1. Introduction
Microwave radar observations of the clear-air (i.e., rain free) atmospheric boundary layer (ABL) are generally accepted to exhibit two primary scattering sources. These are Bragg scattering from refractive index turbulence and Rayleigh scattering from insects, birds, dust, or other airborne particles of sufficient diameter to be detected by radar. Bragg scattering composes a substantial fraction of the backscatter for frequencies below 3 GHz, while Rayleigh scatter tends to dominate for higher frequencies. Operational weather radars in the United States such as the Weather Surveillance Radar-1988 Doppler (WSR-88D) operate near 3 GHz, where both scattering mechanisms are prevalent.
Radar cross sections of insects have been reviewed by Riley (1985) and Vaughn (1985). In general, small nonmigratory “weak flying” insects tend to have cross sections in the range of 10−10–10−7 m2 at X band, whereas larger migratory insects exhibit cross sections greater than 10−5 m2. Observations by typical weather radars, however, are unable to measure insect cross sections, as single insects are rarely encountered within the large-resolution volumes of such systems. When insect population densities are sufficient, however, these weather radars do see insect echo as a volume scattering target. Reported insect reflectivities vary widely, with values often reported greater than 20 dBZ in convergence zones, convective rolls, and outflow boundaries (Achtemeier 1991; Wilson et al. 1994; Russell and Wilson 1997; Lang et al. 2004).
Over land, radar return from insects may be viewed as either an undesired source of clutter, or as a desired, albeit imperfect, tracer of the clear air. Achtemeier (1991) analyzed dual-polarized S-band observations to evaluate insects as a tracer of ABL motion. From the polarization ratio he inferred that insects were reorienting themselves under certain conditions in response to air motion to avoid temperatures less than 10°–15°C. As a result they are not passive tracers during these periods, especially for the purpose of measuring vertical velocities. Vertical motion of insects has been argued by Angevine (1997) to contribute to observed vertical velocity biases in 915-MHz profilers. To evaluate the clear-air return of the WSR-88D radars, Wilson et al. (1994) analyzed observations from multiple radars located in different geographic regions and determined that insects are effective tracers of horizontal wind velocities during summer daylight hours. In addition, the authors showed that insects are useful in identifying microscale updrafts. Kusunoki (2002) observed insect echoes with C-band radar over the Kanto Plain in Japan and found insects to be absent in air colder than 10°C. Zrnić and Ryzhkov (1998) and Lang et al. (2004) reported polarimetric signatures of insects with research S-band weather radars. Using an airborne vertically pointing W-band radar, Geerts and Miao (2005b) characterized insect scattering in the convective boundary layer (CBL) and argued that insects respond to sudden vertical motion and not to temperature.
To investigate whether bird migrations contaminate clear-air wind estimates, Martin and Shapiro (2007) used S-, X-, and W-band radars and showed in two case studies that insects were the dominant source of return in the nocturnal boundary layer (NBL). Bachmann and Zrnić (2007) showed that even with contamination by migratory birds, useful wind and polarimetric information from insects can be isolated using spectral analysis techniques.
These studies have shown insects to be useful for determining atmospheric motions in the absence of precipitation with the primary biases coming from migration and from insect response to vertical motion. The range of equivalent radar reflectivity factor Ze cited in the literature is large (−25 to 20 dBZ) and due to variations in dominant insect size, type, and density.
Recently, interest has grown in the development of networks of short-wavelength (i.e., ≤3 cm) weather radars to monitor conditions within the ABL where longer-range radars lack sensitivity, owing to earth curvature, terrain blockage, and the large spacing between such radar systems (McLaughlin et al. 2007). The large range of insect reflectivities, however, introduces uncertainty about the sensitivity requirements for these radars to monitor clear air. In this paper, we focus on quantifying the clear-air echo of Rayleigh scattering insects in the CBL of the southern Great Plains.
