High temporal and vertical resolution water vapor measurements by Raman and differential absorption lidar systems have been used to characterize the turbulent fluctuations in the water vapor mixing ratio field in convective mixed layers. Since daytime Raman lidar measurements are inherently noisy (due to solar background and weak signal strengths), the analysis approach needs to quantify and remove the contribution of the instrument noise in order to derive the desired atmospheric water vapor mixing ratio variance and skewness profiles. This is done using the approach outlined by Lenschow et al.; however, an intercomparison with in situ observations was not performed.
Water vapor measurements were made by a diode laser hygrometer flown on a Twin Otter aircraft during the Routine Atmospheric Radiation Measurement (ARM) Program Aerial Facility Clouds with Low Optical Water Depths Optical Radiative Observations (RACORO) field campaign over the ARM Southern Great Plains (SGP) site in 2009. Two days with Twin Otter flights were identified where the convective mixed layer was quasi stationary, and hence the 10-s, 75-m data from the SGP Raman lidar could be analyzed to provide profiles of water vapor mixing ratio variance and skewness. Airborne water vapor observations measured during level flight legs were compared to the Raman lidar data, demonstrating good agreement in both variance and skewness. The results also illustrate the challenges of comparing a point sensor making measurements over time to a moving platform making similar measurements horizontally.
The planetary boundary layer (PBL) is the lowest layer of the atmosphere. Because of its proximity to the surface, the PBL is affected by the surface roughness and fluxes of water vapor, sensible heat, and momentum. Turbulent fluxes within the boundary layer transport water vapor, pollutants, and sensible heat throughout the boundary layer, influencing the vertical and horizontal structure of the PBL. Turbulence occurs over a wide range of scales and is a critical process that must be represented in all numerical weather prediction and climate models.
There are several different PBL schemes used today to parameterize turbulence in numerical weather and climate models, and intercomparisons have demonstrated that there are significant differences among them that result in large differences in the model simulations (e.g., Hu et al. 2010; Xie et al. 2012). As an example, differences in the commonly used PBL schemes within the Weather Research and Forecasting Model (WRF) can result in large differences in the daytime mixed layer depth, temperature, and humidity (Milovac et al. 2013), as well as convective available potential energy (CAPE) and convective inhibition (CIN) (Coniglio et al. 2013). Thus, observing and characterizing turbulence in the PBL under a range of atmospheric conditions in order to evaluate and improve the representation of turbulence is an important research topic.
Ground-based water vapor and wind lidar systems have been used for over a decade to provide measurements of turbulence in the boundary layer (e.g., Senff et al. 1994; Wulfmeyer 1999a,b). Unlike other techniques, lidar systems are able to sample profiles of the atmosphere remotely and thus do not create any structurally induced artifacts in the dataset that need to be accounted for in the analysis. However, lidar measurements are inherently noisy, both due to weak backscattered returns and solar noise in the receiver, and thus analysis techniques need to be able to separate the contribution to the variance and skewness profiles from the atmosphere from the noise contributions from the instrument.
Lenschow et al. (2000, hereafter L00) developed a mathematical framework to estimate the lidar noise contribution from the second to the fourth moment and to remove this component when computing atmospheric variance and skewness. This technique has been used in the analysis of wind lidar (e.g., Lothon et al. 2006; Wulfmeyer and Janjić 2005; Newsom and Banta 2004), elastic backscatter lidar (Pal et al. 2010), water vapor differential absorption lidar (DIAL) (e.g., Wulfmeyer 1999a; Kiemle et al. 2011), and Raman lidar (RL; Wulfmeyer et al. 2010).
There are many cases where the noise level in the instrument is sufficiently large that the atmospheric component of the variance is a small fraction of the total variance of the observation. Thus, a natural question to ask is, how well does the L00 method work? The method has been evaluated with Doppler wind lidar measurements (Lenschow et al. 2012) but not with in situ water vapor measurements. To answer this question, we compared turbulent statistics derived from a fast-response in situ airborne water vapor sensor deployed during a 2009 field experiment over the Atmospheric Radiation Measurement Program (ARM) Southern Great Plains (SGP) site (Stokes and Schwartz 1994) with those made by the Raman lidar at that facility. The L00 technique was used to analyze the data from both the airborne in situ sensor and the lidar in order to provide random uncertainties in the variance and skewness statistics, and the sampling uncertainties in both were estimated using the approach in Lenschow et al. (1994). This was done to ensure consistency in the analysis of the two datasets.
