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Mongi Marzoug and Paul Amayenc

Abstract

A class of single- and dual-frequency algorithms that can be used to infer rain-rate profile from a downward-looking spaceborne radar operating at attenuating frequencies is presented. These algorithms rely on use of power-law relations between the radar reflectivity factor Z and the specific attenuation coefficient k. First, they provide estimates of attenuation-related parameters such as the range-profiled specific attenuation coefficient or partial range-averaged specific attenuation coefficients. Then, the corresponding rain rate R range profile can be derived by using a relevant R-k relationship. Profiling may be performed either from the radar or from the surface. The basic purpose of the various algorithms is to correct for several types of range-free scaling errors that may alleviate, for example, requirements on radar calibration and/or storm modeling (cloud, melting layer). Corrections are performed by using an additional measurement of the surface echo, an additional hypothesis (such as uniformity of rain rate versus range near the surface) for the case of single-freqnency algorithms, or by exploiting the correlation between the two attenuation coefficients at both frequencies for the case of dual-frequency algorithm. The present paper (Part I) describes the basic formalism of both single- and dual-frequency algorithms using a unified mathematical framework. Tests of their performances for rain-rate profile retrieval versus range are presented using numerical simulators of spaceborne radar data for the frequency pair (13.75, 24) GHz. Results point out the interest of a dual-frequency radar for future space missions. Validation tests using real data from airborne radar measurements will be presented in a future paper (Part II).

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Paul Amayenc, Jacques Testud, and Mongi Marzoug

Abstract

The potential characteristics and performances of a spaceborne dual-beam radar (or stereo radar) operating at 24 GHz, and devoted primarily to the retrieval of rain-rate structure by using the stereo-radar analysis, were presented in a previous study. This constitutes the starting point of the present paper, which analyzes the feasibility and scientific interest of adding a Doppler capability to the instrument. The constraints imposed by the Doppler mode are elaborated and discussed. Accordingly, the basic design and the expected performances of a low-altitude (≈ 500 km) spaceborne dual-beam Doppler radar are proposed. It is shown that a slight increase in system complexity is needed to perform significant additional Doppler measurements without jeopardizing the primary objective, that is, the quantitative measurement of rain at the global scale.

The scientific interest for Doppler data from space is investigated. Two components of the air velocity can he determined from the dual-beam spaceborne Doppler radar: the along-track component of the horizontal air velocity and a component directed between 0° and 20° off the vertical. Both components could be estimated with an accuracy of approximately 1.2 m s−1 within each resolution cell in standard conditions. Two ways to exploit these data are proposed: monitoring the mesoscale wind field within stratiform precipitation areas, or estimating the horizontal transport of vertical momentum associated with deep convection at the climatological scale.

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Jacques Testud, Paul Amayenc, and Mongi Marzoug

Abstract

This paper investigates the performances achievable in the retrieval of rain-rate profile from a spaceborne radar operating at attenuated frequencies. Results obtained from three radar systems using relevant range-profiling algorithms to estimate rainfall rate are numerically simulated and compared. The three considered systems are a single-beam-single-frequency (SBSF) radar, a single-beam-dual-frequency (SBDF) radar, and a dual-beam-single-frequency (DBSF) radar or “stereoradar.” In each case, the sampling of a typical model rain cell is performed and the data are analyzed according to the selected algorithm for rainfall retrieval. Three possible frequencies for the SRSF and DBSF radars (13.8, 24, and 35 GHz) and two frequency pairs for the SBDF radar (13.8–35 GHz and 13.8–24 GHz) are used. For obtaining objective comparisons, the three instruments are assumed to operate with an identical detection threshold, spatial resolutions, and power measurement accuracy. The main aspects investigated are the dynamical range of rain retrieval and the sensitivity to the measurement noise, to the drop-size distribution variability, and to nonuniform beam-filling effects.

It is concluded that a dual-beam system operating at 24 GHz may be a good candidate for mapping precipitation from space allowing to use optimally the full complementarity of SBSF and DBSF algorithms: SBSF algorithm provides with efficient estimates in light (usually stratiform) and moderate rain, while DBSF algorithm is well adapted to the case of convective rain.

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Paul Amayenc, Jean Philippe Diguet, Mongi Marzoug, and Taoufik Tani

Abstract

In Part I, four single-frequency (SF) algorithms and a dual-frequency (DF) algorithm for range profiling of the rain rate from a spaceborne radar were described and tested from numerical simulations. In Part II, performances of these algorithms are studied using data from a DF (X and Ka bands) near-nadir-pointing airborne radar. The data, gathered over ocean near Wallops Island in 1988, mimic future spaceborne radar measurements.

Rain retrievals are performed for isolated and series of contiguous rain measurements within stratiform and convective rain regions overflown by the aircraft. General features and aspects specific to the experiment conditions are pointed out. The SF algorithms provide more or less scattered results according to their own sensitivities to uncorrected scaling errors. Improvement of the algorithms stability by constraining the total path-integrated attenuation from surface echo measurements is confirmed. The correlation between attenuation coefficients at both frequencies, which forms the theoretical basis of the DF algorithm, is verified from the data. Results from DF algorithm are likely more reliable than SF counterparts since they are globally corrected for scaling errors. Rain-rate thresholds above which “attenuation” algorithms should relay ZR methods to avoid negative bias in rain-rate estimates are found near 12 mm h−1 at X band and 1 mm h−1 at Ka band for a 2.5-km rain depth. Coherent spatial structures of the rain rate within a vertical cross section of the storm are recovered from the “attenuation” algorithms.

The data obtained with a cross-range resolution L 0 ≅ 1 km are also used to perform 2D simulations of beam-averaging, and nonuniform beam-filling (NUBF) effects are used for cross-range resolutions L = 2, 3, and 4 km. Degrading the resolution produces a smoothing of small-scale rain-rate structures and a lowering of the rain-rate estimation. Bias due to NUBF depend on the involved “attenuation” algorithm. It increases with L but remains below 15%, up to L = 4 km for mean rain-rate estimates at large horizontal scale (≈100 km). The ZR methods are weakly affected by the NUBF.

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