A technique for the estimation of humidity in the lower troposphere using simultaneous dual-wavelength radar observations is proposed and tested. The method compares the reflectivity from clouds and precipitation of a non-attenuated wavelength (S-band, 10 cm) and an attenuated wavelength (Ka-band, 8 mm) to compute the clear-air gaseous attenuation at the attenuated wavelength. These estimates are of total gaseous attenuation on radar ray segments that extend from the radar to a cloud/precipitation echo or from one echo to another. The attenuation estimates are then used to compute the path-integrated humidity, which is plotted at the midpoint of the ray segments. Using estimates at several elevation angles and different ranges, a profile of humidity through the lower troposphere can be retrieved. The retrieved humidity compared favorably to proximity in situ soundings with root mean square difference values between the retrieval and sounding ranging from 0.14 to 0.85 g m−3 (approximately 2–6% relative error, respectively).
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 The relatively strong gaseous attenuation of millimeter wavelength radar (e.g., Ka-band, wavelength λ = 8 mm, frequency f = 35 GHz) is typically treated as a source of error that requires correction in order to obtain calibrated equivalent reflectivity (Ze) measurements of clouds and precipitation. Gaseous attenuation at these wavelengths is mostly due to absorption by water vapor and oxygen molecules and is modified by variations in the atmosphere's absorption spectrum line shapes due to Doppler and pressure broadening [Liou, 1992; Stephens, 1994]. Therefore, correction of gaseous attenuation is possible if the atmospheric conditions are known because it depends in a predictable fashion on the temperature, pressure, and humidity [Liebe, 1985]. Conversely, if the gaseous attenuation at millimeter wavelengths is measured, it may be possible to solve the inverse problem, i.e., retrieve information about the atmospheric conditions from the gaseous attenuation value.
 A collocated Ka-band radar was recently added to the National Center for Atmospheric Research (NCAR) 10 cm wavelength (S-band, f = 2.8 GHz) dual-polarimetric radar (S-PolKa) enabling coincident S- and Ka-band measurements [Keeler et al., 2000; Farquharson et al., 2005]. For atmospheric conditions, the gaseous attenuation at S-band is negligible compared to that at Ka-band. Therefore in the right circumstances, it is possible to estimate gaseous attenuation at Ka-band by comparing the equivalent reflectivity factors of the two radars. This requires radar ray segments through the clear atmosphere that intersect Rayleigh scattering conditions at some further range, such as illustrated by the solid black arrows in Figure 1. The Ka-band gaseous attenuation estimates represent the total attenuation over the length of the ray segment. Using wave-propagation model computations, the path-integrated humidity over the ray segment can then be estimated from the gaseous attenuation. Depending on the distribution of suitable echoes and the radar scanning strategy it may be possible to obtain path-integrated humidity estimates at several elevation angles and ranges resulting in estimates through varying layers. These estimates are then used to retrieve humidity profiles in the lowest few kilometers of the atmosphere.
 The goal of this study is to utilize the different gaseous attenuation properties [Lhermitte, 1987; Rinehart, 2004] at different wavelengths through the clear atmosphere to demonstrate the feasibility of using dual-wavelength radar data, specifically S- and Ka-bands, to retrieve atmospheric water vapor in the lower troposphere.
 In section 2 we present some background information concerning the motivation, microwave water vapor retrievals, S-PolKa radar system, the gaseous attenuation properties and the data used in this study. Section 3 provides a description of the dual-wavelength humidity estimate methodology, and section 4 discusses error sources and the strategies to avoid or mitigate them. Results are presented and compared to in situ sounding data in section 5, and section 6 gives a discussion of the results and future work.
 Water vapor is one of the most important atmospheric variables for weather phenomena of many spatial and temporal scales. However, due to its highly variable nature, measurements that are sufficiently representative in both time and space are difficult to obtain [Fabry, 2006]. Weckwerth et al.  provides a meeting summary of the Water Vapor Workshop in Boulder CO, 1998. Representatives from a number of disciplines expressed the need for more and improved water vapor measurements with higher spatial and temporal resolution, including scientists studying: Boundary layer, chemistry/air pollution, hydrology, severe weather and convection, climate, polar regions, numerical weather prediction and quantitative precipitation forecasting. The improvement and development of active and passive remote sensing instruments and techniques for retrieving water vapor was strongly recommended by scientific leaders. For example, operational soundings are typically sparse, e.g., they are nominally performed at 0000 and 1200 UTC in the United States on a distance scale of around 300 km. Changes in the humidity profile that go unmeasured in between soundings can have serious implications for convection initiation and evolution. Both convective available potential energy (CAPE) and total integrated rainwater are sensitive to the boundary layer mixing ratio [Crook, 1996; Weckwerth et al., 1999]. Crook  showed that a change of 1 g kg−1 can be the difference between no storms and convection producing heavy rains and flood potential. Thus, timely and accurate boundary layer humidity profiles are critical for interpretation of storm threat, numerical weather prediction of storms and subsequent quantitative precipitation forecasting. The proposed method cannot address all of these needs, but may provide additional boundary layer/lower troposphere humidity information that is otherwise unavailable.
