NUMERICAL MODELING OF ALTOCUMULUS CLOUD LAYERS

Transcription

1 NUMERICAL MODELING OF ALTOCUMULUS CLOUD LAYERS by Shuairen Liu A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Meteorology The University of Utah March 1998

2 Copyright c Shuairen Liu 1998 All Rights Reserved

3 THE UNIVERSITY OF UTAH GRADUATE SCHOOL SUPERVISORY COMMITTEE APPROVAL of a dissertation submitted by Shuairen Liu This dissertation has been read by each member of the following supervisory committee and by majority vote has been found to be satisfactory. Chair: Steven K. Krueger Gerald Mace Patrick A. McMurtry Jan Paegle Kenneth Sassen

4 THE UNIVERSITY OF UTAH GRADUATE SCHOOL FINAL READING APPROVAL To the Graduate Council of the University of Utah: I have read the dissertation of Shuairen Liu in its final form and have found that (1) its format, citations, and bibliographic style are consistent and acceptable; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the Supervisory Committee and is ready for submission to The Graduate School. Date Steven K. Krueger Chair, Supervisory Committee Approved for the Major Department Jan Paegle Chair/Dean Approved for the Graduate Council Ann W. Hart Dean of The Graduate School

5 ABSTRACT Altocumulus (Ac) clouds are predominately water clouds and typically less than several hundred meters thick. Ac cloud heights are mid-level, from 2 to 8 km. Ac clouds cover large portions of the Earth and play an important role in the Earth s energy budget through their effects on solar and infrared radiation. A two-dimensional cloud resolving model (CRM) and a one-dimensional turbulent closure model (TCM) are used to study Ac clouds with idealized initial conditions. An elevated mixed layer model (MLM) is developed and the results for the MLM are compared with results for CRM. The impacts of large-scale vertical motion, and solar and IR radiation, the utility of the TCM, the mixed layer characteristics and circulation of Ac layers, the turbulent kinetic energy (TKE) budget, and effects of relative humidify (RH) above the cloud are studied with a series of numerical simulations using the CRM and TCM. The results show that weak large-scale vertical motion may allow for a long lifetime of Ac clouds. In the nocturnal case, feedbacks between the liquid water path (LWP), IR radiation, and entrainment lead to an Ac layer with a nearly steady structure and circulation. The solar radiation in the diurnal case leads to decreases in the LWP, circulation intensity, and entrainment rate during the day. The comparison of TCM and CRM simulations suggests that TCM simulations can portray the basic characteristics of Ac clouds. The Ac convective layer includes mainly the cloud region and a shallow subcloud layer. In the Ac convective layers, the updrafts are wide and weak, whereas the downdrafts are narrow and strong. The updrafts are associated with regions of large cloud water mixing ratio, and the downdrafts with the regions of small cloud water mixing ratio. In Ac layers, the TKE is as large as in stratocumulus-topped-boundary-layer (STBL). The TKE is produced by buoyancy in the cloud region, dissipated by viscous dissipation, and

6 redistributed upward and downward through turbulent transport. The Ac clouds become deeper when the RH above the cloud is high and can be maintained even if the RH above cloud is very low. The results and observations suggest that Ac layers are approximately wellmixed and similar to STBL. Therefore, an elevated MLM has been developed and tested for Ac layers. The Ac MLM uses a method for determining the entrainment rate at the mixed layer top that is used in many MLMs of the STBL. At the mixed layer base, the Ac mixed-layer model detrains at a rate that keeps the ratio of buoyant consumption of TKE in the subcloud layer to buoyant production in the cloud layer less than or equal to a critical value. The MLM results were good compared to the CRM results for cloud thickness, and fair for the LWP. The mixed layer magnitudes of conservative variables and flux profiles for the MLM agree reasonably to the results for the CRM. v

7 CONTENTS ABSTRACT... LIST OF FIGURES... LIST OF TABLES... iv vii xii ACKNOWLEDGMENTS... xiii CHAPTERS 1. INTRODUCTION CRM AND TCM SIMULATIONS Initial conditions and simulation cases Comparison to SC A simple analysis of Ac soundings Effect of large-scale vertical motion Effects of radiation Comparison of TCM and CRM Mixed-layer characteristics Circulation characteristics Updarfts and downdrafts TKE budget Different RH above Ac clouds THE ELEVATED MIXED-LAYER MODEL Description of elevated MLM MLM simulations CONCLUSIONS APPENDIX: 2D CRM AND 1D TCM REFERENCES...141

8 LIST OF FIGURES 2.1 Initial profiles of potential temperature for CRM and TCM simulations Initial profiles of water vapor mixing ratio for CRM and TCM simulations Time-dependent behavior of domain averaged liquid water content ( ρ 0 l) in SC and Q Vertical profile of horizontally averaged liquid water content (ρ 0 l)at various times for SC. From Starr and Cox (1985b) Vertical profile of horizontally averaged liquid water content (ρ 0 l)at various times for Q Time-dependent behavior of domain averaged total kinetic energy (TKE) in SC and Q Temperature profiles from soundings at Salt Lake City, Utah at hour 1200 UTC on November 6, 1992 and at hour 1200 UTC on July 18, The profiles of q v from soundings at Salt Lake City, Utah at hour 1200 UTC on November 6, 1992 and at hour 1200 UTC on July 18, Time-dependent behavior of domain averaged liquid water content ( ρ 0 l) for different large-scale vertical velocities (Q24, Q05 and Q27) Time-dependent behavior of liquid water path (LWP) for a nocturnal (Q92, Q93, Q95, Q97, and Q99) and a diurnal case (Q92, Q94, Q96, Q98, and Q90) Contour plot of the field of cloud water mixing ratio (g kg 1 ) for a nocturnal case (Q92, Q93, Q95, Q97, and Q99) Contour plot of the field of cloud water mixing ratio (g kg 1 ) for a diurnal case (Q92, Q94, Q96, Q98, and Q90) Radiative heating rate time-height cross section (K h 1 ) for nocturnal case (Q92, Q93, Q95, Q97, and Q99) IR radiative heating rate time-height cross section (K h 1 ) for diurnal case (Q92, Q94, Q96, Q98, and Q90) Solar radiative heating rate time-height cross section (K h 1 ) for diurnal case (Q92, Q94, Q96, Q98, and Q90)

