Chapter 1:
 

Active Remote Sensing, An Overview

R. E. Carbone
January, 1994
 

1.1. Introduction

Atmospheric remote sensing may be defined as measuring or estimating one or more properties of the atmosphere in a volume which is distant from the sensor. Passive remote sensing relies on the reception of naturally-emitted electromagnetic or acoustic energy by devices which are usually called radiometers. Active remote sensors transmit electromagnetic or acoustic radiation over relatively narrow frequency bands. While the devices go by many names, these are all radar-like in the sense that energy is intermittently or continuously transmitted at known times, and it is received with a known delay. Since the propagation speed of transmitted energy is either known a priori or otherwise can be determined, active remote sensing is better able to resolve the location of atmospheric properties than passive methods. Collectively, atmospheric remote sensors can characterize the kinematic, microphysical, chemical, and thermodynamic conditions, often at very high spatial and temporal resolution. Active remote sensors are principally deployed on land, ships, and aircraft platforms and there is increasing use aboard satellites. The choice of platform determines the size and location of the sampling domain as well as the temporal aspects of sampling.

Atmospheric knowledge is derived from various properties of received electromagnetic and acoustic radiation. Such properties include power, frequency, and the polarimetric state. The energy received is determined by the transmitted waveforms; by energy scattered back to the sensor from a particular point in space; and by cumulative effects along the path of wave propagation. Atmospheric understanding is achieved by tailoring the transmitted waveform characteristics; understanding the potential target scattering modes; and deconvolving the physical or chemical properties along the propagation path.

The most mature technology, from an atmospheric investigative viewpoint, is microwave radar. Many of the analysis techniques at optical and radio wavelengths have been transferred or adapted from the microwave meteorological radar literature. These radars typically operate from about 1.6 cm to 11 cm wavelength (20 GHz to 3 GHz). Scatterers include all forms of precipitation, insects, seeds, birds, and gaseous refractive index variations which are principally associated with water vapor in the planetary boundary layer (PBL). Water vapor absorption is often significant in the troposphere, causing propagation effects on the properties of received signals. Normalized received power, called "reflectivity factor," the first and second moments of the Doppler velocity power spectrum, and various polarimetric quantities are typical measurands. Applications include quantitative precipitation estimation, storm circulations and PBL circulations.

Millimeter-wave radars and UHF/VHF systems are close cousins to the microwave radar. Millimeter-wave systems typically operate near 3 mm and 8 mm wavelength (93 Ghz and 35 Ghz) which are relatively transparent windows with respect to water vapor absorption. Nevertheless, water vapor substantially attenuates millimeter waves over significant propagation paths in the troposphere. Scatterers include non-precipitating cloud water and ice-phase precipitation, insects, and seeds. Such radars are commonly used for dynamical and microphysical cloud studies, and these may also be employed in PBL studies. The equipment is small enough to permit extensive airborne applications.

UHF and VHF radio radars, usually called "profilers," typically operate between about 30 cm and several meters wavelength (1000 MHz and 50 MHz). Scatterers are primarily gaseous water vapor and temperature anomalies (refractive turbulence) but also include rainfall and large ice particles such as hail. The troposphere and stratosphere are nearly transparent to UHF and VHF radiation, so the propagation effects are minimal. Profilers are used primarily to measure mean winds as a function of height, but they also have microphysical applications as well as thermodynamic applications in conjunction with acoustic radiation sources.

At optical and near-optical frequencies so-called "lidars" function most effectively under translucent atmospheric conditions or at cloud and other dense particulate layer boundaries. Scatterers include aerosols, air molecules, cloud water droplets and ice particles. Molecular scatter can be of the ordinary Rayleigh type or through optical excitation of molecular energy states called Raman scattering. Water vapor, ozone, methane and many other substances absorb infrared and optical radiation at specific frequencies which correspond to well-known molecular absorption lines. This propagation effect is used extensively in the application of optical instruments to the measurement of constituent profiles. Capabilities include determining the properties of tenuous clouds, concentrations of aerosol, ozone, and water vapor, and the measurement of winds through the Doppler frequency-shift effect.

1.2. Power, Frequency, Polarization & Propagation

Received power, frequency, and polarization characteristics of signals are the primary measurands from which atmospheric quantities may be deduced. These properties are determined by both the scattering properties and propagation characteristics of the atmospheric medium.