2.2. Microwave Retrievals of Water Vapor
 The idea of using microwave radiation to measure humidity is not new. Humidity is measured routinely with passive dual-channel radiometers using the brightness temperature observations at K-band [Hogg et al., 1983; Padmanabhan et al., 2009] and by the occultation of signals from the array of Global Positioning Satellites (GPS) and receivers at L-band (950–1450 MHz [Bevis et al., 1992]). Both dual-channel radiometer and GPS measurements are used to obtain column integrated precipitable water vapor estimates. Vertical humidity profiles are obtainable from multichannel radiometers that operate at K and V-bands (50–75 GHz [Ware et al., 2003]). Padmanabhan et al.  use tomographic inversion of microwave brightness temperatures to retrieve high spatial and temporal resolution three-dimensional water vapor fields from multiple scanning radiometer measurements. This innovative new remote sensing technique was shown to be accurate within 15% to 20% [Padmanabhan et al., 2009]. In the case of the GPS technique, a network of ground-based receivers and tomography methods on the slant path GPS delay measurements are used to estimate vertical profiles of humidity [MacDonald et al., 2002]. Vertical resolutions of humidity profile estimates vary between 0.5 and 1.0 km for the microwave radiometer and GPS-based techniques. Accuracy of humidity measurements from microwave radiometer and GPS receivers are sensitive to the mean atmospheric temperature profile and zenith hydrostatic delay respectively [Van Baelen et al., 2005].
 Until recently, weather radar has not been used to estimate water vapor. However, recent studies have shown that water vapor estimates can be made from radar using both absolute phase measurements from ground targets [Fabry et al., 1997; Fabry, 2004; Weckwerth et al., 2005] and triple-wavelength measurements through clouds [Meneghini et al., 2005]. Fabry et al.  showed that it is possible to compute, and track changes, in the refractive index of humid air by measuring the absolute phase of the backscattered signal in between stationary ground targets. Using surface temperature and pressure data (along with a reference scan collected during relatively homogeneous conditions), the near-surface humidity can be computed from the refractive index measurements. Meneghini et al.  showed the feasibility of a satellite based, downward looking, triple-wavelength radar technique to retrieve water vapor and precipitation parameters within the clouds. These two techniques and the one proposed here all complement one another well by providing radar-based humidity estimates in different regions, i.e., near the surface, within the clouds and in the clear air. The regions of humidity retrieval for the three techniques from a single ground based radar system are illustrated in the cartoon in Figure 1. The proposed path-integrated dual-wavelength estimates are represented by the solid black arrows, the range-resolved near-surface retrieval by the dashed black line near the ground, and the triple wavelength retrievals by the solid white arrows through the clouds.
2.3. S-PolKa Radar System
 The Ka-band antenna is mounted directly on the side of the larger S-band antenna (Figure 2) and the two radars have matched beam widths (∼0.9 degree) and range resolutions (nominally 150 m). Several investigators have noted the importance of spatially well-matched data for dual-wavelength radar methods [Rinehart, 2004; Hogan et al., 2005; Williams and Vivekanandan, 2007]. This includes matching the radar coverage in range, and pointing angle. The pointing angles of the S- and Ka-band beams are aligned primarily by comparing solar scans and stationary point targets such as towers. To ensure the best possible range matching of the S and Ka-band radar volumes, the two systems are synchronized in time using GPS clocks [Farquharson et al., 2005]. The resulting consistency in range between the two wavelengths is within approximately a few meters.
 The sensitivities of the two radars to Rayleigh scatterers are similar. The increased sensitivity gained by the shorter wavelength Ka-band radar due to the factor of 1/λ2 that appears in the radar equation [Rinehart, 2004], is nearly offset by higher transmit power and lower noise figure at S-band. Additional sensitivity at Ka-band may be lost due to gaseous and liquid water attenuation. The minimum detectable signal for the Ka-band system for a typical dwell time is presented in Table 1 at several ranges for no propagation losses and for average propagation loss of 0.2 dB/km (two-way).
Table 1. Minimum Detectable Signal of the Ka-Band Radara
With SNR equal to 3 dB at several ranges including both no attenuation losses and 0.2 dB km−1 gaseous attenuation loss (two-way). Units are in dBZ.
