The Vertical Redistribution Of A Pollutant Tracer Due To Cumulus Convection

                                                   January 1985
 THE VERTICAL REDISTRIBUTION OF A POLLUTANT TRACER
           DUE TO CUMULUS CONVECTION
  ATMOSPHERIC SCIENCES RESEARCH LABORATORY
    OFFICE OF RESEARCH AND DEVELOPMENT
   U.S.  ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711

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  THE VERTICAL REDISTRIBUTION OF A POLLUTANT TRACER
            DUE TO CUMULUS CONVECTION
                       by
       John A. Ritter and Donald Stedman
Department of Atmospheric and Oceanic  Science
          The University of Michigan
           Ann Arbor, Michigan 48109
     Cooperative Agreement CR807485-01  and 02
                Project Officer

               Jason K.S.  Ching
     Meteorology and Assessment Division
   Atmospheric Sciences Research Laboratory
 Research Triangle Park, North Carolina 27711
   ATMOSPHERIC SCIENCES RESEARCH LABORATORY
     OFFICE OF RESEARCH AND DEVELOPMENT
    U.S. ENVIRONMENTAL PROTECTION AGENCY
 RESEARCH TRIANGLE PARK,  NORTH CAROLINA 27711

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                NOTICE
The information in this document has been
funded partly by the United States
Environmental Protection Agency under
Cooperative Agrements CR807485-01 and -02
to The University of Michigan.  It has been
subject to the Agency's peer and administrative
review, and it has been approved for publication
as an EPA document.

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                               ABSTRACT


          THE VERTICAL REDISTRIBUTION OF A POLLUTANT TRACER
                      DUE TO CUMULUS CONVECTION

                                  by

                          John Andrew Ritter
     This study presents a formalism that incorporates the physi-

cal processes responsible for the vertical redistribution of a

conservative pollutant tracer due to a convective cloud field and

demonstrates that the cloud venting process should not be neglected

in regional-scale modeling.

     Two modeling approaches are presented which, although both are

based on the framework common to the works of Ogura and Cho (1973)

and Johnson (1975), differ in the manner in which the cloud field is

forced.  In the first approach (herein called the implicit model),

which is adapted from Johnson (1975), the vertical cloud development is

limited by the satellite observed value, but the cloud forcing is

determined solely from synoptic-scale heat and moisture budgets.  In

the second approach (herein called the explicit model), the vertical

development is similarly limited, but the forcing functions are

obtained in a unique way by explicitly incorporating the vertical

distribution of cumulus cloud cover, thereby dynamically incorporating

the influences of subsynoptic-scale phenomena.  By comparing the

results of the implicit and explicit models, we may gain some insight

into the importance of subsynoptic-scale phenomena in determining the

vertical pollutant transport due to cumulus convection.


                                i i i

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     The two models give internally consistent results for varying




conditions and give similar results for the total convective upward



mass flux (Mu).  The manner in which the upward mass flux ia appor-




tioned to the various cloud classes, however, differs for the two




models and is shown to affect the vertical profile of detralnment




for a conservative tracer.  This is seen as a consequence of the




vertical profile of forcing functions used in the respective models.




Although the explicit model gave more reasonable profiles, the abso-




lute values stemming from this model must be viewed with caution




due to the sensitivity of the model to its required input.  The




implicit model, on the other hand, whose forcing functions are devoid




of subsynoptic-scale effects, demonstrated an acceptable sensitivity




to its input parameters if the data are prepared judiciously.



     This study has provided two methods by which satellite data can




be used to incorporate the subscale effects of cumulus clouds into



regional transport models.  It has also been shown that regardless of




the method chosen, the concentration increase in the cloud-layer due to



the venting action of cumulus clouds can be as, if not more important



than, the in-situ produciton of some species and should therefore not



be neglected in regional-scale transport models for scenerios




involving convective cloud fields.
                             iv

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                          TABLE OF CONTENTS
Abstract	iii
List of Tables	vt
List of Illustrations	vii
Acknowledgements	xti
Chapter
      1.  Introduction	1
      2.  The Parameterization of Convective Cloud Venting	15
          2.1  Model Perspective	15
          2.2  Data Preparation	36
               a)  Synoptic-scale analysis	36
               b)  Surface analysis	55
               c)  Satellite data	58
               d)  Other data fields	66
          2.3  The Entraining Plume Model	66
          2.4  Determination of the Convective-scale Forcing
               from Synoptic-scale Variables	76
          2.5  Determination of the Convective-scale Forcing
               from a *Bulk' Perspective	80
          2.6  Determination of the Convective Cloud Mass Flux..91
      3.  Model  Evaluation and Intercomparison	98
      4.  Sensitivity Analysis	123
      5.  Summary and Conclusions	13T
Bibliography	136
Appendices	143