9 2.16 Total radiative heating rate time-height cross section (K h 1 ) for diurnal case (Q92, Q94, Q96, Q98, and Q90) Average vertical velocity of updrafts and downdrafts (6-hour average) for nocturnal case (Q92, Q93. Q95, and Q97) Average vertical velocity of updrafts and downdrafts (6-hour average) for diurnal case (Q92, Q94, Q96, and Q98) Time-dependent behavior of domain averaged liquid water content ( ρ 0 l) for vertical grid size of 100 m, initial profiles of type 1, and 1D cases (X25 and X26) and 2D cases (Q05 and Q26) Time-dependent behavior of domain averaged liquid water content ( ρ 0 l) for vertical grid size of 50 m, initial profiles of type 1 (1D case X34 and 2D case Q34), and type 2 (1D case X31 and 2D case Q30) Time-dependent behavior of domain averaged liquid water content ( ρ 0 l) for vertical grid size of 25 m, initial profiles of type 2 and 1D case (X91), and 2D case (Q92, Q93, Q95, Q97, and Q99) Contour plot of the field of cloud water mixing ratio (g kg 1 ) for a nocturnal case X91 with 1D TCM simulation Vertical profiles of liquid static energy at various times for the TCM (X91) and CRM (Q92, Q93, Q95, Q97, and Q99) simulations Vertical profiles of total water mixing ratio at various times for the TCM (X91) and CRM (Q92, Q93, Q95, Q97, and Q99) simulations Vertical profiles of liquid water mixing ratio at various times for the TCM (X91) and CRM (Q92, Q93, Q95, Q97, and Q99) simulations Vertical profiles of radiative heating rate at various times for the TCM (X91) and CRM (Q92, Q93, Q95, Q97, and Q99) simulations Vertical profiles of total water flux at various times for the TCM (X91) and CRM (Q92, Q93, Q95, Q97, and Q99) simulations Vertical profiles of cloud water flux at various times for the TCM (X91) and CRM (Q92, Q93, Q95, Q97, and Q99) simulations Vertical profiles of buoyancy flux at various times for the TCM (X91) and CRM (Q92, Q93, Q95, Q97, and Q99) simulations Contour plot of the cloud water mixing ratio (g kg 1 )attimet=1 hour for case Q Contour plot of the cloud water mixing ratio (g kg 1 )attimet=2 hour for case Q Contour plot of the vertical velocity (m s 1 )attimet=1hour for case Q viii

10 2.33 Contour plot of the vertical velocity (m s 1 )attimet=2hour for case Q Vertical profiles of moist static energy at various times for case Q Vertical profiles of total water mixing ratio at various times for case Q Vertical profiles of temperature at various times for case Q Vertical profiles of virtual potential temperature at various times for case Q Vertical profiles of moist static energy flux at various times for case Q Vertical profiles of total water flux at various times for case Q Vertical profiles of net upward radiative flux at various times for case Q Vertical profiles of sum of net upward radiative flux and moist static energy flux at various times for case Q Vertical profiles of upward and downward radiative flux at various times for case Q Time-dependent behavior of domain averaged kinetic energy, cloud kinetic energy (CKE), and turbulent kinetic energy (TKE) for case Q Vertical profiles of cloud kinetic energy (CKE) at various times for case Q Vertical profiles of turbulent kinetic energy (TKE) at various times for case Q Vertical profiles of total kinetic energy at various times for case Q Evolution of cloud base and top heights, and Ac mixed-layer base and top for the second 6 hours of a nocturnal simulation consisting of cases J01 and J Contour plot of the field of buoyancy flux (W m 2 ) for the second 6 hours of a nocturnal simulation consisting of cases J01 and J Contour plot of the field of updraft buoyancy flux (W m 2 ) for the second 6 hours of a nocturnal simulation consisting of cases J01 and J Contour plot of the field of downdraft buoyancy flux for the second 6 hours of a nocturnal simulation consisting of cases J01 and J Profiles of the average updraft and downdraft vertical velocities for the second 6 hours of a nocturnal simulation consisting of cases J01 and J02 (ML base and top mean the average base and top of mixed-layer). 75 ix