0 dB km−1 attenuation
0.2 dB km−1 attenuation
2.4. Gaseous Attenuation Properties
 Gaseous attenuation in the atmosphere at radio frequencies is mainly due to absorption by water vapor and oxygen molecules. The attenuation of the radar signal depends on the transmit frequency and the temperature, pressure, and concentrations of the absorbing gases [Williams and Vivekanandan, 2007]. The attenuation can accurately be computed for a given atmospheric state by a microwave propagation model, as presented by Liebe , which is used herein. The dependence of gaseous attenuation on frequency and humidity was illustrated clearly in Figure 1 of Lhermitte  and is reproduced here in Figure 3, which shows the gaseous attenuation for the atmosphere (computed with the Liebe  model) as a function of frequency for a variety of water vapor density (g m−3) values [Lhermitte, 1987]. The gaseous attenuation increases with increasing frequency (decreasing wavelength) and with increasing humidity. Comparing the two S-PolKa wavelengths in Figure 3 it can be seen that the gaseous attenuation at S-band (2.8 GHz frequency) is negligible in comparison to the Ka-band (35 GHz). For example, at sea level, 300 K and 80% relative humidity the gaseous attenuation is about 0.3 dB km−1 at Ka-band, and about 0.0079 dB km−1 at S-band, or about 2.6% of the Ka-band attenuation. The Ka-band absorption shows well-separated values for a large range of water vapor density values. This suggests that the water vapor content could be estimated from Ka-band gaseous attenuation measurements. Examining Figure 3, it is clear that the frequency combination of S- and Ka-bands is not the only viable choice for dual-wavelength radar humidity estimates. Considering only the attenuation properties, the longer of the two wavelengths could be S-, C-, or X-band and the shorter wavelength could be Ka-, or W-band.
 The data used in the current study were obtained from the NCAR S-PolKa radar in two field programs: The Rain In Cumulus over the Ocean (RICO) experiment [Rauber et al., 2007] conducted in December and January 2004/2005 on the islands of Antigua/Barbuda in the Caribbean Sea (S-PolKa was on Barbuda), and the Refractivity Experiment For H2O Research And Collaborative operational Technology Transfer (REFRACTT) conducted in the summer of 2006 along the Front Range of Colorado, USA [Roberts et al., 2008]. During RICO, atmospheric soundings measuring temperature, pressure, and dew point temperature were available from the NCAR Global Position Satellite (GPS) Atmospheric Upper air Sounding system (GAUS, http://www.eol.ucar.edu/instrumentation/surface-and-sounding-systems/gaus) located on the island roughly 11 km southeast of S-PolKa and from dropsondes [Hock and Franklin, 1999] deployed from the NCAR C-130 aircraft in close proximity. For verification during REFRACTT, the NCAR Mobile GAUS (MGAUS) sounding system data were available and the Denver National Weather Service Operational soundings (KDNR) were also available. The radar humidity retrievals were made at coincident times and locations with the soundings in order to verify the results.
3. Water Vapor Retrieval Methodology
 The method used to retrieve water vapor from dual wavelength radar observations in this study includes the following steps: (1) estimation of Ka-band atmospheric gaseous attenuation, (2) retrieval of path integrated humidity using microwave propagation computations, and (3) estimation of a vertical profile of humidity. This section is organized as follows: section 3.1 describes the estimation of gaseous attenuation, section 3.2 describes the retrieval of path integrated humidity, and section 3.3 describes a method to combine individual humidity estimates into a single layer based humidity profile.
3.1. Attenuation Estimation
 The difference between S-band and Ka-band reflectivity in the absence of absorption by liquid water, non-Rayleigh scattering and contamination by other radar artifacts are used to obtain estimates of the atmospheric attenuation along a segment of a radar radial. The reflectivity differences are computed on small patches, or kernels, of data spanning several gates in range and azimuth at the edge of echoes. The average of the measured S- and Ka-band reflectivity values ( and , respectively) over the kernel are computed. The averages of reflectivity are computed in linear units (mm6 m−3) and converted back to dBZ. The gaseous attenuation (dB km−1) is estimated simply as
where Ag is the one-way gaseous attenuation in dB km−1 and is the average path length of the gates in the data kernel.
 There are several ways to obtain ray segments suitable for estimating atmospheric attenuation. The first is to consider a ray segment through the clear atmosphere that begins at the radar and ends at the nearest edge of a cloud echo. Such ray segments are called primary rays. An example of a primary ray is illustrated in Figure 4, which shows PPI plots of Ka- and S-band reflectivity obtained during RICO. The solid red arrow represents a primary ray segment extending from the radar to the first cloud echo labeled A.
 It is sometimes possible to account for the total attenuation that has occurred in a radar beam at intermediate ranges between the radar and a suitable target. This enables making a gaseous attenuation estimate over a ray segment through the clear atmosphere that does not begin at the radar. Ray segments that do not begin at the radar are called secondary rays. Two methods to estimate attenuation over secondary rays are illustrated in Figure 4. In the first method the atmospheric attenuation along the primary ray segments from the radar to the cloud echo labeled A (solid red arrow) and the cloud echo labeled B are computed first. Next the total gaseous attenuation to echo A is subtracted from the total attenuation measured to cloud B (illustrated by the dashed red arrow), located at a nearby azimuth to A, but farther in range. The resulting attenuation value is valid over a ray segment extending from the range of cloud A to that of cloud B, indicated by the solid green arrow in Figure 4. The tolerance on valid azimuth differences for secondary rays computed as described above depends on the situation and the application and should be determined by individual investigators. In relatively homogeneous conditions such as the marine environment of RICO larger azimuth differences can be used. The data should be monitored for reflectivity fine lines or radial velocity discontinuities as these are signatures of boundaries and may indicate variable conditions. In the present study, no more than ten degrees of azimuth separation was allowed. Another method to compute gaseous attenuation on a secondary ray segment uses only information along one radar ray that intersects more than one cloud echo. Consider clouds labeled C and D in Figure 4. The difference in S- and Ka-band reflectivity values at the back edge (relative to the radar) of echo C results from a combination of the atmospheric and liquid water attenuation along the path from the radar to that point (solid white arrow). By subtracting this attenuation value from the total attenuation measured at the nearest edge of echo D we are left with the atmospheric attenuation on a secondary ray from the back edge of echo C to the nearest edge of echo D, indicated by the solid green arrow.
