Radar Sampling Volume Research Articles

Estimating the scaling of rain rate moments from radar and rain gauge

Rain rate is a physical parameter that is only defined over some spatial or spatial‐temporal integration volume. The moments of rain rate fields calculated from measurements derived from integration volumes of the same shape and a range of sizes are commonly used as a summarizing statistic of the rain rate process. Ranges of scales are known as stochastically scaling, either simple or multiscaling, when the moments are a power law of integration volume size. The identification of scaling ranges provides information about the dominant physical processes leading to rain rate variation and allow simulation models to be devised. The spatial moment scaling statistics of rain fields have been estimated from radar data many times. In this paper, three real and potential problems with the reported statistics are identified; that is, the existence of moments is not verified, the effects of interpolation have not been considered and the inhomogeneity introduced by variation in radar sample volume with range has been ignored. Radar data from the Chilbolton CAMRa radar in the UK are analyzed, and the existence of positive moments of all orders is demonstrated. An algorithm has been implemented for the calculation of moments from spatially averaged rain data on a regular polar grid. The resulting moments are consistent with cosited rain gauge data and show smooth variation across the scales considered, 300 m to 10 km and 10 s to 6 hours. The resulting moments are well approximated by two multiscaling ranges with a scale break around 3 km or 300 s.

Estimation of the Turbulent Fraction in the Free Atmosphere from MST Radar Measurements

Abstract Small-scale turbulence in the free atmosphere is known to be intermittent in space and time. The turbulence fraction of the atmosphere is a key parameter in order to evaluate the transport properties of small-scale motions and to interpret clear-air radar measurements as well. Mesosphere–stratosphere–troposphere (MST)/stratosphere–troposphere (ST) radars provide two independent methods for the estimation of energetic parameters of turbulence. First, the Doppler spectral width σ2 is related to the dissipation rate of kinetic energy εk. Second, the radar reflectivity, or C2n, relates to the dissipation rate of available potential energy εp. However, these two measures yield estimates that differ with respect to an important point. The Doppler width measurements, and related εk, are reflectivity-weighted averages. On the other hand, the reflectivity estimate is a volume-averaged quantity. The values of εp depend on both the turbulence intensity and the turbulent fraction within the radar sampling volume. Now, the two dissipation rates εp and εk are related quantities as shown by various measurements within stratified fluids (atmosphere, ocean, lakes, or laboratory). Therefore, by assuming a “canonical” value for the ratio of dissipation rates, an indirect method is proposed to infer the turbulent fraction from simultaneous radar measurements of reflectivity and Doppler broadening within a sampling volume. This method is checked by using very high resolution radar measurements (30 m and 51 s), obtained by the PROUST radar during a field campaign. The method is found to provide an unbiased estimation of the turbulent fraction, within a factor of 2 or less.

Local and global statistics of clear‐air Doppler radar signals

A refined theoretical analysis of the clear‐air Doppler radar (CDR) measurement process is presented. The refined theory builds on the Fresnel‐approximated (as opposed to Fraunhofer‐approximated) radio wave propagation theory, and turbulence statistics like locally averaged velocities, local velocity variances, local dissipation rates, and local structure parameters are allowed to vary randomly within the radar's sampling volume and during the dwell time. A local version of the moments theorem and the random Taylor hypothesis are used to derive first‐principle formulations of all higher moments of the Doppler cross‐spectrum. The mth moment is written as a convolution integral of a spectral sampling function and a generalized, mth‐order refractive‐index spectrum or, alternatively, as a convolution integral of a lag‐space sampling function and a spatial cross‐covariance function of the local refractive‐index fluctuations and their local mth‐order time derivatives. Closed‐form expressions of the first three moments (i.e., m = 0, 1, 2) of the Doppler spectrum for the monostatic, single‐signal case are derived. This refined theory, or “local sampling theory,” enables one to correctly interpret CDR observations that are collected under conditions where the applicability of the traditional “global sampling theory” is questionable. The commonly used global sampling assumptions (Bragg‐isotropy, homogeneity, and stationarity of all turbulence statistics within the sampling volume and during the dwell time) may be invalid for small‐scale intermittency in the mixed layer, for refractive‐index sheets corrugated by gravity waves or instabilities, and for layered turbulence in the stably stratified atmosphere.

SOMARE‐99: A demonstrational field campaign for ultrahigh‐resolution VHF atmospheric profiling using frequency diversity

During May of 1999 the sounding system (SOUSY) VHF radar was operated in a demonstrational field campaign specially designed to test the applicability of range imaging (RIM) to radar studies of the atmosphere. The RIM technique utilizes frequency diversity to offer a novel method of improving radar range resolution over that which can be obtained with a conventional pulsed radar with the same bandwidth. During the field campaign, which is being called SOUSY Multifrequency Atmospheric Radar Experiment 1999 (SOMARE‐99), the application of RIM on a VHF radar has been demonstrated. The data from SOMARE‐99 are intended for investigating the dynamics and morphology of fine‐scale vertical structures in the troposphere. This paper gives an overview of SOMARE‐99 and provides some initial scientific results. A central and important result was obtained by comparing RIM‐processed radar observations and data from radiosondes. Profiles of the vertical gradient of the generalized refractive index and the so‐called RIM‐enhanced echo power are found to bear similarities during one particular case, for which the radiosonde was located directly over the radar. Furthermore, a spectral analysis of these two parameters has provided evidence that RIM is successfully identifying multiple structures within the radar sampling volume with scales smaller than the conventional range resolution.

