Subcloud and Cloud-Base Latent Heat Fluxes during Shallow Cumulus Convection

a. Location and day selection

Latent heat fluxes are examined on days with shallow cumulus (ShCu) convection at the Atmospheric Radiation Measurement Southern Great Plains (ARM SGP) site in Oklahoma (Fig. 1). A total of 46 ShCu days from warm seasons (May–September) 2016–18 are used. A list of these days and their boundary layer properties is provided in Table 1. Days are selected by first inspecting MODIS visible satellite data for periods with ShCu in the absence of extensive high clouds and synoptic disturbances. Next Doppler lidar vertical velocity and cloud-base height data are inspected for a set of five Doppler lidars (E32, E37, E39, E41, C1; locations in Fig. 1) distributed within a 50-km radius of the Central Facility at ARM SGP (C1). Only days that have a typical diurnal cycle of CBL and cloud development at all five sites are included to favor spatially homogeneous conditions. While Doppler lidar data from the boundary sites (E32–41) are used in day selection, only data from the Central Facility (C1) are used in the following analysis. Raman lidar data are also manually inspected to ensure data quality, with some days eliminated due to poor signal. We note that 1 day with late afternoon thunderstorms is included, but only hours prior to the arrival of a gust front are used.

MODIS Aqua visible satellite image on a day (17 Jul 2017) with widespread shallow cumulus at ARM SGP. Also shown are location of four boundary site Doppler lidars (E32, E37, E39, E41), the Central Facility Doppler and Raman lidars (C1), and the surface flux station (E14).

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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MODIS Aqua visible satellite image on a day (17 Jul 2017) with widespread shallow cumulus at ARM SGP. Also shown are location of four boundary site Doppler lidars (E32, E37, E39, E41), the Central Facility Doppler and Raman lidars (C1), and the surface flux station (E14).

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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MODIS Aqua visible satellite image on a day (17 Jul 2017) with widespread shallow cumulus at ARM SGP. Also shown are location of four boundary site Doppler lidars (E32, E37, E39, E41), the Central Facility Doppler and Raman lidars (C1), and the surface flux station (E14).

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Table 1.

Summary of the convective boundary layer characteristics on the days used in this study. Values indicate either the mean or maximum over the 1700–2300 UTC period. The single asterisk (*) indicates days excluded from the budget analysis due to missing surface flux data. The double asterisk (**) indicates a day with precipitation late in the afternoon and for which fluxes are only computed for the ShCu portion of the day. The letter M indicates missing data.

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b. Instruments and their application

1. Boundary layer and cloud-base vertical velocity w are observed with a Doppler lidar (DL) located at the ARM SGP Central Facility (C1; Newsom 2010). The DL is an active ground-based infrared (1.5 μm) laser remote sensor that provides range- and time-resolved profiles of radial velocity (i.e., the vertical velocity when pointed vertically) and attenuated backscatter over the lower troposphere. The lidar data are processed at 30-m range-gate resolution and 1.3-s temporal resolution. The DL is sensitive to micron-scale aerosol, which provide a tracer for boundary layer flows. The lidar beam rapidly attenuates in liquid water, which is useful in identifying cloud bases. The DL is also used to identify the time varying CBL height Z_i, based on a threshold of the vertical velocity variance computed for 15-min intervals (Tucker et al. 2009). Here we use a variance threshold of 0.08 m² s⁻², which was found in LZK18 to produce a good representation of CBL heights during ShCu conditions.

2. Boundary layer water vapor mixing ratio q is determined using Raman lidar (RL), which is located adjacent to the DL at C1, and thus provides approximately collocated measurements. The RL employs an ultraviolet (UV) laser that is sensitive to both molecular and aerosol backscatter. The anelastic molecular backscatter is used to retrieve the water vapor mixing ratio in a sample volume (Wulfmeyer et al. 2010). The retrieved water vapor profiles are available at 10-s temporal and 50-m spatial resolution (Raman lidar vertical profiles 10SRLPROFMR1TURN). The RL has high and low field-of-view settings, which produces an overlap in the lower boundary layer (at ~550 m AGL). To avoid issues with the overlap correction in this region we use only data from the “high” field of view for all variance and flux computations. The ability of RL to measure the first through third moments of the boundary layer water vapor mixing ratio is well established (Wulfmeyer et al. 2010; Turner et al. 2014b) and the RL at ARM SGP has been validated against aircraft data (Turner et al. 2014a). The RL backscatter due to clouds also provides a measure of cloud-base height based on a wavelet analysis of the backscatter profile (R. Newsom 2018, personal communication). These cloud-base detections are used in our cloud identification.

3. Surface latent heat fluxes and forcing variables are determined from the observed eddy correlation (ECOR) between vertical velocity and water vapor mixing ratio at site E14, which is very close to the lidar sites at C1 (Fig. 1). We use a quality-controlled version of the surface fluxes (McCoy et al. 2003). The fluxes are computed for 30-min periods. We also use these data, in conjunction with the CBL height, to compute the convective velocity scale $w_{*}={\left[\left(g/\theta \right){\overline{\left(w^{\prime }{\theta }^{\prime }\right)}}_{\mathrm{sfc}}{Z}_i\right]}^{1/3}$ (Stull 1988).

4. The advective tendency for the boundary layer–averaged mixing ratio is estimated from a variational analysis dataset (60VARANARAP). The boundary layer average advection is determined by finding the pressure level of the physical CBL top Z_i, then averaging from the surface to that pressure level in the model output. Data are hourly and later used in hourly CBL budget analyses.

c. Data filtering

2) Noise removal and variance estimates

Both the RL and DL are subject to noise due to daytime random photon detections, low signal-to-noise ratios, and other internal sources. We apply multistep filtering to remove spurious data from both data streams. First, we use physical range checks to flag and remove outliers. For the mixing ratio data, we remove unphysical values (q < 0 g kg⁻¹, q > 24 g kg⁻¹). For the DL we remove all data with absolute value of w > 10 m s⁻¹, which is outside the expected range of boundary layer updrafts and downdrafts. In both instances, the removed data are replaced with the 60-min-mean values at that height.

