FOR PEER REVIEW 11 of 21

mixing ratio at 24 h in Domain 2 for both members. Although the COSMIC-2/FOR- MOSAT-7 RO observations contain implicit information about humidity, the two similar curves indicate that the impact of RO data assimilation tends to become neutral on the moisture field after 24-h model integration posterior to data assimilation. Nevertheless, a slightly positive impact exists in the predicted 24–48-h rainfall. Figure 9 calculates the correlation coefficient, root-mean-square error, and threat score above a 40-mm threshold of the predicted 24–48-h rainfall for both members. It is found that Member 2 mostly has higher correlation coefficients, lower root-mean-square errors, and higher threat scores than Member 1 despite limited differences. The average correlation coefficient, root-mean- square error, and threat score values for Members 1 and 2 are 0.163 and 0.171, 14.5 and 14.3 mm, and 0.0562 and 0.0633, respectively. Paired t-tests are carried out with the whole 152 pairs of rainfall forecasts made by Members 1 and 2. The absolute t values are 1.67 Remote Sens. 2021, 13, 2979 and 1.14 for the correlation coefficient and root-mean-square error, respectively. Both11 val- of 20 ues are smaller than 1.97, which is the critical value with a 95% confidence interval. This infers that the additional assimilation of the RO observations at the initial time has a neutral to slightly positive impact on the moisture and rainfall forecasts during the Meiyu seasonpositive in impact Taiwan. on The the most moisture significant and rainfall improvement forecasts occurs during in the the Meiyu forecast season sample in Taiwan. initial- izedThe mostat 12:00 signiﬁcant UTC 6 June improvement 2020, whose occurs predicted in the 24–48-h forecast rainfall sample maps initialized for Members at 12:00 1 UTC and 26 are June compared 2020, whose with predicted the simultaneous 24–48-h rainfall radar-derived maps for rainfall Members map 1 and in Figure 2 are compared 10. It is found with thatthe simultaneousMember 2 has radar-derived a more similar rainfall rainfall map pattern in Figure and intensity 10. It is foundto the radar-derived that Member 2rain- has falla more than similar Member rainfall 1, which pattern has a and serious intensity overprediction to the radar-derived in central Taiwan rainfall without than Member RO data 1, assimilation.which has a serious overprediction in central Taiwan without RO data assimilation.

FigureFigure 8. The root-mean-square error error of the predicted 850-hPa water vapor mixing ratio at 24 h in Remote Sens. 2021, 13, x FOR PEER REVIEWDomainDomain 2 for for the the 152 152 forecasts forecasts initialized duri duringng 00:00 UTC 26 May–18:00 UTC 2 July 2020, for 12 WRFof 21

MembersMembers 1 (pink curves) and 2 (red curves).

FigureFigure 9.9. TheThe (from(from toptop toto bottom)bottom) correlationcorrelation coefﬁcient,coefficient, root-mean-squareroot-mean-square error,error, andand threatthreat scorescore aboveabove aa 40-mm40-mm thresholdthreshold ofof thethe predictedpredicted 24–48-h24–48-h rainfallrainfall forfor thethe 152152 rainfallrainfall forecastsforecasts initializedinitialized during 00:00 UTC 26 May–18:00 UTC 2 July 2020, for WRF Members 1 (pink curves) and 2 (red during 00:00 UTC 26 May–18:00 UTC 2 July 2020, for WRF Members 1 (pink curves) and 2 (red curves). The green line denotes the forecast initialized at 12:00 UTC 6 June 2020. curves). The green line denotes the forecast initialized at 12:00 UTC 6 June 2020.

Figure 10. The maps of rainfall during 12:00 UTC 7 June–12:00 UTC 8 June 2020, for (from left to right) the radar-derived QPE data and the predicted 24–48-h rainfall of the forecasts initialized at 12:00 UTC 6 June 2020, for WRF Members 1 and 2.

With respect to typhoon prediction, the track forecasts for Typhoon Hagupit, for which CWB issued a sea warning during 2–3 August 2020, are verified with the best track data at 6-h intervals. Figure 11a calculates the total track error within 72 h averaged over the 17 forecasts made by each WRF member. It is found that the positive effect of RO data assimilation is distinguishable since 48 h and more significant since 66 h. For a closer in- spection of the beginning 48 h, Figure 11b calculates the average total track, along-track, and cross-track error differences of Member 1 minus Member 2, where positive values represent the superiority of Member 2. The comparison reveals that RO data assimilation has a neutral impact on the moving speed and slightly positive impact on the moving

Remote Sens. 2021, 13, x FOR PEER REVIEW 12 of 21

Figure 9. The (from top to bottom) correlation coefficient, root-mean-square error, and threat score Remote Sens. 2021, 13, 2979 above a 40-mm threshold of the predicted 24–48-h rainfall for the 152 rainfall forecasts initialized12 of 20 during 00:00 UTC 26 May–18:00 UTC 2 July 2020, for WRF Members 1 (pink curves) and 2 (red curves). The green line denotes the forecast initialized at 12:00 UTC 6 June 2020.

FigureFigure 10. 10. TheThe maps maps of of rainfall rainfall during during 12:00 12:00 UTC UTC 7 7June–12:00 June–12:00 UTC UTC 8 8June June 2020, 2020, for for (from (from left left to to right)right) the the radar-derived radar-derived QPE QPE data data and and the the predic predictedted 24–48-h 24–48-h rainfall rainfall of of the the forecasts forecasts initialized initialized at at 12:0012:00 UTC UTC 6 6June June 2020, 2020, for for WRF WRF Members Members 1 1and and 2. 2.

