Applications of GNSS-RO to Numerical Weather Prediction and Tropical Cyclone Forecast

atmosphere

Review Applications of GNSS-RO to Numerical Weather Prediction and Tropical Cyclone Forecast

Weihua Bai 1,2,3,4,5, Nan Deng 1,2,4,5,*, Yueqiang Sun 1,2,3,4,5, Qifei Du 1,2,4,5, Junming Xia 1,2,4,5, Xianyi Wang 1,2,4,5, Xiangguang Meng 1,2,4,5, Danyang Zhao 1,2,4,5, Congliang Liu 1,2,4,5, Guangyuan Tan 1,2,4,5, Ziyan Liu 1,2,4,5 and Xiaoxu Liu 1,2,4,5 1 National Space Science Center, Chinese Academy of Sciences (NSSC/CAS), Beijing 100190, China; [email protected] (W.B.); [email protected] (Y.S.); [email protected] (Q.D.); [email protected] (J.X.); [email protected] (X.W.); [email protected] (X.M.); [email protected] (D.Z.); [email protected] (C.L.); [email protected] (G.T.); [email protected] (Z.L.); [email protected] (X.L.) 2 Beijing Key Laboratory of Space Environment Exploration, Beijing 100190, China 3 School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China 4 Joint Laboratory on Occultations for Atmosphere and Climate (JLOAC), NSSC/CAS and University of Graz, Beijing 100190, China 5 Key Laboratory of Science and Technology on Space Environment Situational Awareness, CAS, Beijing 100190, China * Correspondence: [email protected]

Received: 10 October 2020; Accepted: 3 November 2020; Published: 6 November 2020

Abstract: The global navigation satellite system (GNSS) radio occultation (RO) technique is an atmospheric sounding technique that originated in the 1990s. The data provided by this approach are playing a consistently significant role in atmospheric research and related applications. This paper mainly summarizes the applications of RO to numerical weather prediction (NWP) generally and specifically for tropical cyclone (TC) forecast and outlines the prospects of the RO technique. With advantages such as high precision and accuracy, high vertical resolution, full-time and all-weather, and global coverage, RO data have made a remarkable contribution to NWP and TC forecasts. While accounting for only 7% of the total observations in European Centre for Medium-Range Weather Forecasts’ (ECMWF’s) assimilation system, RO has the fourth-largest impact on NWP. The greater the amount of RO data, the better the forecast of NWP. In cases of TC forecasts, assimilating RO data from heights below 6 km and from the upper troposphere and lower stratosphere (UTLS) region contributes to the forecasting accuracy of the track and intensity of TCs in different stages. A statistical analysis showed that assimilating RO data can help restore the critical characteristics of TCs, such as the location and intensity of the eye, eyewall, and rain bands. Moreover, a non-local excess phase assimilation operator can be employed to optimize the assimilation results. With denser RO profiles expected in the future, the accuracy of TC forecast can be further improved. Finally, future trends in RO are discussed, including advanced features, such as polarimetric RO, and RO strategies to increase the number of soundings, such as the use of a cube satellite constellation.

Keywords: radio occultation; numerical weather prediction; tropical cyclone forecast

1. Brief Introduction to GNSS-RO Technique The radio occultation (RO) measurement technique can be traced back to the mid-20th century, when Mars atmosphere detection missions, namely Mariner 3 and 4, were launched by scientists from Stanford and Jet Propulsion Laboratory [1]. With the deployment of a GPS constellation, it has been found that the RO technique could also be applied to Earth [2].

Atmosphere 2020, 11, 1204; doi:10.3390/atmos11111204 www.mdpi.com/journal/atmosphere Atmosphere 2020, 11, x FOR PEER REVIEW 2 of 23 Atmosphere 2020, 11, 1204 2 of 23 1.1. Principle of RO 1.1. PrincipleThe RO oftechnique RO is based on the atmospheric refraction phenomenon, which occurs when a GPS/GNSSThe RO signal technique penetrates is based the onEarth’s the atmospheric atmosphere refractionand is then phenomenon, received by low-earth which occurs orbit when (LEO) a GPSsatellites/GNSS behind signal the penetrates earth, as show the Earth’sn in Figure atmosphere 1. During and this is refraction, then received the bending by low-earth angle of orbit the signal (LEO) satellitesis considered behind a primary the earth, parameter as shown in in assimilation Figure1. During systems this used refraction, for operational the bending atmospheric angle of the research. signal isThe considered local and a primarytemporal parameter atmospheric in assimilation characteristics systems determine used for operationalthe bending atmospheric angle α, which research. is Theprincipally local and subjected temporal to atmospheric the vertical characteristics gradient of the determine refractive the index bending (n) along angle αthe, which penetrating is principally path. subjectedThe vertical to thegradient vertical is associated gradient of with the refractiveatmospheric index parameters (n) along such the penetrating as the temperature path. The (T vertical), total gradientpressure ( isp), associated water vapor with partial atmospheric pressure parameters (e), and electron such asnumber the temperature density [3]. (ThisT), total relationship pressure can (p), waterbe expressed vapor partial in the pressureform of an (e), empirical and electron equation: number density [3]. This relationship can be expressed in the form of an empirical equation: 65pe N =×n 10 = 77.6 + 3.73 × 10 (1) TTp e 2 N = n 106 = 77.6 + 3.73 105 (1) × T × T2 where N is the refractivity and n is the refractive index. Based on the assumption of local spherical wheresymmetry,N is the the bending refractivity angle andcan ben transformedis the refractive to refractive index. index Based n via on Equation the assumption (2), i.e., the of localAbel sphericaltransformation. symmetry, the bending angle can be transformed to refractive index n via Equation (2), i.e., the Abel transformation. " Z ∞ α # 11()∞ α(x)dxdx nrn()(r) = expexp (2)(2) a 22 ππ a √xx2 − a2 − where n (r) is the refractive index proﬁles, r is position vector, α is the bending angle, and a is the where n (r) is the refractive index profiles, r is position vector, α is the bending angle, and a is the impact parameter [3]. impact parameter [3].

Figure 1. Schematic of radio occultation [4]. In the legend, the GNOS-BD (BeiDou) /GPS means global Figure 1. Schematic of radio occultation [4]. In the legend, the GNOS-BD (BeiDou) /GPS means global navigation satellite system (GNSS) occultation sounder (GNOS) received signals from Beidou/GPS navigation satellite system (GNSS) occultation sounder (GNOS) received signals from Beidou/GPS satellite. The radio occultation (RO) phenomenon occurs when a GPS signal from the GNSS penetrates satellite. The radio occultation (RO) phenomenon occurs when a GPS signal from the GNSS penetrates the Earth’s atmosphere and is then received by low-earth orbit (LEO) satellites behind the earth. the Earth’s atmosphere and is then received by low-earth orbit (LEO) satellites behind the earth. 1.2. RO Missions 1.2. RO Missions The successful GPS/Meteorology (GPS/MET) experiments conducted in 1995 ushered in the eraThe of successful RO application GPS/Meteorology for atmospheric (GPS/MET) measurements, experiments given conducted that these in 1995 experiments ushered in helpedthe era deriveof RO application 0–60 km atmospheric for atmospheric parameter measurements, proﬁles [given5]. Subsequently, that these experiments scientists helped performed derive several 0–60 studieskm atmospheric on GPS/ METparameter RO meteorological profiles [5]. Subsequently, data and compared scientists the performed results with several those studies obtained on GPS/MET RO meteorological data and compared the results with those obtained using radiosonde

Atmosphere 2020, 11, 1204 3 of 23 using radiosonde [6] and Lidar [7]. These studies have conﬁrmed the accuracy of RO data, although GPS/MET provided only a small amount of RO data. Therefore, a series of RO missions have been scheduled for the following years. These missions include Challenging Mini-satellite Payload (CHAMP) [8,9]; Gravity Recovery and Climate Experiment (GRACE) and Gravity Recovery and Climate Experiment Follow-on (GRACE-FO) [10]; Scientiﬁc Application Satellite-C/D (SAC-C/D) [11]; TerraSAR-X; TanDEM-X; Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC/COSMIC-2, also known as FORMOSAT-3/ FO RMOSAT-7); the Meteorological Operational satellite Programme-A/B/C (MetOp-A/B/C); FengYun-3C/D (FY-3C/D) (Sun, 2018); Communications/Navigation Outage Forecasting System(C/NOFS); Korea Multi-Purpose Satellite-5 (KOMPSAT-5); the Indian Space Research Organization spacecraft Ocean Satellite-2 (OceanSat-2); and Spanish PAZ (peace in Spanish). A few missions have been retired, such as COSMIC-1, GRACE, CHAMP,and SAC-C/D, and some missions will be completed by the end of 2020, such as FY-3C, TanDEM-X/TerraSAR-X, KOMPSAT-5, OceanSat-2, and C/NOFS. More missions have been planned for the future such as MetOp Second Generation (MetOp-SG), FengYun-3E/F/G/H (FY-3E/F/G/H), TerraSAR-X Next Generation (TSX-NG), Jason Continuity of Service-A/B (JASON-CS-A/B, also known as Sentinel 6A/6B), and Meteor-MP N1/N2. By 2025, the planned operational missions will provide approximately 14,700 RO soundings per day [12]. Herein, we introduce three primary missions accounting for most of the RO data: COSMIC, MetOp, and FY-3 series.