3.2. Humidity Estimation
 Using the atmospheric attenuation estimation along a primary or secondary ray segment, the path integrated water vapor content is inferred using simulations with a microwave propagation model. The model used in this study is from Liebe , which computes the attenuation due to water vapor, liquid water and molecular oxygen absorption over propagation paths through atmospheric layers. Each model layer is defined by its depth as well as pressure, temperature, and humidity at the bottom and top of the layers. The model of Liebe  then linearly interpolates in between user-defined layers.
 The model was run numerous times to compute humidity as a function of Ka-band atmospheric attenuation over the range of temperatures and pressures found during RICO in the lower troposphere as observed by soundings taken throughout the project. Figure 5 shows a scatterplot (pluses) of the model water vapor density (g m−3) versus the model-computed one-way atmospheric attenuation (Ag, dB km−1). The scatter along the x axis is due to the dependency of Ag on temperature and pressure. The tight scatter indicates that these dependencies over the range of pressure and temperature in question are small.
 The best fit line is plotted in Figure 5 as the solid line. The third degree polynomial fit yielded the following equation for water vapor density (q, in g m−3),
where Ag is the one-way atmospheric attenuation.
 A similar process was repeated for the conditions at REFRACTT. The equation used on REFRACTT data was
which is plotted as the dashed line in Figure 5. It can be seen that for the same humidity (g m−3) there is slightly less attenuation at the higher altitude of the REFRACTT observations. This is due to the lower concentration of molecular oxygen at the lower surface pressure in Denver (about 850 hPa versus 1013 hPa at sea level). The path-integrated water vapor estimates were computed by simply substituting the value of Ag estimated using equation (1) into equation (2) or (3).
3.3. Estimation of a Layer-Based Humidity Profile
 Next, a layer-based vertical profile of humidity is computed by accounting for the gaseous attenuation measured in lower layers in the estimates of attenuation at higher levels. To illustrate the retrieval, consider two Ka-band attenuation measurements at single elevation angles: The first from 0 to 2 km height above the radar (RAY02) with a total attenuation of 4 dB and the second from 0 to 4 km (RAY04) with a total attenuation of 5 dB. The individual estimated humidity values from RAY02 at the midpoint of the ray segment would result in a humidity estimate at 1 km height that corresponds to 4 dB of attenuation over the 0 to 2 km layer. Similarly the humidity estimate from RAY04 would be at 2 km height and correspond to 5 dB of attenuation over the 0 to 4 km layer. However, the total attenuation measured in the 0 to 2 km layer can be subtracted from the total attenuation in the 0 to 4 km layer. This would provide the additional information that the layer from 2 to 4 km accounts for only 1 dB of the total gaseous attenuation in RAY04. The humidity that corresponds to 1 dB of total attenuation from 2 to 4 km can be computed and is fully consistent with the attenuation measurements of both layers. The following simple algorithm was developed and tested in order to compute such a layer-based profile of humidity from the dual-wavelength estimates.
 First, a number of measurements of average Ka-band gaseous attenuation (dB km−1) were made for different primary ray segments at various maximum heights above the radar. Next, layer mean attenuation values were computed over several different layers. The maximum height variations for the primary ray segments used to define a layer was 0.25 km and the top of the layer (Hi, where i denotes the layer number) was computed as the mean height of the ray segments.
 Now that we have defined a lower troposphere with various average attenuation values over different layers of different thickness, we could then determine the total gaseous attenuation of a Ka-band radar beam propagating through this lower troposphere. Therefore, the total attenuation in dB (AiT) was then computed for each layer at Hi from the layer mean attenuation (dB km−1).
 Next the total attenuation in between layers 1 and 2 (A2T*) could then be computed by subtracting A1 from A2 resulting in the total attenuation from H1 to H2, which is valid at the height of, H*2 = H1 + (H2 − H1)/2. Or in general for n layers,
These total attenuation values were then converted to attenuation in dB km−1. Finally the attenuation values were substituted into equation (2) or (3) to obtain the water vapor density.
4. Error Sources and Mitigation
 This section describes sources of error and the methods to avoid or mitigate them. There are several sources of error that may impact the atmospheric attenuation estimates and subsequently the humidity estimates. In order to check if reasonable humidity estimates can be obtained with the procedure outlined above, it is determined what levels of attenuation estimate error lead to acceptable humidity estimate errors. Therefore the goal is to determine the humidity error that results from errors in the difference, (ΔZ). In this way criteria for the acquisition and processing of ray segments can be designed to keep the humidity errors within a predetermined goal, for example 5% error.
