;LEAI
,OCT 28 1971
    WATER POLLUTION CONTROL ItSSEARCH SERIES • 16130 DNH 01/71
  POTENTIAL ENVIRONMENTAL MODIFICATIONS
               PRODUCED BY
     LARGE EVAPORATIVE COOLING TOWERS
ENVIRONMENTAL PROTECTION AGENCY • WATER QUALITY OFFICE

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          WATER POLLUTION CONTROL RESEARCH SERIES

The Water Pollution Control Research Series describes the
results and progress in the control and abatement of pollu-
tion of our Nation's waters.  They provide a central source
of information on the research, development, and demon-
stration activities of the Water Quality Office, Environ-
mental Protection Agency, through inhouse research and grants
and contracts with Federal, State, and local agencies, re-
search institutions, and industrial organizations.

Inquiries pertaining to the Water Pollution Control Research
Reports should be directed to the Head, Project Reports
System, Office of Research and Development, Water Quality
Office, Environmental Protection Agency, Washington, B.C. 20242.

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              POTENTIAL ENVIRONMENTAL MODIFICATIONS

         PRODUCED BY LARGE  EVAPORATIVE  COOLING TOWERS
                                by
                        E G  & G, Inc.


               Environmental Services Operation

                      Boulder, Colorado
                            for the


                     WATER QUALITY OFFICE

               ENVIRONMENTAL PROTECTION AGENCY
                    Program #16130 DNH 01/71
                       Contract 14-12-542
                           January 1971
Por sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price 75 cents

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                 EPA Review Notice
This report has been reviewed by the Water Quality Office,
EPA, and approved for publication.  Approval does not signi-
fy that the contents necessarily reflect the views and poli-
cies of the Environmental Protection Agency, nor does mention
of trade names or commercial products constitute endorsement
or recommendation for use.

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                               ABSTRACT
The objective of the study was to develop techniques for evaluating the
extent of plumes from large evaporative cooling towers.   Analytical tech-
niques were used to describe the dynamics of the wet cooling tower plume
and its interaction with the environment.  Primary emphasis was placed on
predicting the height of the plume.   Classical atmosphere diffusion theory
was used to determine the downwind spread.

The study showed that the saturation deficit of the atmosphere clearly
controls the downwind spread of the ejected liquid water.  Except for
cases where the relative humidity approaches 100%, downwind propagation
is limited to periods when the air temperature falls below the freezing
point.  For a given set of atmospheric conditions, increases in the tower
radius, the saturation temperature,  and the initial vertical velocity of
the plume contribute to increasing the final plume height.

The potential for adverse atmospheric effects due to cooling towers was
analyzed on a national basis and is  presented in the form of a map of
the United States.

A computer program was developed to perform the necessary calculations.
The Appendix contains a description of the program, including input speci-
fications.

This report was submitted in fulfillment of contract number 14-12-542
under the sponsorship of the Water Quality Office of the Environmental
Protection Agency.

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                          TABLE OF CONTENTS



Section                                                              Page

1. 0     INTRODUCTION                                                 1

        1. 1   Tower Characteristics                                     2
        1. 2   Scope of the Study                                        2

2. 0     TOWER PLUME AND DIFFUSION MODEL                       5

        2. 1   Plume Dynamics                                          5
        2. 2   Downwind Diffusion                                        9
        2. 3   Summary of Numerical Model                            10

3. 0     SATURATION  REQUIREMENTS                                 15

        3. 1   Properties of Natural Fogs                               16
        3. 2   Dropsize Characteristics of Cooling Towers              17
        3. 3   Parameterized Cloud Physics                             17

4.0     CALCULATIONS                                               21
        4. 1   Tower Parameters                                       21
        4. 2   Penetration Height of the Plume                          24
        4. 3   Moisture Effects                                         24
        4. 4   Case Studies                                             24
        4. 5   Topographical Effects                                    27
        4. 6   Summary of Calculations                                 33
        4. 7   Prevention of Adverse  Conditions by Seeding              34

5. 0     REGIONAL  CHARACTERISTICS                                 36

        5. 1   Site Evaluation                                           37
        5. 2   Specific  Criteria                                         37

        REFERENCES                                                 41

        LIST OF FIGURES                                             43

        LIST OF SYMBOLS                                            45

        APPENDIX  A  - Computer Program                             4 8

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                               SECTION  1. 0

                              INTRODUCTION
Recent  studies indicate  that the electrical power needs in the United States
are doubling every  6  or 7 years.   To meet  this need an  increasing number
of steam  electric generating facilities  are  required.   One of the  salient
features of these plants is that they  require  large quantities of cooling water.
This increased  demand  for cooling water has brought forth an environmental
problem called  "thermal pollution", which  is caused by the discharges  of
large quantities  of waste  heat  from the electrical power  plants  into various
natural waterways.   Due  to the likely  adverse consequences of  increased
temperatures from  the  discharged effluent  on aquatic life, there has been
an increasing demand for  alternative methods of cooling  which would  dissipate
the waste  heat in a more  preferable  manner.

One  of  the more favored  means of solving the thermal pollution problem is
the use of large evaporative cooling  towers,  which  dissipate the waste  heat
directly into the atmosphere.   With the recent application of large cooling
towers  in  the United States,  some concern has  been expressed  about  the
possible adverse environmental consequences of the  effluent discharges to  the
atmosphere from the  towers.   In certain climates,  the  evaporation of water  at
rates of several thousands of gallons per minute  may create modifications
to the  local environment through formation of fog, icing  on nearby structures,
and "flashing" of transmission lines  downwind of  the tower.   Other possible
adverse conditions such as haze formation,   icing  of bridges,  and destruction
of crops have also  been suggested.

The  probability of a cooling tower causing adverse  environmental modifications
is a function of  the characteristics of  the tower (height,   exhaust  velocities,
temperature,  etc.)  as well as  the characteristics of the  local climate near
the tower  site.   Certain areas have  wind,  stability,  and humidity conditions
necessary for occurrence  of adverse effects  whereas many areas have  condi-
tions where the  tower effluent  is  dispersed effectively with insignificant environ-
mental  modification resulting.

It is important  to the orderly  development of our national economy that a
rational delineation of the  potential of  inadvertent environmental modification
by cooling towers be  obtained  as  soon as possible.   Thus,  this  study  was
initiated to analyze the  physical consequences of the ejections of cooling tower
effluents and their subsequent  dispersal  into  the environment.   The prime
objective  of the  study has  been to develop  a predictive model from which  the
general behavior of the  cooling tower plume  can be  assessed in terms  of
various meteorological  conditions  and local terrain  features.  In addition,.