WithWith respect respect to to typhoon prediction,prediction, the the track track forecasts forecasts for for Typhoon Typhoon Hagupit, Hagupit, for which for whichCWB CWB issued issued a sea a warning sea warning during during 2–3 August2–3 August 2020, 2020, are verifiedare verified with with the bestthe best track track data dataat 6-h at 6-h intervals. intervals. Figure Figure 11a 11a calculates calculates the the total total track track error error within within 72 72 h averagedh averaged over over the the17 17 forecasts forecasts made made by by each each WRF WRF member. member. ItIt isis found that the the positive positive effect effect of of RO RO data data assimilationassimilation is isdistinguishable distinguishable since since 48 48h and h and more more significant significant since since 66 h. 66 For h. a For closer a closer in- spectioninspection of the of thebeginning beginning 48 h, 48 Figure h, Figure 11b11 cab calculateslculates the the average average tota totall track, track, along-track, along-track, andand cross-track cross-track error error differences differences of of Member Member 1 1minus minus Member Member 2, 2, where where positive positive values values representrepresent the the superiority superiority of of Member Member 2. 2. The The co comparisonmparison reveals reveals that that RO RO data data assimilation assimilation hashas a aneutral neutral impact impact on on the the moving moving speed speed and and slightly slightly positive positive im impactpact on on the the moving moving direction of the predicted typhoon within 48 h. Taking the forecast sample initialized at 12:00 UTC 1 August 2020, for example, the track predicted by Member 2 is closer to the best track than that by Member 1 during 06:00 UTC 3 August (42 h)–06:00 UTC 4 August (66 h) 2020 (Figure 12). As the best track during this period approaches the coastal waters of northern Taiwan, the improvement of the track forecast can benefit the timing of the sea warning issuance. In order to enhance the positive effect, two sensitivity experiments that perform initialization at 00:00 UTC 1 August 2020 and three 6-h assimilation cycles at 00:00, 06:00, and 12:00 UTC (termed as partial cycling) to incorporate earlier observation information are carried out for comparison. One, named as Member 1PC, follows Member 1 to only assimilate the GTS in-situ observations. The other, named as Member 2PC, follows Member 2 to additionally assimilate the RO refractivity profiles. Both partial cycling members use the same configuration of WRF and WRFDA as that in Members 1 and 2. The tracks predicted by Members 1PC and 2PC are found to correct the excessive moving speed of those predicted by Members 1 and 2 (Figure 12). Table1 further lists the total track error differences of Member 2 minus Member 2PC and Member 1PC minus Member 2PC, where positive values represent the superiority of Member 2PC. The result reveals significant outperformance of Member 2PC over Member 2 and Member 1PC. This forecast sample infers that, based on the background provided by global model forecasts, regional model forecasts are likely to benefit from suitable partial cycling assimilation of regional observations, especially the high-resolution, high-quality COSMIC-2/FORMOSAT-7 RO observations. Remote Sens. 2021, 13, x FOR PEER REVIEW 13 of 21

direction of the predicted typhoon within 48 h. Taking the forecast sample initialized at 12:00 UTC 1 August 2020, for example, the track predicted by Member 2 is closer to the best track than that by Member 1 during 06:00 UTC 3 August (42 h)–06:00 UTC 4 August (66 h) 2020 (Figure 12). As the best track during this period approaches the coastal waters of northern Taiwan, the improvement of the track forecast can benefit the timing of the sea warning issuance. In order to enhance the positive effect, two sensitivity experiments that perform initialization at 00:00 UTC 1 August 2020 and three 6-h assimilation cycles at 00:00, 06:00, and 12:00 UTC (termed as partial cycling) to incorporate earlier observation information are carried out for comparison. One, named as Member 1PC, follows Member 1 to only assimilate the GTS in-situ observations. The other, named as Member 2PC, follows Member 2 to additionally assimilate the RO refractivity profiles. Both partial cycling members use the same configuration of WRF and WRFDA as that in Members 1 and 2. The tracks predicted by Members 1PC and 2PC are found to correct the excessive moving speed of those predicted by Members 1 and 2 (Figure 12). Table 1 further lists the total track error differences of Member 2 minus Member 2PC and Member 1PC minus Member 2PC, where positive values represent the superiority of Member 2PC. The result reveals significant outperformance of Member 2PC over Member 2 and Member 1PC. This forecast sample infers that, based on the background provided by global model forecasts, regional model forecasts are likely to benefit from suitable partial cycling assimilation of Remote Sens. 2021, 13, 2979 13 of 20 regional observations, especially the high-resolution, high-quality COSMIC-2/FOR- MOSAT-7 RO observations.

(a) (b)

FigureFigure 11.11. (a) The The total total track track error error within within 72 72 h averaged h averaged over over the the 17 forecasts 17 forecasts for typhoon for typhoon Hagu Hagupitpit initialized initialized during during 12:00 UTC 1 August–12:00 UTC 5 August 2020, for WRF Members 1 (pink curve) and 2 (red curve); (b) the total track error 12:00 UTC 1 August–12:00 UTC 5 August 2020, for WRF Members 1 (pink curve) and 2 (red curve); (b) the total track error difference (black curve), along-track error difference (orange curve), and cross-track error difference (purple curve) of difference (black curve), along-track error difference (orange curve), and cross-track error difference (purple curve) of WRF RemoteWRF Sens. Member2021, 13, x 1 FOR minus PEER WRF REVIEW Member 2 within 48 h averaged over the same 17 forecasts, where positive values represent14 of 21 Memberthe superiority 1 minus of WRFWRF MemberMember 22.within 48 h averaged over the same 17 forecasts, where positive values represent the superiority of WRF Member 2.

FigureFigure 12. TheThe 78-h 78-h track track forecasts forecasts for for typhoon typhoon Hagupit Hagupit initialized initialized at at12:00 12:00 UTC UTC 1 August 1 August 2020, 2020, for forWRF WRF Members Members 1 (pink 1 (pink curve), curve), 2 (red 2 curve), (red curve), 1PC (lig 1PCht (lightpurple purple curve), curve), and 2P andC (dark 2PC purple (dark purplecurve). The black curve denotes the best track at 6-h intervals from CWB. The green dots denote the COS- curve). The black curve denotes the best track at 6-h intervals from CWB. The green dots denote the MIC-2/FORMOSAT-7 RO observations assimilated by WRF Members 2 and 2PC. COSMIC-2/FORMOSAT-7 RO observations assimilated by WRF Members 2 and 2PC. Table 1. The total track error differences (km) of Member 2 minus Member 2PC and Member 1PC minus Member 2PC, where positive values represent the superiority of Member 2PC.