The ARM Raman lidar (RLID) became operational at the SGP site in 1996 (Goldsmith et al. 1998; Newsom et al. 2013), and the system has been operational over 90% of the time since 2005. The RLID backscatter data are processed by operational algorithms in the ARM data management facility to produce profiles of water vapor mixing ratio, aerosol scattering ratio, aerosol backscatter coefficient, aerosol extinction, and linear depolarization ratio (Turner et al. 2002), and the data have been used for a wide range of research topics (e.g., Turner et al. 2001; Ferrare et al. 2001; Comstock et al. 2004). The original resolution of the raw backscattered photon data from this system was 39 m, 1 min; however, the data were typically summed, thereby decreasing the temporal and spatial resolution in order to improve the signal-to-noise ratio. In 2004, the RLID was refurbished and upgraded (Ferrare et al. 2006). As part of this effort, new detection electronics, which performed simultaneous photon counting (PC) and analog-to-digital (AD) detection, were installed (Newsom et al. 2009). This upgrade, which included the replacement of the interference filters that had higher transmission characteristics in the various channels, resulted in signal strengths that were 10–20 times larger than the original system (Ferrare et al. 2006). The new electronics also had higher vertical and temporal resolution: 10 s, 7.5 m, respectively. The higher temporal resolution and the higher signal-to-noise ratio provided a much higher-quality measurement of water vapor mixing ratio in the boundary layer.
Prior to the upgrade of the SGP Raman lidar, only DIAL systems had demonstrated the accuracy and resolution needed to observe turbulent profiles in the convective mixed layer from water vapor profiles. However, Wulfmeyer et al. (2010) demonstrated that the upgraded SGP RLID had the ability to measure atmospheric water vapor variance and skewness profiles using the L00 framework. The RLID needs to collect at least 2 h of data when the convective mixed layer is quasi stationary (i.e., not growing or evolving) in order to have enough data to compute the variance and skewness profiles. In Oklahoma, this generally occurs in the mid- to late afternoon, after the mixed layer has reached its maximum depth. Afternoons that are affected by synoptic events such as frontal or dryline passages are not analyzed with this lidar technique.
b. Twin Otter diode laser hygrometer
ARM has had a focus on liquid water clouds with low optical depths for many years due to the difficulty in characterizing these clouds from ground-based observations and the importance of these clouds in radiative closure, aerosol–cloud interactions, and other processes (Turner et al. 2007). As such, ARM formed the Clouds with Low Optical Water Depths (CLOWD) focus group to develop techniques to improve the program’s ability to observe these clouds and to validate these approaches. One of the important tools available to the CLOWD group were airborne measurements made by the ARM Aerial Facility (AAF), a component of the program that coordinates all aircraft measurements supported by the program.
The CLOWD group proposed and executed the Routine AAF CLOWD Optical Radiative Observations (RACORO) campaign (Vogelmann et al. 2012). RACORO was conducted over a 5-month period, from 22 January to 30 June 2009, over the SGP site. Its primary purpose was to collect a large in situ dataset of continental boundary layer liquid water clouds over a variety of atmospheric conditions. The Twin Otter (TO) aircraft from the Center for Interdisciplinary Remotely-Piloted Aircraft Studies (CIRPAS) was used for RACORO. Because of the routine nature of the experiment, the instruments installed on the TO needed to be mature with a track record of reliable operations and minimum manual maintenance. A full list of instruments carried by the TO during RACORO is given in Table 2 of Vogelmann et al. (2012).
Since it was expected that there could be long stretches of time when boundary layer clouds would not be present, alternative missions were devised that would utilize the multidisciplinary payload on the aircraft to characterize boundary layer properties relevant to RACORO objectives. These missions included “turbulence flights,” where the TO was flown in straight and level legs at various altitudes within the daytime convective mixed layer. One use of these data is to evaluate the turbulent profiles derived from the RLID observations. Because of a relatively large number of clear skies, approximately 40 flight hours were dedicated to this objective, of which two flights were suitable for this analysis.