(1) COSMIC. On 15 April 2006, the first satellite constellation COSMIC designed for RO measurements was launched. It marked the beginning of the wide use of RO data in atmospheric and ionospheric sounding research from an operational standpoint [13]. Since then, COSMIC has provided 1500–2000 soundings per day globally, significantly contributing to numerical weather prediction (NWP) and meteorological studies [14]. Later, its follow-up mission was COSMIC-2, launched in June 2019; COSMIC-2 has provided approximately 5000 soundings per day over 35◦ N–35◦ S, mainly for tropical cyclone (TC) forecasting [15]. Such data are useful for short- and medium-range forecasts in the tropics, given the more accurate measurements of the temperature, humidity, and wind field [16]. The European Centre for Medium-Range Weather Forecasts (ECMWF) started to assimilate COSMIC-2 data at a rate of approximately 5000 soundings per day since March 2020. (2) MetOp. MetOp-A/B/C are three polar-orbiting meteorological satellites that form the space segment component of the overall EUMETSAT Polar System (EPS). MetOp-A was launched in 2006, and its RO data were found to contribute to weather forecasts up to 10 days ahead. This mission was followed by MetOp-B and C. Since March 2019, the ECMWF started to assimilate the bending angle from MetOp-C, with a quality similar to both MetOp-A and B measurements. Currently, the MetOp constellation can provide approximately 2000 soundings per day. As a next step, the EUMETSAT group has planned to launch six MetOp-second-generation (MetOp-SG) satellites. MetOp SG-A is scheduled for launch at the end of 2022. (3) FY-3C/D. FY-3C and D were launched in 2013 and 2017, respectively. The GNSS occultation sounder (GNOS) receiver onboard the FY-3C/D satellites is the first GPS and BeiDou-compatible sounder [17–20]. FY-3C can provide approximately 450–500 RO soundings per day for NWP. The FY-3D launched in 2020 can provide even more RO soundings, approximately 1000 per day. The GNOS-RO data have been used to study climate and TCs [21,22]. GNOS data have been assimilated into the operational NWP system of the ECMWF, Deutscher Wetterdienst (DWD), and Met Office [23]. Moreover, the FY-3-series satellites contain FY-3E/F/G/H and FY-3R, which are intended for rainfall observation. These missions are expected to be launched by 2025 and will provide ten years of continuous RO data. An advanced GNOS receiver (GNOS II) has been designed for the FY-3E satellite, making FY-3E applicable for monitoring sea waves as well [24]. Atmosphere 2020, 11, 1204 4 of 23

With the rapid development of GNSS, such as the Chinese BeiDou Satellite (BDS), Russian GLONASS [25,26], European Galileo [27], GPS, and more LEO satellites deployed with GNSS signal receivers, the frequency and number of RO soundings are expected to improve remarkably [17,18,28–30].

1.3. Advantages of RO RO measurements have many advantages, including global coverage, high accuracy and precision, superior vertical resolution, and a full-time and all-weather observation. Near the top of the tropopause, the departure of the RO soundings with respect to the temperature/pressure/ geopotential temperature is approximately 0.7 K/0.15%/1.4 K. The departure further decreases toward the lower troposphere because of the increased information in the background [31]; its vertical resolutions in the stratosphere and troposphere are approximately 1.5 km and 0.2 km, respectively, even reaching 0.1 km near the surface [32]. RO measurements have a global coverage, particularly including sights over the polar region and oceans, which are blind spots of other detection approaches such as radar and radiosonde [33]. Additionally, RO signals loaded on the L1 (1575.42 MHz) and L2 (1227.60MHz) bands, whose wavelengths are sufficiently long to avoid appreciable attenuation by rain [34]. Therefore, RO measurements are minimally contaminated by aerosol, clouds, and precipitation, thus ensuring a full-time and all-weather observation. RO is a self-calibrated remote sensing technique. Once deployed on an orbiting satellite, the RO sensor requires no further calibration. Hence, RO can provide long-term steady data. Furthermore, an RO measurement is considered a calibration standard [35] and can complement other observations. Given that RO data are independent of the missions and satellites, the data obtained from the different missions always have a high degree of consistency. Owing to this unified benchmark, RO data complement each other well [15,36]. This paper focuses on the impacts of RO measurements on the NWP and TC forecasts. The rest of this paper is organized as follows. In Section2, we introduce the status quo of the application of RO to NWP, including a sensitivity analysis and discussions on the amount of RO data. Section3 presents the positive effects of RO data on TC forecasting through some typical studies. The advances in RO and its prospects are discussed in Section4. Finally, Section5 presents the conclusions drawn from our review.

2. Research and Applications of RO in NWP This section reviews studies that applied RO to NWP. Section 2.1 details the progress made using RO in NWP, including the ﬁrst assimilation of RO data in the assimilation systems of diﬀerent institutes, and the sensitivities of the RO quality to height and region. Section 2.2 introduces a simulation study that focuses on the impact of the amount of RO data. Moreover, the total amount of RO data expected in the future is estimated.

2.1. Progress in the Application of RO to NWP Given the advantages described in Section 1.3, RO measurements can be applied to operational NWP and climate monitoring. Initially, RO data were operationally assimilated into the NWP systems of the ECMWF, NCEP, and Met Office. The results showed that the RO measurements have a significant impact on the NWP. On 12 December 2006, the ECMWF started to assimilate RO data obtained from COSMIC operationally. As shown in Figure2, there is a significant reduction in the mean biases for short-range forecast and analysis in the southern hemisphere [37]. According to [38], after the NCEP incorporated the COSMIC RO data into their assimilation system, the anomaly correlation scores at 500 hPa for the southern hemisphere improved by 4.5 h in a seven-day prediction period. A similar result was obtained in [39] when Met Office assimilated the refractivity of GHAMP and GRACE into their operational forecast system. The forecast was improved significantly for the upper troposphere and lower stratosphere (UTLS) region in the southern hemisphere. AtmosphereAtmosphere2020 2020, 11, 11, 1204, x FOR PEER REVIEW 55 of of 23 23

Figure 2. Time series of the mean and standard deviation of short-range forecast and analysis fitted to Figure 2. Time series of the mean and standard deviation of short-range forecast and analysis fitted the radiosonde temperature measurements in the southern hemisphere, for the operational numerical to the radiosonde temperature measurements in the southern hemisphere, for the operational weather prediction (NWP) system at the European Centre for Medium-Range Weather Forecasts numerical weather prediction (NWP) system at the European Centre for Medium-Range Weather (ECMWF) [37]. With the assimilation of COSMIC RO data operationally by the ECMWF since December Forecasts (ECMWF) [37]. With the assimilation of COSMIC RO data operationally by the ECMWF 2006, there has been an apparent improvement in the short-range forecast and analysis. since December 2006, there has been an apparent improvement in the short-range forecast and Subsequently,analysis. the quality of the RO data was tested gradually. To test the sensitivity of RO data quality to the geopotential height and hemisphere, the authors of [40] studied the effect of COSMIC Subsequently, the quality of the RO data was tested gradually. To test the sensitivity of RO data RO data at different geopotential heights on the ECMWF forecast via comparison experiments with quality to the geopotential height and hemisphere, the authors of [40] studied the effect of COSMIC and without RO data. The group without the RO data was called CTRL, whereas the group with the RO data at different geopotential heights on the ECMWF forecast via comparison experiments with COSMIC RO data was called COS1. The fractional reduction in the root mean square (RMS) means and without RO data. The group without the RO data was called CTRL, whereas the group with the the impact of the RO measurement on the NWP, which is defined as (RMSCTL RMSCOS1)/RMSCTL, COSMIC RO data was called COS1. The fractional reduction in the root mean− square (RMS) means where RMSCTL and RMSCOS1 denote the RMS error for the CTL and COS1, respectively. As shown the impact of the RO measurement on the NWP, which is defined as (RMSCTL − RMSCOS1)/RMSCTL, in Figures3 and4, the RO measurement improves the forecast accuracy at heights of 100 hPa and where RMSCTL and RMSCOS1 denote the RMS error for the CTL and COS1, respectively. As shown in 200 hPa in both the northern and southern hemispheres, which can be attributed to the high vertical Figures 3 and 4, the RO measurement improves the forecast accuracy at heights of 100 hPa and 200 resolution of RO in the UTLS region. However, the results for heights of 1000 hPa and 500 hPa hPa in both the northern and southern hemispheres, which can be attributed to the high vertical are neutral. This is because, in the troposphere, there are already many conventional observations, resolution of RO in the UTLS region. However, the results for heights of 1000 hPa and 500 hPa are such as radiosonde and radar, and the signal-to-noise ratio (SNR) of RO data toward the troposphere is neutral. This is because, in the troposphere, there are already many conventional observations, such relatively low. A comparison of Figures3 and4 shows that the RO measurement performs better in as radiosonde and radar, and the signal-to-noise ratio (SNR) of RO data toward the troposphere is the southern hemisphere than in the northern hemisphere. This is because the emergence of RO data relatively low. A comparison of Figures 3 and 4 shows that the RO measurement performs better in increased the total number of observations in the southern hemisphere, where oceans dominate and the southern hemisphere than in the northern hemisphere. This is because the emergence of RO data where conventional observations, such as radiosonde and ground-based observations, are unavailable. increased the total number of observations in the southern hemisphere, where oceans dominate and Moreover, the RO signal is minimally contaminated by clouds and precipitation, making it suitable where conventional observations, such as radiosonde and ground-based observations, are for detecting atmospheric profiles above oceans. Thus, RO measurements provide more accurate unavailable. Moreover, the RO signal is minimally contaminated by clouds and precipitation, making atmospheric parameters than other observations in the southern hemisphere, such as meteorological it suitable for detecting atmospheric profiles above oceans. Thus, RO measurements provide more satellites based on the detection in the visible and infrared ranges, where the clouds and precipitation accurate atmospheric parameters than other observations in the southern hemisphere, such as could contaminate signals in this band. Many studies also support the superior performance of the meteorological satellites based on the detection in the visible and infrared ranges, where the clouds RO measurement for NWP [36,41–44]. The degradation over day 6 in Figure3a or Figure4a may be and precipitation could contaminate signals in this band. Many studies also support the superior a general phenomenon for many observations associated with synoptic systems in the troposphere, performance of the RO measurement for NWP [36,41–44]. The degradation over day 6 in Figure 3a as these synoptic systems disappear within six days. or Figure 4a may be a general phenomenon for many observations associated with synoptic systems in the troposphere, as these synoptic systems disappear within six days.