To quantify scattering from insects, data are analyzed from the University of Massachusetts S-band frequency-modulated, continuous-wave (FMCW) radar. The radar was developed and is operated by the University’s Microwave Remote Sensing Laboratory (MIRSL). It was deployed to the panhandle of Oklahoma as part of the 2002 International H2O Project (IHOP_2002) (Weckwerth et al. 2004). Similar to the measurements of Richter et al. (1973) and others, the radar measured clear-air backscatter from both refractive index turbulence and from insects. The radar often resolved individual insects that appeared as distinct “dot” echoes in displays of volume reflectivity. Through fairly simple image processing techniques, it is possible to isolate such echoes from distributed Bragg backscatter and consider their contributions to the overall microwave echo.
In section 2, the FMCW radar and its observations are presented, as are the analysis techniques used to isolate and characterize the insects. Once separated insect radar cross sections (RCSs) are calculated, the frequency of occurrence of insects in the sampling volume is determined, and assuming ergodicity, insect number densities are calculated. Following in section 3, the vertical and diurnal distributions of insect RCS are quantified, and the corresponding expected reflectivity factors (Ze) are calculated. We finish with a summary and a discussion of radar requirements for continuous clear-air observations.
2. Methodology
a. FMCW radar observations
Figure 1 shows the University of Massachusetts FMCW radar originally described in İnce et al. (2003). During 13 May–13 June 2002 the radar was located at the “Homestead” site located approximately 12 miles east of the National Center for Atmospheric Research’s (NCAR) S-band dual-polarization Doppler radar (S-Pol) near Bryans Corner, Oklahoma. Several other profiling instruments were also located at this site including a 915-MHz profiler, sodar, sounding systems, and several lidars.
Radar system characteristics for this deployment are summarized in Table 1. The radar operates at S band (10-cm wavelength), and during most of the experiment the radar was configured to operate with a vertical resolution of 2.5 m and a frequency-sweep period of 50 ms. Individual vertical profiles of microwave echo were averaged over 100 sweeps to yield vertical profiles of reflectivity at 5-s intervals. The radar was periodically operated with 5-m vertical resolution when the afternoon CBL grew particularly deep. The observational period for the present analysis was from 13 May through 13 June 2002. During this period there were two extended periods when the radar was not operated: 15–19 May and most of 30 May. Periods of rain were excluded.
The radar is absolutely calibrated by means of an internal calibration loop in which a portion of the transmitted signal is coupled into a surface acoustic wave (SAW) delay line and into the receiver prior to the low-noise amplifier. The resulting calibration signal appears as a synthetic stationary target at the 1.5-km range. The overall attenuation of this passive calibration loop is known, and so the signal can be equated to a reference reflectivity at that range. Drifts in transmitted power and/or receiver gain are reflected in variations of this calibration signal. The synthetic target does not appear in the processed radar imagery, as stationary (clutter) echoes are subsequently removed in the signal processing.
Our observations show that the number of insects in the afternoon boundary layer substantially increases and is consistent with the observations of Geerts and Miao (2005a) that show insect plumes to be collocated with updrafts. At night the depth of the boundary layer decreases and a secondary maximum in reflectivity occurs due to nocturnal insects. Typically, there is strong return at the top of the CBL due to a combination of insects and refractive index turbulence, as well as within insect layers in the NBL.
b. Signal processing
To isolate the contribution of insects from the radar imagery, the following procedure is followed. First, a 7 × 7 median filter was applied over the two-dimensional radar reflectivity image. This filter serves to remove isolated impulsive echoes that occupy fewer than half of the pixels within the filter’s interrogation window. The resulting median-filtered image is subtracted from the original to yield an image of positive (and negative) excursions about the median values. We are interested only in the positive excursions that exceed the median-filtered value by more than 1 dB. The filtered and thresholded image is referred to as the insect echo image. When this image is subtracted from the original image, the result is the Bragg scatter image.
The size of the median filter was chosen after some experimentation on the reflectivity imagery. It was found that results were weakly dependent upon window sizes between 5 × 5 and 11 × 11. The optimum window size actually depends upon the density of insect dot echoes. Ideally, the interrogation window always includes at least one insect target. Small windows suffer from violating this condition frequently, while large windows sacrifice spatial resolution.
The 1-dB threshold corresponds to two standard deviations above the average echo power for our averaged profiles of 100 samples. Pixels exceeding this local threshold are retained, while all others are set to zero. In regions of locally homogeneous Bragg backscatter, the probability of false alarm (identifying a pixel as containing an insect when it does not) is less than 2.5%. This assumes that the local averaged reflectivity estimate is described by a Gaussian random variable with a normalized standard deviation, σ/m = 0.1, where m is the mean.