Next, we eliminate the uncorrelated noise from both the DL and RL data using an adaptive image filter informed by autocovariance function (ACF) filtering. ACF filtering eliminates the noise variance by assuming instrument noise is random and uncorrelated in time, therefore contributing to an unphysical spike in the lag-0 autocovariance (i.e., the variance itself; Frehlich 2001; Tucker et al. 2009; Turner et al. 2014a,b). To remove this noise, the lag-0 covariance can be estimated by linear interpolation (or other method, e.g., structure function) from subsequent temporal lags (e.g., 1–5). This approach is useful for statistical analysis of variance profiles but discards information in coherent structures, including information about individual updraft properties.

To preserve the information about coherent structures, we apply an adaptive variance-based filtering motivated by image processing techniques (Lee 1980) that is informed by the ACF filtering. Specifically, we first compute the profiles of ACF-filtered variance ${\sigma }_{\text{ACF}}^2$in 60-min time blocks. Next, we estimate the noise variance profiles ${\sigma }_{\text{noise}}^2$ using

$\begin{array}{c}{\sigma }_{\text{noise}}^2={\sigma }_{\text{total}}^2-{\sigma }_{\text{ACF}}^2\end{array},$(2)

where ${\sigma }_{\text{total}}^2$ is the unfiltered variance (i.e., the raw lag-0 autocovariance).

From there, following Lee (1980), we compute the unfiltered local mean and variance using a (2n + 1) × (2m + 1) neighborhood applied to the raw data matrix. That is, for each time (i) and height (j) data point x_i,j the local mean and variance are computed as

${\overline{x}}_{i,j}={\displaystyle \frac{1}{\left(2n+1\right)\left(2m+1\right)}}{\displaystyle \sum _{\hspace{0.17em}k=\left(i-n\right)}^{i+n}}{\displaystyle \sum _{\hspace{0.17em}l=\left(j-m\right)}^{j+m}}{x}_{k,l}$(3)

and

${\sigma }_{i,j}^2={\displaystyle \frac{1}{\left(2n+1\right)\left(2m+1\right)}}{\displaystyle \sum _{k=\left(i-n\right)}^{i+n}}{\displaystyle \sum _{l=\left(j-m\right)}^{j+m}}{\left(x_{k,l}-{\overline{x}}_{i,j}\right)}^2,$(4)

respectively. Next, we produce a filtered data matrix $\widehat{\mathsf{x}}$ using

${\widehat{\mathsf{x}}}_{i,j}={\overline{x}}_{i,j}+k_{i,j}\left(x_{i,j}-{\overline{x}}_{i,j}\right),$(5)

where the factor

$k_{i,j}={\displaystyle \frac{\max \left(0,{\sigma }_{i,j}^2-{\sigma }_{{\text{noise}}_{\mathit{j}}}^2\right)}{\max \left({\sigma }_{i,j}^2,{\sigma }_{{\text{noise}}_j}^2\right)}}$(6)

is used to adaptively filter the point-by-point perturbations from the local mean and is informed by the ${\sigma }_{{\text{noise}}_j}^2$ profile, which is based on the ACF filtering. Versions of this filtering are available in a number of coding languages (e.g., “Wiener Filters” in MATLAB and Python), but do not use the ACF informed noise estimate in the k_i,j coefficient. The use of the ACF-estimated noise in our filter provides a statistically defensible and adaptive choice of the noise magnitude, which varies from day to day, with height, and exhibits a significant diurnal variation, all of which make a fixed noise estimate less desirable. We use a 5 × 11 local neighborhood, which corresponds to an approximately 300 m × 550 m region surrounding each pixel (assuming an average translations speed of 5 m s⁻¹). This neighborhood was found to best match the ACF-filtered variance for both the RL and DL data streams.

Figures 2a and 2b shows the qualitative aspects of the adaptive filtering for a 3-h period wherein the CBL is nearly stationary (i.e., Z_i varies slowly). In Fig. 2a, the instrument noise is apparent as appreciable “speckling” imposed on otherwise coherent features in the mixing ratio field (e.g., upward protrusions of high-mixing-ratio air). Figure 2b shows the same data passed through the adaptive filter revealing that the coherent features are preserved while the speckling is substantially reduced while the sharp physical features are preserved.

Overview of data filtering for the Raman lidar data. (a) Raw lidar retrieved water vapor mixing ratio. (b) Mixing ratio data passed through an adaptive noise filter, described in the text. Also shown are the Doppler lidar–derived CBL height (dashed line) and cloud-base detections (filled white circles). (c) Water vapor variance profiles from the raw (black), autocovariance filtere (ACF; red), and adaptive noise filter (green). (d) Power spectra for the raw and adaptive noise–filtered water vapor mixing ratio data in the upper CBL.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Overview of data filtering for the Raman lidar data. (a) Raw lidar retrieved water vapor mixing ratio. (b) Mixing ratio data passed through an adaptive noise filter, described in the text. Also shown are the Doppler lidar–derived CBL height (dashed line) and cloud-base detections (filled white circles). (c) Water vapor variance profiles from the raw (black), autocovariance filtere (ACF; red), and adaptive noise filter (green). (d) Power spectra for the raw and adaptive noise–filtered water vapor mixing ratio data in the upper CBL.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Overview of data filtering for the Raman lidar data. (a) Raw lidar retrieved water vapor mixing ratio. (b) Mixing ratio data passed through an adaptive noise filter, described in the text. Also shown are the Doppler lidar–derived CBL height (dashed line) and cloud-base detections (filled white circles). (c) Water vapor variance profiles from the raw (black), autocovariance filtere (ACF; red), and adaptive noise filter (green). (d) Power spectra for the raw and adaptive noise–filtered water vapor mixing ratio data in the upper CBL.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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The quantitative aspects of the noise reduction are demonstrated in Figs. 2c and 2d. Figure 2c shows the water vapor mixing ratio variance computed using the unfiltered (black), adaptive filter (green), and ACF filter (red). The unfiltered data contain high variance near the surface and aloft, as well as a variance peak at the upper edge of the CBL (Z/Z_i = 1). Both the ACF and adaptive filters remove the variance aloft and at the surface, where the signal is dominated by instrument noise, and preserves the variance peak at the CBL top. A small fraction of the noise aloft persists with the adaptive filter, but since this study focuses on variances, fluxes, and anomalies in the subcloud layer, this does not pose a problem.