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geographical regions throughout the United States have been classified as
to the potential for adverse effects occurring from the  application of cooling
towers.

1. 1    Tower Characteristics

Cooling towers  may be classified as wet type where water and air come in
direct contact or dry type where  cooling is through indirect  contact of heat
exchangers.   The  movement of air for both  types  may  be created either by
mechanical draft with  fans or  by  natural draft through a  chimney.

In the dry type cooling tower,  indirect heat  transfer is by conduction  and
convection through  finned tube  cooler sections,  instead  of evaporation.   There
is no  evaporative loss with subsequent  water makeup requirements,  but greater
air movement  is necessary to  reject  the heat.   Cooled water  from the tower
is introduced into  a direct contact jet condenser where it picks  up heat and
then  is returned to the tower for cooling.   The  dry type  has poorer efficiency
than  the wet type,   and hence is less  economical.  Since  no  water is lost  in
the dry type, it does not represent as  clear a potential for  inadvertent
environment modification as  does the wet type,  and it will not be considered
in this study.

In the wet type cooling tower,  water  is sprayed onto a lattice network (packing)
through which  air  is moved  resulting in evaporative heat  transfer.   One type
of tower  currently  favored,  the hyperbolic natural draft unit,  is  shown in
Figure 1.

The evaporation process  in a tower such  as shown in Figure  1 results in
cooling of the  water by  about  20°F.   The cooled water  is collected in a basin
under the  fill.   Solids in the water accumulate  in  the basin,  and the wastes
are  periodically removed by blow-down.  Make-up water  in  the  order of 3% of
the flow circulated is  necessary to replenish evaporation  and blow-down losses.
The make-up water may be  chemically treated to protect the fill from deterior-
ation  and the spray nozzles  from plugging.

Typical large evaporative towers discharge 10,000 gpm  and several towers  may
be utilized at a given  site.  The  subsequent interaction with the  atmosphere
of these large fluxes of water is  the  primary concern in  terms  of possible
adverse effects.

 1. 2     Scope of the Study

 The  main objective of this study  has been the development of techniques to
 model and predict  the behavior of cooling-tower effluents when discharged into
 the  atmosphere  under various  meteorological conditions.   The study is limited
 to numerical calculations  of the general characteristics of plume  behavior.
 Parameters used in the numerical model are those for typical wet-type natural

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         Hot Water
         Distribution
Asbestos Cement
       Fill
                                                                  DIMENSIONS OF
                                                              KEYSTONE GENERATING
                                                                 STATION TOWERS

                                                              Height - 325 Ft.
                                                              Base Dia.-247Ft.
                                                              Top Did.- IA2 Ft.
                                                              Air Inlet - 26Ft.
                                                              Cold  Water Bavin
                                                                 Depth -6Ft.

                                                              Design Capacity-
                                                                   56O.OOO gpm
                                                                   II8»F to 9O°F

             Cold Water Basin
       FIGURE  I.   NATURAL  DRAFT  WET (Evaporative)  COUNTERFLOW
                              TOWER  FROM  FWPCA
                                      (1968)

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draft  (hyperbolic) towers  such as those at the Keystone  Site in Pennsylvania.
Some consideration is also given to  the behavior of plumes from mechanical
draft  towers.

Due  to the  complexity of  the  problem, a  considerable number of empirical
and parameterized concepts have been employed to develop a practical model.
The  overall aim has  been to  develop a model that is readily useable rather
than one of  rigor and complexity.   Definition  of important parameters  and
their sensitivity to  local variations has been  a part  of the study.

Various  climatic  regions  throughout,  the United States have been classified in
terms of the frequency of meteorological conditions favorable  to adverse effects
from cooling tower plumes.

Clearly, a  firm understanding of environmental  modification by  cooling towers
will have to be established by proper  measurements in the vicinity of operation-
al towers,  in order to validate and  refine the theoretical concepts.   However,
field  measurements  are beyond the scope of the present study.   Besides proper
meteorological  measurements, ecological monitoring will also be necessary
to evaluate the  total influence of the tower  effluent on the environment.

In summary, this study is regarded as one step in what necessarily  must be
a broad program to properly evaluate  the general application of large evap-
orative cooling  towers  throughout the United States.

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                             SECTION  2. 0

                TOWER PLUME  AND DIFFUSION MODEL
Study of the ejection  of  cooling tower effluents into the atmosphere
and  subsequent dispersal into the  environment  involves  knowledge of
several  complex processes.   In this study we  have considered the
problem in the following phases:

      (a)  Dynamics of the wet effluent plume and  its immediate
interaction with environment  through entrainment.   Primary emphasis
has  been placed on predicting the height  to which the plume penetrates.

      (b)  Horizontal  diffusion of the ejected water vapor  and its
contribution to the  local  saturation deficit.

A. subdivision  of the  problem into conditions in the  immediate  vicinity
of the tower (vertical plume) and  those downwind (diffused plume)  is
of obvious  use in clarifying  the  important meteorological  parameters.

2. 1   Plume Dynamics

The phenomena controlling the vertical growth of the wet plumes
from cooling   towers are  different from  those  controlling the movement
of dry particulate  smoke, due to the energies  involved  in evaporation
and  condensation in the  wet  plume and the buoyancy accelerations
produced.   In this  situation,  the  buoyancy forces are produced locally
rather than being a function of the initial temperature of  the effluent
alone.   Thus,  the dynamics of the cooling tower is  more closely
related to that of an  isolated cumulus cloud, where  condensation warms
the core of the plume while evaporation  and chilling occur  near the
edges.

Clearly  the buoyancy of the  wet plume will significantly influence the
vertical  penetration.   In fact, it  is known that the observed plume
rise of cooling tower effluents is  considerably greater than the values
calculated on the basis of initial  effluent temperature alone.   This
additional  penetration is obviously  important in assessing the close-in
characteristics.

Most previous studies of the behavior of effluent from stacks  have
been based on the  concept that the horizontal diffusion is equivalent
to that from a source at an "effective" stack height in  place of the

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actual source, where the effective  stack height  is defined as the
height at which the plume becomes nearly horizontal.  Methods for
determining  effective stack height have  produced varying results.
A summary  of the present  status has been prepared recently by
Briggs  (1968).   In this study we will assume  that the plume grows
in a vertical column (tilted due  to  wind shear) and  that the maximum
height of penetration of the column is of importance for  prediction of
local modification (subsequently  horizontal diffusion will  be  used to
spread  the  column downwind).

Over the past several years  considerable progress  has been achieved
in the application of numerical models to cumulus  clouds (alikened
to moist buoyant plumes).  One of the more widely used cumulus
models  is the one -dimensional  dynamic  model with  parameterized
entrainment  and microphysical  relationships.  In this study, we
proceeded by modifying the cumulus  model (Davis,  1967, Weinstein
and  Davis,   1968) such as to  make  it more applicable to  wet effluent
plumes.