Besides the morphological differences between insect dot echoes and distributed Bragg backscatter, the two sources of scattering also exhibit differing Doppler characteristics. As described in İnce et al. (2003), following the FFT used for converting the detected frequency domain signal to the time domain, the complex (I and Q) samples corresponding to individual range bins may be further processed for Doppler analysis in a manner identical to that for pulsed radars. In this case the effective pulse repetition frequency is the sweep repetition frequency, which is 20 Hz for the data shown here. This rather low pulse rate yields a narrow Nyquist velocity interval of only ±0.5 m s−1. Measured vertical velocities are in many instances aliased; however, the spectrum width can still be interpreted. This is done via pulse-pair analysis as described in Doviak and Zrnić (1993).
By analyzing the correlation coefficient between successive pulses (sweeps) averaged over the 5-s interval, we find that the correlations for the isolated dot echoes tend to be very nearly unity, while those for distributed regions of backscatter tend to be significantly less than unity (Fig. 3). The very high pulse-pair correlation for the dot echoes is indicative of a narrow Doppler spectrum characteristic of a single, simple target, such as an individual insect. Distributed Bragg backscatter, which is volume filling, produces a wider spectrum width because of multiple scattering centers within the pulse volume. Very dense populations of insects will produce a similar signature (i.e., when multiple scatterers are present). It is this evidence and the impulsive dot echo nature of the reflectivity field that supports the dot echoes as due to individual insect returns.
Figures 4a–c show 1 h of unfiltered volume reflectivity η, the corresponding Bragg component of the echo, and the corresponding insect component, respectively. Volume reflectivity is used here because it is simply the radar cross section per unit volume and is independent of the interpretation of the scattering mechanism (i.e., Rayleigh or Bragg). The figure shows the filtering method to be reasonably successful at separating the scattering contributions. Shortcomings of this filter result from the assumption that insect echoes occupy a minority of pixels in the interrogation window. When insect densities become sufficiently large, this condition may be violated, and insect echoes will appear as distributed scatter and will be removed. This occurs when the insect density is greater than about one insect in every two volume cells (or ½ V, where V is the radar sampling volume). Additionally, when insect density is greater than a few per resolution volume, the insects produce a signature that looks like Rayleigh fading. Sharp boundaries of regions dominated by Bragg scattering may also be misidentified as due to insects when the edge of a region occupies fewer than half of the pixels within the interrogation window, although this occurs less frequently than the first effect.
To further illustrate the behavior of the filtering scheme, Fig. 5a shows an unfiltered volume reflectivity image from 0314 to 0330 CDT 1 June 2002, and the corresponding mean η profile (Fig. 5b). During the time period, there was a particularly fine layer consisting of numerous insects and also, possibly, a sharp refractive index gradient. Figure 5c shows the filtered image for the same period and Fig. 5d compares the mean-filtered (gray) and unfiltered (black) profiles. In this layer, the filtering procedure results in a decrease of the volume reflectivity by 5–6 dB. Outside the layer, the mean profile does not deviate much from the unfiltered mean profile. Thus, in cases of particularly dense insect densities, the filtering procedure tends to attenuate the desired insect signal by a few decibels.
It is important to reiterate that the motivation for this research is to quantify the requisite radar sensitivity to reliably measure the clear-air boundary layer. The primary complication of our filter is that it underestimates echoes when insect densities are high and, therefore, the results presented here are conservative estimates.
c. Analysis
Since the identified insects are point targets, it is appropriate to express their amplitudes in terms of radar cross section (RCS or σ), rather than volume reflectivities. The latter description becomes meaningful only when multiple scatterers are distributed throughout the radar’s resolution volume. When this is the case, the volume reflectivity becomes independent of the radar’s resolution volume. In the present dataset, we isolate individual insects or tightly clustered aggregates and as a result, “instantaneous” volume reflectivities are mostly a reflection of the small sampling volume.
