1. Introduction
Extensive marine stratocumulus (Sc) clouds over the southeastern Pacific Ocean play a critical role in the dynamics of the ocean–atmosphere system as well as the global atmospheric circulation in the eastern Pacific (Klein and Hartmann 1993). The tops of the Sc are coincident with the top of the marine boundary layer (MBL). Both the height zi of the inversion atop the MBL and the thickness of the Sc vary in space and time; these variations affect vertical mixing between the ocean and the atmosphere as well as radiative processes within the atmosphere. These attributes are poorly measured by satellites. It is possible that cloud depths could be calculated by using wind-profiler reflectivities to determine zi and ceilometers to measure cloud-base heights. Initial research along those lines (Piña 2010; Lujan 2011) has incidentally revealed deep, long-lasting voids in profiler observations of the Sc-topped MBL, which we explore here.
2. Basic profiler observations
Our data were collected during east Pacific cruises conducted as part of the Pan American Climate Study (PACS). Wind-profiling radars, ceilometers, and radiosondes were among the instruments on the research vessel (R/V) Ronald H. Brown during several boreal autumn deployments. Data from two cruises are used here: autumn 2000 (17 October–12 November) and autumn 2004 (29 October–27 November). The ship tracks and amount of average daytime Sc coverage are shown in Fig. 1.
Track of the R/V Ronald H. Brown during the autumn 2000 and 2004 PACS cruises. Blue shading indicates the average daytime stratocumulus amount, as retrieved from the International Satellite Cloud Climatology Project (ISCCP) D2 dataset (Rossow and Schiffer 1999), during (a) October 2000, (b) November 2000, and (c) November 2004.
Citation: Journal of Applied Meteorology and Climatology 53, 7; 10.1175/JAMC-D-12-0308.1
Wind profilers are dwelling (not scanning) radars and measure signal-to-noise ratio (SNR), radial velocity, and spectral width. A 915-MHz profiling radar receives returns from refractive index fluctuations with a scale size of 16.5 cm, one-half of the transmitted wavelength (i.e., from Bragg scattering), and from Rayleigh scattering by falling hydrometeors. The index of refraction is a nonlinear function of pressure, temperature, and moisture (Gage and Balsley 1978); fluctuations on this scale are created by turbulence. The 915-MHz profiler deployed during these cruises was a five-beam, electronically stabilized, phased-array system (Law et al. 2002); the same radar was present in both cruises. Data used here come from the vertical beam, which operated in two modes primarily differentiated by their height coverage. The “low mode,” with gates spaced 60 m apart, collected data from relatively low altitudes but with higher resolution. The “high mode” had 105-m gate spacing and so provided less resolution but was pulse coded so as to have increased sensitivity and therefore the ability to collect data higher in the atmosphere. In autumn 2000, the dwell duration was about 30 s and the spacing between vertical dwells in the same mode was about 5.3 min. In autumn 2004, the dwell duration was about 40 s for the low mode and 30 s for the high mode and the spacing between vertical dwells of the same mode was about 6 min.
Figure 2 illustrates the effects of our quality control on one day’s low-mode data from each cruise; SNR was converted to relative reflectivity before plotting. The original dataset contains some SNRs and spectral widths that are unrealistically large, and many observations have very low SNRs and large-magnitude velocities (Figs. 2a,b). Three criteria were used to further refine the data. First, whenever SNRs were above 80 dB all variables were excluded. Second, if spectral width was larger than 3 m s−1 then all variables were excluded.1 The effect of this partial thresholding is shown in Figs. 2c and 2d. Also, a minimum threshold of detectability (Riddle et al. 2012) was used to exclude nonatmospheric data with very low SNRs, leaving mostly atmospheric signal.2 Although the Riddle threshold is a good way to remove a great many nonatmospheric echoes fairly quickly, researchers doing detailed quality control on a dataset occasionally find that a slightly higher or lower value makes sense for their situation. Examination of scatterplots of SNR versus vertical velocity and before/after plots showed that, for the autumn 2000 data, subtracting 1.5 dB from this profiler’s Riddle threshold, SNRmin = −14.55 dB, resulted in a beneficial trade-off of many more “good” data points and a few more “bad” data points (Piña 2010). No adjustment was deemed necessary for the autumn 2004 data (Lujan 2011). Therefore, when SNR was less than SNRmin (autumn 2004) or SNRmin − 1.5 dB (autumn 2000) all three variables were excluded. The final “thresholded” data are shown in Figs. 2e and 2f.