The approach used in the model is to apply the vertical  equation
of motion and the first law of thermodynamics with parameterized
relations for plume  mixing,  water  particle growth,  fallout,  and
evaporation.  Numerical  calculations  are carried out by  lifting
incremental portions of the plume  adiabatically  through  successive
vertical steps,  and  at each interval  allowing mixing or  entrainment
to occur with the environment.

The mathematical form of the model will be outlined here with emphasis
on those features unique  to the  cooling  tower  plume.   For  a detailed
derivation of the basic cumulus  model equations,  see Weinstein and
Davis (1968).

The vertical equation of  motion can  be  written  as  (see list  of symbols):
                              2
                          i  dw    dw      1
 where the drag forces will be  provided by the weight of liquid water in
 the  air  and  by mixing with entrained air.  Thus,
 Assuming that  the  plume environment is in hydrostatic  equilibrium,  and
 that there is no horizontal pressure  gradient  between the plume and
 outside  air,

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                                   -  Peg'
   .
and so
1 dw
2  dz
_
" g
T   -  T
 v	ve
  T
    ve
- gQ  -
(1)
Equation (1) is the energy equation for our plume model.  The first term
on the right is the buoyancy term,  the second the drag due to the liquid
water, and the third the loss due to mixing with the slow-moving or station-
ary environmental air.

The temperature distribution with height in the ascending plume can be  derived
using the first  law  of thermodynamics and the Clapeyron  equation for variation
of saturation  vapor pressure with temperature.  The  result  is:
      dT
      dz
             -g


                       e |- u(T-T  ) -
                           ~     O
=
C • •t*' J-
P »
i e
c
P
vq~v
c dz
P
c dz
P
                                                                       (2)
                                      c RT2
                                       P

The terms  on the  right represent  (from left to right) the moist  adiabatic
temperature decrease,  (the change in  temperature resulting  from adiabatic
expansion,  with  latent heat of condensation  released by the condensation of
all vapor over saturation)  the loss of  heat to warm the  entrained air, the
loss of heat to resaturate  the entrained  air, the heat released by freezing
liquid  water,  and the heat realized by the sublimation of the excess vapor
after freezing.   The  last two terms are applicable only to the height incre-
ment,  dz, during which the phase  change is occurring.   After the glaciation
procedure has been completed,  the moist adiabatic process  is assumed to
be  ice saturated and  L  replaces L  in  the first  part  of equation (2).
                       S            6
In this model, it is hypothesized that  mixing or entrainment occurs  through
a continuous incorporation of environmental air around the edges of  the upward
moving plume.   Several theoretical and  observational studies have suggested
that the  entrainment rate is  inversely related  to the plume radius,
        i dM
        M dz
                                             R
                                                                       (3)
                                                "
where the entrainment ^ has  dimensions (length)  ,  R is the plume  radius  and
the dimensionless  constant A depends upon  the  specific character of the plume
and thus  must be determined experimentally.

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Laboratory studies suggest that the value of A should be .15 to . 22.  In
this  study we have used A = . 20.   The variation of R with height along
the plume has been taken  to be:

                             R = R   + z sin a                      (4)
                                  s

where Rs is the  stack  radius,  z is height,  and a is the half-angle of the
plume spread.

The correction to the computed vertical  velocity due to  the shear of the
horizontal wind follows the  concepts outlined by  Malkus  (1952).  The slope
of the plume as  a  result of a vertical shear of the horizontal wind  is given
by:

                                tan  9  -^-
                                          P

where the vertical velocity  is w and the horizontal  speed of the air in the
updraft is Up.   If  the  vertical velocity (wp)  calculated from equation (1)
is taken  as  the hypotenuse of the triangle given  by  the  above relationship,
the  true  vertical velocity  can be calculated.

                                  2     2    /TT \2
                                 w   =  w   - (U )
                                         P     P

Up  is obtained by  considering the horizontal momentum  in the cloud mass
before and after  entrainment of environmental  air.

                          (Momentum) 0 = (Momentum), + (dM)U
                                      2               1         e    or

                           U0 (M + dM)  = MUn  + (dM)U
                             2                 1          e

with the  definition of fi, u = — -j^~ ,  the above relationship  can be  stated as:

                                     U   + ydzlT
                              U  =
                                                 .
                                2      1 + jidz

 Substituting the above into the solution for w given earlier  yields the final
 form  of the relationship:
                               2
                              w

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Utilizing the above  set  of  equations,  along  with  specifications of the  initial
conditions  (tower radius,  initial plume  velocity,  effluent  temperature) and
the environmental conditions (vertical distributions  of  temperature, humidity,
and wind)  calculations of  plume  updraft velocities,  change in plume radius,
liquid-water content,  and maximum plume height can be  obtained.  These
vertical profiles  of plume parameters are used  in the next sections as inputs
for the second phase of the  model which  covers the diffusion  and downwind
spread of  the plume.

2. 2     Downwind Diffusion

The  common practice for  the analysis of diffusion of stack effluents  is to
use an "effective" stack height  in conjunction with relationships derived for
horizontal  and vertical  diffusion.  The  most widely used formulas  are  slight
modifications of those first proposed by Sutton.(1953).   The  relationships selected
for use in the cooling tower problem are of the form
                  X  =  2TT a    u     exp
                              2
v z               2a "~    fia
                    17        y
                                                        2
                                                       y
                                        (6)
                                                *
where X  is the concentration of the effluent,  Q  is the rate of release of the
effluent,  u is  the wind velocity, and ci   and az are the standard  deviations
of the horizontal  and vertical  concentration distributions.   The standard
deviations, a  and  az,  are functions of  the distance downwind from the
source and must  be specified  in equation (6).

Clearly the most important part of using equation (6)  for the  downwind spread
of the effluent relies in obtaining  ze, az,  and a    We assume that the
dynamics  of the plume can be adequately handled as previously described
in order  to obtain ae (defined as the altitude where  w -» 0).   The  dependence
of a   and QZ  on the downwind distance  and on local meteorological and
terrain factors is much more difficult.   In fact,  it is unlikely that  a single
functional relationship can be  found to describe the dependence of a   and az
on the downwind  distance for all  values  of  the  downwind  distance.   During
the early  phase of  the plume propagation the primary mechanism of dispersal
is the self-generated turbulence of the  plume,  or is  due to turbulence generated
by local  structures such  as  buildings and other towers.   On the  other hand,
at sufficiently large times the dispersal is primarily  controlled  by  the ambient
turbulence of the atmosphere.   The dispersion at intermediate times  would
presumably depend on both the self-induced and ambient  turbulence.

