Turbulence and Mass-Transports in Stratocumulus Clouds

Transcription

1 University of Miami Scholarly Repository Open Access Dissertations Electronic Theses and Dissertations Turbulence and Mass-Transports in Stratocumulus Clouds Virendra Prakash Ghate University of Miami, Follow this and additional works at: Recommended Citation Ghate, Virendra Prakash, "Turbulence and Mass-Transports in Stratocumulus Clouds" (29). Open Access Dissertations This Open access is brought to you for free and open access by the Electronic Theses and Dissertations at Scholarly Repository. It has been accepted for inclusion in Open Access Dissertations by an authorized administrator of Scholarly Repository. For more information, please contact

2 UNIVERSITY OF MIAMI TURBULENCE AND MASS-TRANSPORTS IN STRATOCUMULUS CLOUDS By Virendra P. Ghate A DISSERTATION Submitted to the Faculty of the University of Miami in partial fulfillment of the requirements for the degree of Doctor of Philosophy Coral Gables, Florida June 29

3 29 Virendra P. Ghate All Rights Reserved

4 UNIVERSITY OF MIAMI A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy TURBULENCE AND MASS-TRANSPORTS IN STRATOCUMULUS CLOUDS Virendra P. Ghate Approved: Bruce A. Albrecht, Ph.D. Professor of Meteorology Terri A. Scandura, Ph.D. Dean of the Graduate School Brian Soden, Ph.D. Associate Professor of Meteorology Paquita Zuidema, Ph.D. Assistant Professor of Meteorology Frank Marks Jr., Ph.D. Research Meteorologist and Director NOAA, Hurricane Research Division Miami, Florida Pavlos Kollias, Ph.D. Assistant Professor of Atmospheric and Oceanic Sciences McGill University, Canada

5 GHATE, VIRENDRA P. (Ph.D., Meteorology and Physical Oceanography) Turbulence and Mass-Transports in (June 29) Stratocumulus Clouds Abstract of a dissertation at the University of Miami. Dissertation supervised by Professor Bruce A. Albrecht. No. of pages in text. (126) Boundary layer (BL) stratocumulus clouds are an important factor in the earth s radiation budget due to their high albedo and low cloud top heights. Continental BL stratocumulus clouds are closely coupled to the diurnal cycle and the turbulence in the BL affecting the surface energy and moisture budgets. In this study the turbulence and mass-transport structures in continental BL stratocumulus clouds are studied using data from the Atmospheric Radiation Measurements (ARM) s Southern Great Plains (SGP) observing facility located at Lamont, Oklahoma. High temporal (4 sec) and spatial (45 m) resolution observations from a vertically pointing 35 GHz cloud Doppler radar were used to obtain the in-cloud vertical velocity probability density function (pdf) in the absence of precipitation size hydrometeors. A total of 7 hours of radar data were analyzed to report halfhourly statistics of vertical velocity variance, skewness, updraft fraction, downdraft and velocity binned mass-flux at five cloud depth normalized levels. The variance showed a general decrease with increase in height in the cloud layer while the skewness is weakly positive in the cloud layer and negative near cloud top. The updraft fraction decreases with height with the decrease mainly

6 occurring in the upper half of the cloud layer. The downdraft fraction increases with decrease in height with the increase being almost linear. The velocity of eddies responsible for maximum mass-transport decreases from of.4 ms -1 near cloud base to.2 ms -1 near cloud top. The half-hour periods were then classified based on the surface buoyancy flux as stable or unstable and it was found that the variance near cloud top is higher during the stable periods as compared to the unstable periods. Classification was also made based on the cloud depth to BL depth ratio (CBR) being greater or less than.3. The variance profile was similar for the classification while the skewness was almost zero during periods with CBR less.3 and positive during periods with CBR greater than.3. A 14 hour period of stratocumulus cloud on March 25, 25 was analyzed to study the diurnal changes in the turbulence structure and mass transports. The variance near cloud base during the day time when the BL turbulence is primarily due to surface buoyancy production was higher than during the nighttime when the BL turbulence is driven by radiative cooling near the cloud top. Output from a one dimensional radiative transfer model was analyzed to study the vertical structure of the radiative fluxes. A radiative velocity scale analogous to the surface convective velocity scale is proposed to assess the relative importance of radiative cooling near cloud top in generating turbulence compared with the surface buoyancy production. An attempt was also made to calculate the hourly liquid water flux by combining the high temporal resolution (2 sec) liquid water content estimates from the radar reflectivity and a microwave radiometer with the radar observed vertical velocity. The liquid water flux was found to peak at a level

7 below the cloud top and show a divergence with height that was similar to that from model simulations.

8 This dissertation is dedicated to my grandfather Janardan Padmanabh Bhende iii

9 Acknowledgements Many people have been instrumental for the completion of this dissertation. First of all I will like to thank my advisor Dr. Bruce A. Albrecht. He not only taught me cloud physics and radar meteorology but also helped me become a scientist by teaching me ways to approach a scientific problem. The guidance of my committee members Paquita Zuidema, Brian Soden, Frank Marks Jr, and Pavlos Kollias was also very valuable for this study. Pavlos taught me the important engineering tools such as Matlab and explained the radar hardware needed for this study. Dr. Ping Zhu also guided me during the PhD by giving a modeler s view on the observed data. I will also like to thank my current and past group-mates, Ieng, Thymios, Shaunna and Xue. Without them the journey towards PhD would not have been the same. During the PhD program I got a chance to make friends from all around the world. Without the friendship of Marcello, Mehmet, Marcela, Melicie and Aman life in Miami would not have been so much fun. Last but certainly not the least I will like to thank my parents who always encouraged me in this difficult but fun journey. iv

10 Contents List of Figures...vii List of Tables...xvi 1 Introduction Motivation Processes Involved Model Representation of BL Clouds BL Cloud Observations Open Questions Outline and Specific Scientific Objectives Data, Instrumentation and Techniques Dataset and Instrumentation Doppler Cloud Radars Data Processing Techniques Technique to Retrieve Vertical Velocity Retrieval of Cloud Liquid Water Vertical Velocity Climatology Case Descriptions and General Characteristics Variability of Vertical Velocity Surface VSHF Flux Cloud Thickness Summary...62 v

11 4 Diurnal Variations and Liquid Water Transport Case Description Radiation Field Turbulence Structure Liquid Water Structure Summary Summary and Discussion Summary Discussion and Future Outlook Bibliography vi

12 List of Figures Figure 1.1: Schematic diagram of a stratocumulus topped boundary layer. Depicted is the general structure along with the radiative processes. The longwave radiative fluxes (LWR) are shown in blue while the shortwave radiative fluxes (SWR) are shown in yellow...5 Figure 1.2: Schematic diagram of a stratocumulus topped boundary layer. Depicted are the convective and microphysical processes...7 Figure 2.1: Map of the ARM Southern Great Plains observing facility. Image obtained from Figure 2.2: Time-height mapping of ARSCL derived first three Doppler moments for 6 May 26; Reflectivity (top), mean Doppler velocity (middle) and Doppler spectrum width (bottom). The stratocumulus event analyzed is shown in a black box in the reflectivity plot...24 Figure 2.3: Time height map of the first three Doppler moments from WACR for 6 May 26; Reflectivity (top), mean Doppler velocity (middle) and Doppler spectrum width (bottom). Shown in the reflectivity plot are the cloud boundaries...26 vii

13 Figure 2.4: Scatter plot of reflectivity (dbz) and Doppler velocity (V D ) for the period under consideration at four different cloud depth normalized heights...27 Figure 2.5: Power spectra of vertical velocity at five different cloud depth normalized levels (top left), vertical velocity variance (top right), vertical velocity skewness (bottom left) and fractional updraft coverage (bottom right) for hour 22 on 6 May Figure 2.6: Time-height map of reflectivity, Doppler velocity, Doppler spectrum width and liquid water path from top to bottom on 8 April 26. The radar data is from MMCR BL mode while the LWP is from MWR...32 Fig 2.7: Time-height map of the retrieved cloud liquid water content using the radarradiometer technique...33 Figure 3.1: Histograms of observed reflectivity at five cloud depth normalized levels (η) from η =1 at cloud top (top panel) to η= at cloud base (bottom panel). Also reported are the mean and the skewness of the distribution at each level...39 Figure 3.2: Histogram of observed vertical velocity (w) at five different cloud depth normalized levels (η) from η=1 at cloud top (top panel) to η= at cloud base (bottom panel). Also reported are the variance and the skewness of the distribution at each level along with conditionally sampled updraft and downdraft fraction...41 viii

14 Figure 3.3: The cloud depth normalized profile of variance (top left), skewness (top right), updraft fraction (bottom left) and downdraft fraction (bottom right) from half hour periods from all the cases. Also shown is the mean Doppler spectrum width profile (dashed) in the variance panel. The error bars correspond to the standard deviation of the parameter within the 141 half hour periods...44 Figure 3.4: The averaged mass-flux as a function of vertical velocity at five different cloud depth normalized levels (η) with η=1 at cloud top (top panel) to η= at cloud base (bottom panel)...46 Figure 3.5: Average variance (left) and skewness (right) of half hour periods classified based on the surface VSHF values as stable or unstable. Also shown is the average Doppler spectrum width (dashed lines) for the distinction in the variance panel. The error bars denote the standard deviation of the two parameters within those half hour periods...5 Figure 3.6: Average updraft fraction (top panels) and downdraft fraction (bottom panels) for stable periods (left panels) and unstable periods (right panels)...51 Figure 3.7: Ratio of the mean updraft fraction (left) and mean downdraft fraction (right) during the unstable periods to that during the stable periods...52 ix

15 Figure 3.8: The averaged observed mass-flux for stable periods (red) and unstable periods (blue) as a function of vertical velocity at five different cloud depth normalized levels (η) with η=1 at cloud top (top panel) to η= at cloud base (bottom panel)...54 Figure 3.9: Average variance (left) and skewness (right) of half hour periods classified based on the ratio of cloud thickness to BL depth (CBR). Also shown is the average Doppler spectrum width (dashed lines) for the distinction. The error bars denote the standard deviation of the two parameters within those half hour periods...56 Figure 3.1: Average updraft fraction (top panels) and downdraft fraction (bottom panels) during periods with CBR less than.3 (left panels) and periods with CBR greater than.3 (right panels)...58 Figure 3.11: Ratio of the mean updraft fraction (left) and mean downdraft fraction (right) between periods with CBR less than.3 and CBR greater than Figure 3.12: The averaged observed mass-flux for periods with CBR less than.3 (red) and CBR greater than.3 (blue) as a function of vertical velocity at five different cloud depth normalized levels (η) with η=1 at cloud top (top panel) to η= at cloud base (bottom panel)...61 x

16 Figure 4.1: Time-height mapping of ARSCL deduced first three Doppler spectrum moments; reflectivity (top), Doppler velocity (middle) and spectrum width (bottom) from UTC starting on 25 March Figure 4.2: MMCR observed reflectivity, mean Doppler velocity, Doppler spectrum width and MWR observed liquid water path for the event from top to bottom panel for the period under consideration...67 Figure 4.3: Scatter plot between hourly averaged cloud thickness and hourly averaged liquid water path for the entire event...68 Figure 4.4: Surface temperature (temp), relative humidity (RH), wind speed (wspd) and wind direction (wdir) from top to bottom panel. Also shown in the RH panel is the mixing ratio (r)...69 Figure 4.5: Hourly subsidence rate at 7 mb as derived from the ECMWF model over the ARM SGP site...7 Figure 4.6: Potential temperature (top left), mixing ratio (top right), wind Speed (bottom left) and wind direction (bottom right) from radiosondes launched at 12:, 18: and 24: local time on 25 March Figure 4.7: Surface sensible heat flux, latent heat flux and virtual sensible heat flux in the top panel and the surface convective velocity scale in the bottom panel...73 xi

17 Figure 4.8: Surface radiation budget as the upwelling and downwelling shortwave radiative flux (top panel), upwelling and downwelling longwave radiative flux (middle panel) and net radiative flux (bottom panel)...75 Figure 4.9: Half hourly averages of upwelling shortwave radiative flux (SWU) and downwelling shortwave radiative flux (SWD) at cloud top (top panel), middle of the cloud (middle panel) and cloud base (bottom panel) as determined from the RRTM...77 Figure 4.1: Half hourly averages of upwelling longwave radiative flux (LWU) and downwelling longwave radiative flux (LWD) at cloud top (top panel), middle of the cloud (middle panel) and cloud base (bottom panel) as determined from the RRTM...78 Figure 4.11: : Half hourly averages of net longwave radiative flux (Net LW) and net shortwave radiative flux (Net SW) at cloud top (top panel), middle of the cloud (middle panel) and cloud base (bottom panel) as determined from the RRTM...8 Figure 4.12: Half hourly averages of shortwave heating rate (SW Heat Rate) and longwave heating rate (LW Heat Rate) at cloud top (top panel), middle of the cloud (middle panel) and cloud base (bottom panel) as determined from the RRTM...81 xii

18 Figure 4.13: The panels show from top to bottom the net shortwave radiative flux across upper half of cloud layer, the net longwave radiative flux across the upper half of the cloud layer, the net radiative flux across the upper half of cloud layer and the radiation velocity scale respectively...83 Figure 4.14: The convective velocity scale, radiative velocity scale and total velocity scale for the period in consideration...86 Figure 4.15: Time-height mapping of the hourly correlation coefficient between the reflectivity and Doppler velocity (top panel) and the time-height mapping of hourly mean Doppler velocity (bottom panel) for the period under consideration...88 Figure 4.16: Time-height mapping of vertical velocity variance (top panel), hourly averaged Doppler spectrum width (middle panel) and vertical velocity skewness (bottom panel) calculated for each hour in the period of concern...89 Figure 4.17: Time-height mapping of the percent of updraft fraction (top panel) and percent of downdraft fraction (bottom panel) calculated for each hour for the threshold.5 ms -1 for the period under consideration...91 Figure 4.18: Time-height mapping of hourly averaged updraft mass-flux for the period in consideration...92 xiii