11 2.52 Profiles of the average virtual potential temperature within updrafts and within downdrafts, deviating from the horizontal mean value, for the second 6 hours of a nocturnal simulation consisting of cases J01 and J Profiles of the average total water mixing ratio within updrafts and within downdrafts, deviating from the horizontal mean value, for the second 6 hours of a nocturnal simulation consisting of cases J01 and J Profiles of the average liquid water mixing ratio within updrafts and within downdrafts, deviating from the horizontal mean value, for the second 6 hours of a nocturnal simulation consisting of cases J01 and J Profile of the 6 hour average updraft fraction for the second 6 hours of a nocturnal simulation consisting of cases J01 and J Profile of the average convective mass flux corresponding to Fig Time-dependent behavior of velocity scale (w ) simulated by TCM for a 36-hour nocturnal (K01) and a 36-hour diurnal case (K02) Vertical profiles of turbulent kinetic energy at various time for a 36- hour nocturnal case (K01) Vertical profiles of turbulent kinetic energy at various time for a 36- hour diurnal case (K02) Budgets of 3-hour (hour 18 to hour 21) averaged TKE simulated by TCM for nocturnal case (K01). Here, P is pressure transport, T is turbulent transport, B is buoyancy, D is dissipation, and S is storage Budgets of 3-hour (hour 18 to hour 21) averaged TKE simulated by TCM for diurnal case (K01). Here, P is pressure transport, T is turbulent transport, B is buoyancy, D is dissipation, and S is storage Contour plot of buoyant production of the TKE (10 4 m 2 s 3 ) simulated by TCM for a 36-hour diurnal case Contour plot of turbulent transport of the TKE (10 4 m 2 s 3 ) simulated by TCM for a 36-hour diurnal case Contour plot of local storage of the TKE (10 4 m 2 s 3 ) simulated by TCM for a 36-hour diurnal case Time-dependent behavior of liquid water path (LWP) simulated by TCM for different initial relative humility (RH) above cloud Time-dependent behavior of cloud depth simulated by TCM for different initial relative humility (RH) above cloud Contour plot of the field of cloud water mixing ratio for RH 20% above cloud x

12 3.1 Evolution of cloud top, cloud base, and mixed layer base heights for thin cloud CRM and MLM simulations Evolution of cloud top, cloud base, and mixed layer base heights for thick cloud CRM and MLM simulations Evolution of the liquid water path (LWP) for thin cloud CRM and MLM simulations Evolution of the liquid water path (LWP) for thick cloud CRM and MLM simulations Evolution of the liquid water path (LWP) for the CRM and MLM simulations Evolution of cloud top, cloud base, and mixed-layer base heights for the CRM and MLM simulations Evolution of cloud top entrainment velocity for the MLM simulation The vertical profiles of moist static energy for CRM simulation and corresponding mixed-layer values for MLM simulation The vertical profiles of total water mixing ratio for CRM simulation and corresponding mixed-layer values for MLM simulation The vertical profiles of liquid water mixing ratio for CRM simulation and corresponding mixed-layer values for MLM simulation The vertical profiles of moist static flux for CRM and MLM simulations The vertical profiles of total water flux for CRM and MLM simulations The vertical profiles of buoyancy flux for CRM and MLM simulations The vertical profiles of net radiative flux for CRM and MLM simulations Evolution of cloud top, cloud base, and mixed-layer base heights for different BIR max values Evolution of the liquid water path (LWP) for different BIR max values Evolution of cloud top, cloud base, and mixed-layer base heights for different constant A Evolution of the liquid water path (LWP) for different constant A Evolution of cloud top, cloud base, and mixed-layer base heights for different inversion depths Evolution of the liquid water path (LWP) for different inversion depths.128 xi

13 LIST OF TABLES

14 ACKNOWLEDGMENTS I would like to express my sincere appreciation to professor Steven K. Krueger for his guidance, support, patience, and encouragement which have made this research work possible. I would also like to thank the other members of my supervisory committee, Dr. Mace, Dr. McMurtry, Dr. Paegle, and Dr. Sassen, for their support, comments and suggestions. I would especially like to thank Dr. Fu, Dr. Yang, Ms. Chen, and Dr. Lazarus for their helpful discussions and assistance during the course of the study. Finally, I thank my wife Qi, for her patience and encouragement and our daughters Paige and Ashley, for the inspiration to bring this work to fruition. The research work reported in this dissertation was supported by the Environmental Science Division, DOE, under Grant DE-FG03-94ER61769 and by NSF under Grant ATM Computing assistance was provided by NCAR SCD.

15 CHAPTER 1 INTRODUCTION Altocumulus (Ac) and altostratus (As) clouds together cover approximately 22% of the Earth s surface (Warren et al. 1986; Warren 1988). They are prevalent and potentially play an important role in the Earth s energy budget through their effect on solar and infrared (IR) radiation and through the release of latent heats of vaporization and sublimation. However, Ac clouds have not been extensively investigated by either modelers or observational programs. Classified in the International Cloud Atlas (World Meteorological Society 1956), Ac clouds are white or grey, or both white and grey, patches, sheets, or layers of cloud, generally with shading, composed of laminate, rounded massed, or rolls, which are sometimes particularly fibrous or diffuse and which may or may not be merged; most of the regularly arranged small elements usually have an apparent width of 1-5. Synoptic data and observations from the ground are the primary sources of information about Ac formation mechanisms. These mechanisms include: 1) humid air uplifting from and moving ahead of a lower level humidity source in a sheared environment, often in frontal situations; 2) moist air expelled from spreading and decaying convective towers and anvils of cumulonimbus; and 3) humid air condensed in the crests of mountain waves (Gedzelman 1988). Based on aircraft data, Heymsfield et al. (1991) examined two Ac cloud cases at temperature near -30 C. Because these two cases represent only the detailed Ac cloud observations available, we compare them with the results obtained herein. The cloud structure and thermodynamics were similar to stratocumulus (Sc), with extensive cloud top entrainment, a capping temperature inversion, and a dry layer above. Heymsfield et al. (1991) concluded that Ac clouds containing convective