Csanady (1968) proposes that  during the  initial  phase  (within about 2  km  from the
source) the standard  deviations can be  assumed to grow  linearly with distance
from the  source.    That is,  one can  let

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                            CTy  =  pyx and °z  =  pzx

where py and p  are  constant.  Equation (7)  implies  that the concentration
profiles  are self-preserving with  increasing distances from the source.   It
can also be  easily demonstrated that equation (7) is equivalent to  assuming
that  the  entrainment parameter,  A,  is  a constant,  since  equation  (7) essent-
ially  implies a linear  rate  of growth of the plume.   In practice,  we have
chosen p  and pz  empirically to  give observed rates of plume spread con-
sistent with the  angle a.  introduced in equation  (4).

At  sufficiently large distances from the source the influence of the  ambient
turbulence on the dispersion is of primary  importance.   Sutton (1953) gives
the following expressions:
                           0   = .JL  x  V*  •  * /                        (8)
                           z    /2
 where c   and cz are appropriate constants (depending on the atmospheric
 conditions) and the quantity p  is the index corresponding to  a power-law fit
 for  the atmospheric wind profile.   That is,  the wind profile is approximated as

                               / u.    . z v p
                               * ux      z/                             (9)

 where Uj  and Zj,  are convenient reference values.

 Pasquill(1961)  and Turner (1967) have conveniently reduced  these  relation-
 ships and observations of plume spread to a simple set of graphs which
 express ay and a   as functions of distance and stability class.  Turner's
 curves are given  in Figures 2 and  3.

 In the present  study,  equation (7) has been used for  distances less than 2  km
 from the  source,  and for distances  greater than 2 km  values of av  and az
 were obtained from Figures 2 and  3 with  proper selection of  stability class.

 2. 3      Summary of Numerical  Model

 The  model developed to simulate the behavior of the  cooling tower effluent
 can be divided into two  phases;  (a) the immediate stack region (less  than
 2 km from the source),  and (b) the downwind region  where  ambient dispersal
                                      10

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  1,000
   500
   200
   100
 ISI
b
      0.1
I        2        5
 DISTANCE  DOWNWIND, km
10       20
50     100
         FIGURE 2.  VERTICAL  DISPERSION COEFFICIENT AS A FUNCTION OF DOWNWIND  DISTANCE
                           FROM  THE SOURCE.  FROM  TURNER (1969)
                                           11

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10,000!
 5,000
     O.I
12          9        10

   DISTANCE  DOWNWIND, km
                                                                       20
50      100
        FIGURE 3. HORIZONTAL DISPERSION COEFFICIENT AS A FUNCTION OF DOWNWIND DISTANCE
                                FROM  THE  SOURCE.  FROM  TURNER
                                          (1969)
                                           12

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is predominent.   In the immediate stack region the internal  dynamics  and
the vertical penetration of the plume is of prime importance.

Here we  assume  the  cooling  tower effluent to behave as  a moist jet similar
to isolated cumulus  clouds.   We compute  the  temperature  and buoyancy
changes in the plume using equation (2) which accounts for moist adiabatic
ascent, the  losses  due  to  mixing and evaporation,  and  the possible  additional
heat derived from freezing of the effluent water.   The computations are
accomplished using vertical  steps of 50m intervals.  Next,  vertical velocities
of the plume are obtained from  equation (1).   The  local  buoyancy is used to
accelerate the plume while the weight of the  water  material  and the entrain-
ment of environmental  air drag  the  plume  and cause it to  decelerate.

The most critical relation in this phase of the plume  growth  is the para-
meterization used to simulate the self-induced turbulence  and  hence  entrain -
ment.   Our best  information  at  this time  is that the relations in  equation
(3) and (4) appear to be adequate.   However,  further  field measurements
will be necessary to  confirm these relations.

Utilization of initial conditions (tower parameters),  the  atmospheric sound-
ings, and equations  (1-4) allow  the computation of  the vertical profile  of  the
plume core  and yield distributions of plume temperature, vertical velocity,
liquid  water content,  and spread of  plume  radius.   The  horizontal tilt  of
the vertical plume  due  to  wind drag is obtained using equation (5).

In the immediate vicinity of the  tower  (<2km) the diffusion of material from
the edges of the plume is obtained using relations  for az and ay given in
equation  (7),  where pz  and py are related  to the half-angle spread, a,  which
has been determined  empirically.   Due  to  the high  internal vertical velocities
of the plume,  local  erosion near the height of the  stack  is small except
for atmospheric  conditions in which the winds are  gusty  and  the environment
is unstable.   The  emphasis on this  portion of the model is the adequate
determination of plume penetration heights as a function  of the tower para-
meters,  and the local meteorological conditions.

In the second phase of  the model the distributions  of effluent are dispersed
downwind utilizing diffusion parameters  which are related to  the ambient
turbulence.  The  main  result is to diffuse the effluent near  the  maximum
height of the plume  (where the plume vertical velocity approaches zero and
the horizontal tilt  is large) in the downwind direction.   This  is equivalent
to the standard stack-diffusion procedures  which utilize equation (6) and
Figure  2  and 3.

Thus,  the model  simulates in numerical form the buoyant rise  of the  plume,
which is  dragged  by the weight  of the material  and depleted  .by the local
entrain ment  of environmental air.   The height at which the plume's acceler-
ations  are depleted and it is  bent over by  the horizontal  wind is  critical  to
the subsequent downwind spread of the  material by  ambient diffusion.   The
                                       13

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immediate or local diffusion is obtained by linear expansion of the local
entrainment.

Throughout this portion of the model  we have not  discussed the  effluent
water  particle distribution or microphysical processes influencing the
plume.  These  relations will be discussed  subsequently.   Thus far, we
view the  effluent  as  small water droplets moving through the plume area
and evaporating at the edges.   The evaporated  water mass is then diffused
outward and contributes to raising the ambient  water vapor  content.
                                      14

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                                SECTION  3.0

                       SATURATION REQUIREMENTS
The  major emphasis of this  study  is the concern over the modifications to
the local  and downwind environment as the result of the  ejection and diffusion
of the cooling tower vapor effluent.  Specifically, the concern is to determine
what  conditions  are necessary for  the additional  water from the tower  to  be
of sufficient  quantity to raise the local humidity  to  saturation, and hence
lead to formation of fog and haze.   In addition,  the  relative  distances  and
volumes of the  modification are  of concern.

