Liquid water content estimates using simultaneous S and K a band radar measurements

Transcription

1 RADIO SCIENCE, VOL. 46,, doi: /2010rs004361, 2011 Liquid water content estimates using simultaneous S and K a band radar measurements Scott M. Ellis 1 and Jothiram Vivekanandan 1 Received 14 January 2010; revised 15 December 2010; accepted 18 January 2011; published 29 April [1] A technique for the estimation of total liquid water content (LWC; the sum of cloud water and rainwater contents) using simultaneous S and K a band scanning radar observations is proposed and tested using the National Center for Atmospheric Research simultaneous S band and K a band dual polarimetric (S PolKa) radar system. The sources of error for this wavelength pair are evaluated, and the methods to mitigate them are discussed. The results are LWC estimates at each radar volume that are equivalent to specifying a reflectivity (Z) LWC relation constrained by the measured attenuation over 2 km radar ray segments. Because the radars are scanning, the LWC can be mapped out over the spatial volume and temporal evolution of the clouds. The method produces reasonable results that qualitatively compare well to in situ aircraft observations. Citation: Ellis, S. M., and J. Vivekanandan (2011), Liquid water content estimates using simultaneous S and K a band radar measurements, Radio Sci., 46,, doi: /2010rs Introduction 1 National Center for Atmospheric Research, Boulder, Colorado, USA. Copyright 2011 by the American Geophysical Union /11/2010RS [2] The Earth s radiation budget is closely related to cloud fields and their properties [Liou, 1992]. Small changes in cloud properties such as LWC and droplet size produce large variations in the radiative properties of the clouds. These factors are a significant unknown in the global radiation budget, yet can yield large feedbacks to climatic temperature perturbations from other radiative forcings, including increasing CO 2 levels [Liou, 1992]. For example, the properties of stratocumulus have been shown to be an important, yet not fully understood, climate moderator. While aircraft measurements yield useful cloud microphysical information, it is difficult to characterize cloud properties over the lifetimes of an entire cloud or field of clouds due to the small sample size of aircraft probes. Estimates of LWC from a dual wavelength scanning radar system, covering volume scans with relatively high time resolution might prove valuable for studying the microphysical characteristics and processes of these important cloud systems. [3] Another discipline to potentially benefit from scanning radar cloud LWC estimates is numerical weather prediction. There are currently no cloud LWC observations available for quantitative verification of, or assimilation into, numerical models (J. Sun, personal communication, 2007; D. Dowell, personal communication, 2010). Cloud microphysical parameterization errors have been identified as a major source of uncertainty in model prediction of storm evolution and intensity. Thus, verifying model predicted cloud LWC using dual wavelength radar observations has the possibility to lead to improved cloud microphysics parameterizations. Furthermore, assimilation of the radar derived LWC could improve forecasts by improving the initial state of the cloud field. [4] The estimation of liquid water content (LWC) from single radar data is much more ambiguous than estimating the rain rate. The total LWC is the sum of the mass of rain/ drizzle and the mass of nonprecipitating cloud droplets. The measured radar reflectivity (Z in units of dbz) is sensitive to the larger rain or drizzle particles due to its dependence on the sixth power of drop diameter. Often the majority of the total LWC comes from the nonprecipitating cloud droplets [Khain et al., 2008; Hogan et al., 2005; Vivekanandan et al., 1999]. Fox and Illingworth [1997] and Sauvageot and Omar [1987] found that only in the absence of precipitation could a valid and useful Z LWC relation be found. Khain et al. [2008] plotted LWC versus Z computed from in situ aircraft probe data taken over numerous field experiments. Their Figure 1, a composite plot of these measurements, clearly shows that no single Z LWC relationship can fit the wide scatter in the data. For example, the LWC value of 0.2 g m 3 can have Z values from 30 dbz to over 20 dbz [Khain et al., 2008]. The difficulty estimating total LWC from single radar data was recognized by Atlas [1954] who proposed using attenuation measurements to solve the problem. Combining the dual wavelength radar estimates of K a band liquid attenuation with the S band reflectivity, Vivekanandan et al. [1999] have shown it is possible to estimate the median volume diameter (MVD) and radar estimated size (RES). [5] Simultaneous dual wavelength radar measurement capability has been added to the National Center for Atmospheric Research (NCAR) S band (10 cm wavelength) dualpolarimetric transportable research radar (S Pol [Keeler et al., 2000]) with the addition of a K a band (0.86 cm wavelength) radar [Farquharson et al., 2005]. The much smaller K a band antenna was mounted directly onto the edge of the S band antenna so the two radars scan together, 1of15

