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4 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 58, NO. 1, JANUARY 2020
A Distributed Small Satellite Approach forMeasuring Convective Transports in the
Earth’s AtmosphereGraeme L. Stephens , Susan C. van den Heever, Ziad S. Haddad, Derek J. Posselt, Rachel L. Storer,
Leah D. Grant , Ousmane O. Sy, T. Narayana Rao , Simone Tanelli , and Eva Peral
Abstract— The recent successful space-borne demonstrationof a miniaturized CubeSat precipitation radar is highlighted.The low cost of such a radar, together with the availabilityof small satellite, platforms to carry it, now make it feasibleto consider employing a more distributed approach to observeimportant atmospheric processes that relate to precipitation.An approach to quantify the transport of water and air by deepconvection is described based on a clustering of small radarsatellites providing measurements seconds apart. This strategynow adds time as a new dimension for observing such processes.A mission concept, referred to as D-train, comprised of a trainof three satellites 30, 90, and 120 s apart is described, and theexpected performance of it for providing measures of convectivetransport is examined based on a large ensemble of simulationsof convection with an advanced cloud-resolving model.
Index Terms— Atmospheric radar, clouds, convection, meteo-rology, millimeter-wave radar, precipitation, small satellites.
I. INTRODUCTION
AS THE heated air of low latitudes rises and movespoleward, it cools and sinks in the subtropics creating
a massive overturning of the atmosphere that largely deter-mines the weather patterns and climates of the tropical andsubtropical zones. That this rising air is accomplished bytransports by many narrow plumes in deep convection, referredto as hot towers, was one of the most remarkable inferencesabout the atmosphere in the mid-20th century [1]. It wassurmized that the vertical transport of heated air must occurin about 2000 of these hot towers at any given time, butneither the number of hot towers nor the strength of transport
Manuscript received September 20, 2018; revised March 5, 2019; acceptedMay 14, 2019. Date of publication October 14, 2019; date of current versionDecember 27, 2019. This work was supported in part by NASA under GrantNNH15ZDA001N-InVEST. (Corresponding author: Graeme L. Stephens.)
G. L. Stephens, Z. S. Haddad, D. J. Posselt, O. O. Sy, S. Tanelli,and E. Peral are with the Jet Propulsion Laboratory (JPL),California Institute of Technology, Pasadena, CA 91125 USA (e-mail:[email protected]; [email protected]; [email protected]; [email protected]; [email protected];[email protected]).
S. C. van den Heever, R. L. Storer, and L. D. Grant arewith the Department of Atmospheric Sciences, Colorado State Univer-sity, Fort Collins, CO 80523 USA (e-mail: [email protected];[email protected]; [email protected]).
T. N. Rao is with the National Atmospheric Research Laboratory, Gadanki517502, India.
Color versions of one or more of the figures in this article are availableonline at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TGRS.2019.2918090
by deep convection has been measured. We neither know ifthis transport mostly occurs through individual thunderstorms,as first thought, or through larger mesoscale convective sys-tems (MCSs), nor how much is contributed by the most intensetropical storms [2], [3]. Such uncertainties affect our abilityto predict short-term severe weather, weather on subseasonalto seasonal time scales and multi-decadal climate change [4].Specifically: 1) much of the heaviest precipitation and severeweather on earth is associated with these transports [5]; 2) deepconvective transports are the main way that heat, moisture,mass, and trace gases are lifted from low levels into theupper troposphere, and these transports are a significant sourceof high clouds. Although the precipitation radar measure-ments from the NASA Tropical Rainfall Measurement Mission(TRMM) offer information about convective intensity [6] andlatent heating [7], the lack of observational constraints onthe modeling of the processes that produce these clouds andmeasures of transport within them results in a large model-to-model spread in high cloud properties [8] and relatedhigh-cloud feedbacks in models ([9]); and 3) projections ofglobal precipitation change in response to forced climatechange, i.e., “the hydrological cycle acceleration,” can differby a factor of two or more depending on model assumptionsabout tropical deep convective transports [10].
The importance of knowing the vertical transports of watervapor and condensate by atmospheric moist convection cannotbe overstated. Observations of these transports are essentialif we are to advance our ability to predict weather out toseasonal time scales and beyond and if we are to providereliable projections of the effects of climate change on ourweather.
This article describes an approach that provides observa-tions of convective transports made possible through recenttechnology innovation that now offers feasible, low-cost waysto develop weather radars for space-borne applications. Thisenabling technology, together with an ability to fly satellitesin close formation, provides a new dimension in earth obser-vations needed to capture the dynamical nature of convectionand insights on their transports.