19 Figure 4.19: Time-height mapping of the liquid water content for the period under consideration derived using the radar-radiometer technique...94 Figure 4.2: Time-height mapping of hourly averaged liquid water content for the period under consideration...95 Figure 4.21: Liquid water path as a function of time for 16 hour (top) and 21 hour (bottom). Also shown are the 2 nd degree fit, 4 th degree fit and 6 th degree fit to the data...98 Figure 4.22: Time-height mapping of liquid water flux derived for each hour within the period in consideration. The black lines denote the hourly mean cloud boundaries...99 Figure 4.23: Turbulent perturbation of vertical velocity, perturbation of liquid water content, liquid water flux and liquid water path from top to bottom panel for 15 hour. Also shown in the liquid water path panel is the degree fit to the data...11 Figure 4.24 Hourly vertical velocity variance (left) and skewness (right) averaged from 12: LST to 14: LST (day) and from 2: LST to 22: LST (night) as a function of cloud depth normalized height...13 xiv

20 Figure 4.25: Hourly updraft mass-flux (left) and liquid water flux (right) averaged from 12: LST to 14: LST (day) and 2: LST to 22: LST (night) as a function of cloud depth normalized height...15 xv

21 List of Tables Table 2.1: Instrumentation at the ARM-SGP central facility located at Lamont, Oklahoma...19 Table 2.2: Specifications of Ka-band MMCR and WACR at the ARM-SGP central facility...22 Table 3.1: General characteristics of the 11 cases analyzed in this study. The columns are date, day (D) or night (N) event, duration of the event, mean and standard deviation of LWP, surface VSHF, 1 m wind speed, mean and standard deviation of cloud base height, mean and standard deviation of cloud top height, mean and standard deviation of cloud thickness and inversion strength in terms of jump in potential temperature and mixing ratio between 5 m and 3 km...37 xvi

22 Chapter 1 - Introduction 1.1 Motivation Boundary layer (BL) clouds can form at the top of the mixed layer, and are frequently observed on the east side of the oceans, over Polar Regions, and over land in the mid-latitudes (Zhu et al. 21). These low level clouds not only have a large impact on the BL structure, but also strongly affect the earth s radiation budget (Albrecht 1981; Slingo et al. 24). Those over the oceans usually take the form of stratus or stratocumulus, cover vast areas and persist for a long time while over land they take the form of stratocumulus or fair weather cumulus and are highly variable in time and space. The BL clouds are also referred to as shallow clouds, since their cloud top height is generally less than 4 km and their thickness is less than 5 m (Bretherton et al. 24). The impact of these clouds on surface radiation budget is expressed in terms of surface cloud forcing defined as the difference between the measured downwelling radiation at the surface during cloud presence and during clear sky conditions (Cronin et al. 26). The BL clouds have a high albedo (~.6) (Los and Duynkerke 21) and hence are able to reflect most of the incoming solar radiation causing a negative shortwave cloud forcing (~-2 Wm -2 ) at the surface (Ghate et al. 28). As the BL clouds are shallow clouds, the cloud base height is less than couple of kilometers and hence they cause a small positive longwave cloud forcing (<5 Wm -2 ) at the surface. The total effect is a net negative cloud forcing at the surface, resulting in cooling of the underneath sea or land surface. BL clouds affect 1

23 2 the top of atmosphere radiation budget in a similar way. By reflecting most of the incoming shortwave radiation and negligibly modulating the longwave radiation due to the low cloud top height, they increase the net outgoing radiation. Although they reduce the net radiative flux at the surface, it is still sufficient to generate buoyancy and maintain the cloud structure (Discussed later). BL clouds are also the primary means of transporting water vapor and entropy in the lower troposphere. Hence, these clouds have a significant impact on the surface energy and moisture budgets. The continental BL clouds over midlatitudes affect the local climate and weather, and are also closely linked to the surface temperature and water budgets (Kollias and Albrecht 2). The associated moist convection and cloudiness are intimately tied to the diurnal cycle of atmospheric boundary layer, which is an important issue for climate simulations (Slingo et al. 24). These clouds also interact with trace gases which can complicate air pollutions problems such as chemical reaction rates and the removal of pollutants from the boundary layer (Zhu et al. 21). But continental BL clouds have received much less attention in the literature than marine stratus, stratocumulus or cumulus clouds (Del Genio and Wolf 2). The primary reason for this is the relatively large impact of marine clouds on the radiation budget than the continental clouds. Also, traditionally weather forecasting has primarily focused on precipitation and severe weather events (e.g. hurricanes, tornadoes etc.) and BL clouds over land do not a significantly impact these issues. But still these clouds modulate the radiation budget and affect the local weather. Kollias et al. (27) have shown that the fractional cloudiness of boundary layer clouds varies from 1% to

24 3 23% per year in the mid-latitudes over land. Hence, continental BL clouds need to be well represented in Numerical Weather Prediction (NWP) models and General Circulation Models (GCM) and their effect on other physical processes should be well quantified. The focus of this study is one type of continental boundary layer clouds; stratocumulus. Discussed below are the general processes involved in a stratocumulus topped continental BL. 1.2 Processes Involved Shown in Fig 1.1 is a schematic diagram of a stratocumulus topped atmospheric boundary layer and the associated radiative processes. The depth of the BL is usually about 1 km with the cloud occupying the upper third of it. The BL could be shallower or deeper depending on the surface fluxes and the large-scale subsidence (Medeiores et al. 25). The BL is generally well-mixed with the equivalent potential temperature (θ e ) and total water mixing ratio (q T ) conserved within it and is usually capped by a strong temperature and moisture inversion (Albrecht et al. 1981; Stull 1988). The strength of the inversion is controlled by the surface fluxes and large-scale subsidence (Medeiros et al. 25) as well as the relatively high temperature and low moisture content of the free troposphere compared with the well-mixed BL. Hence, the strength of the inversion is an important parameter in determining the entrainment rate (Kruger 1993). The lifting condensation level (LCL) generally coincides with the cloud base indicating a wellmixed sub-cloud layer. The LCL and cloud base height could also differ from each other indicating presence of a stable layer between surface and the cloud leading to

25 4 a decoupled BL (Serpetzoglou et al. 28). The shortwave albedo of these clouds is comparatively much higher (~.6) than the earth s surface (~.3) (Los and Duynkerke 21). Hence, in the presence of these clouds a substantial amount of the incoming shortwave radiation is reflected back to the space. The longwave radiative fluxes are shown by blue arrows in Fig 1.1. Since the earth s surface is always warmer than the cloud base temperature, the surface emitted longwave radiation is higher than the cloud base emitted longwave radiation causing a heating of the cloud base. In the absence of any upper level clouds, the net longwave radiation emitted from the top of the cloud causes strong cooling at cloud top. The difference between the longwave radiation emitted at cloud top and the surface emitted longwave radiation is relatively small compared with the difference between the cloud reflected shortwave radiation at cloud top and the surface reflected shortwave radiation. This is the primary reason for the cooling of the Earth s surface. The cooling caused by the cloud emitted longwave radiation near cloud top and is considered to be one of the factors contributing to turbulence generation near cloud top in the stratocumulus topped BL (Stevens 22; Stevens et al. 23).

26 5 Figure 1.1: Schematic diagram of a stratocumulus topped boundary layer. Depicted is the general structure along with the radiative processes. The longwave radiative fluxes (LWR) are shown in blue while the shortwave radiative fluxes (SWR) are shown in yellow. The convective processes occurring in the stratocumulus topped BL are shown in Fig 1.2. Due to solar heating the earth s surface can heat sufficiently to generate surface turbulent fluxes -- latent heat flux (LHF) and sensible heat flux (SHF). These fluxes give a measure of the convective processes that transport energy and moisture from the surface upwards. The transport is hypothesized to be done by the means of large eddies (Stevens et al. 1999) that scale by the depth of the BL (Stull 1988). These are shown by thick black arrows in the cartoon. In conjunction with these large eddies are also smaller eddies which mix the BL to the

27 6 scales smaller than the larger eddies. These structures of smaller and larger eddies are advected by the synoptic features like high and low pressure systems. Near the top of the cloud, just below the temperature and moisture inversion, it is hypothesized to have a zone in which entrainment is active and hence named the entrainment zone (Kruger et al. 1993; Stevens 22). In this zone the warmer and drier free tropospheric air mixes with the saturated cloudy air resulting in a zone having different properties than either of them (Kruger 1993; Stevens 23). The scales at which entrainment is active and hence determining the entrainment zone have not been observed yet but are hypothesized by microphysical models to be of order of 1 m (Kruger 1993; Yamaguchi and Randall 28). When the large or small eddies carry the sub-cloud layer moisture into the cloud layer, they also carry sub-cloud layer aerosols which could be activated to form cloud droplets above the LCL. During the activation, latent heat is released due to condensation which can increase the temperature of the parcels making it more buoyant than the surrounding atmosphere and hence increasing its updraft velocity (Wang et al. 23). Near cloud top, in the entrainment zone, a sinking parcel is negatively buoyant compared with the surrounding atmosphere. The parcel can have warm and dry free tropospheric air which might cause evaporation of some of the cloud droplet within that air parcels. This evaporation can cause cooling of the parcel due to latent heat of evaporation and can make the parcel more negatively buoyant (Yamaguchi and Randall 28; Wang et al. 23). The cloud liquid water content (LWC) is zero at the cloud base with a linear increase in height as per the adiabatic assumption. But this assumption is known to break-down with higher LWC

28 7 within strong updrafts due to activation of sub-cloud aerosols as compared to downdrafts containing the entrained free tropospheric air due to evaporation. In Fig. 1.2, the darker hydrometeors within updrafts compared to the lighter hydrometeors within downdrafts in Fig 1.2 denote the LWC differences within the two structures. Figure 1.2: Schematic diagram of a stratocumulus topped boundary layer. Depicted are the convective and microphysical processes. 1.3 Model representation of BL Clouds Due to their radiative impacts and close coupling with the BL turbulence, BL clouds need to be represented in some form in all of the meteorological models (Arakawa 24). As described in the previous section, these clouds modify and

29 8 interact with processes occurring at variety of scales. For instance, the advection scales are determined by synoptic systems that have scales of about 1 km; but the microphysical parameters are determined by the updraft and downdraft structures occurring at a few tens of meters (Guo et al. 28). Representing all these phenomena in any type of model is both critical and challenging. In Large Eddy Simulation (LES) models and Cloud Resolving Models (CRM), BL clouds are resolved along with the boundary layer turbulence. Although in these models the subgrid-scale turbulence (~5 m) does need to parameterized. This is generally done using schemes ranging from K-theory to second order closure (Stull 1988). In regional and General Circulation Models (GCM) due to coarser grid resolution BL clouds have to be parameterized. As stated earlier, BL clouds are pivotal in transporting momentum and moisture vertically while they are also closely tied to the turbulence in the boundary layer. Hence, a good cumulus parameterization scheme has to have a turbulence mixing scheme embedded in it (Bretherton et al. 24; Arakawa 24). Many parameterizations have been proposed to represent the effect of these clouds in GCMs. These parameterizations range from using a simple measure of lower Tropospheric stability (e.g. Klein and Hartmann 1993; Wood and Bretherton 26), using a mass-flux approach (Arakawa and Schubert 1974; Bretherton et al. 24), using higher or lower order turbulence closure schemes (Bougeault 1985; Bougeault et al. 1986; Duynkerke and Driedonks 1987; Bechtold et al. 1995), using different BL schemes in a mass-flux approach (Lock et al. 2), by combining the mass-flux and higher order closure approach (Randall et al. 1992; Lappen and Randall 21) or by using a probability density

30 9 function (pdf) based approach (Golaz et al. 22; Zhu and Zhao 28). In all these parameterizations, except those that use a simple measure of tropospheric stability, some measure of vertical velocity within the grid box is used. The grid box mean vertical velocity and the percent of updrafts within the grid-box are used in most of the parameterization based on mass-flux approach (Bretherton et al. 24; Lappen and Randall 21 etc.). Higher-order moments of vertical velocity like variance and skewness are used in parameterizations using higher-order closures, in parameterizations combining mass-flux and higher order closures and in pdf based parameterizations. The dynamics and microphysics interact with each other in stratocumulus clouds and both are critical in determining the cloud fraction, microphysical and radiative properties of these clouds (Wang et al. 23; Guo et al. 28). The aerosols indirect effects (Twomey et al. 1977; Albrecht et al. 1989) and the precipitation effects (Wang and Wang 1994; Stevens et al. 1998) play an important role in determining the stability of stratocumulus clouds. The stratocumulus LWC, which is controlled by both dynamics and the microphysics, is often a factor used in GCM cloud radiative feedback parameterizations (Guo et al. 28). The sub-cloud and cloud layer vertical velocity variations within the grid-box are a key factor in determining the cloud microphysical parameters like effective radius, cloud drop number concentrations, LWC etc. (Jonas 1995; Peng et al 25). The variance and mean of vertical velocity within a GCM grid box is widely used to diagnose the cloud drop number concentration (Jiang and Cotton 25; Lohmann et al. 1999). An explicit bin microphysical (BM) scheme is often used along with a turbulence closure model in

31 1 order to study the aerosol-cloud-precipitation interactions in a LES framework and the model setup is often referred to as LES-BM (Wang et al. 23). Hence, to represent these clouds realistically in any modeling framework, it is necessary to account for dynamical processes associated with the vertical velocity variations, the microphysics controlled by the LWC, and the turbulent interactions between these two. 1.4 BL Cloud Observations Traditionally aircraft have been the primary mode of observing the boundary layer stratocumulus clouds. Especially for studying the turbulence characteristics of these clouds, fast response aircraft instruments are still largely used (e.g. Leaitch et al. 1996; Stull et al. 1997; Guo et al. 28). There have been attempts to study the turbulence in these clouds using ground based remote sensors like Doppler radars. Most of the studies are based on observations from Doppler radars in the form of wind profilers (e.g. Ecklund et al. 1985; Eng et al. 23 etc.) that have large pulse volumes compared with cloud radars (Kollias et al. 21) and hence are unable to detect small-scale features of vertical velocity. But there have been attempts to study these clouds using cloud Doppler radars that have considerably smaller pulse volumes than the traditional weather radars and wind profilers (e.g. Kollias and Albrecht 2; Frisch et al. 1995). Frisch et al. (1995) and Feingold et al. (1999) used a Ka-band cloud radar to study turbulence in marine stratocumulus clouds. Kollias and Albrecht (2) and Kollias et al. (21) made an attempt to characterize the turbulence in the continental stratocumulus and fair weather cumulus clouds