 It can be seen in equation (1) that errors in attenuation estimates due to radar measurement errors are a function of path length and proportional to 1/(2L). Thus, for a given reflectivity difference error, the attenuation error decreases with increasing path length. The water vapor density errors resulting from the errors in atmospheric attenuation estimates can be found using equation (2) or (3) and are plotted using equation (2) in Figure 6. Examine Figure 6 for a reflectivity difference error of 0.5 dB (solid line) within the constraint of a 5% relative error. In a humid environment of water vapor density on the order of 20 g m−3, 5% relative error would be 1 g m−3 and the minimum length for a ray segment is about 15 km. In a drier environment with water vapor density on the order of 10 g m−3, 5% relative error would be 0.5 g m−3 and the minimum length of a ray segment is about 30 km. Thus in a drier climate the horizontal and vertical resolution obtainable is less than in more humid regions.
 Errors in ΔZ can come from several sources including contamination by non-Rayleigh scatterers, or other radar artifacts, measurement fluctuations (or noise), or differences in the absolute calibration of the S- and Ka-band radar reflectivity. Errors due to calibration differences are difficult to mitigate and result in a bias in the humidity retrievals that use primary ray segments. The relative calibrations of the S- and Ka-band radars can be checked comparing uniform drizzle echoes at short ranges. Secondary rays are not impacted by calibration errors. The data selection and processing criteria described below have been designed with the goal to keep the errors in ΔZ at or below 0.5 dB.
4.1. Errors Due to Reflectivity Variance
 The measurement variance of the two radars can be mitigated by averaging a number of radar range gates either in range or in azimuth or some combination. It must be determined how many radar gates must be averaged to bring the variance to 0.5 dB. To this end, the variances of the power measurement of each radar were computed following the procedures described by Keeler and Passarelli , Doviak and Zrnic , and Keeler and Ellis  for typical dwell times. Using the results, the standard deviation values of ΔZ were computed for various spectrum width (SW) values and number of gates averaged and Table 2 presents the results (dB). From Table 2 it can be seen that 10 or more radar gates should be averaged to keep the errors in the reflectivity difference less than 0.5 dB.
Table 2. The Standard Deviations of the Estimated Difference Computed Using Spectrum Width Values of 1, 2, and 3 m s−1, and Number of Averaged Gates of 1, 10, and 20a
SW (m s−1)
Standard Deviation of the Reflectivity Difference (dB) for Number of Gates Averaged
SW, spectrum width.
4.2. Errors Due to Non-Rayleigh Scatterers
 Any contaminant or artifact that violates Rayleigh scattering in one or both wavelengths can cause errors in the humidity estimates. Therefore, several criteria have been developed to help ensure the data used in the water vapor retrieval are appropriate. Non-Rayleigh scatterers at S-band include Bragg scatter, ground clutter contamination, bird echoes, and for Ka-band also include raindrops larger than about 1 mm, insects and other large hydrometeors. Ground clutter and bird echo reflectivity values are much larger at S- than at Ka-band and are therefore easily identified and avoided.
 Contamination by insect echoes is avoided in the analysis using the dual-polarimetric capabilities at S-band. Insect echoes generally have differential reflectivity (ZDR) values greater than 2 dB [Zrnic and Ryzhkov, 1998; Vivekanandan et al., 1999], which is much higher than the drizzle and cloud echoes of interest (ZDR < 0.5 dB). The distinction between insect echoes and the cloud/drizzle echoes of interest can be made automatically using echo classification algorithms as described by Vivekanandan et al.  and Liu and Chandrasekar .
 The echoes used must have reflectivity values that are not significantly impacted by Bragg scattering at S-band. Two criteria were applied to mitigate the impacts of Bragg scattering. The first is based on the findings of Knight and Miller  who observed that in warm Florida cumulus clouds with radar reflectivity above 5 dBZ, Rayleigh scattering was usually the dominant scattering mechanism. Accordingly, no echoes with S-band reflectivity below 5 dBZ were used. However, in some cases the S-band Bragg echo of developing Florida cumulus were observed to be as large as 10 dBZ [Knight and Miller, 1998]. These clouds had an initial S-band “mantle echo” dominated by Bragg scattering and then transitioned to Rayleigh scattering as larger particles formed beginning within the core of the cloud [Knight and Miller, 1998]. To be considered for the humidity retrieval, the second criterion requires the Rayleigh scattering core echo to have at least 9 dB higher reflectivity than any surrounding Bragg echoes. At Ka-band it can be shown that at the range of the minimum ray segment length (15 km) the Bragg scatter echoes are below the minimum detectable level (see Knight and Miller  and Wilson et al.  for computations of relative Bragg scatter power). Therefore, within the limitations of the radar sensitivity, the S-band Rayleigh echo region can be defined by the Ka-band reflectivity. The 9 dB threshold is the level at which the weaker echo would contribute about 0.5 dB to the total reflectivity within a mixed Bragg and Rayleigh echo.