In order to properly define this  aspect of the problem it  is important to point
out how the  water vapor content  necessary to saturate the atmosphere  varies
with temperature in the following manner:
                                                                          _3
        Temperature - °C                  Saturation Vapor Content - g m

              -20°                                      0. 894

              -10°                                      2.158
                 0°                                      4. 847
              +10°                                      9.401

              +20°                                     17.300

Next,  we will define the saturation deficit,  q^ as the difference between the
saturation mixing ratio at  a  given  temperature,  qg,  and  the local ambient
mixing ratio, q  .   Since the  cooling tower effluent  merely adds an incremental
amount of water vapor, Aq,  to the local atmosphere, the relation  of import -
ance  for non-fogging is:


                             qs ' qe = qd >  Aq


The  importance  of ambient temperature can  now be seen  since Aq.  several
kilometers downwind for typical  cooling towers is the order of 0. 1  to  0. 5 g
m~3.   If  the ambient temperature  is 10°C  and the local humidity is  50%
(qe = 4. 7 g  m"3) then qd  = 4. 7  g  m"3.  The addition of  Aq  = 0. 2 g m~3
from a cooling  tower would only change the  humidity 3%.   On the  other hand,
at -10°C and 90% humidity the addition of Aq = 0. 2 g m~3 would lead  to
saturation.   Thus,  clearly the ambient temperature is of prime importance
in determining the saturation deficit  and thus the conditions for the tower
effluent to contribute  enough water vapor to cause fog development.
                                      15

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3. 1    Properties  of Natural  Fogs

The  formation of natural  fog  occurs through local cooling of the  atmosphere
by radiation losses,  or through  advective changes in temperature or moisture,
with subsequent  mixing leading to  saturation.   Table 1 summarizes the
properties of "tyPical"  fogs classified as radiation (inland) and advection   _3
(coastal).   It can  be seen that the typical water contents are  . 1  to . 2 g m  ,
the droplet diameters  average 10/j to 20u,  and particle concentrations vary
from 40 cm~3 to 200 cm"3.   Around industrial areas where sources  of
pollution are prevalent droplet  concentrations will tend to be higher.

The visual range or horizontal visibility in  a fog  is related to the average
size of the fog droplets and the liquid water content by the following  equation
which was  derived by  Trabert in 1901.
V-   .
V  " Q  )      2          Q
      c L, n   r
                                                        c
 where Q  = liquid water content, nr = number of droplets of radius r,
 C = constant,  and K = constant.   Clearly the visibility  decreases with
 increasing liquid water  content and with smaller average droplet diameters.

 Visibility reduction  can begin at humidity  values well below 100% due to water
                                   TABLE 1

                          PHYSICAL FOG MODELS


          Fog Parameters             Radiation (Inland)    Advection  (Coastal)
           at  the Surface               	Fog	    	Fog	

    1.   Average Drop Diameter             10 u                   20 |U

    2.   Typical Drop  Size Range            5-35 ,u                7-65 \i
                                                     3                     3
    3.   Liquid Water  Content               110  mg/m            170  mg/m
                                                  -3                   -3
    4.   Droplet Concentration               200  cm               40 cm

    5.   Vertical Depth  of Fog

           a.     Typical                    100  m                200  m

           b.     Severe                     300  m                600  m

    6.   Horizontal Visibility                100  m                300 m
                                       16

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absorption by hygroscopic  nuclei.   Thus, the characteristics  of the plume
chemicals  and other nearby industrial pollutants become important as  inter-
mixture  with  the water vapor plume may occasionally  enhance the reduction
in visibility.

3. 2      Dropsize Characteristics of Cooling Towers

Very little observational data are available as to the dropsize characteristics
of the cooling tower effluent.   Ledbetter,  (1969) has recently completed
a laboratory study in which he  attempted to simulate the cooling  tower and
subsequently measure  the  dropsize  distributions  generated.

Figure 4 is an  example  of the results obtained by Ledbetter.   The distribution
was  found  to  be bi-modal  with the first  peak <5)u diameter (probably  2-3|i) and
the second in the range  20-40^.   These  experiments suggest  that the water
droplet size  distribution of cooling tower effluents is similar to  that of
natural fogs.   The  reason for the  distinct bi-modal  distribution is not clear,
however.


3. 3      Parameterized Cloud Physics

To simulate  the microphysical processes which occur  in the moist ascent of
the plume  we have  used the parameterized representation  given by Kessler
(1962, 1963,  1964).   It  is assumed  that the development of water droplets
can be divided  into three phases:  condensation (vapor to liquid),   auto con-
version  (bulk process  for  changing the small condensed  droplets to larger
drops),  and coalescence (the  collection of  droplets by  the  larger  drizzle-size
drops).

It is  further assumed  that the liquid water content of the plume  can be
represented by  two groupings called cloud water (droplets with no appreciable
fall velocity)  and hydrometeor water  (larger drops with  fall speeds).

The  change in cloud water is expressed  as:
In addition, the change in  hydrometeor water is:
                       d«h     K!  «. ->   +  •S^cS.0'876
                       "S"  "  (w  - VJ           (w - VJ             U2)
                                       17

-------
     9-10
10-20      20-40     40-60      60-80
       DROPLET  DIAMETER  (ft)
•0-100
FIGURE  4.  DROPLET SIZE DISTRIBUTION FROM LABORATORY EXPERIMENTS
                    (LEDBETTER,  •*«!, 1969)
                             18

-------
where Kj,  K2,  and  (a) are coefficients relating to the microphysical  con-
version rates.  The terminal fall velocity is expressed as:

                                 V, = 4. 5Q °' 125                       (13)
                                  t        n

assuming the drop size distribution given  by Marshall and Palmer (1948).

The model  computes the total rainfall from the plume assuming  that the
fallout is developed  (conversion to hydrometeor water) during the vertical
ascent in the plume, and all  converted hydrometeor water subsequently falls
out of the plume  somewhere  downwind.  The computed rainfall is the max-
imum possible, since  evaporation below the plume is  not included here.
Thus, total rainfall  is given  by:
                               R  = I   oQ, dz                          (14a)
which  is  approximated by:


                                 R  =  )  pR .
                                  o    £  ^ 01

                                   (Q,9 + Qh1)  dz
where                       R .   =    ™  0  ni	                      (14b)
                             Ol          ^


This computation of "total  rainfall" is useful in the original cumulus  cloud
model, as it gives an estimate  of total  precipitation during the lifetime  of
an isolated convective cloud.   However,  total rainfall is not really relevant to
a continuing convective plume,  as from cooling towers,  except as a relative
measure  of precipitation  potential.   But it  is also possible to  convert the
computed water  content into rainfall rate and radar reflectivity.   With the
assumption that  the  hydrometeors are formed into a Mar shall-Palmer drop
size distribution,  the following well-known  relations  are obtained:


