Forward and Backscattering Measurements of Rainfall Over a Path at the Gpm Frequencies
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FORWARD AND BACKSCATTERING MEASUREMENTS OF RAINFALL OVER A PATH AT THE GPM FREQUENCIES Rafael F. Rincon1, Robert Meneghini1, and Roger Lang2 1NASA/Goddard Space Flight Center, Greenbelt, MD 2The George Washington University, Washington, DC 1. INTRODUCTION attenuations, or reflectivity factors, at two frequencies are linearly independent. This paper describes the theoretical basis and conceptual design of a dual-frequency radar and 2.1. Microwave link Dual-wavelength Inversion microwave link (radar/link) system capable of technique measuring simultaneously forward and backscatter from rainfall. The forward and backscattering The microwave link analysis assumes that the path- radar/link system will enable small-scale rain studies average DSD can be represented by a two-parameter essential in understanding the rainfall process, and gamma distribution given by make significant contributions to the investigation of L radar inversion algorithms for the estimation of 1 2 N(DNDzdzNDeeo )=− ( , ') ' = eexp(ΛDe ) , (2.1) precipitation parameters that include liquid water L ∫0 content, median mass diameter, number concentration, and rainfall rate. The system will where N , and Λ are path-average parameters of operate at the frequencies of 13.6 GHz and 35.5 GHz o enabling the testing and validation of established the DSD, and De is the equi-volumetric drop diameter. radar retrieval algorithms such as those used by the Tropical Rain Mapping Mission (TRMM) single- The following approach makes use of attenuation at frequency radar, and those proposed for the Global 13.6 and 35.5 GHz to solve for No and Λ . Precipitation Mission (GPM) dual-frequency radar. The path-average attenuation, A (dB), for a signal The dual frequency radar/link system will be deployed propagating through rain can be expressed as [1] at the NASA/Wallops Island microwave link facility [1], where it will operate in conjunction with a network of Dmax disdrometers, tipping buckets, and optical rain gauges A =−8.686λ LN Im[ f ( D )] D2 exp(Λ D ) dD , (2.2) ννoe∫ νeee to validate the measurements and test the rain Dmin retrieval techniques [1]. This configuration will also serve as an ideal validation site for radar rainfall where ν denotes the signal frequency, λν is the retrievals such as the GPM over flight rainfall wavelength, L is the signal path-length (m), Im[fν (De)] estimates. (m) is the imaginary components of raindrop forward -4 scattering amplitude, N (m ) is the path-average 2. THEORY drop size distribution, and Dmax and Dmin are the maximum and minimum drop sizes in the distribution. The radar/link dual-frequency measurements permit the application of inversion techniques to estimate Using (2.2) and taking the ratio of attenuation at 13.6 parameters of drop size distribution (DSD). In turn, and 35.5 GHz yields the DSD obtained from the inversions can be used to compute important rainfall parameters. The following A λ Dmax 35 13 Im[f (DD )]2 exp(−Λ DdD ) inversion methods are based on the non-Rayleigh ∫ 13 ee e e A13λ 35 scattering characteristics in the interaction of Dmin . (2.3) D microwaves with raindrops exhibited when the signal max −−Im[fDD ( )]2 exp(Λ DdD )= 0 wavelength is comparable to the size of the raindrops. ∫ 35 ee e e D In these methods, at least one of the frequencies min must be in the Mie scattering regime so that the signal Equation (2.3) is a transcendental equation in Λ which can be solved using standard numerical Corresponding Author address: Rafael F. Rincon techniques. Since the A13 and A35 are linearly NASA/GSFC/555, Bldg. 22, Rm. 192B, independent, the roots of this equation yield the value Greenbelt, MD 20771 of Λ for a given attenuation ratio A35 / A13. The (301) 614-5715, E-mail: [email protected] forward scattering amplitudes f and f for non- 13 35 spherical raindrops need to be computed numerically. The numerical method employed would depend on One approach to solve (2.7) is by measuring the the assumption of raindrop shape. For oblate raindrop attenuations at the farthest point of the radar range of shapes, the T-matrix approach is commonly interest, and then estimating the DSD progressively in employed [2]. each cell for all range gates using a backward recursion algorithm [3]. However, measuring the attenuation with space borne radars (the same Having obtained Λ , the value of No can be found applies to ground based radars) cannot be from (2.2). The DSD obtained from this technique accomplished directly, and one must resource to can be used to compute path-average rainfall