Section II briefly describes the technology that now makesthe quantification of convective transports a reality. The Rain-cube [11] demonstration in space was launched in May 2018 tothe international space station. This radar has dramatically
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STEPHENS et al.: DISTRIBUTED SMALL SATELLITE APPROACH FOR MEASURING CONVECTIVE TRANSPORTS IN THE EARTH’S ATMOSPHERE 5
TABLE I
COMPARISON OF THE PROPERTIES OF TWO CONCEPTS FOR ORBITINGRADARS, ONE NOW ORBITING EARTH (RAINCUBE) AND THE OTHER
(THE D-TRAIN RADAR), WHICH IS A DERIVATE OF THE RAINCUBE
RADAR AND HAS BEEN PROPOSED FOR ORBIT
reduced the size and cost of a space-borne radar makingit now feasible to use a distributed small-satellite approachfor observing earth-related processes. Section III describes aconcept for such an approach designed for measuring con-vective transport. This is followed by a presentation of theensemble of simulations using advanced models of convectionto illustrate the expected performance of such an observingapproach. Section V then concludes with a brief description ofa potential mission concept, referred to as D-train, designed toaddress basic questions about the transports by deep convectivestorms.
II. RAINCUBE DEMONSTRATION
Radars are typically thought of as a payload that cannotfit small satellite platforms given their perceived large size,weight, and power requirements. A novel miniature Ka-bandatmospheric precipitation radar (miniKaAR) architecture hasbeen developed at JPL that reduces the number of components,power consumption, and mass by over an order of magnitudewith respect to existing space-borne radars. As such it is com-patible with the capabilities of low-cost satellite platforms suchas CubeSats and SmallSats. Here, we introduce two versionsof this radar, and the properties of each radar are summarizedin Table I. The version of the radar identified as D-train is asmall-satellite version described later. The CubeSat version ofthe radar electronics, referred to as the miniKaAR-C, and anultracompact lightweight antenna referred to as KaRPDA [11]were launched in May 2018 as the technology demonstrationRainCube mission on a 6U CubeSat (Fig. 1). MiniKaAR-Coperates at the center frequency of 35.75 GHz and utilizesoffset I–Q, a novel modulation technique which enablesminiaturization of the radar electronics by directly convertingto/from Ka-band from/to baseband, properly selecting the fre-quency scheme, and using digital filtering to remove unwanted
Fig. 1. 6U CubeSat MiniKaAR-C radar and spacecraft entering thermalvacuum testing at JPL in 2017.
Fig. 2. (a) MiniKaAR-C data from the airborne campaign as a part ofthe PECAN campaign (June 28–July 15, 2015) showing the profile of radarreflectivity Z . The reflectivity color scale is in dBZ. The expected on orbitsensitivity of Raincube of ∼10 dBZ is emphasized with the color scale chosen.(b) MiniKaAR-C reflectivity profiles of rain falling from the nascent hurricaneflorence.
spurious signals. MiniKaAR-C also adopts a solid-state poweramplifier that produces approximately 10 W of RF peak power,and a chirped pulse nominally of 166 μs (with linear frequencymodulation and amplitude tapering) with a duty cycle of 10%.The antenna size for the RainCube technology demonstrationis of 0.5 m, with an antenna gain of 42.6 dB and resultingin a footprint of approximately 8 km from the nominal orbitaltitude of 400 km.
As part of the development, Raincube was integratedand tested in the successful ground and airborne demon-stration experiments before being integrated on a Cube-Sat and launched in space. For the airborne demonstration,the MiniKaAR-C instrument was installed and flown on a Dou-glas DC-8 operated by NASA Armstrong Flight Research Cen-ter. For this application, the KaRPDA antenna was replaced bya horn-lens antenna. Fig. 2(a) shows the Ka-band reflectivity
6 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 58, NO. 1, JANUARY 2020
Fig. 3. Schematic of a three satellite cluster observing a growing convectivecloud. Each profile would be matched to the preceding profile collectedδt seconds before it. One concept being considered is for δt = 30 and 90 s.
profile through a convective cloud system observed duringthe Plains Elevated Convection at Night (PECAN) campaignbetween June 28 and July 15, 2015. Analyses of these fieldexperiment results confirmed the overall performance of theradar including pulse compression, sensitivity, and resolution.
The performance of Raincube was further confirmed withthe profiles of reflectivity observed from the orbit of stratiformrain in the region from 5 to 20 N and from 10 to 30 W asso-ciated with a tropical depression that formed into hurricaneflorence [Fig. 2(b)].
III. DISTRIBUTED RADAR OBSERVING SYSTEM
CONCEPT FOR OBSERVING CONVECTION
The low cost of both the MiniKaAR and small satel-lite platforms to carry it now make it feasible to consideremploying a more distributed approach to observe atmosphericprocesses. An observing system of multiple radars couldbe used in constellation, for example, to provide a broadertemporal and spatial sampling of weather systems than ispossible with a single radar in space. Alternatively, multipleradar satellites could also be flown in a clustered formationto observe very fast changes in convection as, for example,illustrated by the concept shown in Fig. 3. In this hypotheticalexample, a constellation of three small satellites each flying aminiature, nadir-pointing, Ka-band atmospheric radar spaced,respectively, 30 and 90 s apart provide a new dimensionto the observations—one of time. For this case, three time-difference baselines provide the rates of change of convectionfrom weaker (120 s) to the most intense (30 s) systems. Theprincipal measurement delivered by each radar is the range-resolved power returned from atmospheric scatterers (hydrom-eteors) expressed in terms of a radar reflectivity (Z ) factor.The measurement approach also delivers an additional profileof information in the form of a reflectivity difference �Z .Although each profile of Z contains information about convec-tive strength, precipitation, and hydrometeor mass to varyingdegrees [12]–[14], the time-differenced reflectivity measure-ments, by contrast, provide information about rates of changeof condensed mass, a measure of vertical motion as well asother information that can be interpreted in terms of convectivevertical transport as described in the following.