The water vapor measurement from the diode laser hygrometer (DLH) (Diskin et al. 2002) is the primary measurement from the TO used in this analysis. The DLH used an open-path double-pass configuration, where the transmitter/receiver is mounted on the interior of a window of the aircraft and a reflector is placed on the wing strut; the optical pathlength is approximately 220 cm. The DLH was tuned to a weak water vapor absorption line in the 1.4-μm spectral region. The DLH was calibrated in the laboratory over a range of water vapor density and dry air pressure amounts; these calibration coefficients plus the local air temperature and pressure measured by other instruments on the TO were used to derive the water vapor mixing ratio. The DLH observations used in this study were collected at 10 Hz and have been packaged with the aircraft location/attitude dataset for ease of analysis.
The NASA Langley Research Center (LaRC) King Air aircraft joined the RACORO effort during the last month of the campaign. The King Air and TO were typically flown in a stacked formation, with the King Air several kilometers above the TO. The King Air carried the LaRC high spectral resolution lidar (HSRL) (Hair et al. 2008). The HSRL measures both molecular-only and aerosol-plus-molecular backscatter and thus is able to directly measure aerosol backscatter and extinction coefficients simultaneously (Eloranta 2005); the Raman lidar also is able to measure extinction and backscatter directly and simultaneously but using a different approach (e.g., Ansmann et al. 1990). The LaRC HSRL also measures linear depolarization. The backscatter, extinction, and depolarization profiles are very sensitive to aerosol gradients in the atmosphere. Since there is often a gradient in the aerosol concentration at the top of the convective mixed layer, the HSRL is able to detect and quantify the height of this mixed layer (Fast et al. 2012; Scarino et al. 2013). This will prove important for one of the case study days.
While the TO flew many missions to measure turbulence in the mixed layer during RACORO, only two cases were suitable for this intercomparison study. The other days were ruled unsatisfactory due to 1) a large temporal mismatch between the time of the TO flight legs and when the mixed layer became quasi stationary; 2) the mixed layer was not quasi stationary for at least 2 h, or in some cases, was being influenced by the passage of synoptic features such as drylines or fronts; 3) the mixed layer did not become deep enough (at least 1 km) for the RLID to sample it well, since the near-field overlap region hampers the analysis of the data in the lowest 500 m; or 4) the RLID had a very low signal-to-noise ratio for atmospheric water vapor variance, which occurs in very dry seasons (this eliminated a few cases in February and March). Some of the above-mentioned limitations were the result of needing to file flight plans at least 24 h in advance of the mission, and thus inadequacies in the forecast of the boundary layer depth and character resulting in suboptimal conditions for the flight. However, there were two cases that met the conditions needed for the analysis, namely, 31 May and 15 June 2009.
a. 31 May 2009
The synoptic conditions on the afternoon of 31 May over north-central Oklahoma were relatively quiet, with the maximum air temperature at the surface reaching 36°C and southerly afternoon winds at 5–6 m s−1. Earlier in the day (around 0900 UTC), a warm front had passed over the site heading northeast, and by 1800 UTC the front extended from central Nebraska to south-central Missouri. The daytime skies over the SGP site were cloud free, and the surface sensible and latent heat fluxes measured at the SGP site close to the RLID in the late afternoon reached 330 and 150 W m−2, respectively.
The TO flew five separate horizontal legs between 1945 and 2135 UTC, with the lowest and highest legs at approximately 610 and 1670 m AGL, respectively (Fig. 1, top). The legs were oriented with the wind at the flight level (i.e., either flying downwind or upwind; the flight path was chosen to minimize crosswind components). Because of airspace restrictions associated with Vance Air Force Base, which is located to the west of the SGP site, the TO was primarily flying to the north-northeast or northeast of the site; all of the legs ended over the site.
The time–height cross section of the RLID water vapor mixing ratio observations, at 10-s and 75-m resolution, respectively, for the afternoon of 31 May are shown in the top panel of Fig. 2. The depth of the mixed layer is approximately stationary from 1900 to 2100 UTC; RLID data from this period were analyzed to derive the turbulent profiles. The mean height of the mixed layer, determined from the peak in the water vapor variance profile (Lammert and Bösenberg 2006; Pal et al. 2013) over the period from 1900 to 2100 UTC, is 2080 m AGL. Figure 2 (top) clearly shows convective moist updrafts that penetrate the top of the mixed layer and the drier downdrafts that penetrate into this mixed layer. The five TO flight legs, identified as horizontal white/black lines in Fig. 2, were all located within the mixed layer. Note that the upper two TO flight legs are outside this period and that depth of the mixed layer seems to have changed by approximately 600 m between 2100 and 2130 UTC.