Experiments 0 h 6 h 12 h 18 h 24 h 30 h 36 h 42 h 48 h 54 h 60 h 66 h 72 h 78 h Member 2 minus Member 2PC 4.5 -4.5 -2.0 30.7 48.7 90.7 115.3 115.6 150.8 184.0 201.7 190.5 217.4 235.5 Member 1PC minus Member 2PC 33.8 16.4 -8.3 3.7 -0.7 -0.2 8.3 6.9 6.1 37.8 0.6 123.6 27.3 68.0

4. Discussion The 59 sampled pairs of COSMIC-2/FORMOSAT-7 RO and radiosonde profiles around Taiwan exhibit great overall consistency, except for specific humidity at very low levels for the cloudy/rainy group (Figure 5). The exception is similar to the results of a recent study [45] and attributable to the low-level atmospheric instability in precipitation systems. There are also statistically significant differences at high levels, but they are understandable because the true locations of the RO and radiosonde observations can horizontally deviate from the locations of the occultation point and radiosonde station, respectively, as the height increases. The horizontal deviation degrades the representativeness of the comparison, especially for moisture that has a higher spatial variability. Despite these observational uncertainties, the suggested approach of monsoon moisture surveillance using the RO observations still accurately indicates daily moisture variations in the South China Sea and the Bay of Bengal (Figures 6 and 7). An accurate moisture indicator is certainly helpful for anticipating measures against potential droughts or heavy rainfall hazards. The statistics of the 152 moisture and rainfall forecasts for the 2020 Meiyu season in Taiwan (Figures 8 and 9) and the 17 track forecasts for typhoon Hagupit (Figure 11) have

Remote Sens. 2021, 13, 2979 14 of 20

Table 1. The total track error differences (km) of Member 2 minus Member 2PC and Member 1PC minus Member 2PC, where positive values represent the superiority of Member 2PC.

Experiments 0 h 6 h 12 h 18 h 24 h 30 h 36 h 42 h 48 h 54 h 60 h 66 h 72 h 78 h Member 2 minus Member 2PC 4.5 −4.5 −2.0 30.7 48.7 90.7 115.3 115.6 150.8 184.0 201.7 190.5 217.4 235.5 Member 1PC minus Member 2PC 33.8 16.4 −8.3 3.7 −0.7 −0.2 8.3 6.9 6.1 37.8 0.6 123.6 27.3 68.0

4. Discussion The 59 sampled pairs of COSMIC-2/FORMOSAT-7 RO and radiosonde profiles around Taiwan exhibit great overall consistency, except for specific humidity at very low levels for the cloudy/rainy group (Figure5). The exception is similar to the results of a recent study [45] and attributable to the low-level atmospheric instability in precipitation systems. There are also statistically significant differences at high levels, but they are understandable because the true locations of the RO and radiosonde observations can horizontally deviate from the locations of the occultation point and radiosonde station, respectively, as the height increases. The horizontal deviation degrades the representativeness of the comparison, especially for moisture that has a higher spatial variability. Despite these observational uncertainties, the suggested approach of monsoon moisture surveillance using the RO observations still accurately indicates daily moisture variations in the South China Sea and the Bay of Bengal (Figures6 and7). An accurate moisture indicator is certainly helpful for anticipating measures against potential droughts or heavy rainfall hazards. The statistics of the 152 moisture and rainfall forecasts for the 2020 Meiyu season in Taiwan (Figures8 and9) and the 17 track forecasts for typhoon Hagupit (Figure 11) have shown the neutral to slightly positive effects of COSMIC-2/FORMOSAT-7 RO data assimilation. This subsection is to spatially scrutinize the reasons via the forecast samples initialized at 12:00 UTC 6 June and 12:00 UTC 1 August 2020, respectively. Figure 13 shows the 700-hPa temperature and wind differences as well as 850-hPa specific humidity and wind differences of WRF Member 2 minus WRF Member 1 at 0, 24, and 48 h for the Meiyu forecast sample. There is one RO profile (118.31◦E, 26.58◦N) available in Domain 3 at the analysis time, the assimilation of which decreases the temperature and moisture only near the profile location. However, it varies the wind analysis throughout the domain, where a northeasterly difference can be seen over the South China Sea. This suppresses the intensity of the southwesterly flow impinging on Taiwan and, consequently, results in lower temperature and moisture over the Taiwan Strait for the 24-h forecast. For the 48-h forecast, Member 2 still has lower moisture around Taiwan than Member 1 despite higher temperature, and thus the serious overprediction of the 24–48-h rainfall in central Taiwan is successfully corrected by RO data assimilation (Figure 10). Remote Sens. 2021, 13, x FOR PEER REVIEW 15 of 21

shown the neutral to slightly positive effects of COSMIC-2/FORMOSAT-7 RO data assimilation. This subsection is to spatially scrutinize the reasons via the forecast samples initialized at 12:00 UTC 6 June and 12:00 UTC 1 August 2020, respectively. Figure 13 shows the 700-hPa temperature and wind differences as well as 850-hPa specific humidity and wind differences of WRF Member 2 minus WRF Member 1 at 0, 24, and 48 h for the Meiyu forecast sample. There is one RO profile (118.31°E, 26.58°N) available in Domain 3 at the analysis time, the assimilation of which decreases the temperature and moisture only near the profile location. However, it varies the wind analysis throughout the domain, where a northeasterly difference can be seen over the South China Sea. This suppresses the intensity of the southwesterly flow impinging on Taiwan and, consequently, results in lower temperature and moisture over the Taiwan Strait for the 24-h forecast. For the 48-h forecast, Member 2 still has lower moisture around Taiwan than Member 1 despite higher Remote Sens. 2021, 13, 2979 15 of 20 temperature, and thus the serious overprediction of the 24–48-h rainfall in central Taiwan is successfully corrected by RO data assimilation (Figure 10).

