The raindrop size distribution (DSD) is vital for applications such as quantitative precipitation estimation, understanding microphysical processes, and validation/improvement of two-moment bulk microphysical schemes. We trace the history of the DSD representation and its linkage to polarimetric radar observables from functional forms (exponential, gamma, and generalized gamma models) and its normalization (un-normalized, single/double-moment scaling normalized). The four-parameter generalized gamma model is a good candidate for the optimal representation of the DSD variability. A radar-based disdrometer was found to describe the five archetypical shapes (from Montreal, Canada) consisting of drizzle, the larger precipitation drops and the ‘S’-shaped curvature that occurs frequently in between the drizzle and the larger-sized precipitation. Similar ‘S’-shaped DSDs were reproduced by combining the disdrometric measurements of small-sized drops from an optical array probe and large-sized drops from 2DVD. A unified theory based on the double-moment scaling normalization is described. The theory assumes the multiple power law among moments and DSDs are scaling normalized by the two characteristic parameters which are expressed as a combination of any two moments. The normalized DSDs are remarkably stable. Thus, the mean underlying shape is fitted to the generalized gamma model from which the ‘optimized’ two shape parameters are obtained. The other moments of the distribution are obtained as the product of power laws of the reference moments M3 and M6 along with the two shape parameters. These reference moments can be from dual-polarimetric measurements: M6 from the attenuation-corrected reflectivity and M3 from attenuation-corrected differential reflectivity and the specific differential propagation phase. Thus, all the moments of the distribution can be calculated, and the microphysical evolution of the DSD can be inferred. This is one of the major findings of this article.
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Retrieval of lower-order moments of the drop size distribution using CSU-CHILL X-band polarimetric radar: a case study
Abstract. The lower-order moments of the drop size distribution (DSD) have generally been considered difficult to retrieve accurately from polarimetric radar data because these data are related to higher-order moments. For example, the 4.6th moment is associated with a specific differential phase and the 6th moment with reflectivity and ratio of high-order moments with differential reflectivity. Thus, conventionally, the emphasis has been to estimate rain rate (3.67th moment) or parameters of the exponential or gamma distribution for the DSD. Many double-moment “bulk” microphysical schemes predict the total number concentration (the 0th moment of the DSD, or M0) and the mixing ratio (or equivalently, the 3rd moment M3). Thus, it is difficult to compare the model outputs directly with polarimetric radar observations or, given the model outputs, forward model the radar observables. This article describes the use of double-moment normalization of DSDs and the resulting stable intrinsic shape that can be fitted by the generalized gamma (G-G) distribution. The two reference moments are M3 and M6, which are shown to be retrievable using the X-band radar reflectivity, differential reflectivity, and specific attenuation (from the iterative correction of measured reflectivity Zh using the total Φdp constraint, i.e., the iterative ZPHI method). Along with the climatological shape parameters of the G-G fit to the scaled/normalized DSDs, the lower-order moments are then retrieved more accurately than possible hitherto. The importance of measuring the complete DSD from 0.1 mm onwards is emphasized using, in our case, an optical array probe with 50 µm resolution collocated with a two-dimensional video disdrometer with about 170 µm resolution. This avoids small drop truncation and hence the accurate calculation of lower-order moments. A case study of a complex multi-cell storm which traversed an instrumented site near the CSU-CHILL radar is described for which the moments were retrieved from radar and compared with directly computed moments from the complete spectrum measurements using the aforementioned two disdrometers. Our detailed validation analysis of the radar-retrieved moments showed relative bias of the moments M0 through M2 was <15 % in magnitude, with Pearson’s correlation coefficient >0.9. Both radar measurement and parameterization errors were estimated rigorously. We show that the temporal variation of the radar-retrieved mass-weighted mean diameter with M0 resulted in coherent “time tracks” that can potentially lead to studies of precipitation evolution that have not been possible so far.
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- Award ID(s):
- 1901585
- NSF-PAR ID:
- 10232025
- Date Published:
- Journal Name:
- Atmospheric Measurement Techniques
- Volume:
- 13
- Issue:
- 9
- ISSN:
- 1867-8548
- Page Range / eLocation ID:
- 4727 to 4750
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Commonly used disdrometers tend not to accurately measure concentrations of very small drops in the raindrop size distribution (DSD), either through truncation of the DSD at the small-drop end or because of large uncertainties on these measurements. Recent studies have shown that, as a result of these inaccuracies, many if not most ground-based disdrometers do not capture the “drizzle mode” of precipitation, which consists of large concentrations of small drops and is often separated from the main part of the DSD by a shoulder region. We present a technique for reconstructing the drizzle mode of the DSD from “incomplete” measurements in which the drizzle mode is not present. Two statistical moments of the DSD that are well measured by standard disdrometers are identified and used with a double-moment normalized DSD function that describes the DSD shape. A model representing the double-moment normalized DSD is trained using measurements of DSD spectra that contain the drizzle mode obtained using collocated Meteorological Particle Spectrometer and 2D video disdrometer instruments. The best-fitting model is shown to depend on temporal resolution. The result is a method to estimate, from truncated or uncertain measurements of the DSD, a more complete DSD that includes the drizzle mode. The technique reduces bias on low-order moments of the DSD that influence important bulk variables such as the total drop concentration and mass-weighted mean drop diameter. The reconstruction is flexible and often produces better rain-rate estimations than a previous DSD correction routine, particularly for light rain.
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.5194/amt-13-4727-2020
