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  • View in gallery

    Two columns are simulated to account for sea-breeze advection. Ocean and land column states are described by their height zi, moisture qt(z), and temperature θl(z), from which the liquid water profile ql(z) and cloud-base height zb can be derived. Ocean and land have different surface flux conditions, with the ocean having prescribed fluxes of LHF and SHF, while over land the net surface radiative flux F0 is partitioned using a Bowen ratio Bo. At the cloud top, both columns are affected by the net radiative flux Fi and entrainment fluxes that depend on the inversion jumps. Entrainment mixes air into the columns at a rate we, while subsidence reduces column height at a rate wsub. The properties of the ocean column are advected onto the land column with a wind speed u and considering a distance Δx [see Eq. (B5)].

  • View in gallery

    Mixed-layer idealization for 21 Jul 2014. We detect the inversion region from radiosonde data (gray), and compute a well-mixed profile (black) by averaging properties in the ABL and tropospheric regions. The well-mixed profile is compatible with the MLM.

  • View in gallery

    Effect of the steady thickness initialization (STI) for 21 Jul 2014. The changes to the original sounding (dashed lines) for (a) θl(z) and (b) qt(z) are shown in solid lines. MLM simulated cloud boundaries zi and zb for the (c) ocean and (d) land column for the original properties and the modified STI.

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    Correlation coefficient matrix for variables spanning the 195 selected days grouped by their relationship: (a) seasonal trends, (b) initial conditions, (c),(d) boundary forcings divided into two figures for easier presentation—(c) wind and surface fluxes variables and (d) large-scale and radiation parameters. The sign is representative of each correlation coefficient.

  • View in gallery

    (a) The distribution of dissipation time tdiss over coastal land. (b)–(r) The effects of all variables on tdiss for all 195 days. Raw data (gray dots) and a linear fit (dashed black) are shown for the dissipating cases. Distributions (gray box plots) are shown for the persisting cases (marked as P in the tdiss axis), with boxes marking the 25th and 75th percentiles, a circle marking the median, and lines extending between the minimum and maximum values (excluding outliers).

  • View in gallery

    Effect on dissipation time over land of the change of a single variable for the idealized reference case of observed medians. Variables are shown in terms of their Z score, computed by subtracting the observed mean and dividing by the observed standard deviation. (a) Changes of initial-condition variables one at a time, (b) changes of zi|h to maintain constant cloud thickness and the corresponding values of qtBL(zi|h), and changes of h|zi maintaining constant zi and the corresponding changes of qtBL(h|zi), (c) changes in advection and land surface forcing variables, and (d) changes in radiative, subsidence, and SLP variables. Some trends include less than five points as clouds were not present for some configurations.

  • View in gallery

    Relationships between triads of variables: (a) qtBL in the plane described by zi and θlBL and (b) h in the plane described by zi and Δiθl. Gray dots are data points and contours are the best linear fit per the fit equation shown above each panel.

  • View in gallery

    Two-dimensional variable spaces for (a) zi and qtBL, (b) zi and h, (c) zi and Δiθl, and (d) u¯ and h. Data are classified by cases that persist for the whole day (black asterisks, 38 cases) and cases that dissipate during the day (dots colored by dissipation time, 157 cases).

  • View in gallery

    (a) Sky effective radiative temperatures for the dataset of 209 cloudy days as a function of water content above the cloud and below 3 km. The sky effective radiative temperatures were obtained with Streamer (Key and Schweiger 1998). (b) Climatological daily wind profile for the NKX station (10-yr average), showing the original wind speed profile and the wind speed normalized by its 16-h average.

  • View in gallery

    Cloud evolution properties for the ocean column (top row for each panel) and (bottom row for each panel) land columns for single-variable changes of (a) Δiθl, (b) SHF, and (c) Tsky over the idealized reference case. (left to right) Cloud boundaries, entrainment rate, qtBL, Δiqt, θlBL, and Δiθl.

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Coastal Stratocumulus Dissipation Dependence on Initial Conditions and Boundary Forcings in a Mixed-Layer Model

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  • 1 Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California
  • | 2 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
  • | 3 Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California
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Abstract

The impact of initial states and meteorological variables on stratocumulus cloud dissipation time over coastal land is investigated using a mixed-layer model. A large set of realistic initial conditions and forcing parameters are derived from radiosonde observations and numerical weather prediction model outputs, including total water mixing ratio and liquid water potential temperature profiles (within the boundary layer, across the capping inversion, and at 3 km), inversion-base height and cloud thickness, large-scale divergence, wind speed, Bowen ratio, sea surface fluxes, sky effective radiative temperature, shortwave irradiance above the cloud, and sea level pressure. We study the sensitivity of predicted dissipation time using two analyses. In the first, we simulate 195 cloudy days (all variables covary as observed in nature). We caution that simulated predictions correlate only weakly to observations of dissipation time, but the simulation approach is robust and facilitates covariability testing. In the second, a single variable is varied around an idealized reference case. While both analyses agree in that initial conditions influence dissipation time more than forcing parameters, some results with covariability differ greatly from the more traditional sensitivity analysis and with previous studies: opposing trends are observed for boundary layer total water mixing ratio and Bowen ratio, and covariability diminishes the sensitivity to cloud thickness and inversion height by a factor of 5. With covariability, the most important features extending predicted cloud lifetime are (i) initially thicker clouds, higher inversion height, and stronger temperature inversion jumps, and (ii) boundary forcings of lower sky effective radiative temperature.

Corresponding author: Mónica Zamora Zapata, mzamoraz@eng.ucsd.edu

Abstract

The impact of initial states and meteorological variables on stratocumulus cloud dissipation time over coastal land is investigated using a mixed-layer model. A large set of realistic initial conditions and forcing parameters are derived from radiosonde observations and numerical weather prediction model outputs, including total water mixing ratio and liquid water potential temperature profiles (within the boundary layer, across the capping inversion, and at 3 km), inversion-base height and cloud thickness, large-scale divergence, wind speed, Bowen ratio, sea surface fluxes, sky effective radiative temperature, shortwave irradiance above the cloud, and sea level pressure. We study the sensitivity of predicted dissipation time using two analyses. In the first, we simulate 195 cloudy days (all variables covary as observed in nature). We caution that simulated predictions correlate only weakly to observations of dissipation time, but the simulation approach is robust and facilitates covariability testing. In the second, a single variable is varied around an idealized reference case. While both analyses agree in that initial conditions influence dissipation time more than forcing parameters, some results with covariability differ greatly from the more traditional sensitivity analysis and with previous studies: opposing trends are observed for boundary layer total water mixing ratio and Bowen ratio, and covariability diminishes the sensitivity to cloud thickness and inversion height by a factor of 5. With covariability, the most important features extending predicted cloud lifetime are (i) initially thicker clouds, higher inversion height, and stronger temperature inversion jumps, and (ii) boundary forcings of lower sky effective radiative temperature.

Corresponding author: Mónica Zamora Zapata, mzamoraz@eng.ucsd.edu

1. Introduction

Marine stratocumulus (Sc) clouds cover a large area of the planet at the eastern side of oceans where upwelling keeps the sea colder and at latitudes where the subsiding branch of the Hadley cell pushes the atmospheric boundary layer (ABL) down and caps it with warm air, creating an inversion layer that limits the vertical cloud extent. The main physical processes controlling the evolution of Sc clouds are radiation, turbulence, surface fluxes, entrainment, and precipitation (Wood 2012; Stevens 2005; Nieuwstadt and Duynkerke 1996). Sc clouds are maintained by convective turbulent motions, driven mainly by cloud-top radiative cooling that generates sinking plumes and cools the ABL (Lilly 1968). The turbulent motions allow water vapor from the surface to mix and rise up to the condensation level to form a cloud. Near the top of the cloud, there is a complex interface zone exposed to entrainment of air from the free troposphere (Mellado 2017).

Marine Sc clouds have a net cooling effect on the planet (Hartmann et al. 1992) and their impact under climate change conditions is still a matter of research (Zelinka et al. 2017; Bony and Dufresne 2005; Duynkerke and Teixeira 2001). Coastal cities near Sc regions are affected by their presence—not only in terms of climate, but also from the perspective of solar energy generation. As solar heating overcomes cloud-top radiative cooling, clouds over land thin during the day, warming the ABL, and changing its turbulent structure (Fang et al. 2014). No solar radiation is present during the night, resulting in more effective radiative cooling, which causes cloud growth. During the day, solar electricity generation ramps up as Sc clouds dissipate in the morning hours (Jamaly et al. 2013; Wellby and Engerer 2016) or an extended shortfall of solar generation occurs when Sc clouds persist for the whole day. A better understanding of Sc cloud dissipation can help improve solar energy forecasting in these regions.

Different physical processes and meteorological parameters affect the inland coverage of marine Sc clouds and the dissipation time over coastal land. For marine clouds, some parameters have been linked to decreased cloudiness: greater sea surface temperatures (SST) (Hanson 1991; Seethala et al. 2015), weaker lower-tropospheric stability (LTS) (Klein and Hartmann 1993; Wood and Bretherton 2006; Klein et al. 1995), weaker horizontal cold-air advection, weaker surface wind speed, a moister free-troposphere, and lower sea level pressure (SLP) (Klein et al. 1995; Seethala et al. 2015). Research has been less extensive over coastal land, where earlier dissipation has been linked to smaller Bowen ratio (Bo; the ratio between sensible and latent heat fluxes over land) and weaker sea-breeze advection using simple sensitivity analyses (Ghonima et al. 2016; Akyurek and Kleissl 2017).

Most factors do not contribute independently to cloud dissipation because they are interrelated with other variables and covary in nature. Some variables covary due to the nature of physical processes, such as greater SST yielding larger surface heat fluxes. Other variables covary because their definitions are linked, such as lower SST occurring with stronger LTS. Some variables with opposing trends on cloud dissipation can be correlated themselves, causing the total cloud response to be dominated by only one variable and masking the independent effect of the nondominant variable. This is the case for stronger subsidence, which tends to thin Sc clouds, being correlated with larger LTS, which tends to sustain a thicker cloud—their combined occurrence is linked to larger cloudiness due to dominance by LTS (Myers and Norris 2013; Seethala et al. 2015). Such covariability can arise from seasonal trends, such as decreasing LTS cooccurring with increasing SST, which causes cloudiness to decrease from May/June to August/September in Southern California (Clemesha et al. 2016; Klein and Hartmann 1993).

