We present preliminary research on a method to estimate Vertical Air Motion (VAM) at a particular height by comparing the measured rain-rate (RR) by a vertically-pointing S-band Frequency-Modulated Continuous-Wave (FMCW) radar with that of a ground-based disdrometer. The method is based on a constrained parametric solver, assuming high correlation between 5-min averaged rain rates measured by the radar and disdrometer. The method is tested over disdrometer and radar observations during the Verification of the ORigins Tornado EXperiment in South East US (VORTEX-SE) project. Finally, the results are partially validated by means of fitting a gamma distribution to the VAM-corrected DSD profiles and studying its parameters.This research is part of the projects PGC2018-094132-B-I00 and MDM2016-0600 (“CommSensLab” Excellence Unit) funded by Ministerio de Ciencia e Investigación (MCIN)/ Agencia Estatal de Investigación (AEI)/10.13039/501100011033/ FEDER “Una manera de hacer Europa”. The work of A. Salcedo-Bosch was supported under grant 2020 FISDU 00455 funded by Generalitat de Catalunya—AGAUR. The European Commission collaborated under projects H2020 ACTRIS-IMP (GA-871115) and H2020 ATMOACCESS (GA-101008004).Peer ReviewedPostprint (author's final draft

Domínguez Pla, Paula

Frasier, Stephen J.

