1. Introduction

The atmospheric boundary layer (ABL) extends from the ground to the temperature inversion layer at approximately 1 km, although its upper boundary can rise several kilometers in highly convective conditions (Geernaert and Plant 1990). Within the ABL complex three-dimensional turbulent structures, driven by air–ground interaction, are associated with fluxes of heat and moisture. However, the morphology and dynamics of atmospheric turbulence are poorly understood, in large measure because instrumentation has not been available to image clear-air turbulence in multiple dimensions. In recent years, qualitative and quantitative studies of the ABL have been carried out using atmospheric computer models such as large eddy simulation (LES) (Moeng 1984; Moeng and Wyngaard 1988). LES codes are typically used to calculate the three-dimensional, time-dependent structure of the ABL, including velocity fields and local fluctuations in the structure function parameters for temperature C²_T, humidity C²_Q, and temperature–humidity correlation C_TQ (Peltier and Wyngaard 1995); those structure function parameters are proportional to C²_n (Wyngaard et al. 1978), which is equivalent to the radar reflectivity in the absence of precipitation or insect backscatter (Ottersten 1969). The ability of volume-imaging radars to measure three-dimensional velocity fields and local variations in C²_n over time can provide new insights into the structure and dynamics of the ABL and suggests that LES models may be validated or refined by comparison with radar observations.

Radar studies of clear-air turbulence began in the 1950s with efforts to understand the nature of “radar angels” and to explore the prevalence of clear-air scatter as a function of wavelength (Hardy and Gage 1990). By the late 1970s radar wind profilers operating at 50–3000 MHz were exploiting this phenomenon to measure winds and study turbulence at altitudes up to 20 km. Boundary layer profilers employing small antennas and low-power transmitters are effective tools for measuring winds to 5-km altitude with 100-m-height resolution. These systems typically operate near 1 GHz, which provides a good compromise between antenna size and altitude coverage (Ecklund et al. 1988).

Radar wind profilers typically support three to five fixed beams with one vertical beam and the others squinted off zenith along principal compass directions. Coherent integration followed by spectral processing of the echo signal at each range gate along each beam is used to determine the zeroth, first, and second moments of the Doppler spectrum corresponding to total power, mean velocity, and spectral width. Because the beams are widely spaced and somewhat coarsely sampled, it is difficult to obtain a satisfactory picture of finescale atmospheric structure necessary for LES validations. For this reason, the University of Massachusetts has developed a volume-imaging phased array radar for studying boundary layer turbulence.

The turbulent eddy profiler (TEP) is a digital beamforming phased array radar designed to provide finescale imagery of the intensity and motion of turbulence at altitudes from 200 m to 1.5 km. Digital beamforming radars employ multiple receiver elements whose outputs are processed to generate simultaneous beams within the field of view of each element. This is in contrast to active phased arrays that steer a single narrow beam varying in angle from pulse to pulse. First developed for military radar applications, digital beamforming systems have been viewed as costly and complex due to the large amount of RF and digital hardware required to sample the output of multiple antenna elements. However, the recent boom in the commercial RF market has sharply reduced the cost of microwave receivers, making it possible to consider such systems for research applications.

The TEP system may be thought of as a large collection of boundary layer profiler receivers sharing a separate transmitter antenna, as seen in Fig. 1. The signals from these individual profilers are combined in software to generate multiple narrow beams within a 28° field of view. Forming a beam at broadside is achieved by summing the complex element voltages; off-broadside beams are formed by multiplying the element voltages by an appropriate phase taper before summing. More complex adaptive processing may be used to reject interfering signals from clutter or other RF sources (Cherry 1996).

The 30-m vertical resolution of TEP is determined by the transmitted pulse length of 200 ns. Given the full array beamwidth of 3.5°, this yields volume pixels of roughly 30 m on a side at 500-m altitude—approximately equal to the grid size of LES codes. Tables 1 and 2 list the primary system characteristics.

TEP is uniquely suited to measuring boundary layer phenomena that are difficult to measure with existing instrumentation. Volume-imaging lidars (Eloranta and Forrest 1992; Grund et al. 1997), capable of sampling turbulent flows over large areas, do not directly measure C²_n. Conventional boundary layer profilers (Ecklund et al. 1988), while capable of estimating C²_n and mean wind velocity, are limited in spatial resolution by their broad beamwidths and coarse range resolution. The ability to simultaneously image C²_n fluctuations and three-dimensional velocity fields (through Doppler beam swinging) with comparatively high spatial resolution allows the motion of coherent structures to be readily visualized and studied quantitatively. Statistical analysis of the structure function data enables direct comparison with LES model statistics.