 Drops of diameter of less than roughly 1 mm satisfy the Rayleigh scattering condition at Ka-band [Vivekanandan et al., 2001; Lhermitte, 1987]. Therefore, the maximum drop diameter (Dmax) in the radar volume must not exceed 1 mm. To ensure this condition is met, Dmax is computed using the S-band dual-polarimetric data. The median dropsize diameter (D0) is estimated from the S-band Z and ZDR values following Beard and Chuang . The Dmax can be approximated as twice D0 [Vivekanandan et al., 2004], and data with estimated Dmax values exceeding 1.0 mm were rejected.
4.3. Errors due to Attenuation by Liquid
 Errors in the humidity estimates can be caused by attenuation through liquid drops. Liquid attenuation might be attributed to the gaseous attenuation, and the result is an overestimate of Ka-band gaseous attenuation and thus an overestimate of humidity. This can occur in two ways: First the liquid attenuation may become significant if the data kernel collected to compare S- and Ka-band reflectivity values extends too far into the liquid water echo, and second intervening liquid clouds may exist that are below the detection limit of the radar.
 To avoid liquid attenuation contamination from within the selected data kernel, data were not collected more than 0.5 km into any cloud/precipitation echo. At the range resolution of S-PolKa (nominally 150 m), this corresponds to 3 gates in range. Therefore to obtain the required 10 range gates (section 4.1) the data kernel must contain a minimum of 4 adjacent azimuths.
 Clouds that exist in the absence of drizzle or larger precipitation may have reflectivity values below the radar systems detection limit, but enough liquid water content (LWC) to significantly attenuate the Ka-band signal. The minimum detectable reflectivity for the Ka-band radar is listed in Table 1 at various ranges. If clouds below the minimum detectable reflectivity intervene in primary or secondary rays, they will cause errors in the humidity retrievals.
 Studies using in situ data by Fox and Illingworth  and Sauvageot and Omar  found that cumulus clouds in maritime air masses invariably contain drizzle droplets that dominate the reflectivity. Therefore the likelihood of undetected intervening clouds in the maritime environment of RICO is low. It is more likely to encounter undetected intervening cumulus clouds in a continental environment such as the REFRACTT experiment. Although there are no definitive cloud size or LWC thresholds for precipitation formation in cumulus clouds, the likelihood of the formation of larger drops detectable by radar increases with increasing cloud size (vertical and horizontal extent) and LWC [Knight et al., 1983; Rangno and Hobbs, 1994; Prupacher and Klett, 1997; Laird et al., 2000; Wang and Geerts, 2003]. For example, Knight et al.  compared visual histories, in situ aircraft measurements and radar first echoes (defined as 5 dBZ) of growing cumulus clouds in northeast Colorado. They found that the largest values of LWC were associated with vigorous updrafts. Further, the growing cumulus clouds in the study produced the first radar echo within about 10 min of the beginning of the visual record and within 1 min of the cloud top reaching the −20°C level (corresponding to a cloud depth of 3 to 4 km). Furthermore the radar echo spread to fill the visible cloud in 5–10 min of the first echo [Knight et al., 1983]. Rangno and Hobbs  found that continental cumulus clouds needed to be about 3 km wide, or 50% wider than maritime clouds, to have a 95% probability of producing a radar echo. The frequency and severity of intervening cumulus clouds below the radar detection limits are impossible to quantify. However, the implication of these studies is that cumulus clouds below the sensitivity of S-PolKa at the ranges in question (Table 1) would tend to be small (<3 km) in height and width. Raypaths that were impacted by these clouds would appear as outliers in humidity profiles that utilize numerous raypaths and should be removed.
 Stratiform clouds that are undetected by the radar are more problematic. The algorithm should not be applied in the presence of these clouds, which would clearly have to be detected by other observations such as, satellites, ceilometers, lidars, observers, etc.
4.4. Correlation of S- and Ka-Band Reflectivity
 To further identify radar data contaminates, a point-by-point linear (Pearson) correlation coefficient between S- and Ka-band reflectivity values over each data kernel was computed. Data kernels with correlation values less than 0.7 were rejected. The 0.7 threshold was chosen somewhat arbitrarily to ensure the S and Ka data exhibited strong correlations. If the S-band and Ka-band reflectivity values were dominated by different phenomena the reflectivity patterns might be different and the correlation would be lowered. Too high of a threshold would be problematic because the measurement noise at the two wavelengths is independent and therefore reduces the correlation coefficient.
5.1. Vertical Profile Verification
 The water vapor retrievals computed with the RICO data are compared to the proximity GAUS sounding. Figure 7 shows path integrated humidity estimates from 10 January 2005 plotted at the midpoint of primary (secondary) ray segments as pluses (crosses), while the solid line shows the sounding data. The radar was scanning PPI volumes and the 1.5, 2.5, 3.5 and 4.5 deg scans were used in the humidity estimates. Due to partial beam blockage of the Ka-band, the 0.5 deg elevation scan was not used. The dashed line in Figure 7 shows a running average of the sounding computed to mimic the resolution of primary rays. For each height (H) the average humidity was computed from the elevation of the radar (0.0 km in this case) to 2*H and plotted. It can be seen that the small-scale features of the humidity profile cannot be resolved with the primary rays, but that the overall trend and mean values are captured well. The secondary rays, which span from one cloud to another, add some vertical granularity to the retrieved values as can be seen by the crosses in Figure 7. The vertical dashed lines span the vertical extent of the secondary ray segments in the y axis and are plotted on the x axis at the location of the average humidity from the sounding over the extent of the ray segment. The secondary rays increase the vertical resolution of the retrievals. For example, consider the vertical extent of the secondary ray with a midpoint at a height of about 1.5 km, which has a vertical extent from about 0.8 km to 2.2 km in height. This is much smaller than a primary ray with a similar midpoint height, which would span from 0.0 km to 3.0 km above the radar.
