Editorial Type:
Article
Article Type:
Research Article

Attenuation in Rain for X- and C-Band Weather Radar Systems: Sensitivity with respect to the Drop Size Distribution

Guy Delrieu Laboratoire d’Étude des Transferts en Hydrologie et Environnement, Grenoble, France

Search for other papers by Guy Delrieu in
Current site
Google Scholar
PubMed Close
,
Lorenz Hucke Laboratoire d’Étude des Transferts en Hydrologie et Environnement, Grenoble, France

Search for other papers by Lorenz Hucke in
Current site
Google Scholar
PubMed Close
, and
Jean Dominique Creutin Laboratoire d’Étude des Transferts en Hydrologie et Environnement, Grenoble, France

Search for other papers by Jean Dominique Creutin in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Jan 1999
DOI:
https://doi.org/10.1175/1520-0450(1999)038<0057:AIRFXA>2.0.CO;2
Page(s):
57–68
Restricted access

Abstract

This paper is devoted to a sensitivity study of the equation describing attenuation effects in rain for ground-based weather radar systems operating at X- or C-band wavelengths. First, the so-called attenuation equation, also termed the HB solution or HB algorithm in reference to the well-known paper by Hitschfeld and Bordan, is recalled. A procedure aimed at obtaining consistent relations between average values of the equivalent reflectivity factor Ze, the attenuation coefficient k, and the rain rate R as function of two parameters of the drop size distribution (DSD) is also presented. Then, a numerical simulation framework based on a simple description of rainfall characteristics and accounting for some of the radar measurement features is proposed to test the ability of the HB algorithm to perform attenuation correction of hypothetical rain-rate profiles. In a first step, the well-known instability of the solution is illustrated. For instance, it is shown that, even in the absence of radar calibration error and with perfect knowledge of the DSD, the algorithm is not able to correct profiles with path-integrated attenuation (PIA) greater than about 20 dB when typical values are considered for the radar parameters. Owing to this inherent instability, the sensitivity study with respect to the DSD parameters is therefore limited to profiles with PIAs less than 15 dB. The two following results are obtained: 1) a PIA of about 10 dB should be considered as the upper limit that the algorithm is able to correct and 2) given the choice of the (Ze, k, R) relations, optimization of one parameter is necessary and sufficient to obtain improvement over the standard ZR method for this range of PIAs. This parameter plays the role of a correction term for the radar calibration error, the uncertainty in the knowledge of the DSD, and other sources of bias. These results are confirmed by an X-band radar–rain gauge comparison with a dataset collected during the Marseilles Hydrometeorological Experiment.

Corresponding author address: Dr. Guy Delrieu, LTHE, UMR 5564 (CNRS, UJF, INPG, ORSTOM), BP53, 38041 Grenoble Cedex 9, France.

Abstract

This paper is devoted to a sensitivity study of the equation describing attenuation effects in rain for ground-based weather radar systems operating at X- or C-band wavelengths. First, the so-called attenuation equation, also termed the HB solution or HB algorithm in reference to the well-known paper by Hitschfeld and Bordan, is recalled. A procedure aimed at obtaining consistent relations between average values of the equivalent reflectivity factor Ze, the attenuation coefficient k, and the rain rate R as function of two parameters of the drop size distribution (DSD) is also presented. Then, a numerical simulation framework based on a simple description of rainfall characteristics and accounting for some of the radar measurement features is proposed to test the ability of the HB algorithm to perform attenuation correction of hypothetical rain-rate profiles. In a first step, the well-known instability of the solution is illustrated. For instance, it is shown that, even in the absence of radar calibration error and with perfect knowledge of the DSD, the algorithm is not able to correct profiles with path-integrated attenuation (PIA) greater than about 20 dB when typical values are considered for the radar parameters. Owing to this inherent instability, the sensitivity study with respect to the DSD parameters is therefore limited to profiles with PIAs less than 15 dB. The two following results are obtained: 1) a PIA of about 10 dB should be considered as the upper limit that the algorithm is able to correct and 2) given the choice of the (Ze, k, R) relations, optimization of one parameter is necessary and sufficient to obtain improvement over the standard ZR method for this range of PIAs. This parameter plays the role of a correction term for the radar calibration error, the uncertainty in the knowledge of the DSD, and other sources of bias. These results are confirmed by an X-band radar–rain gauge comparison with a dataset collected during the Marseilles Hydrometeorological Experiment.

Corresponding author address: Dr. Guy Delrieu, LTHE, UMR 5564 (CNRS, UJF, INPG, ORSTOM), BP53, 38041 Grenoble Cedex 9, France.