16 2 structures are dynamically forced by radiative cooling. The radiative cooling causes sufficient negative buoyancy in cloud-top parcels to produce the observed downdraft velocities. Heymsfield et al. concluded that a 100-m thick cloud they observed was radiatively cooled throughout, whereas a 400-m thick cloud was radiatively destabilized. They also pointed out that the absence of ice crystals implies a dearth of ice nuclei. Recently, Ryan (1996) noted that observations indicate that middlelevel stratiform clouds less than 1 km deep have either very few ice crystals or no ice crystals. Starr and Cox (SC 1985 a,b) simulated an altostratus case as part of the same study in which they modeled a thin layer of cirrus. Although this calculation was originally described as representing As clouds, it probably better represents Ac stratiformis (Houze 1993). Their model is a two-dimensional (x, z), time-dependent Eulerian numerical model where the focus is on cloud-scale processes (100-m grid resolution). The simulated middle-level cloud retains its hydrometeors through the simulation (1 hour), and is contained in a shallow layer. The radiative heating produces destabilization in the cloud: strong cooling in the upper part of the cloud layer and warming below. Consequently, turbulent kinetic energy is maintained throughout the simulation. Fowler et al. (1996) summarized three classes of prognostic cloud parameterizations for GCMs. The first class has the chief characteristics of cloud parameterizations of Sundquist (1978). Clouds form before the relative humidity (RH) reaches 100%, hence allowing for subgrid-scale cloud cover, and the cloud faction may be expressed as a simple function of the RH in the grid box. The example of the first class of models are Del Genio and Yao (1990 ) and Tiedtke (1993). The second class accounts for the subgrid-scale distribution of the water vapor, condensed water, and temperature in the model (Heise 1984; Smith 1990; Ricard and Royer 1993). The third class uses minimally modified versions of bulk cloud microphysical equations originally developed for mesoscale cloud models (Ghan and Easter 1992; Ose 1993). In contract to Sundqvist-style parameterizations, these cloud parameterizations introduce separate prognostic equations for the mass of

17 3 cloud water and cloud ice. Fowler et al. (1996) indicate that the problem of subgrid-scale cloudiness has not yet been adequately addressed in climate models. The parameterization of the formation and structure of vertically subgrid scale Ac layers has not been previously reported. Randall et al. (1989) simulated grid-scale altocumulus in the UCLA/GLA GCM. However, the thick clouds in their model resemble cirrus and/or anvil clouds more than Ac clouds. Ac clouds have many characteristics that are similar to those of stratocumulus (Sc) clouds in stratocumulus-topped boundary layer (STBL). Basically, both clouds are in shallow layers and are liquid water clouds. In the STBL, turbulence is driven primarily by cloud-top radiative cooling. Cloud top entrainment, surface fluxes, and large-scale subsidence are also important for the formation and maintenance of the STBL. In an Ac layer, turbulent mixing is similarly driven by radiative destabilization. This also suggests that Ac layers can be modeled as elevated mixedlayers. Unlike STBLs, Ac layers are decoupled from the surface. Moisture for Ac formation is transported upward by large-scale ascent or by cumulus convection, instead of by turbulent fluxes as in the STBL. Because of the similarity of Ac and Sc clouds, the research methods used for Sc clouds can be applied to Ac clouds. In general, cloud systems include subgrid scales which cannot be represented explicitly in climate models. The effects of these subgrid-scale processes must be parameterized. In recent years, studies have shown that cloud resolving models (CRMs) are powerful tools for developing and testing parameterizations for GCMs. For example, cloudiness parameterization for use in GCMs are developed with data produced from CRM simulations of observed tropical cloud systems and subtropical stratocumulus (Xu and Randall 1996). These investigations with CRMs have typically ranged from idealized simulations to investigate convection dynamics to simulations aimed at replicating and studying a particular aspect of an observed convective system. These models are not perfect, but they are more accurate than the parameterizations that are to be tested, and they avoid the problems, such as data in limited time and space, associated with observations. In addition, current

18 4 computing power does not allow the use of CRMs directly for climate and weather prediction. Two-dimensional (2D) and three-dimensional (3D) numerical models have been used to study Sc successfully. Large eddy simulation (LES) studies of shallow nocturnal Sc have achieved realistic dynamics (Moeng 1986). Other modeling studies have focused on entrainment (e.g. Deardorff 1980; Kuo and Schubert 1988; Siems and Bretherton 1992; Macvean 1993; Moeng et al. 1995), roll and mesoscale structure (e.g. Sykes et al. 1988; Mason and Sykes 1982; Rand 1995) and explicit representation of the droplet and aerosol microphysics (Kogan et al. 1995; Stevens et al. 1996). The purpose of a CRM is to determine flow statistics, such as horizontally averaged budget terms. In atmospheric convection, the vertical transport terms are usually significant. The corresponding vertical fluxes are primarily due to the large eddies or convective circulations. Many parameterizations of cumulus convection and of boundary layer convection have incorporated this observation by assuming that the vertical fluxes are entirely due to the convective circulations (Randall et al. 1992). The fundamental approach of LES is to explicitly resolve large turbulent eddies, which contain most turbulent kinetic energy (TKE) and do most transport. Only the small, subgrid scale (SGS) eddies are parameterized. The SGS closure provides a way to remove TKE at the smallest resolved scales which has cascaded down scale from the larger eddies. The SGS closure leads to some uncertainty in smallscale mixing. This is particularly important near the ground and near cloud top, where the scales of turbulence are mostly SGS. There is always uncertainty due to numerics. The intercomparison studies of a pure buoyancy-driven clear planetary boundary layer (PBL) (Nieuwstadt et al. 1993) and a pure shear driven clear PBL (Andren et al. 1994) from four different LES codes suggested that the simulation results were not sensitive to the SGS closure and numerical methods. In a one-dimensional (1D) turbulent closure model (TCM), the convective circulations and small-scale turbulence are both parameterized. This kind of model