 For the 10 January case, the overall root mean square difference (RMSD) of the radar retrieved humidity to the sounding data was 1.40 g m−3. It turns out that this statistic was disproportionately influenced by the primary ray that occurs at about 1.8 km height within an unresolvable dry layer of the sounding (Figure 7). Excluding this point, the RMSD is 0.85 g m−3.
Figure 8 shows the dual-wavelength humidity estimates from Figure 7 with the layer-based humidity profile computed as described in section 3.3 plotted as the thick dashed line. For reference, the sounding data were averaged over the same vertical layers used in the layer-based humidity profile and are plotted as the thin dashed line. Despite differences, the layer-based humidity profile generated from the dual-wavelength radar measurements captures the main features, with similar values, as the layer-averaged sounding.
 The next example includes humidity retrieval results for 12 January 2005 and is shown in Figure 9. Similar to the previous example, the retrieved values (pluses) are close to the sounding data and the RMSD for this case is 0.75 g m−3. The trend of decreasing water vapor values with height is again well represented and the results are consistent with the first example. This is also reflected in the resulting layer-based humidity estimate from the dual-wavelength measurements (thick dashed line), which captures the major features of the layer-averaged sounding (thin dashed line).
 Two examples of humidity retrievals from the REFRACTT field campaign are presented in Figure 10. The retrievals were taken near 0000 UTC, on 26 July 2006 (1800 local time), and result only from primary ray segments. First consider the profile denoted by pluses in Figure 10. The profile is valid near the location of the National Weather Service Denver sounding site (KDNR) located southeast of S-PolKa. This facilitated verification of the dual-wavelength radar humidity estimates using the 0000 UTC sounding, which is plotted as the solid line in Figure 10. It can be seen that the dual-wavelength humidity estimates lie close to the NWS sounding. The gradient of humidity with height of the retrievals is in good agreement with the sounding. The RMS difference between the sounding and retrieval values is 0.14 g m−3 in this case, much better than the RICO examples. This is likely because the REFRACTT echoes were at longer ranges at around 40 km as compared to 15 to 20 km in RICO. Recall that water vapor density errors are inversely proportional to path length. Also the fact that the echoes used in REFRACTT were more extensive in the azimuth direction than for the RICO cases, allowed more gates to be averaged and reduced the errors. The water vapor from the sounding in the REFRACTT case is more smoothly varying than in RICO due to the coarser resolution as well as the deeper mixed layer. In these conditions the dual-wavelength water vapor estimation is expected to have lower RMS differences with the sounding.
 The layer-based humidity profile computed from the dual-wavelength measurements near the KDNR sounding site is plotted as the thick dashed line in Figure 10. This profile matches quite well the sounding data and the layer-average of the sounding data (not shown), which nearly overlap in this case.
5.2. Spatial Variability
 The dual-wavelength radar humidity estimates in Figure 10 denoted by the open circles were taken at 0000 UTC but the primary ray segments used were to the north-northeast of the radar. While the variability of these estimates is similar to the 0000 UTC profile taken near KDNR, they show systematically more moisture. This could be explained by the presence of several heavy precipitation systems over the previous hour in the direction of this profile. Thus evaporation could have locally increased the boundary layer humidity in this region.
 The local increase of humidity is evidenced by comparison to the GPS column integrated precipitable water vapor (PWV) estimates shown in Figure 11. The PWV estimates arise from the combination of occultation data from each GPS signal receiving station, shown in Figure 11 as diamonds, in addition to the collocated receiver at S-PolKa, denoted as a stars [Rocken et al., 1995; Ware et al., 2000]. At the analysis time data from 10 satellites were available. It can be seen that the PWV to the northeast of the S-PolKa radar is greater than to the southeast toward KDNR. This supports the idea that the heavy precipitation to the north and northeast of S-PolKa has increased the humidity in that region. The GPS precipitable water vapor estimates are column integrated and do not indicate what level the humidity signal comes from. Therefore, the refractive index estimates [Fabry et al., 1997; Fabry, 2004] from S-PolKa were also examined to verify an increase in low-level humidity.
Figure 12 shows the refractive index computed at 2355 from the S-PolKa radar. The higher values to the north and northeast, as compared to the southeast, of S-PolKa indicate that the near-surface atmosphere is more humid. This is consistent with the GPS findings and supports the moister dual-wavelength retrieval looking north-northeast in Figure 10.