The research to date on coastal Sc dissipation presents several gaps: (i) Only a few parameters have been considered, specifically two in Ghonima et al. (2016), while nine variables have been studied for marine Sc in Seethala et al. (2015). (ii) The parameters do not resemble realistic conditions. Specifically, Ghonima et al. (2016) parameter values for Bowen ratio and sea-breeze advection were chosen ad hoc and only for two idealized cases. (iii) As a result of (ii), covariability effects have been ignored.

In this work, we conduct a comprehensive analysis of how coastal Sc cloud dissipation time depends on initial conditions and boundary forcings, with consideration of covariability. We use a large set of 15 variables measured or derived from realistic meteorological conditions for Southern California as input to a two-column mixed-layer model (MLM) to predict dissipation time (section 2a). The two columns represent ocean and land conditions and allow the modeling of sea-breeze advection over coastal land. Realistic conditions for the MLM are obtained from radiosonde profiles, ground measurements, and NWP models for the 2014–17 summer seasons in Southern California (section 2b). In section 3a, we review the correlations of the variables in the dataset. We perform two analyses in order to consider the impact of covariability on the predicted dissipation time (section 3b). In the first, coastal Sc evolution is simulated for 195 cloudy days in which the initial conditions and forcing parameters covary as in nature. In the second, simulations are performed in which a single forcing parameter is varied around an idealized, composite reference simulation. Because the different parameters covary in nature, the sensitivity to changes in a single parameter will differ between the two approaches: changes in one variable are accompanied by changes in other variables sampled from their climatological covariation. In this paper, “covariability” refers to the effects of these secondary correlations on changes in the evolution of the cloud and, in particular, on the time of its breakup. In section 3c, we quantify and compare the dissipation time trends obtained by the different approaches. Section 4 contains the conclusions. For an easier reading, a nomenclature is included in appendix A.

2. Methods

a. Mixed-layer model framework

The MLM used in this study follows the implementation of Ghonima et al. (2016) (refer to appendix B for further details). In the MLM, the state of the well-mixed ABL is described by three prognostic equations and several parameterizations. The prognostic equations determine the evolution of the thermodynamic state of the ABL, described by the ABL thickness or inversion-base height zi, the mean liquid water potential temperature in the ABL θlBL, and the mean total water content in the ABL qtBL. Cloud thickness h depends on these three variables, where the cloud-top height is also zi and the cloud-base height depends on θlBL and qtBL. The growth of zi depends on the balance between the entrainment of upper air and large-scale subsidence. Changes in θlBL depend on the balance of radiation and turbulent fluxes, while the evolution of qtBL is only determined by turbulent fluxes (precipitation is not considered). Consequently, changes in h are affected by all these factors. Aside from the governing equations, parameterizations in the MLM allow quantifying radiation, entrainment of upper air, large-scale subsidence, and turbulent fluxes at the surface and top of the ABL.

Since we are interested in cloud dissipation over coastal land, a Eulerian framework is preferred, which introduces advection tendencies in the prognostic equations. To account for this effect, we model the evolution of two columns: one over the ocean and the other over land, as illustrated in Fig. 1. The dominant wind direction in this region is from the ocean to the land, during day and night, as a consequence of the North Pacific subtropical high and the continental U.S. thermal low during the summer (Halliwell and Allen 1987). Therefore, advection is considered only for the land column, and the advection terms depend on both ocean and land conditions (appendix B).

Fig. 1.
Fig. 1.

Two columns are simulated to account for sea-breeze advection. Ocean and land column states are described by their height zi, moisture qt(z), and temperature θl(z), from which the liquid water profile ql(z) and cloud-base height zb can be derived. Ocean and land have different surface flux conditions, with the ocean having prescribed fluxes of LHF and SHF, while over land the net surface radiative flux F0 is partitioned using a Bowen ratio Bo. At the cloud top, both columns are affected by the net radiative flux Fi and entrainment fluxes that depend on the inversion jumps. Entrainment mixes air into the columns at a rate we, while subsidence reduces column height at a rate wsub. The properties of the ocean column are advected onto the land column with a wind speed u and considering a distance Δx [see Eq. (B5)].

Citation: Journal of the Atmospheric Sciences 77, 8; 10.1175/JAS-D-19-0254.1

For this study, we are specifically interested in the effect of different variables on cloud dissipation. We accordingly select relevant meteorological variables used by the equations and parameterizations in the MLM. The variables determine the initial conditions and boundary forcings during the simulation. Initial condition variables include the inversion-base height zi, as well as the ABL values of liquid water potential temperature θlBL and total water mixing ratio qtBL, that determine the initial cloud thickness h. Thermodynamic values above the ABL are also part of the initial input, including values at 3 km (θl3km and qt3km) and inversion jumps (Δiθl and Δiqt), which are assumed to occur over an infinitesimally thin layer (Lilly 1968).

The parameters used to determine forcings include large-scale, radiative, and turbulent processes. The large-scale parameters are the ABL large-scale divergence D that determines the subsidence rate at the top of the ABL wsub [Eq. (B2)], an average wind speed u¯ for the advection tendencies (appendix B), and SLP. The radiation parameterization has shortwave and longwave components (section d of appendix B), where the solar irradiance above the cloud SWi along with the cloud properties will determine the shortwave net radiation flux. For the longwave component, the sky effective radiative temperature Tsky represents the longwave radiation gain from the sky above the ABL. Last, turbulent fluxes exist both at the surface and the top of the ABL (section e of appendix B). Surface fluxes depend on the type of column: for the ocean, we prescribe sensible and latent heat fluxes (SHF and LHF) as daily averages, and for the land, we prescribe a Bowen ratio Bo that partitions the sensible and latent heat fluxes. At the top of the ABL, the turbulent fluxes are determined by the inversion jumps Δiθl and Δiqt along with the entrainment rate we. Last, entrainment mixes air from the free troposphere into the ABL through turbulence, which results from a complex combination of radiative cooling, evaporative cooling, and wind shear, among other processes (Mellado 2017). In the MLM, the entrainment parameterization depends on most of the other variables described (section c of appendix B). Entrainment acts as a regulating mechanism in response to cloud thickness as it promotes thinning for thicker clouds (Zhu et al. 2005). Entrainment also favors dissipation over land as larger surface fluxes increase we and both surface fluxes and entrainment promote ABL heating, thinning the cloud.

A comment on the choice of the data/modeling tool for the analysis is in order. We use a MLM because it allows a comprehensive sensitivity analysis in an idealized geometry. Conversely, real observations would introduce unknowns, uncertainties, and errors. For example, real 3D topography affects dissipation time due to differential heating and differences in boundary layer height, while the MLM allows removing these effects. Another example is that boundary layer heights are only observed twice per day in reality while the MLM provides a detailed evolution. A detailed discussion of the benefits of the MLM framework is provided in appendix D.

b. Data

To study how different variables influence Sc dissipation time, we created a comprehensive dataset with realistic Sc conditions for the years 2014–17 in Southern California. It is important to consider realistic conditions to understand if the influence of a variable is actually observable/relevant, as well as to understand which variables need to be measured/obtained to improve cloud dissipation predictions. The dataset contains the variables needed in the MLM: inversion height zi, liquid water potential temperature θl(z) and total water mixing ratio qt(z) profiles, ABL large-scale divergence D, average wind speed u¯, Bowen ratio Bo, incoming solar irradiance above the cloud SWi, sky effective radiative temperature Tsky, SLP, and ocean SHF and LHF. The months of May–September are selected as they constitute the Sc cloud season, and also when the highest solar irradiance is available. The variables are obtained from different sources including radiosondes, numerical weather prediction (NWP) model outputs, observations, and radiative models. Further details are provided in appendix C.

ABL thickness zi and profiles of liquid water potential temperature θl(z) and total water mixing ratio qt(z) are processed from radiosonde data to be compatible with the MLM framework (section b of appendix C). We analyze early morning radiosondes at the NKX Miramar Marine Corps Air Station in San Diego, California. First, the inversion-base height zi is detected as the starting point of the largest temperature inversion. Next, we check if the state of the ABL could be decoupled using the criterion |θυbθυ0| > 1 K (Ghate et al. 2015), where θυb and θυ0 are the virtual potential temperature at the radiosonde cloud base [the point where the relative humidity (RH) exceeds 95%] and at the surface, respectively. Decoupled cases are discarded because the MLM cannot describe the ABL physics appropriately. For the remaining cloudy cases, the state of the ABL is averaged to create a well-mixed profile described by θlBL and qtBL. Last, the free troposphere is included by considering data above the inversion region up to 3 km. While moisture above the inversion is assumed to be constant and represented by an average value of total water mixing ratio qt3km and a sharp inversion jump of total water mixing ratio Δiqt, the liquid water potential temperature is fitted into a linear profile and represented by the value of the fit at 3 km θl3km and by the sharp inversion jump Δiθl. Figure 2 shows an example of the processed well-mixed ABL structure. Since the initial state is derived from the radiosonde launched at 0300 LST (1100 UTC), we use that time to initialize the simulations. Furthermore, we assume that this early state is representative of both ocean and coastal land and thus, start the MLM with the same initial condition for both columns. This assumption is justified as the region experiences a sea breeze during day and night and nighttime surface radiative cooling over land is small due to the Sc cloud cover.

Fig. 2.
Fig. 2.

Mixed-layer idealization for 21 Jul 2014. We detect the inversion region from radiosonde data (gray), and compute a well-mixed profile (black) by averaging properties in the ABL and tropospheric regions. The well-mixed profile is compatible with the MLM.