19 5 had been used to study Sc clouds and other types of clouds (e.g., Oliver et al. 1978; Chen and Cotton 1983 b; Bougeault 1985; and Duynkerke and Driedonks 1987). The 2D CRM approach lies between 1D TCM and LES in its level of physical approximation. A 2D CRM explicitly represents the convective circulations, as does a LES model, but in a more approximate manner. A 2D CRM parameterizes the small scale turbulence using the same closure as a 1D turbulence closure model, but applies the closure only to scales smaller than those of the convective circulations. In 2D CRM simulations, additional uncertainty comes from the assumed two dimensionality of the flow. A recent intercomparison of a simulation of a Sc-topped planetary boundary layer (PBL) by 10 LES codes and four 2D CRMs (Moeng et al. 1996) indicated that the mean and scalar flux profiles predicted by the 2D CRMs was similar to that obtained by the LESs, even though the momentum fluxes, the vertical and horizontal velocity variances, and the turbulence kinetic energy profiles predicted by the 2D CRMs all differ significantly from those of LESs. There are advantages to performing 2D simulations, such as being able to use a finer grid, a larger domain, or a longer time integration than LES models can given the same computer resources. Another type of model used to study Sc clouds is the mixed-layer model (MLM). In mixed-layer models, it is assumed that mean conservative variables are constant with height within the mixed-layer, with a sharp discontinuity between the mixedlayer and the air above. Mixed-layer model have been used to investigate the STBL productively by a large number of authors (e.g., Lilly 1968; Betts 1973; Schubert et al. 1979; Randall 1980 a,b; Suarez et al. 1983; Turton and Nicholls 1987; Bretherton and Wyant 1997). Recently, an intercomparison among six different 1D models for the STBL (Bechtold et al. 1996) showed that 1D models can reasonably represent the main features of the STBL by comparing the results to those from LES models. This study also indicated that bulk models (including only one or two vertical layers), rather than TCMs, seem to be more appropriate for GCMs. But Wyant and Bretherton (1997) have the opposite opinion and indicate that the TCM is better.

20 6 The goal of the research presented herein is to develop a physically-based parameterization for Ac layers for use in GCMs. First, the 2D University of Utah (UU) CRM and 1D TCM are used to increase our understanding of the physical processes that determine the formation, maintenance, and dissipation of Ac clouds and the effects of Ac clouds on the atmosphere. This is necessary before developing an Ac parameterization based on general physical principles. Observations and our numerical simulations of Ac clouds with the CRM and the TCM suggest that Ac layers are well-mixed. This has motivated our development of an elevated mixed-layer model (MLM). This is a step toward incorporating a physically based parameterization for thin Ac layers into a GCM. In the Appendix, we describe the UU CRM and the TCM applied for Ac clouds. In Chapter 2, results from the CRM and the TCM applied to Ac clouds are discussed. The following topics are studied: the role of cloud-scale processes in response to large-scale forcing; radiative effects in diurnal and nocturnal cases; the utility of the TCM; the mixed-layer characteristics and circulation of Ac layers; the circulation characteristics of Ac layers; the TKE budget of Ac layers; the effect of relative humidity (RH) above Ac clouds. The elevated MLM is developed and described in Chapter 3. The sensitivity testing of the elevated MLM and the comparison of results from CRM simulations and MLM calculations are also discussed. A summary and concluding remarks appear in Chapter 4.

21 CHAPTER 2 CRM AND TCM SIMULATIONS In this chapter, the CRM and TCM are used to perform numerical simulations of Ac cloud layers in idealized initial conditions. The purpose is to determine how the process of large-scale motion field, in combination with cloud-scale radiation, microphysics, and cloud convection and turbulence governs the life cycle and structure of Ac layers. A closely related goal is to determine whether or not Ac clouds can be parameterized. As most Ac clouds are water cloud and non-precipitation, neither ice crystals and precipitation is considered in this research. Moeng and Curry (1990) studied the effect of the fall velocity of cloud droplets for a simulated stratus cloud with a LES code. Their results indicated that this effect is insignificant. We neglect the fall velocity of cloud droplets because of the similarity of stratus and Ac clouds. In section 2.1, we introduce the initial conditions and list all simulation cases of CRM and TCM. In section 2.2, results by the CRM are compared to a simulated Ac cloud by Starr and Cox (SC 1985b). In section 2.3, 13 sounding cases at Salt Lake City, Utah are analyzed to illustrate some characteristics of Ac clouds. The effects of large-scale vertical motion are briefly examined in section 2.4. In section 2.5, the radiative effects of Ac clouds by simulating a nocturnal case and a diurnal case are studied. In section 2.6, we compare the results between TCM and CRM simulations under the same initial conditions. The mixed-layer characteristics and circulation of Ac layers are examined in section 2.7 and 2.8, respectively. In section 2.9, we discuss the updraft and downdraft differences in Ac layers. The TKE budget of Ac layers is discussed in section 2.10, and the effects of different relative humidity (RH) above Ac clouds are studied in section 2.11.