 The humidity measured by the surface station at the S-PolKa radar after the locally moistened air has advected over the site at about 0012 UTC is plotted as a diamond in Figure 10. The first raindrops were recorded at the site at 0056 UTC. The surface station humidity value of 12.3 g m−3 is nearly 1.5 g m−3 more than the KDNR sounding at the same altitude, which is consistent with the radar-retrieved profile taken in the same, moister air mass. The square plotted in Figure 10 shows the surface station humidity at 0000 UTC from the NWS Front Range radar site (KFTG), which is located approximately 25 km to the east-southeast of KDNR. The humidity measured at KFTG is consistent with the dryer air mass to the southeast of S-PolKa and is about 0.5 g m−3 dryer than the KDNR sounding value at the same level. Based on the three independent data sources indicating moister air to the north and northeast of S-PolKa at 0000 UTC and the consistency of the radar-retrieved profile with the surface data, it is concluded that the higher humidity profile retrieved from that direction is valid.
 The bias and RMSD of the layer-based humidity estimates from the dual-wavelength radar estimates compared to the sounding data averaged over the same layers were computed using all of the comparison data from both RICO and REFRACTT. The bias was found to be −0.13 g m−3 and the RMSD was 0.46 g m−3.
6. Discussion and Future Work
 The results presented in this study show the utility of S-band and Ka-band dual-wavelength radar to retrieve environmental water vapor profiles through the lower troposphere. Because the estimates are derived from total path atmospheric attenuation estimates of radar ray segments, the retrieved profiles are not able to resolve fine scale features. However, the magnitude of moisture and its gradient with height are well retrieved with root mean square differences to in situ sounding data less than 1 g m−3. The technique worked in both the humid environment of the Caribbean and the dryer environment of Colorado. It was demonstrated that the dual-wavelength radar humidity retrieval detected spatial variation in humidity profiles resulting from changes in the boundary layer humidity due to modification of the air mass by evaporation.
 A technique to combine the humidity estimates from the individual ray segments to estimate a layer-based profile was proposed and demonstrated. The layer-based profile can better represent the vertical variability in the water vapor by taking into account the measured attenuation in successive layers. The vertical resolution of the profiles ranged from about 0.25 to 0.5 km for the data in this study. The vertical resolution is dependent on the radar scanning and distribution of suitable echoes.
 Dual-wavelength radar humidity estimates should also be possible using different wavelength combinations. A potential advantage of using C- or X-band as the long wavelength is that ground clutter and Bragg scatter echoes are not as strong as at S-band. However, the atmospheric attenuation is greater at these wavelengths, thereby reducing the differential attenuation and the sensitivity of the method. Using the more strongly attenuating W-band (Figure 3) as the shorter wavelength has the advantage of increasing the sensitivity and reducing the required ray segment length. However, at W-band drops satisfying Rayleigh scattering are < 0.3 mm making suitable targets more difficult to find.
 The technique is dependent on the clouds that are present to obtain estimates of gaseous attenuation and humidity. For primary rays to be used it is necessary to have ray segments through the clear atmosphere extending from the radar to cloud or precipitation echoes that are greater than 15 km in range in order to keep the retrieval errors below 1 g m−3. For secondary rays to be used, ray segments of 15 km in length must exist in between individual echoes. The conditions favorable for primary rays are much more common than for secondary rays. While the conditions that facilitate the use of the proposed technique are not uncommon, there are also many situations that preclude or limit the method.
 Clearly if no cloud or precipitation echoes are detected the technique is not applicable. Echoes from widespread stratiform clouds (e.g., upslope or marine stratus clouds) present the problem that all primary ray segments will have a midpoint at the same height and therefore would preclude a vertical profile of humidity, although the humidity could be monitored at one height. Humidity retrievals with primary rays are not possible if rain, which attenuates the Ka-band wavelength, is observed over the radar system. Despite these limitations, the technique offers a viable option for accurately observing lower troposphere humidity profiles in many situations with high temporal resolution.
 There are a number of areas of potential future work on this topic. The first would be to automate the algorithm to facilitate real-time use and analysis. Analyzing more data from differing regions and weather conditions is necessary to further define the proposed technique's potential applications and limitations. It is planned to combine the dual-wavelength retrievals with humidity estimates from other radar methods as well as different instruments. The combination of the lower troposphere humidity estimates described here with the near-surface humidity retrievals via measurements of the refractive index [Fabry, 2004], is of particular interest because the estimates are complementary and are both currently available using S-PolKa. The dual-wavelength humidity retrievals could also be combined with other data and model sources to compute updated humidity profiles using objective analysis techniques. Also of interest is the assimilation of the profiles into numerical weather prediction models of various scales.
 The National Center for Atmospheric Research is sponsored by the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors wish to thank Eric Nelson for providing the refractivity analysis, figure, and surface station data, John Braun for providing the GPS analysis and figure, Jeff Keeler for his informative discussions of radar errors, and Wen-Chau Lee, Tammy Weckwerth, Robert Rilling, Wiebke Deierling, and Matthias Steiner for their critical reviews. Special thanks go to the NCAR/Earth Observing Laboratory (EOL) radar engineering and technical staff, Jonathan Emmitt, Al Phinney, Kyle Holden, Gordon Farquharson, and Frank Pratte; without their dedication and talents none of the dual-wavelength radar data presented would have existed.