Benefits of a Closely-Spaced Satellite Constellation of Atmospheric Polarimetric Radio Occultation Measurements

Article Beneﬁts of a Closely-Spaced Satellite Constellation of Atmospheric Polarimetric Radio Occultation Measurements

F. Joseph Turk 1,* , Ramon Padullés 1, Chi O. Ao 1, Manuel de la Torre Juárez 1, Kuo-Nung Wang 1, Garth W. Franklin 1 , Stephen T. Lowe 1, Svetla M. Hristova-Veleva 1 , Eric J. Fetzer 1, Estel Cardellach 2,3 , Yi-Hung Kuo 4 and J. David Neelin 4 1 Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, 4800 Oak Grove Dr., Pasadena, CA 91101, USA; ramon.padulles.rullo@jpl.nasa.gov (R.P.); [email protected] (C.O.A.); [email protected] (M.d.l.T.J.); [email protected] (K.-N.W.); [email protected] (G.W.F.); [email protected] (S.T.L.); [email protected] (S.M.H.-V.); [email protected] (E.J.F.) 2 Institute of Space Sciences (ICE, CSIC), UAB Campus, Can Magrans Street, 08193 Barcelona, Spain; [email protected] 3 Institute for Space Studies of Catalonia (IEEC), Despatch 201, Nexus Building, Grand Captain, 08034 Barcelona, Spain 4 Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, CA 90095, USA; [email protected] (Y.-H.K.); [email protected] (J.D.N.) * Correspondence: [email protected]; Tel.: +1-818-354-0315

Received: 20 September 2019; Accepted: 14 October 2019; Published: 16 October 2019

Abstract: The climate and weather forecast predictive capability for precipitation intensity is limited by gaps in the understanding of basic cloud-convective processes. Currently, a better understanding of the cloud-convective process lacks observational constraints, due to the difficulty in obtaining accurate, vertically resolved pressure, temperature, and water vapor structure inside and near convective clouds. This manuscript describes the potential advantages of collecting sequential radio occultation (RO) observations from a constellation of closely spaced low Earth-orbiting satellites. In this configuration, the RO tangent points tend to cluster together, such that successive RO ray paths are sampling independent air mass quantities as the ray paths lie “parallel” to one another. When the RO train orbits near a region of precipitation, there is a probability that one or more of the RO ray paths will intersect the region of heavy precipitation, and one or more would lie outside. The presence of heavy precipitation can be discerned by the use of the polarimetric RO (PRO) technique recently demonstrated by the Radio Occultations through Heavy Precipitation (ROHP) receiver onboard the Spanish PAZ spacecraft. This sampling strategy provides unique, near-simultaneous observations of the water vapor profile inside and in the environment surrounding heavy precipitation, which are not possible from current RO data.

Keywords: convection; precipitation; moisture; GPM; GNSS; GPS; satellite constellation; cubesat; radio occultation

1. Introduction The climate and weather forecast predictive capability for precipitation intensity is limited by gaps in the understanding of basic cloud-convective processes [1]. Convection is a process by which rapidly rising buoyant air carries moisture (water vapor) from near the Earth’s surface upward, where it condenses. These convective processes are dependent on the environment, the water vapor and

Remote Sens. 2019, 11, 2399; doi:10.3390/rs11202399 www.mdpi.com/journal/remotesensing Remote Sens. 2019, 11, 2399 2 of 19 temperature vertical and horizontal structures in the surrounding region. Much of the water vapor resides in the 2 km nearest the Earth, the approximate top of the boundary layer, which is the layer where air motions are directly influenced by contact with the Earth’s surface. However, increasing evidence points to the control of deep convection by the relatively smaller and more variable amount of moisture above the boundary layer, known as the free troposphere. When abundant, free tropospheric moisture can strengthen convection by making the atmosphere more unstable. Horizontal transport and the mixing of nearby dry air (through a process known as entrainment) can weaken the convection, by decreasing the buoyancy [2,3]. Free-tropospheric moisture thus appears to exert significant control on the development of deep convection, producing heavy precipitation [4–11]. Currently, a better understanding of the cloud-convective process lacks observational constraints, due to the difficulty in obtaining accurate, vertically resolved pressure, temperature, and water vapor (denoted by p, T, and q, respectively) structure in and near convection. Infrared sensors, such as the Atmospheric Infrared Sounder (AIRS), provide water vapor structure outside of clouds and precipitation, but cannot estimate the water vapor inside clouds. Passive microwave (MW) sounding radiometers, such as the Advanced Technology Microwave Sounder (ATMS), operate in millimeter-wave (183 GHz) water vapor bands, which under heavy precipitation, are sensitive to the cloud top ice region [12], limiting their use in studies that require vertically resolved water vapor inside clouds. Passive MW radiometer satellite observations that operate in a longer wavelength water vapor band (near 22 GHz), such as the Tropical Rainfall Measuring Mission (TRMM), Microwave Imager (TMI) and similar passive MW sensors, provide a long record of total column water vapor data [13]. Global radiosonde data provides insitu measurements of the vertical (p, T and q) profile but are generally confined to over-land locations and collected near synoptic times. Ground-based Global Navigation Satellite System (GNSS) stations provide total column water vapor [14]—mostly over land—but do not measure the vertical water vapor profile. In this manuscript, the radio occultation (RO) measurement concept is proposed to address these observational shortcomings [15,16]. An RO occurs when a receiver in low-Earth orbit (LEO) views a GNSS satellite (e.g., the US Global Positioning System, GPS) as it sets or rises behind the Earth’s atmosphere. The measured signal phase and amplitude are analyzed to derive atmospheric refractivity, from which profiles of atmospheric state variables (p, q and T) are derived [17]. A unique aspect of the RO is that the L-band (near 1.4 GHz) GNSS signals suffer minimal attenuation when propagating through even the most severe precipitation events. Owing to the orbital and observation geometry, these measurements represent integrated quantities along each ~150 km propagation ray-path, which is considerably coarser than the spatial scales associated with clouds. Traditionally, RO measurements are collected from GNSS receivers onboard disparate operational and research-based LEO satellites to assimilate into global numerical weather prediction (NWP) models at each update cycle. In order to maximize and homogenize the global sampling density, no particular preference is given to one location or type of weather being observed. Using common metrics such as geopotential height anomaly correlation scores, assimilation of these RO data into NWP models has been demonstrated to lead to an improved overall forecast predictive skill [18,19]. However, the ability of these same RO observations to capture dense vertically resolved (p, T and q) profiles in and near regions of heavy precipitation may provide insight to reveal the role of free tropospheric water vapor influencing underlying cloud-convective processes [20,21]. The idea of using RO for examining the thermodynamic makeup of convective clouds is not new [22,23] and has recently been summarized [24]. In this manuscript, we describe the potential advantages of collecting time-sequential RO from a constellation (or “train”) of closely spaced low Earth-orbiting satellites tracking the same transmitting GNSS satellite. This strategy is driven by the fact that in the acrossray direction, the horizontal resolution of an RO measurement is of a much finer scale than its orthogonal alongray scale, which is essentially limited only by the effective Fresnel zone of ~1 km. A ~2minute spacecraft separation between up to five small LEO satellites would enable each RO receiver to observe the same GNSS transmitter, such that successive RO ray paths are offset Remote Sens. 2019, 11, 2399 3 of 19 from the previous and lie “parallel” to one another. When the RO train orbits near a region of heavy precipitation, there is a possibility that one or more of the RO ray paths will intersect the region of heavy precipitation, whereas others would lie outside of heavy precipitation (Figure1). Remote Sens. 2019, 11, x FOR PEER REVIEW 3 of 18

Figure 1. A graphical depiction of the closely spaced radio occultation (RO) observation strategy. In Figure 1. A graphical depiction of the closely spaced radio occultation (RO) observation strategy. In this this depiction, three polarimetric RO-receiving capable satellites orbit in formation with a time depiction, three polarimetric RO-receiving capable satellites orbit in formation with a time separation separation near two minutes. The short time separation increases the likelihood that all three satellites near two minutes. The short time separation increases the likelihood that all three satellites observe the observe the same occulting GNSS satellite, and one or more ray path profiles transects through the same occulting GNSS satellite, and one or more ray path proﬁles transects through the atmosphere atmosphere containing a region of heavy precipitation (dark grey) and the nearby environment containing a region of heavy precipitation (dark grey) and the nearby environment outside of heavy outsideprecipitation of heavy (light precipitation grey). (light grey).

The p presenceresence of heavy precipitation can can be be discern discerneded by by the the use use of the polarimetric RO RO (PRO) (PRO) techniquetechnique,, recently recently demonstrated demonstrated by by the the Radio Occultations through through Heavy Heavy Precipitation Precipitation (ROHP) (ROHP) receiver onboard the Spanish PAZ spacecraft [[2255],], which is furtherfurther detaileddetailed below.below. This sampling strategy provides unique,unique, near-simultaneousnear-simultaneous observations observations of of the the water water vapor vapor proﬁle profile inside inside and and in the in theenvironment environment surrounding surrounding heavy heavy precipitation, precipitation, which which is not is possiblenot possible from from current current RO data.RO data. Sections 22 andand3 3 describe describe the the RO RO measurement measurement requirements requirements and and a a proposed proposed PRO PRO instrument instrument suitable for small satellite investigations, respectively. Section Section 4 4 examines examines several several possible possible orbital orbital strategies for implementing such such a a c closelylosely spaced RO constellation. To To estimate how frequently RO measurements onboard a constellation “ “train”train” of orbiting satellites will encounter encounter heavy heavy precipitation precipitation inin nature, nature, orbital orbital simulation simulation experiments experiments were were carried carried out out where where the RO the ray RO paths ray paths from a from four-satellite a four- satelliteconstellation constellation were superimposed were superimposed on actual 30minuteon actual precipitation30minute precipitation ﬁelds from thefields Global from Precipitation the Global PrMeasurementecipitation Measurement (GPM) [26] Integrated (GPM) [26 Multi-satellitE] Integrated Multi Retrievals-satellitE for Retrievals GPM (IMERG) for GPM precipitation (IMERG) precipitationproduct [27]. product [27].