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                             LIST OF TABLES
Table 3-1.
Table 4-1.
Table 4-2.
Table


Table


Table
      Basic characteristics of the cloud field for each
      grid cell chosen for an evaluation of the models
      presented.  Units of heat flux are W m"~2
      (ex:  explicit model; im:  implicit model)	
                                                                   .99
      Sensitivity analysis of the explicit model to the
      selection of the lower limit of integration in
      Equation (52)	.	124

      Sensitivity analysis of the explicit model to the
      selection of the approximate minimum bound for the
      determination of cloud half-lives	125
4-3.  Sensitivity analysis of the explicit model to the
      selection of AH/Z^	126
4-4.  Sensitivity analysis of the implicit model to the
      profiles of QR, Qj, Q2> 3X/3p and q^	
                                                            ,127
4-5.  A budget analysis for the terms comprising Q^ and
      0.2 as given by Equations (41) and (42) respectively.
      The data are taken from that of case #1 at 700 and
      800mb.  Units:  °K day"1	128
                              VI

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                        LIST OF ILLUSTRATIONS
Figure 1-1.     The vertical distribution of mixed layer air due
                to the diurnal oscillation of the mixed layer
                height is illustrated.  Parcels transported to
                the upper region of the mixed layer may become
                trapped at that level due to the termination of
                positive heat flux.  Parcels in this region are
                transported by different mechanisms at night than
                those in the nocturnal boundary layer....	3

Figure 1-2.     A depiction of the cloud venting process is shown.
                A cloud-base mass flux, %, enters the cloud from
                the mixed layer.  Cloud layer air enters the
                sides of the cloud by the entrainment process.
                Clouds detrain at their respective cloud tops.
                The total upward mass flux from the clouds
                induces a subsidence in the between cloud
                environment ultimately injecting cloud layer
                air into the mixed layer	5

Figure 2.1-1.   The Regional Oxidant Model domain with the network
                of 60 by 42 grid cells is shown*  The dimensions
                of each grid cell are 1/4° longitude by 1/6°
                latitude	17

Figure 2.1-2.   Summer Experiment study area with individual 1/4°
                longitude by 1/6° latitude grid cells indicated....18

Figure 2.1-3.   Box diagram showing the basic components of the
                modeling approaches used in this study	21

Figure 2.1-4.   Satellite photograph of the Summer Experiment
                study area for 2331$ 7/22/81	23

Figure 2.1-5.   The distribution of clouds in a hypothetical grid
                cell is illustrated.  The dot(s) or circle(s)
                represent hypothetical updrafts for the clouds
                shown.	.....24

Figure 2.1-6.   The model used in this study depicts a real cloud
                field by:
                (a)  choosing a distribution of cloud updrafts to
                     represent the ensemble of clouds present,
                     and by
                (b)  combining the updraft elements of the same
                     height class  (shown in part (a) of this
                     figure) while conserving the total updraft
                     area	.25

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Figure 2.1-7.   Model derived entrainment rates are assigned on
                the basis of cloud-top height,  implying that
                taller clouds have entrained less and therefore
                have retained more of their buoyancy than shorter
                clouds have	27

Figure 2.1-8.   UV-DIAL depiction of pollutant stratification
                in the cloud layer	29

Figure 2.1-9.   A schematic solution of the integral equation used
                to determine the cloud-base mass flux is presented.
                On the left side is a model cloud field (analogous
                to that in Figure 2.1-6'(b).  On the right side is
                the vertical profile of the forcing terms	33

Figure 2.2-1.   The spatial distribution of the rawinsonde obser-
                vation sites used in the analysis of the Summer
                Experiment observational program, July 1981 is
                shown above.  The enclosed region represents the
                study area	38

Figure 2.2-2.   The computational grid domain used for the
                synoptic-scale analysis of the rawinsonde data
                is shown above.  The enclosed region represents
                the study area	39

Figure 2.2-3.   A schematic depiction of how the first derivative
                of a feature with a wavelength X could be
                misrepresented by not having grid points located
                1/4 X apart.  A '+' indicates where additional
                grid points should be* located	40

Figure 2.2-4.   Objectively analyzed 500 mb geopotential heights
                (gpm) for OOZ 7/23/81	43

Figure 2.2-5.   Objectively analyzed 500 mb temperature (K) for
                OOZ 7/23/81	44

Figure 2.2-6.   Objectively analyzed 500 mb specific humidity
                (x 10 g/kg) for OOZ 7/23/81	45