FigureFigure 13. 13. TheThe (top) (top )700-hPa 700-hPa temperature temperature and and wind wind differences differences as as well well as as (bottom) (bottom )850-hPa 850-hPa specific specific humidity humidity and and wind wind differencesdifferences of of WRF WRF Member Member 2 2 minus minus WRF WRF Member Member 1 1 at at (from (from left left to to right) right) 0, 0, 24, 24, and and 48 48 h h for for the the forecast forecast sample sample initialized initialized at 12:00 UTC 6 June 2020. The color shading indicates the temperature and specific humidity differences. The arrows at 12:00 UTC 6 June 2020. The color shading indicates the temperature and specific humidity differences. The arrows indicate the wind difference. The green dot denotes the COSMIC-2/FORMOSAT-7 RO observation assimilated by WRF indicate the wind difference. The green dot denotes the COSMIC-2/FORMOSAT-7 RO observation assimilated by WRF Member 2. The gray shading indicates terrain. Member 2. The gray shading indicates terrain. With respect to the typhoon Hagupit forecast sample, Figure 14 shows the west-east With respect to the typhoon Hagupit forecast sample, Figure 14 shows the west-east cross-sections, which pass through the typhoon center denoted by the black lines, of the cross-sections, which pass through the typhoon center denoted by the black lines, of the temperaturetemperature and and geopotential geopotential height height differences differences of WRF MemberMember 22 minusminus WRFWRF MemberMember 1 1at at 66 h.h. TheThe temperaturetemperature difference is positivepositive at 550–850 hPa hPa west west of of the the typhoon typhoon center center (Figure(Figure 14a), 14a), which which implies thatthat thethe simulatedsimulated condensation condensation heating heating of of the the western western eyewall eye- wallupdraft updraft is strengthened is strengthened and and favorable favorable for thefor warmthe warm core core after after RO dataRO data assimilation. assimilation. The Thegeopotential geopotential height height difference difference is negative is negative at 850–1000 at 850–1000 hPa hPa within within the the rainband rainband areas areas and positive at 250–850 hPa west of the typhoon center (Figure 14b), which implies that the structure of radial inflow at lower levels and outflow at upper levels is further established. Figure 15 shows the 850-hPa geopotential height, wind speed, and wind differences of Member 2 minus Member 1 at 24 h. After 24-h simulation, a dipole pattern is visible around the typhoon center location in both maps because the tracks have become different between the two members (Figure 11). There are extensive decrease of geopotential height and increase of wind speed in the northwest quadrant of the typhoon, which demonstrates that the intensity and symmetry of the typhoon circulation is improved at low levels by RO data assimilation from a weaker and asymmetric circulation simulated in Member 1 (not shown). The improvement of the typhoon structure explains why Member 2 makes more accurate track forecasts to a certain degree (Figure 12). Lastly, to further explore the effect of RO data assimilation with a partial cycling assimilation strategy, Figure 16 shows the 850-hPa geopotential height, wind speed, and wind differences of Member 2PC minus Member 1PC for the analyses and 24-h forecasts. At the final analysis time, the geopotential height difference is negative around the typhoon area but positive in Remote Sens. 2021, 13, x FOR PEER REVIEW 16 of 21

and positive at 250–850 hPa west of the typhoon center (Figure 14b), which implies that the structure of radial inflow at lower levels and outflow at upper levels is further established. Figure 15 shows the 850-hPa geopotential height, wind speed, and wind differences of Member 2 minus Member 1 at 24 h. After 24-h simulation, a dipole pattern is visible around the typhoon center location in both maps because the tracks have become different between the two members (Figure 11). There are extensive decrease of geopotential height and increase of wind speed in the northwest quadrant of the typhoon, which demonstrates that the intensity and symmetry of the typhoon circulation is improved at low levels by RO data assimilation from a weaker and asymmetric circulation simulated in Member 1 (not shown). The improvement of the typhoon structure explains why Mem- ber 2 makes more accurate track forecasts to a certain degree (Figure 12). Lastly, to further Remote Sens. 2021, 13, 2979 explore the effect of RO data assimilation with a partial cycling assimilation strategy,16 ofFig- 20 ure 16 shows the 850-hPa geopotential height, wind speed, and wind differences of Mem- ber 2PC minus Member 1PC for the analyses and 24-h forecasts. At the final analysis time, the geopotential height difference is negative around the typhoon area but positive in its periphery,its periphery, which which demonstrates demonstrates the thereinforcem reinforcementent of the of inner the inner low lowpressure pressure and outer and outer subsidence.subsidence. The wind The wind speed speed difference difference is positive is positive west and west east and of east the typhoon of the typhoon center, center,which whichrepresents represents higher higher intensity intensity in Member in Member 2PC. 2PC.After After 24-h 24-h simulation, simulation, the theimprovement improvement of theof the typhoon typhoon structure structure and and intensity intensity is signific is signiﬁcantlyantly expanded. expanded. As Asa concluding a concluding remark remark on Figureon Figure 12, 12Table, Table 1, 1and, and Figure Figure 16, 16 ,the the effect effect of of one-cycle one-cycle RO data assimilation isis smallersmaller and slower, whereas multi-cycle RO data assimilationassimilation can enhance the quality of typhoon prediction more efﬁciently.efficiently.

(a) (b) Figure 14. The west–east cross-sections of the (a) temperature difference and (b) geopotential height difference of WRF RemoteFigure Sens. 2021 14., The13, x west–eastFOR PEER REVIEW cross-sections of the (a) temperature difference and (b) geopotential height difference of WRF17 of 21 Member 2 minus WRF Member 1 at 6 h for the forecast sample initialized at 12:00 UTC 1 August 2020. The cross-sections Member 2 minus WRF Member 1 at 6 h for the forecast sample initialized at 12:00 UTC 1 August 2020. The cross-sections pass through the typhoon center denoted by the black lines. pass through the typhoon center denoted by the black lines.

