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Anthony J. Illingworth and Dusan Zrnic

A workshop on weather radar polarimetry for research and operational applications was held on 22 and 23 February 1994 at the National Center for Atmospheric Research. Polarization radar can provide estimates of the shapes, sizes, phase, and fall orientations of hydrometeors. This information can be used to remove some of the ambiguities present when only the reflectivity is measured. The morning of 22 February was devoted to 16 short presentations highlighting recent advances in polarimetric radar. The afternoon was dedicated to four discussion sessions that further developed important topics. On the following day, plans for the upgrading and development of the existing NCAR polarization radar capability were presented and debated. The workshop resulted in four recommendations: three of which proposed specific field measurement programs to quantify the potential improvements provided by the polarization techniques.

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Robin J. Hogan and Anthony J. Illingworth

Abstract

Spaceborne millimeter-wave radar has been identified as a possible instrument to make global measurements in ice clouds, which have an important but poorly understood role in the earth’s radiation budget. In this paper, the authors explore the potential of a dual-frequency spaceborne radar to estimate crystal size in cirrus clouds and, hence, determine ice water content and the shortwave extinction coefficient more accurately than would be possible using a single radar. Calculations show that gaseous attenuation is not a serious problem for a nadir-pointing radar measuring down to cirrus altitudes at frequencies between 35 and 215 GHz, provided the frequencies are chosen to lie in the window regions of the atmospheric absorption spectrum. This enables one to exploit the significant benefits of using frequencies too high to be operated from the ground. Radar reflectivity at 35, 79, 94, 140, and 215 GHz has been calculated from aircraft ice particle size spectra obtained during the European Cloud Radiation Experiment (EUCREX) and the Central Equatorial Pacific Experiment (CEPEX), and it is shown that overall the most promising dual-wavelength combination for measuring crystal size and ice water content is 79 and 215 GHz. For a minimum radar sensitivity of −30 dBZ, this combination can measure ice water content and median volume diameter with errors of between 10% and 30% when the reflectivity is greater than −15 dBZ (equivalent to an ice water content of around 0.015 g m−3). If only a single wavelength radar were affordable, then, for estimating ice water content, 215 GHz would be the preferred choice. Since the two radars would be likely to use the same antenna, the authors also consider the effect of cloud inhomogeneities to introduce a random error into the reflectivity ratio because of the different beamwidths at each frequency. It is found, using data from the cloud radars at Chilbolton, England, that this is more than 0.2 dB for frequency pairings that include 35 GHz but for all other combinations is less than 0.1 dB, which is comparable to the other errors in the system and much smaller than the typical values being measured. Nonspherical crystals are shown to have a significant effect on the size measured by a nadir-pointing dual-wavelength radar, but the authors present evidence that this can be largely eliminated by viewing at 45° from nadir.

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Robin J. Hogan and Anthony J. Illingworth

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Cloud variability on scales smaller than the gridbox size of numerical forecast and climate models is believed to be important in determining the radiative effects of clouds, and increasingly attempts are being made to parameterize these fluctuations in the radiation schemes of current models. In order to calculate the radiative effects of an inhomogeneous cloud, a model needs to know not only the degree of variability within a gridbox but also the degree to which the inhomogeneities in vertically adjacent levels are overlapped. In this paper these two parameters are derived for ice clouds from an 18-month midlatitude 94-GHz cloud radar dataset and parameterized in terms of horizontal gridbox size (d), the vertical shear of the horizontal wind (s), and the vertical position in the cloud. The vertical decorrelation length Δz 0 (i.e., the depth over which the correlation coefficient of either ice water content or optical extinction coefficient in separate vertical levels falls to e −1) is found to be well represented in the mean by log10Δz 0 = 0.3 log10 d − 0.031s − 0.315, where Δz 0 and d are in kilometers and s is in meters per second per kilometer. As expected, higher shear results in more rapid decorrelation, although the rms deviation from this expression is around a factor of 2.5. It is found that the probability distribution of ice water content within a gridbox is usually well represented by a lognormal or gamma distribution. The fractional variance in ice water content (f IWC) may be expressed to within a factor of 2 by log10 f IWC = 0.3 log10 d − 0.04s − 0.93, valid for d < 60 km, above which f IWC is constant with increasing d. The expression for the fractional variance of visible extinction coefficient is the same except with the −0.93 term replaced by −0.96. The s dependence indicates a tendency for increased shear to result in decreased cloud variability. This can be explained by the presence of ice fallstreaks in a sheared flow: a parcel of air in the middle of a cloud is alternately fed from above by ice-rich and ice-poor air, resulting in a homogenization of the layer at a rate dependent on the shear. A more complicated formula is derived to express the dependence of f IWC on the vertical position within the cloud; it is found that fractional variance tends to be largest at cloud top and decreases into the interior before increasing again in the lowest third of the cloud. Thicker clouds tend to have lower fractional variance. No significant dependence on temperature or absolute altitude was found for either f IWC or Δz 0.