Citation: Journal of the Atmospheric Sciences 77, 8; 10.1175/JAS-D-19-0254.1

The radiation model in the MLM depends on SWi for the shortwave and Tsky for the longwave radiation fluxes. For obtaining SWi, we assume that there are no other cloud layers overhead—typical for the summer season in Southern California (Christensen et al. 2013)—and calculate the daily maximum of global horizontal irradiance (GHI) from a clear-sky model (Ineichen and Perez 2002). For obtaining Tsky, we solve for the longwave radiative fluxes across the whole atmosphere by inputting the temperature profiles from the radiosonde into the Streamer radiative transfer model (Key and Schweiger 1998) and calculating Tsky as the blackbody temperature from the longwave downwelling flux at the top of the cloud (section c of appendix C).

We estimate u¯ and SLP from measurements at the NKX METAR weather station. We compute u¯ as the average of the westerly wind speeds between 0500 and 2100 LST and scale a 10-yr average daily profile to recreate the diurnal cycle (see Fig. C1b). This daily profile never reaches zero, so advection is continually present during the day (section e of appendix C). We compute SLP as a daily average.

For the turbulent fluxes at the surface, we take different approaches for the ocean and land columns. For the ocean column, the prescribed values of SHF and LHF are computed with a bulk formula (section e of appendix C) from observations of wind speed u¯ and daily averages of SST at the Torrey Pines Outer station obtained from the National Data Buoy Center (NDBC) (NOAA 2017). For the land column, we estimate a daily Bowen ratio Bo at NKX by analyzing in-house operational runs of the Weather Research and Forecasting (WRF) Model. Bo is computed as the ratio between SHF and LHF at the nearest grid point to the NKX station, averaged between 0800 and 1500 LST (section d of appendix C).

Last, we estimate large-scale divergence D from the North American Mesoscale Forecasting System (NAM) as the partial derivative of pressure vertical velocity ω with respect to pressure in the ABL (section d of appendix C).

c. Steady thickness initialization

The MLM is initialized at 0300 LST prior to sunrise, when we expect a stable Sc behavior. Nevertheless, we occasionally observed large changes in modeled cloud thickness in the first few hours after initialization but still prior to sunrise, indicating possible inconsistencies in the initial state. For reference, Duynkerke et al. (2004, their Fig. 4) observed ΔLWP/Δt tendencies of 2.8 and 7.6 g m−2 h−1 at 0300–0400 LST. In contrast, the first-hour average of ΔLWP/Δt for our preliminary MLM runs ranged between −42 and 12 g m−2 h−1.

The reasons for large model tendencies following initialization are multifold: (i) the well-mixed approach fits the radiosonde data to a slightly different state (Fig. 2); (ii) radiosonde measurement errors, especially in the humidity measurement; (iii) LWP is not measured and has to be derived using a crude model [LWP=0ziρ(z)ql(z)dz, where ρ(z) is the density of air]; (iv) the MLM does not adequately describe all ABL physics; and (v) uncertainties in the estimated large-scale divergence. Since the variable interdependencies will be studied as a function of the initial conditions, it is important that the initial conditions are representative of the first few hours of the simulations. While initial variables should reflect real conditions as much as possible, our main objective is to understand the sensitivities of Sc evolution. Therefore, a stable, self-consistent MLM initialization is the priority and slight deviation from measured conditions when needed is tolerated. The steady thickness initialization (STI) method was developed to create a stable initial condition from the measured profiles.

We seek a more stable state by keeping zi constant and varying the set of thermodynamic variables s(θlBL,Δiθl,qtBL,Δiqt). For mathematical consistency, the tropospheric mixing ratio qt3km will also be modified (since it is the sum of ABL and inversion jump quantities). We do not seek a state with zero tendency because (i) we want to avoid deviating too much from the original state, (ii) there is no unique value of s that satisfies the steady thickness condition (van der Dussen et al. 2014, their Fig. 3), and (iii) it has been observed that the zi tendencies at dawn are small but not zero. Instead, we seek for a close, more stable state s by thresholding the rate of change of thickness:

|ht|=|zitzbt|<5×103[ms1].

Using an iterative gradient descent method the four variables change at the same time [Eq. (2)], in an amount proportional to the local gradient of the thickness tendency:

sn+1=snsgn[ht(sn)]ξht(sn),

where ξ is the proportionality constant used to follow the gradient; ξ = 0.1 yielded satisfactory results for most days. We compute the gradient with second-order central finite differences using a step of 0.1 K or 0.1 g kg−1 in each component of s and iterate until the thinning or thickening is less than 5 mm s−1 [Eq. (1)]. An example of the effect of the STI is shown in Fig. 3. The strong thinning experienced in the first hour of simulation with the original initial conditions is greatly reduced, and the STI initial conditions yield −6.4 < ΔLWP/Δt < 12 g m−2 h−1, in better agreement with observations in Duynkerke et al. (2004, their Fig. 4).

Fig. 3.
Fig. 3.

Effect of the steady thickness initialization (STI) for 21 Jul 2014. The changes to the original sounding (dashed lines) for (a) θl(z) and (b) qt(z) are shown in solid lines. MLM simulated cloud boundaries zi and zb for the (c) ocean and (d) land column for the original properties and the modified STI.

Citation: Journal of the Atmospheric Sciences 77, 8; 10.1175/JAS-D-19-0254.1

Finally, we remove STI states that lie far from the original using a squared distance threshold:

d2=i=14(siSTIsisi)2=0.005,

where si and siSTI are the components of s prior and after the STI method is applied, respectively. Twelve cases are removed in this way. For the final set of 195 cases used in the analysis, 115 cases were not modified by the STI, as the original state was already steadier than 5 mm s−1, and for the 80 cases that were modified, the average d2 was 0.0007.

d. Model runs

The STI-adjusted dataset becomes the new input to the MLM. The initial conditions are the STI thermodynamic profiles derived from the radiosonde. The other variables are related to forcings at the boundaries of the ABL, such as airmass advection and fluxes at the surface and inversion levels. The MLM predicts the evolution of the cloud and yields the cloud dissipation time over land. Simulations are terminated when clouds dissipate because the increase in solar heating of the ABL prevents cloud reformation until evening and because several model assumptions (e.g., the entrainment calculation) are no longer valid.

e. Data subsetting

Some of the original 278 cloudy and not decoupled days produced results inconsistent with the MLM assumptions: (i) STI leading to a cloudless state; (ii) negative entrainment values that may be related to decoupling (section c of appendix B); (iii) clouds whose base reached the surface during the simulation (the longwave radiation scheme in the MLM may not represent fog conditions accurately); (iv) otherwise extremely thick clouds that could precipitate (precipitation is not modeled in the MLM), using a threshold of LWP = 250 g m−2; and (v) days with precipitation at the METAR station. After filtering these cases out, we were left with a dataset of 195 days.

f. Sensitivity analyses

1) All variables covary on 195 real days

We analyze the results of the MLM runs for the diverse conditions of 195 days that span a broad range of the parameter space and display covariability. We investigate the trends in dissipation time over land tdiss in relationship to each one of the variables of interest.

2) Single-variable changes from a reference case

The results of the cases with covariability can be difficult to analyze, as different impacts can be enhanced or diminished by the combination of different variables. To aid the understanding of the covariability analysis, we first identify the individual influence of each variable on dissipation time through a traditional sensitivity analysis. We vary one variable at a time from an idealized reference case composed of the medians of all the MLM input variables: zi, qtBL, Δiqt, qt3km, θlBL, Δiθl, θl3km, u¯, SWi, D, Bo, SLP, Tsky, SHF, and LHF. The purpose of using this idealized reference case is to be able to change most variables in their observed ranges. A set of five equidistant points between the percentiles p25 and p75 of the observed distribution for that input variable is simulated.

The other 14 variables are held constant with the following exceptions: (i) Δiqt and the tropospheric mixing ratio are varied together for self-consistency [Eq. (C3)]; (ii) zi is varied following two approaches: (ii-a) variations of zi alone, which yields different cloud thicknesses, and (ii-b) variations of zi with constant cloud thickness obtained by adjusting qtBL; (iii) variations of cloud thickness h with constant zi and θlBL obtained by adjusting qtBL.

The motivation for (ii-b) is to assess the changes of zi without the feedbacks related to the abrupt change in cloud thickness. We refer to (ii-b) as varying zi|h, and we calculate the adjusted qtBL(zi|h) using zb/qtBL [Ghonima et al. 2015, their Eq. (15)] [Eq. (3)]:

(qtBL)new=(qtBL)old+Δziqtzb=(qtBL)old[1+gRdTb(1LlvRdCpRυTb)Δzb],

where (qtBL)new is the value of moisture needed for the updated height (zi)new with respect to the original (qtBL)old. For varying zi|h, h is constant and Δzb = Δzi = (zi)new − (zi)old is the change in cloud thickness from the reference case, with (zi)old the reference case inversion-base height. Tb is the temperature at the original cloud-base height.

Similarly, the motivation for (iii) is to assess the changes of h without the effects of varying zi. We refer to this case as varying h|zi, and the adjusted qtBL(h|zi) is obtained with Eq. (3), taking Δzb = −Δh = (h)old − (h)new because zi is constant. Here, (h)old is the cloud thickness for the reference case and (h)new is the updated cloud thickness.

3. Results and discussion

a. Data statistics and correlations

We present a description of the most important intercorrelations within the dataset, which is crucial for understanding the results of the impacts when all variables covary. Table 1 shows the main statistics, including diagnostic variables from the MLM (cloud-base height zb, cloud thickness h, inversion jump of virtual potential temperature Δiθυ, and liquid water path LWP) and for the well-mixed profiles before and after STI. In the remainder of this section, we describe the main correlations (Fig. 4), distinguished by the nature of their relationship (seasonal trends, initial conditions, and boundary forcings). We emphasize that initial conditions are prior to sunrise and represent both coastal land and ocean conditions.

Table 1.

Statistics for the variables considered in the MLM initialization and complementary variables for describing the cloudy states, corresponding to the 195 available days. Original and STI-derived states are included.

Table 1.
Fig. 4.
Fig. 4.

Correlation coefficient matrix for variables spanning the 195 selected days grouped by their relationship: (a) seasonal trends, (b) initial conditions, (c),(d) boundary forcings divided into two figures for easier presentation—(c) wind and surface fluxes variables and (d) large-scale and radiation parameters. The sign is representative of each correlation coefficient.