The spectral behavior of the filter is shown in Fig. 2d, which compares the power spectral density (Welch 1967) for thefiltered (blue line) and raw (red line) mixing ratio data. Both spectra exhibit nearly identical peaks at frequencies somewhat greater than 10⁻³ Hz (~15 min), which corresponds to the dominant and quasi-periodic “plumelike” features apparent in Figs. 2a and 2b. For successively higher frequencies the filter removes increasing variance, which is especially clear for the noisy parts of the spectrum (10⁻²–10⁻¹ Hz).

The favorable comparisons in Figs. 2d and 2e holds for the broader set of 46 ShCu days, as we show later in the results, and we conclude that the adaptive filter provides the best approach for the current study by preserving the coherent features of interest while reducing the instrument noise that would otherwise strongly affect flux calculations.

d. Defining the anomaly, flux, and flux uncertainty

1) Averaging times

There are numerous ways to define background fields and flux averaging intervals (Lee et al. 2004). Here we choose a centered running mean to define the background and anomaly fields. Specifically, we compare results for sliding 30-, 60-, and 90-min window applied at 15-min intervals. These same time periods are used for flux averaging, such that there is appreciable overlap between flux profiles. We show later that the flux averaging converges for the 60- and 90-min periods.

Within each window, the latent heat flux (LH) is computed as

$\text{LH}=L_{\upsilon }{\overline{\left(w-\overline{w_T}\right)\left(q-\overline{q_T}\right)}}_T,$(7)

where L_υ is the latent heat of vaporization (2500 J g⁻¹) and overbars indicate time averages over the selected time window T. Any time period containing less than 80% good data (e.g., possessing numerous gaps) is discarded from subsequent statistics.

Figure 3 shows an example of the water vapor mixing ratio anomaly field and the corresponding vertical velocity used to compute the fluxes. These data highlight the coherent perturbations proximal to Z_i and occasionally penetrating through the depth of the CBL (e.g., dry intrusion near 1900 UTC). Also apparent is the tendency for upward (downward) vertical motion to coincide with positive (negative) water vapor anomalies, especially in association with cumuli, though as we show later in both a statistical and physical sense, this is not always the case. The instantaneous fluxes (w′q′) are shown in Fig. 3c, showing that the fluxes are strongest in the upper CBL and tend to occur in isolated regions where the vertical velocity and mixing ratio anomalies are correlated.

Example of data used in flux computation. (a) The 30-min-mean water vapor mixing ratio anomalies from the adaptively filtered RL data. (b) Vertical velocity anomalies from the Doppler lidar. (c) Instantaneous kinematic water vapor flux. Shown in each panel are the CBL heights (dashed line) and cloud-base detections (filled white circles).

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Example of data used in flux computation. (a) The 30-min-mean water vapor mixing ratio anomalies from the adaptively filtered RL data. (b) Vertical velocity anomalies from the Doppler lidar. (c) Instantaneous kinematic water vapor flux. Shown in each panel are the CBL heights (dashed line) and cloud-base detections (filled white circles).

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Example of data used in flux computation. (a) The 30-min-mean water vapor mixing ratio anomalies from the adaptively filtered RL data. (b) Vertical velocity anomalies from the Doppler lidar. (c) Instantaneous kinematic water vapor flux. Shown in each panel are the CBL heights (dashed line) and cloud-base detections (filled white circles).

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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e. Conditional sampling

Conditional sampling has been widely used to inspect coherent boundary layer features, including updrafts, downdrafts, and cloud-base properties (e.g., Singh Khalsa and Greenhut 1985; Williams and Hacker 1993; Miao et al. 2006; LZK18). Here we employ two forms of conditional sampling.

First, we identify cloud objects from the RL data as follows: (i) temporally continuous periods with cloud-base detections, (ii) clouds base within 300 m of Z_i, (iii) merging of clouds with gaps less than 30 s, and (iv) eliminating clouds persisting for more than 20 min. Based on the cloud objects, we subsequently extract a subcloud “scene” by normalizing the RL and DL data by the cloud center time, cloud duration, and cloud-base height. These data are later used to inspect the composite subcloud water vapor and vertical velocity distributions.

Second, we conditionally sample updraft objects in the upper CBL as follows: (i) temporally continuous periods with positive vertical velocity (w > 0.5 m s⁻¹) in the DL time series at 0.95Z_i, (ii) merging of objects with short gaps (<10 s), (iii) discarding objects with durations >20 min. From these identified updrafts we further extract time and height normalized scene to probe the differences between clear and cloudy updrafts.

a. Mean and variance profiles

Before examining the latent heat flux profiles, it is informative to examine the underlying mean and variance profiles of water vapor mixing ratio q and vertical velocity w. Figures 4a and 4b shows these height-normalized profiles for the water vapor mixing ratio based on 1104 sixty-minute profiles drawn from the sample of 46 ShCu days for the hours of 1700–2300 UTC [1200–1800 central daylight time (CDT)], corresponding to the portion of the day with slowly evolving CBL heights. The mean profile indicates a quasi-well-mixed CBL up to 0.8Z_i overlaid with a sharp gradient in mixing ratio spanning Z_i that connects the moist CBL with the drier free troposphere (or cloud layer). The mean gradient near Z_i comprises a mix of individual profiles with strong (i.e., jumplike) and weak gradients due to inclusion of both days with very dry air aloft and those with higher humidity in the cloud layer. We later scale some of our analyses by Δq, which we define as the jump in mixing ratio between the 0.2–0.8Z_i layer mean and the 1–1.2Z_i layer mean. The mean Δq values for each day are included in Table 1.