1.2.1 Scattering and Power

A scatterer is a discontinuity in the refractive index of the medium along the propagation path. It may be an aerosol, a hydrometeor, an insect, a gaseous perturbation such as water vapor excess, or a temperature anomaly. A refractive discontinuity is cause for some of the incident energy to be redirected or absorbed. When energy is redirected, the process may be essentially specular (reflection) or multi-directional (scattering), depending on the roughness of the refractive index gradient surface relative to the wavelength of the incident energy. For example, the tropopause may appear essentially specular to radiowaves just as a partially-silvered mirror appears to light. Generally, scatterers are pseudo-randomly distributed throughout measurement volumes in the atmosphere, having no specific relationship to the phase of incident radiation. For this reason, signals from atmospheric targets will fluctuate in amplitude from one realization to another. This is analogous to the so-called "random walk" problem on a complex plane as illustrated in Fig. 1.1 where the instantaneous amplitude and phase of the received signal is the vector sum of the amplitude and phase of from each individual scatterer. Therefore, considerable averaging must be performed before mean power and other moments of the signal distribution can be estimated with useful accuracy.

Average received power is a function of scatterer concentrations, size-distributions and refractive indices. For scatterers smaller than about 0.06 of the electromagnetic wavelength, the backscatter cross-section from a particle goes as D6, where D is particle diameter. This is the so-called Rayleigh scattering regime where average received power is the sixth moment of the particle-size distribution. When scatterers are similar in size to the wavelength (called the Mie region), then the backscatter cross-section exhibits a complicated oscillatory behavior as a detailed function of size. When particles are large with respect to the incident wavelength, then the geometric cross-section scattering limit is reached (D2).

1.2.2 Doppler Frequency Shift

Received mean frequency is a function of scatterer radial motion, the well-known Doppler shift effect. Doppler mean frequency shift, F, is given by F= 2V/lambda, where V is radial velocity and is wavelength. When scatterers move with the ambient air, air motion can estimated directly. The second moment of the Doppler velocity power spectrum may contain contributions from wind shear, turbulence, particle fallspeed variations, molecular motions, and beam-scanning effects.

1.2.3 Polarization

Polarization properties of received signals indicate which fraction of power is associated with a particular electric field vector orientation and the phase relationship among the electric field orientations present in the received signal. This family of measurements is dependent upon the scatterers' refractive index, size, shape, and orientation, therefore having the potential to reveal various microscale properties of the atmosphere.
 

1.2.4 Propagation Effects

Between the scatterers and the remote sensor there is a propagation path which possesses both refractive and absorptive properties. Absorption and scattering by atmospheric constituents will result in signal attenuation or extinction and therefore a reduction in received power and an increased electromagnetic path length (phase delay). Constituent concentration measurements can be made through selection of wavelengths which absorb energy at different rates along the path. In the case of absorber non-isotropy (e.g., raindrops), differential measurements can be made by transmitting two orthogonal polarizations. Constituent concentration estimates can then be calculated from differential electromagnetic phase delay.
 

1.3 Precipitation Estimation & Hydrometeor Classification

1.3.1 Conventional Rainfall Estimation

The first 20 years of radar meteorology were dominated by efforts to establish techniques for rainfall estimation by means of reflectivity factor (Z) - rainfall rate (R) power law relationships of the form Z = aRb. These relationships have a physical basis at 5 cm and 10 cm wavelengths because reflectivity factor, Z, is nearly identical to the sixth moment of the drop-size distribution (DSD)
where D is drop diameter and N(D) is the number density distribution (L-4). Scores of Z-R relationships have been published, but none rival the durability of Marshall and Palmer (1948).