32 11 using W-band cloud radar. But with exceptions of Ecklund et al. (1985) and Feingold et al. (1999), most of the observations of turbulence and vertical velocity from Doppler radar are based on case studies (e.g. Kollias and Albrecht 2; Frisch et al. 1995; Lothon et al. 25 etc.). The cloud microphysical properties like cloud drop size distribution, LWC etc. can only be observed directly using aircraft in-situ instruments. But the in-situ instruments have small sampling volumes and also lack simultaneous vertical profiling. These quantities can be inferred from the observations from the remote sensors. Various retrieval techniques were proposed to do so (e.g. Frisch et al. 1998; Hogan et al. 25; O Connor et al. 25 etc.). The accuracy of the retrieval techniques depend not only on the accuracy of the observations, but also on the assumptions made in the retrieval technique and the meteorological conditions. The interaction between cloud microphysics and turbulence caused by vertical velocity variations was previously by Feingold et al. (1999) by applying the retrieval technique proposed by Frisch et al. (1995 and 1998) to data from a Ka-band cloud radar. Apart from this study, observations of the interaction between cloud microphysics and dynamics using ground-based remote sensors are generally missing Open Questions As described in the previous section, it is both essential and quite challenging to represent BL stratocumulus clouds in meteorological models. But apart from their representation in models, some of the basic phenomena controlling the

33 12 macrophysical, microphysical and turbulence properties of these clouds are not well understood or validated using observations. Below I mention a few of the open questions concerning these clouds which led to the specific objectives of the dissertation. As mentioned earlier, aircrafts were the primary mode of observations of turbulence in these clouds. The aircraft observations are typically from field campaigns which last about a month. Hence, long-term aircraft observations of these clouds are missing. With the exception of Feingold et al. (1999), the observational studies using remote sensors focused on the turbulence structure of stratocumulus clouds were mainly been case studies (Kollias and Albrecht 2; Frisch et al. 1995). Hence, long-term observations of turbulence structure of stratocumulus clouds are still missing. The aircraft observations of turbulence in stratocumulus clouds suffer from a small sample volume and lack of simultaneous vertical profiles. Ground-based vertically pointing cloud Doppler radars are capable of observing the turbulence structure of these clouds. But previous observations, with the exception of Kollias and Albrecht (2), have reported the turbulence structure of these clouds using data averaged over a minute (e.g. Feingold et al. 1999; Hogan et al. 25 etc.). But the strong updraft and downdraft structures are highly variable and occur at very small spatial case (Guo et al. 28). Hence, long-term high temporal and spatial resolution observations of turbulence in these clouds have yet to be done. Stratocumulus clouds have been simulated using different LES and singlecolumn models as a part of the GEWEX (Global Energy and Water Cycle

34 13 Experiment) Cloud System Study (GCSS) s BL cloud working group (BLCWG) objectives. This has led to several studies improving the knowledge of BL clouds (e.g. Brown et al. 22; Zhu et al. 25; Stevens et al. 25; Wyant et al. 27). The models used for inter-comparison differ from each other, not only in the use of parameterizations, but also in model setup and assumptions. The studies concerning BL clouds are tied to the diurnal cycle of the BL (Brown et al. 22), and studies concerning the nocturnal stratocumulus cloud (e.g. Zhu et al. 25) have highlighted major differences between different model simulations. In the earlier case the in-cloud turbulence is driven by buoyant production at the surface due to solar heating, while in the later case the turbulence was maintained by cloud top radiative cooling. Observations of turbulence structure of BL stratocumulus clouds in the above two conditions were unable to validate the model simulations or to understand the associated processes. Moreover, the transition of cloud and BL turbulence structure from a surface forced regime to a cloud top cooling forced regime has not been explored by any study. Observations and study of differences between the turbulence generated through different mechanisms like surface buoyancy forcing, cloud top radiative cooling, shear etc. are still lacking. In most of the GCM, BL clouds are parameterized in terms of mass-flux (Zhu 22). The one dimensional budget equations of the mean liquid water content or the conserved variables have the flux term which is essentially the covariance of vertical velocity and the conserved variable. The model inter-comparisons in the GCSS BLCWG are often based on the simulated mass-flux of the conserved variables. But past observations of mass-flux or liquid water flux have mainly been

35 14 reported through aircraft observations only (e.g. Faloona et al. 25), which suffer from lack of simultaneous vertical sampling. Hence, observations of the vertical profile of mass-flux or liquid water flux are lacking. 1.6 Outline and Specific Scientific Objectives In this study the turbulence and large-eddy structure of boundary layer continental stratocumulus clouds is studied using data from the Atmospheric Radiation Measurement (ARM) s Southern Great Plains (SGP) observing facility. The goal is to address some of the open questions described in section 1.5. The data, instrumentation and retrieval techniques used in this study are described in chapter 2. Eleven cases of nonprecipitating BL stratocumulus clouds, totaling about 7 hours of observations have been analyzed. Presented in chapter 3 is the climatology of the vertical velocity structure of nonprecipitating stratocumulus clouds. Rather than focusing on understanding the cause and effect of the turbulence, a statistical approach is used. The cases are divided based on certain criteria (e.g. surface buoyant production, cloud thickness etc.) and the variations of the vertical velocity structure for the distinction are studied. The vertical velocity structure is characterized using half-hourly values of variance, skewness, updraft fraction and downdraft fraction. Also variations in the mass-flux for the classification are studied. In chapter 4 the results from analysis of a nonprecipitating BL stratocumulus cloud lasting for about 14 hours are presented. This case captures the diurnal variations in the in-cloud turbulence structure as the source of turbulence shifts from

36 15 surface buoyant production during the daytime to cloud top radiative cooling at night. Output from a one-dimensional radiative transfer model is analyzed to assess the radiative flux budget in the cloud layer and to understand the role to radiation in modulating in-cloud turbulence. An attempt is made to derive a simple radiative velocity scale analogous to convective velocity scale. The liquid water flux was also derived by combining the data from cloud radar and microwave radiometer. Vertical structures of turbulent perturbations of liquid water content and vertical velocity are studied in order to understand the resulting liquid water flux. The dissertation is concluded with a summary chapter.

37 Chapter 2 Data, Instrumentation and Techniques 2.1 Dataset & Instrumentation The United States Department of Energy (DOE) s ARM is a major program of atmospheric measurement and modeling, with a particular focus on the influence of clouds and the role of cloud radiative feedback (Stokes & Schwartz 1994; Ackerman & Stokes 23). The Cloud and Radiation Testbed (CART) at the SGP site consists of many observing facilities. It is primarily designed to collect observations for prospective model testing in a shared data environment (Stokes & Schwartz 1994). The SGP site has many boundary facilities, intermediate facilities and one central facility at Lamont, Oklahoma. The design of site is shown in Figure 2.1. Figure 2.1: Map of the ARM Southern Great Plains observing facility. Image obtained from There are many different instruments installed at these sites, but the complete suit of instrumentation is only present at the central facility. A list of the instruments 16

38 17 present at the central facility used in this study are listed in Table 2.1. There are two vertically pointing cloud Doppler radars present at the central facility. As this study is mainly based on the data from the cloud radars their operating characteristics are described in detail in section 2.2. The instruments are described in detail with their operating settings in the respective instrument handbooks available at below is summary of some of the key features of the instruments taken from the handbooks. The ceilometer uses a laser (operating at 95 nm) and can automatically detect up to three cloud base heights along with the backscatter coefficient that is proportional to the square of the hydrometeor diameter. The range of the ceilometer is 7.5 km while the spatial and temporal resolution is 15 m and 15 s respectively. The beam divergence of the field of view of the instrument is.66 milliradians. Since only single layered nonprecipitating stratocumulus clouds are analyzed in this study, the ceilometer data is used only to obtain the cloud base height. Radiosondes are launched every 6 hours from the central facility. They map the vertical profile of temperature, relative humidity, wind speed and wind direction. Although not of high temporal resolution, the soundings data were used to assess the stability of the BL and to observe the temperature and moisture inversion. Data from the soundings was also used to make sure that the clouds analyzed in this study are warm liquid BL stratocumulus clouds with in-cloud temperature greater than -5 C. A 915 MHz wind profiler is also present at the central facility and is equipped with a Radio Acoustic Sounding System (RASS). While the wind profiler data files

39 18 report the first three moments of Doppler spectra every minute, the consensus files report the wind speed and wind direction for every hour. The RASS system provides the vertical profile of virtual potential temperature every hour. Unfortunately the wind profiler and the RASS had technical problems and were not operating during any of the stratocumulus cases analyzed in this study. Since the vertical structure of winds could not be observed, high temporal resolution wind shear observations were also not available for this study. A solar and infrared radiation station (SIRS) is also present at the central facility which observes the surface upwelling and downwelling shortwave and longwave radiative fluxes. The spectral range of the shortwave measurements is 295 nm to 3 microns while that in longwave it is 3.5 microns to 5 microns. All the instruments used in this study have a hemispheric field of view. The temporal resolution of the instruments in this station is 2 s. Since, high resolution radiative flux observations are not needed for this study; 5 minute quality controlled observations were used. The uncertainty in the upwelling and downwelling shortwave radiative fluxes is 1 Wm -2 and 1 Wm -2 respectively. While the uncertainty in the upwelling and downwelling longwave radiative flux is ~4 Wm -2.

40 19 Table 2.1: Instrumentation at the ARM-SGP central facility located at Lamont, Oklahoma. Instrument Name Product Resolution Millimeter Cloud Radar (MMCR) Doppler Spectra Depends on operating mode W-band ARM Cloud Radar Doppler Spectra 4 s, 42 m (WACR) Ceilometer First three cloud base 15 s, 15 m heights Balloon Borne sounding Vertical profile of Every 6 hours system temperature, RH, Winds 915 MHz Wind Profiler BL wind structure & virtual Depends on the Solar and Infrared Radiation Station (SIRS) Microwave Radiometer (MWR) Flux Suite Tower Sensors temperature profile Upwelling/Downwelling longwave/shortwave irradiance Liquid water path and column water vapor Surface sensible heat flux and latent heat flux Surface temperature, RH, wind etc. product parameter. 5 minute 2 s 3 minute 5 minute A microwave radiometer (MWR) is operated at the site and observes the sky brightness temperature at 23.8 GHz and 31.4 GHz. These brightness temperatures are then used to calculate the total water vapor and total liquid water along the line of sight (LOS) by using the algorithm described by Turner et al. (27) and Turner (27). The temporal resolution of MWR is 2 s while the uncertainty in the derived liquid water path (LWP) is 1 gm -2. The field of view is 5.9 at 23.8 GHz and 4.5 at 31.4 GHz. The MWR suffers from a generic problem of precipitated water collection on the instrument which produces unrealistic high values of brightness temperature and LWP. A heater and a blower are deployed near the instrument to solve this problem, but the instrument cannot be used during heavy precipitation.

41 2 A surface eddy correlation flux measurement system (ECOR) present at the site is equipped with high temporal resolution sensors to measure temperature, humidity, wind speed and wind direction. From these instruments half hourly values of surface sensible heat flux and latent heat flux are reported. The values are reported for every half hour period. A meteorological tower is in place to provide surface observations during the radiosonde launches. The tower makes measurement of temperature, humidity, wind speed, wind direction and pressure. The measurements are done every 5 minute. The instrument platform is located 5 m above the ground. 2.2 Doppler Cloud Radars The primary tool for quantifying properties of nearly all radiatively important clouds over the ARM Climate Research Facility (ACRF) sites are the millimeter wavelength cloud radars (Kollias et al. 27). There are two collocated vertically pointing Doppler cloud radars of frequency 35 GHz (Ka-band) and 94 GHz (W-band) at the central facility. The Ka-band radar known as the Millimeter Cloud Radar (MMCR) operates in 4 different modes designed to obtain radar reflectivity factor observations under different conditions. From September 23, the radar has been operated with a new Digital Signal Processor (DSP) and is collecting the raw Doppler spectrum and vertical profiles of the first three Doppler spectral moments every 4 s. The W-band radar, known as the W-band Arm Cloud Radar (WACR) has polarization ability and is operating with a temporal resolution of 4.2 s and spatial

42 21 resolution of 42 m. This radar is also recording the Doppler spectrum and first three Doppler spectral moments in both polarization settings. Although there are two cloud Doppler radars present at the location, we used the observations only from the Ka-band radar because of the long-term availability of MMCR observations compared to the WACR. The operating characteristics and sampling strategies of the MMCR are described in detail by Kollias et al. (25 and 27). The radar operates in four different modes; Boundary Layer (BL), General (GE), Cirrus (CR) and Precipitation (PR). The BL mode is specifically designed to study non-precipitating shallow BL clouds. The sequence of mode operations is BL- GE-BL-CR-BL-PR-BL. Due to the operating settings of each mode, observations are collected every 2 s. As observations from BL mode only are used, no data is recorded for every 2 s making the time resolution 4 s. The time resolution is 4 s because every observation is an average of 2 s and no data collected for another 2 s. The vertical resolution of the BL mode is 45 m. Since the half-power beam width of the radar is.2, the radar pulse volume has horizontal dimension of about 3.5 m at 1 km. Since the data collected is an average of 2 s in time, the advective time scales could be important under high wind conditions. Operating characteristics of the MMCR BL mode and WACR are tabulated in Table 2.2.

