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A. R. Jameson

Abstract

Polynomial expressions are presented for the parameterization of the specific attenuation in rain from 9 to 38 GHz that are applicable to a wide range of naturally occurring drop size distributions and for viewing angles close to nadir. Because the temperature T affects the specific attenuation at some frequencies, expressions for the polynomial coefficients as functions of T are also provided for −10;deg;≤T≤30°C.

The advantage of this parameterization is that even without a detailed specification of the drop size distribution, useful estimates of the specific attenuation are often possible given only two out of three parameters, namely, the rainfall rate R, the rainwater content W, or Dm (the mass-weighted mean drop diameter), particularly if the temperature is also specified.

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A. R. Jameson

Abstract

While there are many microwave techniques for estimating the rainfall rate, there are presently few if any for accurately determining the rainwater content (W). This study shows that the dual-frequency (38, 25 GHZ) differential attenuation (A 38−25) coefficient can provide accurate estimates of W potentially over a wide range of rainwater contents.

While measurements along a microwave link are fairly rally implemented, radar estimate of A 38−25 can become clouded by differences between the radar reflectivity factors at the two frequencies (Z 38, Z 25). Root-mean-square deviations (ε) of the estimated W from the actual Ware calculated for a wide variety of drop-size distributions and rainwater contents. The computed ε include the effects of standard measurement errors and differences between Z 38 and Z 25. Accurate estimates (ε≦∼25%) appear possible using a 38–25-GHZ radar when W≧1.5−2 g m−3, depending upon the desired spatial resolution, and along a microwave link when W≧0.5 g m−3. However, extending microwave measurements to smaller W will probably require frequencies higher than 40 GHz. Consequently, it appears unlikely that microwave techniques for estimating W will ever be capable of the long penetration distances enjoyed by several methods for estimating rainfall rate.

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A. R. Jameson

Abstract

Backscatter amplitude ratios are defined for horizontal and vertical polarizations. These new parameters of linear polarization provide not only a coherent interpretation of the magnitude of the cross-correlation function between horizontally and vertically copolarized backscattered signals (ρL) but also give new meaning and applications for differential reflectivity (ζ).

In particular, it is demonstrated that ρL and ζ can be used to determine the mean and variance of the amplitude ratios. In rain these quantities can be transformed into estimates of the mean and variance of drop axis ratios. This information can potentially improve polarization estimates of rainfall, provided ρL is measured accurately.

Amplitude ratios also appear to be useful for investigating melting processes. Measurements indicate the presence of prolate-like scatterers even where ζ is greater than unity in some bright bands. It is hypothesized that this scattering from apparent prolates is, at least in part, a result of the wetting of the three-dimensional superstructure of dendritic snowflakes. This same process may also be partially responsible for observations of significant linear depolarization (L) in the bright band. Further investigation of this hypothesis requires laboratory experiments, in situ measurements and observations using linear polarization radar capable of measuring ζ, ρL and L simultaneously.

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A. R. Jameson

Abstract

Many hydrological and other scientific problems require nearly instantaneous measurements of rainfall rate. The primary purpose of this paper is to evaluate within a common framework a large number of techniques for nearly instantaneous microwave measurements of rainfall and to determine the range of rainfall rates best suited to the various techniques and estimators.

The physical basis of a technique as transformed by measurement imperfections of real instruments determines the ultimate performance capability of any microwave rain estimator. While many of the defects of the measurement process apply to all techniques, the physics behind each estimator differs. A method is presented for objectively evaluating the physical bases of the techniques and for quantifying estimator performance for perfect instruments. These results, which represent the best possible performance expectations, are then tempered by standard measurement errors to yield more realistic results.

Analysis demonstrates that in general the minimization of rainfall estimate errors over a wide range of rainfall rates requires the simultaneous application of more than one microwave rainfall measurement technique. While this theoretical exercise provides useful guidance, measurement realities highlight the need for definitive experimental studies.

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A. R. Jameson

Abstract

Several investigators propose estimating the rates of attenuation using the difference in the phase with increasing distance between horizontally and vertically polarized microwaves. These attenuation estimates can then be used to correct measured radar reflectivity factors at horizontal and vertical polarizations and their ratio (differential reflectivity) for attenuation biases that may afflict polarization-based quantitative estimates of rainfall, even at frequencies as low as 3 GHz.

Unfortunately, although this polarization phase difference does not depend upon the temperature of the rain, the attenuation is dominated by temperature-sensitive molecular absorption for frequencies below about 9 GHz. Neglecting the effects of temperature when estimating attenuation from the polarization phase difference increases the fractional standard error only slightly at 9 GHz but significantly at 5 and 3 GHz Nevertheless, even though the fractional error is about two to three times larger at 5 and 3 GHz than at 9 GHz, the absolute error (the product of the fractional error and the attenuation) is still greater at higher frequencies. Consequently, in spite of increased sensitivity to temperature, attenuation corrections using polarization phase differences work best at lower frequencies.