Overview of water vapor mixing ratio and vertical velocity statistics using 30-, 60-, and 90-min averaging periods. (a) Mean and interquartile range of the height-normalized water vapor mixing ratio profiles. (b) Mean and interquartile range of water vapor mixing ratio variance profiles. (c) Mean and interquartile range of vertical velocity variance profile. The height normalization is by the CBL height Z_i. In (b) and (c) the autocovariance-filtered (ACV) profiles are shown for reference.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Overview of water vapor mixing ratio and vertical velocity statistics using 30-, 60-, and 90-min averaging periods. (a) Mean and interquartile range of the height-normalized water vapor mixing ratio profiles. (b) Mean and interquartile range of water vapor mixing ratio variance profiles. (c) Mean and interquartile range of vertical velocity variance profile. The height normalization is by the CBL height Z_i. In (b) and (c) the autocovariance-filtered (ACV) profiles are shown for reference.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Overview of water vapor mixing ratio and vertical velocity statistics using 30-, 60-, and 90-min averaging periods. (a) Mean and interquartile range of the height-normalized water vapor mixing ratio profiles. (b) Mean and interquartile range of water vapor mixing ratio variance profiles. (c) Mean and interquartile range of vertical velocity variance profile. The height normalization is by the CBL height Z_i. In (b) and (c) the autocovariance-filtered (ACV) profiles are shown for reference.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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The water vapor mixing ratio variance profiles for the 30-, 60-, and 90-min averaging periods are provided in Fig. 3b, all showing low variance in the lower two-thirds of the CBL, increasing to a pronounced peak of ~1.25 g² kg⁻² at ~ Z_i associated with the coherent moisture anomalies due to updrafts and downdrafts perturbing the humidity gradient at the boundary layer top (as are apparent in Figs. 2a,b and 3a,b). The agreement across the different averaging periods is notable, as is the agreement with the conventional ACF-filtered variance profile (dashed black line) up to 1.1Z_i. Above that level the filter does not fully remove the instrument noise, which does not affect the conclusions of this study. The median and interquartile water vapor variances are slightly larger than those reported using the same RL in Turner et al. (2014a) during clear conditions similar to those in Kiemle et al. (2007) based on sampling with airborne DIAL (cf. their Fig. 3).

The vertical velocity variance profiles (for 30-, 60-, and 90-min sampling), shown in Fig. 3c, match the expected distribution of vertical velocity in buoyancy-driven CBLs (Moeng and Rotunno 1990; Zhou et al. 2019). Namely, the variance peaks at ~0.4Z_i then decays approximately linearly with height to the top of the CBL. As with the water vapor, the adaptively filtered variances closely match the ACF-filtered variances (dashed black line). We do not show the vertical velocity skewness profile, but, as expected it is positively skewed, with skewness peaking in the upper CBL (i.e., near 0.8Z_i). Generally speaking, these velocity variance profiles are consistent with those in Kiemle et al. (2007) and are indicative of turbulence driven by surface buoyancy fluxes (Moeng and Rotunno 1990).

b. Latent heat flux profiles

Figure 5a shows the mean and interquartile ranges of observed latent heat flux as a function of normalized boundary layer height. Also shown are mean and interquartile range of surface latent heat fluxes from site E14 (box and line at the bottom). The profiles for the 30-, 60-, and 90-min sampling periods are all shown, as are the sampling uncertainties for each profile (dotted lines). Notably, the 60- and 90-min profiles are virtually indistinguishable, whereas the 30-min profile is systematically smaller. The sampling uncertainty is smallest (by definition) for the 90-min profiles, but we henceforth focus on the 60 means in our analyses as they allow a finer temporal resolution for examining diurnal changes in flux characteristics. The 30-min data are not further examined.

Overview of latent heat flux profiles. (a) Mean (solid lines), interquartile (dashed lines), and sampling uncertainty ranges (dotted lines) of latent heat flux profiles for the 30-, 60-, and 90-min averaging periods. Also shown are the surface fluxes for the same statistical ranges (box and line). (b) Latent heat flux profiles (solid lines) and standard errors (light lines) stratified by cloud fraction (CF) intervals. The inset shows the distribution of cloud fraction. (c) Latent heat flux profiles (solid lines) and standard errors (light lines) stratified by the humidity jump Δq at the top of the boundary layer.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Overview of latent heat flux profiles. (a) Mean (solid lines), interquartile (dashed lines), and sampling uncertainty ranges (dotted lines) of latent heat flux profiles for the 30-, 60-, and 90-min averaging periods. Also shown are the surface fluxes for the same statistical ranges (box and line). (b) Latent heat flux profiles (solid lines) and standard errors (light lines) stratified by cloud fraction (CF) intervals. The inset shows the distribution of cloud fraction. (c) Latent heat flux profiles (solid lines) and standard errors (light lines) stratified by the humidity jump Δq at the top of the boundary layer.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Overview of latent heat flux profiles. (a) Mean (solid lines), interquartile (dashed lines), and sampling uncertainty ranges (dotted lines) of latent heat flux profiles for the 30-, 60-, and 90-min averaging periods. Also shown are the surface fluxes for the same statistical ranges (box and line). (b) Latent heat flux profiles (solid lines) and standard errors (light lines) stratified by cloud fraction (CF) intervals. The inset shows the distribution of cloud fraction. (c) Latent heat flux profiles (solid lines) and standard errors (light lines) stratified by the humidity jump Δq at the top of the boundary layer.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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The mean 60-min profile indicates flux divergence (i.e., $\partial \overline{w^{\prime }{q}^{\prime }}/\partial z>0$) from the surface to ~0.8Z_i, with flux convergence over the remainder of the CBL depth. Specifically, the mean and upper-quartile fluxes increase linearly with height from the lower to upper CBL, peaking at ~350 and ~600 W m⁻² near 0.8Z_i, then drop rapidly with height to ~0 W m⁻² slightly above the CBL top. The lower-quartile flux profiles, in contrast, are roughly constant with height through the 0.4–0.8Z_i layer indicating a decrease with height with respect to the surface fluxes (i.e., $\partial \overline{w^{\prime }{q}^{\prime }}/\partial z<0$), implying flux convergence (i.e., moistening rate) closer to the surface.