43 22 Table 2.2: Specifications of MMCR and WACR present at the ARM-SGP central facility. Parameter MMCR BL Mode WACR co-pol Frequency 35 GHz 94 GHz Range Resolution 45 m 42 m Temporal Resolution 4.2 s 4.2 s Height of first return 15 m 131 m Range 5 km 15 km Beam Width.2.3 Sensitivity -36 dbz at 5 km -4 dbz at 2 km A novel attempt was made by Clothiaux et al. (1999) and Clothiaux et al. (2) to integrate data from a number of remote sensing instruments to characterize the boundary layer and cloud structure by making a Value Added Product (VAP) named as the Actively Remote Sensed Cloud Locations (ARSCL). The ARSCL dataset has the first three Doppler moments from the cloud radar (MMCR) along with derived cloud boundaries, cloud mask, radiometer wet-window flag etc. The time and spatial resolution of ARSCL dataset is 1 sec and 45 m respectively. The data is quality controlled to remove any insect contamination or spurious radar returns due to instrument settings. Due to lower time resolution, the ARSCL dataset cannot be used to do turbulence studies, but it is an excellent tool to identify periods of operation where BL stratocumulus clouds are present. 2.3 Data Processing Techniques There are several techniques reported in the literature to infer useful meteorological parameters from the observed engineering parameters by the remote sensors. This study is mainly concerned with the retrieval of turbulence statistics and liquid water content from the available suit of remote sensors. The techniques used to retrieve these quantities have been described in the literature but are recited and

44 23 demonstrated here using cases of nonprecipitating stratocumulus clouds. The cases are not analyzed in detail but the techniques are validated Technique to retrieve vertical velocity The technique to retrieve turbulence statistics related to the probability density function (pdf) of in-cloud vertical velocity of stratocumulus cloud using data from vertically pointing cloud Doppler radar is described by Frisch et al. (1995) and by Kollias and Albrecht (2). The same technique is used in this study and is demonstrated by an event on 6 May 26. The first three ARSCL derived Doppler spectrum moments for this day are shown in fig 2.2. The event happened after heavy precipitation between 19 UTC till 24 UTC and is shown in a box. The local time is 6 hours behind Universal Time Constant (UTC) hence the event happened from noon to 18 local time. The land surface might have been wet due the precipitation before the event and the daytime solar heating could have generated enough buoyancy flux at the surface to form stratocumulus clouds. Although both radars were working on this day, the techniques are illustrated using the WACR data. The same technique can also be applied to the MMCR BL mode data to retrieve the turbulence parameters.

45 Figure 2.2: Time-height mapping of ARSCL derived first three Doppler moments for 6 May 26; Reflectivity (top), mean Doppler velocity (middle) and Doppler spectrum width (bottom). The stratocumulus event analyzed is shown in a black box in the reflectivity plot. 24

46 25 Shown in fig 2.3 are the WACR observed first three Doppler moments of the event in consideration. The cloud top and cloud base varied in time with the variations as high as 3 m during some hours. The ceilometer derived cloud base height matched the radar observed first cloudy range gate at all times. Hence, the height where the radar first detects a cloud was used to obtain the cloud base height. The cloud top height was objectively determined using a top-down approach on the radar observed reflectivity profiles. Hence high temporal resolution (4 sec) measurements of cloud base and cloud top heights were made. The derived cloud boundaries are shown in the reflectivity mapping in Fig 2.3. A general feature of the reflectivity increasing with height can be seen, but due to variability in the cloud structure, during some hours (e.g. 19 UTC) the reflectivity peaks in the middle of the cloud. Since the cloud top and cloud base varied in time and the variations were significant on temporal scales intended to calculate turbulence statistics (3 mins or 1 hour), it is necessary to normalize by cloud depth. The determination of cloud boundaries for each sample enables determination of cloud depth normalized values of the variables at each time step. η= z z z z top base base (2.1) Where η gives the cloud depth normalized height at a particular height (z) when the cloud top height is Z top and cloud base height is Z base.

47 Figure 2.3: Time height map of the first three Doppler moments from WACR for 6 May 26; Reflectivity (top), Mean Doppler velocity (middle) and spectrum width (bottom). Shown in the reflectivity plot are the cloud boundaries. 26

48 27 Cloud depth normalized values of reflectivity, Doppler velocity and spectral width at five different η levels (,.25,.5,.75 and 1) were used in the analysis. As we intend to analyze the cloud structure at 5 different levels, for clouds less than 5 gates deep, these parameters were interpolated between cloud base (η = ) and cloud top (η = 1) to get values at intermediate η levels. It can be observed from Fig 2.3 that none of the reflectivity observed is greater than -17 dbz, denoting that no rain or drizzle hydrometeors were present during the event (Frisch et al. 1995). Figure 2.4: Scatter plot of reflectivity (dbz) and Doppler velocity (V D ) for the period under consideration at four different cloud depth normalized heights.

49 28 Shown in Fig 2.4 are scatter plots between reflectivity and mean Doppler velocity at 4 different cloud depth normalized heights for the entire period. It is evident that there is no correlation between the reflectivity and mean Doppler velocity. Since, the cloud droplets have negligible fall velocity, it can be assumed that they are moving up and down with the BL turbulent eddies. Hence, the radar observed mean Doppler velocity can be used as a surrogate for the vertical air motion. Figure 2.5: Power spectra of vertical velocity at five different cloud depth normalized levels (top left), vertical velocity variance (top right), vertical velocity skewness (bottom left) and fractional updraft coverage (bottom right) for hour 22 on 6 May 26.

50 29 Generally in analyzing the turbulence structure of stratocumulus clouds, previous studies (Caughey et al. 1982; Kollias and Albrecht 2 etc.) have calculated at the variance, skewness, updraft fraction and the dominant frequency signal in the vertical velocity. These 4 quantities for hour beginning at 22 UTC are shown in Fig 2.5. The decay of the spectral power with a -2/3 slope denotes that the observed vertical velocity has turbulence signal embedded in it. The slight decrease of vertical velocity variance with height and positive vertical velocity skewness in the cloud layer is consistent with previous modeling studies (e.g. Zhu and Zuidema 29; Moeng and Rotuno 199). The observed fractional updraft area is about 5% for hour Retrieval of cloud liquid water The cloud liquid water content cannot be observed directly through remote sensors but can be retrieved from the observed engineering parameters. Various retrieval techniques are reported in the literature to retrieve the LWC from remotely sensed parameters. The simplest technique is based on retrieving the LWC from the radar observed reflectivity and by using a previously developed Z-LWC relationship. Many Z-LWC relationships are reported in the literature e.g. Atlas (1954), Comstock et al. (24) etc. The Z-LWC relationships are known to vary according to cloud type and geographical location (Meywerk et al. 25). Technique using the reflectivity from two collocated radars of different frequencies is commonly termed as Dual wavelength technique. Various studies in the past have combined reflectivity data from two radars with frequencies like S-band, C-band, X-band, Ka-band and W-band

51 3 to obtain the LWC (e.g. Meneghini et al. 1997; Hogan et al. 25; Vivekanandan et al. 1999; Williams and Vivekanandan 27; etc.) This technique depends heavily on the absolute calibration of both the radars and cannot be applied to high temporal resolution data (Hogan et al. 25). Another type of retrieval technique combines the radar observed reflectivity and ceilometer observed backscatter coefficient (O Connor et al. 25). This technique can only be applied to retrieve drizzle LWC and hence cannot be used for this study as it pertains to retrieval of cloud LWC of nonprecipitating clouds. The technique used in this study is proposed by Frisch et al. (1998) and is often referred to as the Frisch technique or radar-radiometer technique. The technique can be only applied to non-precipitating stratocumulus clouds (reflectivity <-17 dbz) and uses radar reflectivity and radiometer observed LWP. The assumptions made in the retrieval technique are constant cloud drop number concentration with height and linear relationship between square of the third moment of DSD (LWC) and sixth moment of DSD (reflectivity). Hence the integrated liquid water in the atmospheric column as observed by MWR is distributed within the cloud layer by weighting it with the radar observed reflectivity. The liquid water content at a particular radar range gate (i) can be calculated using equation 2.2. lwc i = lwp Z M i= 1 Z 1/2 i 1/2 i Δz (2.2) Z i (mm 6 m -3 ) is the observed reflectivity at a particular range gate, lwp (gm -2 ) is the MWR observed liquid water path, Δz is the radar range resolution and M is the total cloudy range gates observed by the radar. The formulation yields LWP in gm -3.

52 31 Since, data from the cloud radar and MWR is used in the technique and MWR typically have less temporal resolution (~2 sec to 1 min) than the cloud radars (1 sec to 1 sec), the radar data is averaged to match the MWR temporal resolution before the application of the technique. This technique has been previously used by Feingold et al. (1999) to obtain cloud LWC and to analyze its dependence on the in-cloud turbulence. They applied the technique to minute averaged data of both the instruments but argued that application of the technique to high time resolution observations might change the results and give more insights on the microphysics-dynamics relationship. In this study the technique is applied to 2 sec data as the radiometer temporal resolution is 2 sec. The technique is demonstrated using a case from 8 April 26. Shown in Fig 2.6 is the time height mapping of the reflectivity, mean Doppler velocity and Doppler spectrum width observed by MMCR BL mode. It can be seen that none of the observed reflectivity is greater than -2 dbz, denoting the absence of any precipitation size droplets. The reflectivity has the general feature of increase with increase in height, similar to the adiabatic LWC (not shown). The LWP decreases from about 3 gm -2 to 1 gm -2 from 5 UTC to 6 UTC and then remains almost constant. This is consistent with the decrease in the cloud thickness during the first hour and then almost constant cloud thickness for the rest of the event. The event was preceded by precipitation and followed by clear sky periods. Shown Doppler moments are averaged from the radar temporal resolution of 4 sec to 2 sec to match the MWR temporal resolution.

53 Figure 2.6: Time-height map of reflectivity, Doppler velocity, Doppler spectrum width and liquid water path from top to bottom on 8 April 26. The radar data is from MMCR BL mode while the LWP is from MWR. 32

54 33 Shown in Fig 2.7 is the time-height map of the retrieved LWC for the event. It was calculated using equation 2.2. The general feature of LWC increasing with height and then a decrease near the cloud top is seen and is similar to reported by Frisch et al. (1998) and Feingold et al. (1999). Since data from Ka-band radar is used in this study, it is not necessary to correct for any gaseous attenuation or liquid water attenuation while applying the technique (Hogan et al. 25). Figure 2.7: Time-height map of the retrieved cloud liquid water content using the radar-radiometer technique. Although the technique is successfully demonstrated here, it suffers from few shortcomings. The underlying assumption in the technique of the square of the LWC

55 34 proportional to the reflectivity has not been tested for high temporal resolution dataset. While Frisch et al. (1998) and Feingold et al. (1999) have applied the technique to minute averaged data; the application of the technique to a 2 sec data might not be valid and can lead to incorrect results. It is not possible at this time to determine the temporal bounds of the assumptions which can only be done using aircraft data. The other assumption of the technique is a constant cloud drop number concentration with height. Although this is generally true in stratocumulus clouds (Sharon et al. 26; Leaitch et al etc.), this has not been tested in continental stratocumulus clouds. Also the assumption might break-down under conditions of heavy entrainment as the smaller droplets will evaporate faster than the bigger droplets causing little changes in the reflectivity as it is proportional to the sixth moment of DSD. The temporal bounds of this assumption are difficult to determine and not reported in the literature otherwise.

56 Chapter 3 Vertical Velocity Climatology In this chapter an attempt is made to characterize the in-cloud vertical velocity structure of nonprecipitating BL stratocumulus clouds. The technique to retrieve vertical velocity from cloud radar data described in section is used. 3.1 Case Descriptions and General Characteristics Nonprecipitating BL stratocumulus clouds were objectively determined from three years of data (25 to 27) by specifying the following criteria: cloud top lower than 4 km (Kollias et al. 27), reflectivity less than -17 dbz (Frisch et al. 1995), and hourly cloud fraction of 1% for at least three consecutive hours. Soundings from all the cases were analyzed to make sure that all clouds are liquid warm clouds with an in-cloud temperature greater than -5 C. Eleven cases totaling to about 7 hours were identified and are tabulated in Table 3.1. Tabulated are the duration along with the mean LWP, surface virtual sensible heat flux (VSHF), 1 m wind speed, cloud base height, cloud top height, cloud thickness and inversion strength during the event. The standard deviation of LWP, cloud base height, cloud top height and cloud thickness are also reported to assess the variability within the event. The duration of the event is variable with some events lasting for about 1 hours (25325) and some for just 4 hours. The shorter events are often short due to presence of precipitation size droplets (dbz>-17) in them rather than a complete dissipation of the cloud. The mean and standard deviation of LWP is reported. The LWP is highly correlated with the cloud thickness on half-hourly time scales (plot not shown). The mean LWP is 16 gm -2 with average cloud thickness of 315 m. The 35

57 36 standard deviation of the LWP indicates low variability in a number of the cases, although some cases (e.g. 2656) have standard deviations comparable with the mean. The values of surface VSHF suggest that stratocumulus clouds were observed when the surface buoyancy flux contribution to the TKE budget is nonexistent (VSHF<) to when it is substantial. The wind speeds are highly variable with wind speeds as high as about 1 ms -1, and low as about 2 ms -1 and an average of 5.5 ms -1. Unlike marine stratocumulus clouds, where the cloud top is almost constant with very little variations and most of the changes in cloud thickness are attributed to cloud base height changes (Serpetzoglou et al. 28), considerable variations in the cloud top height are observed. During some cases, the BL inversion was difficult to determine from the potential temperature jump across the inversion alone. Hence, reported are the potential temperature and mixing ratio difference between 5 m and 3 km from the averaged soundings during the event. The average pressure at 5 m was 922 mb while at 3 km it was 677 mb. The temperature inversion can be as high as 27 k or low as 14 K. The moisture inversion is always negative with the BL being moister than the free troposphere but showed lot of variations from being strong as 4.7 gkg -1 or weak as -1 gkg -1. It is worth to note that the temperature and moisture inversion did not always coincide with the moisture inversion being at a higher altitude than the temperature inversion in some cases.

58 Table 3.1: General characteristics of the 11 cases analyzed in this study. The columns are date, day (D) or night (N) event, duration of the event, mean and standard deviation of LWP, surface VSHF, 1 m wind speed, mean and standard deviation of cloud base height, mean and standard deviation of cloud top height, mean and standard deviation of cloud thickness and inversion strength in terms of jump in potential temperature and mixing ratio between 5 m and 3 km. Date YYYYMMDD D/N Duration (Hour) LWP (gm -2 ) VSHF (Wm -2 ) Wspd (ms -1 ) Base (m) Top (m) Thick (m) Inversion Strength Mean Std Mean Std Mean Std Mean Std Δθ (k) Δq (g kg -1 ) D D D D N D N D D D D

59 38 Since we intend to compare different cases that have different characteristics (cloud thickness, BL depth etc.), it was necessary to normalize by the cloud depth. The cloud depth normalized height (η) was calculated as per equation 2.1, using cloud base height and cloud top height. The ceilometer observed cloud base height matched the radar observed cloud base height in all the cases. Hence, the radar observed cloud base height and cloud top height was used in calculating the cloud depth normalized height. The top and bottom radar range gate with radar returns above the threshold were removed for each sample to eliminate any partial beam filling effects. These observations were then used to estimate cloud depth normalized values of reflectivity, mean Doppler velocity and Doppler spectrum width for all the cases at a 4 sec temporal resolution. Variance, skewness, fractional updraft and fractional downdraft statistics of the cloud depth normalized vertical velocity were developed for each half-hour period for each case. The half hour averaging period is sufficient in most of the cases for the mean vertical velocity to be zero, but this might not be true for all the half hour periods (Lenschow et al. 1994). Similar analyses performed using hourly averaging did not show any statistically significant changes in the variance or skewness profiles.