Vertical-beam low-mode 915-MHz profiler data from (left) 31 Oct 2000 and (right) 3 Nov 2004: reflectivity, vertical velocity, and spectral width as functions of time and height, together with ship position. Profiler data are plotted only to 2 km to enhance readability. Shown are (a),(b) original processed data; (c),(d) “partially thresholded” data, confined to instances in which spectral width < 3 m s−1 and SNR < 80 dB; and (e),(f) fully “thresholded” data, to which the Riddle threshold was also applied.
Citation: Journal of Applied Meteorology and Climatology 53, 7; 10.1175/JAMC-D-12-0308.1
The data in Fig. 2 are similar to those collected on several days when the ship was not in the ITCZ region. Obvious features are a thin layer of enhanced reflectivity between 1000 and 2000 m, occasional drizzle or rain (e.g., 1100–1200 UTC 3 November 2004), and a layer with small-amplitude vertical motion extending upward from the lowest gates to an undulating height below the enhanced-reflectivity layer. Comparable conditions are observed from 30 October through 3 November 2000 and from 1500 UTC 31 October through 0600 UTC 4 November 2004. (On many other days outside the ITCZ, the noted features were less simple or clear-cut; e.g., multiple layers were present.) For much of our analysis, we concentrate on the two days shown in Fig. 2, but in section 4 we employ data from the longer periods.
Comparison with ceilometer and radiosonde data indicates that the enhanced-reflectivity layer is within the relative humidity gradient atop the boundary layer (Lujan 2011; Hartten et al. 2012). Above that layer, there are few atmospheric returns. Of particular note is the lack of returns within the middle and upper MBL, which also occurs in the high-mode data but to a much lesser extent. What is the absence of detectable atmospheric signal telling us about this MBL?
3. Additional profiler-based measurements
To explore what the frequent lack of atmospheric returns in the upper portion of these Sc-topped MBLs means, we examine the structure-function parameter of the index of refraction 
a. Calibrating the profiler
An Optical Scientific, Inc., model ORG-815 optical rain gauge (see online at http://opticalscientific.com/pdf/brochures/ORG/ORG815DS130405.pdf) was deployed on each cruise; data were postprocessed into 10-min rain rates. These can be used to calibrate the profiler, although ship-based measurements of rain are difficult (Yuter and Parker 2001) and there are temporal, spatial, and sampling-volume size issues associated with using ground-based instruments and vertically pointed radars (Tokay et al. 2009). We have adapted the disdrometer-based technique of Gage et al. (2000, 2002) to the ORG-815 data, using total rain accumulation over several hours to average out some of the temporal and spatial variations. We initially chose one day from each cruise with a clear, long-lived rain episode and good profiler data. As our work progressed, we lost confidence in the ORG-815 data from the autumn 2000 cruise and therefore only used autumn 2004 data. Our calibration constants can be used for both cruises, however; profiling radars are such stable devices that the same calibration factor can be used for a long time (Gage et al. 2000, 2002) and the radar operational modes from both cruises are very similar.