One potentially serious limitation to the ability of any clear-air radar to measure C²_n fluctuations is the presence of insects or other Rayleigh scatterers. Studies by Ecklund et al. (1995) and Wilson et al. (1994) suggest that particulate scattering dominates clear-air scatter in the well-mixed boundary layer, while scattering at and above the top of the boundary layer is dominated by Bragg scattering. As suggested by Ecklund et al. (1996) UHF radars may be operated in combination with a radar operating at a significantly higher frequency to determine whether Rayleigh or Bragg scattering dominates. Future field experiments with the TEP system will be carried out together with a millimeter-wave cloud radar that is highly sensitive to backscatter from insects but insensitive to Bragg scattering. This will allow identification of regions where TEP data, uncontaminated by insects, can be compared to LES models.

This paper introduces the TEP radar system and presents some preliminary results. The radar range equation relevant to TEP is presented in the following section. Section 3 summarizes the hardware design of the instrument, and section 4 presents preliminary atmospheric measurements obtained at The Pennsylvania State University’s Rock Springs, Pennsylvania, field site as examples of system capabilities.

2. Range equation for volumetric beamforming array

The radar range equation for a volume-imaging beamforming radar is essentially the same as that for a conventional wind profiler (Balsley 1978), although care must be taken in using the correct effective area for the antenna:

View Expanded

where S_r/ΔS_n is the ratio of signal to residual noise power spectral densities after averaging Doppler spectra and subtracting the mean noise power; P_ave is the average transmit power; A_et is the effective area of the transmit antenna; F₁ and F₂ are the fractions of received power passing through the predetection filter and coherent integrator, respectively; cτ/2 is the range resolution determined by the pulse length τ and the speed of light c; C²_n is index of refraction structure function parameter averaged over position; λ is the free-space wavelength; α_r is the efficiency of the receive antenna and transmission line; N_ave is the number of spectra averaged; R is the range to the scattering volume; k(T_s + α_rT_c) represents the noise power density due to the receiver noise temperature T_s and the sky temperature T_c (about 80 K for an upward-looking system); k is Boltzmann’s constant; and σ_fd is the spectral width of the received signal.

The spacing between the transmit and receive antennas (15 m) and the receiver diameter (6 m) are both a small fraction of R. Using a single value for R results in differential range errors of 2% or less for altitudes above 200 m. The spectral width of the signal is related to the wind velocity υ_w and beamwidth β as well as the turbulent Doppler variance σ²_υw via

View Expanded

where β_f is the beamwidth of the full array.

Equation (1) includes the simplification λ² = β²_rA_er, where β²_r is the solid angle of the receiver beam and A_er is the effective area of the receiver. The invariance of the product β²_rA_er yields the result that the signal-to-noise ratio is unaffected by the size of beamforming array. In other words, the signal processing gain achieved by focusing the array is offset by the reduction in scattering volume.

Setting S_r/S_n to 1.0 and solving for C²_n gives noise-equivalent C²_n as a function of range. Figure 2 shows TEP’s noise-equivalent C²_n between 0 and 2 km, assuming an upward-looking beam, a turbulent spectral width of 1 m s⁻¹, and a wind speed of 5 m s⁻¹. Atmospheric C²_n ranges from 10⁻¹⁷ on a calm, dry winter night to 10⁻¹² on a warm, turbulent day in a humid environment (Gage 1990). TEP is designed for summertime operation and is able to detect values of C²_n as low as 5 × 10⁻¹⁷.

3. The turbulent eddy profiler

A site plan for TEP is shown in Fig. 3. A 48-ft-long trailer transports the entire TEP system and, during operation, houses the transmitter, data system, and host computer. A corrugated horn transmit antenna, fed by a 25-kW peak-power transmitter, illuminates a 25° wide cone above the receiver array. TEP’s receiver array consists of 90 separate microstrip antennas, each backed by a low-noise receiver, digital integrator, and control and storage electronics. Coherently integrated I and Q data from each receiver is processed using a software beamforming algorithm to produce focused beams of 3.5° width, resulting in approximately 50 beams within the field of view of the radar. Figure 4 shows a photograph of the TEP array under construction in the field.