60 39 % 2 1 Mean = 3.5 dbz Skewness =.42 η=1 % 2 1 Mean = dbz Skewness =.11 η=.75 % 2 1 Mean = 26.9 dbz Skewness =.32 η=.5 % 2 1 Mean = dbz Skewness =.48 η=.25 % 2 1 Mean = dbz Skewness =.57 η= Reflectivity (dbz) Figure 3.1: Histograms of observed reflectivity at five cloud depth normalized levels (η) from η =1 at cloud top (top panel) to η= at cloud base (bottom panel). Also reported are the mean and the skewness of the distribution at each level.

61 4 Fig 3.1 shows a histogram of reflectivity at five different cloud depth normalized levels from all the 4 sec samples from all the cases. Also shown are the mean and the skewness of the distribution at each level. The mean reflectivity increases with height from about -33 dbz at cloud base to -25 dbz at η=.75. The reflectivity then decreases to -3 dbz near cloud top. The increase in reflectivity with height in stratocumulus clouds is due to an increase in the LWC as expected from an adiabatic assumption (Frisch et al. 1998); but the decrease near cloud top may be due to entrainment. The skewness of the distribution decreases with height with a skewness of.57 near cloud base to.11 at η=.75. The skewness is negative (-.42) near cloud top. Positive skewness in the lower 4/5 th of the cloud suggests that there are fewer in number but higher than the mean reflectivity samples present. These might be due to bigger drops transported towards cloud base by downdraft or some giant cloud condensation nuclei (GCCN) activated that are advected from subcloud layer through updrafts. The decrease in the skewness could also be due to increase in the mean reflectivity that shifts the mode of the distribution but it is also noteworthy that the lowest significant reflectivity observed increases with height till η=.75. The results shown represent an ensemble pdf of cloud reflectivity under various conditions at cloud depth normalized heights. As the reflectivity in stratocumulus clouds increases with height, thicker clouds generally have the higher reflectivity near cloud top compared to thinner clouds. This may affect the skewness interpretation near cloud top, but since skewness decreases with height through the cloud layer, the interpretation that entrainment is causing a decrease in bigger drops is plausible.

62 41 % % % % Variance =.1 m 2 s 2 Skewness =.23 η=1 Variance =.15 m 2 s 2 Skewness =.29 η=.75 Variance =.22 m 2 s 2 Skewness =.28 η=.5 Variance =.25 m 2 s 2 Skewness =.31 η=.25 w>.5 ms 1 = 3.9% w>1 ms 1 =.6% w<.5 ms 1 = 5.7% w< 1 ms 1 =.6% w>.5 ms 1 = 7.7% w>1 ms 1 = 1% w<.5 ms 1 = 1% w< 1 ms 1 =.6% w>.5 ms 1 = 1.9% w>1 ms 1 = 2.1% w<.5 ms 1 = 13.9% w< 1 ms 1 = 1.7% w>.5 ms 1 = 11.5% w>1 ms 1 = 2.7% w<.5 ms 1 = 16.1% w< 1 ms 1 = 2.5% % 2 1 Variance =.27 m 2 s 2 Skewness =.27 η= w>.5 ms 1 = 1.9% w>1 ms 1 = 2.8% w<.5 ms 1 = 18.2% w< 1 ms 1 = 3.3% Vertical Velocity w (ms 1 ) Figure 3.2: Histogram of observed vertical velocity (w) at five different cloud depth normalized levels (η) from η=1 at cloud top (top panel) to η= at cloud base (bottom panel). Also reported are the variance and the skewness of the distribution at each level along with conditionally sampled updraft and downdraft fraction.

63 42 The histogram of vertical velocity at five different normalized cloud thickness levels is shown in Fig 3.2. Also shown are the variance, skewness, percent of updrafts observed stronger than.5 ms -1 and 1 ms -1 and percent of downdrafts stronger than -.5 ms -1 and -1 ms -1 at each level. Similar to Fig 3.1, the 4 sec dataset is used in this histogram. The mean vertical velocity is almost zero at all levels. The updrafts are denoted by positive vertical velocity and downdrafts by negative vertical velocity. The variance is highest at cloud base.27 m 2 s -2 and decreases with height. The decrease from cloud base to the middle of the cloud is.5 m 2 s -2 but from the middle of the cloud to cloud top the decrease is.12 m 2 s -2. A positive skewness suggests that the tail of the distribution for updrafts is longer than that of the downdrafts. Hence there are fewer but stronger updrafts present compared with the absolute value of the strongest downdrafts. The skewness is positive at all levels with a value of about.25. Hence the updrafts are stronger than the downdrafts in absolute value at all levels. This is consistent with model simulations denoting positive skewness in the cloud layer (Stevens et al. 25; Golaz et al. 25; Zhu and Zuidema 29). About 11% of updrafts near cloud base are stronger than.5 ms -1 and about 3% are stronger than 1 ms -1. The percent of updrafts decreases with height and only about 4% of updrafts are stronger than.5 ms -1 near cloud top and about.6% are stronger than 1 ms -1. But the decrease is not linear and occurs mainly in the upper half of the cloud with an almost constant profile in the lower half of the cloud. The occurrences of downdrafts stronger than -.5 ms -1 and -1 ms -1 near cloud top are about 5.7% and.6% respectively. The

64 43 downdraft fraction increase in strength with decrease in height, suggesting that the downdrafts get stronger from cloud top to cloud base. As stated previously, half hour statistics of vertical velocity variance, skewness, updraft fraction and downdraft fraction were calculated for all the cases. Fig 3.3 shows the mean profiles of these parameters from all the 141 half hour periods. The updraft and downdraft fraction was also conditionally sampled for 6 different thresholds. Also shown in the variance panel is the mean Doppler spectrum width in all the periods that is representative of the turbulence within the radar pulse volume. The error bars in the variance and skewness plots correspond to the standard deviation of the quantities within the 141 half-hour periods. The variance is a maximum near cloud base and decreases with height. The Doppler spectrum width remains almost constant throughout the cloud layer. The ratio of the variance to the Doppler spectrum width increases with height with the two being comparable near cloud top. This suggests that the processes are occurring at scales smaller than the radar pulse volume and have almost equal amount of energy at scales less than and greater than the radar pulse volume near cloud top. The high variance at the cloud base may result since 7 out of the 11 cases analyzed are associated with surface forced convection. The net longwave radiative flux at the cloud base is always positive as the land surface temperature is always higher than the cloud base temperature. On the other side the longwave cooling near cloud top might be reduced by solar heating due to daytime. This might be another reason for the variance to be higher near cloud base compared with cloud top.

65 44 The mean skewness is positive with a small increase from η= (cloud base) to η=.25. The skewness then remains constant with a decrease to a negative value near cloud top. It can be seen that the standard deviation bars are large compared to the value itself suggesting that the skewness is extremely variable. Almost constant skewness shows that the ratio of the third to the second moment of vertical velocity is also constant. Cloud Depth Normalized Height Variance (m 2 s 2 ) ms 1.1 ms 1.25 ms 1.5 ms 1.75 ms 1 1 ms Updraft Fraction (%) Skewness Downdraft Fraction (%) Figure 3.3: The cloud depth normalized profile of variance (top left), skewness (top right), updraft fraction (bottom left) and downdraft fraction (bottom right) from half hour periods from all the cases. Also shown is the mean Doppler spectrum width profile (dashed) in the variance panel. The error bars correspond to the standard deviation of the parameter within the 141 half hour periods. The mean updraft and downdraft fraction are also shown for six different thresholds. The updraft fractions are always less than the downdraft fraction for the

66 45 same threshold. The updrafts for all thresholds are almost constant from cloud base to the middle of the cloud and then decrease towards the cloud top. The downdrafts increase almost linearly from cloud top to the cloud base. The exact reason for this cannot be deduced from observations alone. The mass-flux was also calculated using the classic plume decomposition approach as explained by Arakawa and Schubert (1974). The mean vertical velocity (w) was calculated for every half hour period as per equation 3.2, using the average vertical velocity within updrafts (w u ), the fractional updrafts within that period (σ u ), the average vertical velocity within downdrafts (w d ) and the fraction downdrafts within that period (σ d ). w= wuσ u + wdσ d (3.2) Then the mass-flux (F kg m -2 s -1 ) was calculated for velocities from -3 ms -1 to 3 ms -1 binned at every.1 ms -1 and having width of ±.5 ms -1 in each direction using equation 3.3. F =ρ ( ) a w w σ (3.3) where w is the average velocity of samples within that bin, σ is the time fraction of samples observed at each height within that bin interval and ρ a is the density of air that is assumed to be constant at 1.2 kg m -3.

67 46 Mass Flux (kgm 2 s 1 ).4.2 η= η= η= η= η= Vertical Velocity (ms 1 ) Figure 3.4: The averaged mass-flux as a function of vertical velocity at five different cloud depth normalized levels (η) with η=1 at cloud top (top panel) to η= at cloud base (bottom panel).

68 47 The mean vertical velocity ( w ) is always close to zero for all the half hour periods at all heights. This is can be noted by no mass transport carried by drafts with velocities near zero. Near cloud base the maximum transport is associated with eddies having velocities of ~.3 ms -1 in the updraft regime and ~.4 ms -1 in the downdraft regime. Mass is being transported by eddies with updrafts greater than 1.5 ms -1, but comparatively little mass is being transported by downdrafts stronger than -1.5 ms -1. The velocity corresponding to the maximum mass-transport decreases with height for both updraft and downdraft regimes. Since the mass transports are for an ensemble of all the 141 half hour periods, the transports by eddies with velocities higher than 1.5 ms -1 in each regime could be greater in some cases. 3.2 Variability of Vertical Velocity Instead of analyzing each case to understand the nature of turbulence and the associated processes, we approach the problem statistically. The half-hour periods were classified based on criteria related to physical processes and the associated differences in the vertical velocity structure are analyzed. The objective is not to understand the cause and effect of the turbulence and the associated vertical velocity structures, but to statistically define how the vertical velocity characteristics vary under different conditions scenarios Surface VSHF Flux One of the factors responsible for maintaining and generating turbulence in the boundary layer is buoyancy (Stull 1988). Hence, an attempt is made to classify

69 48 the half hour periods based on the surface buoyant production. The mean surface VSHF for all the cases is Wm -2, hence the surface values of VSHF are used classify periods as stable (VSHF<1 Wm -2 ) and unstable (VSHF>6Wm -2 ). The words stable and unstable are used as simple indicators and I acknowledge that in the periods classified as stable forced convection may be in play. Application of this criterion gave 5 stable and 44 unstable 3-minute periods. Further, the distinction is not made based on daytime and nighttime periods since in certain cases the surface VSHF is negligible in the afternoon due to heavy precipitation just before the period. In other cases the flux is high in the early evening after sunset when the land surface is still warm due to daytime solar heating. The turbulence generated during the stable cases may be due to cloud top radiative cooling or shear in the BL, although the turbulence or least part of the turbulence generated during the unstable cases is due to surface buoyancy production. Due to the lack of BL wind profiles, it is not possible to fully identify cases where there may be shear production and thus find periods when the turbulence is solely due to cloud top cooling or to surface buoyancy production. Fig 3.5 compares the average variance and skewness for periods where the VSHF is less than 1 Wm -2 (stable) and surface VSHF greater than 6 Wm -2 (unstable). Also shown is the average Doppler spectrum width for these two classifications. The error bars denote the standard deviation of the parameters for the chosen half hour periods. The variance in the lower half of the cloud is higher for unstable periods compared with stable periods. But the variance near the cloud top is higher for stable cases than the unstable cases. The high variance near cloud

70 49 base for the unstable periods compared with the stable periods can be attributed to the presence of buoyant updrafts originating at the surface due to high surface fluxes that are absent in the stable periods. The higher variance near cloud top during the stable periods compared with the unstable periods could be due to presence of turbulence generation at the cloud top due to radiative cooling. The variance at the cloud top during unstable cases is low and is comparable in magnitude to the subgrid scale variance as denoted by the mean Doppler spectrum width. Since cloud top radiative cooling is present at all times, the low variance at cloud top observed during the unstable cases is difficult to interpret. One of the reasons for this might be that as most of the unstable cases are observed during the daytime when solar heating in the cloud top may counter-balance the longwave radiative cooling, resulting in weaker turbulence. The Doppler spectrum width is smaller in the unstable periods than the stable periods. This suggests that more energy is in the resolved large eddies than in eddies smaller than the radar pulse volume in the unstable periods compared with the stable periods. The ratio of the Doppler spectrum width to the variance changes from about.16 at cloud base to almost 1 near cloud top for unstable periods. But for the stable periods it changes from.4 to.8 from cloud base to cloud top. It is difficult to assess from the observations alone if the differences in the Doppler spectrum width observed for this classification are scientifically significant. The skewness is weakly negative throughout the cloud layer for the stable periods. But for unstable cases the skewness is positive throughout the cloud layer and weakly negative near the cloud top. This along with the variance profile

71 5 suggests that the downdrafts are fewer but much stronger than the updrafts near the cloud top in both scenarios. Also it is worth to note that the skewness profile does not change its sign in either case in the lower 4/5 th of the cloud, suggesting that the stronger updraft or downdraft cores make it through the entire cloud layer. Since the skewness profiles in both scenarios are almost constant in the lower 4/5 th of the cloud, the third order moment of vertical velocity ( w variance profile in each case. 3 ' ) also has similar shape as the Cloud Depth Normalized Height Stable Unstable Variance (m 2 s 2 ) Skewness Figure 3.5: Average variance (left) and skewness (right) profiles of half hour periods classified based on the surface VSHF values as stable or unstable. Also shown is the average Doppler spectrum width (dashed lines) for the distinction in the variance panel. The error bars denote the standard deviation of the parameters within those half hour periods.

