Probability-matched Reflectivity-Rainfall Relations for a Hurricane from Aircraft Observations

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  • a Hurricane Research Division, NOAA/AOML, Miami, Florida
  • | b NASA/Goddard Space Flight Center, Greenbelt, Maryland
  • | c Hurricane, Research Division, NOAA/AOML, Miami, Florida
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Abstract

The probability-matching method (PMM) was used to determine the relation between the distribution of equivalent reflectivity Ze measured by an airborne C-band radar and that for concurrently measured rain rate R by a disdrometer on the same aircraft in the eyewall and outer bands of Hurricane Anita in 1977. When the PMM is applied to the disdrometer population of Z's and R's one finds that the Z-R relations differ significantly from those obtained by linear regression of their 1ogarithms. Such regression relations are deceptive. When PMM is applied to the set of Ze's and R's we get a family of Ze-R relations as a function of range which differ significantly from the traditional disdrometer-based Z-R relation for hurricanes by Jorgensen and Willis (JW). These new relations are approximate power laws with slope (exponent) which decrease with increasing range. At ranges less than about 35 km the reflectivity in the eyewall exceeds that in the outer bands and is consistent with the expectation from the disdrometer-based relations. At greater ranges the converse is true due to beamwidth averaging over a broader beam and different vertical profiles of reflectivity in the eyewall and outer bands. We also devise a method to obtain an “effective zero-range” Ze-R relation. This differs from the JW relation by −8.2 dBZ and reflects an error in the radar calibration. This approach is a novel way to calibrate an airborne meteorological radar. The methods may be used with any type of rainstorms and provide a means of using airborne radar and disdrometer systems for air-truthing rainfall measurements from space.

Abstract

The probability-matching method (PMM) was used to determine the relation between the distribution of equivalent reflectivity Ze measured by an airborne C-band radar and that for concurrently measured rain rate R by a disdrometer on the same aircraft in the eyewall and outer bands of Hurricane Anita in 1977. When the PMM is applied to the disdrometer population of Z's and R's one finds that the Z-R relations differ significantly from those obtained by linear regression of their 1ogarithms. Such regression relations are deceptive. When PMM is applied to the set of Ze's and R's we get a family of Ze-R relations as a function of range which differ significantly from the traditional disdrometer-based Z-R relation for hurricanes by Jorgensen and Willis (JW). These new relations are approximate power laws with slope (exponent) which decrease with increasing range. At ranges less than about 35 km the reflectivity in the eyewall exceeds that in the outer bands and is consistent with the expectation from the disdrometer-based relations. At greater ranges the converse is true due to beamwidth averaging over a broader beam and different vertical profiles of reflectivity in the eyewall and outer bands. We also devise a method to obtain an “effective zero-range” Ze-R relation. This differs from the JW relation by −8.2 dBZ and reflects an error in the radar calibration. This approach is a novel way to calibrate an airborne meteorological radar. The methods may be used with any type of rainstorms and provide a means of using airborne radar and disdrometer systems for air-truthing rainfall measurements from space.

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