Rocadenbosch Burillo, Francisco

Salcedo Bosch, Andreu

English

UPCommons. Portal del coneixement obert de la UPC

NUMERICAL SOLVER FOR VERTICAL AIR MOTION ESTIMATION1Salcedo-Bosch, A.1, Domı́nguez-Pla, P.1, Rocadenbosch, F.1,2, Senior Member, IEEE,Frasier, S. J.3, Senior Member, IEEE1CommSensLab-UPC, Department of Signal Theory and Communications (TSC), Universitat Politècnica de Catalunya (UPC)2Institut d’Estudis Espacials de Catalunya (Institute of Space Studies of Catalonia, IEEC), Barcelona, Spain, E-08034 Barcelona, Spain3Microwave Remote Sensing Laboratory, University of Massachusetts, Amherst, MA 01003-92842ABSTRACT3We present preliminary research on a method to estimate Vertical Air Motion (VAM) at a particular height by comparing the4measured rain-rate (RR) by a vertically-pointing S-band Frequency-Modulated Continuous-Wave (FMCW) radar with that of a5ground-based disdrometer. The method is based on a constrained parametric solver, assuming high correlation between 5-min6averaged rain rates measured by the radar and disdrometer. The method is tested over disdrometer and radar observations during7the Verification of the ORigins Tornado EXperiment in South East US (VORTEX-SE) project. Finally, the results are partially8validated by means of fitting a gamma distribution to the VAM-corrected DSD profiles and studying its parameters.9Index Terms— Vertical Air Motion, S-Band radar, Rain Rate, Drop Size Distribution101. INTRODUCTION11Several different ground-based remote sensing instruments are able to assess temperature and/or humidity profiles in the bound-12ary layer including infrared spectrometers and microwave radiometers [1]. However, these instruments have a common draw-13back, which is their poor performance under precipitation scenarios. Alternatively, lower microwave frequency radar observa-14tions are mostly unaffected during precipitation, and hence, they emerge as an alternative in order to reveal details regarding15precipitation microphysical processes [2]. Among the distinct radar technologies available, the S-band (∼ 10 cm) Frequency-16Modulated Continuous Wave (FMCW) radar has been used to monitor boundary layer features since the 1960s [3].17This research is part of the projects PGC2018-094132-B-I00 and MDM-2016-0600 (“CommSensLab” Excellence Unit) funded by Ministerio de Cienciae Investigación (MCIN)/ Agencia Estatal de Investigación (AEI)/ 10.13039/501100011033/ FEDER “Una manera de hacer Europa”. The work of A. Salcedo-Bosch was supported under grant 2020 FISDU 00455 funded by Generalitat de Catalunya—AGAUR. The European Commission collaborated under projectsH2020 ACTRIS-IMP (GA-871115) and H2020 ATMO-ACCESS (GA-101008004).© 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. DOI 10.1109/IGARSS46834.2022.9884354During the VORTEX-SE project, two intensive field campaigns were carried out in 2016 and 2017 [2], in which the Uni-18versity of Massachusetts (UMass) S-Band radar and the Collaborative Lower Atmospheric Profiling System (CLAMPS) [4]19yielded a wealth of observations. The key objectives encompassed the assessment of the atmospheric-boundary-layer evolution20and the characterization of precipitation microphysical processes in northern Alabama in the context of tornado warning and21monitoring [2].22The rainfall rate (RR) and the drop-size distribution (DSD) are key parameters that can be retrieved from vertically pointed23radar observations. RR estimation is influenced by the assumed DSD. In turn, the DSD can be computed from the vertically24pointed radar Doppler spectrum with the assumption that the drops are Rayleigh scatterers falling at their terminal velocities25[5]. However, in practice, the Doppler spectrum is affected by the ambient vertical air motion (VAM). Thus, given the Doppler26spectrum as a function of height, RR and DSD retrievals require height-dependent VAM correction. While raw velocity bins in27the radar observations represent a shifted, and possibly aliased, version of the mean Doppler radial velocity, velocity bins after28VAM correction are expected to represent the true terminal fall velocity of the raindrops.29Different approaches to estimate VAM have been carried out in the literature: Kim et al. [6] obtained VAM estimations30using Doppler spectra derived from a 1290-MHz wind profiler, which showed good agreement in comparison with the VAM31derived at 300 m in height from a K-band micro-rain radar and at surface from a disdrometer. They used the Sans Air Motion32(SAM) gamma-size hydrometeor distribution model introduced by Williams [7], who proposed a method to estimate VAM33based on iterative fitting the DSD retrieved from the velocity-shifted observed spectrum and the SAM-DSD model. In contrast,34this paper tackles VAM estimation relying on RR measurements by a ground-based disdrometer, assuming high RR correlation35between different measurement heights considering 5-min average ensembles. Although collision and coallescence processes36limit radar- and disdrometer-DSD coincidence, correlation coefficients of ρ ' 0.75 are found for the RR between disdrometer37and radar at 500 m in [5]. This paper is organised as follows: Sect. 2 presents the instrumentation including the OTT Parsivel238disdrometer and the UMASS S-band radar, and the retrieval methods for the RR and DSD products and the VAM estimation.39Sect. 3 shows a case study on the proposed VAM estimation method, and Sect. 4 gives conclusion remarks.402. INSTRUMENTS AND METHODS412.1. The UMASS S-Band radar42The S-Band FMCW radar employed during VORTEX-SE was developed by the Microwave Remote Sensing Laboratory from43the University of Massachusetts. This radar is deployed on a truck for mobility and uses two parabolic dish antennas, both44with diameter of 2.4 m and gain of 34 dB, and a 250 W transmitter [3]. This system measures the volume reflectivity spectral45density (with respect to