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Figure 3. Impact of RO data for heights of 100, 200, 500, and 1000 hPa on the ECMWF operational Figureforecast 3. Impactin the northern of RO data hemisphere, for heights where of 100, the 200, posi 500,tive andvalues 1000 indicate hPa on improved the ECMWF NWP. operational The y-axis forecastFigurerepresents in3. Impact the the northern fractional of RO hemisphere, data improvemen for heights wheret in of the the100, root positive 200, mean 500, values square and 1000 indicate (RMS) hPa geopotential improvedon the ECMWF NWP. height Theoperational errors y-axis as a representsforecastfunction in of the the the fractional northern forecast range,hemisphere, improvement which whereis in plotted the the root alposiong meantive the values squarex-axis, indicatein (RMS) the nort geopotentialimprovedhern hemisphere NWP. height The (latitude errors y-axis asrepresents> a20°) function [40]. the The of fractional theerror forecast bars improvemen represent range, which thet in 95% the is confidence plottedroot mean along squareinterval. the (RMS) x-axis, geopotential in the northern height hemisphere errors as a

(latitudefunction> of20 the◦)[ 40forecast]. The range, error bars which represent is plotted the al 95%ong conﬁdence the x-axis, interval.in the northern hemisphere (latitude > 20°) [40]. The error bars represent the 95% confidence interval.

Figure 4. Impact of RO data in 100, 200, 500, and 1000 hPa on the ECMWF operational forecast in Figure 4. Impact of RO data in 100, 200, 500, and 1000 hPa on the ECMWF operational forecast in the the southern hemisphere, where the positive values indicate improved NWP. The y-axis represents southern hemisphere, where the positive values indicate improved NWP. The y-axis represents the the fractional improvement in the RMS geopotential height errors as a function of the forecast range, Figurefractional 4. Impact improvement of RO data in thein 100, RMS 200, geopotential 500, and 1000 height hPa onerrors the ECMWFas a function operational of the forecastforecast inrange, the which is plotted along the x-axis, in the southern hemisphere (latitude > 20◦)[40]. The error bars which is plotted along the x-axis, in the southern hemisphere (latitude > 20°) [40]. The error bars representsouthern the hemisphere, 95% conﬁdence where interval. the positive values indicate improved NWP. The y-axis represents the fractionalrepresent improvementthe 95% confidence in the interval. RMS geopotential height errors as a function of the forecast range, which is plotted along the x-axis, in the southern hemisphere (latitude > 20°) [40]. The error bars represent the 95% confidence interval.

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In addition to the height and region, the amount of RO data is considered considered in a further further sensitivity sensitivity analysis. The The authors authors of of [45] [45] studied studied the the impact of the amount of RO data available at that time at didifferentﬀerent heights usingusing the NWP assimilation system. As shown in Figure 55,, thethe forecastforecast errorerror reducesreduces more in the the stratosphere stratosphere above above 200 200 hPa hPa than than in inthe the troposphere troposphere below below 500 500 hPa hPa when when assimilating assimilating RO ROdata. data. As shown As shown in Figure in Figure 5a–d,5a–d, at heights at heights of 50, of 50,100, 100, 150, 150, and and 200 200 hPa, hPa, increasing increasing the the amount amount of ofassimilated assimilated RO RO data data decreases decreases the the relative relative forecast forecast error. error. This This is is also also consistent consistent with with the the results, shown in Figures 33 and and4 ,4, in in that that the the improvement improvement for for the the southern southern hemisphere hemisphere is is more more signiﬁcant significant than for the northern hemisphere and the tropics.tropics. RO measurements reduced reduced the the forecast error by approximately 10%10% with with assimilating assimilating RO RO data data of onlyof only 5%. 5%. However, However, at 1000 at hPa1000 and hPa 500 and hPa, 500 as hPa, shown as inshown Figure in5 Figuree,f, RO 5e,f, measurements RO measurements have a modest have a impact modest on impact the forecast, on the dueforecast, to the due relatively to the relatively low SNR inlow the SNR troposphere. in the troposphere. Nevertheless, Nevertheless, in actual operation, in actual everyoperation, observation’s every observation’s weight metric weight varies metric with thevaries height. with Therefore,the height. the Therefore, impact ofthe RO impact measurements of RO measurements on the NWP on is the positive. NWP is positive.

Figure 5. SensitivitySensitivity of of height height to the the am amountount of RO data in NWP NWP [45]. [45]. Dependence Dependence of of 24-h 24-h temperature temperature forecast. error error relative relative to 0%-GPS-RO0%-GPS-RO experiment experiment (%) (%) at at (a )( 50,a) 50, (b) ( 100,b) 100, (c) 150,(c) 150, (d) 200,(d) 200, (e) 500,(e) 500,and (andf) 1000 (f) hPa. 1000 The hPa. 24 The h temperature 24 h temperature relative forecast relative error, forecast plotted error, along plotted the y-axis, along decreases the y-axis, with decreasesan increase with in the an GPS-RO increase data in density. the GPS-RO Above 500data hPa, density. more ROAbove data 500 induces hPa, less more error, RO and data the phenomenoninduces lessin error, the stratosphere and the phenomenon is more obvious in than the in stratosphere the troposphere. is more The solid, obvious dotted, than and dashedin the troposphere.lines indicate the The results solid, for thedotted, northern and hemisphere, dashed lines southern indicate hemisphere, the results and tropics,for the respectively. northern hemisphere, southern hemisphere, and tropics, respectively. The authors of [44] analyzed the height at which the RO measurements have the most signiﬁcant impactThe and authors found of that [44] theanalyzed quality the of height the RO at data whic inh the RO lower measurements troposphere have is not the ideal, most particularly significant belowimpact a and height found of 2 that km. the In contrast, quality of RO the has RO apronounced data in the lower positive troposphere impact in the is not UTLS ideal, region, particularly which is approximatelybelow a height of in 2 the km. height In contra rangest, ofRO 10–20 has a km.pronounced Thus, in positive an operational impact NWPin the assimilationUTLS region, system, which theis approximately range between in 10 the and height 20 km range is the of main 10–20 region km. Thus, where in RO an operational data yield optimal NWP assimilation results. system, the rangeTo assess between the impact 10 and of 20 RO km measurement is the main region on NWP, where the RO authors data ofyield [44] optimal evaluated results. the forecast error reductionTo assess of various the impact observations of RO measurement assimilated by on the NW ECMWF.P, the authors Figure6 showsof [44] that,evaluated while the accounting forecast forerror only reduction approximately of various 7% of observations all observations, assimila RO datated by rank the 4th ECMWF. in terms ofFigure the contribution, 6 shows that, reducing while theaccounting error by for approximately only approximately 10%. Notably, 7% of the all assimilated observations, RO dataRO indata the 2014rank ECMWF4th in terms assimilation of the systemcontribution, are estimated reducing to the be error less thanby approximately 3000 soundings 10%. per Notably, day. With the such assimilated a modest RO amount data in and the yet2014 a tremendousECMWF assimilation impact on system the NWP, are the estimated RO data to are be deemed less than promising. 3000 soundings per day. With such a modest amount and yet a tremendous impact on the NWP, the RO data are deemed promising.