2. RO RO Measurement Measurement R Requirementsequirements During a ann RO RO,, t thehe transmitted GNSS signal undergoes refractive bending bending,, causing a phase shift inin the the signal signal due due to to variations variations of of the the atmospheric atmospheric refractive refractive index. index. Atmospheric Atmospheric refractivity refractivity is is directly directly related to the density of the atmosphere (temperature (temperature and and pressure) pressure) and and its its water water vapor vapor conte content.nt. Typically, anan RORO receiverreceiver trackstracks two GNSS carrier frequencies (denoted L1 and L2) to separate the dispersive ionospheric ionospheric delay delay from from the the non-dispersive non-dispersive atmospheric atmospheric delay delay (refractive (refractive index-based index-based delay delayinduced induced by the by tropospheric the tropospheric constituents). constituents). For GPS, For L1GPS,= 1.57542 L1= 1.57542 GHz GHz and L2and= L2=1.22760 1.22760 GHz. GHz. The key measurement required from a GNSS GNSS-RO-RO instrument is a time series of phase delays relative to an initial arbitrary phase. Knowing Knowing the the precise precise positions positions and clock clock drifts of of the the transmitter transmitter and receiver, the receiver phase delays are converted to excess phase delay due to the atmo atmospheresphere as the ray paths cut through successive atmospheric layers [[1717].]. The a atmospherictmospheric refractive refractive index index is obtained successively from each layer from top to bottom, like peeling an onion [1616].]. The theoretical vertical resolution of the retrieval is limite limitedd by diffraction diffraction within the atmosphere and estimated to be ~60 m [[24]24].. In practice, measurement noise noise limits limits the obtainable vertical resolution resolution to to ~200 m in the lower troposphere [28,29], providing a horizontal resolution in the range of ~100 km, sufficient for the synoptic scale structures addressed in Section 1. In the low to middle troposphere (below ~10 km altitude in the tropics), the relevant altitude range for the free troposphere, retrieval of water vapor profile requires a priori information on temperature [16,30]. Given the reasonable estimates of the temperature and refractivity uncertainties, tropospheric specific humidity can be determined to within 0.5 g/kg per profile [31–33]. Remote Sens. 2019, 11, 2399 4 of 19 lower troposphere [28,29], providing a horizontal resolution in the range of ~100 km, sufficient for the synoptic scale structures addressed in Section1. In the low to middle troposphere (below ~10 km altitude in the tropics), the relevant altitude range for the free troposphere, retrieval of water vapor profile requires a priori information on temperature [16,30]. Given the reasonable estimates of the temperature and refractivity uncertainties, tropospheric specific humidity can be determined to within 0.5Remote g/kg Sens. per 2019 profile, 11, x FOR [31– PEER33]. REVIEW 4 of 18

2.1. Polarimetric RO Concept However, conventional RO provides no unique capability for distinguishing the presence or absence of of precipitation precipitation along along each each RO RO ray ray path path.. A large A large collection collection of close of close-time-time coincidences coincidences of RO of- RO-basedbased soundings soundings with with Tropical Tropical Rainfall Rainfall Measuring Measuring Mission Mission (TRMM) (TRMM) Precipitation Precipitation Radar Radar (PR) (PR)and andCloudSat CloudSat radar radar observations observations was was examined examined by by [34] [34 to] to differentiate diﬀerentiate the the vertical vertical distribution of atmospheric layers layers stable stable to convection to convection during during precipitating precipitating events. In eventsthis manuscript,. In this a combinationmanuscript, ofa suchcombination RO soundings of such with RO thesoundings polarimetric with ROthe (PRO)polarimetric concept RO is proposed(PRO) concept for directly is proposed distinguishing for directly RO proﬁlesdistinguishing whose propagation RO profiles ray whose paths propagation traverse regions ray paths of heavy traverse precipitation regions (Figure of heavy2), characterized precipitation by(Figure increasingly 2), characterized larger numbers by increasingly and sizes of larger aspherical number (oblate-shaped)s and sizes of hydrometeors aspherical (oblate as the-shaped) rainfall ratehydrometeors increases. as the rainfall rate increases.

Figure 2. 2. AA depiction depiction of of the the polarimetric polarimetric RO RO measurement measurement concept. concept As the. As right-hand the right- circularlyhand circularly (RHC) polarized(RHC) polarized transmitted transmitted GNSS signal GNSS propagates signal propagates through a region through of heavy a region precipitation of heavy characterized precipitation bycharacterized aspherical hydrometeors,by aspherical hydrometeors, an orthogonal (i.e.,an orthogonal cross-polarized) (i.e., cross left-hand-polarized) circularly left (LHC)-hand polarizedcircularly component(LHC) polarized is induced. component The co-is induced. and cross-polarized The co- and signalscross-polarized are measured signals by are a GNSSmeasured receiver by a atGNSS two linearreceiver (horizontal at two linear and (horizontal vertical, denoted and vertical H and, V)denoted orthogonal H and polarizations. V) orthogonal polarizations.

PRO enhances standard RO by observing the GNSS signals signals in in two two orthogonal orthogonal polarizations polarizations [3 [355].]. The co- co- and and cross-polarized cross-polarized radio radio signals signals propagating propagating through through heavy precipitation heavy precipitation media will media experience will diexperiencefferent phase different delays phase(phase delaysdelay is ( denotedphase delay by φ ), is measurable denoted by by 휙 the), receiver’smeasurable polarimetric by the receiver’s antenna. Realisticpolarimetric scattering antenna. simulations Realistic scattering performed simulations using collocated performed COSMIC using RO collocated and TRMM COSMIC precipitation RO and retrievalsTRMM precipitation have shown thatretrievals the phase have di shownfference that between the phase the horizontally difference (H)between and vertically the horizontally (V) polarized (H) 1 signalsand vertically (defined (V) as polarized∆φ) is large signals enough (defined to detect as ∆ a휙 path-averaged) is large enough rain to rate detect exceeding a path 2-averaged mm h− withrain overrate exceeding 70% probability 2 mm [ 35hr].-1 with The PROover concept 70% probability has recently [35 been]. The proven PRO concept by the ROHP has recently instrument been onboard proven theby the Spanish ROHP PAZ instrument satellite launchedonboard the in February Spanish PAZ 2018, satellite a proof-of-concept launched in experiment February 2018 [25,36, a]. proof Further-of- calibrationconcept experiment and validation [25,36]. accounting Further calibration for the antenna and validation pattern, accounting Faraday eff ectsfor the and antenna other factors pattern, is detailedFaraday ineffects [37]. and other factors is detailed in [37]. As an example of ROHP data in the presence and absence of heavy precipitation, Figure3 3 shows shows fivefive ROHPROHP observationsobservations (labeled (labeled A A through through E) E) on on 23 23 May May 2018 2018 near near tropical tropical cyclone cyclone Mekunu. Mekunu. Large Large∆φ exceeding∆휙 exceeding 25 mm 25 weremm obtainedwere obtained up to 10 up km to in 10 height km in regionsheight associated in regions with associated heavy precipitation with heavy precipitation surrounding the eyewall near 55E/10N (label A), whereas regions of no precipitation (labels B, C and D) exhibit no significant ∆휙 anywhere in the profile. ∆휙 near 10 mm (label E), associated with thin cold clouds, suggests that ROHP may also be sensitive to frozen crystalline ice shapes, similar to the differential phase observed by the ground-based polarimetric radars [38]. Remote Sens. 2019, 11, 2399 5 of 19 surrounding the eyewall near 55E/10N (label A), whereas regions of no precipitation (labels B, C and D) exhibit no significant ∆φ anywhere in the profile. ∆φ near 10 mm (label E), associated with thin cold clouds, suggests that ROHP may also be sensitive to frozen crystalline ice shapes, similar to the

Remotediﬀerential Sens. 2019 phase, 11, x observed FOR PEER byREVIEW the ground-based polarimetric radars [38]. 5 of 18

Figure 3. ROHP observations onon MayMay 23,23, 20182018 in in the the presence presence of of tropical tropical cyclone cyclone Mekunu Mekunu (Category (Category 3). The3). The tangent tangent point point location location and and ray orientationray orientation of five of ROHPfive ROHP observations observations are represented are represented by the by circle the circlesymbol symbol and the and thick the blue thick line. blue The line five. The insets, five correspondinginsets, corresponding to each Radio to each Occultations Radio Occultations through throughHeavy Precipitation Heavy Precipitation (ROHP) ( observation,ROHP) observation, show the show measured the measured H-V diff Herential-V differential phase shift phase in shift mm asin mma function as a function of height of (green),height (green) alongside, alongside the profile the ofprofile temperature of temperature (orange) (orange) and water andvapor water partialvapor pressurepartial pressure (blue) obtained (blue) obtained from PAZ from at thePAZ same at the time. same Large time polarimetric. Large polarimetric phase di ffphaseerences differences were obtained were obtainedup to a 10 up km to height a 10 km from height the ROHP from observations the ROHP observations in regions associated in regions with associated heavy precipitation with heavy precipitationsurrounding thesurrounding eyewall near the 55Eeyewall/10N. near Regions 55E/10N of no. Regions precipitation of no nearprecipitation 40E/3S show near no40 significantE/3S show nosignal. significant The background signal. The colorbackground represents color the represents observed the geostationary observed geostationary satellite infrared satellite brightness infrared brightnesstemperature temperature (Kelvin), which (Kelvin) is shown, which as is a shown proxy as for a cloud proxy top for heightcloud and top height associated and convective associated precipitationconvective precipitation intensity. intensity.

The locations locations of of strong strong convection convection and and associated associated heavy heavy precipitation precipitation have have implications implications for the for orbitalthe orbital design design strategy strategy outlined outlined in Section in Section 3. ROHP3. ROHP is currently is currently (late (late 2019) 2019) providing providing about about 200 observations200 observations per perday. day. To Toshow show geographically geographically where where the the strongest strongest observed observed ∆∆휙φ occuroccur and and how how this correlates withwith known known precipitation precipitation climatologies, climatologies Figure, Figure4 shows 4 shows the locations the locations of the upper of the percentile upper (upperpercentile 2%) (upper of ROHP 2%) observationsof ROHP observations that results that after results∆φ isafter averaged ∆휙 is averaged from the from RO rays the RO whose rays tangent whose pointtangent intercepts point intercept three disff threeerent different vertical regions vertical (0–5, regions 5–10 (0 and–5, 5 10–15–10 and km 10 height).–15 km Theheight) top. panel The top includes panel includesonly data only from data June–July–August from June–July (JJA),–August and the (JJA) lower, and panel the from lower December–January–February panel from December–January (DJF).– TheFebruary color (DJF). background The color map background depicts the map average depicts rain the rate average during rain these rate months during derived these m fromonths the derived GPM fromIMERG the precipitation GPM IMERG product. precipitation During product JJA, there. During is a good JJA, agreement there is a ofgood<∆ φagreement> in the 10–15 of <Δϕ> km regionin the (red10–15 symbols) km region with (red known symbols) areas with of convection, known areas notably of convection, the Maritime notably continent, the Maritime the Pacific continent, Intertropical the PacificConvergence Intertropical Zone (ITCZ) Convergence and the African Zone (ITCZ Sahel.) and During the DJF, African the maximum Sahel. During shifts DJF to the, the Amazon maximum and shiftsthe Western to the PacificAmazon Ocean. and the The Western strong precipitation Pacific Ocean. in theThe 0–5 strong km layers precipitation (black colors) in the is 0 not–5 km restricted layers (blackto the tropics,colors) is but not also restricted captures to heavythe tropics but shallow, but also oceanic captures rain heavy events but below shallow 40S oceanic latitude, rain and events cold below 40S latitude, and cold season precipitation poleward of 50 degree latitude (RO events poleward of 60 degrees latitude are not shown since their location lies outside the range of the IMERG product). Remote Sens. 2019, 11, 2399 6 of 19

season precipitation poleward of 50 degree latitude (RO events poleward of 60 degrees latitude are not Remoteshown Sens. since 2019 their, 11, x locationFOR PEERlies REVIEW outside the range of the IMERG product). 6 of 18