22 8 2.1 Initial conditions and simulation cases The initial profiles of potential temperature θ and water vapor mixing ratio q v we used for the CRM simulations are similar to those used by SC. We consider three types of profiles, which are shown in Figs. 2.1 and 2.2. The type 1 profile is nearly the same as the SC profile. For type 2 the supersaturation region is only half as thick as for type 1. For type 3 the height of the supersaturation region is lower than for type 1 and type 2. Because the Ac cloud depth from SC simulation is thicker than that (less than or equal to 50 mbar) of the typical Ac cloud (Cotton and Anthes 1989), we consider types 2 and 3. Another reason to consider type 3 is that the height of Ac clouds for SC is higher than average Ac cloud height. The base temperatures of supersaturation region, i.e., the cloud base in the beginning, are -31.5, -30.3, and C for types 1, 2, and 3, respectively. The base temperatures of two Ac clouds Heymsfield et al. (1991) measured are and C. The cloud domain vertically includes a region where the vertical resolution is uniform and small (called main model vertical domain below) and several layers with large vertical resolutions. Here a layer means the depth between two levels. The main model vertical domain is from 5.5 to 8.9 km (from 4.5 to 7.9 km for type 3). The horizontal domain is 6.4 km (3.2 km for vertical grid 25 m). Below the main domain, there is one 500 m layer and several 1 km layers down to the surface (sea level). There are six levels above the main vertical domain with heights of 9.5, 11, 16, 20, 50, and 60 km, respectively. These six levels are used only for radiation calculations. The horizontal grid size, vertical grid size in the main domain, and time step for the CRM and TCM simulations are listed in Table 2.1. A simulated Ac cloud case with the cloud height between 3 and 4 km was also examined and its characteristics is similar to above cases. A part of reason using type 1 and type 2 is that our results can be compared with SC s Ac case. But the cloud base temperature for those types is very low. As the cloud ascends with time, temperature in cloud will decrease below -40 C for some simulation cases. Water droplets will become ice crystals while temperature is below -40 C. Therefore, our results are not physically real for temperature less than

23 9 Height (m) type 1 type 2 type Potential temperature (K) Figure 2.1. Initial profiles of potential temperature for CRM and TCM simulations. -40 C. However, our results of low cloud heights for type 3 are similar to those for type 1 and 2, which indicates that simulations for type 1 and type 2 are dependable if they are used to study water clouds. The reference state is the U.S. Standard Atmosphere (USSA). At the levels below 5.5 km (4.5 km for type 3), θ and q v are the same as in the USSA, but q v is linearly adjusted so that relative humidity (RH) is the USSA value at the surface and 0.6 at the level just below 5.5 km (4.5 km for type 3). For the thick cloud simulation (type 1), θ and q v from 5.5 km to 8.9 km are initialized the same as in SC. The relative humidity (RH) is 108% from 7.15 to 7.55 km and θ is moist adiabatic from 6.95 to 7.55 km. For type 2, RH is 108% only from 6.95 to 7.15 km and θ is moist adiabatic from 6.85 to 7.15 km. For type 3, RH

24 type 1 type 2 type 3 Height (m) Water vapor mixing ratio (g kg -1 ) Figure 2.2. simulations. Initial profiles of water vapor mixing ratio for CRM and TCM

25 11 Table 2.1. Cases of CRM and TCM simulations. D means dimensions and PT physical times. Case Type D PT (h) z (m) t (s) w 0 (cm/s) radiation Q24 1 2D nocturnal Q05 1 2D nocturnal Q26 1 2D nocturnal Q27 1 2D nocturnal Q28 1 2D diurnal X25 1 1D nocturnal X26 1 1D nocturnal Q30 2 2D nocturnal X34 2 1D nocturnal Q34 1 2D nocturnal X31 1 2D nocturnal Q92 2 2D nocturnal Q93 2 2D nocturnal Q94 2 2D diurnal Q95 2 2D nocturnal Q96 2 2D diurnal Q97 2 2D nocturnal Q98 2 2D diurnal Q99 2 2D nocturnal Q90 2 2D diurnal J01 3 2D nocturnal J02 3 2D nocturnal J03 3 2D diurnal X91 2 1D nocturnal X92 2 1D nocturnal X93 2 1D nocturnal X94 2 1D nocturnal K01 2 1D nocturnal K02 2 1D diurnal

26 12 is 108% from 5.45 to 5.65 km and θ is moist adiabatic from 5.35 to 5.65 km. There are 300 m transition regions below and above the supersaturated region where RH changes from 108% to 60% continuously. Outside these regions in the main domain RH is 60%. Heymsfield et al. obtained the satuaration as high as 105% with a parcel model. To initiate motions, random perturbations in potential temperature are used between heights 7.2 and 7.5 km for type 1, between heights 6.95 and 7.15 km for type 2, and 5.45 and 5.65 km for type 3. The maximum magnitude of the perturbations is 0.1 K. These perturbation regions are in the supersatuation region for each type. The ground temperature is fixed at the USSA surface air temperature. The resulting surface turbulent flux is near zero. The effective cloud droplet radius used is 9 µm. The average radii from the observations of Heymsfield et al. are about 7.5 µm in a 400 m deep cloud and only 3 µm in a 100 m deep cloud. The large-scale vertical velocity, radiative condition, and duration are also listed in Table 2.1. The simulation times of cases Q24, Q05, Q27, X25, X27, Q30, X31, Q34, X34, Q92, J01, X91, X92, X93, X94, K01, and K02 are started at midnight. Other cases continue from one of cases above. Note that Q26 and Q28 are continued from Q05, and J02 and J03 are continued from J01. The cases Q92, Q93, Q95, Q97, and Q99 are a series of 36-hour simulation under nocturnal condition, and the cases Q92, Q94, Q96, Q98, and Q90 are under diurnal condition. As a whole, Q05 and Q26 are a 12 hour nocturnal case, Q05 and Q28 are a 12-hour diurnal case. Note also that J01 and J02 are a 36-hour nocturnal case, and J01 and J03 are a 36-hour diurnal case. 2.2 Comparison to SC We simulate a nocturnal case (Q24) which is the same as the case of SC (1985 b) with w 0 =2cms 1. As mentioned in the introduction, SC simulated an Ac case successfully. They also considered cloud-scale processes, radiation, and large-scale processes as in our model. Therefore, their results should be comparable to our results under the same conditions. SC s Ac simulation is only 1 hour long. So we compare the first hour results of Q24 to SC s simulation. In Fig. 2.3, the