From the aforementioned insect echo images, we first calculate the probability of encountering an insect within the radar scattering volume, P(Insect). This is simply the relative frequency of occurrence of an echo within the time series for each height observation. Figure 6 shows the vertical profile of P(Insect) averaged over the entire observational period, regardless of hour. Overall, insects were encountered in roughly 10%–20% of the volume cells with three distinct maxima evident in the profile: ∼200, 1000, and 2100 m.
Ergodicity is necessarily assumed in this analysis such that the temporal average of detections within a small volume over 1 h is representative of the spatial average in a substantially larger volume. The diurnal relative frequency of encountering insects is shown in Fig. 7. Here, P(Insect) has been composited by hour of the day over the observational period. The maximum relative frequency of about 0.25 occurs from the surface up to about 200 m AGL within the NBL and, as discussed, it may be an underestimate due to the appearance of dense nocturnal insect layers. However, the density of nocturnal insects is relatively high throughout the lower 1.5 km of the atmosphere; that is, they often extend well beyond the top of the NBL. The minimum probability of an insect occurs after sunrise until roughly 1000 CDT. A secondary maximum in the probability occurs in the afternoon and extends throughout the convective boundary layer. At about 1700 CDT, prior to the sun setting, convection subsides and the density of insects decreases. With nightfall the low-level nocturnal insect layer quickly develops.
3. Results
a. RCS: Gross and diurnal statistics
For the pixels containing insect echoes, we calculate the distribution of observed insect radar cross sections. This is the conditional distribution of RCS values given that an insect is present, p(σ∣Insect). The RCS value when no insect is present is, of course, zero. Figure 9a shows the distribution of insect cross sections as a function of height for all of the IHOP data.
Figure 9b also shows profiles of F, the cumulative distribution function of insect RCS. The figure shows that roughly 5%–10% of insects throughout the lower 2.5 km of the atmosphere have S-band RCS values exceeding 1 × 10−9 m2, which corresponds to 1 × 10−7 m2 at X band, the largest of the “small” insects reported by Riley (1985).
Figures 10 and 11 show RCS cumulative distribution profiles for nighttime and daytime hours, respectively. Each panel in the figures corresponds to the indicated hour. At about 2300 CDT (Fig. 10b), a low-level maximum begins to develop at 200 m. As the night progresses (Figs. 10c,d) the relative frequency of insects increases with roughly 10%–20% of RCS values greater than 1 × 10−9 m2 at 0300 CDT. With sunrise, nocturnal insects disappear and the frequency of occurrence decreases by more than an order of magnitude.
As shown in Figs. 11a,b, the number of insects below 1500 m remains low in the morning. As the CBL grows, starting late morning, insect densities increase (Figs. 11e,d) and reach a maximum at about 1700 CDT (Fig. 11e) between 500 and 1500 m. This maximum consists of more than 10% of the measurements having cross sections greater than 1 × 10−9 m2, 5% greater than 1 × 10−8 m2, and 1% greater than 1 × 10−7 m2, which is in the range of “large” insects reported by Riley (1985).
b. Expected effective reflectivity factor 〈Ze〉
Figure 13 shows the diurnal modulation of the average radar reflectivity factor. We find on average that the maxima in reflectivity in the nocturnal boundary layer and in the afternoon convective boundary layer are 10–20 dBZ greater than the minima observed in the morning and at dusk. The maximum at night (the afternoon) is confined to the lower 700 (lower 1100) m.
4. Summary and discussion
The FMCW radar provides a unique view of the atmospheric boundary layer with very fine temporal and spatial resolutions. It is the fine space–time resolution that enables the segregation of point scatterers (in this case, Rayleigh scattering insects) from distributed scatterers and allows the study of insect number densities, cross sections, vertical distributions, and average reflectivity.
The observed backscatter shows a strong diurnal signal with a low-level maximum in the NBL and another maximum in the afternoon CBL between 500 and 1500 m around 1700 CDT. RCS values at this maximum have values ranging from less than l × l0−12 m2 to greater than l × l0−7 m2 (or 0.4 mm2). These insects are “microinsects” (<10 mm in diameter) and, when the wavelength of radiation is considered, are consistent with the cross-section measurements of Riley (1985).