Citation: Journal of the Atmospheric Sciences 77, 8; 10.1175/JAS-D-19-0254.1

Given the large number of variables, principal component analysis (PCA) would seem to be a relevant tool. We do not report PCA results for this dataset because the reduction of dimensions is limited (it takes 10 variables to explain 90% of the variance) and the resulting parameter space is nonphysical.

1) Variables affected by seasonal trends

Our dataset includes measurements taken between May and September, a time span that is long enough to show seasonal patterns that influence the correlation between some variables (no detrending is performed in this dataset). While solar irradiance above the cloud SWi varies during the year, peaking on June 21, the set of temperature variables SST, θlBL, and Tsky peak in early August. The time lag between SWi and the temperature variables is influenced by the seasonal pattern of SST, which in turn is affected by the oceanic upwelling that is stronger during June and July for Southern California (Clemesha et al. 2016) as well as the thermal inertia of the ocean. The time lag is long enough to cause a negative correlation between temperatures and SWi as shown in Fig. 4a.

The strong correlation between SST and θlBL results from the strong influence of ocean SST on the early morning coastal air temperature through horizontal advection.

2) Variables that determine initial conditions

The initial state, prior to sunrise, comprises zi, qt(z), and θl(z), which together determine h. By definition, a warmer ABL that is cloudy is at (in-cloud) or near (below-cloud) saturation and can contain more water due to the Clausius–Clapeyron relationship; this makes θlBL and qtBL highly correlated. Conversely, conditions that are warm and dry (causing a negative correlation) are less likely to sustain a cloud and are therefore underrepresented in the dataset.

Inversion-base height zi is strongly anticorrelated with qtBL; a deeper ABL is associated with lower temperature at the inversion base, requiring less water content to be present to saturate and form a cloud. Entrainment also supports this relationship, as prolonged or stronger entrainment can result in deeper ABLs and a lower qtBL. Interestingly, the relationship between the primary 3 ABL variables qtBL, zi, and θlBL is observed to be linear (R2 of linear fit is 0.945; Fig. 7a) and closely follows saturation conditions (see appendix E). Although a linear relationship exists, only two of the three pairs are correlated, as zi and θlBL do not correlate; therefore, qtBL acts like a dependent variable.

Cloud thickness h is defined as the difference between cloud top zi and cloud base zb heights. One might expect lower cloud base to mean greater cloud thickness, but instead variations in cloud thickness are dominated by variations in ABL-top height (deeper ABLs have more room for thick clouds). The correlation between zi and qtBL causes thicker clouds to be strongly associated with smaller qtBL. Cloud thickness is also strongly correlated with Δiθl because a stronger temperature inversion limits the entrainment of drier and warmer air into the ABL, which thins the cloud. Figure 4b shows that both zi and Δiθl influence h. Although the linear correlation coefficient is only 0.61, both variables combined explain nearly all the variance in h: ABLs with lower (higher) tops and weaker (stronger) capping inversions are related to thinner (thicker) clouds. Note that Δiθl and zi are not correlated in our dataset (Fig. 4). While this may seem counterintuitive as strong LTS has been linked to shallower ABLs (Klein and Hartmann 1993), LTS not only depends on Δiθl but also on zi. Following Wood and Bretherton (2006), the correlation coefficients of zi and Δiθl with LTS are −0.48 and 0.84, respectively.

For the tropospheric quantities, qt3km correlates with qtBL: a smaller qt in the ABL is related to a smaller qt above. The same logic explains the correlation between θl3km and θlBL.

3) Variables that determine boundary forcings

Here, correlations between parameters that specify the boundary forcing of the ABL from above and below are described. Large-scale subsidence, represented by the horizontal divergence D, is weakly correlated with zi even though subsidence pushes the ABL top down. At −0.08, the correlation coefficient is small, which could be related to errors in estimating divergence, or to the different values of entrainment that also affect zi, or due to time lags/phase shifts between when changes in D affect zi, thus weakening the correlation between the two variables. From Myers and Norris (2013), we would expect subsidence to also influence Δiθl, but the correlation between D and Δiθl is weak. This disagreement may be explained also by the variables being out of phase and by the exclusive use of well-mixed Sc-capped ABLs in our dataset [vs all ABLs in Myers and Norris (2013)], since other ABL types tend to be associated with smaller D and smaller Δiθl.

Surface fluxes affect both temperature and moisture in the ABL. Over the ocean, LHF and SHF correlate with u¯ by definition [Eqs. (C8) and (C9)]. LHF is correlated with zi while SHF is not. A larger LHF was also related to a larger zi in (Bretherton and Wyant 1997) probably because a larger LHF is related to a smaller qtBL (by definition), which in turn correlates to a larger zi. In contrast, SHF depends on θlBL, which is not correlated to zi.

Over land, Bo is negatively correlated to qtBL as an ABL with stronger surface latent heat fluxes causes both a larger qtBL and a smaller Bo. Secondary variable correlations (qtBL to θlBL and zi) explain the correlation of Bo to θlBL and zi.

The last set of forcings are the radiative fluxes. For the shortwave portion, the yearly variations of solar irradiance causes SWi to be anticorrelated with temperature metrics [section 3a(1)]. For the longwave portion, Tsky is correlated with qt3km due to the longwave absorption and emission by water molecules above the cloud (Fig. C1a). Secondary variable correlations (qt3km to qtBL and zi) explain the correlation of Tsky with qtBL and zi.

b. Dissipation time dependence

We now review the results of the sensitivity analyses of modeled dissipation time, defined as the time when cloud thickness h becomes zero. The main focus of this section is to compare the covariability results of the 195 simulated days to the single-variable changes as well as previous studies. The discussion is subdivided into initial conditions and forcing parameters.

The covariability results for the 195 MLM simulations are shown in Fig. 5. The tdiss histogram (Fig. 5a) shows that clouds either dissipate before 1300 LST or persist for the whole day. We refer to these two categories as dissipating and persisting cases, respectively, so tdiss is defined for dissipating clouds only. Some of the variables influence tdiss, while others differ markedly between dissipating and persisting cases, and some show unclear trends or nonmonotonic tendencies. Figures 5b–r show the top 17 trends with linear fits for tdiss with R2 > 0.02 or with a noticeable difference between persisting and dissipating cases. Dissipation time is strongly related to h, zi, LWP, qtBL, Δiθl, Tsky, and oceanic SHF; while u¯, Bo, and D show weaker trends.

Fig. 5.
Fig. 5.

(a) The distribution of dissipation time tdiss over coastal land. (b)–(r) The effects of all variables on tdiss for all 195 days. Raw data (gray dots) and a linear fit (dashed black) are shown for the dissipating cases. Distributions (gray box plots) are shown for the persisting cases (marked as P in the tdiss axis), with boxes marking the 25th and 75th percentiles, a circle marking the median, and lines extending between the minimum and maximum values (excluding outliers).

Citation: Journal of the Atmospheric Sciences 77, 8; 10.1175/JAS-D-19-0254.1

The results for the single-variable changes from an idealized reference case while holding all other variables constant are shown in Fig. 6, where simulated dissipation time for the land column is plotted against the variables’ Z score (subtracting observed mean and dividing by the standard deviation) for ease of comparison. The idealized reference case corresponds to a coastal cloud that dissipates around 0800 LST (continuous line in Fig. F1 in appendix F).

Fig. 6.
Fig. 6.

Effect on dissipation time over land of the change of a single variable for the idealized reference case of observed medians. Variables are shown in terms of their Z score, computed by subtracting the observed mean and dividing by the observed standard deviation. (a) Changes of initial-condition variables one at a time, (b) changes of zi|h to maintain constant cloud thickness and the corresponding values of qtBL(zi|h), and changes of h|zi maintaining constant zi and the corresponding changes of qtBL(h|zi), (c) changes in advection and land surface forcing variables, and (d) changes in radiative, subsidence, and SLP variables. Some trends include less than five points as clouds were not present for some configurations.

Citation: Journal of the Atmospheric Sciences 77, 8; 10.1175/JAS-D-19-0254.1

1) Initial ABL state

The initial state of the ABL affects the dissipation time more than the forcing parameters. The components of the initial state are zi, qtBL, and θlBL, which have an intricate relationship [section 3a(2) and Fig. 7], and together determine h. Although h is not an explicit input variable to the MLM, we include it in the analysis because of its strong trend, the fact that it is readily observable, and its importance for entrainment and radiation.

Fig. 7.
Fig. 7.

Relationships between triads of variables: (a) qtBL in the plane described by zi and θlBL and (b) h in the plane described by zi and Δiθl. Gray dots are data points and contours are the best linear fit per the fit equation shown above each panel.

Citation: Journal of the Atmospheric Sciences 77, 8; 10.1175/JAS-D-19-0254.1

For all the approaches considered, h has the most robust relationship with tdiss, followed by zi. Thicker clouds or deeper ABLs either dissipate later or persist for the whole day. Similar to marine Sc (Burleyson and Yuter 2015), clouds that are thicker at dawn can withstand more solar heating and delay dissipation. For both h and zi, covariability weakens the single-variable change trends on tdiss (Figs. 5e,b and 6a) because the independent effects are diminished by the effects of the variables that covary with them, such as qtBL. For zi, the covariability trend is more similar to the experiment where cloud thickness is held constant by varying zi|h together with qtBL (Fig. 6b). This means that even when we control for the strong effects of h, other variables with weaker independent trends also impact the final trend for zi. The trends for h and zi imply a strong trend for LWP as well (Fig. 5q). Since zi and h are correlated, we analyze the trend of tdiss with respect to both variables. Figure 8b shows that dissipation time varies with both h and zi, but it is more strongly correlated with cloud thickness.

Fig. 8.
Fig. 8.

Two-dimensional variable spaces for (a) zi and qtBL, (b) zi and h, (c) zi and Δiθl, and (d) u¯ and h. Data are classified by cases that persist for the whole day (black asterisks, 38 cases) and cases that dissipate during the day (dots colored by dissipation time, 157 cases).

