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Daniele Hauser and Paul Amayenc

Abstract

Raindrop-size distributions and vertical air motions are deduced from vertically pointing C-band Doppler radar data by using a new method (described in Hauser and Amayenc, 1981) which assumes the raindrop sizes are exponentially distributed [N 0 exp(−λD)]. Results gathered in stratiform rain precipitation after the passage of a cold front are presented and compared with those obtained by using the well-known Rogers approach. The new method which does not a priori require the knowledge of N 0 values is capable of detecting spatial and temporal variations much better than the Rogers method. Taking this variability into account allows one to find relationships involving three rainfall parameters with good accuracy.

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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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Taoufik Tani and Paul Amayenc

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Rain measurements of the airborne Tropical Rainfall Measurement Mission (TRMM) radar simulator Airborne Rain-Mapping Radar in a typical event of Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment are used to compare near-nadir rain-rate profiles retrieved from a set of deterministic attenuation-compensating algorithms. This set includes generic algorithms such as the Hitschfeld–Bordan (HB) estimate and the surface reference (SR) methods constraining the total path-integrated attenuation (PIA), and two hybrid algorithms of which one uses the same principle as the “standard” TRMM radar-profiling algorithm. In absence of reference rain data for validating the retrievals, the study is based upon an intercomparison of the results and analyzes their features in relation with theoreretical predictions. The rain data sequence is the same as used previously in a companion paper, which allowed the authors to get rain relations better adjusted to the observed rain system than those associated to a Marshall–Palmer (MP) drop size distribution. These two sets of rain relations are used here to study subsequent changes in the various rain retrievals. How comparing the results among the generic and/or the hybrid algorithms may help identify the physical assumptions and error sources in the various methods is pointed out.

With the MP relations, all methods provide almost similar retrievals in stratiform light rain. In convective heavy rain, the retrievals are largely scattered; erroneous HB-derived PIA estimates are responsible for a downward collapsing effect in the HB and the TRMM-like radar algorithms, which prevents them from recovering a credible cell-like structure. With the adjusted relations, the rain estimates from all methods are generally increased and in much better agreement. A mirror image algorithm performing PIA profiling from the surface is also exploited. The direct estimate of the surface backscatter coefficient, obtainable below very light rain only, agrees with the value measured in clear air. The one-way PIAs, immune to errors in the radar calibration and the rain relations, are found to be well correlated with those derived from SR algorithms over a 5-dB range, provided that a bulk correction factor involving these two error types be adjusted in the latter case.

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Daniele Hauser and Paul Amayenc

Abstract

Using the hypothesis of an exponential hydrometeor-size distribution characterized by the two classical intercept (N 0) and slope (λ) parameters, a method is presented for simultaneously deducing N 0, λ and the vertical air velocity w from a Doppler spectrum measured at vertical incidence. It is based on a least-squares fitting of a theoretical spectrum depending on N 0, λ and w, which are the adjusted parameters, to the measured one. The principle, sensitivity and limitations of the method are discussed in detail. It is expected that this method applies mainly to the case of stratiform rain.

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Danièle Hauser and Paul Amayenc

Abstract

This paper describes the retrieval of cloud water and water vapor contents from Doppler radar data. The convective part of a tropical squall line (22 June 1981) observed during the COPT 81 (Convection Profonde Tropicale 1981) West African experiment, was chosen for developing a two-dimensional and steady state model for the retrieval of these parameters. The model is based upon the solution of the continuity equation for the total water substance, with wind and rain water fields specified from Doppler radar observations. The results are consistent with the previous kinematic analysis of the convective part of this squall line. Cloud water mixing ratios up to 4 g kg−1 are found in the warm and unstable inflow while unsaturated air is observed in the low level frontward cold flow. At high altitude, an important amount of condensate is transferred rearward into the stratiform part of the squall line. The paper also presents sensitivity tests of the model in order to discuss the main assumptions used to cope with the problem.

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Anthony J. Illingworth, Daniele Hauser, and Paul Amayenc

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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, 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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Danièle Hauser, Frank Roux, and Paul Amayenc

Abstract

Microphysical and thermodynamic retrieval studies using a specified wind field can provide a means for analysing the different processes occurring within an observed precipitating system. Up to now, the retrieval of microphysical variable fields or thermodynamic fields have been performed separately, though the interest of associating both types of retrieval has been already noted by several authors.

The research reported here presents a new retrieval method allowing consistent and simultaneous derivation of the microphysical and thermodynamic variable fields using the whole set of governing equations (momentum, thermodynamic, and microphysical equations) with the wind field specified from Doppler radar observations. The microphysical retrieval makes use of the continuity equation for the total water substance and for the precipitating substance. Two types of precipitating particles are considered (rain and graupel), and a parameterization derived from that proposed by Kessler is chosen. In practice, the microphysical retrieval is coupled to the retrieval of thermodynamic variables, which is derived from Roux. A more classical approach taking into account the thermodynamic equation and the microphysical equations, but not the momentum equation is also used for comparison.

Results obtained from both approaches in the convective region of a tropical squall line observed during COPT81 (22 June 1981) are presented and discussed. It is found that both approaches provide results in mutual agreement, and which are consistent with the observed reflectivity structure, and with surface measurements. The respective advantages and drawbacks of each approach are also discussed.

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Peter Bauer, Paul Amayenc, Christian D. Kummerow, and Eric A. Smith

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The objective of this paper is to establish a computationally efficient algorithm making use of the combination of Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and precipitation radar (PR) observations. To set up the TMI algorithm, the retrieval databases developed in Part I served as input for different inversion techniques: multistage regressions and neural networks as well as Bayesian estimators. It was found that both Bayesian and neural network techniques performed equally well against PR estimates if all TMI channels were used. However, not using the 85.5-GHz channels produced consistently better results. This confirms the conclusions from Part I. Generally, regressions performed worse; thus they seem less suited for general application due to the insufficient representation of the nonlinearities of the TB–rain rate relation. It is concluded that the databases represent the most sensitive part of rainfall algorithm development.

Sensor combination was carried out by gridding PR estimates of rain liquid water content to 27 km × 44 km horizontal resolution at the center of gravity of the TMI 10.65-GHz channel weighting function. A liquid water dependent database collects common samples over the narrow swath covered by both TMI and PR. Average calibration functions are calculated, dynamically updated along the satellite track, and applied to the full TMI swath. The behavior of the calibration function was relatively stable. The TMI estimates showed a slight underestimation of rainfall at low rain liquid water contents (<0.1 g m−3) as well as at very high rainfall intensities (>0.8 g m−3) and excellent agreement in between. The biases were found to not depend on beam filling with a strong correlation to rain liquid water for stratiform clouds that may point to melting layer effects.

The remaining standard deviations between instantaneous TMI and PR estimates after calibration may be treated as a total retrieval error, assuming the PR estimates are unbiased. The error characteristics showed a rather constant absolute error of <0.05 g m−3 for rain liquid water contents <0.1 g m−3. Above, the error increases to 0.6 g m−3 for amounts up to 1 g m−3. In terms of relative errors, this corresponds to a sharp decrease from >100% to 35% between 0.05 and 0.5 g m−3. The database ambiguity, that is, the standard deviation of near-surface rain liquid water contents with the same radiometric signature, provides a means to estimate the contribution from the simulations to this error. In the range where brightness temperatures respond most sensitively to rainwater contents, almost the entire error originates from the ambiguity of signatures. At very low and very high rain rates (<0.05 and >0.7 g m−3) at least half of the total error is explained by the inversion process.

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