(a) (b)

Figure 15. The 850-hPa ( a) geopotential heig heightht difference and ( b) wind speed difference of WRF Member 2 minus WRF Member 1 at 24 h for the forecast sample initialized at 12:00 UTC 1 August 2020. The arrows indicate the wind difference. Member 1 at 24 h for the forecast sample initialized at 12:00 UTC 1 August 2020. The arrows indicate the wind difference. The green dots denote the COSMIC-2/FORMOSAT-7 RO observations assimilated by WRF Member 2. The dark blue shad- The green dots denote the COSMIC-2/FORMOSAT-7 RO observations assimilated by WRF Member 2. The dark blue ing indicates terrain. shading indicates terrain.

Remote Sens. 2021, 13, x FOR PEER REVIEW 17 of 21

(a) (b) Figure 15. The 850-hPa (a) geopotential height difference and (b) wind speed difference of WRF Member 2 minus WRF RemoteMember Sens. 2021 1, 13at ,24 2979 h for the forecast sample initialized at 12:00 UTC 1 August 2020. The arrows indicate the wind difference.17 of 20 The green dots denote the COSMIC-2/FORMOSAT-7 RO observations assimilated by WRF Member 2. The dark blue shading indicates terrain.

Figure 16. The 850-hPa (top) geopotential height difference and (bottom) wind speed difference of WRF Member 2PC minus WRF Member 1PC for the (left) analyses at 12:00 UTC 1 August 2020, and (right) 24-h forecasts. The arrows indicate the wind difference. The green dots denote the COSMIC-2/FORMOSAT-7 RO observations assimilated by WRF Member 2. The

dark blue shading indicates terrain.

5. Conclusions This study utilizes COSMIC-2/FORMOSAT-7 RO observations to suggest a moisture indicator and design numerical model experiments for the purposes of monsoon moisture surveillance and severe weather prediction, respectively. Prior to the experiments, a comparison between 59 sampled RO profiles and nearby radiosonde profiles around Taiwan, divided into the sunny and cloudy/rainy groups, is made to verify the RO data quality. The comparison exhibits great overall consistency, except for specific humidity at very low levels for the cloudy/rainy group. Despite the exception, the suggested moisture indicator, which calculates total precipitable water out of the 1DVar-retrieved humidity profile, accurately monitors daily moisture variations in the South China Sea and the Bay of Bengal throughout the 2020 monsoon rainy season. With respect to the numerical model experiments, the performances of two operational 84-h WRF forecast members with and without RO data assimilation are compared. The statistics of 152 moisture and rainfall forecasts for the 2020 Meiyu season in Taiwan show a neutral to slightly positive impact brought by RO data assimilation. A forecast sample with the most significant improvement reveals that not only the temperature and moisture fields, but also the wind field is appropriately adjusted by model integration posterior to data assimilation. The statistics of 17 track forecasts for typhoon Hagupit (2020) also show the positive effect of RO data assimilation. A forecast sample reveals that the member with RO data assimilation Remote Sens. 2021, 13, 2979 18 of 20

simulates better typhoon structure and intensity than the member without, and the effect can be larger and faster via multi-cycle RO data assimilation. It is noteworthy that even though there are globally more than 4000 COSMIC-2/ FORMOSAT-7 RO profiles per day, there may sometimes be very few or no RO profiles available in a regional domain at the analysis time such as Figure 13. Therefore, the partial cycling (or even full cycling) assimilation strategy becomes a key factor in propagating more RO observation information into the regional domain and indeed improves the typhoon forecast sample in this study. For future prospects, the statistics of operational multi-cycle forecasts can be carried out as well for a more systematical evaluation. It is also to be emphasized that even though the relatively cheaper 3DVar assimilation scheme and local refractivity observation operator are employed for the consideration of operational costs, this study still explores the benefits of the cutting-edge COSMIC-2/FORMOSAT-7 RO observations in both observational and modeling aspects. The statistical results can provide a benchmark for more advanced assimilation schemes or observation operators.