Citation: Journal of the Atmospheric Sciences 77, 8; 10.1175/JAS-D-19-0254.1

While colder ABLs are related to later dissipation, as expected, moister ABLs dissipate earlier with covariability. For θlBL, the trend with covariability (Fig. 5c) is weaker than for the single-variable changes (Fig. 6a), and for qtBL, the trend with covariability (Fig. 5d) is completely opposite to the single-variable changes (Fig. 6a). This seeming contradiction is actually in agreement with the strong correlations observed between larger qtBL and both lower h and zi and larger θlBL, which shorten cloud lifetime.

The fact that qtBL does not dominate the trend with covariability also agrees with the linear dependence of qtBL on zi and θlBL [section 3a(2)], and with the cloud thickness regulation feedback. Cloud thickness is regulated toward an equilibrium state in that thicker clouds enhance cloud radiative cooling and entrainment, which in turn thin the cloud and regulate h (Zhu et al. 2005). At nighttime, thinner clouds will experience weaker entrainment due to the regulating feedback, keeping the ABL moister and shallower and supporting the negative correlation between zi and qtBL, and between h and qtBL. For these initially thin clouds experiencing reduced entrainment, we expect a shorter cloud lifetime, which agrees with the trend of weaker first hour initial entrainment rates we,1h¯ and earlier tdiss (Fig. 5p). Last, Fig. 8a visually shows the lack of dominance of qtBL on tdiss when compared to zi: the gradient of dissipation time, as well as the region of persisting clouds, are more strongly correlated with zi than qtBL, meaning that the trend between qtBL and tdiss in Fig. 5d is a consequence of the anticorrelation between zi and qtBL.

2) Inversion jumps and free-tropospheric conditions

While the inversion jumps and free-tropospheric state are part of the initial conditions, we analyze them separately because they represent the interaction between the ABL and free troposphere, rather than the ABL state. Stronger temperature inversion jumps Δiθl and weaker moisture inversion jumps Δiqt (moister troposphere) delay dissipation time (Figs. 5f,g), in agreement with most previous studies.

The effect of stronger temperature inversion jumps Δiθl agrees with the result for the single-variable changes (Fig. 6a) for our reference case. Ma et al. (2018) obtained a Δiθl trend that opposed ours and that of Xu and Xue (2015), and argued that the impacts of the temperature inversion jump might depend on the reference case selected. There are competing effects of Δiθl: while a stronger temperature inversion jump reduces the entrainment rate, it also means that the entrained air is warmer. Mathematically, the net warming heat flux is the product of a reduced entrainment rate and a stronger inversion jump, and the direction of the effect for the product could vary for different conditions [Eq. (B15)]. For our reference case, the diminished entrainment rate dominates the over the warmer entrained air, delaying the dissipation by maintaining the ABL moister and colder over land and ocean (Fig. F1a). Our results with covariability support the trend of Xu and Xue (2015) and van der Dussen et al. (2015), as well as the trend of increased cloudiness with stronger Δiθl in previous climate studies (Seethala et al. 2015; Klein and Hartmann 1993; Klein et al. 1995; Wood and Bretherton 2006). Nonetheless, we note that persisting clouds do not predominantly exhibit stronger inversion jumps.

As was the case with h, the influence of Δiθl on tdiss is not dominated by zi. This is evident in the two-dimensional space of zi jointly with Δiθl. Figure 8c shows that earlier dissipation (persisting clouds) occurs for shallow (deeper) ABLs under a weak (strong) inversion, which also corresponds to the conditions for thinner clouds shown in Fig. 4b.

For moisture, weaker inversion jumps Δiqt (relatively moister free troposphere) are linked to persisting clouds, although dissipation time (as a continuous variable) is not strongly correlated to Δiqt (Fig. 5g). The trend is consistent with the single variations due to reduced entrainment drying (Fig. 6a), in agreement with the LWP responses reported by van der Dussen et al. (2015), Xu and Xue (2015), and Ma et al. (2018).

At first glance, the covariability trends of Δiqt and qt3km seem contradicting: weaker Δiqt (relatively moister free troposphere) and also lower qt3km (drier free troposphere) lead to persisting clouds (Figs. 5g,h). However, a weaker Δiqt is only a free troposphere that is similar in moisture to the ABL, and not necessarily a moister free troposphere. Thus, a very dry free troposphere can have a weak inversion jump if the ABL is also dry. Nevertheless, the trend of a dry troposphere extending dissipation time is still unexpected since it opposes the single-variable changes (Fig. 6a). The strong correlations between drier qt3km to higher zi and lower Tsky, both of which extend cloud lifetime, explain the trend. Previous studies have related a moister free troposphere to reduced cloudiness (Dal Gesso et al. 2014; Seethala et al. 2015), where the latter (correctly) speculated that correlations rather than physical processes are responsible for the trend.

The combined effects of moisture and temperature inversion jumps have been studied for the cloud-top entrainment instability (CTEI), a process that can trigger cloud dissipation (Deardorff 1980; Kuo and Schubert 1988; van der Dussen et al. 2014; Xu and Xue 2015). Even though the stability parameter criterion κ ≥ 0.23 was found to be insufficient to predict the CTEI, Fig. 5r shows a trend between larger κ and earlier dissipation, suggesting that CTEI could be contributing to cloud dissipation for larger κ. Nevertheless, the great dispersion precludes us from stating this conclusively (R2 = 0.03).

Similarly to qt3km, θl3km has a stronger effect with covariability than in the single-variable changes (Figs. 5i and 6a). The enhanced effect of θl3km can be explained by the strong correlation to θlBL.

3) Sea-breeze advection

Since sea-breeze advection is crucial in extending the lifetime of coastal Sc (Ghonima et al. 2016), a robust trend between u¯ and tdiss is expected, as shown by the single-variable changes (Fig. 6c). In actuality, the trends with covariability show u¯ exhibiting a nonlinear behavior where larger wind speeds are associated with both persisting clouds and early dissipation time (Fig. 5j).

The nonlinear trend of u¯ is not related to the physics, but it is caused by a sampling issue. To explain this misleading trend, we look at the influence of initial cloud thickness on the relationship between u¯ and tdiss. Figure 8d shows first that h dominates the dependence of dissipation time in the u¯ and h space. Second, separating analyses for thick (h > 150 m) and thin clouds is enlightening. Thicker clouds persist with larger u¯, as expected, and the critical wind speed for clouds to persist decreases with greater initial cloud thickness. For thinner clouds, the dissipation time is not affected by u¯. Since the persisting clouds are not part of the trend lines in Fig. 7, a misleading anticorrelation of wind speed and dissipation time is observed. This analysis suggests that advection is irrelevant for thin clouds as they already dissipate before the onset of advection around 0700 LST. Advection does play an important role for thicker clouds that survive through the weak advection period, which then benefit from the cooling associated with stronger advection. This effect was not observed by Ghonima et al. (2016) as they only analyzed two reference cases with the presence or absence of sea breeze.

Another aspect that could cause our results to deviate from real observations is the wind speed input for the MLM. For ease of comparison, we have assumed that the wind speed for all 195 days has the same diurnal variation (i.e., the onset of sea breeze is fixed, but the magnitude changes). However, we speculate that the timing of the sea-breeze onset may be as or more important than the wind speed magnitude. By 0800 LST, when the wind speed increases in our simulation (Fig. C1b), 116 days are already clear or have clouds that are already so thin that the heat input from solar radiation dominates over cooling from horizontal advection. For these early morning dissipation cases, the wind speed is irrelevant. This timing dependence was also mentioned by Burleyson and Yuter (2015) for marine Sc, as cloud breakup rates strengthen near noon.

4) Surface fluxes

For coastal Sc clouds, both the surface fluxes over the ocean and over land can affect the cloud evolution. A larger SHF over the ocean is linked to earlier dissipation time, agreeing with previous studies for marine Sc (McMichael et al. 2019; Chlond and Wolkau 2000). The effect of SHF under covariability is greater than for the single-variable changes (Figs. 5k and 6c). In contrast, the influence of LHF on tdiss is weak with covariability, despite the existence of persistent clouds for larger LHF (Fig. 5l) supporting the trend of the single-variable changes (Fig. 6c). This difference between the effect of SHF and LHF suggests that the importance of the ocean fluxes, which influences coastal clouds through advection, may be greater for temperature than for moisture, agreeing with Ghonima et al. (2016).

Over land, the influence of Bo on dissipation time does not show a strong trend when covariability is considered, but persistent cases are related to higher Bo (Fig. 5m), contradicting Ghonima et al. (2016) and the trends of single-variable changes. This unexpected effect is a consequence of the correlation between Bo and qtBL.

5) Large-scale forcings

Subsidence is known to be of great importance for the evolution of Sc clouds. Stronger D reduces cloud lifetime by thinning the cloud from the top, and the clouds that persist have lower D (Fig. 5n), agreeing with the single-variable changes (Fig. 6d), as well as the response in LWP in previous sensitivity studies (McMichael et al. 2019; Ma et al. 2018; van der Dussen et al. 2016; Noda et al. 2014; Blossey et al. 2013) and the response in cloudiness for independent changes of subsidence (Myers and Norris 2013).

Aside from subsidence, SLP is an indicator of the synoptic conditions over the coast of California. Although there is not a robust impact of SLP on tdiss with covariability (not shown), we note that the physical impact of a smaller SLP yields later tdiss because—for constant θlBL—a colder temperature profile is needed to balance the change in pressure, resulting in a thicker cloud.

6) Radiative forcings

We have two radiation parameters of importance for dissipation of coastal clouds representing radiative cooling and solar heating. Stronger radiative cooling, represented by a lower Tsky, delays dissipation with the most robust trend of all the forcing parameters (Fig. 5o). This effect agrees with the single-variable changes (Fig. 6d) and previous studies (Kopec et al. 2016; Chlond and Wolkau 2000).