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FigureFigure 6. 6.Evaluation Evaluation of various various observations observations assimilated assimilated by bythe theECMWF. ECMWF. (a) Data (a) DataPercentage; Percentage; (b) (b)Frequency Frequency of of Error Error Reduction. Reduction. Wh Whileile accounting accounting for for only only 7% 7% of ofthe the total total observations observations in inthe the assimilationassimilation system, system, RO RO has has the the fourth-largest fourth-largest impactimpact onon NWP. Adapted from from [44]. [44]. 2.2. Impact of the Amount of RO Data on NWP and Future Trends 2.2. Impact of the Amount of RO Data on NWP and Future Trends As a small amount of RO observation data has an impressive impact on the NWP, the authors As a small amount of RO observation data has an impressive impact on the NWP, the authors ofof [46 [46]] analyzed analyzed the the upper upper limit limit ofof thethe amountamount of RO data data that that benefits beneﬁts NWP. NWP. The The authors authors of of[46] [46 ] simulatedsimulated the the impact impact of of the the number number of ofassimilated assimilated RO observations varying varying from from 2000 2000 to to 128,000 128,000 on on NWPNWP using using the the ensemble ensemble of of data data assimilation assimilation (EDA)(EDA) approach, namely namely the the OSSE OSSE (Observing (Observing System System SimulationSimulation Experiment). Experiment). The The operational operational ECMWFECMWF NWP analysis analysis is is used used as as the the proxy proxy of ofthe the truth truth to to simulatesimulate the the bending bending angle. angle. FigureFigure7 shows 7 shows that that increasing increasing the amountthe amount of assimilated of assimilated RO data RO leads data to leads a continuous to a continuous reduction in thereduction EDA spread, in the EDA a parameter spread, a that parameter estimates that the estima forecasttes the error. forecast Speciﬁcally, error. Specifically, Figure7a–c Figures indicate 7(a)– that, at heights(c) indicate of 500 that, and at 100heights hPa, of the 500 simulated and 100 hPa, temperature the simulated and geopotential temperature heightand geopotential show better height results in theshow southern better results hemisphere in the thansouthern in the hemisphere tropics and th thean northernin the tropics hemisphere. and the Furthermore,northern hemisphere. the higher theFurthermore, geopotential the height, higher the the greater geopotential the error height, reduction. the greater For example, the error the reduction. statistical For errors, example, shown the in Figurestatistical7a,b, aterrors, 500 hPa shown decrease in Figure by approximately 7a,b, at 500 hPa 20%, decrease whereas by they approximately decrease by 20%, approximately whereas they 50% at 100decrease hPa. Notably,by approximately the maximum 50% at error 100 hPa. reduction Notably, is80% the maximum when using error 128,000 reduction observations, is 80% when and using impact saturation128,000 observations, has not been and reached, impact i.e., saturation if the amount has not of been RO reached, data keeps i.e., increasing, if the amount the of forecast RO data error keeps will keepincreasing, decreasing. the forecast However, error 128,000 will keep is far decreasing. from achievable, However, as 128,000 the total is amountfar from ofachievable, RO observations as the total amount of RO observations in 2020 is only approximately 10,000. Therefore, the greater the in 2020 is only approximately 10,000. Therefore, the greater the amount of RO data, the better the amount of RO data, the better the accuracy of the NWP. accuracy of the NWP. Another notable result in Figure7 is that half of the maximum impact can be attained using only 16,000 RO observations, a more reachable number. However, the current RO data in the assimilation system are far from reaching 128,000 and 16,000. So far, the ECMWF could assimilate approximately 5000 soundings per day from the seven missions. As listed in Table1, these missions include COSMIC-2, MetOp-A/B/C, FY-3C/D, TanDEM-X, TerraSAR-X, KOMPSAT-5, and PAZ. The total amount of RO data received by these missions is approximately 9000; however, the actual received number is only approximately 6000. After the quality control, there are only 5000 soundings left in the assimilation system. As for the NCEP Global Data Assimilation System (GDAS), there were 2000–3000 RO soundings per day until 2019, according to [47], as shown in Figure8.

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Figure 7. Normalized ensemble of data assimilation (EDA) spread (%) as a function of the assimilated Figure 7. Normalized ensemble of data assimilation (EDA) spread (%) as a function of the assimilated numbernumber of simulated of simulated RO RO proﬁles profiles [46 [46].]. The The EDAEDA spreadspread is is an an error error statistic statistic of ofthe the ECMWF ECMWF NWP NWP theoreticaltheoretical forecast forecast and analysis. and analysis. (a) Temperature (a) Temperature at 100 at hPa; 100 (b hPa;) temperature (b) temperature at 500 hPa;at 500 (c) geopotentialhPa; (c) heightgeopotential at 500 Pa; (heightd) relative at 500 humidity Pa; (d) relative at 850 humidity hPa. The at more 850 hPa. the ROThe observations,more the RO observations, the better the the NWP, and therebetter is the no NWP, saturation and there even is withno saturati 128,000on even soundings with 128,000 per day. soundings per day.

Table1.AnotherAssimilated notable radio result occultation in Figure (RO) 7 is that data half in the of European the maximum Center impact Medium-Range can be attained Weather using Forecast only (ECMWF)16,000 RO operational observations, numerical a more reachable weather prediction number. Ho (NWP)wever, system the current (adapted RO from data ECMWF)in the assimilation [48]. system are far from reaching 128,000 and 16,000. So far, the ECMWF could assimilate approximately Mission Soundings/Day 5000 soundings per day from the seven missions. As listed in Table 1, these missions include COSMIC-2, MetOp-A/B/C, FY-3C/D,COSMIC-2 TanDEM-X, TerraSAR-X, KOMPSAT-5, 5000 and PAZ. The total amount of RO data received byMetOp-A these missions/B/C is approximately 19059000; however, the actual received number is only approximately 6000.FY-3C After/D the quality control, there 1000 are only 5000 soundings left in TanDEM-X 100 the assimilation system. As for the NCEP Global Data Assimilation System (GDAS), there were 2000– TerraSAR-X 200 3000 RO soundings per day until 2019, according to [47], as shown in Figure 8. KOMPSAT-5 500 PAZ 300 Table 1. Assimilated radio occultation (RO) data in the European Center Medium-Range Weather Total data 9005 AtmosphereForecast 2020 (ECMWF), 11, x FOR PEERoperationalActual REVIEW numerical received dataweather prediction (NWP) ~6000 system (adapted from ECMWF)10 of 23 [48]. Data used ~5000 Data used ~5000 Mission Soundings/Day COSMIC-2 5000 MetOp-A/B/C 1905 FY-3C/D 1000 TanDEM-X 100 TerraSAR-X 200 KOMPSAT-5 500 PAZ 300 Total data 9005 Actual received data ~6000 Figure 8. Daily total RO proﬁles in the National Centers for Environmental Prediction (NCEP) Global Figure 8. Daily total RO profiles in the National Centers for Environmental Prediction (NCEP) Global Data Assimilation System (GDAS) from 01/2017 to 09/2019. Taken from [47]. Data Assimilation System (GDAS) from 01/2017 to 09/2019. Taken from [47].

The amount of RO observations will thrive in the future. According to the OSCAR website, there were approximately 10,000 soundings per day in 2020. Commercial RO data from Spire and other companies are not included. As shown in Figure 9, the possible amount of RO observations may reach 14,700 soundings per day in 2025. Moreover, it may reach a maximum of approximately 18,400 soundings per day in 2027. According to [46], if the assimilated number reaches 16,000 soundings per day, the error in the NWP can be reduced by 25% compared with the error in 2013. This can probably be achieved by 2027.

Figure 9. Planned RO data amount from 2020 to 2030 from all missions. The shadow area represents the estimates of possible RO data; the bold lines indicate three primary missions, namely, COSMIC, FY-3, and MetOp [12].

3. Research and Applications of RO to TC Forecast This section details how the RO measurement benefits TC forecast. Section 3.1 states the current status of TC forecast. Section 3.2 presents case studies that demonstrate how the RO measurement impacts TC forecast. In Section 3.3, we discuss how the assimilation operator, mainly the non-local excess phase operator, optimizes the TC forecast.

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Data used ~5000

FigureAtmosphere 8. Daily2020 ,total11, 1204 RO profiles in the National Centers for Environmental Prediction (NCEP) Global 10 of 23 Data Assimilation System (GDAS) from 01/2017 to 09/2019. Taken from [47].

The amountThe amount of RO ofobservations RO observations will thrive will thrivein the infuture. the future. According According to the toOSCAR the OSCAR website, website, there there were approximatelywere approximately 10,000 10,000 soundings soundings per day per in day 2020. in 2020.Commercial Commercial RO data RO from data Spire from and Spire other and other companiescompanies are not are included. not included. As shown As shown in Figure in Figure 9, the9 possible, the possible amount amount of RO of observations RO observations may may reach reach14,700 14,700 soundings soundings per day per in day 2025. in Moreover 2025. Moreover,, it may it reach may a reach maximum a maximum of approximately of approximately 18,400 18,400 soundingssoundings per day per in day 2027. in According 2027. According to [46], to if [th46e], assimilated if the assimilated number number reaches reaches 16,000 16,000soundings soundings per per day, theday, error the in error the inNWP the NWPcan be can reduced be reduced by 25% by co 25%mpared compared with the with error the in error 2013. in This 2013. can This probably can probably be achievedbe achieved by 2027. by 2027.