Figure 2.2-7.   A schematic representation of a situation in
                which the interpolation of the horizontal compon-
                ents of the wind field do not yield the same
                results as the interpolation of the wind speed
                (see text for discussion)........	46

Figure 2.2-8.   Synoptic-scale relative vorticity fields
                (x 106 s"1) at 500 mb for OOZ 7/23/81:
                (a)  from initial u and v component interpolation,
                (b)  from the interpolated centroid point values
                     of £  and
                         Viii

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                (c)  from the final wind field determined from
                     Equation (9)	49

Figure 2.2-9.   Synoptic-scale divergence fields (x 106 s""1) at
                500 mb for OOZ 7/23/81:
                (a)  from initial u and v component interpolation,
                (b)  from the interpolated centroid point values
                     of 6, and
                (c)  from the final wind field determined from
                     Equation (9N	50

Figure 2.2-10.  Wind field (kt) at 500 mb for OOZ 7/23/81:
                (a)  from initial u and v component interpolation,
                (b)  from the Schaefer-Doswell variational
                     technique.	51

Figure 2.2-11.  Vertical velocity field (mb hr"1) at 500 mb for
                OOZ 7/23/81	54

Figure 2.2-12.  The spatial distribution of surface meteorological
                observation sites used in the analysis of the
                Summer Experiment observational program,
                July 1981	56

Figure 2.2-13.  The computational grid domain used for the surface
                meteorological data is shown above.  The enclosed
                region represents the study area	57

Figure 2.2-14.  Surface observations of
                (a)  temperature (K), and
                (b)  dew-point temperature (K)
                for OOZ 7/23/81	59
Figure 2.2-15.
Figure 2.2-16.
Figure 2.3-1.
An illustration of the process by which the fre-
quency distribution of cumulus cloud-top heights
is used to give the vertical distribution of
fractional cumulus cloud cover:
(a)  profile of IR pixel data obtained from
     satellite observations;
(b)  the corresponding profile of cumulus cloud
     coverage via a regression analysis between
     observed IR pixel data and fractional cumulus
     cloud cover observed from the satellite
     visible imagery; and
(c)  final normalized cloud cover distribution	63

Regression curve showing the relationship between
the IR pixel count and the area of cumulus
coverage.	65

A vertical profile of the normalized mass flux
distribution of n(XjL,p), for a typical cloud
class	69

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Figure 2.3-2.

Figure 2.5-1.
Figure 3-1.
Figure 3-2.
Figure 3-3.
Figure 3-4,
Figure 3-5.
Figure 3-6.
Figure 3-7.
Example of model derived entrainment rates
An illustration of the entrainment zone which
exists between the mixed layer and the more
stable cloud layer above is shown.  H2
represents the highest level to which mixed
layer air can penetrate.  HI marks the highest
level at which most of the air can be identified
as mixed layer air. . . ..... ......
                                                                   83
(a)
     fractional cumulus cloud coverage as a
     function of pressure as determined from
     satellite data, and
     model derived entrainment rates as a
     function of cloud class
for cell (5,20) at 20Z (case #1)	
                (b)
                                                                  100
(a)
     fractional cumulus cloud coverage as a
     function of pressure as determined from
     satellite data, and
     model derived entrainment rates as a
     function of cloud class
for cell (7,20) at 20Z (case #2)	
                (b)
                                                                  101
(a)
     fractional cumulus cloud coverage as a
     function of pressure as determined from
     satellite data, and
     model derived entrainment rates as a
     function of cloud class
for cell (12,16) at 20Z (case #3)..	
                (b)
                                                                  ,102
Vertical mass flux distribution for
(a)  explicit model, and
(b)  implicit model
at 20Z (case #1)	
                                                                  ,105
Cloud-base mass flux distribution mg(p) for
(a)  explicit model, and
(b)  implicit model
at 20Z (case #1)	
                                                                  ,106
Concentration increase in the cloud layer of a
conservative tracer assuming a mixing ratio of
60 ppbv in the mixed layer and 40 ppbv in the
cloud layer for
(a)  explicit model, and
(b)  implicit model
at 20Z (case //I).	
                                                                  ,108
Vertical mass flux distribution for
(a)  explicit model, and
(b)  implicit model
at 20Z  (case #2)	
                                                                  ,110

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Figure 3-8.     Cloud-base mass flux distribution mjj(p) for
                (a)  explicit model, and
                (b)  implicit model
                at 20Z (case #2)	112

Figure 3-9.     Concentration increase for the same conditions
                of Figure 3-6 for
                (a)  explicit model, and
                (b)  implicit model
                at 20Z (case #2)	113