For the solar heating, SWi shows no clear trend with tdiss under covariability (not shown). Meanwhile, the effect observed for single-variable changes is that increased heating shortens cloud lifetime (Fig. 6d), as the additional heating of the cloud and the land surface accelerates dissipation. Although SWi was found to strongly influence the rate of cloud breakup for marine clouds (Burleyson and Yuter 2015), that effect may be reduced by the dominance of other factors such as ABL depth and cloud thickness.

c. Summary, quantification, and discussion of dissipation trends

Most of the impacts of different variables on cloud dissipation time over land were either diminished or increased when considering covariability, while others were unexpected due to the correlations among parameters related to forcings and initial conditions. In this section, we summarize and quantify the most robust trends when all variables covary and compare them to the trends resulting from changes in a single variable when all others are held constant.

The trends are expressed as δψ/δtdiss, quantifying how much change in a variable ψ is needed to delay tdiss by 1 h. Thus, the greater the number, the less sensitive tdiss is for that variable. For the analysis of changes with all variables covarying, we obtain one-dimensional linear fits for all dissipating cases. For the analysis of changes in a single variable from a reference case with all other variables held constant, we calculate the slope δψ/δtdiss also for all dissipating cases. We also compute trends for the two-dimensional space spanned by strongly correlated variables zi and qtBL as a two-dimensional linear fit of all the points to estimate the relationship between tdiss and the two variables (zi,qtBL) as

ΔtdissδtdissδziΔzi+δtdissδqtBLΔqtBL.

The results of the different methods are shown in Table 2. We acknowledge that for the single-variable changes the linear trend results depend on the reference case and only a single reference case is considered here. For the dissipation time trends when all variables covary, the different linear fits are also an approximation since the behavior is likely to be nonlinear based on the nonlinearities in the entrainment and radiation parameterizations. The estimated trends should be interpreted with caution, as they are marginal views of the behavior in the multidimensional space and other variables will naturally vary and contribute to the overall impact.

Table 2.

Comparison of dissipation time trends for different variables; single-variable changes from a reference case, and when all variables covary. Only the most robust trends are included.

Table 2.

The most consistent trend is the δψ/δtdiss response to changes in zi. A greater change of zi is needed to influence tdiss when all variables covary (163.9 m h−1) compared to when only zi varies and other variables are held constant (50.40 m h−1). The δψ/δtdiss response is least sensitive for changes in inversion-base height with cloud thickness held constant (zi|h, 320.9 m h−1) probably because the zi change is not reinforced by changes in initial h. For h, we find a similar effect of covariability, requiring greater changes (319.6 m h−1) compared to when only h|zi was varied (78.74 m h−1).

The impact of qtBL on tdiss is strong, but the different approaches yield contradictory trends, as discussed in section 3b(1). While the single-variable changes yielded a positive δψ/δtdiss response (0.359 g kg−1 h−1), the fit for qtBL when all variables covary (−2.826 g kg−1 h−1) and the fit in the 2D (qtBL, zi) space (−21.11 g kg−1 h−1) are both negative. Meanwhile, the constant cloud thickness analysis varying zi|h yields a similar value to the trend with covariability (−1.891 g kg−1 h−1).

The comparison of the sensitivity of dissipation time when a single variable changes to sensitivity when all variables covary highlights the difficulty in finding universal cloud response trends because of the multidimensionality and intercorrelations in the dataset. Changing a single variable ignores its correlations with other variables and may create unrealistic meteorological conditions. Simplified covariability, such as variations of zi|h together with qtBL to minimize feedbacks related to strong changes of cloud thickness, can yield more realistic trends. However, we are not able to isolate the unique influence of one variable on dissipation time when all variables covary, and the net effects are composed of all the correlated variable contributions. However, the trends in cloud dissipation time when all variables covary can quantify the marginal impact of a variable in the most realistic way, in the sense that it is what we would observe in nature if we were to measure a limited number of variables. Still, covariability effects are found to be too important to ignore, and thus, they should be considered in sensitivity analyses in order to improve prediction models.

The timing of dissipation may also affect the importance of some variables, as noted by Burleyson and Yuter (2015) in explaining why breakup rates of marine Sc are stronger in the late morning. Over coastal land, when tdiss is closer to noon, wind speed and solar irradiance are greater than in the early morning and the same relative change in these variables would cause a larger absolute change in advective cooling and solar heating. This dependence on dissipation timing could apply to all variables with diurnal cycles, such as u¯, Bo (as it is applied to surface fluxes over land), and SWi. In fact, Figs. 5j–o show that most cases resulting in early dissipation times are caused by a larger range of forcing variables than later dissipation times. Because of this spread in the early morning cases, the dissipation trends can be affected. Elucidating the extent of this impact is left for future work and it can indeed help to move forward to more realistic predictions.

While the physical processes described are consistent with the statistical results in this paper, simplifications may affect real dissipation trends: 1) The wind speed time series was simplified to allow a more standardized comparison. 2) Uncertainties exist in the estimation of D and Bo. 3) The ABL is assumed to be well mixed. 4) Decoupling is not considered in the MLM, which might influence the real trends related to zi and dissipation time even though cases that were initially decoupled were removed from the analysis. Even though this means that the prediction skill of the model is currently not sufficient to predict real dissipation times (as discussed in appendix D), it also means that the complex results obtained are a pure consequence of the covariability within the dataset. If covariability has such a great influence on the results of a simple model such as the MLM, it will probably have it to a greater extent in more complex models and in nature.

4. Conclusions

We have studied the effects of several variables on the predicted dissipation time of Sc clouds over a coastal region using a realistic dataset and a two column mixed-layer model. The dataset included 195 Sc days in the summers of 2014–17 in Southern California, with 15 variables acting as initial and forcing parameters in the MLM.

The main findings are summarized as follows:

  • This work confirmed the importance of initial ABL height and cloud thickness in coastal Sc dissipation, in agreement with the trends of cloudiness for marine Sc. If these two variables could be measured more accurately and time-resolved in coastal areas using lidar, solar forecasts in the area could be improved.
  • Covariability results, in which perturbations to one variable are accompanied by correlated variations in other variables related to initial conditions and forcings from a sample of 195 cloudy days, differ greatly from a traditional, single-variable sensitivity analysis. In most cases, covariability only strengthened or diminished the trend of a variable (albeit sometimes substantially), while in other cases the trend was the complete opposite.
  • For example, lower ABL total water mixing ratio and larger Bowen ratio delay cloud dissipation with covariability while they accelerate dissipation time as single variables or in previous studies (Ghonima et al. 2016).
  • Covariability also provides a different perspective on how sea-breeze advection can affect dissipation time compared to previous Sc studies over coastal land (Ghonima et al. 2016), affecting initially thinner clouds more than thicker ones.
  • Covariability effects are uniquely observable in our analysis and could not have been observed with a traditional sensitivity analysis. The use of a model instead of observed data ensures that the trends observed are solely a consequence of the covariability in the dataset and not of unknown or unobservable effects stemming from real-world complexities. Given the importance of covariability, modeling studies with sensitivity analyses should include covariability in the scenario generation.
  • Dissipation times predicted by the MLM correlate only weakly to observed dissipation times, likely due to the simplicity of the model.

Future work should examine correlations in other coastal Sc regions in order to study the extent of regional influence on the variables. Another topic of interest is the influence of realistic wind conditions on coastal dissipation time.

Acknowledgments

We thank E. Wu, H. Yang, B. Akyurek, and X. Zhong for helpful discussion and comments for this work. We thank the reviewers for their comments that improved the manuscript. MZZ is funded by CONICYT PFCHA/Doctorado Becas Chile/2015—72160605. The authors declare no conflict of interest. We thank Minghua Ong for editorial assistance.

APPENDIX A

Nomenclature

a. Roman symbols

A

In-cloud entrainment efficiency

ACBL

Convective ABL entrainment efficiency

A1, A2

Constants for the shortwave radiative flux

c1, c2

Constants for the longwave radiative flux

Cf

Bulk transfer coefficient for surface fluxes

Cp

Mean heat capacity of dry air in the ABL

d2

Squared distance for the STI method

D

ABL large-scale horizontal divergence

fw

Filter for westerly wind

F

Total net radiative flux

FLW

Net longwave radiation flux

FSW

Net shortwave radiation flux

g

Gravitational acceleration

h

Cloud thickness

k

Constant for the shortwave radiative flux

L

Mean latent heat of vaporization in the ABL

LW↓i

Downwelling longwave flux at zi

nbRH

Points below zbRH in the radiosonde

p

Pressure

p00

Reference pressure (1000 hPa)

q

Constant for the shortwave radiative flux

ql

Liquid water mixing ratio

qsat

Water saturation mixing ratio

qt

Total water mixing ratio

qυ

Water vapor mixing ratio

Rd

Specific gas constant for dry air

Rυ

Specific gas constant for water vapor

Ri

Bulk Richardson number

s

Auxiliary variable for the STI method

SWi

Shortwave irradiance above the cloud

tdiss

Predicted dissipation time

Tb

Temperature at cloud base

Tcld

Mean cloud temperature

Tsc

Mean temperature below cloud

Tsky

Effective sky temperature

u

Wind speed for large-scale advection

u(t)

Wind velocity vector

u¯

16-h average wind speed

wθl¯

Vertical turbulent flux of θl

wθυ¯

Buoyancy flux

wqt¯

Vertical turbulent flux of qt

w*

Convective vertical velocity scale

we

Entrainment rate

wsub

Subsidence rate

z

Height

zb

Cloud-base height

zbRH

Radiosonde cloud-base height

zi|h

Changes of zi maintaining constant h

zi

Inversion-base height

zi+

Just above inversion-base height

zit

Inversion-top height

b. Greek symbols

α

Constant for the longwave radiative flux

αw(t)

Wind direction

β

Constant for the shortwave radiative flux

γ

Constant for the longwave radiative flux

δψ/δtdiss

Change in ψ to delay tdiss by 1 h

Δx

Distance between ocean and land columns

ΔT

Temperature inversion strength

θ

Potential temperature

θl

Liquid water potential temperature

θυ

Virtual potential temperature

μ0

Cosine of the solar zenith angle

ξ

Tuning parameter for the STI method

Π

Exner function

ρ

Air density in the ABL

σ

Stefan–Boltzmann constant

τSW(z)

Cloud optical depth for shortwave radiation (zero at cloud top)

τLW(z)

Cloud optical depth for longwave radiation (zero at cloud top)

τLW,b

Cloud optical depth at cloud base for longwave radiation

ϕ

Conversion efficiency for land surface fluxes

ω

Pressure vertical velocity

h

Horizontal gradient operator

c. Abbreviations

Bo

Bowen ratio

GHI

Global horizontal irradiance

LHF

Latent heat flux at the ocean surface

LTS

Lower-tropospheric stability

MLM

Mixed-layer model

Sc

Stratocumulus

SHF

Sensible heat flux at the ocean surface

STI

Steady thickness initialization

SZA

Solar zenith angle

d. Subscripts and superscripts

ψBL

Well-mixed value of ψ in the ABL

ψ3km

Value of ψ at z = 3 km

ψ0

Value of ψ at the surface

ψb

Value of ψ at the cloud base

ψcld

Value of ψ evaluated in the cloud region

ψi

Value of ψ at the inversion base

(ψ)new

New value of ψ to maintain constant h

(ψ)old

Original value of the variable ψ

Δiψ

Inversion jump of ψ

APPENDIX B

Mixed-Layer Model

a. Governing equations

The state of the well-mixed ABL is described by inversion-base height zi, total water mixing ratio qt = qυ + ql, and liquid water potential temperature θlθLql/(CpΠ), where qυ is the water vapor mixing ratio, ql is the liquid water mixing ratio, Π=(p/p00)Rd/Cp is the Exner function, L is the latent heat of vaporization, Cp is the heat capacity of dry air, p is pressure, p00 = 1000 hPa, and Rd is the specific gas constant for dry air.