The general shape and magnitude of our mean flux profiles are consistent with previous observational (e.g., Giez et al. 1999; Kiemle et al. 2007) and modeling studies (e.g., Larson et al. 2012). Kiemle et al. (2007), for example, found peak fluxes in the upper CBL of 600–800 W m⁻² with strong flux divergence through the lower three-quarters of the CBL, implying upward transport of moist air and downward entrainment of dry air into the CBL resulting in a net drying of that layer. Not all previous studies, however, indicate a linear or monotonically increasing profile (e.g., Senff et al. 1994; Kiemle et al. 2011). To that end, individual profiles (not shown) contributing to the statistics in Fig. 5a can differ markedly, including profiles that decrease or vary nonmonotonically with height, presumably due to temporal variations in the vertical extent of thermals and plumes within the single column sampled by the lidars.

To examine variations in latent heat fluxes between cloudy and cloud-free periods we stratify the flux profiles by cloud fraction (CF), deeming all 60-min-mean profiles with CF < 0.05 to be ostensibly clear, profiles with 0.05 < CF < 0.15 as low cloud fraction, profiles 0.15 < CF < 0.35 as medium cloud fraction, and CF > 0.35 as high cloud fraction (noting that high ShCu CF is still a low CF). This binning results in a sample of 682 clear, 330 low-CF, 296 medium-CF, and 68 high-CF profiles. The results are shown in Fig. 5b (note the distribution of CFs is shown in an inset panel, showing the preponderance of clear profiles and a mean CF of ~11% for all profiles). These data clearly show that the low- and medium-CF periods (green and blue profiles) are associated with substantially larger latent heat fluxes than the clear or high-CF profiles near 0.8Z_i but minimal differences in the surface forcing (cf. square markers). This implies stronger drying of the CBL during these periods. The standard error is shown for each profile, which helps visualize the statistically significant differences among profiles.

These results echo those of Giez et al. (1999) wherein “cloud-induced flux” profiles showed a notable peak in the upper CBL as compared to the “between cloud” profiles. These results do not, however, imply a feedback between clouds and subcloud fluxes, but rather that the underlying vertical velocity and moisture perturbations are most pronounced during the cloudy periods and thus force the clouds.

Next, we examine the variation in the flux profiles with the strength of the mean jump Δq at the top of the CBL. Specifically, we stratify the flux profiles by Δq ranges of <2, 2–4, 4–6, and >6 g kg⁻¹. There is a systematic and statistically significant (see standard errors) shift to larger latent heat fluxes and stronger flux divergences in the upper CBL in association with larger humidity jumps aloft. Compare, for example, the fluxes at 0.8Z_i of ~194, 317, and 484 W m⁻² for the second through fourth Δq bins, respectively. The profiles associated with the weakest humidity jumps (Δq < 2) are weakly convergent through the depth of the CBL, implying net moistening during these periods. Notably, the sensitivity of the flux profile to Δq suggests the potential to parameterize these fluxes based on better-resolved mean-state profiles. We examine this in section 5.

c. Diurnal cycle and humidity budget

Here we examine the composite diurnal cycle of the latent heat flux profile and its impact on boundary layer drying. The composite is for a subset of 42 out of the 46 ShCu days due to missing surface flux data. The days included in the budget analysis are indicated in Table 1. Figures 6a–h show the time variation in the composite latent heat flux profile along with the surface latent heat flux. Note that these profiles are presented in physical height coordinates, rather than normalized heights, which is accomplished by multiplying the height normalized profiles by the mean CBL depth for each composite 1-h time bin.

Overview of the diurnal cycle of latent heat flux profiles and the CBL humidity budget. (a)–(h) Composite hourly latent heat flux profiles including sampling uncertainty bounds (black dashed), mean CBL height (solid blue), 0.8Z_i (dashed blue), and a key indicating the cloud fraction (CF) and flux integral time scale (IS). (i) Time evolution of the mean mixing ratio profile, with colors corresponding to time stamps in (a)–(h). (j) Budget analysis showing storage (magenta), flux divergence (red), and advection (green) for the composite day. Negative values indicate CBL drying.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Overview of the diurnal cycle of latent heat flux profiles and the CBL humidity budget. (a)–(h) Composite hourly latent heat flux profiles including sampling uncertainty bounds (black dashed), mean CBL height (solid blue), 0.8Z_i (dashed blue), and a key indicating the cloud fraction (CF) and flux integral time scale (IS). (i) Time evolution of the mean mixing ratio profile, with colors corresponding to time stamps in (a)–(h). (j) Budget analysis showing storage (magenta), flux divergence (red), and advection (green) for the composite day. Negative values indicate CBL drying.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Overview of the diurnal cycle of latent heat flux profiles and the CBL humidity budget. (a)–(h) Composite hourly latent heat flux profiles including sampling uncertainty bounds (black dashed), mean CBL height (solid blue), 0.8Z_i (dashed blue), and a key indicating the cloud fraction (CF) and flux integral time scale (IS). (i) Time evolution of the mean mixing ratio profile, with colors corresponding to time stamps in (a)–(h). (j) Budget analysis showing storage (magenta), flux divergence (red), and advection (green) for the composite day. Negative values indicate CBL drying.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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The flux profiles show the growth of the CBL (bold dashed blue line), the tendency for the flux to peak or inflect at ~0.8Z_i (light dashed blue line), and the tendency for a minimum in the latent heat flux near Z_i. Also shown are the hourly median cloud fractions, which peak at ~13% between 1400 and 1500 CDT, and the hourly CBL-averaged flux integral time scales, which range from 34 to 40 s.