27 13 Domain Avg LWC (mg m -3 ) SC Q Time (min) Figure 2.3. Time-dependent behavior of domain averaged liquid water content ( ρ 0 l) in SC and Q24. time-dependent behavior of the domain-averaged liquid water content( ρ 0 l) is shown for SC and Q24. The agreement between SC and Q24 is good. For both SC and Q24, in the first 25 minutes, the liquid water content increases quickly, and after 25 minutes, it increases slowly. In Figs. 2.4 and 2.5, profiles of horizontally-averaged liquid water content (ρ 0 l) are shown at various times for SC and Q24, respectively. The agreement is also reasonable. In Q24, the cloud top and base height increase faster than those in SC. The cloud depth for Q24 is about 600 m, which is comparable to a 400 m deep cloud of Heymsfield et al. (1991) analyzed. Their peaks value of ρ 0 l is 70 mg m 3, which is about the same as those for Q34 after 30 minutes (see Fig. 2.5).

28 Figure 2.4. Vertical profile of horizontally averaged liquid water content (ρ 0 l)at various times for SC. From Starr and Cox (1985b). 14

29 min Height (m) min 30 min Horizontal Avg LWC (mg m -3 ) Figure 2.5. Vertical profile of horizontally averaged liquid water content (ρ 0 l)at various times for Q24.

30 Domain Ave TKE (mj kg -1 ) SC Q Time (min) Figure 2.6. Time-dependent behavior of domain averaged total kinetic energy (TKE) in SC and Q24. The time-dependent behavior of the domain-averaged TKE for SC and Q24 is shown in Fig In the beginning the TKE increases slowly when liquid water content is small. The TKE then increases to 100 mj kg 1 for both cases during the next 15 minutes when the liquid water content increases quickly, though Q24 lags several minutes. After this period the TKE oscillates for SC and Q24. Though there are some difference between the TKE magnitudes, the agreement for TKE between the cases is reasonable.

31 2.3 A simple analysis of Ac soundings In this section, sounding data at Salt Lake City, Utah are studied for primitive knowledge of Ac clouds. Only the soundings with evident Ac clouds from ground observation are used here. There are 13 sounding cases from November 1992 to October The Ac clouds are supposed to occur in the region where the relative humidity (RH) is larger than 92% for this simple analysis of Ac soundings. Wang and Rossow (1995) obtained the cloud region based on three criteria: maximum RH in a cloud of at least 87%, minimum RH of at least 84%, and RH jumps exceeding 3% at cloud top and base. They pointed out that cloud characteristics are changed a little if the minimum RH is changed to 74%. So, I believe our criterion is fine for a primitive analysis. Ac clouds are differentiated from As clouds by examining cloud depth. Ac clouds are shallow, up to several hundred meters deep, but As clouds are usually deeper. Also, Ac clouds have evident q v or temperature jumps at the cloud top. Temperature and q v profiles from two soundings at Salt Lake City are shown in Fig. 2.7 and Fig. 2.8, respectively. The Ac cloud regions are marked. The surface height at Salt Lake City is 1288 m above sea level. The Ac are obviously shallow clouds and temperature with q v jumps at cloud top. The cloud base height, cloud depth, and temperatures at cloud top and base for Ac clouds are listed in Table 2.3. The average cloud base is 5439 m, from a low of 2897 m to a high of 6830 m. The average cloud depth is 295 m; ranging from 96 m to 681 m. The average cloud temperature is about -15 C. The temperature and q v jumps at cloud top and base are important features of Ac clouds. The inversion layer heights (base and top) and the changes of temperature, RH, and q v are illustrated in Table 2.3. Because the vertical resolution from soundings is large, it is impractical to get accurate magnitudes of the jumps. The results obtained here are for quantitative study. The base of the inversion layer is the sounding level near cloud top, and the top is one or two sounding levels above the base level as the temperature increases with height. The average temperature jump is 0.9 K. The average RH jump is -43%. The average q v jump 17

32 /06/ /12/94 Height (m) Temperature (K) Figure 2.7. Temperature profiles from soundings at Salt Lake City, Utah at hour 1200 UTC on November 6, 1992 and at hour 1200 UTC on July 18, 1994.

33 /06/ /12/94 Height (m) Water vapor mixing ratio (g kg -1 ) Figure 2.8. The profiles of q v from soundings at Salt Lake City, Utah at hour 1200 UTC on November 6, 1992 and at hour 1200 UTC on July 18, 1994.