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A. R. Jameson

Abstract

Scaling studies of rainfall are important for the conversion of observations and numerical model outputs among all the various scales. Two common approaches for determining scaling relations are the Fourier transform of observations and the Fourier transform of a correlation function using the Wiener–Khintchine (WK) theorem. In both methods, the observations must be wide-sense statistically stationary (WSS) in time or wide-sense statistically spatially homogeneous (WSSH) in space so that the correlation function and power spectrum form a Fourier transform pair. The focus here is on developing an explicit understanding for the requirement. Statistically heterogeneous (either in space or time) data can produce serious scaling errors. This work shows that the effects of statistical heterogeneity appear as contributions from cross correlations among all of the distinct contributing rainfall components using either method so that the correlation function and its FFT do not form a transform pair. Moreover, the transform then also depends upon the time and location of the observations so that the “observed” power spectrum no longer represents a “universal” scaling function beyond the observations. An index of statistical heterogeneity (IXH) defined in previous work provides a way of determining whether or not a set of rain data may be considered to be WSS or WSSH. The greater IXH exceeds the null, the more likely the derived power spectrum should not be used for general scaling. Numerical simulations and some observations are used to demonstrate all of these findings.

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A. R. Jameson

Abstract

As radar waves having different polarizations propagate through a collection of nonspherical oriented hydrometeors, a phase difference between the waves appears. In a collection of uniformly horizontally oriented quiescent water drops, the rate of change of the propagation differential phase shift with increasing distance from the radar is proportional to the product of the liquid water content and the departure from unity of the mass-weighted mean axis ratio of the drops provided the radar wavelength is much larger than the drops. The appropriateness however, of such a simple relation to natural rain 'in which some drops assume complex shapes and a variety of orientations through the processes of collision, coalescence, break-up and oscillation remains to be determined.

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A. R. Jameson

Abstract

This paper presents the theoretical bases and detailed polynomial expressions applicable to a wide range of naturally occurring drop size distributions for more accurate parameterizations of the specific attenuations at both horizontal and vertical polarizations from 5 to 25 GHz as well as for the specific polarization propagation differential phase shift ΦDP from 3 to 13 GHz. Because temperature affects the specific attenuation (and to a much lesser degree ΦDP) particularly at frequencies below 10 GHz, temperature-dependent expressions for the polynomial coefficients are also provided.

This approach is appealing because even without a detailed knowledge of the drop size distribution, the radar parameters can be well estimated (particularly if the temperature is also specified) given only two out of three parameters, namely R, W, or Dm, the mass-weighted mean drop diameter, often available in numerical simulations or simple conceptual models. Examples are given for a wide variety of drop size distributions. These parameterizations of microwave variables in terms of bulk meteorological quantities may also be quite useful for those needs, such as communication studies that require estimates of microwave parameters with a minimum of assumptions.

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A. R. Jameson

Abstract

The attenuation of microwaves is caused not only by precipitation but also by clouds. Consequently, the presence of liquid cloud can affect estimates of rainfall rate computed from attenuation and reflectivity factors measured at higher frequencies typically used for spaceborne and airborne radars. Cloud attenuation also affects ground-based radar measurements of rainfall at frequencies as low as 5 GHz.

This paper suggests an approach for determining the attenuation due to cloud (AC) and for estimating the cloud water content (WC) even in moderate rain by using radars operating at two frequencies with one of them capable of dual-linear (horizontal-vertical) polarization measurements. This analysis suggests that useful “instantaneous” estimates of AC and WC should be possible when an upper frequency of 13.8 GHz is used in conjunction with a lower frequency. These measurements could also be used to derive cloud attenuation statistics, potentially useful for developing techniques to help compensate for the effect of cloud attenuation on spaceborne, airborne, and ground-based radar estimates of rainfall.

While this algorithm appears promising, it is particularly challenging to devise approaches to test this technique, not only because the necessary instruments do not yet exist but also because of a lack of a standard for comparison. Although a complete test appears out of reach at this time, it should be possible at least to explore the validity of certain aspects of the technology. One possible approach using measurements over extended volumes is discussed at the end of this paper.

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A. R. Jameson

Abstract

Radar polarization measurements are influenced by the distribution of shapes (weighted by the index of refraction) and the fall behaviors of the hydrometeors. In so far as precipitation-sized hydrometeors are symmetric oblates in the Rayleigh-Gans scattering regime, the effects of canting and shapes can, in principle, be separated using the co- and cross-polarized backscattered signals at both horizontal and vertical polarizations. These measurements yield estimates of the variance of a two-parameter distribution of canting angles as well as the refractive index weighted estimates of the mean and variance of the shape (axis ratio) distribution. To the extent that hydrometeor asymmetries can be neglected, these quantities provide a possible framework for precipitation identification from radar polarization measurements at long wavelengths.

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