The strength of the drying or moistening (i.e., flux divergence or convergence) can be visually approximated from these profiles as the difference between the surface flux and that at 0.8Z_i: greater increases with height indicate stronger drying. Notably, for 1030–1130 CDT, the peak fluxes aloft are either less than or nearly equal to the surface fluxes, such that the profiles imply moistening or no change to the lower CBL humidity budget. In contrast, from 1230 to 1330 CDT the flux aloft increases significantly, reaching a peak of ~470 W m⁻², which is more than twice the surface flux magnitude (204 W m⁻²), implying strong drying. Thereafter, the flux aloft slowly decreases, with the flux profile becoming approximately constant with height by 1630 CDT.

Figure 6i shows the corresponding time variation in the mean mixing ratio profile, which supports the interpretation provided by the flux profiles. Namely, the CBL evolution is characterized first by overall moistening and deepening from 0930 to 1130 CDT, then by strong drying over the lower 80% of the CBL from 1120 to 1630 CDT. Further aloft, in the 0.8–1.0Z_i layer, strong moistening due to flux convergence is apparent.

The evaluated storage (left side) and flux divergence (right side) terms of Eq. (8), shown in Fig. 5j, indicating good agreement both in time and magnitude: the observed CBL drying is well described by the computed flux divergence. Specifically, 1) the observed moistening in the midmorning is consistent with the flux convergence, 2) the storage term crosses zero (i.e., becomes drying) at the same time that the flux profile becomes divergent (at 1130 CDT), 3) the drying is strongest (~0.3 g kg⁻¹ h⁻¹) at ~1330 CDT, consistent with the flux divergence (Fig. 5d), and 4) the drying then diminishes through the afternoon. Interestingly, the flux divergence persistently exceeds the observed drying by ~0.06 g kg⁻¹ after 1300 CDT. This difference agrees well with the timing of the advective moistening (green line, from the variational analysis), though the magnitude of the advection does not fully account for the residual. That the advection is smaller than the residual may be due to errors in the flux calculation (note the sampling error bounds), errors in the surface flux data, errors in the boundary layer height, or underestimation of the by the variational analysis. For example, the ECOR surface fluxes used here sample a crop field, whereas the land use surrounding SGP is both spatially and temporally variable (e.g., pasture, crop, winter harvested wheat vs summer irrigated crops).

We also note that the magnitude of the drying is less than half the peak drying documented in Kiemle et al. (2007), but this difference is not surprising given our sample is the average over a large 42-day sample as compared to 1 day. In addition, while advection can impact the CBL moisture budget, by averaging over many days with varying conditions this contribution becomes quite small during the midday period.

d. Joint probability density function

The relationship between water vapor and vertical velocity anomalies in the upper CBL (0.7 ≤ Z/Z_i < 1) can also be cast as a joint probability density function (JPDF), which is a component of some parameterizations and closure schemes (e.g., Golaz et al. 2002; Larson et al. 2012). Figure 7 shows the JPDF for both the cloud-free (Fig. 7a) and cloudy periods (Fig. 7b), here defined as all periods with CF > 0.05 and CF < 0.35, as well as the difference between the two distributions (Fig. 7c). Irrespective of cloud cover the JPDFs are approximately isotropic and centered around zero. This implies that despite the visual indication of coherent “moist updrafts” in RL and DL data (e.g., Figs. 3a,b) that there exist many data points in all quadrants of the JPDF (i.e., a mix of moist downdrafts, moist updrafts, dry downdrafts, and dry updrafts).

JPDFs for water vapor mixing ratio anomalies and vertical velocity in the upper CBL for (a) clear and (b) cloudy (CF > 0.05) periods. (c) Difference between cloudy and clear JPDFs. Red and blue contours bound regions of positive and negative changes in probability, respectively.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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JPDFs for water vapor mixing ratio anomalies and vertical velocity in the upper CBL for (a) clear and (b) cloudy (CF > 0.05) periods. (c) Difference between cloudy and clear JPDFs. Red and blue contours bound regions of positive and negative changes in probability, respectively.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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JPDFs for water vapor mixing ratio anomalies and vertical velocity in the upper CBL for (a) clear and (b) cloudy (CF > 0.05) periods. (c) Difference between cloudy and clear JPDFs. Red and blue contours bound regions of positive and negative changes in probability, respectively.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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The difference between the cloudy and cloud-free JPDFs, however, shows that cloudy periods do in fact possess a larger population of moist updrafts, dry downdrafts, and moist downdrafts (red shaded regions), with fewer weak anomalies distributed around zero (blue shaded regions). This finding supports the flux differentiation between cloudy and clear periods shown in Fig. 5b. In the following sections we will examine some of the physical reasons for the breadth of the JPDF.

e. Subcloud water vapor and vertical anomalies

In this section we move from a statistical representation of the subcloud circulation (i.e., variances, fluxes profiles, etc.) to a process-based perspective (i.e., updraft composites) in order to probe the underlying physics contributing to the fluxes of water vapor in the subcloud layer. To do so, we extract a subcloud “scene” of vertical velocity and water vapor for each cumulus based on the conditional sampling of cloud objects. These “scenes” are normalized by cloud-base height Z_cb and by cloud duration and then averaged such that the composite cloud resides between unitless time −0.5 and 0.5 with cloud-base height Z_cb of 1. We note that the normalization by cloud-base height, not Z_i, allows compositing of individual ShCu occurring at varying heights (±300 m) relative to Z_i. In the mean, Z_cb is ~20 m higher than Z_i. The resulting composite includes 933 cumuli sampled over the full set of 46 days included in the study.