72 51 Shown in Fig 3.6 is the mean half hourly updraft and downdraft fraction for stable and unstable periods. The updrafts and downdrafts are also conditionally sampled for six different threshold values as in Fig 3.3. Since the unstable periods are surface forced, the updraft fraction for all the thresholds is greatest at the cloud base and decreases in the upper half of the cloud. For the stable periods the updraft fraction is about the same at all levels with a slight decrease in the upper half of the cloud. The downdraft fraction increases with height in both scenarios. The increase in downdraft fraction from cloud top to the middle of the cloud is higher than from middle of the cloud to cloud base in case of unstable periods. Cloud Depth Normalized Height Stable Updraft Fraction (%) Downdraft Fraction (%) Unstable ms ms 1.25 ms ms ms 1 1 ms Updraft Fraction (%) Downdraft Fraction (%) Fig 3.6: Average updraft fraction (top panels) and downdraft fraction (bottom panels) profiles for stable periods (left panels) and unstable periods (right panels).

73 52 In the stable periods the downdraft fraction increases almost linearly from cloud top to base. The higher cloud base downdraft fraction for a threshold of -1 ms -1 compared with the equivalent updraft fraction in the stable cases suggests that the variance observed near the cloud base is mostly due to downdrafts rather than the updrafts. The increase of downdraft fraction with height is difficult to explain from these observations alone. But it may be due to evaporative cooling in the entrained free Tropospheric air that can make the parcel more negatively buoyant. Cloud Depth Normalized Height Ratio of Unstable to Stable 1 ms 1.1 ms 1.25 ms 1.5 ms 1.75 ms 1 1 ms Updraft Fraction Ratio Downdraft Fraction Ratio Fig 3.7: Ratio of the mean updraft fraction (left) and mean downdraft fraction (right) during the unstable periods to that during the stable periods.

74 53 To further characterize the differences between updrafts and downdrafts in the two scenarios, the ratio of the mean updraft fraction and the mean downdraft fraction for the unstable to that for stable periods are shown in Fig 3.7. The ratio is almost unity throughout the cloud layer for a threshold of less than.5 ms -1, but there are differences in the ratios for higher thresholds. The updraft fraction ratio for velocities greater than.5 ms -1 is greater than unity in the lower 4/5 th of cloud but decreases to less than unity near cloud top. This suggests that compared with stable periods, the unstable periods have about twice as much updrafts stronger than.75 ms -1 near cloud base. Since the ratio is less than unity near cloud top, there are more updrafts near cloud top in the stable periods compared with unstable periods. There are about 1 times more updrafts greater than 1 ms -1 near cloud top during stable cases compared with the unstable cases. The result is difficult to interpret from these observations alone, but this may be due to mass-conservation alone since there are more downdrafts observed in the stable case compared with the unstable cases. The downdraft fraction ratio is less than unity in the upper half of the cloud and almost unity below that. Hence there are more strong downdrafts (<-.5 ms -1 ) in stable periods compared with the unstable periods in the upper half of the cloud. While in the lower half of the cloud same amount of downdrafts are observed in both scenarios.

75 54 Mass Flux (kgm 2 s 1 ).4.2 η= η= η= η= η=.2 Stable Unstable Vertical Velocity (ms 1 ) Figure 3.8: The averaged observed mass-flux for stable periods (red) and unstable (blue) as a function of vertical velocity at five different cloud depth normalized levels (η) with η=1 at cloud top (top panel) to η= at cloud base (bottom panel).

76 55 The mass-flux transport as a function of velocities was also calculated and the averaged mass-flux for the two stability classifications is shown in Fig 3.8. Although the peak of the distribution in the updraft regime at the cloud base is lower in unstable periods as compared to stable periods, transport by eddies with higher velocities (>1 ms -1 ) is much higher in unstable periods compared with stable periods. The structure is similar in the lower half of the cloud, but above it the transport by eddies stronger than.5 ms -1 is higher in stable periods compared with unstable periods. This is consistent with the stronger (>1ms -1 ) updrafts observed in the stable cases compared with the unstable cases near cloud top. The mass-flux in the downdraft regime, although different for the two scenarios in the upper half of the cloud, is nearly the same in the lower half. The velocity of eddies causing a maximum mass transport is lower during unstable periods compared with the stable periods in the downdraft regime near cloud top Cloud Thickness Previous modeling studies (Brown et al. 22; Zhu and Zhao 28; Zhu and Zuidema 29 etc.) have shown that the variance peaks in the middle of the BL. But the ground-based vertically pointing cloud radar can only observe the cloudy portion of the BL. Hence, to put the results reported earlier into perspective and to assess if any distinct vertical structure of the variance and skewness can be observed, the ratio of cloud thickness to the BL depth (CBR) is used to develop a classification scheme. The cloud top height is used as a surrogate for the BL depth. A total of 69 half hour periods were observed with a CBR of less than.3 with an average BL

77 56 depth of 13 m, a surface VSHF of 39 Wm -2, and a cloud thickness of 245 m. For a CBR greater than.3 there were a total of 72 half hour periods with an average BL depth of 861 m, a cloud thickness of 382m and a surface VSHF of 31 Wm -2. Cloud Depth Normalized Height CBR<3% CBR>3% Variance (m 2 s 2 ) Skewness Figure 3.9: Average variance (left) and skewness (right) of half hour periods classified based on the ratio of cloud thickness to BL depth (CBR). Also shown is the average Doppler spectrum width (dashed lines) for the distinction. The error bars denote the standard deviation of the two parameters within those half hour periods. Fig 3.9 shows the variance and skewness profile for the CBR classifications. The variance is similar regardless of the percent of the BL occupied by the cloud. But the variance within the pulse volume is higher in periods when the CBR is greater than.3 compared to periods when CBR is less than.3. The skewness is

78 57 almost zero at all levels for a CBR less than.3, but the skewness is weakly positive for periods with CBR greater than.3. The skewness is negative at the top in both cases. This suggests that stronger updrafts with roots in the mixed layer may extend to the cloud base when the cloud occupies a larger portion of the BL, but cannot when the cloud is thin and at a higher height above the surface. Furthermore, positive skewness with a similar variance as periods with negative skewness shows that the variance is modulated by updrafts rather than downdrafts in both cases. Hence, there are strong updrafts for a CBR greater than.3 with no strong downdrafts. But with a CBR less than.3, similar strengths of updrafts and downdrafts are present making the skewness almost zero. Since the variance is similar in magnitude, the near zero skewness for cases with CBR less than.3 suggests that the third moment of vertical velocity ( w 3 ' ) is almost negligible in those periods, but it is considerably higher in periods for CBR greater than.3. The updraft and downdraft fraction for the CBR classifications are shown in Fig 3.1. Although the skewness is almost zero or slightly positive in the two cases, the updraft fraction is less than the downdraft fraction for both classifications. The general structure of updraft fraction decreasing with height, but the downdraft fraction increasing from cloud top towards cloud base is observed in both scenarios. Apart from the magnitude, the updraft and downdraft vertical profiles are similar.

79 58 Cloud Depth Normalized Height CBR<3% Updraft Fraction (%) Downdraft Fraction (%) CBR>3% ms ms ms ms ms 1 1 ms Updraft Fraction (%) Downdraft Fraction (%) Figure 3.1: Average updraft fraction (top panels) and downdraft fraction (bottom panels) during periods with CBR less than.3 (left panels) and periods with CBR greater than.3 (right panels). Shown in Fig 3.11 is the ratio of average updraft fraction and average downdraft fraction for CBR less than.3 to periods with a CBR greater than.3. It can be seen that the downdraft fraction is similar regardless of the amount of BL occupied by the cloud. This suggests that the processes generating and maintaining downdrafts are independent of the location of cloud within the BL. A process such as cloud top radiative cooling or entrainment that mainly depends on the cloud top height, inversion strength and the tropospheric stability could be responsible for this. The updraft fractions ratios are almost constant vertically for updrafts less than.5

80 59 ms -1. The updraft fraction ratio increases in the upper half of the cloud for thresholds greater than.5 ms -1, denoting more updrafts in the upper half of the cloud in periods with CBR greater than.3 compared with periods with CBR less than.3. This is consistent with surface forced turbulent updrafts decelerating as they approach the top of the boundary layer. 1 Ratio of CBR<3% to CBR>3% 1 Cloud Depth Normalized Height Updraft Fraction Ratio ms 1.1 ms 1.25 ms 1.5 ms 1.75 ms 1 1 ms Downdraft Fraction Ratio Figure 3.11: Ratio of the mean updraft fraction (left) and mean downdraft fraction (right) between periods with CBR less than.3 and periods with CBR greater than.3. The observed mass-flux as a function of velocity at five cloud depth normalized levels for the CBR classification is shown in Fig Apart from few

81 6 differences in the middle of the cloud, the mass-flux is almost similar in shape and magnitude in the downdraft regime under both conditions. This is consistent with the conclusion from Fig 3.11 that the downdraft structure is nearly the same for all the conditionally sampled thresholds. The mass-flux in the updraft regime shows different characteristics for the two cases with more transport occurring at higher velocities in the CBR greater than.3 case than the CBR less than.3 case.

82 61 Mass Flux (kgm 2 s 1 ).4.2 η=1.2 CBR<3% CBR>3% η= η= η= η= Vertical Velocity (ms 1 ) Figure 3.12: The averaged observed mass-flux for periods with CBR less than.3 (red) and CBR greater than.3 (blue) as a function of vertical velocity at five different cloud depth normalized levels (η) with η=1 at cloud top (top panel) to η= at cloud base (bottom panel).

83 Summary Eleven cases of nonprecipitating continental BL stratocumulus clouds were analyzed to characterize the vertical velocity structure of these clouds. High temporal (4 sec) and vertical resolution (45 m) data from a vertically pointing Doppler cloud radar was used for this purpose. This study provided observations of strong updrafts and downdrafts structures that are narrow and highly variable (Guo et al 28). The Doppler velocity provided the mean vertical air motion at these resolutions and the Doppler spectrum width gave an indication of the variance of the vertical velocity at scales within the radar pulse sampling volume (45m; ~2 m). Cloud depth normalized values of reflectivity, vertical velocity and spectrum width were obtained for all the cases to generate ensemble statistics. The mean reflectivity increases almost linearly with height in the lower 4/5 th of the cloud and then decreases near cloud top. This decrease can be due to entrainment that causes the LWC to be sub-adiabatic. The mean vertical velocity is near zero at all levels, and the variance decreased with height within the cloud layer. The ensemble skewness (Fig 3.3) is positive at all levels suggesting that the magnitude of the updrafts is always stronger than that of the downdrafts at all levels. The ratio of the spectrum width to the variance increases with height from about.2 at cloud base to almost 1 at cloud top, suggesting that the dominant scales of motions near cloud top are smaller than the radar pulse volume and are comparable to the energy in the resolvable scale eddies. In general the updraft fraction decreases with height in the cloud layer and the downdraft fraction is highest at cloud base decreasing with height. The mass-flux transport was also calculated as a function of updraft and

84 63 downdraft velocities. The mass transport by eddies with velocities greater than 1 ms -1 in the updraft regime are small compared with the transports by downdrafts less than -1 ms -1. Statistics of variance, skewness, updraft fraction, downdraft fraction and velocity binned mass-flux based on 3-minute averages were calculated for each case. The half hour periods were then classified based on the surface VSHF (stable or unstable) and the ratio of the cloud thickness to the BL depth ratio (CBR). It was found that the variance near cloud top is higher in periods with surface VSHF less than 1 Wm -2 (stable) compared with the periods when the surface VSHF is greater than 6 Wm -2 (unstable). The reverse is true at cloud base. The skewness is negative during stable periods but positive during unstable periods. The ratio of the updraft fraction of the two scenarios revealed that there are about 1 times more updrafts greater than 1 ms -1 near cloud top in stable compared with the unstable periods. Also there are 2.5 times more strong (>1 ms -1 ) updrafts near cloud base during unstable periods compared with stable periods. The classification based on the ratio of cloud thickness to BL depth (CBR) revealed that there are more strong (>1 ms -1 ) updrafts present when for a CBR greater than.3 as compared with the CBR less than.3 cases. Although the variance for this classification was similar in magnitude and structure, the skewness was almost zero for periods with CBR less than.3 and weakly positive for periods with the CBR greater than.3.