                            Qh  = 72 x 10"3 Rj0'88                     (15)


where  Q^  is in  g/kg and R , the  rainfall rate,  is in mm/hr;  thus,
                                       19

-------
                                 R,  =  14 Q  *'136                     (16)
                                   i        n
                                         fi   q
and radar  reflectivity Z,  in units of mm /m  is
                                 Z  =  200
At temperatures below 0°C,  freezing  is  allowed  to  occur and release  additional
latent heat.  The microphysical  conditions are handled in  a similar manner
as above,  but  with  different  values for Kj, K^.  a,  and  V^..   Experience  has
shown that natural freezing of moist plumes in the  atmosphere is unlikely
until the ambient temperatures approach -20°C.
                                     20

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                                SECTION  4. 0

                              CALCULATIONS
The  computerized version of the model that has been presented was used
to analyze the behavior and subsequent  downwind spread  of cooling tower
plumes.   The  input data used were the tower parameters and the vertical
distributions of ambient temperature,  wind and relative humidity.   A
number of model runs were obtained to analyze the effects of various
parameters on the general plume behavior.


4. 1      Tower Parameters

Most computer runs were conducted using the following tower characteristics:
Height = 50m, Velocity = 5.0 m/sec,  Radius  =  30m,  and Saturated Temp-
erature of 90°F.  However, variations of these  parameters were also studied.
Figure 5  shows  a typical profile of vertical velocity,  and plume temperature
along with the variation of plume radius as  derived by the model.   The
effect of tower radius is shown in Figure 6.   It  can be readily seen that
the penetration height is significantly  greater  for increasing tower  radii.
This is due to the fact that local entrainment and erosion is inversely
proportional to the  radius of the local updraft.

The  height of the tower above  ground  was found to have  a negligible effect
on the penetration of  the  plume.   This is due to the large buoyancy of  the
initial updraft,  which overshadows any reasonable changes in tower height.
The  height of the tower must  be considered when other structures  are
placed in the  vicinity, however,  because local turbulence generated by
additional structures  can change the above results.

Increases in tower  temperature (saturation)  and in the initial vertical velocity
clearly increase the penetration height of the  tower plume.   Thus, in the
design of towers, factors which promote greater penetration  are first the
tower radius,   and secondly  the  effluent temperature and  draft velocity.

The  preceding results are directly  relevant  to natural  draft cooling towers.
The  model is  equally applicable to  mechanical draft towers,  since  the only
tower parameters that need to be specified are  height, radius,  velocity, and
temperature.   Since individual mechanical draft towers are  limited in
radius to approximately 10 meters  or less,  it can be  seen from Figure  6
that  mechanical  draft towers generally have limited penetration height
compared to the larger natural  draft towers.
                                     21

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   2000
    1800
    1600
    1400
    1200
    1000
     800
o    600
Cu
     400
     200
                                  	VERTICAL VELOCITY

                                  	TEMPERATURE  EXCESS


                                          RADIUS
       -2
                                                           I	1
             6      8      10     12     14
               VERTICAL  VELOCITY -m/sec


             4      6      8     10     12

               TEMPERATURE  EXCESS - 0°C
                                                          16     18     20
       14     16
20    40     60
                                 80     100    120

                                  RADIUS -m
18
140    160    180    200
  FIGURE  5.  EXAMPLE  OF NUMERICAL MODEL RESULT FOR  A COOLING TOWER  PLUME,
                                    22

-------
    2000
     1800
I
oc
UJ
     1600
     1400
s
CD
X
(9
<


UJ

UJ
Q.
     1200
     1000
     800
     600
     400
     200
10     15    20     25     30     35    40

                STACK  RADIUS - m«ter«
                                                                   45
50     55
                                                                                      60
       FIGURE  6.  EFFECT OF  STACK RADIUS  ON PENETRATION  HEIGHT
                                          23

-------
Several mechanical draft towers  are  usually  used to provide a capacity equal
to a single large natural draft  tower.  In general,  the combined plume from
the mechanical towers will have  less vertical penetration than would a plume
from a single hyperbolic tower having  equal  volume.   The discrete small
plumes may merge, but they do  so with  a large initial increase in entrain-
ment,  because  of the dry environmental  air from between individual towers.
The modeling  results indicate that mechanical draft towers as currently
used will always result  in less penetration and  greater potential for adverse
environmental effects than typical large natural  draft towers.


4. 2      Penetration Height of the Plume

Figure 7  shows the effects of atmospheric stability on the penetration  height.
Distributions are given  for isothermal  conditions,  for  a 5°C inversion and
a 10°C inversion (up to  300m,  then isothermal above,  all for surface T-0°C).
These curves  clearly show that the initial buoyancy of the cooling tower
plume is  sufficient to penetrate many low-level  inversions if the wind  is  not
strong.

Wind and wind shear tend to  accentuate the effects  of  stability and  bend the
plume over,  reducing the total penetration height.   This is due to the increased
momentum exchange and the  overall  drag,  causing the plume  to yield to the
horizontal momentum of the  atmosphere.    Calculations show that  the plume
core has  vertical velocities  in  excess of  10 m/sec  for the first few ten's  of
meters and  then decelerates  very rapidly to  the  plume top (see Figure  7).
The large decelerations  when coupled with horizontal wind drag result in
decreasing the effective  plume  height and lead to increases of water vapor
downwind, which under proper  saturation deficit  can yield fog formation.


4.3.     Moisture Effects

As pointed out in Section  3. 0,  the moisture deficit  in the atmospheric layer
penetrated by  the plume is of most significance in evaluating  the  adverse
conditions caused by fogging  downwind  from cooling towers.   Figure 8 shows
a set of   computations  for a situation  with a 10°C  inversion  and  relative
humidity  in  the  plume layer  varying  from 50% to 100%.   It is clear that
the  atmosphere's capacity to  receive  water fluxes typically generated by
cooling towers is generally good for  these temperatures  and normal humidities.
Thus,  it  can be clearly  established that  conditions suitable for fogging and
downwind visibility effects from cooling towers  are related to moisture
deficits,  which are  controlled by the  local relative  humidity and temperature.

4. 4     Case  Studies

Several couMivcer runs  using  actual atmospheric  data have been made.   These
will be use   .-ore to further  indicate  the behavior of the cooling tower plunv.-
                                       24

-------
iSOOr
1600 -
 • 0°C  ISOTHERMAL
—  0°C  5° INVERSION TO 300m
— 0°C  10° INVERSION TO  300m
   WIND IS  CALM
                 46      8     10     12      14
                         VERTICAL  VELOCITY -m/*ec
                16      IB
       FIGURE  7.   EFFECT  OF STABILITY  ON PENETRATION HEIGHT
                                25

-------
   2200}
   2000-
   !300<-
   iSOO
E
I
a
U!