The composite cloud (Fig. 8a) is linked to a region of high water vapor mixing ratio air extending upward from the well-mixed portion of the CBL (Z/Z_cb < 0.8) to cloud base (Z/Z_cb = 1).

Summary of composite subcloud and cloud-base properties. (a) Composite subcloud water vapor mixing ratio. (b) Composite subcloud mixing ratio anomaly. (c) Composite vertical velocity overlaid on the mixing ratio anomaly. Positive vertical velocity is contoured every 0.1 m s⁻¹, and negative vertical velocity is contoured every 0.05 m s⁻¹. (d) Cross section of vertical velocity (red) and mixing ratio (green) at 0.95Z_cb. All data are normalized to the cloud-base height and cloud duration and centered on the cloud center time (i.e., 0).

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Summary of composite subcloud and cloud-base properties. (a) Composite subcloud water vapor mixing ratio. (b) Composite subcloud mixing ratio anomaly. (c) Composite vertical velocity overlaid on the mixing ratio anomaly. Positive vertical velocity is contoured every 0.1 m s⁻¹, and negative vertical velocity is contoured every 0.05 m s⁻¹. (d) Cross section of vertical velocity (red) and mixing ratio (green) at 0.95Z_cb. All data are normalized to the cloud-base height and cloud duration and centered on the cloud center time (i.e., 0).

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Summary of composite subcloud and cloud-base properties. (a) Composite subcloud water vapor mixing ratio. (b) Composite subcloud mixing ratio anomaly. (c) Composite vertical velocity overlaid on the mixing ratio anomaly. Positive vertical velocity is contoured every 0.1 m s⁻¹, and negative vertical velocity is contoured every 0.05 m s⁻¹. (d) Cross section of vertical velocity (red) and mixing ratio (green) at 0.95Z_cb. All data are normalized to the cloud-base height and cloud duration and centered on the cloud center time (i.e., 0).

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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The associated water vapor anomaly, shown in Fig. 8b, peaks (in the mean) at greater than ~0.6 g kg⁻¹ in the 0.8–1.0Z_cb layer, which corresponds to the layer of peak variance (Fig. 4b). The adjacent regions (outside of the cloud) are characterized by negative water vapor mixing ratio anomalies. The structure of the moisture anomaly matches that described in Miao et al. (2006), wherein radar detected CBL plumes showed homogeneous mixing ratio air in their lower portions but pronounced positive anomalies near the top of the CBL.

Figure 8c shows the mean vertical velocity (determined from the DL; red contours indicate updrafts) overlaid on the water vapor mixing ratio anomalies (replicated from Fig. 8b). These combined data reveal the canonical structure of the subcloud circulation as a central moist updraft flanked by broad dry downdrafts and compact downdrafts along the updraft edge in the upper CBL. The updraft and the water vapor anomaly are both slightly asymmetric in time.

These composite data also indicate a systematic difference in the characteristic width and structure of the water vapor and vertical velocity anomalies: the high water vapor air (green shading) is broader than the updraft, and especially near 0.95Z_i. This observation is reinforced by considering cross sections through the water vapor and vertical velocity fields averaged over the heights of 0.9–0.97Z_i (Fig. 8d). The vertical velocity (red line) is characterized by a narrow quasi-Gaussian updraft flanked by downdrafts, which arise due to a combination of mechanical forcing (LZK18), evaporative cooling (Rodts et al. 2003; Hues and Jonker 2008), and radiative cooling (Endo et al. 2019). The full width at half-maximum (FWHM) amplitude of the updraft is ~1 in normalized time units. In contrast the water vapor anomaly is less peaked and broader, with an FWHM of ~1.5.

This difference in characteristic width results in regions of high-mixing-ratio air coinciding with the cloud edge downdrafts and the nearly stagnant regions of air (i.e., the inflection point between updraft and downdraft). The implied result is that the covariance of water vapor and vertical velocity near cloud base is less positive than might otherwise be thought, contributing to the broad JPDF with a mix of wet updrafts, dry downdrafts, and wet downdrafts that was apparent in Fig. 7.

The geometric differences in water vapor and vertical velocity anomalies follows from the structure of velocity and scalar distributions observed in laboratory and simulated thermals and plumes (Turner 1979; Tarshish et al. 2018). Specifically, thermals transport scalar properties through their central updraft, diverge them at the thermal cap, then transport them downward in flanking downdrafts. Thus the scalar properties of the air in the downdraft region are a mix of the air rising through the updraft (i.e., high mixing ratio) and entrained dry air from above the rising thermal (note that if the air suffered no entrainment, then the water vapor cross section would have a top-hat profile rather than a Gaussian shape). The resulting difference in shape and width of velocity and moisture fields has also been previously noted in aircraft observations of shallow cumulus, which show, in some instances, a top-hat-like distribution of water vapor anomalies and a tripole vertical velocity structure (e.g., Fig. 7 in Crum et al. 1987). This geometric difference is a fundamental attribute of the thermals, their water vapor fields, and their fluxes and should be considered in parameterizations.

f. Cloud-base latent heat flux

In this section we isolate the flux of water vapor that exits the CBL through cloud venting [i.e., M_q in Eq. (1)] thereby augmenting the typical CBL entrainment process. This is accomplished by computing the covariance of the cloud-base vertical velocity $\left(w_{\text{cb}}^{\prime }\right)$ and water vapor mixing ratio anomaly $\left(q_{\text{cb}}^{\prime }\right)$ time series,

${\text{LH}}_{\text{cb}}=\rho L_{\upsilon }\overline{w_{\text{cb}}^{\prime }{q}_{\text{cb}}^{\prime }},$(13)

where the temporal averaging is over the cloud duration (and thus often quite short and analogous to an instantaneous flux). The resulting distribution of cloud-base fluxes is shown in Fig. 9a.