Figure 3-10.    Vertical mass flux distribution for
                (a)  explicit model, and
                (b)  implicit model
                at 20Z (case #3)	115

Figure 3-11.    Cloud-base mass flux distribution mg(p) for
                (a)  explicit model, and
                (b)  implicit model
                at 20Z (case #3)	116

Figure 3-12.    Concentration increase for the same conditions
                of Figure 3-6 for
                (a)  explicit model, and
                (b)  implicit model
                at 20Z (case #3)	118

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                          ACKNOWLEDGEMENTS

     The work presented in this report is the culmination of the efforts of
several people, all to whom I am gratefully indebted.  This research topic
was suggested to me by Dr. Jason Ching.  I am grateful to him for the many
fruitful discussions we have had and for the continued support for my work
that he has shown.  The enthusiasm, energy and personal interest exuded by
my major advisor, Dr. Donald Stedman, did much to help me over numerous research
and academic hurdles in the past several years.  His friendship and example
as a scientist has influenced me greatly during this, period.  I have benefited
greatly from  the insightful suggestions given to me by Dr. Francis Binkoski.
Mr. 0. Russell Bullock was extremely helpful in providing a firm base from which
to start.  The technical support of Adrian Busse, Dale Coventry, and Jim Regan
has been invaluable.  Administrative responsibilities were admirably fulfilled
by Bobbi Walunas.
     I would also Tike to thank the Meteorology and Assessment Division of
EPA for providing me with the environment and computer resources necessary
for the completion of this work which was funded by EPA under Cooperative
Agreements CR807485-01 and -02.
                                  xn

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                              CHAPTER 1



                             INTRODUCTION



    In recent years there has been an increasing awareness and concern

over the fate of pollutants that are emitted as a result of normal

human activity and their resulting impact on the air quality and ulti-
       ,                                    •
mately on the quality of human life for those who reside in the wake

of the pollutant plume.  Several studies have shown that pollutants

are capable of being transported over long distances.  Spicer et^ al.

(1977) along with White et ajL. (1976) have shown that urban pollutant

plumes can be identified up to 250 km from their sources.  Wolff et

al. (1977) have similarly shown enhanced ozone concentrations along

the 'northeast corridor1 extending from Washington, B.C., to Boston,

Mass.   The long—range transport of ozone under high pressure condi-

tions has also been addressed by Samson and Ragland (1977).  With the

advent of faster computers and the knowledge gained from previous

studies, the level of complexity of the numerical models used to study

the transport and transformation processes of pollutants has increased

tremendously (Rodhe and Crutzen, 1981; Baboolal et_ al., 1981; Eliassen

£t_al., 1982; Lamb, 1983).  Johnson (1983) reviews several different

modeling approaches used today in the study of the long-range trans-

port and transformation of pollutants.

    The horizontal transport of pollutants has been the focal point of

many of the current transport models.  However, pollutants are also

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                                  2




subject to vertical dispersion above the mixed layer due to several




mechanisms.  Figure 1-1 illustrates the vertical redistribution of




mixed-layer pollutants as a result of the diurnal oscillation of the



mixed-layer height (Carson, 1973; Manins, 1982).  We see from the




figure that pollutants emitted into the mixed layer during the period




of strong daytime convection become well-mixed throughout the layer.




However, as the surface-heat flux subsides in the late afternoon, the




pollutants located in the upper region of the layer remain there as




the mixed-layer height collapses.  Eventually, a nocturnal inversion




is established which separates the now aged mixed layer, above the




nocturnal inversion base, from the surface layer.  The pollutants in



the inversion layer, which were of mixed layer origin, are now free to




be advected independently of the transport occurring in the surface




layer (Zeman, 1979).




    Another mechanism by which pollutants can be vertically dispersed



is through the action of convective clouds.  The role that such clouds




play in influencing the transport and transformation of pollutants has



received increasing attention in the past few years.  Emmitt (1978)



has traced the mixed-layer thermals associated with convective clouds




from just above the cloud base to the surface.  This indicates that




pollutants emitted in the surface layer are able to be transported




vertically into the cloud layer as a result of these 'cloud roots'.




This upward transport of mixed-layer air causes a compensating amount




of cloud layer air, deficient in pollutant load, to return to the



mixed layer thereby diluting the mixed-layer concentrations.  As a




result of this process, the mixed-layer height, another important




variable in transport models, is modulated.  These processes are

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         Mixed layer top
                     I
                    SR
T
 N
T
 ss
Figure 1-1.  The vertical distribution of mixed layer air due to
             the diurnal oscillation of the mixed layer height
             is illustrated.   Parcels transported to the upper
             region of the mixed layer may become trapped at that
             level due to the termination of positive heat flux.
             Parcels in this  region are transported by different
             mechanisms at night than those in the nocturnal
             boundary layer.