FigureFigure 4. 4. TheThe g geographicaleographical distribution distribution of of the the upper upper percentile percentile (top (top 2 2%)%) of the measured ∆휙φ fromfrom all all ROHPROHP observations observations between between 60S 60S and and 60N 60N latitudes latitudes.. Each Each color color denotes denotes a avertical vertical region region where where the the ∆∆휙φ fromfrom all all rays rays were were averaged averaged.. Black, Black, orange orange and and red red symbols symbols represent represent cases cases where where the the average average ∆∆휙φ waswas obtained obtained by by averaging averaging all all RO RO rays rays whose whose tangent tangent point point lies lies between between 0 0–5,–5, 5 5–10–10 and and 10 10–15–15 km km height,height, respectively. respectively. The The top top panel panel includes includes all all data data for for June June–July–August–July–August (JJA); (JJA); the the lower lower panel panel for for DecemberDecember–January–February–January–February (DJF) (DJF).. The The color color background background map map de depictspicts the the average average rain rain rate rate during during thesethese months months derived derived from from the the GPM GPM IMERG IMERG precipitation precipitation product. product. 2.2. The Cion RO Receiver 2.2. The Cion RO Receiver Early RO-based satellites such as the FORMOSAT-3/COSMIC RO constellation carried the IGOR Early RO-based satellites such as the FORMOSAT-3/COSMIC RO constellation carried the IGOR (Integrated GPS Occultation Receiver) GNSS receiver, which is based on the BlackJack receiver designed (Integrated GPS Occultation Receiver) GNSS receiver, which is based on the BlackJack receiver at JPL, and flown on such missions as PAZ, CHAMP, SAC-C, and GRACE. The recently deployed designed at JPL, and flown on such missions as PAZ, CHAMP, SAC-C, and GRACE. The recently (June 2019) six-satellite COSMIC-2 constellation [39] carries the TriG GNSS receiver (the name implies deployed (June 2019) six-satellite COSMIC-2 constellation [39] carries the TriG GNSS receiver (the the first letter of each of three common GNSS systems, namely GPS, Galileo and GLONASS), the name implies the first letter of each of three common GNSS systems, namely GPS, Galileo and follow-on to BlackJack [40]. However, IGOR or TriG are much too large to be flown on small satellites, GLONASS), the follow-on to BlackJack [40]. However, IGOR or TriG are much too large to be flown such as a 6U cubesat. on small satellites, such as a 6U cubesat. Recently, a low-cost, low-power, and low-mass GNSS receiver (Cion) was developed at JPL [41]. Recently, a low-cost, low-power, and low-mass GNSS receiver (Cion) was developed at JPL [41]. The Cion receiver was designed for two commercial firms, Tyvak and GeoOptics, for use in the GeoOptics The Cion receiver was designed for two commercial firms, Tyvak and GeoOptics, for use in the CICERO (Community Initiative for Continuing Earth Radio Occultation) constellation [42]. Cion uses GeoOptics CICERO (Community Initiative for Continuing Earth Radio Occultation) constellation a commercial off-the-shelf (COTS) computer along with existing space-qualified RF downconverters, [42]. Cion uses a commercial off-the-shelf (COTS) computer along with existing space-qualified RF software, and firmware to produce the precise timing needed to generate RO profiles (Figure5). downconverters, software, and firmware to produce the precise timing needed to generate RO The Cion is capable of recording both setting and rising occultations, and the processing uses the profiles (Figure 5). The Cion is capable of recording both setting and rising occultations, and the processing uses the open-loop (OL) tracking implemented in the receivers for COSMIC and COSMIC- 2 for extended water vapor profiling through the moist lower troposphere [43]. A JPL version of the Cion receiver suitable for NASA small satellite missions has been designed and is currently being built for the SigNals of Opportunity P-band Investigation (SNOOPI) In-Space Validation of Earth Remote Sens. 2019, 11, 2399 7 of 19 open-loop (OL) tracking implemented in the receivers for COSMIC and COSMIC-2 for extended water vaporRemote Sens. profiling 2019, 11 through, x FOR PEER the moistREVIEW lower troposphere [43]. A JPL version of the Cion receiver suitable7 of 18 for NASA small satellite missions has been designed and is currently being built for the SigNals Science Technologies (InVEST) mission and for the Navigation Technology Satellite (NTS-3), a of Opportunity P-band Investigation (SNOOPI) In-Space Validation of Earth Science Technologies technology demonstration for the next-generation GNSS transmitter. It has also been proposed for (InVEST) mission and for the Navigation Technology Satellite (NTS-3), a technology demonstration numerous other missions, primarily in conjunction with other observations that require precise time for the next-generation GNSS transmitter. It has also been proposed for numerous other missions, tags at the level of a few picoseconds. A follow-on NASA Instrument Incubator Program (IIP) called primarily in conjunction with other observations that require precise time tags at the level of a few Genesis is building on this design to enable a next-generation GNSS reflections receiver for small picoseconds. A follow-on NASA Instrument Incubator Program (IIP) called Genesis is building on this satellites as well. design to enable a next-generation GNSS reflections receiver for small satellites as well.

FigureFigure 5.5. A picture of the Cion RO receiver instrument flyingflying onboard the CICERO 6U-sized6U-sized cubesatscubesats (right),(right), shown shown alongside alongside the the size size of the of thelarger larger TriG TriG receiver receiver (left) flying (left) onboard flying onboard each of the each six of satellites the six insatellites the COSMIC-2 in the COSMIC constellation.-2 constellation. 3. Results 3. Results To estimate how frequently RO measurements from a constellation of low Earth-orbiting satellites To estimate how frequently RO measurements from a constellation of low Earth-orbiting will encounter heavy precipitation in nature, orbital simulation experiments were carried out where satellites will encounter heavy precipitation in nature, orbital simulation experiments were carried the RO ray paths were superimposed on the nearest 30minute GPM IMERG precipitation product [27]. out where the RO ray paths were superimposed on the nearest 30minute GPM IMERG precipitation A number of different orbit scenarios were examined, varying the number of satellites, orbital altitudes product [27]. A number of different orbit scenarios were examined, varying the number of satellites, and inclinations, and the relative time separation between satellites in the constellation configuration. orbital altitudes and inclinations, and the relative time separation between satellites in the For brevity, one such configuration (three satellites) is described in Section 3.1, with summaries of constellation configuration. For brevity, one such configuration (three satellites) is described in findings for other orbit scenarios described in Section 3.2. Section 4.1, with summaries of findings for other orbit scenarios described in Section 4.2. 3.1. Three-Satellite Constellation 3.1. Three-Satellite Constellation This simulation consists of an LEO constellation of three satellites orbiting in a 45-degree inclination planeThis at an simulation elevation of consists 500 km. of The an three LEO satellites constellation are separated of three by satellites two minutes. orbiting Each insatellite a 45- carriesdegree ainclination polarimetric-capable plane at an ROelevation receiver of with 500 akm. receiving The three antenna satellites capable are ofseparated collecting by GNSS two minutes telemetry. Each data satellite carries a polarimetric-capable RO receiver with a receiving antenna capable of collecting within a 45◦ antenna azimuth range (relative to boresight), capable of tracking both rising and setting occultationsGNSS telemetry from data the GPSwithin and a 45° GLONASS antenna satellites.azimuth range Each (relative RO is characterized to boresight) by, capable the location of tracking of the tangentboth rising point and when setting the occultations straight line from between the GPS the and transmitter GLONASS and satellite the receivers. Each is RO 100 is km characterized below the surface,by the location corresponding of the tangent roughly point to a when ray grazing the straight the surface. line between For the the purpose transmitter of this and study, the thereceiver choice is of100 straight-line km below the tangent surface height, corresponding is unimportant roughly since to athe ray locationsgrazing the of surface simulated. For RO the dopurpose not depend of this sensitivelystudy, the choice on the height.of straight-line tangent height is unimportant since the locations of simulated RO do notThe depend RO captured sensitively by these on the three height satellites. have been simulated for 30 consecutive days and then repeatedThe RO to complete captured aby full these year. three A precessionsatellites have of been3 deg simulated/day is included for 30 consecutive in the simulations days and of then the − satellite’srepeated to orbits complete to obtain a full a realistic year. A samplingprecession over of the-3 deg/day Earth. With is included this configuration, in the simulations around of 1.2E6 the occultationssatellite’s orbits are to obtained obtain a over realistic the coursesampling of oneover year. the Earth. Note thatWith this this quantityconfiguration, stands around for possible 1.2E6 occultations,occultations arebut obtainedno spacecraft over duty the course cycle nor of processingone year. Note losses that are this taken quantity into account. stands An for RO possibleevent isoccultations, defined as abut clustered no spacecraft group ofduty near-simultaneous cycle nor processing occultations, losses are which taken happen into account. when theAn diROff erentevent is defined as a clustered group of near-simultaneous occultations, which happen when the different satellites obtain an RO from the same GNSS transmitter. Such events can be complete (the three satellites capture an RO from the same transmitter within a few minutes), or non-complete (one or two of the three satellites miss or truncate an RO tracking opportunity). This latter condition typically happens when the transmitted GNSS ray path is oriented in such a way that it is received near the Remote Sens. 2019, 11, 2399 8 of 19 satellites obtain an RO from the same GNSS transmitter. Such events can be complete (the three satellites capture an RO from the same transmitter within a few minutes), or non-complete (one or twoRemote of Sens. the 2019 three, 11 satellites, x FOR PEER miss REVIEW or truncate an RO tracking opportunity). This latter condition typically8 of 18 happens when the transmitted GNSS ray path is oriented in such a way that it is received near the edge ofedge the of antenna the antenna pattern pattern (e.g., >(e.g.,45◦ antenna >45° antenna azimuth), azimuth and) the, and occultation the occultation falls outside falls outside the azimuth the azimuth cutoff threshold,cutoff threshold as implemented, as implemented in the occultation in the occultationscheduler. Considering scheduler. eventsConsidering instead events of individual instead ROs, of overindividual one year, ROs, 400,000 over eventsone year are, captured,400,000 events and 97% are ofcaptured, these are and complete 97% of events these (i.e., are allcomplete three satellites events capture(i.e., all three an RO satellites from the capture same GNSS an RO transmitter). from the same GNSS transmitter). A sample ofof wherewhere thesethese clustersclusters of of RO RO appear appear when when projected projected onto onto the the Earth Earth is is shown shown in in Figure Figure6, where6, where only only those those RO eventsRO events that havethat have crossed crossed the extreme the extreme precipitation precipitation are shown. are shown Heavy.and Heavy extreme and precipitationextreme precipitation is defined is defined when the when cumulative the cumulative differential differential phase shift phase (defined shift (defined as ∆φ) as exceeds ∆휙) exceeds 2 mm and2 mm 6 mm, and respectively 6 mm, respectively (discussed (discussed further in further Section in 3.1.1 Section). In this 4.1.1.). one-day In this scenario, one-day 1173 scenario, (about 0.1%1173 of(about thetotal) 0.1% eventsof the total) are shown. events are Note shown. that the Note RO that locations the RO from locations this trainfrom ofthis satellites train of tendsatellites to clump tend together,to clump increasingtogether, increasing the likelihood the likelihood that one or that more one observations or more observations fall inside andfall inside outside and the outside regions the of heavyregions precipitation. of heavy precipitation.