Use of standard Z-R relationships assumes that local variability in DSDs will be "averaged out" and that, over the domain specified, a quasi-equilibrium condition is prevalent. As discussed by Carbone (1985), DSDs achieve equilibrium only if there is sufficient time for the processes of condensation, evaporation, collision coalescence and breakup, spontaneous breakup, and sedimentation to achieve a balanced state. Marshall and Palmer's results proved to be durable because they addressed the circumstance of widespread, stratiform rain where equilibrium DSDs are likely. In convective precipitation (e.g., Carbone and Nelson, 1978), equilibrium DSDs are often the exception in dynamically active regions. When the time available is insufficient to achieve equilibrium, the DSDs implicit in Z-R relationships are not present. It follows that estimates of rainfall from measurements of the sixth moment will not correlate well with a quantity dependent on the product of mass (the third moment) and terminal fall speed (roughly the 0.7th moment). Wilson and Brandes (1979) summarize rainfall rate estimation techniques that combine rain gauge data with radar observations. The basic premise is that rain gauges provide accurate, spot checks of rainfall. Radar then provides the relative pattern, thus permitting temporal and spatial integrals of precipitation in the domain. When there is coherence in rainfall amounts at the characteristic rain gauge spacing, then objective analyses estimate cumulative rainfall with uncertainty of roughly 20 percent.

Longer term average precipitation estimates can be made by means of areal or volumetric integrals of Z (e.g., Donnead et. al., 1984; Calheiros and Zawadski, 1987; Atlas and Ulbrich, 1990; Rosenfeld et. al., 1990). Rosenfeld claims accuracy of 5 to 10 percent in tropical maritime conditions. In these applications Z is employed as a random variable that is climatologically correlated with rainfall. Implicit in these techniques is a statistical relationship between the historical probability density function of rainfall rate (as measured by rain gauges) and the probability density function of spatial Z integrals. The mapping of these functions against each other constitutes a relationship which is not based on the sixth moment of the drop-size distribution and implicitly takes into account various other sampling factors. It is attractive from the hydrological perspective because it has a plausible statistical basis when results are averaged over periods of roughly seasonal duration.

1.3.2 Multiparameter Microphysical Techniques

1.3.2.1 Dual Frequency

Dual frequency rainfall estimation methods rely on the measurement of differential attenuation which is sensitive to the 3rd to 5th moments of the DSD, depending upon radar frequency and drop-size. Generally speaking, for 10 GHz (= 3 cm) frequency, there is an average 4th moment dependency in the cloud-droplet through raindrop size range. This is very attractive for rainfall estimation, given the nominal 3.7th moment dependency for ordinary DSDs. Jameson (1990) has recently examined this method, along with other dual-parameter and multiparameter methods. He finds the method applicable as a local estimator in very high rainfall rates (250 mm/hr). The method is also applicable as an integral constraint along paths of lighter rainfall. For example, the attenuation calculated along a radar radial path from a (DSD-derived) Z-R relationship must be consistent with the measured attenuation, else the Z-R relationship is not applicable. Dual frequency methods may also be applied to non-Rayleigh scatter situations such as hail detection at microwave wavelengths, ice crystal detection at millimeter wavelengths, and aerosol spectrum measurements at optical wavelengths.

Drawbacks to the dual-frequency rainfall estimation technique include the failure to discriminate between cloud water and precipitation; applicability to relatively high rainfall rates only; dependence on accurate calibration of and beam-matching for two radars; and sophisticated initialization techniques to correct for calibration uncertainties. Jameson also points out that, despite average 4th moment dependency, details of instantaneous DSDs lead to significant deviations from the mean, since drops of 1-4 mm diameter have a 5th moment dependence and drops from 4-6 mm diameter have a 3.2nd moment dependence at the 10 cm wavelength.

1.3.2.2 Linear Co-polar Differential Reflectivity Method

Seliga and Bringi (1976) introduced the differential reflectivity method, ZDR. It requires nearly simultaneous transmission and reception at two orthogonal polarizations which are usually selected to be horizontally and vertically oriented. The method is termed "co-polar" because transmission and reception are at the same polarization. ZDR relies on the fact that small drops are essentially spherical and large drops are oblate as illustrated in Fig. 1.2 (courtesy R. Wakimoto). The quantity ZDR is merely 10 log (Zh/Zv) where h and v represent the horizontal and vertical polarization states, respectively. Typical values are 1-4 dB, measured to roughly 0.1 dB accuracy. The ZDR measurement is very sensitive to breadth of the DSD, closely tracking the median volume diameter for well-behaved DSDs. When used in conjunction with Z, it can be an improved estimator of instantaneous rainfall rate. It also effectively discriminates rain from hail as well as some other forms of convectively-generated ice. Hail typically has a ZDR value near zero together with a reflectivity value characteristic of heavy rainfall. Furthermore, ZDR often identifies melting levels when such conditions may not be evident from Z alone. In mid-latitude convection, ZDR is important to rainfall estimation if only because it readily detects the presence of ice-phase hydrometeors. Jameson (1990) reports that ZDR-Z rainfall estimation, compared to other methods, is most favored for rainfall rates of 10 mm/hr or less with uncertainties of order 20 percent.