Figure 9. Planned RO data amount from 2020 to 2030 from all missions. The shadow area represents Figure 9. Planned RO data amount from 2020 to 2030 from all missions. The shadow area represents the estimates of possible RO data; the bold lines indicate three primary missions, namely, COSMIC, the estimatesFY-3, and of possible MetOp [ 12RO]. data; the bold lines indicate three primary missions, namely, COSMIC, FY-3, and MetOp [12]. 3. Research and Applications of RO to TC Forecast 3. Research and Applications of RO to TC Forecast This section details how the RO measurement benefits TC forecast. Section 3.1 states the current Thisstatus section of TC details forecast. how Section the RO 3.2 measurement presents case benefits studies TC that forecast. demonstrate Section how3.1 states the RO the measurementcurrent status impactsof TC forecast. TC forecast. Section In 3.2 Section presents 3.3, wecase discuss studies how that the demonstrate assimilation how operator, the RO mainly measurement the non-local impactsexcess TC forecast. phase operator, In Section optimizes 3.3, we thediscuss TC forecast. how the assimilation operator, mainly the non-local excess phase operator, optimizes the TC forecast. 3.1. Status of TC Forecast NWP is one of the primary methods for predicting the TC; however, it is hard to improve the accuracy. The authors of [49] investigated the predictions of TC using global NWP models, including Climate Change Canada’s Global Environmental Multiscale Model (CMC), European Center’s Medium-Range Weather Forecast Global Model (ECMWF), American National Center’s Environmental Prediction Global Forecast System (GFS), and Met Office Global Model (UKMET), based on three verification metrics defined in [50], namely, the hit, false alarm, and miss. Here, the metric hit means a successful prediction whose location is within 5◦ against the target TC and whose time is within 24 h against the target TC; the metric miss means a failed prediction; the false alarm indicates a successful TC forecast modeling, but with incorrect time and track. As shown in Figure 10, all the institutes performed suboptimally, as most of the predictions fell in the low critical success index portion with a low detection probability, which is far from the perfect forecast. Atmosphere 2020, 11, x FOR PEER REVIEW 11 of 23

3.1. Status of TC Forecast NWP is one of the primary methods for predicting the TC; however, it is hard to improve the accuracy. The authors of [49] investigated the predictions of TC using global NWP models, including Climate Change Canada’s Global Environmental Multiscale Model (CMC), European Center’s Medium-Range Weather Forecast Global Model (ECMWF), American National Center’s Environmental Prediction Global Forecast System (GFS), and Met Office Global Model (UKMET), based on three verification metrics defined in [50], namely, the hit, false alarm, and miss. Here, the metric hit means a successful prediction whose location is within 5° against the target TC and whose time is within 24 h against the target TC; the metric miss means a failed prediction; the false alarm indicates a successful TC forecast modeling, but with incorrect time and track. As shown in Figure Atmosphere10, all the2020 institutes, 11, 1204 performed suboptimally, as most of the predictions fell in the low critical success11 of 23 index portion with a low detection probability, which is far from the perfect forecast.

Figure 10. TropicalTropical cyclone (TC) forecast model perf performanceormance of four institutes during 2007–2014. Probability of detection (POD) = hit is given along they y-axis; Success ratio (SR)= hit Probability of detection (POD) hit+miss is given along the -axis; Success ratio (SR) hit+ f alse alarm is hit+f alse alarm givenis given along along the the x-axis; x-axis; the the dashed dashed line line indicates indicates the the bias bias= ; the; solidthe solid line line indicates indicates the hit+miss hit criticalthe critical success success index index (CSI) (CSI)= hit +f lase alarm+miss . The solid. The circle solid and circle triangle and triangle indicate indicate the North the Atlantic North (NATL) and eastern North Paciﬁc (EPAC) basins. Higher values of POD, SR, and CSI indicate a better Atlantic (NATL) and eastern North Pacific (EPAC) basins. Higher values of POD, SR, and CSI indicate forecast of the TC genesis. On the top right corner is the perfect forecast [49]. a better forecast of the TC genesis. On the top right corner is the perfect forecast [49]. 3.2. Eﬀect of RO Data on TC Forecasts 3.2. Effect of RO Data on TC Forecasts Theoretically, TCs form in the environment of reduced wind shear, a deep layer of warm sea surface Theoretically, TCs form in the environment of reduced wind shear, a deep layer of warm sea (temperatures above 27 ◦C), enhanced vorticity, humidity, and deep convection. These conditions are basedsurface on (temperatures the TC forecast above model 27 [51 °C),]. If theseenhanced initial vort conditionsicity, humidity, in the TC and forecast deep model, convection. such as These wind, temperature,conditions are and based water on the vapor, TC forecast are more model accurate, [51]. the If these TC forecast initial conditions will be improved. in the TC forecast model, such Theas wind, RO data temperature, are conducive and to water improving vapor, the are accuracy more accurate, and precision the TC of forecast TC prediction will be via improved. enhancing the accuracyThe RO ofdata the intensityare conducive and track to ofimproving the TCs. Mostthe accuracy TCs are generatedand precision above of oceans, TC prediction and the inner via structuresenhancing ofthe a accuracy TC are moist. of the The intensity conventional and track measurements, of the TCs. Most such TCs as radiosondeare generated and above some oceans, of the satellites,and the inner are eitherstructures incapable of a TC of are detecting moist. The the co atmosphericnventional measurements, systems above oceanssuch as orradiosonde inaccurate and in detectingsome of the the satellites, water vapor. are Aseither mentioned incapable in Sectionof detecting 1.3, the the RO atmospheric signals can propagatesystems above through oceans clouds or andinaccurate obtain in water detecting vapor the condition water vapor. above As the mentioned oceans. Thus, in Section this feature 1.3., the makes RO thesignals RO measurementscan propagate feasiblethrough forclouds TC forecasts. and obtain water vapor condition above the oceans. Thus, this feature makes the RO measurementsMany studies feasible show for that TC ROforecasts. measurements have a positive impact on the TC forecast [52–59]. The most famous one is the NCAR (National Center for Atmospheric Research) 4-Day forecast of Ernesto in 2007. As shown in Figure 11, in the second and third column, the generation of hurricane Ernesto is successfully predicted in the group with the RO data, whereas the group without the RO data failed. Atmosphere 2020, 11, x FOR PEER REVIEW 12 of 23

Many studies show that RO measurements have a positive impact on the TC forecast [52–59]. The most famous one is the NCAR (National Center for Atmospheric Research) 4-Day forecast of

AtmosphereErnesto in2020 2007., 11, 1204As shown in Figure 11, in the second and third column, the generation of hurricane12 of 23 Ernesto is successfully predicted in the group with the RO data, whereas the group without the RO data failed.

FigureFigure 11.11. LeftLeft columncolumn showsshows thethe imageimage ofof Ernesto’sErnesto’s genesisgenesis takentaken byby aa satellitesatellite afterafter 54,54, 78,78, andand 102102 h;h; the middle middle column column shows shows the the model model result result with with RO ROdata; data; the right the rightcolumn column shows shows the model the modelresults results without the RO data. Ernesto’s genesis is predicted successfully after assimilating the RO without the RO data. Ernesto’s genesis is predicted successfully after assimilating the RO observation observation [60]. [60]. This case was further studied in [61]. Because of the strong correlation between T, e, and p as in This case was further studied in [61]. Because of the strong correlation between T, e, and p as in Equation (1), while solving equations, it is difficult to know which parameter induces the error. Thus, Equation (1), while solving equations, it is difficult to know which parameter induces the error. Thus, it is difficult to accurately estimate the error RO data brings to the TC forecast. The authors of [61] it is difficult to accurately estimate the error RO data brings to the TC forecast. The authors of [61] solved this problem using an ensemble mean assimilation system. In the paper, one observation set solved this problem using an ensemble mean assimilation system. In the paper, one observation set (ObS) using the NCEP reanalysis was set, and three experiments were set: CTRL, RO, and RO6km. (ObS) using the NCEP reanalysis was set, and three experiments were set: CTRL, RO, and RO6km. The CTRL assimilated the conventional measurements, such as those obtained from radiosonde, aircraft, The CTRL assimilated the conventional measurements, such as those obtained from radiosonde, and satellite cloud drift wind; the RO assimilated all the RO refractivity profiles; and the RO6km aircraft, and satellite cloud drift wind; the RO assimilated all the RO refractivity profiles; and the assimilated only the RO refractivity profiles above a height of 6 km. In Figure 12a, the central sea RO6km assimilated only the RO refractivity profiles above a height of 6 km. In Figure 12a, the central level pressure in the RO is approximately 15 hPa lower than those in CTRL and RO6km, which makes sea level pressure in the RO is approximately 15 hPa lower than those in CTRL and RO6km, which the TC in RO stronger. This is because the assimilated RO data provided a more accurate pressure makes the TC in RO stronger. This is because the assimilated RO data provided a more accurate field and helped adjust the initial wind field through forecast multivariate correlations between the pressure field and helped adjust the initial wind field through forecast multivariate correlations provided parameters RO and wind, which affects the cyclone’s intensification. In Figure 12b, the track between the provided parameters RO and wind, which affects the cyclone’s intensification. In Figure error of the RO is approximately in the range of 30–50 km, which is lower than that in other groups. 12b, the track error of the RO is approximately in the range of 30–50 km, which is lower than that in From the image of the total column cloud liquid water shown in Figure 12c, the RO prediction is similar other groups. From the image of the total column cloud liquid water shown in Figure 12c, the RO to the satellite infrared cloud image, which verified fact that RO data provide better measurements of prediction is similar to the satellite infrared cloud image, which verified fact that RO data provide the water vapor field. Therefore, the RO data have a positive impact on the TC prediction. Notably, better measurements of the water vapor field. Therefore, the RO data have a positive impact on the the results of RO6km are neutral, emphasizing the importance of RO data below 6 km. As mentioned TC prediction. Notably, the results of RO6km are neutral, emphasizing the importance of RO data in Section2, the main benefits of RO for the NWP are in the height range of 10–20 km. However, for the below 6 km. As mentioned in Section 2, the main benefits of RO for the NWP are in the height range TC prediction, RO data below 6 km are crucial as they provide more accurate initial conditions of the of 10–20 km. However, for the TC prediction, RO data below 6 km are crucial as they provide more water vapor and help adjust wind analysis above oceans. accurate initial conditions of the water vapor and help adjust wind analysis above oceans.