85 Chapter 4 Diurnal Variations and Liquid Water Transport 4.1 Case Description To further gain insights about the source, nature and effect of turbulence in nonprecipitating boundary layer stratocumulus clouds, a case on March 25, 25 is analyzed. Shown in Fig 4.1 are the time-height maps of the reflectivity, Doppler velocity and Doppler spectrum width for a two day period starting from UTC on 25 March 25. The spectral moments are from the ARSCL derived product. It can be seen that broken BL clouds, possibly broken stratus or fair weather cumulus are observed from 6: to 13: hours. A solid stratus structure is then observed for 16 hours starting from hour 16 to hour 32 of the event as shown in the Fig Since the local standard time (LST) is 6 hours behind UTC, the solid stratus structure formed at about 1: LST on March 25, 25 and continued till 2: LST on March Some high clouds were also observed, mainly in the form of falling ice particles as can be seen from a positive Doppler velocity. The positive Doppler velocities denote a motion towards the radar in Fig 4.1. After the stratocumulus event, rain was observed mainly originating from the higher clouds. Although this cannot be proven substantially, a few Doppler spectra analyzed for the period between hours 34 and 35 showed two separate peaks for cloud and precipitation droplets. The surface temperature, humidity and wind fields as observed by the tower sensors did not show any significant changes that could be attributed to a frontal passage. This was also confirmed by the surface weather maps for both days. 64

86 65 Height (km) Height (km) Height (km) ARSCL dbz ms UTC Time (Hour) ms 1 Figure 4.1: Time-height mapping of ARSCL deduced first three Doppler spectrum moments; reflectivity (top), Doppler velocity (middle) and spectrum width (bottom) from UTC starting on March 25, 25. The focus of this case study is on the non-precipitating stratocumulus cloud occurring from 16 to 32 starting from UTC on March 25, 25. LST is six hours behind UTC and all the observations in the rest of the study are reported in LST. Thus the solid stratocumulus event analyzed in detail is observed from about 1: LST to 24: LST (midnight) on March 25, 25. Shown in Fig 4.2 is the time-height map of reflectivity, mean Doppler velocity, Doppler spectrum width and LWP for the period under consideration as observed by

87 66 the MMCR and the MWR. Also shown is the LCL (blue) and ceilometer observed cloud base height (black) in the reflectivity panel. The observed reflectivity is always less than -2 dbz. The reflectivity shows a general increase with increasing height. In general, the top most cloudy range gate has a reflectivity less than the gate below. This could be due to partial beam filling or due to entrainment effects. The reflectivity near cloud top is highest at 2: LST to 22: LST. The cloud thickness is almost uniform throughout the event with a sudden decrease seen at 19: LST. The ceilometer observed cloud base height matches well the radar observed first cloudy range gate, suggesting that the radar is able to capture the entire cloud structure from base to top. The LCL follows the increase in the cloud base height until 16: LST, suggesting a surface coupled turbulent boundary layer; but after 16: LST the LCL diverges substantially from the cloud base height. The increased difference between LCL and the cloud base height indicates an increase in the degree of decoupling of the BL. Updrafts and downdraft structures can be seen in the Doppler velocity image throughout the event. The Doppler spectrum width is about.2 ms -1, throughout the event. A slight decrease in the spectrum width can be seen during 17: LST. The bottom panel in Fig 4.2 shows the LWP for the event as recorded by the MWR at a 2 sec temporal resolution. The LWP fluctuated from about 5 gm -2 to 18 gm -2 throughout the event and the changes were well correlated with changes in the cloud thickness.

88 Height (m) dbz 4 1 Height (m) Height (m) LWP (gm 2 ) ms 1 1 ms Local Time (Hour) Figure 4.2: MMCR observed reflectivity, mean Doppler velocity, Doppler spectrum width and MWR observed liquid water path for the event from top to bottom panel for the period under consideration

89 68 Shown in Fig 4.2 is a scatter plot between hourly averaged cloud thickness and the hourly averaged LWP for the event. It can be seen that the LWP is almost linearly related to the cloud thickness. Possibly the least square fit will correspond to the adiabatic value of LWP while the scatter around it denotes the deviation from the adiabatic value. Although changes of the order of 5 gm -2 within an hour could be attributed to changes in the cloud structure, the small scale high frequency fluctuations in LWP could be due to updrafts and downdrafts modifying the cloud LWC Cloud Thickness (m) LWP (gm 2 ) Figure 4.3: Scatter plot between hourly averaged cloud thickness and hourly averaged liquid water path for the entire event.

90 69 Temp ( C) RH (%) wspd (ms 1 ) wdir ( ) RH r Local Time (Hour) Figure 4.4: Surface temperature (temp), relative humidity (RH), wind speed (wspd) and wind direction (wdir) from top to bottom panel. Also shown in the RH panel is the mixing ratio (r). r (g kg 1 ) Shown in Fig 4.4 are the surface meteorological variables during the event. The surface air temperature was nearly constant and only varied between 6 C to 9 C. The surface air temperature increased from about 7 C during the start of the event to about 9 C at 16: LST and then decreased to about 6 C at midnight. The surface RH showed little variation with a decrease from about 85% at 1: LST to about 75% at 16: LST and then a linear increase to about 9% at midnight. The surface air mixing ratio varies between 3 gkg -1 and 5 gkg -1 during the event. The mixing ratio peaked at 13: LST and then decreased almost linearly to about 3.2

91 7 gkg -1 at midnight. The surface wind speed showed almost negligible variability and remained constant at 5 ms -1 from the north ω (mb day 1 ) Local Time (Hour) Figure 4.5: Hourly subsidence rate at 7 mb as derived from the ECMWF model over the ARM SGP site. Shown in fig 4.5 is the hourly subsidence rate as reported by European Center for Medium Range Weather Forecasting (ECMWF). The values are averages within a domain that has northeast and southwest points of 98.3 W 37 N and 97 W 36 N respectively. The subsidence rate is reported in pressure coordinates; hence, positive values denote downward motion while negative values upward motion. The model subsidence rate was about 1 mb day -1 until 16 LST and dipped sharply to about -4 mb day -1 at 18 LST. It then increased to about 2 mb day -1 at 2

92 71 LST and then gradually reduced to about 5 mb day -1 till the midnight. The reason for the sharp decrease and then increase from 16 to 2 hours is difficult to explain from these results only. A general decrease in the cloud top height and hence the BL depth can be seen during the 19 hour from the radar image. This might be a result of high subsidence rate during the previous hour. But it is difficult to assess if the changes in the cloud top height are due to the changes in the subsidence rate or due to variability in the clouds Height (km) θ (k) r (g kg 1 ) Wspd (ms 1 ) Wdir ( ) Figure 4.6: Potential temperature (top left), mixing ratio (top right), wind Speed (bottom left) and wind direction (bottom right) from radiosondes launched at 12:, 18: and 24: local time on 25 March 25.

93 72 Shown in Fig 4.6 are the profiles of potential temperature (θ), mixing ratio (r), wind speed (Wspd) and wind direction (Wdir) derived from the three radiosondes launched during the event. The θ profiles show a sharp inversion at the cloud top at about 12 m. The potential temperature in the cloud layer follows the moist adiabatic lapse rate in all the three soundings. An unstable θ is observed in the lowest 2 m during the 12: LST sounding due to the surface heating at this time. Two mixed layers and the cloud layer can be seen in the potential temperature profile for the 24: LST sounding. The observed θ during the 18: LST is higher compared with the other two soundings and indicates the warmer atmosphere during that time. The mixing ratio profiles show a well-mixed structure in the 12: LST and 18: LST soundings. In the 24: LST sounding the mixing ratio shows a decoupled BL with two mixed layers. The bottom mixed layer is from the surface to 2 m and the mixed layer above is from 2 m to 1 km. The top of the lower mixed layer is approximately equal to the LCL during that hour. This further validates the decoupled BL structure observed at night. The 12: LST sounding indicates a wind speed of about 6 ms -1 near the surface, increased to about 8 ms -1 in the middle of the BL and then decreased to 6 ms -1 near the top of the BL. The wind speed near the inversion is about 4 ms -1 in all of the sounding with linear increase in the free troposphere. Comparatively weak but constant with height winds were observed during the 18: LST sounding. The wind direction showed similar vertical structure in all the sounding with northerly winds within the BL and easterly winds above the BL.

94 73 Flux (Wm 2 ) Surface W* (ms 1 ) 12 1 LHF SHF VSHF Local Time (Hour) Figure 4.7: Surface sensible heat flux, latent heat flux and virtual sensible heat flux in the top panel and the surface convective velocity scale in the bottom panel. The surface SHF, LHF and VSHF for the event is shown in fig 4.7. The LHF is always positive and peaks to about 5 Wm -2 during local noon dropping to about 1 Wm -2 at night. This suggests that moisture transport was always from the surface to the air above and the transport was higher during the daytime as compared with the nighttime period. This also suggests that the land surface was always more moist than the air above. The SHF peaked at about 11 Wm -2 during local noon and then gradually dropped to below zero at might. This is consistent with the land surface warming during the daytime due to solar heating and then cooling at night. The negative SHF at night indicates that the land surface is colder than the air above it.

95 74 The VSHF follows the SHF closely and hence the surface buoyant production is highest during the day and peaks at about local noon; no buoyant production at night. The convective velocity scale (w S *) was calculated using the formulation by Stull (1988) and using the LCL as the scaling height. ( ) 1/3 ' w Tv gzlcl ws* = ' Tv (4.1) w S * was about.9 ms -1 from 1 to 16 hours and then dropped to zero at 18: LST. A w S * of about.2 ms -1 was observed from 22: to 24: LST. Since this period corresponds to night time and the surface SHF is very small, it seems reasonable that the reported positive values of SHF are due to instrument errors rather than any meteorological conditions. 4.2 Radiation Fields The observed surface upwelling longwave (LWU), downwelling longwave (LWD), upwelling shortwave (SWU), downwelling shortwave (SWD) and net radiative flux are shown in Fig 4.8. Although stratocumulus clouds have a high albedo (~.6 Los and Duynkerke 21), considerable solar radiation is able to reach the surface. The downwelling shortwave radiation peaks to about 3 Wm -2 at 13: LST and then decreases almost linearly to zero at about 18: LST. The surface also reflects some of the incident shortwave radiation which is about 4 Wm -2. The shape of the SWD is consistent with the solar radiation peaking around the middle of the day. The few high level clouds also impact the SWD and appear to decrease the SWD by about 1 Wm -2 at about 13: LST.

96 75 SW Flux (Wm 2 ) LW Flux (Wm 2 ) Net Flux (Wm 2 ) Surface Radiative Flux on SWD SWU LWD LWU Local Time (Hour) Figure 4.8: Surface radiation budget as the upwelling and downwelling shortwave radiative flux (top panel), upwelling and downwelling longwave radiative flux (middle panel) and net radiative flux (bottom panel). The observed surface LWD showed little variation throughout the event and remained at about 33 Wm -2. Due to absence of the solar heating at night and the subsequent cooling of the surface, the LWU decreased from its daytime value of about 36 Wm -2 to about 34 Wm -2 at night. The LWU is always greater than the LWD since the land surface is always warmer than the source of the LWD, which in this case is the emission from the stratocumulus clouds above. Hence there is always some cooling of the surface in the longwave part of the radiative spectrum. The net radiative flux at the surface exhibits a Gaussian type curve during the

97 76 daytime with a peak of about 2 Wm -2 on 13: LST. The net flux is negative after 18: LST since there is no solar heating after this time. To further characterize the radiation field for the case study, output from the Atmospheric and Environmental Research Inc. (AER) Rapid Radiative Transfer Model (RRTM) was analyzed. (The model output was kindly provided by Dr. Sally McFarlane through the ARM broad band heating rate profile (BBHRP) working group framework). The model includes output from RRTM-LW (Mlawer et al. 1997) and RRTM-SW (Mlawer et al. 1998). The model output vertical resolution is 5 m with 1 m resolution within the cloud layer. The optical properties of liquid clouds are implemented in the RRTM based on the parameterization by Hu and Stamnes (1993). The model run was made every minute using the atmospheric profile from the merged sounding VAP, the cloud properties from the ARSCL VAP, aerosol properties from the aerosol best estimate VAP and the shortwave surface albedo from the MultiFilter Rotating Shadowband Radiometer (MFRSR). The carbon dioxide mixing ratio was set at 36 ppmv, while the ozone properties were obtained from the total ozone mapping spectrometer (TOMS). The model settings are described in detail by Mlawer et al. (22). Since the model has inputs from various instruments and derived quantities and high temporal resolution radiative fluxes were not needed for this study, to minimize the random errors the model fluxes were averaged for 3- minute periods.

98 77 Radiative Flux (W m 2 ) 1 8 Cloud Top SWD SWU Cloud Middle Cloud Base Local Time (Hour) Figure 4.9: Half hourly averages of upwelling shortwave radiative flux (SWU) and downwelling shortwave radiative flux (SWD) at cloud top (top panel), middle of the cloud (middle panel) and cloud base (bottom panel) as determined from the RRTM. Shown in Fig 4.9 are the half hourly averaged SWD and SWU near cloud top, in the middle of cloud and near cloud base for the period in consideration. The SWD near cloud top peaks to a maximum at about 12: LST and then drops to zero at about 18: LST. The SWU, which is mostly the reflected shortwave radiation by the clouds, peaks to about 6 Wm -2 at 12: LST, giving a cloud albedo of about.6. A sudden decrease can be seen in the SWD and correspondingly in SWU during the 13: LST due to high-level clouds discussed earlier and shown in Fig 4.1. The SWU and SWD show a similar variation but are smaller in magnitude in the middle

99 78 of the cloud and at cloud base. The decrease in the SWD with height is partly due to its reflection and partly due to its absorption by the cloud. The SWD at cloud base has a peak of about 4 Wm -2 at 12: LST. This is about 1 Wm -2 lower than the observed SWD at the surface during that hour. Although the model calculated SWD at cloud base differs from the SWD at the surface by about 1 Wm -2 but show a similar shape; hence the model output can be used to gain insight on the impact of radiation on cloud processes. Radiative Flux (W m 2 ) 4 35 Cloud Top Cloud Middle Cloud Base LWD LWU Local Time (Hour) Figure 4.1: Half hourly averages of upwelling longwave radiative flux (LWU) and downwelling longwave radiative flux (LWD) at cloud top (top panel), middle of the cloud (middle panel) and cloud base (bottom panel) as determined from the RRTM.

100 79 The LWU and LWD at cloud top, middle of the cloud and at cloud base for the period in consideration is shown in Fig The LWD at cloud top is mainly controlled by the atmospheric profile of water vapor and carbon dioxide and the upper level clouds. It remained almost constant at about 25 Wm -2 during the first 6 hours and with a increase to about 3 Wm -2 during 17: LST with some variability after that. The later increase and fluctuations correspond well with the upper level clouds as seen by the radar (Fig 4.1). The LWU at the cloud top remains constant at about 32 Wm -2 throughout the period. The LWU at cloud top is mainly controlled by the cloud top temperature. The LWD and LWU in the middle of the cloud are almost the same and show very little variation. The LWU at cloud base is about 5 Wm -2 higher than the LWD at cloud base as the surface below is always warmer than the cloud base. The surface observed LWU is about 3 Wm -2 higher than the LWU at the cloud base as calculated by the model. On the other hand the LWD at the surface is about 1 Wm -2 lower than the model calculated LWD at the cloud base.