1.3.2.3 Co-Polar Differential Phase Method

This method makes use of the phase component of the complex received signal for the same transmitted waveform as ZDR. Rather than relying on differences in received power due to drop oblateness, this is a measure of differential radio path length between the orthogonal polarizations. The path-integrated quantity is usually referred to as PhiDP and this is measured in units of degrees. Specific differential phase shift rate is usually referred to as KDP. In moderate to heavy rainfall at 10 cm wavelength, KDP is of order 1 deg/km. It is sensitive roughly to the 4th moment of the DSD. According to Jameson (1990), KDP is somewhat less prone to errors resulting from non-equilibrium DSDs than dual-frequency differential attenuation techniques. Because of limitations to the accuracy in measurement of electromagnetic phase, differential phase shift methods are best suited for moderate to heavy rainfall rate estimation, perhaps in combination with Z - ZDR ice detection. Since cloud water droplets are spherical, the PhiDP signal is from water at precipitation sizes only. It fails to "see" spherical cloud water. In principal, dual-frequency differential attenuation measurements, combined with dual polarization differential phase measurements can partition rain and cloud water.

1.3.2.4 Co-Polar Differential Attenuation

This quantity is closely related to PhiDP and dual-frequency differential attenuation, having a central moment dependency. Its use as a rainfall estimator is in the earliest stages of investigation. It must be deduced somewhat indirectly from dialectrically (if not physically) spherical hydrometeors at the trailing edge of rainfall regions or in ice-phase regions of precipitation. Indications are that it may be less practical to implement than competing methods.

1.3.2.5 Linear Cross-Polar Methods

Linear depolarization ratio (LDR) is defined as P/P where P and P are the received powers at orthogonal and parallel polarizations, respectively. P is Z after normalization for range and radar constants. LDR is very sensitive to degree of orientation in the ensemble of particles and not very useful to rainfall estimation per se. It can be useful in hydrometeor phase and ice habit discrimination in convective storms.

1.3.2.6 Linear Cross-Correlation Method (rhohv)

The correlation of instantaneous amplitude, rhohv, received at orthogonal polarizations is extremely high for like ensembles of particles such as drizzle drops. When a diversity of sizes, shapes, orientations, and refractive indices is present within the measurement volume, the amplitude cross-correlation decreases markedly. One example of such a circumstance is the 0oC melting level in precipitation. This measurement is similar in some ways to LDR, but its implementation is quite distinct, having strong advantages in weak signals.

1.3.2.7 Circular Polarization Methods

Similar capabilities to the aforestated linear polarimetric methods can be achieved with a circularly polarized waveform as reviewed by Bringi and Hendry (1990). There are advantages for some hardware implementations and for some research objectives. The reader is referred to the reviews of Bringi and Hendry (1990) and Metcalf (1990) for details.

1.3.3 Kinematic Method for Precipitation Estimation

 

In reasonably widespread precipitation, Doppler harmonic wind field analyses can yield accurate estimates of the horizontal divergence field. By means of integrating the equation of mass-continuity, and using a representative sounding for estimation of cloud base height and temperature, condensate production rate (CPR) may be calculated

where w is vertical air velocity, m is water vapor mixing ratio, and t is time. Wilson and Carbone (1984), using the so-called "VAD" technique have shown this can be an effective means to estimate stratiform rainfall rate and snowfall, particularly in circumstances where the potential for evaporation is low. It is necessary to assume a precipitation efficiency which, for stratiform precipitation, typically approaches unity. Conversely, measurement of strong mesoscale ascent in the absence of commensurate precipitation (estimated by Z for example), indicates storage of cloud liquid water.