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Figure 12. Forty-eight-hour prediction results of Storm Ernesto: (a) central sea level pressure; (b) track

error; and (c) total column cloud liquid water obtained from three experiments and satellite infrared cloudFigure image 12. Forty-eight-hourForty-eight-hour of the actual storm. prediction The central results sea of leve Storml pressure Ernesto: (SLP) ( a) central in the ROsea grouplevel pressure; is approximately (b) track 15error; hPa and lower (c)) than totaltotal those columncolumn in cloudCTRLcloud liquidliquidand RO6km, waterwater obtainedobtainedwhich makes fromfrom the three TC experiments in RO stronger and [61]. satellite infrared cloud image of the actual storm. The central central sea leve levell pressure pressure (SLP) in the RO RO group group is is approximately approximately Similarly,1515 hPahPa lowerlower the thanthan authors thosethose ininof CTRLCTRL [62] investigatedandand RO6km,RO6km, whichwhich the impact makesmakes theofthe COSMIC TCTC inin RORO strongerstrongerRO data [[61].61 on]. the track of the super cyclone Gonu. Considering the error of the lower troposphere, they assimilated only the RO Similarly, the authors of [62] investigated the impact of COSMIC RO data on the track of the super data Similarly,in the UTLS the region. authors The of results[62] investigated show that thethe impact72–96 h of forecast COSMIC of Gonu’sRO data track on the was track improved of the cyclone Gonu. Considering the error of the lower troposphere, they assimilated only the RO data in becausesuper cyclone the RO Gonu. data Consideringprovided more the erroraccurate of the temperature lower troposphere, information they in assimilated the UTLS onlyregion. the TheRO the UTLS region. The results show that the 72–96 h forecast of Gonu’s track was improved because energydata in forthe theUTLS development region. The ofresults a mature show TCthat comes the 72–96 from h forecastthe cold ofair Gonu’s above track the TC.was Therefore,improved the RO data provided more accurate temperature information in the UTLS region. The energy for the assimilatingbecause the RORO datadata in provided UTLS region more can accurate improve temperature the TC forecast information in the later in the stage. UTLS The region. above twoThe development of a mature TC comes from the cold air above the TC. Therefore, assimilating RO data in studiesenergy emphasizedfor the development that RO dataof a matureboth in TCthe comesUTLS regionfrom the and cold below air 6above km arethe essentialTC. Therefore, to TC UTLS region can improve the TC forecast in the later stage. The above two studies emphasized that prediction.assimilating RO data in UTLS region can improve the TC forecast in the later stage. The above two RO data both in the UTLS region and below 6 km are essential to TC prediction. studiesTo furtheremphasized study thathow RO RO datameasurements both in the help UT imprLS regionove the and accuracy below of6 TCkm forecast, are essential the authors to TC To further study how RO measurements help improve the accuracy of TC forecast, the authors ofprediction. [63] used RO data to simulate the vertical structure of forty-two cases of TCs formed over the North of [63] used RO data to simulate the vertical structure of forty-two cases of TCs formed over the AtlanticTo furtherbasin during study 2002–2010.how RO measurements The TC parameters help impr wereove statistically the accuracy analyzed of TC forecast, as a function the authors of the North Atlantic basin during 2002–2010. The TC parameters were statistically analyzed as a function distanceof [63] used from RO thedata eye to simulate of the cyclones.the vertical In structure comparison of forty-two with the cases ECMWF of TCs formedreanalysis, over the the Northresult of the distance from the eye of the cyclones. In comparison with the ECMWF reanalysis, the result confirmedAtlantic basin that during the RO 2002–2010. observation The could TC parametersresolve the weremajor statistically characteristics analyzed of the as TC a functionstructure—the of the confirmed that the RO observation could resolve the major characteristics of the TC structure—the eye eyedistance and eyewall; from the the eye inflow, of the which cyclones. is the markIn comparison of a mature with TC; thethe outflow ECMWF layers; reanalysis, and even the the result rain and eyewall; the inflow, which is the mark of a mature TC; the outflow layers; and even the rain bands bandsconfirmed at a confidencethat the RO level observation of 95%. Thecould relative resolve humidity the major of characteristicsthe simulated ofrain the bands TC structure—the 200 km from at a confidence level of 95%. The relative humidity of the simulated rain bands 200 km from the center, theeye center,and eyewall; shown the in Figureinflow, 13, which is approximately is the mark of 25% a mature higher TC; than the ECMWF outflow reanalysis.layers; and However, even the rain the shown in Figure 13, is approximately 25% higher than ECMWF reanalysis. However, the location of locationbands at of a theconfidence rain bands level may of 95%.not be The that relative distinct humidity because of the simulatedlow horizontal rain bandscoverage 200 of km the from RO the rain bands may not be that distinct because of the low horizontal coverage of the RO water vapor waterthe center, vapor shown data. Therefore,in Figure 13, the is improvement approximately in the25% TC higher forecast than can ECMWF be attributed reanalysis. to assimilating However, ROthe data. Therefore, the improvement in the TC forecast can be attributed to assimilating RO data. data.location of the rain bands may not be that distinct because of the low horizontal coverage of the RO water vapor data. Therefore, the improvement in the TC forecast can be attributed to assimilating RO data.

Figure 13. TC relative humidity fractional diﬀerence between GPS simulation and ECMWF reanalysis. Figure 13. TC relative humidity fractional difference between GPS simulation and ECMWF As the vertical proﬁle of the TC, the humidity is statistically analyzed as a function of the altitude and reanalysis. As the vertical profile of the TC, the humidity is statistically analyzed as a function of the distance from the eye of the cyclones. The relative humidity of the simulated rain bands 200 km from altitudeFigure and13. TCdistance relative from humidity the eye of fractionalthe cyclones. diffe Therence relative between humi dityGPS of simulation the simulated and rain ECMWF bands the center is approximately 25% higher than ECMWF reanalysis [63]. 200reanalysis. km from As the the center vertical is approximately profile of the TC, 25% the higher humi thandity isECMWF statistically reanalysis analyzed [63]. as a function of the altitude and distance from the eye of the cyclones. The relative humidity of the simulated rain bands 200 km from the center is approximately 25% higher than ECMWF reanalysis [63].

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3.3.3.3. Eff ectEffect of RO of RO Assimilation Assimilation Operator Operator on TCon TC Forecasts Forecasts To furtherTo further improve improve the accuracy the accuracy of TC forecastof TC foreca usingst RO using measurements, RO measurements, the forecast the model forecast should model considershould the consider assimilation the assimilation approaches approaches and associated and operatorsassociated in operators the assimilation in the assimilation system. The system. popular The assimilationpopular assimilation approaches approaches include 3D-Var, include 4D-Var, 3D-Var, and 4D-Var, ensemble and Kalman ensemble filter Kalman [64]. filter In terms [64]. ofIn theterms assimilationof the assimilation operator, operator, as listed inas Tablelisted2 in, the Table RO 2, provides the RO provides two measurements: two measurements: the refractivity the refractivity and theand bending the bending angle. These angle. two These can be two used can to derivebe used several to derive assimilation several operators. assimilation The operators. refractivity The includesrefractivity the local includes refractivity, the local non-local refractivity, refractivity non-loca [65],l andrefractivity non-local [65], excess and phase;non-local the bendingexcess phase; angle the includesbending the angle 2D/3D includes ray tracer the [ 662D/3D] and ray local tracer bending [66] angleand local [67]. bending On the oneangle hand, [67]. the On first the operatorone hand, of the thefirst bending operator angle, of i.e.,the bending the ray tracer, angle, is i.e., computationally the ray tracer, is expensive. computationally The local expensive. bending operatorThe local ofbending the bendingoperator angle of the is theoretically bending angle equivalent is theoretically to the local equiva refractivitylent to the operator local refracti becausevity theoperator bending because angle the canbending be transformed angle can to abe refractive transformed index to via a refractive Abel transformation. index via Abel However, transformation. the local bendingHowever, angle the islocal morebending accurate angle and is has more a wider accurate range and [67 ].has On a thewider other rang hand,e [67]. the On local the refractivity other hand, used the tolocal be therefractivity most popularused operatorto be the for most avoiding popular complex operator computations for avoiding [68 complex]. In the assimilationcomputations system [68]. forIn the TCs, assimilation a better choicesystem is the for non-local TCs, a better excess choice phase is operator the non-local (EPH), ex ascess the phase high moistureoperator environment(EPH), as the inhigh the moisture inner regionsenvironment of a TC resultsin the ininner strong regions local-refractivity of a TC results horizontal in strong gradients, local-refractivity which break horizontal the spherically gradients, symmetricwhich break atmosphere the spherically assumption, symmetric resulting atmosphere in multipath assumption, effects [69]. resulting In such circumstances, in multipath theeffects local [69]. refractivityIn such wouldcircumstances, induce significant the local representativenessrefractivity would errors. induce Nevertheless, significant representativeness the EPH can avoid thiserrors. issue,Nevertheless, as proven in the many EPH papers can avoid [68,70 this–73 issue,]. Here, as theproven non-local in many value papers represents [68,70–73]. a more Here, accurate the non-local value estimatedvalue represents under the a mathematical more accurate assumption. value estimated The under EPH is the a virtual mathematical value obtained assumption. by integrating The EPH is a thevirtual refractivity value along obtained an arbitrary by integrating trajectory, the refractivi which passesty along the an tangent arbitrary point trajectory, closer to which the actual passes ray the pathtangent [74]. point closer to the actual ray path [74].