Save
Cover Journal of Applied Meteorology and Climatology
Journal of Applied Meteorology and Climatology

  • Amayenc, P., J. P. Diguet, M. Marzoug, and T. Tani, 1996: A class of single- and dual-frequency algorithms for rain-rate profiling from a spaceborne radar. Part 2: Tests from airborne radar measurements. J. Atmos. Oceanic Technol.,13, 142–164.

  • Atlas, D., and H. C. Banks, 1951: The interpretation of microwave reflections from rainfall. J. Meteor.,8, 271–282.

  • ——, and C. W. Ulbrich, 1974: The physical basis for attenuation–rainfall relationships and measurement of rainfall parameters by combined attenuation and radar methods. J. Rech. Atmos.,8, 275–298.

  • Beard, K. V., 1976: Terminal velocity and shape of cloud and precipitation drops aloft. J. Atmos. Sci.,33, 851–864.

  • Delrieu, G., J. D. Creutin, and I. Saint-André, 1991: Mean K–R relationships: Practical results for typical weather radar wavelengths. J. Atmos. Oceanic Technol.,8, 467–476.

  • ——, S. Caoudal, and J. D. Creutin, 1997: Feasibility of using mountain return for the correction of ground-based X-Band weather radar. J. Atmos. Oceanic Technol.,14, 368–385.

  • Geotis, S. G., 1975: Some measurements of the attenuation of 5-cm radiation in rain. Preprints, 16th Conf. on Radar Meteorology, Houston, TX, Amer. Meteor. Soc., 63–66.

  • Haddad, Z. S., I. Eastwood, and S. L. Durden, 1995: Intrinsic ambiguities in the retrieval of rain rates from radar returns at attenuating wavelengths. J. Appl. Meteor.,34, 2667–2679.

  • Hildebrand, P. H., 1978: Iterative correction for attenuation of 5-cm radar in rain. J. Appl. Meteor.,17, 508–514.

  • Hitschfeld, W., and J. Bordan, 1954: Errors inherent in the radar measurement of rainfall at attenuating wavelengths. J. Meteor.,11, 58–67.

  • Joss, J., and A. Waldvogel, 1967: Ein Spektrograph für Niederschlagstropfen mit Automatisher Auswertung. Pure Appl. Geophys.,68, 240–246.

  • ——, and ——, 1969: Raindrop size distribution and sampling size error. J. Atmos. Sci.,26, 566–569.

  • Kozu, T., and K. Nakamura, 1991: Rainfall parameter estimation from dual-radar measurements combining reflectivity profiles and path-integrated attenuation. J. Atmos. Oceanic Technol.,8, 259–270.

  • Marshall, J. S., and W. K. Palmer, 1948: The distribution of raindrops with size. J. Meteor.,5, 165–166.

  • Marzoug, M., and P. Amayenc, 1991: Improved range profiling algorithm of rainfall rate from a spaceborne radar with a path-integrated constraint, IEEE Trans. Geosci. Remote Sens.,GE-29, 584–592.

  • ——, ——, 1994: A class of single- and dual-frequency algorithms for rain-rate profiling from a spaceborne radar. Part 1: Principle and tests from numerical simulations. J. Atmos. Oceanic Technol.,11, 1480–1506.

  • Meneghini, R., 1978: Rain-rate estimates for an attenuating radar. Radio Sci.,13, 459–470.

  • ——, and T. Kozu, 1990: Spaceborne Weather Radar. Artech House, 199 pp.

  • ——, J. Eckerman, and D. Atlas, 1983: Determination of rain rate from a spaceborne radar using measurements of total attenuation. IEEE Trans. Geosci. Remote Sens.,GE–21, 34–43.

  • Sauvageot, H., and J. P. Lacaux, 1995: The shape of averaged drop size distributions. J. Atmos. Sci.,52, 1070–1083.

  • Sempere-Torres, D., J. M. Porra, and J. D. Creutin, 1994: A general formulation for raindrop size distribution. J. Appl. Meteor.,33, 1494–1502.

  • ——, ——, ——, 1998: Experimental evidence of a general description for raindrop size distribution properties. J. Geophys. Res.,103 (D2), 1785–1797.

  • Testud, J., and P. Amayenc, 1989: Stereoradar Meteorology: A promising technique for observation of precipitation from a mobile platform. J. Atmos. Oceanic Technol.,6, 89–108.

  • ——, ——, X. Dou, and T. Tani, 1996: Tests of rain profiling algorithms for a spaceborne radar using raincell models and real data precipitation fields. J. Atmos. Oceanic Technol.,13, 426–453.

  • Weible, M. L., and D. Sirmans, 1976: Simulation of attenuation by rainfall at a wavelength of 5 cm. Preprints, 17th Conf. on Radar Meteorology, Seattle, WA, Amer. Meteor. Soc., 75–78.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 799 371 49
PDF Downloads 458 233 20