1.3.4 Electrical Effects

The atmosphere is well-known to generate very strong electric fields near and within convective clouds which contain ice. The water molecule possesses a large dipole moment and therefore ice-phase hydrometeors are subject to reorientation in strong electric fields. Ensemble hydrometeor reorientation has been observed in convective storms by both linear and circular polarization methods. This is a difficult observation because electric fields are often highly transitory. To facilitate cloud electrification studies, microwave radar beams are often pointed at regions of radio emissions from lightning as located by passive radio detection systems.

1.4 Doppler Methods in Mesoscale Kinematics

Doppler radar is a very important tool in the study of mesoscale circulations. In the U.S., a national network of microwave Doppler radars (WSR-88D) is beginning to serve many purposes in short period weather forecasting and warnings. A permanent VHF Doppler wind-profiling network will likely be established, thus providing continuous time series of tropospheric winds on a continental scale. Several other nations are installing, or plan to install significant networks of operational microwave and UHF or VHF Doppler radars for similar purposes. It should also be noted that acoustic Doppler systems, called "sodars," are sometimes employed for monitoring surface layer and lower PBL winds.

Another dimension of improved kinematic sampling relies on airborne microwave and millimeter-wave Doppler systems, and optical Doppler lidars. Airborne research observing systems can be transported to remote regions of the globe including vast areas over the oceans and polar regions.

Doppler profilers, radars, lidars, and sodars measure one component of motion, called "radial velocity," along the axis of the sensors' beam. Measuring two-dimensional or three-dimensional vector wind fields generally requires more than one beam position or more than one radar receiver. Multi-angle sampling requirements are often satisfied either by continuously scanning or discretely repositioning the sensor beam. In convective scale research, it is common practice to employ dual or multiple radars or highly mobile radars on research aircraft.

1.4.1 Quasi-stratified Airflow and Profiling

A traditional quantitative analysis method is the so-called "Velocity Azimuth Display" (VAD) technique which exploits the multiple-look angles that are acquired during the course of a 360 scan. This technique was pioneered by Lhermitte and Atlas (1961) and Caton (1963). As illustrated in Fig. 1.3, Browning and Wexler (1968) formalized the method and showed how a standard harmonic analysis of the time series could yield the mean horizontal divergence from the 0th harmonic, the wind speed and direction from the 1st harmonic, and the deformation rate and axis of dilatation from the 2nd harmonic. The harmonic analysis concept has been elaborated upon and its applications have been extended by many (e.g., Wilson, 1970; Waldteufel and Corbin, 1979; Kropfli, 1986; Srivastava et. al., 1986; Johnston et. al., 1990, Lee et. al., 1994). Excepting the methods of Johnston et. al., and Lee et. al., these forms of harmonic analysis assume no particular model for the wind field other than quasi-linear properties. A complete formulation of the harmonic terms in a linearly varying wind field is given in Doviak and Zrni (1984). Strong non-linearities, as might be expected in vigorous convection and across sharp frontal discontinuities, are not appropriate domains for application of most harmonic techniques. Rotational circulation terms (e.g., relative vorticity) are not resolved in the basic VAD technique, since these manifest themselves as velocity components purely tangential to the Doppler sensor.

VAD analyses provide a time-height cross-section of winds representative of the mean conditions surrounding a lidar or radar on horizontal scales up to 100 km. The horizontal divergence profiles may be vertically integrated by means of the mass-continuity equation to obtain the mesoscale ascent and descent time-height history as illustrated in Figs. 1.4 and 1.5 (after Carbone et al., 1990). Advanced versions of harmonic analysis permit the determination of hydrometeor fallspeed and improved divergence estimates; wind field properties in regions not centered on the radar location; more detailed and quantitative analyses of quasi two-dimensional circulations; and the determination of momentum fluxes and heat fluxes.

If mean horizontal wind is the only quantity desired, this may be accomplished by sampling in as few as two orthogonal directions. This is the method of most UHF and VHF wind profilers, for which continuous scanning may be too expensive or otherwise impractical. Fig.1.6 illustrates the beam positions for a five-beam profiler, which requires fewer assumptions about the vertical velocity field and is therefore subject to fewer errors than the simplest two-beam approach.