2 Table 1. Comparisons Between Different Wavelengths of Reflectivity Measurement Variance, the Attenuation, and the Maximum Size of Liquid Drop Allowed for Rayleigh Scattering to Hold Radar Wavelength Z Measurement Variance (db) Attenuation (db km 1 (g m 3 ) 1 ) Maximum Diameter (mm) S band C band X band K a band W band resulting in simultaneous, overlapping measurements at the two wavelengths. By comparing the reflectivity in Rayleigh scattering of the (nearly) nonattenuating S band wavelength to that of the attenuating K a band wavelength, it is possible to estimate the K a band liquid attenuation. The goal of this study is to develop and demonstrate a technique to retrieve LWC, and subsequently MVD and RES, from scanning dual S and K a band radar measurements. [6] In section 2 there is a review of the general theory and the sources of error in dual wavelength LWC estimates along with a description of the data used. Section 3 describes the method including the mitigation of the errors described in section 2 for the particular radar configuration of S PolKa with scanning, simultaneous S and K a band radar observations. Section 4 gives results of the algorithm on real data, and section 5 provides a summary and discussion. 2. Background 2.1. Review of Theory [7] The premise of dual wavelength LWC estimates is that the LWC can be computed from the measured differential attenuation of two radars at different wavelengths, which is estimated by comparing the measured reflectivity values (Z) from the two radars. In Rayleigh scattering, Z is a measurement of the intrinsic equivalent reflectivity factor after subtracting the path losses due to attenuation by gases and cloud/precipitation particles. It can be shown that the LWC at range r is proportional to the range derivative of the dualwavelength ratio (DWR) adjusted by the gaseous attenuation with a proportionality constant of the difference between the liquid attenuation coefficients (db km 1 (g m 3 ) 1 )of the two wavelengths [Hogan et al., 2005; Williams and Vivekanandan, 2007], ðdwrþ ð a Gð 2 ; rþ a G ð 1 ; rþþ = ða L ð 2 ; rþ a L ð 1 ; rþþ ð1þ where l is the wavelength, a is the attenuation coefficients, the subscripts L and G refer to the liquid and gas attenuation respectively and the DWR is defined in units of db as DWRðdBÞ ¼ Zð 2 Þ Zð 1 Þ: ð2þ The liquid attenuation coefficients are functions of temperature. Different wavelengths have different dependencies on temperature. Because the estimate uses the difference of reflectivity, it is not sensitive to the absolute calibrations of the two radars and any path losses encountered prior to the measurements used for comparison including attenuation or partial beam blockage. Therefore major sources of error in the radar measurements are avoided with DWR based techniques. Detailed discussion of the theory behind DWRbased LWC estimates can be found in the works of Williams and Vivekanandan [2007] and Hogan et al. [2005]. [8] Previously reported dual wavelength radar estimates of LWC include collocated vertically pointing 94 and 35 GHz radars [Hogan et al., 2005], 10 and 35 GHz data with long dwell times [Vivekanandan et al., 1999] and scanning measurements at 10 and 35 GHz [Martner et al., 1993]. Accurate estimates of LWC are contingent on the accuracy of the estimated DWR and temperature Review of Error Sources [9] Williams and Vivekanandan [2007] and Hogan et al. [2005] give comprehensive and general discussions of the sources of error in dual wavelength LWC estimates which are summarized below. The error sources include: reflectivity measurement noise, magnitude of differential attenuation, radar beam geometry mismatches, violation of the Rayleigh scattering assumption, and errors in the specification of temperature Mie Scattering [10] Errors in estimated LWC can occur due to the violation of the Rayleigh approximation (Mie scattering). Mie scattering can impact the estimated LWC in two ways. First the propagation medium no longer attenuates in the Rayleigh regime. The impact of non Rayleigh attenuation is small because the majority of the liquid water (responsible for attenuation) is contained in the small cloud drops [Atlas and Ulbrich, 1977; Hogan et al., 2005]. The second impact of Mie scattering on the estimated LWC is that the measured reflectivity can deviate substantially from the Rayleigh values causing errors in the estimated attenuation. This source of error is much more severe than non Rayleigh attenuation by drops [Hogan et al., 2005]. Therefore the estimate of attenuation must not utilize reflectivity measurements in regions of Mie scattering. Table 1 shows the approximate maximum drop diameters for which Rayleigh scattering applies for S, C, X, K a,andwbands[rinehart, 2004; Vivekanandan et al., 2001; Lhermitte, 1987]. It can be seen that the choice of W band would limit the analysis to nonprecipitating clouds Reflectivity Measurement Noise and Differential Attenuation [11] Each choice of wavelength pair has a different measurement noise and differential attenuation level. The total measurable DWR increases with increasing path length (i.e., resolution) and with increased differential attenuation of the two radar wavelengths. The DWR signal must be large enough in comparison to the measurement noise to obtain reasonably small LWC errors. Therefore the maximum obtainable resolution of the LWC estimates depends on both the measurement noise and the differential attenuation of the radars. For comparison of the different wavelengths, Table 1 lists the reflectivity measurement variance (assuming high SNR) and attenuation coefficients for S, C, X, K a, and W bands. The variance estimates were made using the formulation of Doviak and Zrnic [1993] assuming a spectrum width of 2 m s 1 and typical scan parameters for the 2of15