Author Contributions: Conceptualization, Y.-C.C.; methodology, Y.-C.C. and Y.-c.W.; software, Y.-C.C., Y.-c.W., A.-H.W. and H.-H.L.; validation, Y.-C.C. and Y.-c.W.; formal analysis, Y.-C.C., C.-C.T., C.-J.W., H.-H.L. and D.-R.C.; writing—original draft preparation, C.-C.T.; supervision, C.-C.T. and Y.-C.Y.; funding acquisition, C.-C.T. and Y.-C.Y. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Taiwan’s National Science and Technology Center for Disaster Reduction (NCDR). Data Availability Statement: The operational products for monsoon moisture surveillance and severe weather prediction are available online: https://watch.ncdr.nat.gov.tw/watch_fs7, accessed on 23 May 2021. The digitial data are not publicly available due to NCDR’s right of privacy. Acknowledgments: The authors are grateful to Ying-Hwa Kuo at UCAR for the insightful sugges- tions and Shao-Chin Huang and Chung-Yi Lin at NCDR for the discussions about this study. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Lin, H.-H.; Tsai, C.-C.; Liou, J.-C.; Chen, Y.-C.; Lin, C.-Y.; Lin, L.-Y.; Chung, K.-S. Multi-weather evaluation of nowcasting methods including a new empirical blending scheme. Atmosphere 2020, 11, 1166. [CrossRef] 2. Hofmann-Wellenhof, B.; Lichtenegger, H.; Wasle, E. GNSS—Global Navigation Satellite Systems: GPS, GLONASS, Galileo, and More; Springer Wien: Vienna, Austria, 2008; pp. 1–518. [CrossRef] 3. Hein, G.W. Status, perspectives and trends of satellite navigation. Satell. Navig. 2020, 1, 22. [CrossRef] 4. Melbourne, W.G.; Davis, E.S.; Duncan, C.B.; Hajj, G.A.; Hardy, K.R.; Kursinski, E.R.; Meehan, T.K.; Young, L.E.; Yunck, T.P. The Application of Spaceborne GPS to Atmospheric Limb Sounding and Global Change Monitoring; Jet Propulsion Laboratory Publication 94-18: Pasadena, CA, USA, 1994; pp. 1–142. 5. Kursinski, E.R.; Hajj, G.A.; Schofield, J.T.; Linfield, R.P.; Hardy, K.R. Observing earth’s atmosphere with radio occultation measurements using the global positioning system. J. Geophys. Res. 1997, 102, 23429–23465. [CrossRef] 6. Ware, R.; Exner, M.; Feng, D.; Gorbunov, M.E.; Hardy, K.; Herman, B.; Kuo, Y.-H.; Meehan, T.; Melbourne, W.; Rocken, C.; et al. GPS sounding of the atmosphere from low earth orbit: Preliminary results. Bull. Amer. Meteor. Soc. 1996, 77, 19–40. [CrossRef] 7. Wickert, J.; Reigber, C.; Beyerle, G.; König, R.; Marquardt, C.; Schmidt, T.; Grunwaldt, L.; Galas, R.; Meehan, T.K.; Melbourne, W.G.; et al. Atmosphere sounding by GPS radio occultation: First results from CHAMP. Geophys. Res. Lett. 2001, 28, 3263–3266. [CrossRef] 8. Hajj, G.A.; Ao, C.O.; Iijima, B.A.; Kuang, D.; Kursinski, E.R.; Mannucci, A.J.; Meehan, T.K.; Romans, L.J.; de la Torre Juárez, M.; Yunck, T.P. CHAMP and SAC-C atmospheric occultation results and intercomparisons. J. Geophys. Res. 2004, 109, D06109. [CrossRef] 9. Tapley, B.D.; Bettadpur, S.; Ries, J.C.; Thompson, P.F.; Watkins, M.M. GRACE measurements of mass variability in the earth system. Science 2004, 305, 503–505. [CrossRef] 10. Anthes, R.A.; Bernhardt, P.A.; Chen, Y.; Cucurull, L.; Dymond, K.F.; Ector, D.; Healy, S.B.; Ho, S.-P.; Hunt, D.C.; Kuo, Y.-H.; et al. The COSMIC/FORMOSAT-3 mission: Early results. Bull. Amer. Meteor. Soc. 2008, 89, 313–334. [CrossRef] 11. Schreiner, W.S.; Weiss, J.P.; Anthes, R.A.; Braun, J.; Chu, V.; Fong, J.; Hunt, D.; Kuo, Y.-H.; Meehan, T.; Serafino, W.; et al. COSMIC-2 radio occultation constellation: First results. Geophys. Res. Lett. 2020, 47, e2019GL086841. [CrossRef] Remote Sens. 2021, 13, 2979 19 of 20