Fig. 4. Relation between the time differences of the radar reflectivity andthe vertical motion of the same volume of air.
Fig. 5. Maps of vertically averaged reflectivity (Top) and associated timederivative adjusted for the horizontal advection (Bottom) as observed by theKDAX radar on January 4, 2008: temporally averaged from 22:11 to 22:16(Left) during the presence of the squall line, from 18:14 to 20:53 (Middle)before the formation of the squall line, and from 21:02 to 01:00 (duringsquall).
IV. INFORMATION CONTENT OF TIME-DIFFERENCED
RADAR DATA: OBSERVATIONAL SUPPORT
The observing approach described above and its relation-ship to convective transport are not easily tested with air-borne observations. The approach has been motivated by andverified to some degree with time sampled surface radarobservations [15]–[18]. Fig. 4 shows one example of analysisof joint surface radar data matched to wind profiling dataof monsoon rain systems over from National AtmosphericResearch Laboratory, Gardanki, India. Although anecdotal,Fig. 4 shows a broad correlation between observations of�Z/�t and observations of vertical motion (w) at differentlevels within convective storms. The underpinning basis ofsuch a relation is described in the following.
The results highlighted in Fig. 5 are from analysis ofsurface radar echoes that offer further illustration of the natureof the relation between time-differenced radar echoes andvertical transports in storms. The data are a sequence of
STEPHENS et al.: DISTRIBUTED SMALL SATELLITE APPROACH FOR MEASURING CONVECTIVE TRANSPORTS IN THE EARTH’S ATMOSPHERE 7
NEXRAD volume scans from the WSR-88D radar KDAX atSacramento, taken during the storm that passed over NorthernCalifornia on January 4, 2008. The radar reflectivities fromJanuary 3, 2008 1800Z to January 5, 2008 0100Z reveal asquall line sweeping through from the West–Northwest tothe East–Southeast (refer to the top row of Fig. 5, whichshows the vertically integrated radar reflectivities averagedover three different time intervals). The radar produced avolume scan approximately every 4.5 min. The reflectivitydata were interpolated to a grid with a horizontal resolutionof 1.5 km and a vertical resolution of 250 m. The horizontalwind advection field U = (u, v) was estimated directly fromthe gridded reflectivity data at each vertical level, by movinga horizontal 15 km × 15 km square window over the domainscanned by the radar and identifying, for the center of eachwindow position in the domain, the vector U which maximizesthe correlation between the reflectivities measured at thebeginning of the given 4.5-min interval and those measuredat the end of the time interval. For robustness, criteria verysimilar to those used to estimate Atmospheric Motion Vectorswere adopted. The resulting advection field was then usedto correct the simple partial derivative of the reflectivitieswith respect to time, to allow the estimation of the numeratorin (2). This numerator, once corrected for advection, thusrepresents the combined sources of condensed water by totaleffect of any increased local condensation and any verticaltransport (positive values pointing upward). The bottom ofFig. 5 shows this source term averaged over the three differenttime intervals. Despite the changing patterns of the reflectivityaverages (top rows), the averages of the total source termreveal strong sources fixed over the coastal ranges and to alesser extent at the west-facing slope of the Sierras inland,and a fixed sink located on the east-facing slope of the coastalranges. This event was an “atmospheric river” and remarkablyhighlights the orographic influences on moist air being liftedthat is not visible in the reflectivity data. The bottom rowsclearly highlight the presence of vertical transport from thesouthwest onto the coast, the coastal ranges, with a similarif less pronounced effect by the Sierras themselves furtherinland. This is a form of phenomenological “validation” thatthe time-difference measurements indeed reflect the verticaltransport of water in storm systems.
V. OBSERVING SYSTEM SIMULATIONS
An ensemble of numerical model simulations of deepconvection produced a synthetic database of observationsthat can be connected to properties of convection. Thesesimulations were conducted using an advanced convectiveresolving cloud model with a detailed treatment of cloudand ice hydrometeors [19], [20]. The synthetic observationsso created are a valuable way of testing the measurementconcept and evaluating retrieval performance. The simulationapproach developed for this purpose is schematically por-trayed in Fig. 6. The cloud model evolves the dynamical andthermodynamical properties of the environment along withthe distribution of clouds and precipitation associated withthe convective system that forms. Cloud model simulations
Fig. 6. Flow diagram of the simulation approach developed to explorethe relation between the proposed space-borne radar measurements and theconvective transport.