However, the average reflectivity factor observations are notably smaller than those observed by Achtemeier (1991), Wilson et al. (1994), and others, who have focused on episodic periods of intense clear-air features in the convective boundary layer where number densities may be especially high. The FMCW radar measurements during IHOP_2002 were made continuously from a fixed position and sampled “extreme” events only as they passed over the radar. The FMCW observations agree well with the coincident measurements of microinsects made by Geerts and Miao (2005b, a).
Recent interest in the use of short-wavelength radar networks for monitoring of precipitation and winds in the ABL motivates the consideration of insects as tracers of the ABL winds. The analysis here suggests that the maximum sensitivity for continuous all-day monitoring of the ABL is approximately −25 to −20 dBZ, which is consistent with the sensitivity of most millimeter-wave cloud radars. However, targeted measurements of the CBL in the afternoon (i.e., for monitoring convective initiation) would require substantially less sensitivity: −10 to 0 dBZ. Such sensitivity is not beyond the capabilities of short-wavelength meteorological radars. These results provide a framework for system design and highlight the utility of making targeted observations.
Another important factor in determining the usefulness of clear-air X-band radar return is knowledge of the presence, size, and spatial distribution of insects. This is especially important because shorter-wavelength radars are insensitive to Bragg scattering turbulence and, therefore, their utility depends upon there being insects from which to scatter. As mentioned, insects are absent over the ocean or when temperatures are less that 10°C. Even if they are present, prior work has shown a wide range of clear-air return (−25 to 20 dBZ). As has been shown here, variations in Ze and RCS throughout the day can span many orders of magnitude, a range that calls for broader observations. Broader observations of insect backscatter would not only be of value to entomologists but would provide radar scientists and engineers with guidance in developing operational radars capable of monitoring the clear-air boundary layer using insects.
Acknowledgments
The authors gratefully acknowledge the helpful comments of the anonymous reviewers. This work was supported primarily by the Engineering Research Centers Program of the National Science Foundation under Award 0313747 to the Center for Collaborative Adaptive Sensing of the Atmosphere (CASA). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation.
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The University of Massachusetts S-band FMCW radar deployed at the “Homestead” site during IHOP_2002.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
The University of Massachusetts S-band FMCW radar deployed at the “Homestead” site during IHOP_2002.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
The University of Massachusetts S-band FMCW radar deployed at the “Homestead” site during IHOP_2002.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
FMCW measured reflectivity for 10 Jun 2002. The ordinate is altitude AGL and the abscissa is CDT.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
FMCW measured reflectivity for 10 Jun 2002. The ordinate is altitude AGL and the abscissa is CDT.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
FMCW measured reflectivity for 10 Jun 2002. The ordinate is altitude AGL and the abscissa is CDT.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) Unfiltered volume reflectivity η and (b) the pulse-to-pulse (or sweep to sweep) correlation coefficient.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) Unfiltered volume reflectivity η and (b) the pulse-to-pulse (or sweep to sweep) correlation coefficient.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) Unfiltered volume reflectivity η and (b) the pulse-to-pulse (or sweep to sweep) correlation coefficient.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) Unfiltered volume reflectivity η due to both Rayleigh and Bragg scattering, (b) the separated Bragg component of the echo, and (c) the corresponding excursion image (i.e., the insect echo).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) Unfiltered volume reflectivity η due to both Rayleigh and Bragg scattering, (b) the separated Bragg component of the echo, and (c) the corresponding excursion image (i.e., the insect echo).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) Unfiltered volume reflectivity η due to both Rayleigh and Bragg scattering, (b) the separated Bragg component of the echo, and (c) the corresponding excursion image (i.e., the insect echo).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) Unfiltered volume reflectivity η image during the night of 10 Jun 2002. (b) Profile of mean η over the same period. (c) Median-filtered insect η image and the corresponding (d) mean profiles of unfiltered (black) and filtered (gray) η over the period.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) Unfiltered volume reflectivity η image during the night of 10 Jun 2002. (b) Profile of mean η over the same period. (c) Median-filtered insect η image and the corresponding (d) mean profiles of unfiltered (black) and filtered (gray) η over the period.