The power spectral density was computed from the DLH observations for each TO leg (Fig. 3). These traces demonstrate that the DLH observations were able to resolve the inertial subrange at all flight levels on both days, as indicated by the − power-law behavior seen in the data at higher frequencies (Kolmogorov 1941). Also, there is very little evidence of a flattening of the power spectra at high frequencies, which suggests that the random noise level in these data is low.
A comparison of the RLID and TO mean water vapor concentration is shown in Fig. 4 (left), showing good agreement between the RLID and DLH on the aircraft. The error bars in the mean water vapor profiles denote the square root of the total variance of the water vapor observations from each sensor. The larger error bars in the RLID data are primarily due to the larger amount of (random) instrument noise in the lidar system, relative to the DLH observations. The total variance and uncorrected skewness of the water vapor observations from the RLID are shown as the green lines in the center and right-hand panels of Fig. 4. Using the L00 approach, the atmospheric variance and skewness were derived from the RLID observations (dark circles with error bars); these profiles are markedly different than the total variance and uncorrected skewness profiles and illustrate the importance of accounting for the instrument noise. Both random and sampling errors were computed from the RLID variance and skewness profiles in Fig. 4 using the L00 method and Lenschow et al. (1994), respectively. In general, the sampling errors in the RLID variance and skewness profiles (denoted with error bars) are 1–2 times as large as the random errors (denoted with thick horizontal lines), except in the RLID skewness profile below 1000 m AGL, where the random errors exceed the sampling errors.
The variance and skewness computed from the DLH observations on each TO leg are shown as blue squares in Fig. 4. The sampling uncertainties in these statistics are represented as error bars and the random errors in these DLH statistics are negligible.
The DLH atmospheric variance observations agree very well with the RLID observations for the first four levels and agree reasonably well for the uppermost level. This comparison clearly shows that the L00 approach to separate the atmospheric variance from the total variance is very good. The atmospheric skewness results are a bit mixed, with the first three TO levels agreeing well with the RLID, but there is poorer agreement on the fourth level at 1420 m AGL and fair agreement at the uppermost level at 1680 m. Recall, however, that the upper two flight legs were near the end or outside of the RLID analysis time, and also that the mixed layer seemed to be changing character at that time as its depth changed about 600 m after 2115 UTC. Furthermore, sampling errors are becoming increasingly important for higher-order turbulent moments, which could be affecting this comparison.
b. 15 June 2009
The weather conditions on 15 June over the SGP site were very similar to those on 31 May, including the passage of a warm front at approximately 1200 UTC moving toward the northeast. By 1300 UTC, the front extended from northwest Kansas to south-central Missouri. The skies were cloud free behind the front, and surface air temperature reached 38°C in the late afternoon. The winds behind the front were from the south-southwest at approximately 5 m s−1. The sensible heat flux at the surface at the SGP site was large, but the latent heat flux was small (approximately 500 and 50 W m−2, respectively) in the late afternoon.
The TO flew three horizontal legs from 1845 to 1945 UTC 15 June, with the legs located at roughly 660, 980, and 1310 m AGL (Fig. 1, bottom). Like 31 June, the flight legs radiated out from the SGP site to the northeast, again located along the wind direction at flight level. The time–height cross section of water vapor mixing ratio observed by the RLID is shown in the bottom panel of Fig. 2. The mixed layer is more than a factor of 2 moister in the 15 June case than in the 31 May case. RLID data from 1830 to 2030 UTC were processed to derive the turbulent profiles, and the peak of the variance profile was again used to determine that the mean top of the mixed layer during this period was at 1120 m AGL. Like 31 May, moist updrafts extending above the mean top height of the mixed layer can be seen in this figure as well as downdrafts that mix drier air from the free troposphere into the mixed layer. The three TO legs seem to be within, near the top of, and above the mixed layer (Fig. 2, bottom). The TO observations are well matched temporally with the RLID analysis.
Figure 5 shows the comparison between the mean, variance, and skewness of the water vapor mixing ratio for 15 June, where the DLH observations were derived over each of the approximate 39-km flight legs (blue squares). For the RLID water vapor skewness profile, only levels where the derived uncertainty was less than 1.5 are shown. The mean water vapor mixing ratio values show a slight bias between the two (Fig. 5, left panel), with the DLH observations being slightly wetter than the RLID. There is reasonable agreement in the atmospheric variance between the RLID and the DLH for the lower two TO legs, but the uppermost leg has large differences in both variance and skewness between the DLH and RLID observations.