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                                  4




illustrated in Figure 1-2, where n^ indicates the upward mass flux




(in units of mass area"* time""1 ) entering through the cloud bases and




where M represents the downward compensating mass flux of cloud-




layer air.  Other studies have shown how the presence of clouds can




modify the thermodynamic structure of the subcloud layer (Deardorff,



1975; Betts, 1976; Seguin and Garstang, 1976; Johnson, 1976).  Con-




vective clouds have long been known to redistribute heat and moisture




(Riehl and Malkus, 1958, 1961; Ooyama, 1964; Charney and Eliassen,




1964; Kuo, 1965; Yanai et_al., 1973; Arakawa and Schubert, 1974;




Johnson, 1976).  However, to date, the field of air pollution meteor-




ology has been virtually silent about the influence these clouds may



have in vertically redistributing pollutants.  The proper treatment




of this process must be incorporated into long-range transport models




if the results are to be considered credible.




    As a result of the growing concern for a more realistic depiction




of the physical processes involved in long-range transport, the U.S.




Environmental Protection Agency (EPA) has initiated the Northeast



Corridor Regional Modeling Project (NECRMP).  The focal point of this




project is the development of the Regional Oxidant Model (ROM), a




regional-scale Eulerian transport and photochemistry model (Lamb,



1983).  In order to initialize and validate this model, several field




studies have been undertaken, the results of which are summarized by




Clarke ejt ad. (1983).  The results of these observational programs




have given even more evidence of the importance of convective clouds




in venting pollutants from the mixed layer (Vaughan et al., 1982).  An




especially interesting observation was made by Greenhut e_t_ a!U (1983).




They observed peak ozone concentrations of 130 ppb over Philadelphia's

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                m
                                                        m
                 u
                                                         u
Figure 1-2.
A depiction of the cloud venting process is shown.
A cloud-base mass flux, m , enters the cloud from
the mixed layer.  Cloud layer air enters the sides
of the cloud by the entrainment process.  Clouds
detrain at their respective cloud tops.  The total
upward mass flux from the clouds induces a subsi-
dence in the between cloud environment ultimately
injecting cloud layer air into the mixed layer.

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                                  6




urban area, whereas to the southeast and northwest values of 90 ppb




were observed.  In addition, in a cloud penetration by an aircraft




they estimated that the flux of ozone in the updraft was two orders




of magnitude larger than the turbulent eddy flux.  These observations




indicate that turbulent diffusion alone is inadequate to account for




the redistribution of pollutants due to the presence of a convective




cloud field and that the effects of the updrafts that are associated




with these clouds must be incorporated into pollutant transport




models..




    Until the recent studies of Chatfield (1982) and Gidel (1983), the




process of cloud venting was either ignored or a bulk eddy-diffusion




constant was assumed (Chameides and Stedman, 1977; Liu, 1977).




Chatfield used transition probabilities to parameterize the effects of




cloud transport on various sulfur species in the tropics, while Gidel




used an approach similar to the one proposed in this work.  Although




both of these works reached the important conclusion that an increas-




ing specie mixing ratio with height in the free troposphere can be



explained by the venting action of cumulus clouds, both works used



an assumed distribution of vertical mass transport due to clouds.




In the present work the distribution of cloud-base mass flux used to



describe the vertical redistribution of a conservative tracer will




not be assumed a priori, but will be determined by the model.




    Parameterization techniques for determining how clouds influence,




and are forced by, the large-scale thennodynamic fields have come




through a long evolution.  A brief history of this evolution will now




be given so that a better perspective of this complex problem can be




obtained.

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                                  7




    The depth to which clouds may penetrate depends on the environmen-




tal profiles of temperature, moisture, and wind shear.  Methods used



to determine the extent of growth vary.  Two fundamental, approaches,




however, are the parcel method and the slice method.  In the parcel




method, a parcel of cloud air is assumed to follow the moist adiabat




upwards on an adiabatic diagram.  The intersection of this moist




adiabat and the line representing the environmental lapse rate defines




the cloud top.  In the slice method, Bjerknes (1938) allowed compen-




sating, unsaturated downward motion to match the saturated ascent of




the cloud parcel by applying the continuity equation as a constraint.




This induced motion acts to dry and warm the environment by adiabatic




compression, thereby altering the environment by increasing the sta-




bility of the cloud layer.  In addition, the subsidence field acts to




retard the growth of the mixed layer (Johnson, 1978; Pielke, 1974).