velocity), η(v), with averaged spatial and temporal resolutions of 5 m and 16 s, respectively. From46these it is possible to obtain profiles of the spectral reflectivity factor, Z(v), vertical velocity, v, and spectrum width, w. This47radar enables to study the atmospheric boundary layer behaviour as well as precipitation events, because it is able to detect both48clear-air echo and precipitation [5].492.2. The OTT Parsivel2 disdrometer50The OTT Parsivel2 disdrometer used for VORTEX-SE measurement campaign is deployed as a part of the Portable In situ Pre-51cipitation Station (PIPS), designed and developed by Purdue University and the U.S. National Severe Storms Laboratory. This52is a ground-based instrument that measures optically at 1 dimension the precipitation size particle-by-particle. The disdrometer53has an approximate temporal resolution of '10 s and measures different rain-related parameters such as the DSD and the RR,54among others [8].552.3. Data products and Vertical Air Motion correction56Data products.- The steps to estimate the RR and DSD from radar measurements begin with the measured radar volume57reflectivity η(v) as a function of velocity (see details in Appendix of [5] and physical basis in [9]). The DSD is defined as58N(D) =η(D)σ(D), (1)where σ(D) is the single-particle backscattering cross section of a drop of diameterD, and η(D) is the radar reflectivity density59as a function of diameter. The rain rate is computed as60RR = π/6∫ ∞0N(D)D3v(D)dD, (2)which is essentially the third order moment of the DSD and fall velocity as a function of drop diameter, v(D).61VAM correction.- The fundamental raindrop terminal-velocity-to-diameter relationship, denoted v(D) in Eq. 2, assumes62that there is no vertical air motion [9],63v(Dn) = (9.65− 10.3e−0.6·Dn)δv(h), (3)where Dn is the raindrop diameter, δv(h) is an air density correction for the terminal velocity as a function of height, and64velocities are positive down. In the presence of VAM, the Doppler velocity measured by the vertically-pointing radar is given65by66vDoppler = v + vV AM , (4)where v = v(D) is the terminal fall velocity for raindrops of diameter D, vDoppler is the corresponding Doppler velocity67measured by the radar, and vV AM is the VAM velocity. In what follows, dependency with diameter D will be skipped because68VAM is a property related to atmospheric dynamics and turbulence and therefore, it is equally affecting all particle sizes. Size69retrieval from Doppler velocity measurements must include the correction, v = vDoppler − vV AM when computing Eq. 370inverse function, D(v), and subsequent retrieval of the DSD and RR via Eq. 1 and Eq. 2, respectively. Therefore, in practice,71the RR product can be defined as a function of the VAM velocity correction as RR(V AM).72VAM estimation.- The VAM estimation method consists on an optimisation problem by solving Eq. 2 as a function of the73VAM velocity correction. The optimization problem can be formulated as74V AM = arg minV AM||RRdisdro −RR(V AM)||2, (5)whereRR(V AM) is the RR radar product obtained as a function of the V AM velocity correction solving Eq. 2. Eq. 5 above is75posed assuming that RRdisdro and RR(V AM) are correlated in height (at altitudes considerably lower than the melting layer)76when considering 5-min averages. The VAM optimization is carried out by means of a constrained non-linear Least-Squares77algorithm, minimizing the squared error between RRdisdro and RR(V AM).783. RESULTS AND DISCUSSION79The algorithm presented in subsection 2.3 has been applied to radar and disdrometer measurements (5-min averaged) taken80during April 30, 2016 00:00-01:00 UTC in the context of VORTEX-SE measurement campaign. The algorithm estimated VAM81values that, when used to correct the radar reflectivity measurements at 500 m height, provided RR values virtually identical82to RRdisdro (||RRdisdro − RR(V AM)||2 < 0.002mm · h−1). Fig. 1 compares the radar-measured RR at 500 m, with and83without VAM correction (solid black and gray traces, respectively), to RRdisdro (dashed blue). It can be observed that without84correction, radar-derived RR shows considerably lower values (' 0.1 mm ·h−1) compared to RRdisdro (' 0.4 - 0.8 mm ·h−1)85mainly due to VAM-velocity-induced error [10]. With VAM correction, the radar-derived RR trace overlaps RRdisdro time86series, and the estimated VAM time series is obtained (dashed brown trace), showing a nearly constant value of ' 4 m · s−1.87The background color map depicts the 5-min averaged DSD measured by the FMCW radar after VAM correction.88In order to validate the VAM-corrected DSDs obtained for each 5-min average, and thus, the estimated RRs and VAM89velocities, the gamma distribution parameterization of DSD was derived by means of the method of moments [11]. The gamma90distribution representation of N(D) is formulated as91N(D) = N0Dµe−ΛD, (6)being characterized by N0, µ, and Λ parameters. Fig. 2 shows a DSD parameterization example in which the average DSD92measured by the radar between 00:00 UTC and 00:05 UTC, with and without VAM correction (solid trace, b) and a) panels,93respectively), is plotted along its gamma parameterization (dashed trace). It can be observed that without VAM correction94(Fig. 2 a)) the measured DSD is poorly fitted to a gamma distribution, showing a great bias between the modelled and measured9500:10:00 00:20:00 00:30:00 00:40:00 00:50:000.20.40.60.811.21.4D[mm]0246810Rain Rate [mmh-1]; VAM [m/s]0 1 2 3 4 5log(N [m-3mm-1])Radar VAM correctedRadar uncorrectedDisdrometerVAMFig. 