have a horizontal grid-spacing of 250 m, much finer thatthe footprint expected of a miniKaAR. This allows us totest the effects of nonuniform cloud effects on radar reflec-tivity over a variety of simulated footprint sizes. Simulationof radar retrieved convective vertical mass flux consists ofthree main components. First, an ensemble of model initialconditions is created for three cases of observed convection,with initial humidity, temperature, and wind in each caseare then perturbed over ranges consistent with uncertainty inradiosonde observations [21], creating an ensemble of 25 dif-ferent simulations of convection for each case. In the secondcomponent, simulated liquid and ice hydrometeors from thecloud model are input into four different cloud microphysicalmodules to produce inputs to the radar simulator. The radarsimulator has been documented in [17], [18], and [22]. Thescattering properties of each category of water in the cloudmodel’s microphysical scheme are based on T-matrix codefor liquid and discrete-dipole scattering (DDSCAT) approx-imations for ice. Simulated radar on the 250-m model grid isthen convolved with D-train’s expected antenna point spreadfunction to produce observations on a 3-km scale, the expectedfootprint of the space-borne miniKaAR when configured witha 1.6-m antenna and assumed on a 500-km orbit. In thisway, the results can be assessed as a function of the assump-tions inherent to these different microphysics schemes. Thus,the simulation approach provides a way of assessing thesensitivity of the entire process to assumption about micro-physical properties that are not observed or remain uncon-strained. The third main component then uses these syntheticobservations to: 1) explore the extent that the observed radarinformation relates to the convective transports as predicted;2) the extent that 3-km scale observations represent the actualtransports averaged to the 3-km scale; and 3) the extent thatthe observations are sensitive enough to reveal the depen-dence of the transports on changing environmental properties.An important environmental parameter that influences convec-tion and its transport is the environmental relative humidity(RH) [23]–[25], and the sensitivity of the retrieved information
8 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 58, NO. 1, JANUARY 2020
Fig. 7. Example simulation of the 3-km footprint miniKaAR measurementstaken from one ensemble member of each case identified by date. (Top row)Synthetic along-orbit nadir simulation of Z (in units of dBZ). (Middle row)90-s Z difference expressed as dBZ/min. (Bottom row, red) The deepestprofiles and greatest changes in Z occur where the updrafts are strongest.A precision on each radar of 1 dBZ is approximately an order of magnitudesmaller than the expected changes in the deepest convection over 90 s.
on RH can also be assessed against the model truth. Theproduction of synthetic observations using highly realisticfine-scale simulations of convection constitutes a valuable wayof testing the measurement concept and evaluating retrievalperformance.
A. Radar Simulations of a Convective Storm
Fig. 7 shows one example of miniKaAR simulated level 1reflectivity data for one member of each case study ensemble.The Z profiles (top row) are from reflectivities calculated atthe model 250-m resolution then averaged to 3 km. The 90-sprofile differences (�Z , middle row of panels), however, arewhere the dynamical imprints of the convective transports canbe found. This is highlighted in the bottom panels showingthe maximum vertical motion and maximum �Z within each3-km column above the melting level. The stronger verticaltransports, indicated by larger vertical motions, stand out asbeing highly correlated with the largest reflectivity changesthat typically occur in the deepest convective columns. TheAug 11th case serves to highlight how the relation between themaximum vertical motion and the reflectivity difference breaksdown away from the convective cores. In this example, thecorrelation breaks down in regions of stratiform precipitationin the region of 0–40 km.
B. Vertical Motion
The simulations described above, together with analysis ofobservations from surface radars (Figs. 4 and 5 and [15]–[17]),clearly illustrate how information about the vertical movementof air within convection is contained in the time-differenceradar observations. An intuitive demonstration of this con-nection follows by tracking the rise of a given Z surface ina storm, such as the echo top height of, say, the 10-dBZsurface as schematically presented in Fig. 3. Tracking thissurface offers a way of indexing the upward motion of
condensed water in the convective core. Different resolutionsof these upward motions are thus implied in using different δtbaselines. For example, a range resolution of 250 m with δtof 30, 90, and 120 s hypothetically corresponds to a resolvedvertical motion of 8, 2.8, and 2 ms−1, respectively. Unlikethe instantaneous nature of the Doppler motion measurements,the motions and transports inferred from time-difference mea-surements represent the sustained mean motion and transportsover the given δt baseline
Although the relation between time-differenced radar mea-surements and vertical motion of hydrometeors can be con-ceptually understood in terms of the movement of Z surfacesas described above, a more formal relation between the obser-vations and motion follows by considering the time rate ofchange of the radar reflectivity Z of a given radar volume,namely,
∂z
∂ t+ u
∂z
∂x+ v
∂z
∂y+ wC
∂z
∂h= C (1)
where the term ∂ Z/∂ t ∼ �Z/�t is the observed time differ-ence obtained with two radars observations, and the secondtwo terms are the horizontal advection of cloud particlesthrough the volume by the horizontal wind components uand v. The vertical advection of Z by the vertical windcomponent wc is the term associated with the vertical transportby convection representing, in this case, the vertical motion ofcondensed water and is thus directly analogous to a Dopplervelocity that convolves both air and particle speeds. The factorC contains all cloud processes acting within the volume tochange the mass of condensate observed by the radar asexpressed by Z such as by vapor deposition on particles andother processes. The ensemble cloud model simulations revealthat these cloud physical conversion processes primarily varylinearly with wc [Fig. 8(a)] with a proportionality constant thatis a remarkably well-behaved function of temperature [21].Given this behavior it reasonable to approximate C ∼ αwc,resulting in a rearrangement of (1) as[
�z
�t+ u
�z
�x+ v
�z
�y
] [α − �z
�h
]−1
= WC . (2)
Since the coefficient α can be robustly deduced from sim-ulations and temperature regardless of the convective stormtype [Fig. 8(b)], (2) underscores how the vertical motionthat advects Z is directly related to the observables of timedifference measures of Z (i.e., �Z/�t) and the vertical profileof Z (i.e., �Z/�h) with the contribution from horizontaladvection also being diagnosed from across track multi-beamradar observations. A swath of 15 km composed of fivefootprints side by side has been proposed in order to accountfor the cross-track advection. For convection that develops inthe tropical environment, the latter contributions of advectionare, however, often small and can be neglected.