On 14 November 2004 (0000–1000 UTC) the gauge accumulated 12.818 mm, mostly from 0500 to 0900 UTC. We classified this rain as stratiform on the basis of the relative reflectivities and velocities (Fig. 3a) measured by the radar during this period3 (Williams et al. 1995). We used the Marshall–Palmer relationship Z = 200R1.6 mm6 m−3 (Marshall et al. 1955) to convert reflectivity Z to rain rate R. This is the stratiform Z–R relationship from the National Weather Service’s Quantitative Precipitation Estimation system (Zhang et al. 2011); most other stratiform Z–R relationships are a variation of it, and it therefore seems to be a reasonable choice for a basic calibration. We did the calibration separately for each profiler mode, only using range gates with linear power response and uncontaminated by sea clutter. The radar reflectivities contributed to the rain accumulation only when our postprocessing software identified rainfall [cf. the cluster analysis of Williams et al. (2000)], and we assumed that the rain was constant over the time between records. We are not concerned about loss to evaporation because, once fall times were accounted for, there was very good agreement between the profiler and ORG-815 time series.
(a) The thresholded but uncalibrated low-mode reflectivity, vertical motion, and spectral width, together with ship location, on 14 Nov 2004. (b) The accumulated rain measured by the ORG-815 on 14 Nov 2004 (black line), together with the accumulated rain measured by the profiler gates that were used to obtain the calibration factor for the radar (gray lines). For the low mode, these gates were centered at 270, 330, 390, and 450 m; for the high mode, they were centered at 623 and 728 m. The gray bar shows how the accumulated profiler rain after the 10-h calibration period would change if the calibration factor were increased or decreased by 1.5 dB.
Citation: Journal of Applied Meteorology and Climatology 53, 7; 10.1175/JAMC-D-12-0308.1
We determined the radar calibration constants using an iterative process, matching the accumulated rain observed by the radar to the accumulated gauge rainfall (P. E. Johnston et al. 2014, unpublished manuscript). The calibration constant for the low (high) mode is the value for which the average of four (two) consecutive range gates is within 0.001 mm of the gauge accumulation. The accumulation from each gate closely matches the ORG-815 data, both during and after the calibration period (Fig. 3b). The high mode is more sensitive than the low mode because of its longer pulse length and use of pulse coding. Changing the radar constant by ±1.5 dB would change the accumulation by amounts from +3.11 to −2.49 mm. We believe the calibration to be within ±1.5 dB, although this belief relies on our assumption that we have a good precipitation dataset.
b. Finding the structure-function parameter of the index of refraction
By using Eqs. (2)–(5), the SNR thresholds applied in section 2 can be converted to Ze and 
(a) Minimum detectable reflectivity factor Ze and (b) minimum detectable refractive index structure-function parameter 
Citation: Journal of Applied Meteorology and Climatology 53, 7; 10.1175/JAMC-D-12-0308.1
4. Understanding “missing” profiler reflectivities
Our final thresholding step, application of a minimum SNR threshold, is not universal practice in the profiling community. Therefore we start our last analysis with a less-refined dataset to highlight the impact of the threshold and differences between the profiler modes. We focus on 
a. Statistical view of 
Profiles of the minimum, median, and maximum 
Profiles of minimum, median, and maximum 
Citation: Journal of Applied Meteorology and Climatology 53, 7; 10.1175/JAMC-D-12-0308.1
b. Relating 
Parameter 
Either view of 
c. Other evidence of MBL decoupling
Section 4b was theoretical and somewhat hypothetical. It would be pleasing if we were able to link other observational indications of decoupling with the gaps in the profiler data. There were a limited number of balloon soundings during these two multiday cruise segments, but launch times were determined by clock rather than by conditions, and therefore sampling with respect to profiler gaps is not robust. We therefore consider other BL metrics with higher time resolution.