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Neil I. Fox and Anthony J. Illingworth

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The radar reflectivity and liquid water content of stratocumulus clouds have been computed from cloud droplet spectra recorded during more than 4000 km of cloud penetrations by an aircraft, and the probability of detecting various values of liquid water content as a function of the radar sensitivity threshold has been derived. The goal of the study is to specify the sensitivity required for any future spaceborne cloud radar. In extensive marine stratocumulus deeper than about 200 m, occasional but ubiquitous drizzle-sized droplets of up to 200 μm dominate the radar return and increase it by between 10 and 20 dB above the cloud droplet contribution to the return, making radar detection easier, although the concentration of the drizzle drops is so low that they have no effect on the liquid water content or effective radius. These occasional drizzle-sized droplets are present throughout the vertical and horizontal extent of such clouds but should evaporate within 200 m of cloud base. On occasion, the drizzle can fall farther and may yield a false measurement of cloud-base altitude, but such cases can be recognized by examining the vertical profile of reflectivity. A radar sensitivity threshold of −30 dBZ would detect 80%, 85%, and 90% of the marine stratocumulus, with a liquid water content above 0.025, 0.05, and 0.075 g m−3, respectively. Because nonprecipitating drizzle droplets are rare in continental stratocumulus, the equivalent figures are reduced to 38%, 33%, and 25%. Improving the sensitivity to −40 dBZ increases detection probability to nearly 100% for both types of cloud. These figures are based on the assumption that the cloud is deep enough to fill the radar pulse volume.

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Nicolas Gaussiat, Henri Sauvageot, and Anthony J. Illingworth

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Cloud liquid water and ice content retrieval in precipitating clouds by the differential attenuation method using a dual-wavelength radar, as a function of the wavelength pair, is first discussed. In the presence of non-Rayleigh scatterers, drizzle, or large ice crystals, an ambiguity appears between attenuation and non-Rayleigh scattering. The liquid water estimate is thus biased regardless of which pair is used. A new method using three wavelengths (long λ l, medium λ m, and short λ s) is then proposed in order to overcome this ambiguity. Two dual-wavelength pairs, (λ l, λ m) and (λ l, λ s), are considered. With the (λ l, λ m) pair, ignoring the attenuation, a first estimate of the scattering term is computed. This scattering term is used with the (λ l, λ s) pair to obtain an estimate of the attenuation term. With the attenuation term and the (λ l, λ m) pair, a new estimate of the scattering term is computed, and so on until obtaining a stable result. The behavior of this method is analyzed through a numerical simulation and the processing of field data from 3-, 35-, and 94-GHz radars.

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Anthony J. Illingworth, Daniele Hauser, and Paul Amayenc

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Anthony J. Illingworth and T. Mark Blackman

Abstract

Polarization radar techniques essentially rely on detecting the oblateness of raindrops to provide a measure of mean raindrop size and then using this information to give a better estimate of rainfall rate R than is available from radar reflectivity Z alone. To derive rainfall rates from these new parameters such as differential reflectivity Z DR and specific differential phase shift K DP and to gauge their performance, it is necessary to know the range of naturally occurring raindrop size spectra. A three parameter gamma function is in widespread use, with the three variables N o, D o, and μ providing a measure of drop concentration, mean size, and spectral shape, respectively. It has become standard practice to derive the range of these three variables in rain by comparing the 69 published values of the constants a and b in the empirical relationships Z = aR b with the values of a and b obtained when R and Z are derived by integrating the appropriately weighted gamma function. The relationships in common use both for inferring R from Z, Z DR, and K DP, and for developing attenuation correction routines have been derived from a best fit through the values obtained by cycling over these predicted ranges of N o, D o, and μ. It is pointed out that this derivation of the predicted range of N o, D o, and μ arises using a flawed logic for a particular nonnormalized form of the gamma function, and it is shown that the predicted ranges give rise to some very unrealistic drop spectra, including many with high rainfall and very small drop sizes. It is suggested that attenuation correction routines relying on differential phase may be suspect and the commonly used relationships between rainfall rate and Z, Z DR, and K DP need to be reexamined. When more realistic drop shapes are also used, it may be that published relationships for deriving R from Z and Z DR are in error by over a factor of 2; a new equation is proposed that, in the absence of hail and attenuation, should yield values of R accurate to 25%, provided that Z DR can be estimated to 0.2 dB and Z is calibrated to 1 dB. Relationships of the form R = a KbDP, with b = 1.15, are in widespread use, but more realistic drop spectra and drop shapes yield a value of b closer to 1.4, similar to the exponent in ZR relationships. In accord, although K DP has the advantage of insensitivity to hail, it may have the same sensitivity to variations in drop spectra as Z does. In addition, the higher value of the exponent b implies that the proposed use of the total phase shift to give the path-integrated total rainfall is also questionable. However, the consistency of Z, Z DR, and K DP in rain can be used to provide absolute calibration of Z to 0.5 dB (12%), and when it fails it indicates that hail is present, in which case a relationship of the form K DP = aR 1.4 should be used. The technique should work at S, C, and X band, but, in all cases, paths should be chosen so that the total phase shift is not large enough to introduce significant attenuation of Z and Z DR.