Fig. 9 exemplifies the connection between the verticalmotion in the form of an equivalent Doppler velocity thatis retrieved from time-difference measurements of reflectivityfrom the ensemble of cases derived using the February 23rdcase study. These profiles are derived from time differencesof Z of 90 s and apply to an ensemble of measurements
STEPHENS et al.: DISTRIBUTED SMALL SATELLITE APPROACH FOR MEASURING CONVECTIVE TRANSPORTS IN THE EARTH’S ATMOSPHERE 9
Fig. 8. (Top) Relation between the conversion of vapor to condensatemass and vertical motion calculated using an advanced cloud resolving modelreveals a strongly linear growth process regardless of the model of what typeof cloud particle is growing and regardless of the environmental atmosphericstate in which convection forms. This relation only applied above the freezinglevel. (Bottom) αcoefficient for various cases presented as a function of radarvolume temperature [21].
Fig. 9. Retrieval of vertical motion principally based on reflectivity differencemeasurements. Retrieval errors are shown as they apply to the ensemblesimulation for the 90 s �Z > 5 dB and |wmax| > 1 m/s. Retrieval perfor-mance is shown for different assumed measurement errors on Z (expressedin dBZ). The 0-dB noise is the ideal no-measurement-noise case, illustratingthe intrinsic retrieval uncertainty due to the imperfect information content ofthe observation. The 2-dB case is what would be expected for a space-borneradar.
for �Z > 5 dB and |wmax| > 1 m/s. Retrieval performanceis shown for different assumed measurement errors on Z(expressed in dBZ). The 0-dB noise profile is the idealno-measurement-noise case, illustrating the intrinsic retrievaluncertainty due to the imperfect information content of theobservation. The 2-dB measurement noise case is a conserva-tive estimate of the expected performance of a radar in space
Fig. 10. (a) (Top) Relation between the maximum vertical updraft speed andthe heaviest rains of storms expressed by the 99% rate of surface precipitationderived from the model ensemble. (b) (Bottom) Relation between maximumupdraft speed in column and the 1/2
√CAPE, which is the maximum expected
of an idealized buoyant plume rising in air where CAPE is a measure of energyavailable to lift air. The dashed line is the prediction from this idealized theoryand the points are that derived from the ensemble of model simulations.
both this result and that shown in Fig. 7(a) underscore howtime-difference radar reflectivity measurements map directlyonto the vertical motion within the column observed, espe-cially above 5 km. The maximum column updraft speed thatcan be inferred from such profiles is a fundamental measureof convective intensity correlating to the more extreme precip-itation produced by storms [Fig. 10(a)]. This maximum speedalso connects to the environmental conditions, like convectiveavailable potential energy (CAPE), through simple theoret-ical relationships that can be tested with such information[Fig. 10(b)].
C. Water Mass Changes
Radar reflectivity Z itself provides valuable informationabout the mass of condensed water M in the radar volume.Time-difference measurements of Z relate to rates of changeof condensed mass M in the volume in a more direct waythan does Z relate to M . The basis of this result follows fromthe simple Z–M relationship typically expressed as a powerlaw [12], [26]
Z ∼ M2/N0 ∼ aMb (3)
10 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 58, NO. 1, JANUARY 2020
Fig. 11. (a) Z–M relationship. (b) Z–dlogM/dt relationship. These rela-tionships are derived from the ensemble of simulations with three differenttypes of microphysical models in the simulations of Z . The spread in theZ–M relation is a result of these different assumptions about microphysics,whereas the Z -dlogM/dt is much less sensitive to the effects of microphysics.
where M = mass of condensed water (rain water, hail, snow,cloud water, and ice), No = hydrometeor concentration, andthe coefficients a and b vary depending on the details ofthe cloud itself. Fig. 11(a) shows an example of a Z–Mrelationship derived from the entire 75 ensemble member sim-ulations described above. The consequence of the approximatenature of the power-law relation (3) is that reflectivity Z isnot a unique measure of M varying by about two ordersof magnitude for a given value of Z . The largest rangeof uncertainty in this relationship is represented by the acoefficient that is poorly known and depends on the types ofhydrometeors in the volume that are typically either unknownor not unmeasured [26].