TableTable 2. RO 2. RO operator operator in data in data assimilation. assimilation.

ObservationObservation AssimilationAssimilation Operator Operator Accurac Complexity LocalLocal refractivity refractivity Refractivity Non-local refractivity Refractivity Non-local refractivity y Non-local excess phase Non-local excess phase Local bending angle Bending angle Local bending angle Bending angle 2D/3D Ray tracer 2D/3D Ray tracer

BasedBased on tenon ten tropical tropical cyclones cyclones that that occurred occurred during duri 2008–2010,ng 2008–2010, the the authors authors of [of75 ][75] investigated investigated thethe impact impact of ROof RO measurements measurements on on the the tropical tropical cyclogenesis cyclogenesis using using the the WRF WRF data da assimilationta assimilation system. system. TheThe study study demonstrated demonstrated that that the the EPH EPH can can help help improve improve the the probability probability of successfulof successful TC TC predictions predictions fromfrom 30% 30% to 70%,to 70%, whereas whereas the the local local refractivity refractivity operator operator (LOC) (LOC) improved improved this this value value by by onlyonly 10%.10%. A A casecase study on on the the typhoon typhoon Nuri Nuri revealed revealed that that the theexperiment experiment using using the EPH the EPHshows shows a higher a higher moisture moisturecontent content near the near ocean the ocean surface surface and and vertical vertical motion, motion, as as indicated indicated by by the redred circlecircle in in Figure Figure 14 a.14a. Additionally,Additionally, the the dashes dashes in Figure in Figure14b 14b indicate indicate a stronger a stronger mid-level mid-level vorticity vorticity development development in the in EPHthe EPH experimentexperiment against against the the LOC LOC experiment. experiment. Therefore, Therefore, the the non-local non-local excess excess phase phase operator operator is ais better a better assimilationassimilation operator. operator.

Atmosphere 2020, 11, 1204 15 of 23 Atmosphere 2020, 11, x FOR PEER REVIEW 15 of 23

Figure 14. DifferencesDifferences between the excess phase operator (EPH) and local refractivity refractivity operator operator (LOC) (LOC) experiments in a time–pressure section from 72 to 0 h for Typhoon Nuri (2008) in (a) vertical velocity experiments in a time–pressure section from −72 to 0 h for Typhoon Nuri (2008) in (a) vertical velocity (colors; m s −1 ) and water vapor mixing ratio (contours; g kg −1), and (b) vertical velocity (colors; m s −1) (colors; m s− ) and water vapor mixing ratio (contours; g kg− ), and (b) vertical velocity (colors; m s− ) 5 1 and vorticity (contours, 10−5 s−−1 )[75]. and vorticity (contours, 10 s ) [75]. All the above studies prove that assimilating the RO data can promote the accuracy of TC forecast. RO dataAll the below above 6 km studies are essential prove that as they assimilating play an important the RO data role incan the promote initial stagesthe accuracy of TC genesis. of TC Theforecast. RO data RO indata the below UTLS 6 region km are have essential a positive as they influence play onan theimportant forecast role over in three the initial days owing stages to of their TC highgenesis. vertical The RO resolution. data in Throughthe UTLS the region vertical have studies a positive of TC, influence RO data on provide the forecast a more over accurate three initial days fieldowing above to their the high sea surface, vertical including resolution. su ffiThroughcient water the vertical vapor, which studies restores of TC, theRO dynamic data provide structures a more of TCsaccurate such initial as the eyewallfield above and rainthe sea bands. surface, Therefore, including the TC sufficient forecast iswater improved vapor, significantly which restores owing the to thedynamic RO measurement. structures of However,TCs such as the the current eyewall number and rain of RObands. measurements Therefore, the is insu TC ffiforecastcient. Theis improved planned missions,significantly such owing as COSMIC-2, to the RO measurement. MetOp, and FY-3, Howeve are expectedr, the current to increase number the of RO daily measurements number of RO is soundingsinsufficient. in The the planned future.This missions, will bring such remarkableas COSMIC improvements-2, MetOp, and forFY-3, TC are prediction expected [76 to]. increase the daily number of RO soundings in the future. This will bring remarkable improvements for TC 4.prediction Outlook [76]. This section introduces some new perspectives in the application of the RO technique in NWP 4. Outlook and TC forecast. It is worthwhile to exploit other potential features of the GNSS signal, particularly to increaseThis the section frequency introduces and amount some ofnew RO perspectives soundings. Therein the are application trends toward of the increasing RO technique the amount in NWP of ROand soundings TC forecast. and It expanding is worthwhile the new to exploit features other of the potential RO. Section features 4.1 illustrates of the GNSS three emergingsignal, particularly strategies to overcomeincrease the the insufrequencyfficiency and in the amount amount of of RO RO soun data,dings. including There multi-system-compatible are trends toward increasing RO receivers, the commercialamount of RO cube soundings satellite constellation,and expanding and the the new airborne features RO of technique. the RO. Section Section 4.1 4.2 illustratesintroduces three two advancedemerging strategies RO features, to overcome including the the insufficiency polarimetric ROin the technique amount andof RO multi-feature data, including receiver. multi-system- compatible RO receivers, commercial cube satellite constellation, and the airborne RO technique. 4.1.Section Trends 4.2 Towardintroduces Increasing two advanced the Amount RO offeatures, RO Soundings including the polarimetric RO technique and multi- feature receiver. 4.1.1. Multi-System-Compatible RO Receivers 4.1. TrendsThe authors Toward ofIncreasing [47] demonstrated the Amount of that RO there Soundings is no saturation in NWP, even with 128,000 RO observations assimilated. However, there may be only 18,400 soundings per day in 2027, as estimated in4.1.1. Section Multi-System-Compatible 2.2. Therefore, the frequency RO Receivers of RO soundings should be enhanced. Other than more missions,The authors a multi-system-compatible of [47] demonstrated RO that sounder there isis anno economical saturation andin NWP, efficient even strategy with 128,000 to improve RO theobservations frequency assimilated. of RO soundings. However, there may be only 18,400 soundings per day in 2027, as estimated in SectionTable3 2.2.lists Therefore, some of the the primary frequency GNSS of sounders RO soundings in operation should or in be the enhanced. planning stage. Other The than popular more TriGmissions, (Tri-GNSS) a multi-system-compatible receiver on COSMIC-2 RO andsounder GRACE is an collects economical signals and from efficient GPS andstrategy GALILEO to improve with approximatelythe frequency of 500 RO soundings soundings. per day per satellite. The next-generation, TriG (JASON-CS), can receive Table 3 lists some of the primary GNSS sounders in operation or in the planning stage. The popular TriG (Tri-GNSS) receiver on COSMIC-2 and GRACE collects signals from GPS and

Atmosphere 2020, 11, 1204 16 of 23 additional data from GLONASS, with the amount of data reaching 1000 soundings per day. According to [77], the next-generation TriG will be compatible not only with GPS, Galileo, and GLONASS, but also with BeiDou, DORIS (The Doppler Orbitography by Radio positioning Integrated on Satellite), Japan’s QZSS (Quasi-Zenith Satellite System), and IRNSS (India’s Regional Navigation Satellite Systems). Moreover, China’s GNOS (GNSS Occultation Sounder) onboard FY-3C/D is the ﬁrst BeiDou and GPS-compatible RO sounder [17–20]. With the complete deployment of BeiDou satellites, the soundings have reached 1000 soundings per day. Furthermore, the next sounder for MetOp, namely the RO Sounder, may increase the tracked GNSS constellation to three constellations. More multi-system-compatible RO receivers are required. With the development of multi-system RO receivers, a further increment in the amount of RO soundings is foreseen. As a result, this will further improve the NWP and TC forecast.

Table 3. Global navigation satellite system (GNSS) sonders (adapted from OSCAR website).

Sonder GNSS Tracked Soundings/Day Satellite Status ~500 COSMIC-2 TriG GPS, GALILEO In orbit ~600 GRACE-FO GPS, GALILEO, TriG (JASON-CS) ~1000 JASON-CS-A/B Planned GLONASS GNOS FY-3D In orbit GPS, BeiDou ~1000 GNOS-2 FY-3E/F/G/H/R Planed GRAS GPS ~650 MetOp-A/B/C In orbit GPS, Galileo, GLONASS, RO ~1100-1500 MetOp-SG-A/B Planned Beidou (2 or 3 of them) ~100 TanDEM-X In orbit IGOR GPS TerraSAR-X ~200 TSX-NG Planned ARMA-MP GPS, Galileo, GLONASS ~2000 Meteor-MP Planned TriG: Triple G (GPS, Galileo, GLONASS); GRAS: GNSS Receiver for Atmospheric Sounding; IGOR: Integrated GPS Occultation Receiver; ARMA: Radio occultation instrument for Meteor-MP.