101 8 Net Radiative Flux (W m 2 ) Cloud Top Cloud Middle Net SW Cloud Base Net LW Local Time (Hour) Figure 4.11: Half hourly averages of net longwave radiative flux (Net LW) and net shortwave radiative flux (Net SW) at cloud top (top panel), middle of the cloud (middle panel) and cloud base (bottom panel) as determined from the RRTM. Fig 4.11 shows the net longwave and net shortwave fluxes at cloud top, middle of the cloud and at cloud base for the period under consideration. The upward flux is considered positive while the downward flux is considered negative. The net longwave flux at the cloud top is positive resulting in cooling of the layer. The net longwave flux in the middle of the cloud and at cloud base is almost zero denoting negligible heating or cooling to the layer. The net shortwave flux is negative and shows little variation in magnitude and structure at all levels. It reduces in

102 81 magnitude by about 3 Wm -2 from the cloud top to the middle of the cloud while remains almost the same below that. Heating Rate (k day 1 ) 3 3 Cloud Top Cloud Middle Cloud Base SW Heat Rate LW Heat Rate Local Time (Hour) Figure 4.12: Half hourly averages of shortwave heating rate (SW Heat Rate) and longwave heating rate (LW Heat Rate) at cloud top (top panel), middle of the cloud (middle panel) and cloud base (bottom panel) as determined from the RRTM. It can be deduced from Fig 4.11 that radiative flux changes from the top of the cloud layer to the middle of the cloud are greater than from middle of the cloud to the cloud base. Hence, the heating or cooling of the cloud layer is greater in the upper half of the cloud layer compared with the lower half. To further emphasize that, shown in Fig 4.12 are the shortwave and longwave heating rates near cloud top, middle of the cloud and near cloud base. The heating or cooling is highest near

103 82 cloud top while minimal in the middle of the cloud and near cloud base. Previous modeling studies have pointed out that the maxima of longwave cooling is higher than the maxima of the shortwave heating (e.g. Rogers and Koracin 1992), but probably due to coarser vertical resolution that distinction is not captured by the RRTM. The shortwave heating near cloud top is ~2 k day -1, while the longwave cooling near cloud top is heavily modulated by upper level clouds and fluctuates between -5 kday -1 to zero. It can be noticed that there is almost no heating of the cloud layer between 16: to 2:. Shown in Fig 4.13 is the divergence of radiative flux for the upper half of cloud layer. Hence, shown is the difference between the radiative flux at the middle of the cloud to that at cloud top. The positive value of flux divergence denotes heating of the upper half of the cloud layer, while negative values denote cooling of the upper half of the cloud layer. The shortwave flux divergence is always positive denoting heating and remains constant at about 4 Wm -2 during the first five hours and then gradually decreased to zero around 18: LST. The kink in the shortwave flux divergence observed at 13: LST is due to reduction in the incoming solar radiation due to upper level clouds rather than changes in the cloud absorption properties. The longwave flux divergence is always negative denoting cooling of the upper half of the cloud layer. During the first four hours, due the absence of any high level clouds, the longwave flux divergence is about -6 Wm -2. The longwave cooling at cloud top is reduced due to the presence of high level clouds from 16: to 2: LST with the longwave flux divergence reducing to almost zero during that period.

104 83 SWF (Wm 2 ) LWF (Wm 2 ) Net Flux (Wm 2 ) Rad. W* (ms 1 ) Local Time (Hour) Figure 4.13: The panels show from top to bottom the net shortwave radiative flux across upper half of cloud layer, the net longwave radiative flux across the upper half of the cloud layer, the net radiative flux across the upper half of cloud layer and the radiation velocity scale respectively.

105 84 The longwave flux divergence then decreases again with some fluctuations due to some high-level cloudiness. The net flux divergence (shortwave + longwave) is negative for the most part indicating cooling of the upper half of the cloud layer. During the first five hours, the net flux divergence is about -2 Wm -2 due to a longwave flux divergence of about -6 Wm -2 and shortwave flux divergence of about 4 Wm -2. Hence, some of the cooling of the upper half of the cloud in the longwave spectrum is balanced by the heating in the shortwave spectrum. The net flux divergence is almost zero during 16:3 LST as the longwave cooling is completely counteracted by the shortwave heating of the layer. During the nighttime, due to absence of solar heating, the net flux divergence is same as the longwave flux divergence. The net flux divergence is almost zero around 19: LST (night time) due to the presence of upper level clouds which balanced the longwave cooling. The cooling is a maximum (most negative net flux divergence) at midnight. Analogous to the surface convective velocity scale (Stull 1988), an expression is proposed for a radiative velocity scale w R * that is relevant to the turbulence generated by cloud top cooling. It is calculated as * Zthick ( ΔFR ) wr = g ct ρ p 1/3 (4.2) Equation 4.2 is used to calculate the radiative velocity scale w R * (ms -1 ) using the acceleration due to gravity g (ms -2 ), thickness of the layer Z thick (m), net flux divergence across the layer ΔF R (Wm -2 ), density of air ρ (kgm -3 ), specific heat of dry air (Jkg -1 k -1 ) and layer average temperature T (k). Radiative velocity scale is proposed to assess the impact of radiation on the BL turbulence and also to assess

106 85 the relative importance of cloud top radiative cooling and surface buoyancy flux in driving the BL turbulence. The radiative velocity scale for the period in consideration is shown in Fig 4.13 bottom panel. It was calculated for using half-hour values of net flux divergence and using the layer average temperature from the nearest sounding. It can be seen that the radiative velocity scale is negatively correlated with the net flux divergence. It is about.5 ms -1 during the first five hours and then reduces to near zero at 16:3 LST. During night when high level clouds were present, the longwave radiative cooling at cloud top was balanced by the longwave heating from the high level clouds. This can be seen during 19: LST when the radiative velocity scale is zero and shows that radiative cooling was not generating any turbulence in the cloud layer. The velocity scale is at a maximum (.6 ms -1 ) at night during and when no high-level clouds are present. Shown in Fig 4.14 are the radiative velocity scale and the surface convective velocity scale. Also shown is the total velocity scale (W T *) which is the square root of the sum of the square of the convective velocity scale and the square of the radiative velocity scale. During the first five hours, the radiative velocity scale is about half of the surface convective velocity scale. The total velocity scale is about.2 ms -1 higher than the surface convective velocity scale. This suggests that the cloud top radiative cooling is also active during the daytime despite solar heating and acts to increase the turbulence in the BL beyond the surface driven value. The surface convective velocity scale drops to zero at night due to absence of any surface buoyancy production. Hence, during the night, the total velocity scale is the same as

107 86 the radiative velocity scale. The turbulence is purely driven by the radiative cooling occurring at the cloud top. It is worthwhile to note that although the longwave flux at the cloud top is primarily a function of the cloud top temperature; the longwave cooling is heavily modulated by the presence or absence of high level clouds. It can be seen that during the absence of any high level clouds (21: LST), the total velocity scale is about.6 ms -1, while during the presence of high level clouds and diminished cooling, the velocity scale drops to about.3 ms -1 (22: LST). W* (ms 1 ) 1.2 W * 1.1 R W 1 S * W *.9 T Local Time (Hour) Figure 4.14: The convective velocity scale, radiative velocity scale and total velocity scale for the period in consideration.

108 Turbulence Structure Since all of the radar returns were lower than -2 dbz (Fig 4.2), an attempt is made to characterize the turbulence structure of the cloud using the technique described earlier in chapter 2. The necessary condition for the application of the technique is absence of any precipitation size droplets, which can be tested from the correlation between the reflectivity and mean Doppler velocity. Shown in Fig 4.15 is a time-height mapping of hourly correlation coefficient (r) between the reflectivity and mean Doppler velocity for the period under consideration. A positive correlation coefficient denotes higher reflectivity within updrafts and lower reflectivity within downdrafts. While a negative correlation coefficient denotes lower reflectivity within updrafts and higher reflectivity within downdrafts. It can be seen that the values of the correlation coefficient are low (-.2<r<.2) for most of the event except in the lower half of the cloud during 19: to 22: LST where the correlation coefficients are highly negative (<-.5). A scatter plot between the reflectivity and mean Doppler velocity for those periods (not shown) revealed that the negative correlation is mainly due to comparatively higher reflectivity within downdrafts as opposed to lower reflectivity within updrafts.

109 88 Height (m) Height (m) Local Time (Hour) ms 1.2 Figure 4.15: Time-height mapping of the hourly correlation coefficient between the reflectivity and Doppler velocity (top panel) and the time-height mapping of hourly mean Doppler velocity (bottom panel) for the period under consideration. Hence, although the reflectivity values are less than -2 dbz, a few precipitation size hydrometeors are present within the radar sampling volume during some periods. The hourly mean Doppler velocity shown is the lower panel does not show any significant changes and remains within ±.2 ms -1 throughout the event. This further suggests that precipitation size hydrometeors were only present during some of the radar returns during 19: to 22: LST. It is difficult to identify the radar returns that may have precipitation size hydrometeors in them. The turbulence parameters retrieval technique is applied here to the entire event and it is

110 89 acknowledge that the retrieved turbulence parameters near the cloud base during 19: to 22: LST may not be valid due to presence of precipitation size hydrometeors. But the retrieved parameters might still provide some additional information regarding the turbulence structure of the cloud. Height (m) Height (m) Height (m) Local Time (hour) m 2 s 2 m 2 s Figure 4.16: Time-height mapping of vertical velocity variance (top panel), hourly averaged Doppler spectrum width (middle panel) and vertical velocity skewness (bottom panel) calculated for each hour for the period under consideration. Shown in fig 4.16 is the variance, Doppler spectrum width and skewness of the vertical velocity calculated for each hour. Also shown are the mean cloud base height and mean cloud top height for every hour. A general structure of variance

111 9 decreasing with height is seen throughout the event. The variance at the cloud base is high during the daytime compared with that at nighttime. The variance at the cloud base gradually increases in time to peak around 15: LST and then decreases to about.15 m 2 s -2 and remains almost constant for the rest of the event. The Doppler spectrum width, which gives a measure of the vertical velocity variations within the radar pulse volume, is also shown in Fig It is about.5 m 2 s -2 and constant with height throughout the event. The spectrum width during 17: LST and 18: LST is less as compared to during other hours. The skewness varies from about -1 to 1 during the event. The skewness is generally positive during the daytime (1: to 16: LST) and negative during nighttime (17: to 23: LST). Positive skewness during the daytime suggests that the variance is controlled by the updrafts rather than the downdrafts during the daytime, while negative skewness during nighttime suggests that the variance is controlled by the downdrafts. Some of the negative skewness during the later hours may result due to precipitation size droplets within some of the radar returns. Updraft and downdraft fraction were also calculated for every hour. The fractions were also calculated using different thresholds similar to chapter 3. Shown in Fig 4.17 are the time-height maps of updraft and downdraft fraction greater than.5 ms -1 and less than -.5 ms -1 respectively. The updraft fraction is always less than the downdraft fraction with both decreasing from cloud base to cloud top. The updraft fraction increased to about 2% near the cloud base from 1: LST to 15: LST. Then it decreased to about 5% and remained the same for the rest of the event except for 21: and 23: LST. The increased updraft fraction during these

112 91 hours is well correlated with the total velocity scale calculated earlier and shown in Fig Although fewer, updrafts stronger than.5 ms -1 were present near the cloud base from 19: LST to 22: LST, where high negative correlation between reflectivity and mean Doppler velocity was found. This further indicates that some of the radar samples during those hours had precipitation size droplets in them. Height (m) % Height (m) Local Time (hour) 8 % 4 Figure 4.17: Time-height mapping of the percent of updraft fraction (top panel) and percent of downdraft fraction (bottom panel) calculated for each hour for the threshold.5 ms -1 for the period under consideration The downdraft fraction at the cloud base was about 2% from 1: to 18: LST and decreased to about 1% at 19: LST The decrease in the downdraft fraction during that hour corresponds well with the zero total velocity scale for that

113 92 hour and further validates the formulation of radiative velocity scale. The downdraft fraction then increased again to about 15% remained almost constant for the rest of the event. These changes also correspond well with the total velocity scale discussed earlier. 15 Mass Flux Height (m) Local Time (Hour) kgm 2 s 1 Figure 4.18: Time-height mapping of hourly averaged updraft mass-flux for the period in consideration. Also calculated was the mass-flux using equation 3.3 and discussed in chapter 3. Shown in Fig 4.18 is the updraft mass-flux for the period under consideration. The downdraft mass-flux was similar in magnitude but opposite in sign, conserving the total mass. The mass-flux showed a decrease with increase in height. Mass-flux at cloud base was higher during than day compared to that at

114 93 night. These periods also have higher variance and updraft fraction compared to other hours. Lower values of mass-flux during 18: and 19: LST correspond well with almost zero total velocity scale during those hours. The mass-flux during 23: LST is comparatively greater than any nighttime hour and the same is true for the total velocity scale. This further validates the formulation of the radiative velocity scale and total velocity scale. 4.4 Liquid Water Structure The radar-radiometer technique to derive the cloud LWC described earlier in Chapter 2 was applied to the event to retrieve cloud liquid water. Although few precipitation size droplets were present at the cloud base from 19: to 22: LST, the technique is applied to the entire event. The retrieved LWC near cloud base during those hours might not be accurate, since the assumptions in the technique break down in the presence of precipitation (Pujol et al. 27). But the technique has been applied in the past to weakly drizzling clouds (Meywerk et al. 25) when the reflectivity was peaking near cloud top due to higher LWC rather than near cloud base due to comparatively larger drizzle drops falling out of the cloud. As similar conditions are observed during from 19: to 22: LST, the application of the technique to retrieve the LWC during those hours seems reasonable. Shown in fig 4.19 is the retrieved LWC per equation 2.2 for the entire event. The MMCR data was averaged to match the MWR temporal resolution of 2 sec. Hence, the retrieved LWC has temporal resolution of 2 sec and spatial resolution of 45 m in vertical. Since the data is an average of 2 sec and the radiometer pulse

115 94 volume has horizontal dimension of about 8 m at 1 km, the advective scales dominate the horizontal spatial resolution of the retrieved LWC. The LWC has the general feature of increase with increase in height. The LWC near cloud top during 17: LST is about.6 gm -3. The LWC at the top most cloud gate is less than the maximum value either due to partial beam filling of the radar pulse volume lowering the reflectivity or due to entrainment effects. The LWC near cloud top during 2: LST to 22: LST is lower than during 16: LST to 18: LST, although the cloud thickness is almost similar during those hours. This indicates that the cloud was more sub-adiabatic during 2: to 22: LST compared with 16: to 18: LST. Figure 4.19: Time-height mapping of the liquid water content for the period under consideration derived using the radar-radiometer technique.