Decoupling within Sc-topped MBLs is identified in various ways throughout the literature. One commonly noted feature of decoupled MBLs is a great discrepancy between the cloud-base height zb and the lifting condensation level (LCL) height zLCL computed from lower BL conditions. Jones et al. (2011, hereinafter JBL2011) obtained zb and zLCL from data collected during 88 subcloud flight legs (~150 m MSL) over the subtropical eastern Pacific during the Variability of American Monsoon Systems (VAMOS) Ocean–Cloud–Atmosphere–Land Study Regional Experiment (VOCALS-REx; October–November 2008). They computed the difference between high-resolution (1 Hz) values and then computed the leg-average5 difference Δzb, which they called a subcloud decoupling index. Their Δzb values fell within the range 0–1100 m. After comparing Δzb with adjacent aircraft soundings that they had already identified as well mixed or decoupled, they set Δzb ≤ 150 m as the criterion for well-mixed Sc-topped MBLs in their study region (70°–85°W, 17°–30°S). According to this criterion, about 45% of the subcloud legs were in well-mixed conditions; for comparison, 28% of the aircraft profiles collected were identified as well mixed. All of the legs with heavy drizzle and 44% of the legs with light drizzle were decoupled.
We have used ship-based observations to compute a similar measure of decoupling. The R/V Ronald H. Brown instrumentation included a ceilometer and near-surface meteorological instruments; from these we have obtained mean cloud-base and LCL heights at 10-min resolution during the multiday periods identified in section 2. Details of the datasets and computations are given in the appendix. We calculated the height difference between contemporaneous cloud bases and LCLs (see Figs. A1a and A1b) and then averaged the differences into hourly values Δz = 
The distributions of Δz are shown in Fig. 6. The 2000 values are clearly bimodal in distribution; the 2004 values are less clearly so and are perhaps even trimodal. The maximum values are considerably smaller than those of JBL2011. Two of the hourly 2004 values (and 27 of the 418 10-min values) are negative; this fact might be due to our use of surface values instead of 150-m observations, to our location 5°–8° from the equator, or to different synoptic conditions. What constitute the criteria for “well mixed” is open for debate and may even vary from year to year. If we assumed that 28% of the observed MBLs were well mixed, corresponding to the JBL2011 aircraft profiles, the cutoff would be ~300 m in 2000 and ~250 m in 2004; if we assumed a value of 45%, corresponding to the JBL2011 Δzb, the cutoff would be ~300 m. Something in the range from 150 (as per JBL2011) to 400 m (the break point in the autumn 2000 distribution) seems a reasonable estimate. In any event, MBLs that are not well mixed were clearly common and fall into a continuum of decoupled states.
Distributions of hourly averaged decoupling index Δz = 
Citation: Journal of Applied Meteorology and Climatology 53, 7; 10.1175/JAMC-D-12-0308.1
A quick visual comparison between time series of Δz (not shown) and plots such as Figs. 2e and 2f indicated some correspondence between large Δz and deep gaps and between small Δz and minimal gaps. The visual results were equivocal enough that we wanted a more objective and methodical comparison between the decoupling index Δz and the MBL gaps, but quantifying the gaps proved to be difficult. We decided to use very small 
Each high-mode profile’s 
For each hour, we counted the number of profiles in which the high-mode 
Distributions of the percentage of high-mode 
Citation: Journal of Applied Meteorology and Climatology 53, 7; 10.1175/JAMC-D-12-0308.1
To address this question, we compared these hourly percent-below values with the hourly Δz (Fig. 8). The correlation for all paired points in 2000 (Fig. 8a) is 0.44, indicating that hours with a larger percentage of very small atmospheric 
The hourly decoupling index Δz = 
Citation: Journal of Applied Meteorology and Climatology 53, 7; 10.1175/JAMC-D-12-0308.1
Hours with no more than 40% of 
5. Final thoughts
Because wind profilers observe returns from several different types of phenomena [clear air (
Acknowledgments
Thanks are given to Laura Bianco for MATLAB code; to Aaron Piña and Javier Lujan for sharing their enthusiasm and creativity; to Wayne Angevine for thought-provoking conversations; to Holger Voemel for providing guidance on water vapor pressure formulations (available at http://cires.colorado.edu/~voemel/vp.html); and to Ludovic Bariteau, Chris Fairall, Sergio Pezoa, Dave Welsh, and Dan Wolfe for helpful discussions about cruise instrumentation and data. We appreciate the questions and comments from Peggy LeMone and two anonymous reviewers, which led us to improve our analysis, thoughts, and presentation. The ISCCP D2 data were obtained online in June 2011 from the International Satellite Cloud Climatology Project (http://isccp.giss.nasa.gov, maintained by the ISCCP research group at the NASA Goddard Institute for Space Studies). Colors in figures are based on values from ColorBrewer.org. This work was supported by grants from NOAA’s Climate Program Office to the NOAA/ESRL/Physical Sciences Division.