1. Time series representing the radar-measured RR, with and without VAM correction, the disdrometer-measured RR andthe VAM estimation results. The DSD is represented on the background.DSDs. This is further evidenced by the gamma distribution parameters obtained, with µ = −3.574 which is out of the accepted96range in the literature for µ values (µ ∈ [−3, 8]) [9]. On the other hand, after VAM correction (Fig. 2 b)), the obtained DSD can97be nicely fitted to a gamma distribution. This result is quantitatively validated as well by the gamma distribution parameters98obtained, now with µ = −2.185 within the expected ranges.990 0.2 0.4 0.6 0.8 1 1.2D [mm]102104106N(D) [m-3mm-1]Measured N(D)N(D)=N0D e- DN0 = 97 = -3.574 = 1.9958a)0 0.5 1 1.5D [mm]102104106N(D) [m-3mm-1]Corrected N(D)N(D)=N0D e- DN0 = 1.47e+04 = -2.1854 = 3.875b)Fig. 2. Case example showing the gamma distribution fitting to a radar-measured DSD without (panel a)) and with (panel b))VAM correction.Table 1 depicts the gamma distribution parameters obtained for each of the 5-min averaged DSD measurements after VAM100correction. N0 values range from a minimum of 5.94·103 at 00:35 UTC, corresponding to the lowest RR within the measurement101period under study, to a maximum of 6.66 · 104. µ values remain approximately constant around µ = −2, and finally, Λ ranges102from a minimum of 3.87 at 00:05 UTC to a maximum of 7.44 at 00:55 UTC. The obtained values are in accordance with the103ranges found in the literature [9] and their temporal correlation seem to validate the VAM estimations obtained. However, all we104have shown is that the radar-derived RR can be made to match the disdrometer-derived RR, and that the resulting radar-derived105Time (UTC+2) N0 µ Λ00:05:00 1.47 · 104 -2.19 3.8700:10:00 3.15 · 104 -2.19 4.5000:15:00 2.33 · 104 -2.12 4.4900:20:00 5.76 · 104 -1.91 5.0700:25:00 3.95 · 104 -1.97 4.7800:30:00 1.43 · 104 -2.19 4.5800:35:00 5.94 · 103 -1.99 4.5800:40:00 8.85 · 103 -2.01 4.500:45:00 1.45 · 104 -2.33 4.5300:50:00 2.35 · 104 -1.53 5.4500:55:00 6.66 · 104 -1.99 7.44Table 1. Gamma distribution N0, µ, and Λ fit parameters found for the VAM-corrected radar-measured DSDs for the measure-ment period under study (April 30, 2016 00:00-01:00 UTC) in the context of VORTEX-SE campaign. Each row correspondsto a DSD 5-minute average.DSD seems realistic. The Gamma distribution parameters obtained still need to be validated according to the rain type present106in the scenario under study, and the DSDs from the two instruments should be compared in light of their respective sensitivities.107The rather substantial apparent VAM over the course of 1 hour also deserves further investigation.1084. CONCLUSIONS109A methodology to estimate VAM velocity from radar and disdrometer RR measurements has been presented. The method110consists on fitting the radar-retrieved RR, as a function of VAM velocity correction, to the disdrometer-measured RR using111constrained non-linear Least-Squares optimization.112The methodology was tested over experimental data captured during a 1-hour period by an S-band FMCW radar and an OTT113Parsivel2 disdrometer in the context of VORTEX-SE measurement campaign. The estimation results found a nearly constant114VAM velocity of '4 m/s during the observation period. After VAM correction, the radar-measured RR was found to match115almost ideally the disdrometer-measured RR. In order to validate these results, the gamma distribution parameterization was116derived for each of the estimated DSD. It was found that without VAM correction, the gamma distribution parameters showed117unrealistic values, outside of the accepted bounds for a precipitation process. On the other hand, after VAM-correction, realistic118values for all parameters were found with a coherent temporal continuity, showing the methodology improvement of the radar119measurements.120Although good performance of the algorithm has been observed, it needs to be tested over different experimental data,121validating the VAM estimations by means of radar wind profilers. Moreover, the effect of reflectivity density aliasing needs to122be studied as well.1235. REFERENCES124[1] U. Löhnert and O. Maier, “Operational profiling of temperature using ground-based microwave radiometry at Payerne:125Prospects and challenges,” Atmos. Meas. Tech, vol. 5, pp. 1121–1134, May 2012.126[2] R. L. Tanamachi, S. J. Frasier, J. Waldinger, A. LaFleur, D. D. Turner, and F. Rocadenbosch, “Progress toward Character-127ization of the Atmospheric Boundary Layer over Northern Alabama Using Observations by a Vertically Pointing, S-Band128Profiling Radar during VORTEX-Southeast,” J. Atmos. Ocean. 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Lee, “Raindrop size distribution properties associated with vertical air motion in the stratiform137region of a springtime rain event from 1290 mhz wind profiler, micro rain radar and parsivel disdrometer measurements,”138Meteorol. Appl., vol. 23, no. 1, pp. 40–49, 2016.139[7] C. R. Williams, “Simultaneous ambient air motion and raindrop size distributions retrieved from uhf vertical incident140profiler observations,” Radio Sci., vol. 37, no. 2, pp. 1–22, 2002.141[8] A. Tokay, D. B. Wolff, and W. A. Petersen, “Evaluation of the new version of the laser-optical disdrometer, ott parsivel2,”142Journal of Atmospheric and Oceanic Technology, vol. 31, no. 6, pp. 1276 – 1288, 2014.143[9] R. J. Doviak et al., Doppler radar and weather observations. Courier Corporation, 2006.144[10] D. Rajopadhyaya, P. May, R. Cifelli, S. Avery, C. Willams, W. Ecklund, and K. Gage, “The effect of vertical air mo-145tions on rain rates and median volume diameter determined from combined uhf and vhf wind profiler measurements and146comparisons with rain gauge measurements,” J. Atmos. Ocean Technol., vol. 15, 12 1998.147[11] A. Tokay and D. A. Short, “Evidence from tropical raindrop spectra of the origin of rain from stratiform versus convective148clouds,” Journal of Applied Meteorology and Climatology, vol. 35, no. 3, pp. 355 – 371, 1996.149

Numerical solver for vertical air motion estimation

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Numerical solver for vertical air motion estimation

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