Figure 6.6. The l locationocation of the RO tangent points for the events where thethe intersectedintersected precipitationprecipitation induced a propagation cumulative differential diﬀerential phase shift ( ∆Φ) )> >66 mm.mm. The didifferentﬀerent colorscolors indicate each lowlow earth-orbitingearth-orbiting (LEO)(LEO) satellite, satellite, where where LEO LEO=1= 1 (blue) andand LEOLEO=3= 3 (green) (green) are are the leading and trailing satellitesatellite inin thethe constellation,constellation, respectively.respectively.

Further analysisanalysis of Figure 66 shows shows that that this this configurationconfiguration yields yields eventsevents with with di differentfferent RO orientation geometries. Depending Depending on on the the location of the transmitter and the azimuth at which the signal arrives to the receiver receiver,, the separation distance between the three RO tangent points can change, change, as well as the time didifferencefference separatingseparating eacheach ofof thethe ROs.ROs. This condition can be exploited to achieve sampling of convection and itsits environmentenvironment overover aa rangerange ofof separations.separations. The distribution of these separations is further explored explored i inn Figure Figure 7. Figure 77a (a) showsshows the the frequency frequency distribution distribution (histograms) (histograms) of the distance between between the the RO RO tangent tangent points points obtained obtained by by two two different different combinations combinations of ofsatellites satellites in inthe the train train (first (first versus versus second second and and first first versus versus third), third), and and Figure Figure 7 7(b)b showsshows thethe histogramhistogram ofof thethe corresponding time didifference.fference. It can be seen how the most frequent distance separation between the firstfirst and the third RO lies around 100 km for thethe consecutiveconsecutive satellites, and around 200 km for the furthest ones, although these separationsseparations areare distributeddistributed overover aa widewide rangerange ofof distances.distances. Remote Sens. 2019, 11, 2399 9 of 19 Remote Sens. 2019, 11, x FOR PEER REVIEW 9 of 18

Figure 7. ((a)) Histogram of of the the distance distance (km) (km) between the the tangent tangent point point locations locations of of the the RO RO acquired with the first first and second satellite of the train train constellation constellation (blue), and with the first first and third satellites (orange). (b ()b )Same Same as asleft left panel, panel, but but for forthe thetime time difference difference (seconds) (seconds) between between the RO the tangent RO tangent point locations.point locations.

A similar situation happens with the time separation. Notice that al althoughthough the time separation between the satellites is two minutes, the the time time difference difference between the corresponding acquired RO i iss not necessarily twotwo (or(or fourfour forfor the the ones ones in in the the edges) edges) minutes, minutes due, due to theto the relative relative motion motion between between the theGNSS GNSS and and the receivingthe receiving satellites. satellite Thes. mostThe most frequent frequent time ditimefference difference between between the first the and first the and second the secondis around is around 140 s, while 140 s between, while between the first the and first the and third the RO third is around RO is around 280 s. 280 s. 3.1.1. Representation of Precipitation at RO Observation Times 3.1.1. Representation of Precipitation at RO Observation Times Superimposing the RO events simulated above on actual coincident precipitation data allows Superimposing the RO events simulated above on actual coincident precipitation data allows for a physically realistic characterization of the number of cloud structures associated with heavy for a physically realistic characterization of the number of cloud structures associated with heavy precipitation that will be sampled per year, such that the constellation will be able to provide RO precipitation that will be sampled per year, such that the constellation will be able to provide RO soundings inside and nearby heavy precipitation almost simultaneously. Following the detectability soundings inside and nearby heavy precipitation almost simultaneously. Following the detectability threshold proposed by Cardellach et. al. [35], a precipitation detection threshold of ∆φ > 1.5 mm is set. threshold proposed by Cardellach et. al. [35], a precipitation detection threshold of ∆휙 > 1.5mm is This detection threshold has been confirmed with ROHP data as a conservative threshold for rays with set. This detection threshold has been confirmed with ROHP data as a conservative threshold for rays a tangent point height of ~2 km [25,37]. In Padullés et. al. [37], detectability was defined as vertical with a tangent point height of ~2 km [25,37]. In Padullés et. al. [37], detectability was defined as averages of ∆φ, but since IMERG is providing only surface precipitation, for the purpose of this study, vertical averages of ∆휙, but since IMERG is providing only surface precipitation, for the purpose of a single ray close to the surface is assumed to represent the precipitation conditions at the time of this study, a single ray close to the surface is assumed to represent the precipitation conditions at the the RO. time of the RO. In the following discussion, the definition of “outside precipitation” is better expressed as In the following discussion, the definition of “outside precipitation” is better expressed as “undetected precipitation” (i.e., when ∆φ < 1.5 mm) for the purposes of this study. This is because one “undetected precipitation” (i.e., when ∆휙 < 1.5 mm) for the purposes of this study. This is because is not able to completely rule out the possibility that there is precipitation present when the ∆φ that is one is not able to completely rule out the possibility that there is precipitation present when the ∆휙 induced is below the instrument detectability threshold [37]. that is induced is below the instrument detectability threshold [37]. For the computation of the full end-to-end contributions to ∆φ along each ray path, [36] carried For the computation of the full end-to-end contributions to ∆휙 along each ray path, [36] carried out scattering computations using the T-matrix approach for liquid- and solid-phase precipitation. out scattering computations using the T-matrix approach for liquid- and solid-phase precipitation. Since IMERG only provides surface precipitation, to calculate the precipitation-induced ∆Φ in a Since IMERG only provides surface precipitation, to calculate the precipitation-induced  in a computationally efficient fashion, a simplified power-law equation that relates the rain rate (R) to the computationally efficient fashion, a simplified power-law equation that relates the rain rate (R) to the specific differential phase shift (KDP) at the GNSS L-band frequency (1.575 GHz) was derived [44] and specific differential phase shift (퐾퐷푃) at the GNSS L-band frequency (1.575 GHz) was derived [44] and is as follows: is as follows: b KDP = cR (1) 퐾 = 푐푅푏 (1) 퐷푃 1 1 where c = 0.00868 and b = 1.218, R is in mm hr− and KDP is in units of deg km− . The rain rates -1 -1 whereprovided c= 0.008 by IMERG68 and areb= 1.2 interpolated18, R is in mm into hr the and representative 퐾퐷푃 is in units RO ray,of deg which km is. The simulated rain rate bys aprovided straight byline IMERG of 300 kmare (i.e.,interpolated 150 km on into either the siderepresentative of the tangent RO ray, point which in the is azimuthal simulated direction by a straight between line the of 300 km (i.e., 150 km on either side of the tangent point in the azimuthal direction between the GNSS GNSS satellite and the RO receiver). KDP is integrated along the ray path to obtain ∆φ. satellite and the RO receiver). KDP is integrated along the ray path to obtain ∆휙. Remote Sens. 20192019, ,1111, ,x 2399 FOR PEER REVIEW 10 of 1810 of 19

To use a single straight-line ray is a simplification of the actual ray paths that result as the receivingTo use and a singletransmitting straight-line satellites ray occult is a simpliﬁcation each other. In of thereality, actual the ray set paths of RO that rays result do not as thecreate receiving a andperfect transmitting vertical plane satellites while occult descend eaching other. deeper In into reality, the theatmosphere, set of RO raysbut rather do not a createslant collection a perfect verticalof planerays that while follow descending the geometry deeper created into the by atmosphere, the relative but motion rather of a slant the receiver collection with of rays respect that to follow the the geometrytransmitter. created In Figure by 8 the, anrelative RO event motion captured of theby three receiver satellites with is respect shown to in the Figure transmitter. 8 (a), where In Figuretwo 8, anof the RO observations event captured intersect by three precipitation satellites is, while shown the in Figurethird is8 a,sounding where two outside of the of observations the precipitation intersect precipitation,structure. while the third is sounding outside of the precipitation structure.

Figure 8. 8. AA simulated simulated three three-satellite-satellite RO ROorbit orbit scenario, scenario, superimposed superimposed upon n uponearest nearest 30 minu 30te IMERG min IMERG precipitation pattern. pattern. (a) (a )Representation Representation of of an an event event where where two two of the of the RO RO observations observations (RO (RO-1-1 and andRO- RO-2; 2;green green and and orange, orange, respectively) respectively) provide provide profiles profiles that that intersect intersectprecipitation, precipitation, whilewhile aa thirdthird (RO-3;(RO-3; blue) blue)profiles profiles the environment the environment outside outside of the of precipitating the precipitating structure. structure. The The colored colored rays rays represent represent a realistic a realisticrepresentation representation of RO rays of RO generated rays generated with a with ray-tracer a ray-tracer and are and positioned are positioned here forhere illustration for illustration purposes. purposes.Only the portionOnly the of portion the rays of the below rays 6below km is 6 shown.km is shown. For each For RO,each theRO, associatedthe associated “X” “ symbolX” symbol depicts depictsthe location the location of the tangentof the tangent point. point. The black The black dashed dashed line showsline shows a single a single simplified simplified 300 300 km km ray ray used to usedcharacterize to characterize each RO. each (b RO.) The (b) same The s ROame event RO event as (a as), depicting(a), depicting the the diff differenceerence that that the the relative relative angle angle(α) between () between the azimuth the azimuth on the on surfacethe surface and and the the along-track along-track occultations occultations has has from from the the geometry geometry of the of the observations. In this event, the angle is almost 90, with an across-RO separation (denoted by observations. In this event, the angle is almost 90◦, with an across-RO separation (denoted by d) of d)about of about 100 100 km. km (c). ( Thec) The same same as as ( b(b),), but but aa different different RO RO event event where where the the relative relative angle angle () is (α around) is around 10. The effective distance deff between the rays is reduced to near 20 km, even though the separation 10◦. The effective distance deff between the rays is reduced to near 20 km, even though the separation between the the tangent tangent points points d dremain remain nearly nearly the the same same as event as event (b). ( b).