O
CO
-.(
X
O
x
                                                                                                                              •100
                                                                                                                             100
            .02
.04    .06
1.0
2.0
                                                                  3.0
                                                DOWNWIND  DISTANCE —km
                   FIGURE 6.   DOWNWiNO SPREAD  OF LIQUID-WATER  CONTENT, O.O5 g/m3  CONTOURS  FOR VARIOUS

                                 VALUES OF RELATIVE  HUMiDITY EXPRESSED  IN  %

-------
The first case is for the Pittsburgh,  Pennsylvania, sounding of 1200Z on
February 28,  1968 (Figure 9).  Conditions for the Keystone Site were
utilized; Figure 10 shows the vertical profile of the plume parameters
while Figure 11 shows the results of the downwind dispersion of the
plume.   Verification for this case was obtained through personal communications
with Dr. Charles Hosier*,  who observed that the height of the plume was
at about 7000 ft. MSL and that the plume  spread downwind for a considerable
distance with very light snow flurries falling from the plume.  Photographic
measurements of the width of the individual  tower plumes indicated a
radius of about 300 meters near the top,  which is in close agreement with
the computed radius in Figure 10.

Another example is the Salem,  Oregon,  sounding for 1200Z on November 11,
1969 (Figure 12).  This case is used to demonstrate the effects of a deep
layer of atmospheric moisture which is capped by an inversion and dry
air aloft.  Figure  13 shows the distribution of liquid water downwind from
a typical hyperbolic tower.
Many additional runs have been completed which contribute to the general
under standing of the movement of moisture downwind from typical towers.
They will not be presented here but the overall results are given in Section 4. 7.

4. 5       Topographical Effects

Since it is desirable to extrapolate the results of dispersion of cooling-tower
effluents at  one location to other locations, one of the necessary assessments
that has to be made is the influence of topographical variations on plume
dispersal.  The influence of topography on the plume dispersal may occur
in three ways;  firstly,  through an effect on the local wind speed and direction,
secondly, through an effect on the characteristics  of the atmospheric
turbulence,  and thirdly, through the distribution of local moisture sources.

Most of the  analyses  mentioned above apply to an idealized "infinite-plane1'
ground for which the  roughness characteristics are assumed to be
statistically uniform.   Moreover, all ambient conditions are assumed to
be uniform  and parallel to the ground. Such conditions are seldom realized
in the  atmosphere and even over "gently rolling  terrain influences can
occasionally be significant.  A wind blowing more  or less parallel to a
valley may  be "channeled" in a direction parallel to the sides of the valley.
*Dean,  College of Earth and Mineral Sciences, Pennsylvania State University,
University Park, Pennsylvania.
                                   27

-------
to
OS
                a
                £
LJ
K
.0
Vi
if}
UJ
1C
Q.
                     500-
                     600-
     700h
                    800-
                                                                                                   345-08
                                                                                                                   355-02
                    900 -,
                   1000-
           MOIST
           ADIABATS   \
               DRY.
                                                                                                                           Q
                                                                                                                           UJ
                                                                                                                           LU
                                                                                                                           CL
                                                                                                                           CO
O
h-
o
IU
K
O

O
                                                                                                   100-08

                                                                                                   100-08

                                                                                                   105-06

                                                                                                   110-06
                            FIGURE 9.   PITTSBURGH SOUNDING, FEBRUARY  28,1968  1200?
                                            O TEMPERATURE     ADEWPOINT

-------
    2400
    2200
                                                 —— VERTICAL VELOCITY


                                                 	RADIUS

lit
    1000
UJ

o
m    800
                                     \
                                          \
                                            •*
                                              •»
                                                ^
                                                  \
r
a
     600
     400
     200
              20
40
                                   8     10     12      14


                                VERTICAL  VELOCITY -m/sec
60
80     100     120

  RADIUS - m
140
160
180
200   220
                     FIGURE 10.  VERTICAL  PROFILES  FOR  PITTSBURGH CASE
                                         29

-------
CO
o
                          2000 -
                          1800 -
                       M
                       ec.
                       ui
                       X

                       —
                       lil
                       X
                                                           PLUME CENTERLINE CONCENTRATIONS - gm'3
                                                                              2.0
3.0
                                                               DISTANCE - km.
                                                       FIGURE 11. Predicted Downwind Liquid Water Content for

                                                                 Pittsburgh  Sounding

-------
500
                                                                                                 260-40
                         MOIST '  -15 \
                        AOIABATS  /     \
                         DRY    /        \
1000^-
295-10
285-06
200-05
180-08
            FIGURE 12.   SALEM  SOUNDING,  NOVEMBER  11,1969,  I200E
                          O TEMPERATURE,

-------
co
to
                                                                 PLUME CENTERLINE CONCENTRATIONS  Qm
                                                                                                  -3
                                                  1.0
            2.0


DISTANCE — km.
                                                                                                    3.0
                                               FIGURE 13.   Pr»cJif!.ecl Downwind Liquid Water  Content for

                                                           SI.K '''og Sounding  -  11 Nov.  196M

-------
Moreover, when a strong geostrophic wind is blowing parallel to the
valley there may be a funnel effect, and this may influence the  cooling-
tower plume.  When the geostrophic wind is blowing nearly normal to
the axis of the valley, complex downwash and upwash effects may occur
along the  slopes  of the  valley.  The effects of aerodynamic downwash on
chimney plumes have been studied in laboratory wind tunnels.  The
cooling-tower plumes from sources located in valleys may also be in-
fluenced significantly by the katabatic and anabatic winds due to differential
cooling or heating.

Topographical features may also influence the dispersion of cooling-tower
effluents through their effect on the characteristics of the ambient
atmospheric turbulence.  Topograhical features may cause different rates
of heating at different places,  and thus create convective turbulence.

Local sources of water vapor such as rivers,  lakes, ponds, etc. will
influence  the local saturation deficit and hence be of importance in deter-
mining the cooling tower effects.

4. 6       Summary of Calculations

From the series of model runs the following results were obtained:

          (a)  For a given set of atmospheric  conditions,  increases in the
radius of  the tower, the saturation temperature, and the stack  velocity
contribute to increasing the  penetration height of the tower plume.  The height
of the tower above ground has a negligble influence on penetration height.
          (b)  For a given set of tower parameters,  stability influences the
penetration height as does the bending-over effect of wind and wind shear.
The most significant parameter in determining the vertical plume dynamics
is the entrainment relation,  which is determined by  the stack radius and the
angular spread of the plume.  Environmental relative humidity is important
in controlling the evaporative cooling at the plume edges and hence the  rate
of depletion of thermal  buoyancy.