The time rate of change of mass content and the corre-sponding temporal differences of the radar reflectivity moredirectly relate to each other as shown in Fig. 11(b) becausebiases inherent in Z–M relationships through the a coefficientlargely cancel when data are differenced over short enoughtime intervals (seconds). It is from dZ/dtthat the relative rateof change dlogM/dtcan be derived for each radar range binabove the melting level (∼5 km for tropical storms), and theslope of such a relation in Fig. 11(b) represents the exponentb. These results indicate how invariant the exponent b isbetween different cloud microphysical models uses to createthe synthetic observations (Fig. 6). Interpretation of time-difference observations below about 5 km, for the most part,is problematic because of a number of factors (attenuation,multiple scattering) that cannot easily be quantified, and thus,the analysis is really only applicable above the freezing level.These results reproduce those obtained in [17] and [18], basedon simulations of very different atmospheric scenes (tropicaldepression Isabel in the East-Atlantic, 2003, and Pineapple-Express atmospheric river in California, 2008) with an entirelydifferent model.
Fig. 12. (a) (Top) Bayesian retrieval versus actual model mass flux (truth)of condensed water mass flux at 350 hPa. (b) (Bottom) Isolated case fromFebruary 23rd ensemble showing a correlation between the vertical fluxes ofdry-(x-axis, Q A) and moist-air (y-axis, QC ) mass fluxes.
D. Convective Mass Fluxes
This time-difference radar measurements contain informa-tion both about the time change of condensed mass and thevertical movement of water mass in storms, especially whereair is moving upward at velocities exceeding 1 ms−1, suggeststhat these measurements can serve as a reasonable close proxyfor the vertical flux of condensed water QC = ρwC M whereρ is the density of air. Information content analysis confirmsthat the combination of both time-differenced (�Z) and time-averaged Z profiles directly relate to this flux for profileswhere vertical motions exceed 1 ms−1 [16], and the resultsof such an analysis are shown in Fig. 12. It also turns outthe mass flux of vertically rising dry air (Q A) also correlatesdirectly to QC [Fig. 12(b)].
Thus, estimates of QC provide direct insights on Q A
and thus insights on the convective mass fluxes of dry air,a principal parameter that describes convective transports.
Profiles of dry-air mass flux Q A retrieved from a syn-thetic level-1 radar data are compared to actual mass fluxesderived from the cloud model-averaged to that same scale(3×3 km2 horizontally) in Fig. 13. These results are presentedas percentiles within two RH regimes to illustrate the rangeof transports that occur conditioned on RH and the abilityof the retrieval to reproduce this range of behavior. Thevertical profiles of Q A presented in this example are forthe lowest 10% RH [Fig. 12(a)] and the upper most 10%RH [Fig. 13(b)] of the environments used in the simulations.These results demonstrate how the retrieval of mass flux
STEPHENS et al.: DISTRIBUTED SMALL SATELLITE APPROACH FOR MEASURING CONVECTIVE TRANSPORTS IN THE EARTH’S ATMOSPHERE 11
Fig. 13. February 23rd case study: vertical profiles of the convective massflux conditioned on the environmental humidity. Shown are the percentilesof the vertical fluxes of dry air Q A compared to model truth (circles) andBayesian retrievals (solid line) that use observations of a convoy of twominiKaAR radars. Profiles are for all (a) high-moisture and (b) low-moistureenvironments.
captures both the variability within a given environmental RHstate and the variability across changes in environmental RH.The results also illustrate how the retrieval breaks down below5 km as expected for reasons described above. Although theinstantaneous errors on individual flux profiles are estimated tobe approximately 40%, when averaged over many profiles suchas on the scale of a storm, or composited by environmentalhumidity, as in the example of Fig. 13, these errors aretypically less much than 15% and small enough to capturecredibly the dynamic range of variability of mass flux.
VI. D-TRAIN MISSION CONCEPT
The dynamical train (D-train) mission concept proposesmaking time-difference observations with three small satellites30 and 90 s apart, each flying a miniKaAR with a fixedantenna of 1.6 m in diameter on a small 100-kg class satellite.This concept would deliver time-difference measurements onthree-time baselines. When placed in an orbit of 500 km,each miniKaAR with a 1.6-m antenna (Table I) is projected toprovide reflectivity profiles with a footprint of approximately3 km at the surface and a vertical profile with a 250-mresolution. A concept for a five beam radar delivering cross-track swath of approximately 15 km has been proposed.A swath provides the ability to examine the geometry ofconvective cores as well as enhances the ability to overlapconvective core regions observed seconds apart. The missionconcept also has a pointing requirement of 0.07◦ 2−σ , whichis one-fifth of the antenna beamwidth, to ensure the requiredminimum footprint overlap of 80%, which has been assessedto be sufficient to reduce the confounding factors due tofootprint mismatch [15], [16]. Such geolocation requirementimposes specific requirements to antenna alignment, and plat-form navigation and control systems, which are well withinthe capabilities of available small satellite platforms and notunprecedented as, for example, demonstrated by the formationflying of CloudSat and CALIPSO satellites.