If this process were allowed to continue, the convection could actu-




ally be cut off in'that the subsidence field may cause the mixed-




layer height to decrease until the moisture supply is no longer



sufficient to sustain the cloud field.  Therefore, in order for the




convection to be maintained, a forcing mechanism must exist that will



counteract the effects of stabilizing subsidence motion.  Several such



such mechanisms exist.  Over land, the diurnal heating of the surface




layer, topographical influences, and land-sea breeze convergence




zones are typical examples of these mechanisms.  Over oceanic regions,




however, the convergence of moist-air provides the major impetus for




cloud growth.  Bjerknes (1938) also found that the greatest efficiency




of convection was attained when the area of the rising air was only a




small percentage of the total area.  This is an important point, the

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                                   8




 relevance of which will  be  discussed  in  this work.   The  inclusion




 of synoptic-scale  vertical  motion  into this framework was  done  by




 Cressraan (1946), thereby allowing  the dynamics  of  the environment to




 Influence cloud development.




     A major weakness  of the  slice method is that  no provision  has




 been made for  the  entrainment of environmental  air into  the  cloud




 •parcel.   It has been observed,  for example  (Warner,  1955;  Squires,




 1958),  that the water  content in nonprecipitating  cumulus  clouds  can




 3*ot be approximated by the  mixed-layer water-vapor mixing  ratio,




 hence  implying the existence  of the entrainment process.   Stommel




 (1947,  1951) envisioned  the entrainment  process in terms of  a. turbu-




 lent stream or Tjet? moving through a nonturbulent environment.   In




 his studies, he determined  the rate of entrainment from  profiles  of




 temperature and specific humidity  taken  both inside and  outside of




 curauli.   Due to the continual entrainment of outside air,  the mass



 flux within the jet was  shown to increase with  height.   Scorer  and




 Lodlam (1953)  introduced the  'bubble1 or thermal model for convection.




"This model, most applicable to small  cumuli, models the  rising  element



 as a puff of air that  expands as if it were contained in a conelike



 container with the vertex at  the originating point of the  thermal.




 Unlike the plume or jet  approach of Stommel, entrainment in  this  model




 occurs at the  leading  face  of the  bubble.   Squires and Turner  (1962)




 furthered the  development of  the entraining plume  or 'jet' proposed




 by Stommel by  employing  the results of Morton  (1957) who found  that




 the inflow velocity from a  quiescent  environment is proportional  to




 the upward 'jet* velocity.  The thermodynamical treatment  of Squires




 and Turner was built on  a firmer physical basis than previous efforts

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                                  9




and yielded results of in-cloud properties that were reasonably con-




sistent with the available observational data.  The latter two mixing



models (plume or jet and bubble) have served as the basis for convec-




tion models up to the present.  As would be expected, each method has




strengths and weaknesses.  As for the plume model, any mixing at the




top, or leading face of the plume, is neglected.  It is also assumed




that the plume detrains into the environment only at the cloud top.




The bubble theory, on the other hand, is incapable of treating rising




thermals from a steady source, either below or within the bubble




itself.




    The previous discussion has dealt only with a single cloud ele-




ment.  However, if conditions present are conducive to cloud growth,



as a result of any of the aforementioned mechanisms, a population, or




ensemble, of clouds instead of a single cloud will actually be formed.




The relationship, however, between such a convective cloud population




and the larger synoptic field is a complex one that is not yet fully




understood.  Riehl and Malkus (1958, 1961) made some of the first




advances in understanding this relationship.  Their work showed that




the transport of sensible heat and water vapor by cumulus clouds in




the tropics is important in maintaining the energy budget of the



tropical atmosphere.  Efforts to parameterize this relationship could




be categorized into three basic approaches:  convective adjustment,




boundary-layer convergence, and moisture convergence through an entire




air column.  A complete review of these methods is provided by Bates




(1972) and will be briefly described here.




    In the convective adjustment technique (Manabe and Strickler,



1964) the conditional instability of a layer is removed in such a way

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                                  10




that the total energy is conserved.  Realizing that the tropical



boundary layer has a high moisture content relative to the air above,




Ooyama (1964), along with Charney and Eliassen (1964), related the




convergence of moisture in the boundary layer to the growth rate for




tropical cyclones.  Charney and Eliassen named this process the




Conditional Instability of the Second Kind (CISK).   This was an impor-




tant development since in this process the synoptic-scale features




actually cooperate with a population of cumulus clouds, in that the




cumulus clouds provide the heat which aids the growth of the synoptic-




scale waves while the synoptic-scale feature supplies the moisture



that maintains the cumulus clouds.  Kuo (1965) parameterized the




growth of tropical cyclones in terms of the net moisture convergence




integrated over an entire column of the atmosphere and added to this



the evaporation from the sea surface.