3 S PolKa radar including a Pulse Repetition Frequency (PRF) of 1000 Hz, and 100 samples per beam. The attenuation coefficients were computed using the microwave propagation model of Liebe [1985] with a temperature of 20 C and a pressure of hpa. [12] Hogan et al. [2005] derived an equation relating the LWC error due to measurement fluctuations as a function of the radar wavelengths, dwell time, spectral width, signal tonoise ratio (SNR) and the number of range gates used to estimate DWR (i.e., the resolution of DWR). A similar relation was also formulated by Williams and Vivekanandan [2007]. Thus for a given dual wavelength radar configuration it is possible to estimate the highest range resolution allowed to achieve acceptably low LWC errors for different wavelength pairs. The level of acceptably low errors depends on the user and the types of clouds being analyzed. [13] For example the vertically pointing K a and W band measurements at a resolution of 75 m required a dwell time of close to 8 min to achieve an accuracy of approximately 10% or ± 0.04 g m 3 [Hogan et al., 2005]. The measurement variance can be reduced by averaging the range gates. They found when two range gates were averaged lowering the spatial resolution to 150 m, the necessary dwell time was reduced to about 1 min Radar Measurement Geometry [14] Williams and Vivekanandan [2007] found that in order to accurately retrieve LWC using dual wavelength radars, the beams must be matched in space and time. Displaced beams result if the two radar systems are too far apart and misaligned beams result if the radar antennas are not pointing in the same directions. Williams and Vivekanandan [2007] also found that differing radar beam widths will cause LWC estimation errors due to inhomogeneities in the observed cloud or due to the difference in observation time and space as clouds move through the differently illuminated volumes at the two wavelengths. A mismatch between the two radar range resolutions will also cause LWC estimate errors [Williams and Vivekanandan, 2007]. While the LWC estimate errors due to these radar measurement geometry differences can be reduced by time averaging and spatial smoothing, Williams and Vivekanandan [2007] found that well matched beams are required for routine, robust and reliable LWC estimates with dualwavelength radars Errors in Temperature [15] Because the liquid attenuation is a function of the temperature, errors in the specification of temperature will lead to LWC errors [Hogan et al., 2005; Williams and Vivekanandan, 2007]. Williams and Vivekanandan [2007] show that in the range 20 to 20 C a temperature error of 4 C results in a 10% error in LWC for the S and K a band wavelength pair. Therefore for the proposed method to yield reasonable results the specified temperature must be within about 4 C. This is generally possible if suitable sounding data or model predictions are used Data [16] The data used in the current study were obtained from the Rain In Cumulus over the Ocean (RICO) experiment conducted in December and January 2004/2005 in the Caribbean Sea [Rauber et al., 2007]. The observations were typically of shallow trade wind cumulus that did not contain any ice phase. For comparison, in situ aircraft measurements of LWC were available. [17] The aircraft in situ data were used for qualitative comparisons to radar derived LWC and size parameter values. Quantitative comparisons of radar and aircraft data are difficult for a number of reasons. For example the errors of representativeness contribute to differences in radar/aircraft data comparisons due to very different measurement volumes. The radar measurement volume varies with range and can be on the order of 1 km by 1 km by 150 m (the range resolution does not vary) and the in situ probes have volumes on the order of centimeters. Because cloud and precipitation properties can vary significantly (by as much as 30 50%) within the volume of one radar pixel [Paluch and Knight, 1984; Prupacher and Klett, 1997; Jaffrain et al., 2009], it is very difficult to ensure the aircraft probe measurements are representative of the radar measurements. The aircraft data can be averaged along the flight path to match the horizontal extent of the radar volume in one dimension. This one dimensional averaging, however, does not account for variations in the other horizontal axis nor in the vertical. Because of the aircraft motion, the in situ data cannot be averaged in time as is typically done with comparisons of ground based in situ data to radar data. These differences limit the accuracy and usefulness of quantitative comparisons between radar and aircraft data. The in situ data in this study are used to ensure that the radar estimated LWC is reasonable. 3. Estimating LWC and Size Parameters From S PolKa Measurements [18] In order to make attenuation based estimates of total liquid water content within acceptable error limits using scanning S and K a band radars, the sources of error, as summarized in section 2.2, must be addressed for this radar configuration. In this section the methods used to mitigate the errors and estimate the LWC on the radar resolution are presented. The estimates of median volume diameter and radar estimated size are also summarized Mitigation of Error Sources [19] In this section the mitigation of the general error sources described in section 2.2 are described for the specific radar configuration and wavelength pair of the S PolKa Mie Scattering [20] Gaussiat et al. [2003] and Meneghini et al. [2005] showed that Mie scattering can be identified using observations with three wavelengths. Hogan et al. [2005] took advantage of the vertical pointing geometry to identify Mie scattering using the differential Doppler velocity. They found that if the difference in mean Doppler velocities exceeded 0.1 m s 1 there was significant Mie scattering causing errors in DWR. The scanning S PolKa radar requires a different approach because only two wavelengths are available and the radial velocity differences cannot be used at nonvertical incident to identify regions of Mie scattering contamination. [21] Drops of diameter of less than roughly 1 mm satisfy the Rayleigh scattering condition at K a band [Vivekanandan et al., 2001; Lhermitte, 1987]. Therefore the maximum drop diameter (D max ) in the radar volume must not exceed 1 mm. To ensure this condition is met, D max is computed using the 3of15