A realistic realistic representation representation of ofthe the RO RO ray ray projection projection onto onto the Earth the Earth surface surface is shown is shown in Figure in Figure8 (a) 8a (colored(colored collection collection of of rays) rays),, in in addition addition to tothe the simplified simplified 300 300 km kmray rayfor each for each RO (black RO (black dashed dashed line). line). The realistic rays rays are are generated generated using using actual actual ray ray-tracing-tracing from from the theretrievals retrievals of a ofreal a realRO observation RO observation that occurred in a different location and time, and have been transported here for illustration that occurred in a different location and time, and have been transported here for illustration purposes. purposes. Only the portion of these rays that lie below 6 km are shown, which are the portions that Only the portion of these rays that lie below 6 km are shown, which are the portions that are more are more likely to be affected by precipitation. Therefore, the shortest colored rays (in this case, the likely to be affected by precipitation. Therefore, the shortest colored rays (in this case, the ones closer ones closer to the N-W corner of Figure 8) represent the highest rays (shorter portions of them are to the N-W corner of Figure8) represent the highest rays (shorter portions of them are below 6 km), below 6 km), while the longest represent the rays closer to the surface (Figure 9). while the longest represent the rays closer to the surface (Figure9). Remote Sens. 2019, 11, x 2399 FOR PEER REVIEW 11 of 18 19

Figure 9. 9. AA depictiondepiction of of the the horizontal horizontal extent extent of the of rays the correspondingrays corresponding to RO rayto RO paths ray whose paths bending whose bendingfalls below fall as ﬁxedbelow height a fixed (shown height here(shown at 6 here km). at The 6 km). lower The rays lower project rays a project longer horizontala longer horizontal distance distancerelative torelative upper to rays. upper rays.

Another quantity to take into consideration is the angle between the projection on the surface of the along along-ray-ray direction and the line joining the different different satellite tangenttangent pointspoints ((α).). In the the right right panels panels of F Figureigure 8, th thisis angle angle α isis defined defined as as the the angle angle between between any any of the of thedashed dashed lines lines and andthe gray the grayline. line.The topThe and top bottom and bottom right right panels panels in Figure in Figure 8 (8a8 and(Figure 8b) 8highlighta,b) highlight the importance the importance of such of an such angle: an angle: in the topin the panel top,  panel, is aroundα is around 90 and 90 the◦ and distance the distance between between the rays theremains rays remainssimilar to similar the distance to the between distance tangentbetween points, tangent while points, in while the bottom in the bottom panel, panel, where where  < 10α<, the10◦ , effective the effective distance distance between between rays rays is significantlyis significantly reduced. reduced. Such Such effective effective distance distance is isdefined defined as as the the distance distance between between rays rays following following a perpendicular line line:: de f f = d cos(90 α) (2) 푑푒푓푓 = 푑 cos(90−− 훼) (2) where d is the distance between tangent points. where d is the distance between tangent points. 3.1.2. Near-Simultaneous RO Inside and Outside of Heavy Precipitation 3.1.2. Near-Simultaneous RO Inside and Outside of Heavy Precipitation The example presented in Figure8 highlights the case where there is (at least) one RO sounding insideThe heavy example precipitation presented andin Figure (at least) 8 highlights one sounding the case outside, where there the occurrences is (at least) one of whichRO sounding permit insidethe analysis heavy ofprecipitation relationships and between (at least) soundings one sounding inside outside heavy, the precipitation occurrences and of which in its immediatepermit the analysisenvironment. of relationships For assessing between the probability soundings of inside this condition heavy precipitation across a one-year and in period, its immediate there are environment21,500 events. For where assessing at least the one probability of the observations of this condition crosses across detectable a one-year precipitation, period, there and are 15,50021,500 eventsthat have where at least at least one one observation of the observations crossing detectablecrosses detectable precipitation precipitation and one, and crossing 15,500 undetectable that have at leastprecipitation. one observation While scientific crossing inferences detectable regarding precipitation the vertical and one moisture crossing structure undetectable can be gatheredprecipitation. from Whilethe events scientific where inferences all soundings regarding are inside the vertical precipitation, moisture for thisstructure study, can we be are gathered primarily from focused the events on the whereevents all with soundings (at least) oneare inside RO sounding precipitation, inside heavyfor this precipitation study, we are and primarily (at least) focused one sounding on the outside.events withThe distribution(at least) one of RO the sounding distances betweeninside heavy theobservations precipitation with and these(at least) desired one observingsounding outside conditions. The is distributionshown in Figure of the 10 . distances between the observations with these desired observing conditions is shown in Figure 10. Remote Sens. 2019, 11, 2399 12 of 19 Remote Sens. 2019, 11, x FOR PEER REVIEW 12 of 18

FigureFigure 10. 10.( a()a A) A 2-dimensional 2-dimensional (2-D) (2- histogramD) histogram of the of relative the relative angle (α angle) between () between the along-ray the along direction-ray anddirection the line and joining the the line tangent joining points, the tangent as a function points, of the as associated a function tangent of the point associated separation tangent difference point dseparation(see Figure difference8). Only thosed (see RO Figure events 8). thatOnly had those at leastRO events one observation that had at that least detected one observation precipitation that (i.e.,detected∆Φ > precipitation1.5 mm, denoted (i.e., as  “inside > 1.5 precipitation”) mm, denoted and as at“inside least one precipitation”) observation that and did at not least detect one precipitationobservation that (i.e., did∆Φ not< 1.5 detect mm, denotedprecipitation as “outside (i.e.,  precipitation”) < 1.5 mm, denoted are considered. as “outside (b) p Anrecipitation”) associated 1-Dare considered. histogram of (b the) An tangent associated point 1- separationD histogram di ffoference the tangentd.(c) Anpoint associated separation 1-D difference histogram d. of(c) theAn distributionassociated 1 of-D angleshistogram between of the the distribution along-ray direction of angles and between the line the joining along the-ray tangent direction points. and the line joining the tangent points. The joint distribution in Figure 10a exhibits a bimodal shape, arising from the fact that the constellationThe joint distribution consists of in three Figure satellites. 10 (a) Therefore,exhibits a the bimodal occurrences shape, of arising sounding from inside the fact and that outside the precipitationconstellation cancons comeists of from three two satellites consecutive. Therefore satellites, the occurrences (e.g., RO-1 of and sounding RO-2), orinside the leadingand outside and trailingprecipitation satellites can (RO-1 come and from RO-3). two Along consecutive with the satellites histogram (e.g., of RO the-1 distance and RO separation-2), or the in leading Figure 10 andb, thetrailing histogram satellites for (ROα is- plotted1 and RO in- Figure3). Along 10c. with For the this histogram orbit configuration, of the distance most separation of the observations in Figure are 10 confined(b), the histogram within 20 for◦ < α is< plotted160◦. in Figure 10c. For this orbit configuration, most of the observations are confined within 20 <  < 160. 3.2. Other Orbit Constellation Scenarios 3.2. OtherIn the Orbit discussion Constellation in Section Scenarios 3.1, the 3-satellite orbit simulation was done for a non-sun-synchronous orbitIn with the a discussion 45◦ inclination in Section plane. 4.1, In the this 3-satellite section, orbit simulations simulation are w carriedas done out for witha non a-sun 98◦- (sun-synchronous)synchronous orbit with orbit a inclination 45 inclination and aplane. 45◦ non-sun-synchronous In this section, simulation orbit,s are each carried with fourout with receiving a 98 satellites,(sun-synch eachronous) separated orbit inclination from its neighbor and a 45 by non two-sun minutes.-synchronous For bothorbit, cases, each with the corresponding four receiving precessionsatellites, each is included. separated These from four its neighbor satellites byhave two their minutes own. location, For both identified cases, the as corresponding 1, 2, 3 and 4. Toprecession examine theis included. quantity ofThese events four that satellites will be obtainedhave their meeting own location, the “at least identified one RO as inside 1, 2, and3 and at least4.To oneexamin ROe outside” the quantity criteria of events defined that above, will dibeff obtainederent configurations meeting the of“at the least four one satellites RO inside are considered.and at least one RO outside” criteria defined above, different configurations of the four satellites are considered. For example, the configuration whereby all four satellites are considered is identified as “1-2-3-4” and Remote Sens. 2019, 11, 0 13 of 19