4. Sample measurements

During August 1996, TEP was deployed at the Rock Springs, Pennsylvania, field experiment facility operated by The Pennsylvania State University’s meteorology department. For this deployment 60 of the 90 receivers were fielded (the outermost ring of the array was omitted). Figure 11 shows a 28-min-long height versus time profile of volume backscattering coefficient as sensed by a single element of the receiver array. The peak signal-to-noise ratio in this image is approximately 20 dB, measured at a height of 1000 m. The two-way, 6-dB beamwidth of this image is approximately 28°, as given by the geometric mean of the transmit and receiver 3-dB beamwidths. The color scale is chosen to maximize contrast of features within the boundary layer. The data were gathered on a hot August afternoon (1510 LT 22 August) with widely scattered fair weather clouds, temperature 26°C, RH = 60% with low ground winds (1.5–2 m s⁻¹) from the west.

The lowest range gates up to about 200 m are corrupted by ground clutter. The top of the boundary layer is evident at a height of between 1000 and 1200 m, indicated by a region of enhanced radar backscatter (White et al. 1991). A vertical feature evident near t = 800 s appears to elevate the top of the boundary layer. We take this to be evidence of an updraft. This is followed a few minutes later by a downdraft feature beginning at t = 1200 s, where the top of the boundary layer dips dramatically reaching a minimum at t = 1400 s.

Figure 12 displays volume images of reflectivity and velocity resolved using the focusing capability of the TEP system. Each horizontal slice corresponds to the distribution observed over the field of view for the range gate indicated on the vertical axis. An estimate of the antenna element pattern, determined by averaging power over all range gates and over time, has been removed from each image. This set of horizontal slices covers the top of the boundary layer (900–1290-m height) averaged for 5 s and corresponding to the t = 1250 s point of Fig. 11. Finer detail of the structure at the top of the boundary layer is evident, as the brightest backscatter feature follows a narrow, vertically oriented tendril shape. The corresponding Doppler images show mean Doppler velocities consistent with a downdraft in the upper range gates. In this figure, positive velocities are moving away from the radar.

A short time sequence of horizontal slices at an altitude of 1050 m is shown in Fig. 13 beginning with the time interval shown in Fig. 12. At this altitude, the range of zenith angles shown corresponds to a cross-range distance of 460 m. The advection of the brightest reflectivity features across the field of view from west to east is readily apparent from frame to frame. The rapid evolution of the velocity field is shown by the arrows in Fig. 13, where the length of the tail indicates the magnitude of the velocity. Convergence of the velocity field in the region of strongest reflectivity is clearly apparent in this figure. The horizontal velocity vectors here are calculated using a simplification of the Velocity Azimuth Display technique, sometimes called the fixed beam Doppler method (Röttger and Larsen 1990). Each velocity pixel represents an average over a 5 × 5 grid, equivalent to 9° resolution.

Figure 14 shows a rendered three-dimensional volume derived from the crosswind slice of the TEP field of view as a function of time. This image was produced by casting rays through the volumetric data and reporting the maximum intensity observed along each ray. Two small gaps in the data of 70 s each occurred at 700 and 1400 s, which we assumed was zero length in processing the image. Data in such a format are useful for qualitative comparison and validation of LES models that produce predictions on a similar sized grid.

5. Discussion

The data presented above demonstrate that digital beamforming radar techniques can be successfully applied to clear-air scattering applications. Although the data presented above has features that are clearly connected to convective processes, it is still unclear to what degree the reported C²_n data are contaminated by Raleigh scattering from insects. Future field experiments will include simultaneous millimeter-wave cloud radar observations to estimate the radar cross section of insects or other particulates at various altitudes.

While a direct comparison of atmospheric features between TEP and LES output is not feasible, statistical comparisons of local fluctuations of C²_n are currently being investigated. Peltier and Wyngaard (Peltier and Wyngaard 1995) defined “local” C²_n values from pixel-sized, volume-averaged quantities available from LES;such values will be statistically compared to TEP measured values. Other comparisons will include three-dimensional velocity fluctuations and eddy dissipation rates from TEP and LES.