34 20 Table 2.2. Temperature, height, and depth of Ac clouds from soundings at Salt Lake City, Utah. sounding cloud base cloud temperature (K) temperature (K) time Height (m) depth(m) at cloud base at cloud top average is g kg 1. Heymsfield et al. (1991) mentioned that the RH decreases rapidly below cloud base and above cloud top. There is a 0.6 C jump in temperature for their 400 m deep cloud and no jump for a 100 m deep cloud. There are no clear temperature jumps at cloud base based on the soundings. Whether q v and RH are continuous at cloud base is checked from q v and RH profiles. There is only one case with discontinuous q v and two cases with discontinuous RH. Therefore, Ac clouds exhibit evident temperature and q v jumps at the cloud top and no clear jumps at the cloud base. 2.4 Effect of large-scale vertical motion In this section, the effects of large-scale vertical motion via w 0 are briefly examined. The radiation is nocturnal. In Fig. 2.9, the temporal behavior of ρ 0 l is shown for three simulations (Q24, Q05, Q27) with various specified values of w 0. Similar to the analysis of SC (1985b) for cirrus clouds, each simulation may also be partitioned into three stages. During the initial stage, the response to the

35 21 Table 2.3. The jumps of temperature, q v, and RH above Ac clouds from soundings at Salt Lake City, Utah. sounding T (K) change inversion q v (gkg 1 ) change RH (%) change time in inversion layer in inversion in inversion not available average initial conditions dominates. This is followed by a transition or adjustment period. Then the solutions are dominated by the response to the continuing production of available water vapor and latent heat via w 0 as modulated by cloud-scale processes. With w 0 =2 cm s 1, ρ 0 l increases because additional water vapor is available. With w 0 = 2 cms 1, ρ 0 l decreases to zero. It is interesting that ρ 0 l is almost steady when w 0 =0. It suggests that altocumulus clouds may last a long time when there is no large-scale vertical motion. 2.5 Effects of radiation We studied the radiative effects of Ac clouds by simulating a nocturnal case and a diurnal case. The starting time for both simulations is midnight local time. The diurnal case uses the radiative conditions at latitude 30 N on July 15. The total simulation time is 36 hours for each case. The nocturnal case is the combination of Q92, Q93, Q95, Q97, and Q99, and the diurnal case is the combination of Q92, Q94, Q96, Q98, and Q90. The simulation conditions are listed in Table 2.1. The

36 22 Domain Avg LWC (mg m -3 ) w 0 (cm s -1 ) Time (hr) Figure 2.9. Time-dependent behavior of domain averaged liquid water content ( ρ 0 l) for different large-scale vertical velocities (Q24, Q05 and Q27).

37 23 12 Liquid Water Path (g m -2 ) Nocturnal Diurnal Time (hr) Figure Time-dependent behavior of liquid water path (LWP) for a nocturnal (Q92, Q93, Q95, Q97, and Q99) and a diurnal case (Q92, Q94, Q96, Q98, and Q90). initial profiles of temperature and moisture are type 2, e. g. the thin cloud. The vertical grid interval in the main vertical domain (from 5.5 to 8.9 km) is 25 m. The time step is 2.5 seconds. In Fig. 2.10, the time evolution of the liquid water path (LWP) is shown for the nocturnal and diurnal cases. The LWP decreases slowly for the nocturnal case. In the diurnal case, heating by absorbed solar radiation has a strong effect on the LWP. In the diurnal case, the LWP decreases rapidly after sunrise, decreases slowly during the afternoon, then increases again after sunset until sunrise. The evolution of the profiles of the horizontally-averaged liquid water mixing ratio for the nocturnal and diurnal cases are shown in Figs and 2.12, respec-

38 Height (m) Time (hr) Figure Contour plot of the field of cloud water mixing ratio (g kg 1 ) for a nocturnal case (Q92, Q93, Q95, Q97, and Q99).

39 Height (m) Time (h) Figure Contour plot of the field of cloud water mixing ratio (g kg 1 ) for a diurnal case (Q92, Q94, Q96, Q98, and Q90).

40 26 tively. For the nocturnal case, the cloud layer ascends and the cloud depth is almost constant. During the daytime in the diurnal case, the cloud top height is nearly constant and the cloud depth decreases. After sunset, the cloud depth increases in the diurnal case. A decreased cloud depth during the daytime under diurnal conditions also occurred in the stratocumulus simulations of Bougeault (1985), Turton and Nicholls (1987), and Wyant and Bretherton (1997), and the marine stratocumulus observation of Hignett (1991). The effects of radiation on the Ac layer depend on the radiative heating rate profile within the cloud layer. Fig displays the evolution of the total radiative heating rate profile for the nocturnal case. Figs. 2.14, 2.15, and 2.16 display the evolution of the IR, solar, and total radiative heating rate profiles, respectively for the diurnal case. In the nocturnal case, there is a thin region of strong cooling in the upper part of the cloud layer, and a thick region of weak heating in the lower part of the cloud layer. These regions develop as the cloud ascends and the general pattern is quite stable, although the radiative heating rates in the lower part of the cloud layer and the radiative cooling rates in the upper part of the cloud layer decrease slowly with time. In the diurnal case, IR radiation still has a cooling effect in the upper part of the cloud layer and a heating effect in the lower part, while the solar radiation has only a heating effect. Comparing Figs and 2.15, we find that the maximum solar heating and IR cooling rates occur in the same region. This also occurred in a simulation of a stratocumulus-topped boundary layer under diurnal conditions (Krueger et al. 1995a). In the Ac layer, this pattern produces net heating in the cloud layer during the morning (Fig. 2.16) which decreases the cloud depth and LWP. The total radiative heating rate in the diurnal case (Fig. 2.16) has an upperlevel cooling region and a lower-level heating region most of the time. But in the late afternoon, the cloud region is almost totally radiatively cooling, although the cooling rate is very small. This agrees with the radiative cooling observed in the

41 Height (m) Time (h) Figure Radiative heating rate time-height cross section (K h 1 ) for nocturnal case (Q92, Q93, Q95, Q97, and Q99).

42 Height (m) Time (h) Figure IR radiative heating rate time-height cross section (K h 1 ) for diurnal case (Q92, Q94, Q96, Q98, and Q90).

43 Height (m) Time (h) Figure Solar radiative heating rate time-height cross section (K h 1 ) for diurnal case (Q92, Q94, Q96, Q98, and Q90).