4 Figure 1. (a) S and K a band reflectivity versus range and (b) DWR versus range for an echo observed during Rico on 10 January 2005 at 1128 UTC at an elevation angle of 4.5 deg. S band dual polarimetric data. The median dropsize diameter (D 0 ) is estimated from the S band Z and Z DR values following Beard and Chuang [1987]. The D max can be approximated as twice D 0 [Vivekanandan et al., 2004], and data with estimated D max values exceeding 1.0 mm were excluded from the DWR computation Reflectivity Measurement Noise and Differential Attenuation [22] Using the equation derived by Hogan et al. [2005] relating the LWC error due to measurement fluctuations as a function of the radar wavelengths, dwell time, the number of range gates, spectral width and the signal to noise ratio it is possible to evaluate different radar wavelength pairs and configurations. This includes S PolKa and the vertically pointing K a and W band radars used by Hogan et al. [2005] with the goal of obtaining high resolution LWC profiles through low level stratus and stratocumulus clouds. They found that 150 m resolution was needed to produce 0.04 g m 3 error (roughly 10% error) for a dwell time of 1min.UsingstaringXandK a band data at low elevation angles, Vivekanandan et al. [1999] achieved 0.04 g m 3 accuracy with 750 m resolution and 30 s dwell time. [23] The long dwell times of Hogan et al. [2005] and Vivekanandan et al. [1999] are not obtainable with S PolKa in scanning mode, necessitating coarser resolution to obtain reasonable results. Following the calculations of Hogan et al. [2005] for typical S PolKa dwell times and spectrum width values, it was estimated that 2 km resolution is required to achieve an accuracy of 0.04 g m 3 (approximately 10% error). Experiments on the RICO data using different resolutions to compute DWR were performed. It was found that the minimum resolution required to obtain reasonable measurement noise was also about 2 km, consistent with the theoretical results computed from Hogan et al. [2005]. Therefore the DWR measurements in this study are made over a ray segment with a minimum length of 2 km. Using the total attenuation measurements over the ray segments, estimates of DWR at the resolution of S PolKa (nominally 150 m) are then made following the methodology of Tuttle and Rinehart [1983] as described in section Radar Measurement Geometry [24] Beam angle and range gate alignment can be difficult to obtain using two separate radar systems, particularly in the case of separate scanning radar systems. Vivekanandan et al. [1999] and Hogan et al. [2005] achieved good results by utilizing side by side radars that were fixed or staring. In this way, sufficiently accurate alignment could be obtained, resulting in high quality LWC estimates. [25] The S PolKa K a band antenna is mounted directly on the side of the larger S band antenna so that the two radars scan together. The two radars have matched beam widths ( 0.9 degree) and range resolutions (nominally 150 m). The pointing angles of the S and K a 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 K a 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. This configuration provides spatially and temporally well matched dual wavelength radar data at S and K a bands, minimizing the errors from mismatched radar resolution volumes Cloud Liquid Water Content Estimation [26] The attenuation is estimated over ray segments of 2 km or more using data found to be Rayleigh scattering using the criteria described in section 3.1. The S band liquid attenuation is less than 1% of the K a band attenuation (Table 1). Thus the total attenuation (db) over the ray segment at K a band can be estimated simply as the difference in the DWR value at the end of the ray segment and the DWR value at the beginning. Figure 1 shows plots of S and K a band reflectivity values (Figure 1a) and DWR (Figure 1b) versus range. As the range increases through the cloud echo, the difference between S and K a band reflectivity values increases due to attenuation. This is also seen in the 4of15