ancillary techniques, such as the surface reference parameters such as liquid water content, median technique, to estimate the path-average attenuation mass diameter, number concentration, and rainfall [4]. rate. As in the microwave link case, the backscattering 2.2. Radar dual-wavelength Inversion technique cross-section and the scattering amplitudes in (2.7) must be computed numerically for non-spherical This approach makes use of measured reflectivity raindrops. factors and path-integrated attenuation at 13.6 and 35.5 GHz to solve for N and Λ . o 3. SYSTEM DESCRIPTION The radar analysis assumes that the DSD can be represented by a two parameter gamma distribution The dual-frequency radar/link system will measure the forward and the backscattered signals from rain 2 N(,)Dreo=− N ()exp(()) rDΛ rDe, (2.4) simultaneously using a combination of radar and microwave link techniques. This approach will allow to solve equation (2.7) can be solved readily with out where No and Λ are the free parameters of the DSD, which are functions of the range r. the introduction of uncertainties from estimates of attenuation. The effective reflectivity factor, Ζe, from a volume of raindrops at a distance r from the transmitter can be The radar/link system will be deployed at the expressed as [3] NASA/Wallops Island microwave link facility where it will operate in conjunction with a ground network of Dmax Z e ()rCNr= ()σ ( DDedD ) 2 −Λ()rDe , (2.5) impact disdrometers, tipping buckets, and optical rain ν ννobee∫ e Dmin gauges that provide the DSD spectra, rainfall accumulation, and rainfall rate directly under the 4 5 2 microwave signals path. The ground network will not where C = λ /(π |K | ), K = (ε - 1) / (ε + 2), ε is the ν ν ν ν ν only help validating the measurements and testing the dielectric constant of a raindrop, and σ is the b rain retrieval techniques, but it will also help evaluate backscattering cross-section. any differences between elevated-path-averages m e estimates and point ground measurements, and to The measured reflectivity factor, Ζ , is related to Ζ by study the DSD time evolution and spatial variability over the microwave path. Z m= ArZr()e (). (2.6) ν νν A block diagram of the radar and the link transmitter is Using (2.5) and (2.6), and taking the ratio of shown in figure 1, and the microwave link receiver is measured reflectivity factors at 13.6 GHz and 35.5 shown in figure 2. The line-of-sight, microwave link GHz yields system will consist of a two-channel transmitter and receiver system characterized by coherent operation Z m Dmax at the frequencies of 13.6 GHz, and 35.5 GHz. The 35 A ()rDDedσ ( ) 2 −Λ()rDe D microwave link will share the radar transmitter (fig. 1), Z m 13 ∫ bee13 e 13 Dmin and a use a coherent receiver (fig. 2) synchronized to . (2.7) Dmax the incoming radar signals. The system will measure −=Ar()σ ( DDe ) 2 −Λ()rDe dD 0 35 ∫ bee35 e path-integrated attenuation (A13.6 and A35.5) and path D min integrated frequency phase-shift (Φ35.5-13.6). The radar will employ Frequency Modulated Equation (2.7), which is similar to (2.3), is a Continuous Wave (FMCW) signals to measure rainfall transcendental equation in Λ which can be solved backscatter, and provide reflectivity profiles along the using standard numerical techniques for a given ratio path. Both 13.6 GHz and 35.5 GHz signals will be of reflectivity factors Ζ35 / Ζ13. However, in order to transmitted simultaneously (fig 1). solve (2.7), the attenuations A13 and A35 must be known for any given r. 35 GHz 34.97749 GHz Multiplier LPF IF AMP Data 13.5 KHz System LNA 35 GHz 22.5135 MHz Output LPF IF AMP 13 GHz 22.5 MHz 5 MHz Multiplier 5 MHz Divider LO Radar/link transmitter 35 GHz LNA Multiplier 35 GHz 5 MHz PLL Amp 15 MHz Sweep 13 GHz 15.009 MHz 2-W 9 KHz Oscillator Divider Output 13 GHz Amp PLL 13 GHz 12.98499 GHz 12.98499 GHz 2-W 9 KHz PLL Divider LO Figure 1. FMCW radar system / Microwave link Figure 2. Microwave link receiver transmitter 2Br f = 1 . (Hz) (3.4) The radar range resolution will be determined by 1 cT the choice of three FMCW parameters. These s are the sweep bandwidth, sweep duration, and IF filter bandwidth. The transmitter will generate a Equation (3.4) can also be obtained by inspection from fig. 1 by noting that B / TR = f / TR. frequency sweep of bandwidth B = fmax - fmin (Hz), Δ Similarly, the frequency of a signal return from a during a time Ts (sec). Each sweep is repeated contiguous rain volume located a r2 is at interval Ts as shown in figure 1. T 2Br2 R B f2 = . The bandwidth of the IF filter, BIF, fmax cTR fΔ at the receiver required two resolved the frequencies is 2BΔr Bff=−= . (3.5) f IF 21 min cTs Ts ___ Fig.