The governing equations of the MLM are the air mass, energy, and moisture balances [Eqs. (B1), (B3), and (B4)], which describe the average state of the ABL through the well-mixed variables qtBL and θlBL. In the airmass balance [Eq. (B1)], entrainment, subsidence velocity, and large-scale advection determine the evolution of the ABL depth zi:

zit=we+wsubuhzi,

where we is the entrainment rate, wsub is the subsidence rate, u is horizontal wind speed, and ∇h is the large-scale horizontal gradient operator. The subsidence rate at the top of the ABL, wsub, is parameterized by constant horizontal divergence D within the ABL:

wsub=D×zi.

In the heat balance [Eq. (B3)], turbulent fluxes, radiation, and large-scale advection drive the evolution of the temperature in the ABL:

θlBLt=z(wθl¯(z)+F(z)ρCp)uhθlBL,

where wθl¯(z) is the turbulent flux of liquid potential temperature and F(z) is the vertical profile of radiative flux.

In the total water content balance [Eq. (B4)], we do not consider precipitation fluxes and subsequently, only turbulent fluxes and large-scale advection are present:

qtBLt=zwqt¯(z)uhqtBL,

where wqt¯(z) is the turbulent flux of total water mixing ratio.

b. Horizontal advection

To describe ocean–land interaction, we model the evolution of two columns: one over the ocean and the other over land (Fig. 1). Due to the dominant wind direction from the ocean to the land, the ocean column model does not contain any advection terms, i.e., the last terms in [Eqs. (B1), (B3), and (B4)] are removed. For the land column, the advection terms depend on both ocean and land conditions:

uhθlBL=uΔx(θl,landBLθl,oceanBL),
uhqtBL=uΔx(qt,landBLqt,oceanBL),

where u is the wind speed and Δx = 30 km is the distance between the two columns. The associated coupling time scales Δx/u range between 1.3 and 3.6 h at noon, when the wind speed is maximum, and between 3.1 and 8.4 h at night.

c. Entrainment parameterization

The entrainment rate is parameterized through buoyancy flux contributions (Ghonima et al. 2016, their section 4b). The total entrainment rate is the sum of contributions from surface and cloud regions, where each amount is proportional to a convective velocity scale, w*, and inversely proportional to a bulk Richardson number, Ri:

we=we,0+we,cld=ACBLw*0Ri0+Aw*cldRicld=1.25ACBLΔiθυwθυ¯|0+2.5AhΔiθυzbziwθυ¯(z)dz,

where, at the surface, the constant ACBL = 0.2 (Deardorff 1976) is a clear convective boundary layer (CBL) entrainment efficiency, w*0 is the surface convective velocity scale, and Ri0 is the surface bulk Richardson number. For the cloud region, A is an entrainment efficiency coefficient (Grenier and Bretherton 2001) that includes evaporative enhancement effects, w*cld is a cloud convective velocity scale, and Ricld is the bulk Richardson number in the cloud region. Last, Δiθυ is the inversion jump of virtual potential temperature, and wθυ¯(z) is the buoyancy flux with wθυ¯|0 as its surface value. The buoyancy flux uses a vertical profile of dry and moist coefficients that were updated at each iteration and were calculated differently for the subcloud and cloud regions, following Cuijpers and Duynkerke (1993, their appendix A).

Some cases resulted in negative entrainment when using this parameterization, and were discarded from the analysis. When analyzing the entrainment rate, algebraic manipulation yields an explicit equation:

we=we,0+2.5AhΔiθυzbzi{C1[(1zzi)(wθl¯|0+F0ρCp)+zziFiρCpF(z)ρCp]+C2[(1zzi)wqt¯|0]}dz1+2.5AhΔiθυzbzizzi(C1Δiθl+C2Δiqt)dz,

where C1 and C2 are the moist coefficients. The denominator can be negative depending on the value of the integral. Assuming C1 and C2 are constants (which is a reasonable assumption), the criterion for negative entrainment becomes

h2zi(C1Δiθl+C2Δiqt)<Δiθυ2.5A,

which depends on many parameters and cannot be analyzed in a simple way. If we explore the condition for r.h.s. = 0, with referential moist coefficients C1 = 0.5 and C2 = 970 K (Ghonima et al. 2016, their section 4b), we obtain: Δiθl < C2/C1iqt| ≈ 1.94|Δiqt|. The CTEI criterion also relates the inversion jumps [van der Dussen et al. 2014, their Eq. (1)] and can be rewritten as Δiθl < 0.77L/Cpiqt| ≈ 1.915|Δiqt|. Both conditions are very similar, suggesting that the cases close to the critical CTEI criterion can yield negative entrainment rates when using this parameterization. Our physical interpretation is that for cases where negative subcloud fluxes should develop, the integrated buoyancy flux in the ABL cannot be described by the positive in-cloud buoyancy flux alone, resulting in an artificial negative entrainment velocity.

d. Radiative model

The net upward radiative flux includes longwave and shortwave contributions: F = FLWFSW:

FSW(z)=43SWi(qA1ekτSW(z)qA2ekτSW(z)βeτSW(z)/μ0)+μ0SWieτsw(z)/μ0,

where SZA is the solar zenith angle, μ0 = cos(SZA), τSW(z) is the cloud optical depth (zero at cloud top) [Duynkerke et al. 2004, their Eqs. (6) and (7)] calculated with an effective radius of 10 μm, A1 and A2 come from boundary conditions of the radiative transfer equation, and k, q and β are constants that depend on μ0 and optical properties of cloud droplets (Duynkerke et al. 2004, their appendix).

The longwave contribution FLW depends on three temperatures: Tsc taken as the mean temperature of the subcloud region; Tcld taken as the mean temperature in the cloud region, and Tsky taken as an effective radiative temperature of the sky:

FLW(z)=γσ[(Tcld4Tsky4)c1eατLW,b+(Tsc4Tcld4)c2]eατLW(z)+[(Tcld4Tsky4)c2eατLW,b+(Tsc4Tcld4)c1]eατLW(z),

where σ is the Stefan–Boltzmann constant, τLW(z) is the cloud optical depth [Larson et al. 2007, their Eqs. (6) and (7)], and τLW,b is the maximum optical depth (at cloud base). The parameters α, c1, c2, and γ are terms derived from the radiation transfer equation (Ghonima et al. 2016, their appendix B).

e. Surface and cloud-top fluxes

The surface fluxes of moisture wqt¯|0 and temperature wθl¯|0 depend on the type of the surface. For the ocean column, the SHF and LHF are fixed during the day. For the land column, the surface fluxes depend on the Bowen ratio Bo. A part of the net radiation flux at the surface F0 is converted into a moisture and a heat flux released to the ABL [Eqs. (B12) and (B13)]:

wqt¯|0,land=ϕ11+BoF0ρCp,
wθl¯|0,land=ϕBo1+BoF0ρCp,

where ϕ = 0.88 is the efficiency at which net radiation is converted into surface fluxes (Ghonima et al. 2016).

At the top of the ABL, the turbulent fluxes of moisture wqt¯|i and temperature wθl¯|i depend on the entrainment rate we and the sharp inversion jumps of moisture [Eq. (B14)] and temperature [Eq. (B15)], respectively (Lilly 1968):

wqt¯|i=weΔiqt,
wθl¯|i=weΔiθl.

APPENDIX C

Data

a. Variables

The parameterizations and equations included in the MLM determine our variables of interest. We gather data from different sources for the years 2014–17, May–September. In the following, variables are grouped by their data source.

b. Radiosondes: zi, θl(z), qt(z)

We obtain 1200 UTC radiosonde data (reported at 0400 LST, launched at 0300 LST) from the NKX Miramar Marine Corps Air Station in Southern California (32.85°N, 117.2°W). The station is located 10 km away from the coast, where the shoreline is aligned meridionally.

Radiosonde profiles are postprocessed into well-mixed layers to make them compatible with the MLM. First, temperature inversions in the lowest 3 km are detected. The largest temperature inversion is assumed to cap the mixed layer if it is sufficiently strong (ΔT > 3 K), yielding inversion-base and -top heights, zi and zit respectively. Clouds are assumed to exist where RH exceeds 95% below zi, with the radiosonde cloud base zbRH defined as the lowest point that meets that condition. Decoupled days cannot be represented in an MLM, and thus, we discard these days using the criterion |θυbθυ0| > 1 K (Ghate et al. 2015), where θυb and θυ0 are the virtual potential temperature at the radiosonde cloud base and at the surface, respectively.