The range of vertical motions resolved by time-differencemeasurements of 120, 90, and 30 s is shown in Fig. 14(a)derived from the entire model ensemble. A 120-s time dif-ference corresponds to vertical motions of 2 m/s and greater.
Fig. 14. (a) Cumulative distribution of vertical velocity derived from theensemble of simulations at different heights in deep convection for updraftsexceeding 1 m/s. The shaded regions convey where vertical motions cansimply be inferred from height changes of reflectivity observe 30, 90, and10 s apart. This illustrates how a mission concept as described detects motionsof 2 m/s and larger. (b) Cumulative distribution of dry air mass flux inisolated convective storms at three different levels. D-train potentially samples80–90 of the total mass flux of these storms.
According to the simulations performed, this detection thresh-old corresponds to about 50% of all vertical motions containedin the ensemble database of deep convection and to about80%–90% of all transport above 5 km calculated from the75 member ensemble [Fig. 14(b)]. At 90 s, the upper 35%of all motions would be detected corresponding to between70% and 85% of all convective transports above 5 km, whilemeasurements 30 s apart detects approximately the upper10% of motions corresponding to 40%–60% of all convectivetransports above 5 km.
VII. CONCLUSION
The recent successful space-borne demonstration of a minia-turized, low-cost CubeSat precipitation radar, together with theavailability of small satellite platforms to carry it, now makeit feasible to consider employing a more distributed approachto observe important atmospheric processes that relate to pre-cipitation. This article described progress toward such a goalboth presenting a rationale of why time differenced, clusteredmeasurements provide a quantitative approach to estimatingthe vertical transport of air by deep convective storms. Bothsurface observations and observing system simulations supportthe credibility of the measurement strategy being proposed.A mission concept, referred to as D-train, comprised of atrain of three satellites 30, 90, and 120 s apart each carrying
12 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 58, NO. 1, JANUARY 2020
a version of this small radar is described. The expected per-formance of it for providing measures of convective transportis described, and the expected performance of the observingsystem is examined using a large ensemble of simulations ofconvection with an advanced cloud-resolving model. Furtherresearch in testing the measurements approach using bothother surface observations as well as further model simulationsis underway.
The topics addressed by this measurement approach arecentral to the clouds convection and precipitation designatedobservable recommendation of the National Academy decadalstudy that calls for measurements of vertical motion in convec-tion. This recommendation is currently under study by NASA,and the relative merits of this approach compared to Dopplermeasurements, for example, are being explored through furthermodel simulations. The proposed approach introduced in thisarticle is novel, while the collective uncertainty associatedwith the method is addressed in Fig. 9 for vertical motion,the individual error sources, such as effects of attenuation,multiple scattering, microphysical assumptions inherent to(2), and other observational factors like pointing errors andpartially filled footprints, all need further investigation.
ACKNOWLEDGMENT
The research was carried out at the Jet Propulsion Labora-tory, California Institute of Technology, Pasadena, CA, USA,under a contract with the National Aeronautics and SpaceAdministration. The development of Raincube was fundedunder the Science Mission Directorate’s (SMD) In-Space Val-idation of Earth Science Technologies (InVEST) solicitation.
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Graeme L. Stephens received the Ph.D. degreein meteorology from the University of Melbourne,Melbourne, VIC, Australia, in 1977.
He was a University Distinguished Professor withColorado State University, Fort Collins, CO, USA.Since 2010, he has been the Director of the Cen-ter for Climate Sciences, Jet Propulsion Laboratory(JPL), Pasadena, CA, USA. His work over the yearshas focused on the influence of clouds on the earthsystem. He has authored or coauthored more than260 peer-reviewed publications and several chapters
in books. He has authored a book, Remote Sensing.Dr. Stephens is a member of the National Academy of Engineering, a fellow
of the Royal Society, AAAS, AGU, and AMS. He was a recipient of theMason Gold Medal of the Royal Meteorological Society, the Gold Medalof the International Radiation Commission of IAMAP/IUGG, the Houghtonand Charney Awards of the AMS, and a number of awards from NASA andColorado State University.
STEPHENS et al.: DISTRIBUTED SMALL SATELLITE APPROACH FOR MEASURING CONVECTIVE TRANSPORTS IN THE EARTH’S ATMOSPHERE 13
Susan C. van den Heever received the M.Sc. degreein atmospheric science from the University of theWitwatersrand, Johannesburg, South Africa, in 1994,and the Ph.D. degree in atmospheric science fromColorado State University, Fort Collins, CO, USA,in 2001.
Since 2008, she has been a Professor with theDepartment of Atmospheric Sciences, ColoradoState University, and a CSU Monfort Professorin 2015. She has authored a book Storm Dynamics,a book chapter on factor separation analysis and
almost 70 articles on cloud physics, cloud dynamics, and mesoscale modeling.She also oversees the development of a sophisticated cloud-resolving model.