    Ooyama (1971) was the first to introduce the concept of an ensem-




ble, or spectrum of cloud sizes.  The ensemble was defined in terms



of a dispatcher function which gives the rate of generation of



bubbles from the surface layer.  The issue of a cloud spectrum was




again addressed by Arakawa and Schubert (1974).  They pointed out



that the parameterization scheme used by Ooyama (1971) was not closed




since the exact nature of the dispatcher function was not known.




They closed the parameterization problem by explicitly linking the




characteristics of a cumulus ensemble to the large-scale fields of




temperature, moisture and radiative cooling.  Their results showed




that cumulus detrainment cooled and moistened the environment while



the cumulus induced subsidence caused large-scale warming and drying.




The cloud ensemble they employed was divided into cloud classes based

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                                  11




on the fractional rate of mass entrainment, which was uniquely de-




scribed for each cloud class.  The budgets of moist static energy,




mass and total water content were then determined for each cloud




class.  The cloud-base mass flux was subsequently determined by the




solution of these budget equations subject to the environmental




profile of moist static energy and the forcing resulting from the




large-scale fields of temperature, moisture and radiative cooling.




Their method was designed to be used in the U.C.L.A. general circu-




lation model and was prognostic in nature.  The control of the cloud




field in the temporal sense was accomplished by defining a cloud work




function which is a measure of the kinetic energy generation for each




cloud class.  The required assumptions were that each cloud class be




in a  'quasi-equilibrium* with the large-scale forcing and that the



region under consideration is small in comparison to the large-scale,




but large enough to contain a statistically representative sample of




the cloud population.




    Ogura and Cho (1973) and Nitta (1975) have used the Arakawa-




Schubert theory in a diagnostic sense to determine how, for different



situations, the cumulus field interacted with, and was determined by,



the large-scale budgets of heat and moisture.  Cho and Ogura (1974)




applied this same approach to yet another tropical data set and found




that deep and shallow cumulus clouds were controlled by separate mech-



anisms.  Lewis (1975) tested the diagnostic model described above on




a situation involving a prefrontal squall line.  He compared the ob-




served frequency of tall clouds (from a WSR-57 radar) and total area




covered, to that obtained from the model with favorable results.




Johnson (1975, 1976) incorporated convective-scale downdrafts into

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                                  12




the diagnostic approach of Ogura and Cho (1973) and found that the




magnitude of the downdraft mass flux in the lower troposphere was




between one-quarter and one-half that of the updraft mass flux.  He




concluded that neglecting the contribution of convective-scale down-




drafts to the net mass flux budget in precipitating cases could result




in an excessively warm and dry lower troposphere.  Johnson (1977)




incorporated lateral detrainment into his diagnostic model, following



the results of Fraedrich (1976) who found that lateral detrainment




and not cloud top detrainment was the dominant detrainment mechanism.




Johnson found that the inclusion of this process may decrease the net



cumulus mass flux by 15% - 20%.  Johnson (1980) further modified the




diagnostic model to include the effects of mesoscale downdrafts.




    As the above discussion indicates, the formalism of the Arakawa-




Schubert approach has proven to be flexible in regard to the inclusion




of additional mechanisms that may provide a more realistic depiction




of the actual interaction between the convective and large-scale



fields.  It should be noted that neither the Arakawa-Schubert scheme




nor its diagnostic counter-part require any empirical or observed



cloud data as input.  This can be very advantageous when working



with, for example, a data set that is zonally averaged or when only




rawinsonde data are available.  There are however, two major problems




that are encountered when this approach is applied to a mid-latitude




situation on a regional scale with a grid spacing of « 20 km on a




side.  The first problem is the assumption that each grid cell con-




tains a representative sample of the cumulus population.  This may



be easily violated if only a few cumulonimbus clouds (with a radius




of approximately 5 km) are present in the cell.  Secondly, the

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                                  13




connection between the large-scale and convective-scale motions, as




defined by the synoptic-scale rawinsonde data, precludes the ability




of the model to be influenced by forces or phenomena tha^t have spatial




scales smaller than that of the rawinsonde separation distance or time




scales shorter than the 12 hours between rawinsonde observations.