Overview of cloud-base latent heat fluxes. (a) Distribution of cloud-base latent heat flux with the percentage of positive latent heat flux clouds along with the mean and median cloud-base fluxes shown in the key. (b),(c) Subcloud composite water vapor mixing ratio and vertical velocity for (b) positive flux and (c) negative flux clouds.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Overview of cloud-base latent heat fluxes. (a) Distribution of cloud-base latent heat flux with the percentage of positive latent heat flux clouds along with the mean and median cloud-base fluxes shown in the key. (b),(c) Subcloud composite water vapor mixing ratio and vertical velocity for (b) positive flux and (c) negative flux clouds.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Overview of cloud-base latent heat fluxes. (a) Distribution of cloud-base latent heat flux with the percentage of positive latent heat flux clouds along with the mean and median cloud-base fluxes shown in the key. (b),(c) Subcloud composite water vapor mixing ratio and vertical velocity for (b) positive flux and (c) negative flux clouds.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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The latent heat flux distribution contains both negative and positive latent heat flux clouds but is positively skewed such that 66% of clouds have positive fluxes. This is similar to the fraction of clouds (62%) with positive mass flux documented in LZK18. The positive moisture flux clouds occasionally have very large cloud-base fluxes (10 kW m⁻²). These values, which seem spurious at first, are consistent with the hypothetical flux that would be generated by the upper end of the observed cloud-base velocity and humidity perturbations (e.g., 10 000 W m⁻² for a cloud with a ~2 m s⁻¹ mean updraft and ~2 g kg⁻¹ mean mixing ratio anomaly; see Figs. 5a and 5b). However, while the fluxes due to individual clouds are sometimes large, the net latent heat flux out of the CBL due to clouds is a function of the total cloud-base updraft area (or fraction of time), which is typically just a few percent (VS14) such that upon averaging over all times (clear and cloudy) the net fluxes, as seen in Fig. 5, are much smaller (e.g., 500 W m⁻²).

Whereas the positive mass flux clouds are morphologically similar to the mean of all clouds (Fig. 9b) the clouds that contribute to the negative water vapor flux lack a coherent subcloud updraft (Fig. 9c). These clouds correspond with the negative mass flux clouds documented in LZK18. Interestingly these cumuli remain linked to weak, but positive water vapor mixing ratio anomalies in the subcloud layer, suggesting that either 1) even as the updraft decays a “wake” of detrained high humidity air remains, or 2) “glancing” lidar observations along the subsiding edges of a broader cloud that possess a central, but unsampled, updraft. This occurrence of moist remnant thermals with no central updraft has been noted in the past, including in Giez et al. (1999), and is consistent with aircraft observations of cumuli (e.g., Crum et al. 1987). Ultimately, these negative flux clouds, characterized by sinking moist air, are another reason for the breadth and isotropic character of the JPDF.

While these cloud-base statistics contain some uncertainty due to the unknown location of the sampled cloud chord relative to the broader cloud, they remain useful in that they can be directly compared with synthetic lidar observations of subcloud fields in LES. This utility was recently evidenced in a study diagnosing the provenance of biases in lidar-sampled cloud-base vertical velocity distributions with those from LES output (Endo et al. 2019).

g. Cloudy versus clear updrafts

We next ask the following question: are cloudy updrafts wetter than clear updrafts? To answer this question, we compare a conditionally sampled cloudy (N = 683) and clear (N = 961) updrafts near the upper edge of the CBL (Z/Z_i = 0.95). As apparent in Fig. 10, the cloudy updrafts are wetter and stronger than the clear updrafts. Specifically, Fig. 10c shows that the wet updrafts have a peak water vapor mixing ratio anomaly of ~0.5 g kg⁻¹ as compared to ~0.35 g kg⁻¹ in the clear updrafts, a difference that is statistically significant (95% confidence using at two-tailed t test) through most of the updraft cross section (filled dots show significantly different points). This result implies that the lifting condensation level (LCL) in the cloud-free updrafts is slightly higher than in the cloudy updrafts and supports the narrative that clouds preferentially form above the strongest and wettest updrafts. These updraft composite also supports our earlier interpretation that the water vapor anomaly is systematically wider than the updraft (irrespective of cloudiness), and thus further reinforces the notion that the broad JPDF of water vapor and vertical velocity is intrinsic to the structure of the CBL and rising thermals.

Updraft composites based on conditional sampling at 0.95Z_i. (a),(b) Water vapor mixing ratio and vertical velocity for (a) cloudy and (b) clear updrafts. (c) Comparison of clear (dashed) and cloudy (solid) vertical velocity (red) and water vapor mixing ratio (green) cross sections sampled at 0.95Z_i. The line segments with dots indicate locations of statistical significance in the cloudy vs clear mean values.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Updraft composites based on conditional sampling at 0.95Z_i. (a),(b) Water vapor mixing ratio and vertical velocity for (a) cloudy and (b) clear updrafts. (c) Comparison of clear (dashed) and cloudy (solid) vertical velocity (red) and water vapor mixing ratio (green) cross sections sampled at 0.95Z_i. The line segments with dots indicate locations of statistical significance in the cloudy vs clear mean values.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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Updraft composites based on conditional sampling at 0.95Z_i. (a),(b) Water vapor mixing ratio and vertical velocity for (a) cloudy and (b) clear updrafts. (c) Comparison of clear (dashed) and cloudy (solid) vertical velocity (red) and water vapor mixing ratio (green) cross sections sampled at 0.95Z_i. The line segments with dots indicate locations of statistical significance in the cloudy vs clear mean values.

Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0122.1

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