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) Unfiltered volume reflectivity η image during the night of 10 Jun 2002. (b) Profile of mean η over the same period. (c) Median-filtered insect η image and the corresponding (d) mean profiles of unfiltered (black) and filtered (gray) η over the period.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Vertical profile of the probability of an insect in the radar sampling volume P(Insect) from 13 May to 13 Jun 2002 regardless of the hour of the day.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Vertical profile of the probability of an insect in the radar sampling volume P(Insect) from 13 May to 13 Jun 2002 regardless of the hour of the day.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Vertical profile of the probability of an insect in the radar sampling volume P(Insect) from 13 May to 13 Jun 2002 regardless of the hour of the day.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Diurnal composite of profiles of the probability of encountering an insect in FMCW sampling volume during IHOP_2002.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Diurnal composite of profiles of the probability of encountering an insect in FMCW sampling volume during IHOP_2002.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Diurnal composite of profiles of the probability of encountering an insect in FMCW sampling volume during IHOP_2002.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Diurnal composite of the number density of insects with S-band cross sections greater than 10−10 m2. The density is plotted as number per 104 m3.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Diurnal composite of the number density of insects with S-band cross sections greater than 10−10 m2. The density is plotted as number per 104 m3.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Diurnal composite of the number density of insects with S-band cross sections greater than 10−10 m2. The density is plotted as number per 104 m3.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) PDF profiles of insect RCS measured during IHOP_2002, regardless of hour of the day. (b) Corresponding cumulative distribution function profile (F).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) PDF profiles of insect RCS measured during IHOP_2002, regardless of hour of the day. (b) Corresponding cumulative distribution function profile (F).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a) PDF profiles of insect RCS measured during IHOP_2002, regardless of hour of the day. (b) Corresponding cumulative distribution function profile (F).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a)–(f) Profiles of cumulative distribution function F of RCS measured during the night [except for (f), which is morning] at the Homestead site in Oklahoma over the IHOP_2002 experiment: May and June 2002.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a)–(f) Profiles of cumulative distribution function F of RCS measured during the night [except for (f), which is morning] at the Homestead site in Oklahoma over the IHOP_2002 experiment: May and June 2002.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a)–(f) Profiles of cumulative distribution function F of RCS measured during the night [except for (f), which is morning] at the Homestead site in Oklahoma over the IHOP_2002 experiment: May and June 2002.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a)–(f) Profiles of cumulative distribution function F of RCS measured during daylight hours at the Homestead site in Oklahoma over the IHOP_2002 experiment: May and June 2002. (e) Densities of large insects reach a maximum at 1700 CDT from 500 to 1500 m AGL.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a)–(f) Profiles of cumulative distribution function F of RCS measured during daylight hours at the Homestead site in Oklahoma over the IHOP_2002 experiment: May and June 2002. (e) Densities of large insects reach a maximum at 1700 CDT from 500 to 1500 m AGL.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
(a)–(f) Profiles of cumulative distribution function F of RCS measured during daylight hours at the Homestead site in Oklahoma over the IHOP_2002 experiment: May and June 2002. (e) Densities of large insects reach a maximum at 1700 CDT from 500 to 1500 m AGL.
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Vertical profile of the gross expected effective reflectivityfactor 〈Ze〉 over IHOP_2002; 〈Ze〉 is calculated using Eq. (1).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Vertical profile of the gross expected effective reflectivityfactor 〈Ze〉 over IHOP_2002; 〈Ze〉 is calculated using Eq. (1).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Vertical profile of the gross expected effective reflectivityfactor 〈Ze〉 over IHOP_2002; 〈Ze〉 is calculated using Eq. (1).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Diurnal composite of expected effective reflectivity factor 〈Ze〉 during IHOP_2002; 〈Ze〉 is calculated using Eq. (1).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Diurnal composite of expected effective reflectivity factor 〈Ze〉 during IHOP_2002; 〈Ze〉 is calculated using Eq. (1).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
Diurnal composite of expected effective reflectivity factor 〈Ze〉 during IHOP_2002; 〈Ze〉 is calculated using Eq. (1).
Citation: Journal of Atmospheric and Oceanic Technology 25, 12; 10.1175/2008JTECHA1059.1
FMCW system characteristics and sampling strategy.