5 increasing DWR with range (Figure 1b). Note that the nonzero DWR at the shortest range shown if Figure 1 is due to any liquid and gas attenuation that occurred at shorter ranges. The total attenuation over the chosen ray segment includes gaseous and liquid attenuation. The gaseous attenuation that occurs over the ray segment is removed assuming saturation in cloud or using a nearby sounding below cloud base similar to Hogan et al. [2005]. The result is an estimate of the total liquid attenuation, A Lt (db). [27] Because LWC estimates at higher range resolution than 2 km are desired, the next step is to estimate the liquid attenuation (db km 1 ) at the range resolution of the radar from the coarser DWR estimates. Following Tuttle and Rinehart [1983], the attenuation is apportioned along the ray segment using the S band reflectivity data as, A L ¼ Cz p s ; where A L is the one way K a band liquid attenuation (db km 1 ), and z S is the S band reflectivity in mm 6 m 3. The coefficient p is well approximated as a constant [Tuttle and Rinehart, 1983] and the coefficient C is determined for each ray segment. Summing z s over the ray segment and using the total liquid attenuation A Lt (db), equation (3) becomes A Lt ¼ CSz p s : The coefficient C is computed for each ray segment using (4). [28] The constant p was computed for the wavelength combination S and K a band following the technique developed by Tuttle and Rinehart [1983] for S and X bands. Taking the log 10 of equation (3) and rearranging we have ð3þ ð4þ log 10 ða L Þ ¼ log 10 ðcþþp log 10 ðz s Þ; ð5þ where S subscript signifies S band, and Z is in units of dbz. About 500 ray segments were collected from RICO data and the total attenuation A Lt and mean S band reflectivity values were computed. Next a linear least squares fit was made to the data to determine average values of p and C. The average value of p was about 0.2. [29] With the computed C and p coefficients, equation (3) is used to estimate the K a band liquid attenuation at the resolution of the radar (150 m for S PolKa). It should be kept in mind that only path integrated attenuation along ray segments can be reliably measured for the clouds observed and the ending points of the path should be free of non Rayleigh scattering. The accuracy of the range resolved attenuation estimated from the measured total attenuation depend on the validity of equation (3). [30] With these range resolved liquid attenuation estimates, the liquid water content (g m 3 ) was estimated using, LWC ¼ KT ð ÞA L : where K is a constant that is a function of temperature [Vivekanandan et al., 1999] Estimation of Drop Size Parameters [31] Next the median volume diameter (MVD) was computed from the LWC estimates and S band reflectivity ð6þ values following the relationship proposed by Vivekanandan et al. [1999], MVD 3 ¼ 2: z=lwc where MVD is in mm, z is in mm 6 m 3 and LWC is g m 3. Equation (7) assumes an exponential dropsize distribution. The MVD is defined as the drop diameter at which half of the mass of water is contained within drops of larger diameter and half of the mass is contained within drops of smaller diameter. [32] A particle size characteristic that is a direct function of the radar measurables known as the radar estimated size (RES) was introduced by Vivekanandan et al. [2001]. They defined the RES as the ratio of reflectivity, z, and K a band liquid attenuation, which can be written as, RES ¼ 7: z 1=3 ; ð8þ A L where RES is in mm, z is in mm 6 m 3 and A L is in db km 1. The RES has the advantage that it is derived directly from radar measurables and does not assume any DSD. It is generally weighted toward the larger end of the particle size spectrum and is equal to or greater than the MVD [Vivekanandan et al., 2001]. [33] The technique proposed here uniquely combines and extends of the principles used by Hogan et al. [2005], Williams and Vivekanandan [2007], and Vivekanandan et al. [1999] to estimate the dual wavelength LWC and associated errors using the unique combination of scanning S and K a band radar observations. The attenuation study of Tuttle and Rinehart [1983] is further used to obtain LWC estimates at the range resolution of the radar. Total LWC (cloud plus precipitation content) have not previously been estimated from scanning S and K a band simultaneous radar measurements. 4. Results [34] Figure 2 shows PPI plots of the measured S band reflectivity and the LWC estimate for a plan position indicator (PPI) scan collected during the RICO field experiment on 12 January 2005 at 1707 UTC. The NCAR C 130 aircraft was in a region measuring LWC with the in situ King probe. The C 130 aircraft signature (or so called skin paint) is visible in the reflectivity field as it exited a cumulus cell (Figure 2). Both the King probe measurements and the dualwavelength estimates of LWC varied between 0.05 and 0.1 g m 3 of cloud water in the region indicated by the red oval in Figure 2. [35] Figure 3 shows PPI plots of the estimated median volume diameter and radar estimated size for the same data as shown in Figure 2. The MVD values are reasonable in the domain. The estimated RES shown in Figure 3 are also reasonable and greater than or equal to the MVD, in agreement with Vivekanandan et al. [2001]. [36] Figure 4 shows PPI plots of S band reflectivity and radar estimated LWC at elevation angles of 1.5 deg and 4.5 deg from a volume scan of precipitating trade wind cumulus collected on 10 January 2005 during RICO. The ð7þ 5of15