Space and Time Filtering of Remotely Sensed Velocity Turbulence

Abstract It is well known that the width of a clear-air Doppler radar spectrum can be used to estimate the small-scale variability of the wind. To do this accurately requires that all contributions to the spectral width be accounted for. Recently, an approximate formula for correcting Doppler spectral widths for spatial and temporal filtering effects was proposed. The formula assumes independent additive contributions to the spectral width from the inherent volume averaging of the radar-sampling volume and the finite measurement interval. In the present paper the approximate formula is compared to an exact triple-integral formulation in which the spatial and temporal effects are shown to be coupled in a nonlinear fashion. The required integrations are evaluated numerically and are carried out over the full range of scales in wavenumber space, in contrast to earlier work, where truncated forms of isotropic, inertial-subrange spectral forms were used to obtain a simple, closed-form expression. Comparisons s...

Doppler radar spectral width broadening due to beamwidth and wind shear

Abstract. The spectral width observed by Doppler radars can be due to several effects including the atmospheric turbulence within the radar sample volume plus effects associated with the background flow and the radar geometry and configuration. This study re-examines simple models for the effects due to finite beamwidth and vertical shear of the horizontal wind. Analytic solutions of 1- and 2-dimensional models are presented. Comparisons of the simple 2-dimensional model with numerical integrations of a 3-dimensional model with a symmetrical Gaussian beam show that the 2-dimensional model is usually adequate. The solution of the 2-dimensional model gives a formula that can be applied easily to large data sets. Analysis of the analytic solutions of the 2-dimensional model for off-vertical beams reveals a term that has not been included in mathematical formulas for spectral broadening in the past. This term arises from the simultaneous effects of the changing geometry due to curvature within a finite beamwidth and the vertical wind shear. The magnitude of this effect can be comparable to that of the well-known effects of beam-broadening and wind shear, and since it can have either algebraic sign, it can significantly reduce (or increase) the expected spectral broadening, although under typical conditions it is smaller than the beam-broadening effect. The predictions of this simple model are found to be consistent with observations from the VHF radar at White Sands Missile Range, NM.

Doppler radar spectral width broadening due to beamwidth and wind shear

The spectral width observed by Doppler radars can be due to several effects including the atmospheric turbulence within the radar sample volume plus effects associated with the background flow and the radar geometry and configuration. This study re-examines simple models for the effects due to finite beamwidth and vertical shear of the horizontal wind. Analytic solutions of 1- and 2-dimensional models are presented. Comparisons of the simple 2-dimensional model with numerical integrations of a 3-dimensional model with a symmetrical Gaussian beam show that the 2-dimensional model is usually adequate. The solution of the 2-dimensional model gives a formula that can be applied easily to large data sets. Analysis of the analytic solutions of the 2-dimensional model for off-vertical beams reveals a term that has not been included in mathematical formulas for spectral broadening in the past. This term arises from the simultaneous effects of the changing geometry due to curvature within a finite beamwidth and the vertical wind shear. The magnitude of this effect can be comparable to that of the well-known effects of beam-broadening and wind shear, and since it can have either algebraic sign, it can significantly reduce (or increase) the expected spectral broadening, although under typical conditions it is smaller than the beam-broadening effect. The predictions of this simple model are found to be consistent with observations from the VHF radar at White Sands Missile Range, NM.

Velocity Spectra of Vortices Scanned with a Pulse-Doppler Radar

Abstract Doppler velocity spectra of a combined Rankine model vortex are computed by assuming a Gaussian antenna pattern, various vortex sizes, pulse volume depths, and reflectivity profiles. Both very narrow and very broad antenna beamwidths may produce bimodal spectra. Most often, the theoretically derived spectra exhibit a rapid power decrease for spectral components near maximum velocity which agrees with an experimental observation previously reported. In spring 1973, NSSL's 10 cm, high-resolution Doppler radar scanned the vicinity of a large tornado that devastated Union City, Okla. Digital radar samples were recorded and Fourier-analyzed to derive power spectra for sample volumes spaced about the vortex location. Power spectra were examined for white noise type signatures that indicated vortex rotation contained within the radar sample volume. Spectra were simulated using radar and tornado cyclone parameters matched to those existing during the observations to determine spectral features for compar...

Simultaneous Radar and Instrumented Aircraft Observations in a Clear Air Turbulent Layer

Some characteristics of a scattering, turbulent region near the 3-km level were measured with radar and an instrumented aircraft. It was found that the weakly scattering region was near a thin (20 m) layer of extreme stability (0.1C m−1) which seemed to cap a region of light to moderate turbulence. For the most turbulent run lasting 110 sec, an average eddy dissipation rate was found to be 16 cm2 sec−2. Smaller intervals (7.5 see) showed ε to be as large as 45 cm2 sec−2. An RHI photograph taken just before the measurements showed two wave-like layers similar to structures previously interpreted as Kelvin-Helmholtz waves. The wave-like structure disappeared within 15 min and only an extremely weak single layer remained after ∼30 min. In general, stronger turbulence was associated with larger temperature variations and thus with greater reflectivity. Radar and radiosonde data were used for the first time to calculate eddy dissipation rates. These agreed to within a factor of 4 with the more dependable estimates of dissipation derived from airborne hot wire anemometer velocity spectra. Provided the radar scattering occurs within a layer ∼35 m thick (as appears reasonable from the aircraft data) rather than from the entire radar sample volume, then the eddy dissipation rates calculated from the radar and radiosonde data become consistent with those derived from velocity spectra.