While conventional Doppler wind profiling is the dominant method in use for the troposphere, research continues in the application of other methods such as "spaced antenna drift" and interferometric Doppler processing. Interferometry (Van Baelen and Richmond, 1993) shows promise for PBL momentum flux estimation at UHF frequencies. It is implemented by electronically dividing the receive antenna into several parts and processing the time-rate-of-change in signal phase for each antenna section independently. A three dimensional wind vector can be calculated for every illuminated volume because the rate of phase change differs at each receiver. There are substantial advantages to vector wind measurements in a single volume as opposed to conventional, multiple-beam implementations. Possible drawbacks include reliability and sensitivity in weak signals.

1.4.2 Convective Scale Airflow - Single Doppler Techniques

In convection, single Doppler techniques are limited, for the most part, to qualitative inspection of flow features and identification of various convective circulation features. A few convective-scale circulations lend themselves quite readily to single Doppler quantitative analysis. These include convergence lines, small scale vortices, and low-level wind shear resulting from intense downdrafts which descend to the surface. Convergence lines may be readily observed and evaluated given assumptions of two-dimensionality when the line is oriented nearly orthogonal to the radar's beam. In this case, confluence may be calculated from the range derivative of Doppler velocity and vertical air motion. Confluence may be interpreted in whole or in part as horizontal convergence. For example, the convection initiation work of Wilson and Schreiber (1986) is a superb example of circumstances in which this assumption is generally applicable. Similarly, frontal circulations (e.g., Hobbs and Persson, 1982) are readily identified by integration of the 2-D mas-continuity equation.

Small scale vortices are particularly easy to identify with Doppler radar. Vortices are always accompanied by a couplet of azimuthal shear as shown in Fig 1.7. Maxima of approaching and receding radial velocities appear in adjacent azimuth sectors and convergence will skew the receding branch closer in radar range for a cyclonic vortex (Wood and Brown, 1983). The rotational sense and amplitude of vortices are easily determined by inspection when the vortex is larger than characteristic beam dimensions. When the vortex is comparable in diameter to the beamwidth, then some method of deconvolution is required to estimate the true tangential velocity (Zrnic et. al., 1985).

Cylindrically symmetrical divergence fields are another flow pattern easily recognized by single Doppler analysis. The radial velocity pattern is a couplet which is oriented along the radar radial, clearly indicating radial shear (see Fig.1.8). In the case of divergent flow, the range derivative of radial velocity is positive, and for convergence it is negative. Well known cases of convectively-driven windshear from microbursts may be detected in this manner (Fujita and Wakimoto, 1983; Wilson et. al., 1984).

1.4.3 Convective Scale Airflow, Multiple-Doppler Techniques

The object of dual- and multiple-Doppler experimentation is to measure 3-dimensional wind fields and their evolution. As shown in Fig.1.9, with two or more Doppler radars or lidars it is possible to measure two or more quasi-independent Doppler velocity components (Vr1, Vr2 , ...Vrn) of scatterer motion. In most circumstances, the horizontal components of scatterer motion are faithful representations of the horizontal wind components. The vertical component of scatterer motion, W, is the sum of vertical air motion, w, and any scatterer terminal fallspeed, VT. Typically, for lidar applications and many millimeter-wave radar applications, scatterer terminal fallspeed is negligible. Typically, a microwave Doppler velocity field contains a component of motion attributable to the mean reflectivity-weighted fallspeed of precipitation particles.

1.4.3.1 Dual-Doppler Techniques

The dual-Doppler approach was pioneered by Lhermitte and Miller (1970). It is mathematically under-determined, since the information available to the analysis are the fields of Vr1, Vr2, and the anelastic form of the equation of mass continuity given by
where u and v are the horizontal wind components; w is the vertical wind component, and is air density. This is insufficient to recover the 3 independent components of air motion plus hydrometeor terminal fallspeed. While more than one approach is possible, it is common to employ a Z-VT relationship for the purpose of correcting radial velocities for hydrometeor fallspeed bias. Assumption of upper and/or lower boundary conditions for the integration of the mass continuity equation then permits calculation of the vertical air motion. Analyses are usually performed either in Cartesian or cylindrical coordinates, the latter being a natural system for dual-Doppler analysis.