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Neil I. Fox and Anthony J. Illingworth

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The radiative characteristics of stratocumulus clouds are dependent upon their microphysical properties, primarily the liquid water content and effective radius of the drop population. Aircraft observations of droplet spectra in warm stratocumulus over the North Atlantic and around the British Isles by the Hercules C-130 aircraft of the U.K. Meteorological Office Meteorological Research Flight have been used to calculate the radar reflectivity, liquid water content, and effective radius. Empirically derived relationships, found from more than 4000 km of flight data on 11 separate days, that link reflectivity with either liquid water content or effective radius have been derived. These empirical relationships are significantly different from those predicted if the cloud droplet spectrum is modeled as a gamma function. Occasional drizzle-sized drops are frequently present within the cloud, and even though their concentration is very low, they dominate the reflectivity and these empirical relationships fail. However, although the drizzle drops increase the reflectivity, they have a negligible effect on the liquid water content and effective radius of the cloud. As these drops have a significant fall velocity in comparison to the cloud droplets, it is suggested that a ground-based Doppler radar could separate the components of the reflectivity due to bimodal drop spectra and the vertical structure of the cloud properties that determine radiative transfer could be retrieved.

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Chun-Lei Liu and Anthony J. Illingworth

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There has been considerable discussion concerning the accuracy of values of ice water content (IWC) in ice clouds derived from measurements of radar reflectivity (Z). In this paper, the various published relationships that are based on ice particle size spectra recorded from aircraft are analyzed, and it is shown that a relationship between ice water content and reflectivity can be derived (IWC = 0.137Z 0.64 at 94 GHz and IWC = 0.097Z 0.59 at 35 GHz), which only varies by 20%–30% for different climatological areas, providing the same ice density as a function of particle size is assumed. Uncertainty as to the true variation of density of ice particles with size may reduce the average IWC for a given Z by up to 30% for an IWC of ≈0.1 g m−3 and 20% for an IWC of ≈0.01 g m−3. Individual values of IWC derived from a single measurement of Z are likely to have an error of about +100% and −50%, but if some characteristic size estimate is available, this is reduced to about +50% and −30%. The remaining errors are due to deviations of the size spectra from exponentiality, so there is no advantage in measuring the characteristic size more precisely than this limit. Remote sensing of ice particle size is not trivial, and it is shown that if instead of size, an estimate of the temperature of the ice cloud to within 6 K is available, then, rather surprisingly, the reduction in the error of IWC is almost as good as that achieved using size. Essentially this result is reflecting the well-known correlation of crystal size with temperature. When the mean values of IWC for a given Z and T are compared for a tropical and midlatitude dataset using a common ice density variation with size, then the difference is usually less than 25%. A spaceborne instrument may need to integrate over horizontal distances of 10 km to achieve sufficient sensitivity; this necessity may introduce a bias into the retrieved IWC because the relationship between IWC and Z is not linear, but analysis shows that any bias should be less than 10%.

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Ewan J. O'Connor, Anthony J. Illingworth, and Robin J. Hogan

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In this paper a technique for autocalibration of a cloud lidar is demonstrated. It is shown that the lidar extinction-to-backscatter ratio derived from integrated backscatter for stratocumulus is, in the absence of drizzle, constrained to a theoretical value of 18.8 ± 0.8 sr at a wavelength of 905 nm. The lidar can be calibrated by scaling the backscatter signal so that the observed lidar ratio matches the theoretical value when suitable conditions of stratocumulus are available. For a beam divergence of 1–1.5 mrad, multiple scattering introduces an uncertainty of about 10% into the calibration and for a narrow-beam ground-based lidar, with negligible multiple scattering, calibration may be possible to better than 5%. Some examples of the mean lidar ratio of supercooled liquid water layers and ice clouds inferred using this technique are also shown.

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