While the agreement between the variance and skewness statistics from the RLID and DLH on 31 May and the lower two flight legs on 15 June were reasonable (Figs. 4 and 5), the differences between the RLID and the DLH for the uppermost flight leg at 1314 m AGL on 15 June was initially difficult to interpret. On this day, the King Air was flying directly above the TO, and the HSRL was providing profiles of aerosol backscatter, extinction, and depolarization from the King Air’s altitude (approximately 9 km) to the surface. Using a Haar wavelet approach adapted from the one described by Brooks (2003), the top of the mixed layer was identified from gradients in the aerosol concentration using the HSRL data. These observations showed that the depth of the mixed layer changed with distance away from the SGP site, with the mixed layer becoming progressively deeper to the northeast of the site (Fig. 6). However, the HSRL-observed ground altitude over this 30-km flight leg was relatively constant at 330 m ± 20 m MSL; therefore, the change in the depth of the mixed layer along this flight path is presumably due to local differences in the surface heat fluxes. The TO was flying a constant altitude leg, and thus during this uppermost leg it spent part of the flight above the mixed layer (brown), in the interfacial layer between the mixed layer and free troposphere (red), and in the mixed layer (green). Thus, using the entire flight leg to estimate the atmospheric mean, variance, and skewness (i.e., the blue symbols at 1314 m in Fig. 5) results in large sampling error, because the flight cannot be prescribed to being in a single height within the convective mixed layer.
Thus, we computed the mean, variance, and skewness from subsets of this uppermost TO leg, with the subsets chosen based on the HSRL observations showing when the TO was above, at, and below the top of the convective mixed layer (brown, red, and green points in Fig. 6, respectively). The power density spectra for these three sublegs are indicated in Fig. 3b with the same colors, and they demonstrate that even though the flight paths were shorter that the DLH data still resolved the inertial subrange. Using the TO height normalized by the HSRL-observed mixed layer height and then scaled to the RLID boundary layer height, these mean, variance, and skewness values derived from the shorter TO flight subsets were overplotted on the mean, variance, and skewness panels of Fig. 5 as a green cross, red triangle, and brown diamond, respectively (again, the colors correspond to the subsets of data in Fig. 6). Note in Fig. 6 that the TO sampled a very significant updraft between 4.5 and 6.0 km away from the SGP. This updraft, which had very moist and cool air, was excluded from the analysis of the 0–9-km subset of this flight leg, as it was deemed that this singular event was not representative of the water vapor environment above the mixed layer. However, this may be debatable, as there is a single deep penetrating plume seen in the RLID time–height cross-section image at 2005 UTC that reaches near 1600 m—well above the top of the mixed layer—and the power spectrum that corresponds to the flight leg above the mixed layer (brown spectrum at 1314 m AGL) shows the presence of a − power-law relationship along some portions of its frequency range. The DLH variance and skewness derived from the partial legs agree very well with the RLID observations, especially for the 10–17-km (red) and 19–29-km (green) subsections; there is poorer agreement for the 0–9-km (brown) subsection. However, because of the shorter flight lengths, the sampling uncertainties in the variance and skewness values derived from the DLH are larger than the values for the lower two flight legs. Nonetheless, the level of agreement in the water vapor variance and skewness measures between the remote sensing and the in situ methods is remarkable.
This comparison between aircraft and lidar data also demonstrates the advantage of deriving turbulence profiles using ground-based lidar systems. The lidar is capable of measuring turbulence at different heights simultaneously, thereby reducing the difficulties in the interpretation of the results due to nonstationarity or horizontal variability of the mixed layer. Furthermore, the structure of turbulence profiles in the interfacial layer between the mixed layer and free troposphere can be measured with higher vertical resolution using lidar systems. In this work, we found significantly different maximum values and widths of the peaks of the RLID variance profiles. These variance profiles contain important information about the entrainment processes, as indicated in Sorbjan (2005) and Wulfmeyer et al. (2010). For example, the variance peak in the interfacial layer depends on both the magnitude of the moisture gradient and the Brunt–Väisälä frequency. Further analysis is beyond the scope of this paper, as it requires more synergetic information, such as temperature and wind profiles, and will be the subject of a future work. However, studying the interfacial layer with aircraft in situ data is difficult due to the uncertainty in knowing whether the aircraft is indeed within this layer (e.g., Fig. 6). Thus, improvement in the PBL schemes requires that we develop better understanding of the slopes of turbulent profiles in the interfacial layer, which suggests that long-term lidar measurements of turbulence are necessary.