1.4.3.2 Multiple-Doppler Techniques

Direct Method (Armijo, 1969)
Given three radars, the analysis system is fully determined. In principal, it is straightforward to calculate u,v,W directly. The mass-continuity equation, permits computation of w and therefore the field of VT. Alternatively, application of a Z-VT relationship summed with W provides an independent estimate of w. In practice, the combination of errors and uncertainties prevents application of the direct method. This is due to geometrical considerations, spatial sampling deficiencies, non-stationarity of the circulation, boundary condition uncertainties, and the uncertainty in Doppler velocity estimation.
Modified Direct Method
A three-radar direct solution can be used to obtain the horizontal wind field and vertical air motion can be obtained exclusively through application of the continuity equation. W, and VT are not explicitly determined. This method of analysis is a relatively common one. A Z-VT relationship can be applied for the purpose of calculating W in hydrometeor trajectory analyses.
Over-Determined Methods (Kessinger et. al., 1987)
Under certain circumstances (mostly related to geometry, domain size, and vertical boundary conditions) it may be advantageous to obtain three (or more) under-determined dual-Doppler analyses from three (or more) radars. These solutions may be reconciled in a number of ways. Most often, consensus is determined in a least squares sense among the solutions.
Bistatic Method
It has been demonstrated by Wurman (1994) that multiple-Doppler data may be acquired with only one active sensor and one or more additional passive receivers. The active radar transmits and receives Doppler information in the usual manner. The other receivers, typically located tens of kilometers away, receive bistatically scattered energy at angles which are oblique to that of the radar beam. The Doppler shift observed is that which corresponds to the component of scatterer motion between the illuminated volume and the bistatic receiver.

1.4.3.3 Airborne Doppler Radar

Owing to the geometrical difficulties associated with vertical velocity estimation from ground-based Doppler radars, and the desire to observe atmospheric circulations in remote locations, airborne Doppler capabilities have been developed by NOAA/ERL and NCAR (in collaboration with the CRPE and CNRS, France). Airborne Doppler radars have been used with considerable effectiveness in the study of tropical storms and other precipitation systems at mid-latitudes. The NCAR Electra Doppler RAdar (ELDORA) capabilities permit high resolution, dual-Doppler kinematic fields over very large domains as illustrated in Fig. 1.10. Because the hours of flight operation are limited, airborne radars are not well-suited to the acquisition of climatological datasets. In those instances where long timeseries of data are required, permanent ground-based and shipboard installations are preferred.

1.4.4 Thermodynamic and Other Retrievals

Gal-Chen (1978) first proposed application of the equations of motion for the purpose of thermodynamic retrieval from Doppler-derived wind fields. As described by Hane and Ray (1985), the horizontal momentum equations, in terms of non-dimensional pressure, can be solved in a least squares sense.
where is non-dimensionalized pressure and f is the Coriolis parameter as given by Gal-Chen (1978), the above can be solved from observations in the least squares sense.

This provides independent, horizontal planes of the pressure perturbation field throughout the depth of the storm volume. In a quasi-steady storm circulation the local time derivatives may be excluded and the horizontal pressure perturbation field can be checked for repeatability with successive Doppler volumes. Typically, convective circulations are unsteady and local time derivatives must be retained. Only the horizontal derivative of pressure is known at the lateral boundaries of the Doppler wind field. It follows that only the perturbation pressure from some unspecified mean is known. Knowledge of absolute pressure deviation from the undisturbed environmental state at the lateral boundaries determines the extent to which one can interpret vertical pressure gradients and therefore buoyancy estimates. Gal-Chen and Kropfli (1984) have demonstrated that retrieved pressure perturbation fields can be checked, in a least squares, cross-correlation sense, for consistency between the local accelerations and the retrieved pressure gradients. This consistency check provides a summary assessment of the quality of the Doppler wind field and the significance of the retrieved thermodynamic features.

The term "retrieval" often has been used for numerical modeling where the kinematic framework is provided by Doppler analyses. This is distinct from thermodynamic retrievals which are a relatively straightforward extrapolation of the kinematic measurements. Foremost among this latter class of "retrievals" is microphysical modeling. Storm electrification modeling and aqueous chemistry modeling have also employed Doppler flow fields. Examples of pioneering studies in these areas include Rutledge and Hobbs (1983, 1984), Ziegler (1985, 1988), Ziegler et. al. (1986), Rutledge (1986), Rutledge and Houze (1987). Hauser et. al. (1988) took this process one step farther by coupling microphysical and thermodynamic aspects of the retrieval.