RemoteFor example, Sens. 2019 the, 11, configuration 0 whereby all four satellites are considered is identified as “1-2-3-4”13 ofand 19 Remotethe separation Sens. 2019, 11 distance, 0 is always two minutes. If only the first and third satellites are considered,13 of the?? Remoteconfiguration Sens. 2019, 11 is, 0 denoted by “1-3” and the separation distance is 2 + 2 = 4 min, etc., Table1 lists13 of the 19 For example, the configuration whereby all four satellites are considered is identified as “1-2-3-4” and six scenarios. Fortheexample, separationRemote Sens. the distance2019 configuration, 11, 2399 is always whereby two minutes. all four If satellites only the are first considered and third is satellites identified are as considered, “1-2-3-4” and the13 of 19 the separation distance is always two minutes. If only the first and third satellites are considered, the Forconfiguration example,Table 1. theSix is configurationdi denotedfferent orbital by “1-3” whereby scenarios and all summarizedthe four separation satellites in Figure distance are considered11. Each is 2 + row2 is= in identified4 the min, table etc., corresponds as Table “1-2-3-4”1 lists to and the theconfigurationsix separation scenarios. distance is denoted is always by “1-3” two and minutes. the separation If only the distance first and is 2 third+ 2 = satellites4 min, etc., are Tableconsidered,?? lists the the theFor same example, row in the Figure configuration 11. whereby all four satellites are considered is identified as “1-2-3-4” and configurationsix scenarios. is denoted by “1-3” and the separation distance is 2 + 2 = 4 min, etc., Table1 lists the Tablethe separation 1. Six different distance orbital is scenarios always two summarized minutes. in If Figure only the11. Each first androw in third the tablesatellites corresponds are considered, to the six scenarios.Name Satellite Configuration Orbital Depiction Separation (min) Tabletheconfiguration same 1. Six row diff inerentis Figure denoted orbital 11. scenarios by “1-3” summarized and the separation in Figure ?? distance. Each row is 2 in+ the2 = table4 min, corresponds etc., Table to1 lists the 1 1-2 2 the same row in Figure ??. Tablesix scenarios. 1. Six different orbital scenarios summarized in Figure 11. Each row in the table corresponds to Name2 Satellite Configuration 1-3 Orbital•• Depiction## Separation4 (min) the sameName row in Figure 11 Satellite. Configuration Orbital Depiction Separation (min) Table31 1. Six different orbital scenarios 1-41-2 summarized in Figure•#• 11# . Each row in the table62 corresponds to the same row in Figure 11. Name142 Satellite Configuration 1-2-3 1-2 1-3 Orbital••• Depiction####• Separation2,24 2 (min) ## 1253Name Satellite 1-2 1-2-4 1-3 1-4 Configuration Orbital••••# Depiction•# Separation2 (min)2,46 4 ### # 23641 1-2-3-4 1-3 1-2-3 1-4 1-2 •••##•#• 2 2,42,6 2, 2 2 2 1-3 #### 4 345 1-41-2-3 1-2-4 •••••••••• •# 2,62, 2 4 3 1-4 6 ## # The total456 number4 of cases that 1-2-3 1-2-3-4 1-2-4have 1-2-3 at least one observation••••••#• crossing• detectable2, precipitation 22,2,2, 2 2, 4 2 and # one crossing56 undetectable5 precipitation 1-2-41-2-3-4 1-2-4 and the distance between•••••••••#• the tangent points2,d 4,2, is2,4 computed 2 for six prescribed configurations.6 These results 1-2-3-4 are depicted in Figure# 11( in grey box2, 2, and 2 as a blue The total6 number of cases that 1-2-3-4 have at least one observation••••••• crossingd detectable precipitation2, 2, 2deff and line). The left and right columns refer to the 45- and 98-degree inclination scenarios, respectively, and one crossingThe total undetectable number of cases precipitation that have and at least the distance one observation between•••• crossing the tangent detectable points d precipitation, is computed and for each of theThe six total rows number corresponds of cases to thethat row have in at Table least1. one observation crossing detectable precipitation and onesix prescribedThe crossing total undetectable number configurations. of cases precipitation that These have results and at least the are onedistance depicted observation between in Figure crossing the 11 tangent( d detectablein grey points box precipitationd, and is computeddeff as a and blue for Theone firstcrossing thing undetectable to notice is that precipitation the total number and the of distance cases increases between with the tangent the number points ofd satellites,, is computed onesixline). crossing prescribed The left undetectable and configurations. right columns precipitation These refer results and to the the are 45- distance depicted and 98-degree between in Figure inclination the?? tangent(d in scenarios, grey points boxd, and is respectively, computeddeff as a blue for and but alsofor sixwith prescribed the maximum configurations. time separation Thesebetween results are these depicted satellites. in Figure This 11 is( ad directin grey consequence box and d ff as a sixline).each prescribed of The the left six configurations. and rows right corresponds columns These refer to resultsthe to row the are 45-in depictedTable and 98-degree1. in Figure inclination 11( d in scenarios,grey box and respectively,d as a blue ande of havingblue line). more The chances left and of hitting right columns precipitation refer to by the increasing 45- and 98-degree the number inclination of satellites scenarios, (i.e.,eff number respectively, line).each The ofThe the left first six and thing rows right tocorresponds columnsnotice is thatrefer to the the torow the total 45- in number Table and 98-degree?? of. cases inclination increases with scenarios, the number respectively, of satellites, and of observations)and each of theand six increasing rows corresponds the likelihood to the of row observing in Table1simultaneously. inside and outside the eachbut of alsoThe the firstwith six rowsthing the maximum corresponds to notice is time that to the separation the row total in number Table between1. of thesecases increasessatellites. with This the is a number direct consequence of satellites, precipitationThe structures first thing by to notice increasing is that the the nominal total number separation. of cases In increases general, with there the are number more cases of satellites, of butof havingThe also first with more thing the chances maximum to notice of hittingis time that separationthe precipitation total number between by ofincreasing cases these increases satellites. the number with This the of is satellites anumber direct consequence of(i.e., satellites, number simultaneousbut alsoinside withthe and maximum outside precipitation time separation observations between with these the satellites. 98◦ orbit Thisconfiguration, is a direct since consequence the butofof having alsoobservations) with more the chances maximum and increasing of hitting time separationthe precipitation likelihood between byof observingincreasing these satellites.simultaneously the number This of isinside satellitesa direct and consequence (i.e., outside number the separationof having between more the chances observations of hitting is larger. precipitation by increasing the number of satellites (i.e., number ofofprecipitation having observations) more structures chances and increasing of by hitting increasing the precipitation likelihood the nominal by of increasing observing separation. thesimultaneously In number general, of satellitesthereinside are and (i.e., more outside number cases the of Itof is observations) also noticeable and how increasing the distribution the likelihood of effective of distances observing changessimultaneously with respectinside to the and distances outside the ofprecipitationsimultaneous observations)inside structures and and increasing outside by increasing theprecipitation likelihood the nominal observations of observing separation. withsimultaneously the In general, 98◦ orbitinside there configuration, are and more outside since cases the the of betweenprecipitation the tangent structures points. However, by increasing the cases the nominal where de separation.ff > 25 km is Inmore general, than the there 85% are of more the total cases of precipitationsimultaneousseparation between structuresinside and the by outside observations increasing precipitation is the larger. nominal observations separation. withIn the general, 98◦ orbit there configuration, are more cases since theof cases for all configurations. The is remarkably similar to the distance between tangent points for Itsimultaneous is also noticeableinside how and the outside distributiondeff precipitation of effective observations distances with changes the 98with◦ orbit respect configuration, to the distances since the simultaneousseparation betweeninside and the outside observations precipitation is larger. observations with the 98◦ orbit configuration, since the the casesseparation with an between orbital plane the observations of 98◦. The reason is larger. is that for this configuration, α is closer to 90◦. This is separationbetweenIt is also the between noticeabletangent the points. observations how the However, distribution is larger. the cases of effective where distancesdeff > 25 km changes is more with than respect the 85% to the of distances the total a consequenceIt is also of the noticeable orbit inclination, how the distribution and the relative of eff inclinationective distances between changes the GNSS with respect satellites to theand distances the betweencasesIt is for also the all noticeable configurations.tangent points. how the TheHowever, distributiondeff is remarkably the casesof effective where similar distancesdeff to> the25 changes km distance is more with between than respect the tangent to 85% the of distances points the total for receivingbetween satellites. the tangent For such points. a configuration, However, the most cases of the where occultationsdeff > 25km are collectedis more than at the the edges 85% of the total betweencasesthe cases for the all with tangent configurations. an orbital points. plane However, The ofd 98eff◦is. The theremarkably reason cases where is similar thatd for> to this25 the configuration, km distance is more between thanα is the closer tangent 85% to of 90 points the◦. This total for is receiving antenna beam pattern (i.e., away from the velocityeff or anti-velocity direction of the receiving a consequencecases for all of theconfigurations. orbit inclination, The d andeff is the remarkably relative inclination similar to between the distance the GNSS between satellites tangent and points the for casesthe cases for all with configurations. an orbital plane The ofd 98eff ◦is. The remarkably reason is similar that for to this the configuration, distance betweenα is closer tangent to 90 points◦. This for is satellite),the cases while with for anthe orbital 45◦ inclination plane of 98 orbit,. The the reason observations is that for are this more configuration, likely to beα collectedis closer with to 90 the. This is theareceiving consequence cases with satellites. an of orbital the For orbit plane such inclination, ofa configuration, 98 . The and◦ reason the most relative is that of the inclinationfor thisoccultations configuration, between are collected theα GNSSis closer at satellites the to 90 edges. andThis of◦ thethe is centrala consequence part of the antenna of the orbit beam inclination, pattern◦ (RO and geometry the relative more inclination aligned with between the velocity the GNSS or anti-velocity satellites◦ and the areceivingreceiving consequence satellites. antenna of the beam For orbit such pattern inclination, a configuration, (i.e.,and away the from relative most the of velocity inclination the occultations or anti-velocity between arethe collected direction GNSS at satellites the of the edges receiving and of the the directionreceiving of the satellites. receiving For satellite). such a configuration,Besides the changes most of in thedeff occultations, this also means are collected that the observationsat the edges of the receivingreceivingsatellite), satellites. antenna while for beam For the such 45 pattern◦ inclination a configuration, (i.e., away orbit, from most the the observations of velocity the occultations or are anti-velocity more are likely collected direction to be at collected the of edges the receiving with of the the collectedreceiving with theantenna 98◦ orbit beam configuration pattern (i.e., awaycan su fromffer from the velocity a larger or tangent anti-velocity point drift direction and its ofderived the receiving receivingsatellite),central part antenna while of the for beam antenna the 45pattern◦ inclination beam (i.e., pattern away orbit, (RO from the geometry the observations velocity more or aligned are anti-velocity more with likely the direction to velocity be collected of or the anti-velocity receiving with the uncertaintiessatellite), [45 while]. for the 45◦ inclination orbit, the observations are more likely to be collected with the satellite),centraldirection part while of of the the for receiving antenna the 45 inclination satellite). beam pattern Besides orbit, (RO the the geometry observations changes more in d arealignedeff, this more also with likely means the to velocity be that collected the or observations anti-velocity with the central part of the antenna◦ beam pattern (RO geometry more aligned with the velocity or anti-velocity centraldirectioncollected part of with of the the the receiving antenna 98◦ orbit beam satellite). configuration pattern Besides (RO can geometry the su changesffer from more in ad aligned largereff, this tangent withalso means the point velocity that drift the or and anti-velocity observations its derived direction of the receiving satellite). Besides the changes in deff, this also means that the observations directioncollecteduncertainties of with the [45 the receiving]. 98◦ orbit satellite). configuration Besides can the su changesffer from in ad larger, this tangent also means point that drift the and observations its derived collected with the 98 orbit configuration can suffer fromeff a larger tangent point drift and its derived collecteduncertainties with[ the? ]. 98 orbit◦ configuration can suffer from a larger tangent point drift and its derived uncertainties [◦45]. uncertainties [45]. Remote Sens. 2019, 11, 2399 14 of 19 Remote Sens. 2019, 11, x FOR PEER REVIEW 14 of 18

Figure 11. 11.A A summary summary of the of distribution the distribution of distances of distances for the cases for the with cases inside with and outsideinside precipitationand outside

precipitatiobservationson (gray observations box histogram), (gray box and histogram), the effective and distances the effectivedeff between distances rays accountingdeff between for rays the accountingangle α (blue for line the histogram) angle  (blue for theline di histogram)fferent orbit for configurations. the different orbit (Left configurations. panels) The results (Left forpanels a 45◦) Theorbit results inclination. for a 45 (Right orbit panelsinclination.) The ( resultsRight panels for a 98) ◦Theorbit results inclination. for a 98 In orbit each inclination. of the left In and each right of thesides, left from and topright to sides, bottom, from the top results to bottom, are shown the results for the are number shown and for positions the number ofRO-capable and positions receiving of RO- capablesatellites receiving indicated sa intellites Table 1indicated. The labels in Table embedded 1. The within labels eachembedded panel providewithin each the absolutepanel provide numbers the absolutecorresponding numbers to each corresponding histogram, to and each the histogram, ratio between and the the cases ratio with betweendeff > the25 kmcases with with respect deff > 25 to km the withtotal casesrespect (green to the font). total cases (green font).