Turbulence is a process that is parameterized in most numerical models of the atmosphere, and measurements of turbulence in the atmosphere, especially above the surface and in the interfacial layer where few observations exist, are critical so that these parameterizations can be evaluated and improved. The RLID at the SGP site is a valuable tool for this effort because it has sampled an extensive range of atmospheric conditions since it was upgraded in 2004.
Wulfmeyer et al. (2010) demonstrated that the upgraded SGP RLID has the sensitivity to provide measurements of water vapor mixing ratio variance and skewness in daytime convective mixed layers. We have used aircraft observations during the RACORO field experiment to evaluate the accuracy of these turbulence profiles. Two cases from RACORO satisfied the conditions that proved necessary for the analysis.
The total variance in the water vapor mixing ratio signal observed by the RLID is much larger than the atmospheric water vapor mixing ratio variance due to random instrument noise in the RLID observations. The L00 method was used to estimate the contribution of the instrument noise and to derive variance and skewness profiles with the instrument noise removed. The atmospheric variance in the mixed layer spanned a range of values from near 0 to approximately 4 (g kg−1)2, and the skewness ranged from values near −3 to as large at 3. The atmospheric variance and skewness profiles derived from the RLID agreed well with the DLH observations from the TO, and they demonstrate that the L00 method does a good job accounting for the instrumental error when deriving these higher-order statistics.
However, this analysis also demonstrated that there can be significant sampling differences between the lidar and aircraft, and that these sampling differences could point to misleading results. The addition of the King Air and the HSRL above the TO, which provided the spatial context of the TO observations relative to the top of the mixed layer for the 15 June case, was a great benefit to this analysis. The HSRL observations showed that the mixed layer deepened toward the northeast away from the SGP site and, consequently, that the TO flight path, which started above the mixed layer at the SGP site, crossed into the mixed layer as it flew its level leg away from the site. The HSRL data were used to subdivide the DLH observations into above, at, and below the mixed layer top for this leg, and the variance and skewness of these subsections agreed very well with the corresponding RLID measurements.
This analysis provides confidence in the RLID-derived variance and skewness profiles, and that further analysis of the longer RLID dataset will be meaningful. Our study demonstrates that ground-based lidar profiling provides better resolution and interpretation of turbulent profiles in the interfacial layer, which is of particular importance for process studies and model evaluation. However, future intercomparisons of turbulent statistics between RLID and airborne in situ instruments would benefit greatly by having a much larger number of cases than the two mixed layer cases presented here, so that a statistically significant intercomparison can be performed. Nonetheless, this study provides a nice starting point for the analysis of the multiyear RLID dataset that is currently in process, which will provide a statistical description of the turbulence profiles in the convective mixed layer.
NOAA’s National Severe Storms Laboratory and the Department of Energy (DOE) Atmospheric System Research (ASR) program supported this work. We thank the Raman lidar mentor team of Chris Martin, John Goldsmith, and Rob Newsom for their efforts in maintaining the Raman lidar. We would also like to thank the entire RACORO team: Andy Vogelmann for his leadership before, during, and after the experiment; the RACORO scientific steering committee; Haf Jonsson for the analysis and processing of the Twin Otter flight data; Glen Diskin for the DLH processing; and the AAF for its coordination of the RACORO flight activities. The data used in this paper were collected as part of ARM, and are available via its online data archive (http://www.archive.arm.gov). HSRL operations were supported by the NASA Science Mission Directorate, the ASR program (Interagency Agreement DE-AI02-05ER63985), the DOE Office of Science, Office of Biological and Environmental Research (OBER), and the NASA CALIPSO project. The authors thank the NASA Langley King Air B-200 flight crew for its outstanding work supporting these flights and measurements. Finally, we thank Mike Coniglio, Andy Vogelmann, Glenn Diskin, and Haf Jonsson for providing comments on an earlier draft of this manuscript, and especially the two anonymous reviewers for their excellent input, which improved this manuscript.