1.5 Scalar Profiling and Fluxes

There exists a family of emerging techniques for constituent and thermodynamic profiling. When these are combined with Doppler techniques, it may prove possible to calculate flux divergence profiles from which the sources and sinks of constituents and thermodynamic energy can be estimated remotely. Some of the techniques are presently being pursued on research aircraft platforms for future application to global change process studies.
 

1.5.1 Radio-Acoustic Temperature/Humidity Profiling

Simultaneous transmission of electromagnetic and acoustic energy permits the measurement of acoustic wave propagation speed and therefore a measure of atmospheric density or virtual temperature. The principle of this measurement is identical to gaseous refractive index scattering but the refractive anomaly is manufactured by compression and rarifaction within the transmitted acoustic wave. A Bragg backscatter resonance occurs when the acoustic pulse is exactly one-half of the electromagnetic wavelength. Radio-acoustic sounding systems (RASS) usually operate at UHF in the PBL and at VHF through a deeper tropospheric layer. Acoustic sources are a common adjunct to Doppler wind profilers for the purpose of virtual temperature profiling. In principle, it is possible to separate contributions to the air density from temperature and water vapor, thereby deriving profiles of both.

1.5.2 Dual-Wavelength Backscatter Techniques

At optical and infrared frequencies it is possible to distinguish between molecular and aerosol scatter, thereby providing an improved basis for aerosol burden computation. The molecular backscatter cross-section is a well-known function of pressure, temperature, and humidity in the troposphere, and this contribution is significant at the higher optical frequencies. At lower frequencies, backscatter is usually from aerosol alone, thus permitting calculation of the aerosol backscatter component. Translation of this information into aerosol mass-density is difficult because the size spectrum of particles typically spans the Rayleigh, Mie, and geometric scatter regimes. In principle, multiple wavelengths may be employed to span a wide range aerosol sizes.

1.5.3 Differential Absorption (DIAL) Techniques

Perhaps the most established technique in scalar profiling is dual-frequency differential absorption in the optical and infrared range. The two most common gases targeted for profiling are water vapor and ozone. Absorption is calculated over the two-way path based upon the difference in received power. Since gaseous absorption is directly in proportion to the molecular number density of the targeted species, so-called DIAL techniques offer the promise of highly quantitative concentration profiles at high vertical resolution. An important complication in the measurement is differential aerosol backscatter at two frequencies which must be removed from the propagation component. Efforts to combat this error source include independent aerosol spectrum measurements and selection of absorption lines close enough in frequency to minimize the effect of aerosol distribution assumptions.

1.5.4 Raman Scatter Technique

Raman scatter relies on a very powerful lidars to excite emissions in rotational sidebands from species such as water vapor. This method is similar to DIAL in that it is an absolute measure of molecular concentration. An advantage over the DIAL approach is that only one active lidar frequency is required for a measurement. A disadvantage is that the backscatter is relatively weak and often cannot be discriminated from ambient radiation in daytime conditions. Weight and power consumption of the equipment is also a consideration for airborne applications.

1.5.5 Doppler-Scalar Eddy Correlation

One of the most exciting future applications of active remote sensors generally and optical systems specifically is the combination of Doppler and constituent-profiling sensors to approximate classical insitu eddy correlation measurements. A Doppler radial velocity timeseries at vertical incidence is analogous both to a timeseries of in situ vertical velocity from towers near ground level and at flight level from aircraft. A critical difference is the ability to perform this measurement over a substantial depth of the troposphere or stratosphere in conjunction with highly-resolved profiles of constituents such as ozone and water vapor from DIAL and Raman lidars. Such capabilities, if available on research aircraft, can provide quasi-synoptic flux profiles over deep layers and very large domains.

The effectiveness of Doppler-scalar remote sensing methods will be dependent upon signal-to-noise ratio given realistic statistical uncertainties in both the velocity and constituent concentration estimates. Another potential limitation will be the size of the measurement volume in comparison to the scale of turbulent flux perturbations. Low-pass filtering effects could diminish effectiveness of such measurements.
 
 

1.6 REFERENCES

 
Armijo, L., 1969: A theory for the determination of wind and precipitation velocities with Doppler radars. J. Atmos. Sci., 26, 570-573.

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