12. Luntama, J.-P.; Kirchengast, G.; Borsche, M.; Foelsche, U.; Steiner, A.; Healy, S.; von Engeln, A.; O’Clerigh, E.; Marquardt, C. Prospects of the EPS GRAS mission for operational atmospheric applications. Bull. Amer. Meteor. Soc. 2008, 89, 1863–1876. [CrossRef] 13. Brusch, S.; Lehner, S.; Fritz, T.; Soccorsi, M.; Soloviev, A.; van Schie, B. Ship surveillance with TerraSAR-X. IEEE Trans. Geosci. Remote. Sens. 2011, 49, 1092–1103. [CrossRef] 14. Saeed, N.; Elzanaty, A.; Almorad, H.; Dahrouj, H.; Al-Naffouri, T.Y.; Alouini, M.-S. CubeSat communications: Recent advances and future challenges. IEEE Commun. Surv. Tutor. 2020, 22, 1839–1862. [CrossRef] 15. Maiwald, F.; Brown, S.T.; Koch, T.; Milligan, L.; Kangaslahti, P.; Schlecht, E.; Skalare, A.; Bloom, M.; Torossian, V.; Kanis, J.; et al. Completion of the AMR-C instrument for Sentinel-6. IEEE J. Sel. Top. Appl. Earth Obs. Remote. Sens. 2020, 13, 1811–1818. [CrossRef] 16. Rocken, C.; Anthes, R.; Exner, M.; Hunt, D.; Sokolovskiy, S.; Ware, R.; Gorbunov, M.E.; Schreiner, W.; Feng, D.; Herman, B.; et al. Analysis and validation of GPS/MET data in the neutral atmosphere. J. Geophys. Res. 1997, 102, 29849–29866. [CrossRef] 17. Poli, P.; Joiner, J.; Kursinski, E.R. 1DVAR analysis of temperature and humidity using GPS radio occultation refractivity data. J. Geophys. Res. 2002, 107, 4448. [CrossRef] 18. Kuo, Y.-H.; Zou, X.; Huang, W. The impact of Global Positioning System data on the prediction of an extratropical cyclone: An observing system simulation experiment. Dynam. Atmos. Ocean. 1998, 27, 439–470. [CrossRef] 19. Zou, X.; Wang, B.; Liu, H.; Anthes, R.A.; Matsumura, T.; Zhu, Y.-J. Use of GPS/MET refraction angles in three-dimensional variational analysis. Q. J. R. Meteorol. Soc. 2000, 126, 3013–3040. [CrossRef] 20. Smith, E.K.; Weintraub, S. The constants in the equation for atmospheric refractive index at radio frequencies. Proc. IRE 1953, 41, 1035–1037. [CrossRef] 21. Phinney, R.A.; Anderson, D.L. On the radio occultation method for studying planetary atmospheres. J. Geophys. Res. 1968, 73, 1819–1827. [CrossRef] 22. Zou, X.; Vandenberghe, F.; Wang, B.; Gorbunov, M.E.; Kuo, Y.-H.; Sokolovskiy, S.; Chang, J.C.; Sela, J.G.; Anthes, R.A. A ray- tracing operator and its adjoint for the use of GPS/MET refraction angle measurements. J. Geophys. Res. 1999, 104, 22301–22318. [CrossRef] 23. Poli, P.; Joiner, J. Effects of horizontal gradients on GPS radio occultation observation operators. I: Ray tracing. Q. J. R. Meteorol. Soc. 2004, 130, 2787–2805. [CrossRef] 24. Poli, P. Effects of horizontal gradients on GPS radio occultation observation operators. II: A fast atmospheric refractivity gradient operator (FARGO). Q. J. R. Meteorol. Soc. 2004, 130, 2807–2825. [CrossRef] 25. Sokolovskiy, S.; Kuo, Y.-H.; Wang, W. Assessing the accuracy of a linearized observation operator for assimilation of radio occultation data: Case simulations with a high-resolution weather model. Mon. Weather Rev. 2005, 133, 2200–2212. [CrossRef] 26. Sokolovskiy, S.; Kuo, Y.-H.; Wang, W. Evaluation of a linear phase observation operator with CHAMP radio occultation data and high-resolution regional analysis. Mon. Weather Rev. 2005, 133, 3053–3059. [CrossRef] 27. Sasaki, Y. An objective analysis based on the variational method. J. Meteorol. Soc. Jpn. 1958, 36, 77–88. [CrossRef] 28. Liu, H.; Zou, X.; Shao, H.; Anthes, R.A.; Chang, J.C.; Tseng, J.-H.; Wang, B. Impact of 837 GPS/MET bending angle profiles on assimilation and forecasts for the period June 20–30, 1995. J. Geophys. Res. 2001, 106, 31771–31786. [CrossRef] 29. Zou, X.; Liu, H.; Anthes, R.A.; Shao, H.; Chang, J.C.; Zhu, Y.-J. Impact of CHAMP radio occultation observations on global analysis and forecasts in the absence of AMSU radiance data. J. Meteorol. Soc. Jpn. 2004, 82, 533–549. [CrossRef] 30. Healy, S.B.; Thépaut, J.-N. Assimilation experiments with CHAMP GPS radio occultation measurements. Q. J. R. Meteorol. Soc. 2006, 132, 605–623. [CrossRef] 31. Healy, S.B.; Eyre, J.R.; Hamrud, M.; Thépaut, J.-N. Assimilating GPS radio occultation measurements with two-dimensional bending angle observation operators. Q. J. R. Meteorol. Soc. 2007, 133, 1213–1227. [CrossRef] 32. Cucurull, L.; Derber, J.C.; Treadon, R.; Purser, R.J. Assimilation of Global Positioning System radio occultation observations into NCEP’s Global Data Assimilation System. Mon. Weather Rev. 2007, 135, 3174–3193. [CrossRef] 33. Cucurull, L.; Derber, J.C. Operational implementation of COSMIC observations into NCEP’s Global Data Assimilation System. Weather Forecast. 2008, 23, 702–711. [CrossRef] 34. Aparicio, J.M.; Deblonde, G.; Garand, L.; Laroche, S. Signature of the atmospheric compressibility factor in COSMIC, CHAMP, and GRACE radio occultation data. J. Geophys. Res. 2009, 114, D16114. [CrossRef] 35. Rennie, M.P. The impact of GPS radio occultation assimilation at the Met Office. Q. J. R. Meteorol. Soc. 2010, 136, 116–131. [CrossRef] 36. Anlauf, H.; Pingel, D.; Rhodin, A. Assimilation of GPS radio occultation data at DWD. Atmos. Meas. Tech. 2011, 4, 1105–1113. [CrossRef] 37. Huang, C.-Y.; Kuo, Y.-H.; Chen, S.-H.; Vandenberghe, F. Improvements in typhoon forecasts with assimilated GPS occultation refractivity. Weather Forecast. 2005, 20, 931–953. [CrossRef] 38. Kuo, Y.-H.; Liu, H.; Guo, Y.-R.; Terng, C.-T.; Lin, Y.-T. Impact of FORMOSAT-3/COSMIC data on typhoon and Mei-yu prediction. In Recent Progress in Atmospheric Sciences: Application to the Asia-Pacific Region; Liou, K.-N., Chou, M.-D., Eds.; World Scientific: Singapore, 2008; pp. 458–483. [CrossRef] Remote Sens. 2021, 13, 2979 20 of 20