Dr. van den Heever was a recipient of the American Geophysical Union’sASCENT Award, the American Meteorological Society’s Lorenz Award, andseveral other awards from CSU and NASA. She has received several editorawards. She is currently the Editor of the Journal of the Atmospheric Sciencesand a Guest Editor of the Atmospheric Chemistry and Physics.
Ziad S. Haddad received the Ph.D. degree from theMassachusetts Institute of Technology, CambridgeMA, USA, in 1983.
Since 1991, he has been a Technical Staff Memberwith the Jet Propulsion Laboratory (JPL), Pasadena,CA, USA. His research interests include remotesensing estimation of environmental variables andprocessing using radars and passive microwaveradiometers.
Derek J. Posselt received the B.S. and M.S.degrees in atmospheric science from the Univer-sity of Wisconsin–Madison, Madison, WI, USA,in 1997 and 2001, respectively, and the Ph.D. degreein atmospheric science from Colorado State Univer-sity, Fort Collins, CO, USA, in 2006.
From 2006 to 2007, he was a Post-DoctoralResearcher with Colorado State University. He wasan Assistant Research Scientist from 2007 to 2011,an Assistant Professor from 2011 to 2014, and anAssociate Professor from 2014 to 2016 with the
University of Michigan, Ann Arbor, MI, USA. From 2012 to 2016, he servedas the Deputy Principal Investigator for the Cyclone Global NavigationSatellite System (CYGNSS) Mission. He is currently a Research Scientist withthe Jet Propulsion Laboratory, California Institute of Technology, Pasadena,CA, USA. He has authored a book chapter on Bayesian MCMC methods.He has authored or coauthored 53 peer-reviewed publications. His researchinterests include weather–climate interactions, nonlinear data assimilationfor cloud and precipitation processes, remote sensing retrievals, and high-resolution numerical modeling.
Rachel L. Storer received the B.S. degree in meteorology from Penn StateUniversity, State College, PA, USA, in 2006, and the M.S. and Ph.D. degreesin atmospheric science from Colorado State University, Fort Collins, CO,USA, in 2009 and 2012, respectively.
She is currently a Research Scientist with Colorado State University. Shehas authored several peer-reviewed publications on convection. She has morethan 10 years of experience in numerical modeling of clouds and convection.Her research interests include convective dynamics, microphysics, and cloud-resolving modeling.
Leah D. Grant received the Ph.D. degree in atmospheric science fromColorado State University, Fort Collins, CO, USA, in 2018.
She is currently a Research Scientist with Colorado State University.She has more than 7 years of experience in numerical modeling and fieldobservations of convective clouds. She has authored seven peer-reviewedpublications on convective processes. Her research interests include dynamicaland microphysical processes in atmospheric convection.
Dr. Grant received a number of awards and fellowships from the NSF,AMS, AGU, and Colorado State University.
Ousmane O. Sy received the Ingénieur degree inaerospace from Ecole Nationale de l’Aviation Civile,Toulouse, France, in 2003, the M.Sc. degree inelectrical engineering from Paul Sabatier Univer-sity, Toulouse, in 2003, and the Ph.D. degree inelectromagnetics from the Eindhoven University ofTechnology, Eindhoven, The Netherlands, in 2009.
From 2004 to 2005, he was a Test Engineerof aeronautical navigation systems with Airbus.In 2009, he joined the Jet Propulsion Laboratory,Pasadena, CA, USA. His research interests include
space-borne remote sensing, electromagnetics, and uncertainty quantification.Dr. Sy was a recipient of the Young Scientist Award during the general
assembly of URSI, Chicago, in 2008, and the Best Student Paper Award atZürich’s international symposium on EMC, Switzerland, in 2009.
T. Narayana Rao, photograph and biography not available at the time ofpublication.
Simone Tanelli received the M.Sc. and Ph.D.degrees in electrical engineering and remote sensingfrom the University of Florence, Florence, Italy,in 1995 and 1998, respectively.
Since 2001, he has been with Radar Scienceand Engineering Section, Jet Propulsion Laboratory,Pasadena, CA, USA. He has covered a number ofroles spanning from engineering to science on air-borne and space-borne cloud and precipitation radarssuch as CloudSat’s CPR, GPM’s DPR, RainCube’sminiKaAR, and the airborne radars APR-2 and
APR-3. He has authored or coauthored over 50 peer-reviewed publications.
Eva Peral received the Ph.D. degree in telecommunications engineeringfrom the Universidad Politecnica de Valencia, Valencia, Spain, in 1998, andthe Ph.D. degree in electrical engineering from the California Institute ofTechnology, Pasadena, CA, USA, in 1999.
She is currently an Instrument System Engineer for Ka-band radar interfer-ometer (KaRIn) instrument in the Surface Water Ocean Topography Mission(SWOT) and the Principal Investigator of the RainCube Mission at JPL,Pasadena, CA. She has more than 15 years of experience in radar systemengineering, radar on-board processing, fiber optics, semiconductor lasers,and optoelectronics. She holds eight U.S. patents. She has coauthored a bookreview chapter on wide-swath radar altimetry. She has authored multiple peer-reviewed publications.