6 Figure 2. PPI plots of (a) S band reflectivity and (b) estimated LWC. The data were collected on 12 January 2005 at 1707 UTC. trade wind cumuli are shallow and confined below the freezing level ( 5 km), so there is no ice phase. Cloud base is approximately 800 m [Derksen et al., 2009], corresponding to a range of about 30 km at 1.5 deg elevation and about 10 km for the 4.5 deg elevation data. Therefore, the majority of the 1.5 deg scan data are below cloud base and the 4.5 deg scan data are above cloud base. It can be seen that the estimated LWC values are much lower at 1.5 deg than at 4.5 deg even though the reflectivity values are similar or even greater at 1.5 deg. This makes physical sense considering the 1.5 deg scan data are below cloud base and the 4.5 deg scan data are above cloud base. The data below cloud base has reflectivity values consistent with the presence of drizzle and raindrops, but the total LWC is relatively Figure 3. PPI plots of (a) MVD and (b) RES for the data presented in Figure 2. 6of15

7 Figure 4. PPI plots of S band reflectivity at (a) 1.5 and (b) 4.5 deg elevation, and (c and d) the corresponding LWC estimates, respectively. The data were collected on 10 January 2005 at about 1130 UTC. low due to the absence of cloud drops. At 4.5 deg the cloud drops are responsible for larger LWC values despite the reflectivity values being similar or lower than below cloud base. [37] Figure 5 shows the RES for the data presented in Figure 4. In contrast to the LWC in Figure 4, the RES is larger below cloud base (1.5 deg elevation) than higher in the cloud (4.5 deg elevation). [38] Because the estimates can be made with a scanning radar system (S PolKa in this case), the LWC and size parameters can be mapped over the volume of the cloud as illustrated in Figures 6 and 7, respectively, which show PPI s of selected elevation angles (1.5, 3.5, 5.8, and 9.8 deg) of the convective cloud visible in Figure 4 (bottom). It can be seen in Figure 6 that the LWC increases from very low levels below cloud base at 1.5 deg to middle of the cloud at 5.8 deg and then decreases again near the top of the cloud at 9.8 deg. The RES values shown in Figure 7 are generally larger at 1.5 deg elevation angle below cloud base and smoothly decrease with height. An exception is a maximum in RES at 5.8 deg elevation angle evident in Figure 7c. [39] Vertical cross sections of the radar data, LWC and size parameter estimates were constructed using the volume scan depicted in Figures 4 and 5. The cross sections are through the maximums in LWC of the echoes to the southwest and northwest of the radar denoted by the circles labeled echoes A and B, respectively, in Figure 4d. The vertical cross sections of reflectivity, radial velocity (VR), LWC, and MVD of echo A are shown in Figure 8. The contours represent constant values as indicated on the color scale. The maximum in LWC is at an altitude of about 1.5 km with a magnitude near 0.5 g m 3 and the maximum in MVD is lower at 1.0 km altitude with a maximum of about 2.5 mm. Although there are no direct verification data to compare to the cross sections, Derksen et al. [2009] compiled the LWC measurements from C 130 the cloud 7of15