39. Chen, S.-Y.; Huang, C.-Y.; Kuo, Y.-H.; Guo, Y.-R.; Sokolovskiy, S. Assimilation of GPS refractivity from FOMOSAT-3/COSMIC using a nonlocal operator with WRF 3DVAR and its impact on the prediction of a typhoon event. Terr. Atmos. Ocean. Sci. 2009, 20, 133–154. [CrossRef] 40. Kueh, M.-T.; Huang, C.-Y.; Chen, S.-Y.; Chen, S.-H.; Wang, C.-J. Impact of GPS radio occultation refractivity soundings on a simulation of Typhoon Bilis (2006) upon landfall. Terr. Atmos. Ocean. Sci. 2009, 20, 115–131. [CrossRef] 41. Huang, C.-Y.; Kuo, Y.-H.; Chen, S.-Y.; Terng, C.-T.; Chien, F.-C.; Lin, P.-L.; Kueh, M.-T.; Chen, S.-H.; Yang, M.-J.; Wang, C.-J.; et al. Impact of GPS radio occultation data assimilation on regional weather predictions. GPS Solut. 2010, 14, 35. [CrossRef] 42. Liu, H.; Anderson, J.; Kuo, Y.-H. Improved analyses and forecasts of Hurricane Ernesto’s genesis using radio occultation data in an ensemble filter assimilation system. Mon. Weather Rev. 2012, 140, 151–166. [CrossRef] 43. Chen, Y.-C.; Hsieh, M.-E.; Hsiao, L.-F.; Kuo, Y.-H.; Yang, M.-J.; Huang, C.-Y.; Lee, C.-S. Systematic evaluation of the impacts of GPSRO data on the prediction of typhoons over the northwestern Pacific in 2008–2010. Atmos. Meas. Tech. 2015, 8, 2531–2542. [CrossRef] 44. Huang, C.-Y.; Chen, S.-Y.; Anisetty, S.K.A.V.P.R.; Yang, S.-C.; Hsiao, L.-F. An impact study of GPS radio occultation observations on frontal rainfall prediction with a local bending angle operator. Weather Forecast. 2016, 31, 129–150. [CrossRef] 45. Ho, S.-P.; Zhou, X.; Shao, X.; Zhang, B.; Adhikari, L.; Kireev, S.; He, Y.; Yoe, J.G.; Xia-Serafino, W.; Lynch, E. Initial assessment of the COSMIC-2/FORMOSAT-7 neutral atmosphere data quality in NESDIS/STAR using in situ and satellite data. Remote Sens. 2020, 12, 4099. [CrossRef] 46. Cao, C.; Wang, W.; Lynch, E.; Bai, Y.; Ho, S.-P.; Zhang, B. Simultaneous radio occultation for intersatellite comparison of bending angles toward more accurate atmospheric sounding. J. Atmos. Ocean. Technol. 2020, 37, 2307–2320. [CrossRef] 47. NCDR WATCH. Available online: https://watch.ncdr.nat.gov.tw/watch_fs7 (accessed on 22 May 2021). (In Chinese) 48. TACC-Taiwan Data Process Center. Available online: https://tacc.cwb.gov.tw/v2/en/index.html (accessed on 22 May 2021). 49. Tsonis, A.A. An Introduction to Atmospheric Thermodynamics, 2nd ed.; Cambridge University Press: Cambridge, UK, 2007; pp. 1–187. 50. Gorbunov, M.E.; Gurvich, A.S. Algorithms of inversion of Microlab-1 satellite data including effects of multipath propagation. Int. J. Remote Sens. 1998, 19, 2283–2300. [CrossRef] 51. Liu, H.; Kuo, Y.-H.; Sokolovskiy, S.; Zou, X.; Zeng, Z.; Hsiao, L.-F.; Ruston, B.C. A quality control procedure based on bending angle measurement uncertainty for radio occultation data assimilation in the tropical lower troposphere. J. Atmos. Ocean. Technol. 2018, 35, 2117–2131. [CrossRef] 52. Wang, B.; LinHo. Rainy season of the Asian–Pacific summer monsoon. J. Clim. 2002, 15, 386–398. [CrossRef] 53. Wang, B.; LinHo; Zhang, Y.; Lu, M.-M. Definition of South China Sea monsoon onset and commencement of the East Asia summer monsoon. J. Clim. 2004, 17, 699–710. [CrossRef] 54. LinHo; Wang, B. The time-space structure of the Asian–Pacific summer monsoon: A fast annual cycle view. J. Clim. 2002, 15, 2001–2019. [CrossRef] 55. Saha, S.; Moorthi, S.; Pan, H.-L.; Wu, X.; Wang, J.; Nadiga, S.; Tripp, P.; Kistler, R.; Woollen, J.; Behringer, D.; et al. The NCEP Climate Forecast System Reanalysis. Bull. Amer. Meteor. Soc. 2010, 91, 1015–1058. [CrossRef] 56. Skamarock, W.C.; Klemp, J.B.; Dudhia, J.; Gill, D.O.; Barker, D.M.; Duda, M.G.; Huang, X.-Y.; Wang, W.; Powers, J.G. A Description of the Advanced Research WRF Version 3; NCAR Technical Note NCAR/TN-475+STR; NCAR: Boulder, CO, USA, 2008; pp. 1–125. [CrossRef] 57. Tao, W.-K.; Simpson, J.; Baker, D.; Braun, S.; Chou, M.-D.; Ferrier, B.; Johnson, D.; Khain, A.; Lang, S.; Lynn, B.; et al. Microphysics, radiation and surface processes in the Goddard Cumulus Ensemble (GCE) model. Meteor. Atmos. Phys. 2003, 82, 97–137. [CrossRef] 58. Kain, J.S. The Kain-Fritsch convective parameterization: An update. J. Appl. Meteor. 2004, 43, 170–181. [CrossRef] 59. Jiménez, P.A.; Dudhia, J.; González-Rouco, J.F.; Navarro, J.; Montávez, J.P.; García-Bustamante, E. A revised scheme for the WRF surface layer formulation. Mon. Weather Rev. 2012, 140, 898–918. [CrossRef] 60. Chen, F.; Dudhia, J. Coupling an advanced land surface-hydrology model with the Penn State-NCAR MM5 modeling system. Part I: Model implementation and sensitivity. Mon. Weather Rev. 2001, 129, 569–585. [CrossRef] 61. Hong, S.-Y.; Noh, Y.; Dudhia, J. A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Weather Rev. 2006, 134, 2318–2341. [CrossRef] 62. Iacono, M.J.; Delamere, J.S.; Mlawer, E.J.; Shephard, M.W.; Clough, S.A.; Collins, W.D. Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models. J. Geophys. Res. 2008, 113, D13103. [CrossRef] 63. Zhang, J.; Howard, K.; Langston, C.; Vasiloff, S.; Kaney, B.; Arthur, A.; Van Cooten, S.; Kelleher, K.; Kitzmiller, D.; Ding, F.; et al. National Mosaic and Multi-Sensor QPE (NMQ) system: Description, results, and future plans. Bull. Am. Meteorol. Soc. 2011, 92, 1321–1338. [CrossRef] 64. Kim, T.K. T test as a parametric statistic. Korean J. Anesthesiol. 2015, 68, 540–546. [CrossRef]