Examples of these phenomena would be land-sea breeze circulations



(Pielke, 1974), orographic influences (Orville, 1968), mesoscale con-




vergence patterns (Fritsch and Maddox, 1981a,b; Chen and Orville,




1980), or inhomogeneities caused by differing land use patterns. •




     In regard to the first problem mentioned above, it will be




pointed out later in this work that the limitations of this problem




may be mitigated if a frequency distribution of cumulus cloud top



heights is available to augment the input data.  It will also be




shown that the limitations inherent to the second problem mentioned




above can be avoided if the same frequency distribution is used to




directly force the cloud field; although in this case, some of the




calculations are sensitive to parameters that may be difficult to




determine in an operational sense.




     The process of cloud venting is a very complex one due to the



spatial distribution, temporal nature, and subgrid-scale nature of




these clouds.  This study presents a formalism, based on the diag-




nostic counterpart of the Arakawa-Schubert scheme, that incorporates



the physical processes responsible for the vertical redistribution




of a conservative pollutant tracer due to a convective cloud field




and demonstrates that the cloud venting process should not be neglec-




ted in regional-scale modeling.

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                                  14




     The following chapter describes the parameterization techniques




utilized in this study, as a well as a description of the various




data bases employed and how they were determined.  The results of the



modeling approaches used are described in Chapter 3.  A sensitivity




analysis is provided in Chapter 4, while Chapter 5 presents a summary




of the findings of this study.

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                               CHAPTER 2




            THE PARAMETERIZATION OF CONVECTIVE CLOUD VENTING





                         2.1 Model Perspective




    This section will give a broad overview of the modeling approaches


employed herein.  The overview will include a discussion on the goal


and motivation for this study, as well as an outline of some of the


problems encountered and assumptions inherent to the approaches taken.


The mathematical formalization for these approaches will be presented


in detail in Sections 2.3 - 2.6.  The preparation and description of


the data bases used in this study are outlined in Section 2.2.


    The goal of this study is to determine the impact that cumulus


clouds have on venting a conservative tracer from the subcloud layer
         x

and to investigate the subsequent redistribution of the tracer in the


vertical.  Two modeling approaches are presented which, although both


are based on the framework common to the works of Yanai et_ al*, (1973,


1976), Ogura and Cho (1973), Arakawa and Schubert (1974), Nitta (1975)


and Johnson (1975, 1977), differ in the manner in which the cloud


field is forced.  The first approach (called an implicit model) is


adapted from Johnson (1975) wherein the cloud forcing functions are


determined from the synoptic-scale heat and moisture budgets as


determined from rawinsonde and radiative cooling data.  Realizing


that clouds may also be forced from subsynpotic-scale phenomena, an



                                 15

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                                  16



alternative model (called an explicit model) was developed to




provide a formalism in which satellite data can be used in a unique




way to determine the cloud forcing functions for use in the above



framework.  By comparing the results of the implicit and explicit




models, we may gain some insight into the importance of subsynoptic-




scale phenomena, which have not been dynamically included into the




implicit model, in determining the cloud-top detrainment of a conser-




vative pollutant that has been vented from the subcloud layer.




    The motivation for this effort was to develop a formalism that




could be integrated into EPA's ROM (Lamb, 1983) which would account




for the influence that a convective cloud field has on subcloud layer




pollutant levels.  Since the ROM will be used to study the transfor-




mation and transport of pollutants across the northeast quadrant of




the U.S., an assessment of the Influence that such a cloud field may




have on the subcloud pollutant levels would be of great value.  The




related study area for the ROM is shown in Figure 2.1-1.  The model



domain is comprised of a network of 60 by 42 grid cells.  The dimen-




sions of each grid cell are 1/4° longitude by 1/6° latitude.  It is



this scale on which the calculations of cloud-base mass flux will be



made.  Since the ROM is not yet fully operational, the models pre-



sented in this report will be applied to the region associated with




the Summer Experiment study conducted jointly by the National Aero-




nautics and Space Administration (NASA) and the EPA during July 1981.




Figure 2.1-2 illustrates the Summer Experiment study area.  The




dimensions of the grid cells have been chosen to match those of the




ROM in order to facilitate the subsequent adaptation of the models




described in this report into said model.

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I
•U
•o -a
c
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If an account is to be made of the vertical transport of pollu-

tants due to convective clouds, one must not only incorporate the

appropriate physics of the process, but one must also require that

the real cloud field, as determined from satellite imagery, be ade-

quately depicted by the model cloud field. This is one example of

an instance where an actual process or situation has to be approxi-

mated by a numerical idealization of the same. As is the case in

any modeling approach, many assumptions will have to be made in the

course of this work. Some of the assumptions, however crude they may

seem to be, are actually at the state-of-the-art and only underscore

the need for more observational programs so that these assumptions