8 Figure 5. PPI plots of estimated RES at (a) 1.5 and (b) 4.5 deg elevation, for the data presented in Figure 4. Figure 6. PPI plots showing the LWC of selected elevation angles, (a) 1.5 deg, (b) 3.5 deg, (c) 5.8 deg, and (d) 9.8 deg, of the convective cloud visible in Figure 4 (bottom). 8of15

9 Figure 7. PPI plots showing the RES of selected elevation angles of the convective cloud visible in Figure 4 (bottom). Shown are (a) 1.5, (b) 3.5, (c) 5.8, and (d) 9.8 deg. 9of15

10 Figure 8. Vertical cross sections of (a) reflectivity (dbz), (b) radial velocity (m s 1 ), (c) LWC (g m 3 ), and (d) MVD (mm) through the echo labeled A in Figure 4d. The cross sections are reconstructed from the volume scan presented in Figures 4 and of 15

11 Figure 9. Vertical cross sections of (a) reflectivity (dbz), (b) radial velocity (m s 1 ), (c) LWC (g m 3 ), and (d) MVD (mm) through the echo labeled B in Figure 4d. The cross sections are reconstructed from the volume scan presented in Figures 4 and 5. penetrations during RICO. The data presented by Derksen et al. [2009] represent the combination of many clouds at various stages of development. The altitude of the maximum median value of C 130 observed LWC occurs at an altitude of 1.5 km, similar to the data in Figure 8c. The median and 90% values of the C 130 measured LWC at 1.5 km altitude were near 0.35 and 0.55 g m 3, respectively. It is not surprising that echo A would have a maximum LWC near the maximum of the in situ data considering this is a growing cumulus as evidenced by the convergence at low levels and divergence at upper levels seen in the VR plot of Figure 8b. The LWC maximum being located above cloud base and above the maximum in drop size are also consistent with a growing cumulus cloud [Prupacher and Klett, 1997]. The MVD values estimated in Figure 8d are in the range of the observations of Baker et al. [2009] who found that the cumulus clouds of RICO frequently contained drops of 3 mm and greater with narrow drop size distributions with a lack of many smaller drops. [40] Vertical cross sections similar to those in Figure 8 but through the maximum LWC in echo B (Figure 4d) are shown in Figure 9. The reflectivity maximums of echoes A and B are similar, but echo B has the maximum near cloud base and echo A has the maximum at higher altitudes. In echo B the LWC maximum is also much lower in altitude than echo A and is located near cloud base. The LWC also has lower magnitude than echo A, with a maximum near 0.2 g m 3. The MVD values of the cross section of echo B have a maximum similar to echo A, but are located near cloud base indicating the larger raindrops have descended. The low level convergence and upper level divergence indicated in the VR field of echo B is also much weaker than in echo A. This implies that the updraft in echo A is more vigorous than echo B. Stronger updrafts produce higher LWC values [Prupacher and Klett, 1997], so it is consistent that echo A would have higher LWC values than echo B. The largest drops being located near cloud base is consistent with a cumulus cloud near the end of its lifetime [Prupacher and Klett, 1997] and echo B indeed dissipated about 10 to 15 min after the cross section in Figure 9. The LWC values in Figure 9c are well within the range of C 130 observed LWC reported by Derksen et al. [2009]. [41] Time series of the LWC and RES for full volumes of individual clouds are also possible with the scanning dualwavelength S PolKa estimates thereby documenting the evolution of total LWC and drop growth. Figure 10 shows a 10 min time series of LWC estimates of the cells in Figure 4 (bottom), and Figure 11 shows the accompanying RES 11 of 15

12 Figure 10. A time series PPI plots at 4.5 deg showing the LWC of the convective clouds visible in Figure 4 (bottom). The times shown are (a) 1131, (b) 1134, (c) 1137, and (d) 1141 UTC. 12 of 15

13 Figure 11. A time series PPI plots at 4.5 deg showing the estimated RES of the convective clouds visible in Figure 4 (bottom). The times shown are (a) 1131, (b) 1134, (c) 1137, and (d) 1141 UTC. 13 of 15