4. Discussion For these orbit simulations, two different orbital planes were considered. The study first examined the RO sampling conditions from a 3-satellite LEO constellation orbiting in non-sun- synchronous 45 inclination plane, where each satellite is separated by 2 minutes. To assess how the Remote Sens. 2019, 11, 2399 15 of 19

4. Discussion For these orbit simulations, two different orbital planes were considered. The study first examined the RO sampling conditions from a 3-satellite LEO constellation orbiting in non-sun-synchronous 45◦ inclination plane, where each satellite is separated by 2 min. To assess how the RO sampling from this low inclination differs from the sampling conditions of the more common polar (98◦ inclination, sun-synchronous) orbit, a 4-satellite LEO constellation was simulated for both inclinations, all other aspects being the same. These simulations showed that:

1. Over one year, a 3-satellite constellation 45◦ inclination plane will collect 400,000 events and 97% of these are complete events (i.e., all three satellites capture a RO from the same GNSS transmitter). 2. Of these complete events, the superposition of GPM IMERG data reveals that 15,500 will have at least one observation crossing detectable precipitation and one crossing un-detectable precipitation.

3. The 98◦ orbit resulted in more events meeting the criteria in (2) above than the 45◦ inclination orbit, because there is more distance separation between the RO observations. However, the relative inclination with the GPS and GLONASS satellites also makes these observations more likely to have α ~90◦ deg, and hence smaller deﬀ distances. From a scientiﬁc standpoint, it is better to have smaller distances to be able to characterize the convection inside and in the nearby environment (too far apart is less desirable). With this rationale, the 98◦ orbit is less optimal for the study of the immediate surrounding of precipitation.

4. Collections of RO observations with α closer to 90◦ are more perpendicular to each other, but also suffer a larger tangent point drift. In other words, even though deff is small in general for the 45◦ case, the tangent point drift will be smaller. Therefore, there is less likelihood of a ray path overlap between adjacent RO soundings. Over one year, these event sampling numbers are sufficient for comparing convective transition statistics amongst climate models over tropical oceans, such as comparing the sharp pickup in precipitation as column water vapor exceeds a critical threshold [10], as well as sensitivity to the free-tropospheric moisture [11].

5. Conclusions To address fundamental open questions in the cloud-convective process, a sequence of polarimetric RO measurements collected from a closely spaced LEO satellite constellation is proposed. Currently, this process lacks observational constraints, due to the difficulty in obtaining accurate, vertically resolved pressure, temperature and water vapor structure inside and near convective clouds with global coverage over land and oceans. The recent launch of the COSMIC-2 (6-satellite, 24◦ inclination plane) RO constellation in mid-2019 may provide RO sampling internal and external to many convective systems, but relatively few close-time events at the short time scales of moisture transport in and near convective cloud processes. From the technology aspect, the polarimetric RO concept has been proven from space with the data collected from the modified IGOR receiver (ROHP) flying onboard the Spanish PAZ satellite since early 2018. An RO receiver (Cion) suitable in size and power requirements for small 6U-sized cubesats has been successfully flown and operated. The unique sampling offered by closely-spaced (p, q and T) profiles obtained from RO is complementary to other small satellite-based observations of the cloud structure as obtained from space-based radar, such as the RainCube Ka-band radar currently (mid-2019) being tested from space [46]. RO obtained by compact, low-power Cion-sized instruments could orbit together with small high-frequency (e.g., 183 GHz water vapor complex) passive MW sounders on the same platform, or separately in formation flying. Depending upon the orientation of the RO antenna on the receiving satellite, the RO tangent point locations can be tailored to lie outside of the MW sounder swath (effectively expanding the total coverage area), or more internal to the swath. In the Remote Sens. 2019, 11, 2399 16 of 19 latter case, the coarse along-ray but high-vertical-resolution RO data are complementary to the finer horizontal scale, but the coarse vertical-resolution-passive MW data enables the potential tomographic reconstruction of 3-D water vapor structure [47]. In addition, knowledge of the moist thermodynamic profile within heavy precipitation is useful towards the improvement and evaluation of the microphysical parameterizations used in NWP forecast models, and advancement of the state of rain-affected data assimilation [48]. The use of PRO for NWP data assimilation will require a forward observation operator that can simulate all contributions to ∆Φ along realistic RO propagation paths [37]. In addition, other applications can benefit from such a constellation (e.g., inferring horizontal wavelengths of gravity waves from multiple RO temperature profiles) [49].

Author Contributions: Conceptualization, F.J.T., R.P., C.O.A., M.d.l.T.J., G.W.F., S.T.L., S.M.H.-V., E.J.F., J.D.N.; methodology, F.J.T., R.P., C.O.A., M.d.l.T.J., K.-N.W., G.W.F., S.T.L., S.M.H.-V., E.J.F., E.C., Y.-H.K., J.D.N.; software, F.J.T., R.P., C.O.A., M.d.l.T.J., K.-N.W., S.T.L., S.M.H.-V., E.C., Y.-H.K.; validation, F.J.T., R.P., C.O.A., M.d.l.T.J., K.-N.W., G.W.F., S.T.L., S.M.H.-V., E.J.F., E.C., Y.-H.K.; formal analysis, F.J.T., R.P., C.O.A., M.d.l.T.J., K.-N.W., G.W.F., S.T.L., S.M.H.-V., E.J.F., E.C., Y.-H.K.; investigation, F.J.T., R.P., C.O.A., M.d.l.T.J., K.-N.W., G.W.F., S.T.L., S.M.H.-V., E.J.F., E.C., J.D.N.; resources, F.J.T., R.P., C.O.A., M.d.l.T.J., K.-N.W., G.W.F., S.T.L., S.M.H.-V., E.J.F., E.C., J.D.N.; data curation, R.P., M.d.l.T.J.; writing—original draft preparation, F.J.T., R.P., G.W.F., C.O.A., K.-N.W., J.D.N.; writing—review and editing, F.J.T.; visualization, F.J.T., R.P., S.T.L.; supervision, F.J.T., C.O.A., M.d.l.T.J., J.D.N.; project administration, F.J.T., J.D.N.; funding acquisition, F.J.T., M.d.l.T.J., C.O.A., J.D.N. Funding: FJT, COA, MTJ and KNW acknowledge support from NASA US Participating Investigator (USPI) program element 14-ESUSPI14-0014. RP was supported by an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory, administered by Universities Space Research Association under contract with NASA. JDN and YHK acknowledge support from National Science Foundation under grant AGS-1540518. EC contribution partially funded by Spanish Grant RTI2018-099008-B-C22 (MCIU/AEI/EU). Acknowledgments: This work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Copyright 2019. All rights reserved. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

References

1. Stephens, G.L.; L’Ecuyer, T.; Forbes, R.; Gettlemen, A.; Golaz, J.-C.-C.; Bodas-Salcedo, A.; Suzuki, K.; Gabriel, P.; Haynes, J. Dreary state of precipitation in global models. J. Geophys. Res. 2010, 115, D24211. [CrossRef] 2. Brown, R.G.; Zhang, C. Variability of mid-tropospheric moisture and its eﬀect on cloud-top height distribution during TOGA COARE. J. Atmos. Sci. 1997, 54, 2760–2774. [CrossRef] 3. Holloway, C.E.; Neelin, J.D. Moisture vertical structure, column water vapor, and tropical deep convection. J. Atmos. Sci. 2009, 66, 1665–1683. [CrossRef] 4. Sherwood, S.C.; Wahrlich, R. Observed evolution of tropical deep convective events and their environment. Mon. Weather Rev. 1999, 127, 1777–1795. [CrossRef] 5. Parsons, D.B.; Redelsperger, J.-L.; Yoneyama, K. The evolution of the tropical Western Paciﬁc atmosphere-ocean system following the arrival of a dry intrusion. Q. J. R. Meteorol. Soc. 2000, 126, 517–548. [CrossRef] 6. Tompkins, A.M. Organization of Tropical Convection in Low Vertical Wind Shears: The Role of Cold Pools. J. Atmos. Sci. 2001, 58, 1650–1672. [CrossRef] 7. Redelsperger, J.L.; Parsons, D.B.; Guichard, F. Recovery processes and factors limiting cloud-top height following the arrival of a dry intrusion observed during TOGA-COARE. J. Atmos. Sci. 2002, 59, 2438–2457. [CrossRef] 8. Derbyshire, S.H.; Beau, I.; Bechtold, P.; Grandpeix, J.Y.; Piriou, J.M.; Redelsperger, J.L.; Soares, P.M.M. Sensitivity of moist convection to environmental humidity. Q. J. R. Meteorol. Soc. 2004, 130, 3055–3079. [CrossRef] 9. Sahany, S.; Neelin, J.D.; Hales, K.; Neale, R.B. Temperature-moisture dependence of the deep convective transition as a constraint on entrainment in climate models. J. Atmos. Sci. 2012, 69, 1340–1358. [CrossRef] Remote Sens. 2019, 11, 2399 17 of 19