APPENDIX
Cloud-Base Measurements, Surface Meteorological Conditions, and Calculation of Lifting Condensation Level
Our time periods of interest for this portion of the study are from 30 October through 3 November 2000 (5.0 days) and from 1500 UTC 31 October through 0600 UTC 4 November 2004 (3.625 days). During these times, the ships were located outside the ITCZ region and within the approximate bounds 4°–8°S, 92°–110°W, and profiler reflectivities showed the same features seen in Figs. 2e and 2f and discussed in section 2.
a. Cloud-base heights
Cloud-base measurements were made during both cruises with a Vaisala, Inc., CT25K. During the autumn 2000 cruise, there were no ceilometer data available from 1850 UTC 29 October until 1750 UTC 1 November. The original 15-s data were processed into 10-min values of 15th-, 50th-, and 85th-percentile heights. We used the median cloud bases, discarding all values above 2000 m because our interests were confined to levels near or below the thin layer of reflectivity seen between 1000 and 2000 m. The 10-min values are variable (Figs. A1a,b), but exhibit more short-term variability (scatter) in 2004 than in 2000.
Ten-minute time series of various relevant meteorological parameters during portions of the (left) autumn 2000 and (right) autumn 2004 cruises. Yellow bars along the top axes indicate the average daily duration of insolation. (a),(b) Median cloud-base heights (orange dots), LCL heights (blue line), and their difference (black dots). A solid horizontal line across the lower right portion of the plots indicates zb − zLCL = 0. (c),(d) Sea surface temperature (blue line), air temperature (brown line), and specific humidity (black line).
Citation: Journal of Applied Meteorology and Climatology 53, 7; 10.1175/JAMC-D-12-0308.1
b. Surface meteorological conditions
During both cruises, sea surface temperature Ts was measured at a nominal depth of 0.05 m with a thermistorA1 mounted inside a Brookhaven National Laboratory “sea snake” in a fashion similar to that originally described by Fairall et al. (1997). Air temperature Ta and specific humidity q were measured with an aspirated Vaisala HMP-235 mounted 15.5 m above the ship's local sea level. Humidities were increased by 3% after intercomparison with psychrometer values. The 10-s samples were averaged into 1-min values; these data were postprocessed into 10-min values, which are shown in Figs. A1c and A1d. Temperatures Ts and Ta showed greater long-term variability and q showed a larger range in 2000 than in 2004; Ts ranged from 21.6° to 24.3°C in 2000 and from 21.9° to 22.7°C in 2004, and Ta ranged from 20.5° to 24.9°C in 2000 and from 19.7° to 23.4°C in 2004. Specific humidity ranged from 15.7 to 18.6 g kg−1 in 2000 and from 16.1 to 16.9 g kg−1 in 2004.