4.1.2. Commercial Cube Satellite Constellation As discussed in Section 2.2, 16,000 soundings can be a closer target. For such a substantial number, at least one hundred satellites with RO receivers are required. Fortunately, RO receivers are inexpensive, light, small, and less power consuming. RO receivers have been additional payloads on many satellites such as CHAMP, SAC-C/D, and GRACE. This approach has been commercially applied to cube satellites (10 cm 10 cm 30 cm and 4.7 0.1 kg) by companies, such as Spire, GeoOptics, × × ± and PlanetIQ, to establish a constellation network for providing critical weather data to NWP, ship, and aircraft tracking. Here, only the part regarding NWP of our interest is introduced. Spire is one of the largest commercial producers of RO measurement systems. Up to 2019, Spire launched more than 80 nanosatellites in LEOs for full global sampling [78], and the sounder Lemur-2 on these cube satellites can receive signals from GPS, GLONASS, QZSS, and Galileo, providing approximately 6000 RO proﬁles per day. According to the initial assessment and test run in the Met oﬃce NWP system, as reported in [79], Spire’s data are as good as the operational GNSS-RO data below 30 km. The research also showed that assimilating Spire data as a replacement of MetOp-C data into the NWP system can further improve the forecast. The Climate Community Initiative for Continuing Earth Radio Occultation (CICERO) is another cube satellite constellation project designed as a follow-up and augmentation for COSMIC by GeoOptics Cooperation. Up to 2017, 48 cube satellites have been deployed in orbit [80]. If the data from these projects can be incorporated into the operational NWP assimilation systems, a considerable improvement will be seen in the accuracy of the NWP and TC forecast. Atmosphere 2020, 11, 1204 17 of 23

4.1.3. Airborne RO Technique To some extent, most of studies we reviewed were the Spaceborne RO (SRO) technique, because the receivers are onboard LEO satellites. The GNSS also has a ground-based observation, which provides its signal delays as a source of the water vapor contents for NWP, such as zenith total delay (ZTD) and integrated water vapor (IWV) [81]. However, in the case of receivers onboard aircrafts, the Airborne RO [82] technique is employed. The ARO is a solution to the shortcomings of the SRO, i.e., the insufficient observations and random temporal and spatial distributions. For instance, in the face of a target location where a TC is generated, the obtained profiles from the SRO are sparse. The ARO addresses this issue by maneuvering the aircraft to the target location and by collecting the samples several times. The drawbacks of the ARO are the less stable receiver platform and the low SNR of the current antennas. The authors of [83] used the ARO to study Hurricane Karl in 2010 and the heavy rainfall over Colorado in September 2013. The results showed improvement in the initial moisture and pressure field measurements, resulting in a better 36 h rainfall forecast. That dissertation reported that if all U.S. continental flights were to set up this receiver, the estimated RO soundings could reach 3000 every 12 h. If the drawbacks of the ARO can be solved, it will be a step forward in the application of RO in NWP and TC monitoring.

4.2. Trends Toward Expanding New Features of RO

4.2.1. Polarimetric RO Technique A new feature of the RO is the detection of heavy precipitation via polarimetric RO (PRO). Although the RO profiles have a high vertical resolution and are minimally affected by clouds and precipitation, they have a low horizontal resolution of approximately 100 km. If the horizontal resolution can be improved, it will benefit short-/medium-range weather forecasts such as rainfall and TC forecasts. The PRO technique aims to address the low horizontal resolution of RO. The approach involves deploying a closely spaced RO satellite train for a denser sampling. This strategy provides near-simultaneous observations of the water vapor proﬁles surrounding the target heavy-precipitation region. The PRO receivers launched in February 2018 are onboard the Spanish PAZ (peace in Spanish) spacecraft, and a concept-of-proof experiment has been carried out [84]. The authors of [84–86] studied the probability of the train constellation in encountering heavy-precipitation regions, and possible orbital strategies for implementing such a constellation. If the concept can be proven, the precipitation forecast can be improved. This will be conducive to the precipitation forecasts in NWP and TC monitoring.

4.2.2. Multi-Feature GNSS Receiver In addition to navigation and RO, another function of the GNSS signal is GNSS reflectometry (GNSS-R), which can be used for observing oceans, ice, soil, and other geophysical parameters. This feature is also important for TC and NWP as it provides a sufficient wind field measurement, particularly over oceans. So far, this spaceborne GNSS-R technique has been implemented in The Cyclone Global Navigation Satellite System (CYGNSS) mission [87,88], Jason-2/OSTM satellite, OceanSat-2 [89], and Disaster Monitoring Constellation (DMC) [82]. The GNOS sounder onboard FY-3E integrated the RO function and GNSS-R function in one receiver to save space and power for the satellites. Thus, the sounder measures the ionosphere, neutral atmosphere, sea wave, and wind field [24] simultaneously. In the future, multi-feature GNSS receivers will also be a trend. If more integrated receivers are developed, more RO missions will help increase the use of GNSS-R data. This will provide more atmospheric parameters for TC forecasts and NWP.

5. Conclusions As an advanced atmospheric sounding technique, RO eﬀectively complements other conventional observations owing to its unique advantages. RO measurements have contributed signiﬁcantly to Atmosphere 2020, 11, 1204 18 of 23

NWP and TC forecasts. In this paper, we mainly reviewed the applications of RO observations in NWP and TC forecasts. RO has many advantages such as global coverage, high accuracy and precision, superior vertical resolution, and full-time and all-weather observation. In terms of the contribution to NWP,RO promotes the accuracy of NWP,particularly in the southern hemisphere and poles, where most of the conventional measurements are unavailable. Through studies on the sensitivity of RO data to the height, the core region where RO data make most contribute to the NWP assimilation system was found to be in the range of 10–20 km. While accounting for only 7% of the total observations made in 2014 in the assimilation system, RO has the fourth-largest impact on NWP. Moreover, the amount of current RO data is approximately 10,000 soundings per day, far from the upper limit, i.e., 128,000 soundings per day, which means that more RO data can benefit NWP. In the future, with the amount of assimilated RO data expected to reach up to 16,000 soundings per day, the error in NWP can be reduced by 25% compared with the error in 2013, which is a considerable improvement. In the tropical cyclone monitoring field, RO represents a solution that overcomes the long-lasting problem of false or missed predictions. With the assimilation of RO data, the intensity and track predictions of the TC can be improved significantly. RO data, from both below 6 km and the UTLS region, contribute to this improvement. RO data below 6 km are critical in the initial stage of TC genesis, and the data in the UTLS positively influence the forecast over three days owing to the high vertical resolution of RO. Moreover, through an analysis of the simulated vertical structure of TCs, the essential structures could be restored, particularly the eye, eyewall, and rain bands, because the RO technique provides more accurate measurements of the initial water vapor fields and helps adjust the wind fields. Because of the high horizontal gradient of the water vapor and temperature of TC, the assimilation of RO data in such regions remains challenging. New approaches, such as the non-local excess phase operator, can partly solve this problem and further improve the TC forecast. With denser RO data expected in the future, a more accurate TC forecast can be anticipated. Finally, to better serve NWP and TC forecasts, the potentials of RO should be exploited. New RO techniques and strategies have emerged to increase the frequency of RO soundings, such as the Airborne RO technique, multi-system compatible receiver, and Cube Satellite Constellation. Moreover, the superior behaviors of RO can yield original features, such as the polarimetric RO technique to measure heavy precipitation, and the multi-feature receiver, which helps integrated RO and GNSS-R. With more RO missions and satellite launches, a consistent improvement in NWP and TC forecast can be expected. Some problems in the application of RO in NWP and TC forecast remain unresolved. First, the horizontal resolution of RO data remains low [63], approximately 100 km. Additionally, the water vapor and temperature below a height of 10 km cannot be solved independently [61], resulting in further bias in the assimilation system. There are noises in the lower troposphere (0–5 km) due to the comprehensive effect of multipath effects, super-refractivity, and receiver errors [75]. To solve these issues and increase the total number of RO missions, more advanced algorithms are required. Further development in the application of RO in NWP and TC forecast can be realized using original methods such as deep learning, machine learning, and big data [90]. These methods may improve the quality of RO data below a height of 10 km, based on the reanalysis of RO data accumulated over the past several decades. Furthermore, as RO measurements contain important parameters of the atmosphere and ionosphere, we could explore the possible relationships between space weather or stratospheric dynamics and weather forecast in the troposphere to improve NWP and TC forecast [91]. We believe that the development of RO will bring more promising results for NWP and TC forecasts.

Author Contributions: Writing—original draft/editing, W.B., N.D.; Data curation G.T., Z.L., X.L., N.D.; Resources, W.B., N.D., Y.S., C.L.; Funding acquisition, Y.S., Q.D., J.X., X.W., X.M., D.Z., C.L. All authors have read and agreed to the published version of the manuscript. Atmosphere 2020, 11, 1204 19 of 23

Funding: This research was supported by the National Natural Science Foundation of China, grant numbers 42074042, 41505030, 41606206, and 41775034; Strategic Priority Research Program of Chinese Academy of Sciences, grant number XDA15007501. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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