14 Figure 12. Scatterplot of S band reflectivity versus estimated LWC. The data were grouped into regions with RES values of less than 1 mm (blue) between 1 and 2 mm (red) and greater than 2 mm (black). estimates.it can be seen in Figure 10 the LWC steadily decreases with time indicating mature cells that are raining out and evaporating. A similar trend can be seen in the RES time series (Figure 11). [42] The LWC estimates from the complete volume scan (including 6 PPIs ranging from 1.5 to 9.8 deg) collected on 10 January 2005 were plotted against the S band reflectivity and are shown in Figure 12. There is a considerable range of LWC values for a given reflectivity value. For example a reflectivity of 20 dbz is associated with LWC values ranging more than a factor of 10 from about to 0.2 g m 3. This is a direct result of using the attenuation to estimate LWC as opposed to the reflectivity alone. A single Z LWC relationship would appear as a single straight line in Figure 12 and would fail to capture the variability seen by the attenuationbased estimates. Numerous straight lines can be seen in Figure 12 indicating that the technique proposed in this study is equivalent to specifying a Z LWC relationship that is consistent with the measured total attenuation for each ray segment of at least 2 km in length. The data shown in Figure 12 have been grouped into three ranges of the estimated radar estimated size: RES < 1 mm are plotted blue, 1 < RES < 2 mm are plotted red, and RES > 3 mm are plotted black. The results show that the RES is strongly related to measured Z, but has no relation to LWC. This is consistent with the fact that Z is dominated by the larger precipitation sized drops while the LWC is dominated by the smaller cloud droplets. Therefore no relation between LWC and RES is expected. 5. Summary and Discussion [43] A technique to estimate the total cloud liquid water content using a scanning S and K a band dual wavelength radar system was proposed and tested using data collected with the NCAR S PolKa radar during RICO. The errors associated with this wavelength pair in a scanning configuration were analyzed following Hogan et al. [2005] and Williams and Vivekanandan [2007]. The proposed method applied to RICO data yielded LWC values that were consistent with, and within the range of, the in situ aircraft probe data LWC measurements compiled by Derksen et al. [2009]. The results also compared well to nearly coincident in situ measurements. Time series of LWC estimates showed that the algorithm was stable with time. [44] The total liquid attenuation at K a band is measured over ray segments with a minimum length of 2 km. The attenuation at the radar range resolution is then estimated following Tuttle and Rinehart [1983] and used to estimate the LWC. The results are analogous to specifying a different Z LWC relationship for ray segments of 2 km or more in length constrained by the measured total liquid attenuation. The advantage of estimating LWC from dual wavelength radar measurements is that the estimate is not confounded by variations in drop size distributions and the presence of drizzle as is the case for single wavelength measurements. The method is applied to scanning weather radar data allowing the LWC and size parameters to be documented over the volume of cloud systems and tracked in time. [45] The dual wavelength radar LWC estimates are lacking direct quantitative verification to date. Future work must include verifying the results of the algorithm. There are several approaches for data collection that can provide opportunities for quantitative verification of the LWC estimates. One approach is to collocate a radiometer that measures the total liquid path with S PolKa similar to the procedure outlined by Vivekanandan et al. [1999]. The scanning of the radar and the radiometer could be coordinated such that the time and azimuth resolution of both could be matched. The radar estimated LWC could then be integrated in range and compared to the radiometer measurements [Vivekanandan et al., 1999]. Another approach involves coordinated in situ aircraft and S PolKa measurements. The aircraft could be flown along radar radials and then the in situ measured LWC could be averaged to the resolution of the radar. This would allow comparisons of the range resolved LWC as well as the total liquid path estimated by the radar and measured with the aircraft. Another verification involves vertically pointing K a and W band radars in the S PolKa domain for comparison to the LWC estimates of Hogan et al. [2005]. Finally, there is a robust verification that does not require additional LWC measurements. Stratocumulus clouds have been shown to have adiabatic LWC values [Prupacher and Klett, 1997; Paluch and Knight, 1984; W. A. Cooper, personal communication, 2010]. Therefore if dual wavelength radar LWC estimates are made in stratocumulus clouds and proximity sounding data are available, the adiabatic LWC values could be computed and compared to the radar estimates. Therefore if regular soundings could be launched during observations of stratocumulus clouds, this would be a straightforward and robust method of verification for the LWC estimates. [46] Acknowledgments. The National Center foratmospheric 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 would like to thank Paul Field for helpful discussions concerning the aircraft data, and Tammy Weckwerth and Wiebke Deierling for helpful reviews and discussions. 14 of 15

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