Surface pressure Psfc and sea level pressure (SLP) were not recorded during the cruises. During the times of interest, the ship was generally between the 5° and 8°S Tropical Atmosphere-Ocean array (TAO) buoys at 95° and 110°W (McPhaden 1995); the only pressure data available are from the 95°W buoys in 2000, however (Cronin et al. 2002). Analysis showed that the 8°S surface pressures were about 0.7 hPa higher than the 5°S values from 29 October to 4 November and the mean daily cycle (from 29 October through 1 November) at 8°S had a range of almost 4 hPa about a mean value of 1015.0 hPa. Composite mean maps of SLP from the Twentieth Century Reanalysis project (Compo et al. 2011), averaged over those same four days, were about 0.5 hPa less than the TAO mean at 95°W, 8°S. A 6-day mean (from 29 October through 3 November 2000) was within 1.0 hPa of the 4-day TAO mean and showed a gradient at 8°S of 0.5 hPa between 95° and 115°W. A 5-day mean from 2004 (from 31 October through 5 November) showed that gradient to be 0.2 hPa across a field of pressures that were approximately 2.0 hPa less than in the 2000 composite.
Confident that pressure gradients were low across the ship’s relevant cruise tracks, we tested the effect of using Psfc = 1010 hPa versus Psfc = 1015 hPa (the high pressure dropped the height of the LCL by about 10 m) and the effect of incorporating a 4-hPa daily cycle (this increased the standard deviation of LCL heights from ~0.1 m to a value of ~2 m). We ultimately decided to use a constant Psfc = 1010 hPa in our LCL calculations.
c. LCL computations
Computing LCL from Ta, q, and Psfc required several steps, which we briefly outline for completeness. Specific humidity was converted to mixing ratio and then to vapor pressure; saturation vapor pressure was computed from Ta using the formula of Hyland and Wexler (1983). Dewpoint temperature was computed using the formula of Bolton (1980), and the temperature of the LCL TLCL was computed from the formula of Barnes (1968). This was converted to the pressure PLCL using Poisson’s equation. Next, we followed the methods of Wilde et al. (1985). Virtual temperature Tυ was computed as per Wallace and Hobbs [1977, their Eqs. (2.17) and (2.14)]. By assuming that the mixing ratio was constant between the surface and the LCL, we were able to compute the vapor pressure at the LCL eLCL; we used this, together with PLCL and TLCL, to compute the virtual temperature at the LCL TυLCL. The height of the LCL ZLCL was computed from the hypsometric equation with Rd/g0 = 29.3 [Wallace and Hobbs 1977, their Eq. (2.30)] and z0 = 3 m, the height of the pressure measurements on the Autonomous Temperature Line Acquisition System (ATLAS) and TAO moorings. The resulting ZLCL for both cruise segments are shown in Figs. A1a and A1b; they are highly variable on subhourly and subdaily scales, ranging from ~300 to ~1100 m, although the character of that variability is somewhat different in each cruise.
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These empirical values can be justified on physical grounds. An 80-dB SNR at about 1000 m yields a relative reflectivity of about 85 dBZ, larger than that usually associated with hail, and a 3 m s−1 spectral width corresponds to a 2.25 m2 s−2 vertical velocity variance.
We are confident that insects are not an issue in this marine environment.
The high-mode profiler reflectivity shows a bright band at about 4.5 km during the 0500–1000 UTC rain, which rules out warm-rain processes during that time. Reflectivities above the bright band were too weak for convective precipitation: hence, the choice of the stratiform algorithm. The short-lived rain events between 0000 and 0230 UTC were shallow (below 4.4 km) and produced no bright band, and therefore they might have been warm rain. They made only a small contribution to the accumulated rain during the calibrating period, however.
Although it can be possible to extract information on turbulent intensity from radar observations of spectral width, this particular profiler was unfortunately configured in a way that renders its data unsuitable for such work.
Legs were approximately 12 min (70 km) long.
This exclusion was accomplished through a combination of our postprocessing algorithm and hand analysis and removed 16 of 1318 profiles in 2000 and 68 of 871 profiles in 2004.
Measurement Specialties, Inc., model 46040 superstable thermistor (resistance 3000 Ω at 25°C).