10. Kuo, Y.-H.; Neelin, J.D.; Mechoso, C.R. Tropical Convective Transition Statistics and Causality in the Water Vapor-Precipitation Relation. J. Atmos. Sci. 2017, 74, 915–931. [CrossRef] 11. Schiro, K.A.; Neelin, J.D. Deep Convective Organization, Moisture Vertical Structure, and Convective Transition Using Deep-Inflow Mixing. J. Atmos. Sci. 2019, 76, 965–987. [CrossRef] 12. Haddad, Z.S.; Sawaya, R.C.; Kacimi, S.; Sy, O.O.; Turk, F.J.; Steward, J. Interpreting millimeter-wave radiances over tropical convective clouds. J. Geophys. Res. Atmos. 2017, 122, 1650–1664. [CrossRef] 13. Wentz, F.J. A 17-Yr Climate Record of Environmental Parameters Derived from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager. J. Clim. 2015, 28, 6882–6902. [CrossRef] 14. Adams, D.K.; Fernandes, R.M.; Holub, K.L.; Gutman, S.I.; Barbosa, H.M.; Machado, L.A.; Calheiros, A.J.; Bennett, R.A.; Kursinski, E.R.; Sapucci, L.F. The Amazon Dense GNSS Meteorological Network: A New Approach for Examining Water Vapor and Deep Convection Interactions in the Tropics. Bull. Am. Meteorol. Soc. 2015, 96, 2151–2165. [CrossRef] 15. Ware, R.; Rocken, C.; Solheim, F.; Feng, D.; Herman, B.; Gorbunov, M.; Businger, S. GPS sounding of the atmosphere from low earth orbit: Preliminary results. Bull. Am. Meteorol. Soc. 1996, 77, 19–40. [CrossRef] 16. 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. Atmos. 1997, 102, 23429–23465. [CrossRef] 17. Hajj, G.A.; Kursinski, E.R.; Romans, L.J.; Bertiger, W.I.; Leroy, S.S. A technical description of atmospheric sounding by GPS occultation. J. Atmos. Sol.-Terr. Phys. 2002, 64, 451–469. [CrossRef] 18. Bauer, P.; Radnóti, G.; Healy, S.; Cardinali, C. GNSS Radio Occultation Constellation Observing System Experiments. Mon. Weather Rev. 2013, 142, 555–572. [CrossRef] 19. Cucurull, L.; Atlas, R.; Li, R.; Mueller, M.J.; Hoffman, R.N. An Observing System Simulation Experiment with a Constellation of Radio Occultation Satellites. Mon. Weather Rev. 2018, 146, 4247–4259. [CrossRef] 20. Kuo, Y.-H.; Schiro, K.A.; Neelin, J.D. Convective Transition Statistics over Tropical Oceans for Climate Model Diagnostics: Observational Baseline. J. Atmos. Sci. 2018, 75, 1553–1570. [CrossRef] 21. Padullés, R.; Cardellach, E.; Wang, K.-N.; Ao, C.O.; Turk, F.J.; Torre-Juárez, M.D.L. Assessment of global navigation satellite system (GNSS) radio occultation refractivity under heavy precipitation. Atmos. Chem. Phys. 2018, 18, 11697–11708. [CrossRef] 22. Biondi, R.; Randel, W.J.; Ho, S.-P.; Neubert, T.; Syndergaard, S. Thermal structure of intense convective clouds derived from GPS radio occultations. Atmos. Chem. Phys. Discuss. 2011, 11, 29093–29116. [CrossRef] 23. Murphy, M.J.; Haase, J.S.; Padullés, R.; Chen, S.-H.; Morris, M.A. The Potential for Discriminating Microphysical Processes in Numerical Weather Forecasts Using Airborne Polarimetric Radio Occultations. Remote Sens. 2019, 11, 2268. [CrossRef] 24. Bonafoni, S.; Biondi, R.; Brenot, H.; Anthes, R. Radio occultation and ground-based GNSS products for observing, understanding and predicting extreme events: A review. Atmos. Res. 2019, 230, 104624. [CrossRef] 25. Cardellach, E.; Oliveras, S.; Rius, A.; Tomás, S.; Ao, C.O.; Franklin, G.W.; Iijima, B.A.; Kuang, D.; Meehan, T.K.; Padullés, R.; et al. Sensing Heavy Precipitation with GNSS Polarimetric Radio Occultations. Geophys. Res. Lett. 2019, 46, 1024–1031. [CrossRef] 26. Skofronick-Jackson, G.; Kirschbaum, D.; Petersen, W.; Huffman, G.; Kidd, C.; Stocker, E.; Kakar, R. The Global Precipitation Measurement (GPM) mission’s scientific achievements and societal contributions: Reviewing four years of advanced rain and snow observations. Q. J. R. Meteorol. Soc. 2018, 144, 27–48. [CrossRef] 27. Huffman, G.J.; Bolvin, D.T.; Braithwaite, D.; Hsu, K.; Joyce, R.; Kidd, C.; Nelkin, E.J.; Xie, P. NASA Global Precipitation Measurement (GPM) Integrated Multi-satellitE Retrievals for GPM (IMERG); Algorithm Theoretical Basis Document, version 4.5; NASA Precipitation Measuring Missions, Goddard Space Flight Center: Greenbelt, MD, USA, 2015. Available online: http://pmm.nasa.gov/sites/default/files/document_files/ IMERG_ATBD_V4.5.pdf (accessed on 11 October 2019). 28. Gorbunov, M.E.; Lauritsen, K.B. Analysis of wave fields by Fourier integral operators and their application for radio occultations. Radio Sci. 2004, 39, RS4010. [CrossRef] 29. Zeng, Z.; Sokolovskiy, S.; Schreiner, W.S.; Hunt, D. Representation of Vertical Atmospheric Structures by Radio Occultation Observations in the Upper Troposphere and Lower Stratosphere: Comparison to High-Resolution Radiosonde Profiles. J. Atmos. Ocean. Technol. 2019, 36, 655–670. [CrossRef] Remote Sens. 2019, 11, 2399 18 of 19

30. Healy, S.B.; Eyre, J.R. Retrieving temperature, water vapour and surface pressure information from refractive-index profiles derived by radio occultation: A simulation study. Q. J. R. Meteorol. Soc. 2000, 126, 1661–1683. [CrossRef] 31. Kursinski, E.R.; Hajj, G.A. A comparison of water vapor derived from GPS occultations and global weather analyses. J. Geophys. Res. Atmos. 2001, 106, 1113–1138. [CrossRef] 32. Kursinski, E.R.; Gebhardt, T. A Method to Deconvolve Errors in GPS RO-Derived Water Vapor Histograms. J. Atmos. Ocean. Technol. 2014, 31, 2606–2628. [CrossRef] 33. Vergados, P.; Mannucci, A.J.; Ao, C.O. Assessing the performance of GPS radio occultation measurements in retrieving tropospheric humidity in cloudiness: A comparison study with radiosondes, ERA-Interim, and AIRS data sets. J. Geophys. Res. Atmos. 2014, 119, 7718–7731. [CrossRef] 34. Juárez, M.D.L.T.; Padullés, R.; Turk, F.J.; Cardellach, E. Signatures of Heavy Precipitation on the Thermodynamics of Clouds Seen from Satellite: Changes Observed in Temperature Lapse Rates and Missed by Weather Analyses. J. Geophys. Res. Atmos. 2018, 123, 13033–13045. 35. Cardellach, E.; Tomás, S.; Oliveras, S.; Padullés, R.; Rius, A.; Juárez, M.; Turk, F.J.; Ao, C.O.; Kursinki, E.R.; Schreiner, R.; et al. Sensitivity of PAZ LEO Polarimetric GNSS Radio-Occultation Experiment to Precipitation Events. IEEE Trans. Geosci. Remote Sens. 2015, 53, 190–206. [CrossRef] 36. Cardellach, E.; Padullés, R.; Tomás, S.; Turk, F.J.; Ao, C.O.; Torre-Juárez, M.D.L. Probability of intense precipitation from polarimetric GNSS radio occultation observations. Q. J. R. Meteorol. Soc. 2018, 144, 206–220. [CrossRef][PubMed] 37. Padullés, R.; Ao, C.O.; Turk, F.J.; de la Torre-Juárez, M.; Wang, K.-N.; Iijima, B.; Cardellach, E. Calibration and Validation of the Polarimetric Radio Occultation and Heavy Precipitation experiment Aboard the PAZ Satellite. Atmos. Meas. Tech. Discuss. 2019.[CrossRef] 38. Andrić,J.; Kumjian, M.R.; Zrnić,D.S.; Straka, J.M.; Melnikov, V.M. Polarimetric Signatures above the Melting Layer in Winter Storms: An Observational and Modeling Study. J. Appl. Meteor. Climatol. 2013, 52, 682–700. [CrossRef] 39. Anthes, R.; Schreiner, W. Six new satellites watch the atmosphere over Earth’s equator. Eos 2019, 100. [CrossRef] 40. Esterhuizen, S.; Franklin, G.; Hurst, K.; Mannucci, A.; Meehan, T.; Webb, F.; Young, L. TriG—A GNSS Precise Orbit and Radio Occultation Space Receiver. In Proceedings of the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2009), Savannah, GA, USA, 22–25 September 2009; pp. 1442–1446. 41. Franklin, G.; Esterhuizen, S.; Galley, C.; Iijima, B.; Larsen, K.; Lee, M.; Liu, J.; Meehan, T.; Young, L. A GNSS receiver for small satellites enabling precision POD, radio occultations, and reflections. In CubeSats and NanoSats for Remote Sensing II; International Society for Optics and Photonics: Bellingham, WA, USA, 2018; p. 1076905. 42. Jasper, L.; Nuding, D.; Barlow, E.; Hogan, E.; O’Keefe, S.; Withnell, P.; Yunck, T. CICERO: A Distributed Small Satellite Radio Occultation Pathfinder Mission. In Proceedings of the 27th AIAA/USU Conference, Small Satellite Constellations, Logan, UT, USA, 10–15 August 2013; Paper SSC13-IV-5. Available online: http: //digitalcommons.usu.edu/cgi/viewcontent.cgi?article=2936&context=smallsat (accessed on 11 October 2019). 43. Ao, C.O.; Hajj, G.A.; Meehan, T.K.; Dong, D.; Iijima, B.A.; Mannucci, A.J.; Kursinski, E.R. Rising and setting GPS occultations by use of open-loop tracking. J. Geophys. Res. Atmos. 2009, 114, D04101. [CrossRef] 44. Bringi, V.N.; Chandrasekar, V. Polarimetric Weather Radar: Principles and Applications; Cambridge University Press: New York, NY, USA, 2001. 45. Foelsche, U.; Syndergaard, S.; Fritzer, J.; Kirchengast, G. Errors in GNSS radio occultation data: Relevance of the measurement geometry and obliquity of profiles. Atmos. Meas. Tech. 2011, 4, 189–199. [CrossRef] 46. Peral, E.; Im, E.; Wye, L.; Lee, S.; Tanelli, S.; Rahmat-Samii, Y.; Horst, S.; Hoffman, J.; Yun, S.; Imken, T.; et al. Radar Technologies for Earth Remote Sensing from CubeSat Platforms. Proc. IEEE 2018, 106, 404–418. [CrossRef] 47. Möller, G.; Landskron, D. Atmospheric bending effects in GNSS tomography. Atmos. Meas. Tech. 2019, 12, 23–34. [CrossRef] Remote Sens. 2019, 11, 2399 19 of 19

48. Geer, A.J.; Baordo, F.; Bormann, N.; Chambon, P.; English, S.J.; Kazumori, M.; Lawrence, H.; Lean, P.; Lonitz, K.; Lupu, C. The growing impact of satellite observations sensitive to humidity, cloud and precipitation. Q. J. R. Meteorol. Soc. 2017, 143, 3189–3206. [CrossRef] 49. Faber, A.; Llamedo, P.; Schmidt, T.; De La Torre, A.; Wickert, J. On the determination of gravity wave momentum ﬂux from GPS radio occultation data. Atmos. Meas. Tech. 2013, 6, 3169–3180. [CrossRef]

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