The well-mixed qt [Eq. (C1)] is an ABL average of the radiosonde measurements. Since ql is not measured by radiosondes, qt will be underestimated, but in view of the limited resolution of the data and that qtql, this approach is reasonable. Above the inversion, we consider qt to be constant, and also compute it as an average up to 3 km:

qt(z)={qtBL=1zi0ziqυ(z)dzifz<ziqt3km=13kmzitzit3kmqυ(z)dzifzzi.

For θl(z), we follow a similar averaging approach [Eq. (C2)]. If there are more than 5 data points below zbRH, the average is computed in the subcloud region to avoid phase-change heating effects on θ(z); otherwise, all points in the ABL are averaged (including all the points is not a major concern for qt since qtql). Above the ABL, we obtain a linear fit for θ(zit < z < 3 km):

θl(z)={θlBL=1zi0ziθ(z)dzifz<ziandnbRH5θlBL=1zbRH0zbRHθ(z)dzifz<ziandnbRH>5az+bifzziwitha,bfrom linear fit forθ(zit<z<3km),

where nbRH is the number of points below zbRH.

We assume that the inversion occurs over an infinitesimally thin layer, defining the inversion jumps of total water mixing ratio and liquid water potential temperature:

Δiqt=qt3kmqtBL,
Δiθl=θl(z=zi+)θlBL,

where zi+ is just above the inversion height.

c. Radiative and clear-sky models: Tsky and SWi

We obtain the effective sky temperature Tsky for the longwave radiative model using the Streamer radiative transfer model (Key and Schweiger 1998). Inputs are the temperature and relative humidity soundings, which are extended to 100 km with a U.S. Standard Atmosphere, 1976. We compute Tsky as the blackbody temperature from the longwave downwelling flux at the top of the cloud as LWi=σTsky4. Figure C1a shows that skies with more water content experience a smaller net radiative cooling at the cloud top.

Fig. C1.
Fig. C1.

(a) Sky effective radiative temperatures for the dataset of 209 cloudy days as a function of water content above the cloud and below 3 km. The sky effective radiative temperatures were obtained with Streamer (Key and Schweiger 1998). (b) Climatological daily wind profile for the NKX station (10-yr average), showing the original wind speed profile and the wind speed normalized by its 16-h average.

Citation: Journal of the Atmospheric Sciences 77, 8; 10.1175/JAS-D-19-0254.1

For the shortwave radiation model, SWi is the solar irradiance incident on the top of the Sc cloud. We estimate SWi as the GHI from a clear-sky model (Ineichen and Perez 2002). Monthly climatological Linke turbidities for that location are input to the clear-sky model.

d. NWP models: Bo, D

We estimate the Bowen ratio Bo at NKX by analyzing in-house operational runs of the WRF Model using the Noah land surface model (Skamarock et al. 2008). Bo is the ratio between SHF and LHF at the surface at the nearest grid point to the NKX station. Hourly output is averaged between 0800 and 1500 LST to yield a (constant) daily Bo that is input to the MLM simulations. Land surface models in WRF are known to differ from measurements (Wharton et al. 2016); land surface models tend to produce Bo ≈ 1 with small temporal deviations.

We estimate large-scale divergence D from the NAM Forecasting System as the partial derivative of pressure vertical velocity ω with respect to pressure in the ABL. The differences are computed between 975 and 850 hPa [Eq. (C5)]. We average D spatially over an area of 21 grid points over the ocean around (38.15°N, 117.5°W) and then temporally with a 3-day moving average:

D=ωpω(975hPa)ω(850hPa)975hPa850hPa.

e. METAR and NDBC: u¯, SLP, SHF, LHF

For coastal regions in Southern California, the sea breeze acts during the day with a strong westerly component, usually beginning around 0800 LST and peaking around 1200 LST. A 16 h average (between 0500 and 2100 LST) wind speed u¯ is computed from the METAR weather station at NKX. All westerly winds (with direction between 180° and 360°) are scalar averaged:

u¯=116ht=0500LSTt=2100LSTfw[u(t)]dt,

where u(t) is the wind velocity with magnitude u(t) and direction αw(t) and fw[u(t)] is the filter for considering westerly directions only:

fw(u)={u(t)ifαw(t)(180°,360°)0else.

A 10-yr average daily wind profile is shown in Fig. C1b. The daily profile is normalized by its 16-h average wind speed and then rescaled with the daily u¯.

We estimate SLP as the daily average SLP at the METAR weather station at NKX.

Surface turbulent fluxes in the ocean column, which are fixed in the MLM, are computed from wind and sea surface temperature data. Daily averages of SST are obtained at the Torrey Pines Outer station from the NDBC (NOAA 2017). Surface fluxes are computed using a bulk transfer coefficient Cf = 1.2 × 10−3 (Blossey et al. 2013), the average SST and wind speed, and assuming that the temperature and moisture above the surface is the same as that of the initial state of the ABL:

SHF=ρCpu¯Cf(SSTθlBL),
LHF=ρLlvu¯Cf[qsat(SST)qtBL],

where qsat is the saturation mixing ratio.

APPENDIX D

Dissipation Time Comparison

We estimate dissipation time over NKX tdissSAT using a satellite derived low cloudiness product (Clemesha et al. 2016; Wu et al. 2018). This dataset has a 4-km spatial resolution and 30-min time resolution. We obtain tdissSAT at the closest pixel to NKX as the time when skies are clear for at least 1 h afterward. We neglect tdissSAT before 0500 LST since they are unlikely to be caused by Sc, which would thicken during the night.

We also estimate dissipation time tdissGHI from 1-s global horizontal irradiance data measurements at the UC San Diego campus, 5 km west of NKX (Zamora Zapata et al. 2019). Only Sc to clear transitions are included; a Sc cloud is assumed to exist if the early sounding is well mixed and has a cloud presence (RH > 95%), while also checking sky imagery at the time of the breakup to discard other cloud types or the presence of upper-level clouds. A tdissGHI event is recorded when the clear-sky index is close to 1 for the following 5 min.

There is a strong correlation between tdissSAT and tdissGHI (0.79, R2 = 0.6), while the correlation between MLM modeled dissipation time and tdissSAT and tdissGHI is 0.26 and 0.28 with R2 of 0.06 and 0.07, respectively.

Ideally the MLM dissipation times would be more correlated to the observed dissipation times. But given the MLM assumptions, parameter uncertainties, adjustment of initial conditions, and neglect of some physical processes, the relatively small correlation is not surprising. We maintain that the MLM based analysis of parameter correlations is valuable and superior to the alternatives. Strengths of the MLM application in this analysis include the following: (i) The MLM represents most of the physical processes. (ii) The MLM has been validated by Ghonima et al. (2016) against LES, demonstrating that the MLM is capable of correctly predicting the evolution of an idealized coastal Sc cloud. (iii) Initial conditions are approximated through elaborate sourcing from best available models and measurement sources. (iv) The simple geometric domain of the MLM prevents real-world complexities such as varying topography and 3D effects from affecting the results. (v) Simulation days are limited to conditions that are represented in the model, e.g., days with decoupling are removed. However, as evidenced by the need for adjustment of initial conditions, there are inconsistencies in the initial conditions and/or shortcomings in the model. As a result, the MLM results live in a virtual/model world. But we maintain that to analyze variability and covariability between variables an internally consistent albeit somewhat idealistic modeling approach is preferable over sparse measurements and 3D models such as WRF that also perform poorly and introduce additional complexities. This paper is the first to attempt a comprehensive evaluation of variability and covariability of atmospheric parameters for Sc dissipation over land. It is our hope that in the future models are improved and models can be better coupled to measurements to narrow the gap between model results and observations.

APPENDIX E

Linear Approximation to qtBL(zi,θlBL)

For a cloud to form given ABL height zi and well-mixed liquid water potential temperature θlBL, the total water content at ABL top must surpass saturation by a small amount, which is condensed into a cloud: qtBL=qsat(zi,θlBL)+ql(zi). Since ql(zi)qtBL, we investigate the behavior of qsat(z, θl):

qsat=εp(z)/es(z,θl)1,

where ε = 0.622 and pressure follows the hydrostatic assumption p(z) ≈ p0ρgz. The water saturation pressure es is given by the August–Roche–Magnus approximation:

es=κ1exp(κ2Tcκ3+Tc),

where κ1 = 610.94 Pa, κ2 = 17.625, κ3 = 243.04, and Tc is temperature in degrees Celsius. To estimate temperature near the cloud top, we will assume that we are just surpassing saturation with an infinitesimally thin cloud and use the dry adiabatic lapse rate:

Tc=T0Γdz273.15K,

where Γd = g/Cp is the dry adiabatic lapse rate and T0 is surface temperature, which is related to the well-mixed θl and surface pressure p0:

T0=θl(p0p00)Rd/Cp.

With these assumptions, we can estimate ∂qsat/∂z and ∂qsat/∂θl and evaluate them at the observed means of zi, θl, and p0 (Table 1), obtaining

qsatθl=εp(pes1)2pκ2κ3es(κ3+Tc)20.6964gkg1K1,
qsatz=ε(pes1)2pκ2Γdκ3es(κ3+Tc)2ρgeses20.0055gkg1m1,

which yields results similar to the linear fit coefficients in Fig. 7a. This indicates that even with the assumptions made here, the linear relationship between zi, θlBL, and qtBL closely follows the saturation condition.

APPENDIX F

Detailed Cloud Evolution for Single-Variable Changes

We present the time evolution of the ocean and land columns for the single-variable changes of three parameters in Fig. F1. For stronger Δiθl, the resulting colder θlBL indicates that the effect of weaker entrainment dominates over the warmer entrained air. For SHF, the changes over the ocean column barely affect the land column. Last, a lower Tsky results in a cooler ABL, indicating that the radiative cooling dominates over the increased entrainment of warmer air.

Fig. F1.
Fig. F1.

Cloud evolution properties for the ocean column (top row for each panel) and (bottom row for each panel) land columns for single-variable changes of (a) Δiθl, (b) SHF, and (c) Tsky over the idealized reference case. (left to right) Cloud boundaries, entrainment rate, qtBL, Δiqt, θlBL, and Δiθl.

Citation: Journal of the Atmospheric Sciences 77, 8; 10.1175/JAS-D-19-0254.1

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