David Atlas

Path- and Area-Integrated Rainfall Measurement by Microwave Attenuation in the 1–3 cm Band

Abstract The reasons for the linear relationship between microwave attenuation A and rainfall rate R near 1 cm wavelength are explained. This linearity also implies independence of the A-R relationship from the drop size distribution (DSD), thus making attenuation measurements near this wavelength attractive for path-averaged rainfall. Regression equations of the form A = KRα are calculated for four radar wavelengths from 0.86 to 3.2 cm from drop size spectra. As predicted, α increases from about 1.04 to 1.16 and average errors of estimate of R from the regression equations increase from about 9 to 21% from 0.86 to 3.2 cm, respectively. The larger errors at 3.2 cm reflect the increased dependence on the form of DSD. Even at 3.2 cm, the errors are typically less than half those incurred from the use of reflectivity factor Z and a priori Z-R relations. Various methods of measuring path- and area-averaged R are studied. Radar methods using standard targets fail over 30 km paths at wavelengths of 0.86 and 1.2...

Advances in Radar Meteorology

Publisher Summary In this chapter there were two main objectives: To summarize significant developments in radar meteorology since 1958 and to integrate them properly within the framework of knowledge existing prior to that time. The emphasis in this chapter is on the basic principles and concepts of radar meteorology. In order to relate the measured reflectivity to the size and concentration of the particles in the scattering volume, and thus to the conventional meteorological parameters, such as liquid water content and precipitation rate, this chapter is first to determine the radar cross section of an individual scatterer as a function of its refractive index, size, shape, and orientation. Because of the importance of precipitation rate in a variety of meteorological problems, ranging from flood warning to research on the water budget of a storm, extensive consideration is given to its measurement by radar. Radar measurements of storm structure and dimensions suffer from beam width and side lobe effects. In particular, the problem of estimating true storm height is discussed in some detail in the next section, and it is shown how the heights of intense storms may be greatly overestimated by the effects of side lobes, while the visible tops of some weaker storms may be underestimated. The use of Doppler or coherent radar techniques permits the measurement of the velocities of the scatterers, and so, provides a vital new dimension in radar probing of the atmosphere. The basic Doppler theory and the relation of the Doppler spectrum of the scatterers to the fluctuation spectrum of echo intensity on incoherent (conventional) pulse radar are reviewed in some detail. The final section is devoted to a comprehensive review of the long-elusive phenomenon of “angel” echoes.

General Probability-matched Relations between Radar Reflectivity and Rain Rate

Abstract A method of deriving the relation between radar-observed reflectivities Ze and gauge-measured rain intensity, R is presented. It is based on matching the probabilities of the two variables. The observed reflectivity is often very different from the true reflectivity near the surface due to the averaging of the real reflectivity field aloft by the beam, path attenuation, and variations in the drop-size distribution (DSD) between the pulse volume and the surface. The probability-matching method (PMM) inherently accounts for all of these differences on average. The formulation of the Ze − R functions is constrained such that 1) the radar-retrieved probability density function (PDF) of R is identical to the gauge-measured PDF, and 2) the traction of the time that it is raining is identical for both the radar and for simultaneous, collocated gauge measurements. This ensures that the rain measured by the radar is equal to that observed at the gauges. The resultant Ze − R functions are not constrained t...

Systematic variation of drop size and radar‐rainfall relations

Time histories of the characteristics of the drop size distribution of surface disdrometer measurements collected at Kapingamarangi Atoll were partitioned for several storms using rain rate R, reflectivity factor Z, and median diameter of the distribution of water content D0. This partitioning produced physically based systematic variations of the drop size distribution (DSD) and Z-R relations in accord with the precipitation types viewed simultaneously by a collocated radar wind profiler. These variations encompass the complete range of scatter around the mean Z-R relations previously reported by Tokay and Short [1996] for convective and stratiform rain and demonstrate that the scatter is not random. The systematic time or space variations are also consistent with the structure of mesoscale convective complexes with a sequence of convective, transition, and stratiform rain described by various authors. There is a distinct inverse relation between the coefficient A and the exponent of the Z-R relations which has been obscured in prior work because of the lack of proper discrimination of the rain types. Contrary to previous practice it is evident that there is also a distinct difference in the DSD and the Z-R relations between the initial convective and the trailing transition zones. The previously reported Z-R relation for convective rain is primarily representative of the transition rain that was included in the convective class. The failure of present algorithms to distinguish between the initial convective and the trailing transition rains causes an erroneous apportionment of the diabatic heating and cooling and defeats the primary intent of discriminating stratiform from convective rains.

Rainfall Microphysics and Radar Properties: Analysis Methods for Drop Size Spectra

Abstract Analyses are performed of experimental drop size spectra to explore the relationships among integral parameters for rain. The data used in this work were acquired with an airborne optical 2D precipitation probe in TOGA COARE during a 4-month period in 1992–93. It is assumed that the experimental size spectra can be described by a gamma drop size distribution (DSD) of the form N(D) = N0Dμ exp(−ΛD) involving three parameters (N0, μ, Λ), which are determined using a new method of truncated moments. The method allows for truncation of the DSD at the large-diameter end of the spectrum due in part to instrumental effects and also in part to the trajectory of the aircraft through a rain streamer that has been sorted by wind shear. An effect analogous to truncation can occur at the small-diameter end of the size spectrum due to evaporation. However, truncation of the spectrum at the small-diameter end is not considered in this work. It is found that spectra with small space and timescales display conside...

Climatologically tuned reflectivity-rain rate relations and links to area-time integrals

Abstract Relations between either the point- or beam-averaged effective reflectivity, Ze, and surface rain rate, R, are determined by a probability matching method similar to that of Calheiros and Zawadzki, and Rosenfeld. The cumulative density functions (CDF) of reflectivity and rain rate are matched at pairs of Ri, Zi, which give the same percentile contribution. One obtains range dependent Ze − R relations by stratifying the Ze data by range. Truncation of the Ze distribution by too large a threshold causes the threshold rain rate retrieved from the radar data to exceed that in the matching gage distribution. Forcing a match between the mean rate measured by the gages and those retrieved by use of a set of trial Ze − R equations provides for the adjustment of the final Ze − R relation and compensates for the truncation. The radar retrieved CDFs of rain rate then replicate the CDF of gage measured rates nicely. In the case of GATE the probability matching scheme produces a Ze − R relation that agrees wi...

On the Separation of Tropical Convective and Stratiform Rains

Abstract This work resolves an apparent conflict between the results of Yuter and Houze and Atlas et al. concerning relations between radar reflectivity factor Z and rainfall rate R derived from essentially the same drop size data observed aloft during the Tropical Ocean and Global Atmosphere programs (TOGA) Coupled Ocean–Atmosphere Response Experiment (COARE). It is shown that the single relation found by Yuter and Houze is founded upon distinct underlying Z–R relations for stratiform and convective rains. This result occurs despite the fact that errors in rain types classified by different methods and the variability of the effective drop sizes within each type tend to obscure the distinction. This newly found agreement between the two distinctly different methods of analysis also suggests the essential equivalence of the classification methods of Steiner et al. (based upon the existence of a maximum in the observed reflectivity field) and of Atlas et al. (based upon the magnitude of the drafts). Howev...

Early Foundations of the Measurement of Rainfall by Radar

Shortly before the outbreak of World War II, there was very intense research activity in the United States and the United Kingdom involving the development of radar. The exact date on which precipitation echoes were first detected with this new instrument is not certain (see the Appendix), but Ligda (1951) recorded that a shower was tracked on a 10-cm radar to a range of 7 miles off the English coast on 20 February 1941. On 7 February 1941, a 10-cm radar was used at the Radiation Laboratories in Cambridge, Massachusetts, to detect aircraft over the Boston airport about 5 miles away. Using reasonable assumptions, it can be shown that echoes from rain or snow of intensity about 1 to 3 mm h−1 could have been detected by this radar at short ranges. Thus, the first precipitation echoes quite probably were detected very shortly after 7 February 1941, or almost simultaneously with the date of the first reported detection in England. We have been unable to document such an event in the United States until the work of Bent (1943) in 1942–43. It soon became obvious that microwave radar would be an excellent tool for the observation of storms and for tracking balloon-borne targets for wind-finding. This review highlights the key research steps leading to the development of techniques for the quantitative estimation of rainfall by radar. We use the word “estimation” because a variety of factors produce both scatter and bias in the radar rainfall observations.