For most cases of light winds ( < 3 msec  ), penetration heights of
300-1000  meters are obtained but for stable air with strong wind, the
penetration heights are reduced to a few hundred meters.
          (c)  The saturation deficit of the  atmosphere clearly  controls the
downwind spread of the ejected liquid water.  Except for cases where the
relative humidity approaches 100%, downwind propagation is limited to
the colder temperature periods typical of fall  and winter (< 0°C).

Under calmer winds, penetration is sufficient and little problem is to be
expected near the tower.  However, stability can limit penetration such
that strong winds can cause looping.  On the other hand, typical moisture
                                    33

-------
deficits occurring with windy conditions may be sufficient to completely
eliminate the appearance of the plume in a very short distance.

In summary, moderate winds with stable lapse rates and low moisture
deficits (high humidity and generally temperatures colder than about 0°C)
provide proper conditions for possible fogging and adverse modifications
downwind of typical cooling towers.

4.7       Prevention of Adverse Conditions by Seeding

It is well known that seeding of stable liquid-water clouds with properly
sized particles of sodium chloride or other hygroscopic materials can
modify the drop-size distribution in the clouds and, under certain conditions,
lead to an improvement in visibility.  The  physical process is one of
producing an initial small population of relatively large  droplets.  The
hygroscopic particles grow faster and have a larger equilibrium size  than
natural droplets which have formed on less hygroscopic condensation nuclei.
Given the artificially broadened drop-size  distribtuion,  the large droplets
continue to  grow to precipitation-particle size.

In terms of our cooling-tower model, the affect of seeding would be to change
the conversion constants, K  and K  in eqns.  (11) and (12).  The end result
would be a more rapid conversion from cloud water to hydrometeor water.
(Conversely,  seeding with very large numbers of uniformly small hygroscopic
particles will produce a cloud of large numbers of small droplets with no
large droplets.  Such a cloud, similar to many natural fogs, is extremely
stable with  very slow conversion to precipitation. )

The beneficial affects on visibility to be obtained by broadening the drop-size
distribution can readily be seen from Trabert's equation for visibility given
previously.  An increase in the mean droplet radius, for constant liquid water
content,  leads directly to an increase in horizontal visibility.  Any subsequent
decrease in water  content due to precipitation further improves the visual range.

Results of the model calculations and limited observations from cooling towers
suggest that where tower plumes have large vertical penetration, natural
conversion  will take place, leading to formation of precipitation particles.
With more limited vertical rise,  less liquid water is condensed, and a
narrower drop-size distribution such as  shown in Figure 4 would be expected.

When persistent stable plumes form downwind of cooling towers,  there  is
little question that the visibility in the plume could be improved by seeding with
properly  sized hygroscopic particles.  It is less  clear that routine seeding
in a wide range of  meteorological conditions would be advantageous.   Certainly
                                    34

-------
the production of fallout (precipitation) downwind of the tower would not
ordinarily be regarded as a beneficial effect.  Further,  an increase in
the number  of large droplets will usually  lead to longer travel times
and distances before the plume completely dissipates.

In the case of serious  fogging episodes from towers, seeding offers a
technique for reducing the adverse effects.  For optimum results the
seeding should probably be done  downwind of the tower where the effects
are most serious, rather than at the tower itself.  The most efficient
practical methods for  performing the seeding would have to be determined
by experiment.  Such  experiments at a tower location where adverse effects
are relatively frequent are recommended.

The above discussion has been directed toward warm (above 0°C) plumes.
Supercooled tower fogs could be  effectively dissipated by seeding with
freezing nuclei such as silver iodide, or with dry ice.  In tower locations
where fogs are occasionally formed at temperatures lower than  about -5°C,
silver iodide seeding of the plume at the tower  could be utilized  in problem
situations to change the fog into ice crystals which would fall out in a
relatively short travel distance.
                                    35

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                               SECTION 5. 0

                      REGIONAL CHARACTERISTICS
Based on the  results obtained from the  model computations,  it is now
possible to  investigate  various geographical regions of the  United States
in order to rate these  areas in terms of the potential for adverse effects
downwind of cooling towers.   The  model results  show that typical summer
conditions with  warm temperatures  (high moisture  deficit) and unstable
lapse rates generally will not lead to downwind propagation of a  cooling
tower  plume.    The prime season  of interest is the  late fall and  winter
where stable  air and colder temperatures are prevalent.

Statistical data  necessary for proper definition of low-level moisture deficit,
stability,  and  general dispersion is typically difficult to obtain on a regional
basis.  For the purposes of this study we  have used the following three
sources as  a  means of evaluating the geographical potential for  cooling
tower  production of fog:

         (a)   "Fog  Frequency  in the United States",  A. Court, and R.
            Gerston,   The  Geographical  Review,  p.  545.

         (b)  "Low-Level Inversion Frequency  in the Contiguous United
            States", C.  R. Hosier,  Monthly Weather  Review, Vol.  89,
            No. 9, September 1961, p.  319-339.

         (c)  "Estimates of Mean Maximum Mixing  Depths in the  Contiguous
            United States", G.  C.  Holzworth,  Monthly Weather Review,
            Vol. 92,   No.  5,  May 1964,  p. 235-242.

A qualitative  classification for the potential for adverse cooling  tower affects
has  been made  based on the following criteria:

         (a) High Potential;  Regions where heavy fog is observed over
            45 days per year,  where during October  through  March  the
            maximum  mixing depths are low  (400-600m), and the frequency
            of  low-level inversions is at least 20-30%.

         (b)  Moderate  Potential;  Regions where heavy fog  is observed over
            20 days per year,  where during October  through  March  the
            maximum  mixing depths are less than 600m, and the frequency
            of  low-level inversions is at least 20-30%.

         (c) Low Potential:  Regions where heavy fog  is  observed less than
             20 days per year,  and where October through March the max-
            imum mixing depths  are moderate to high (generally >600m).
                                     36

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Figure  14 is  a depiction of the results of this  evaluation for the United
States.   The  main areas  of high  potential are the West Coast, Pacific
Northwest,  the Appalachian Valleys,  and the far  Northeast Coast.   The
areas of  moderate potential are the Gulf and Atlantic  Coasts,  the Great
Lakes  region,  and leeward of the Continental Divide.

From the  data obtained with the  model calculations, these  areas have the
most suitable  climatic conditions for producing adverse effects downwind from
cooling towers.  However,  since the local microclimate  of a  given  region
can  vary  considerably from the larger-scale features,  each site  will have
to be evaluated on the basis of the local parameters.   As  pointed out in
Section 4. 6, local topographic influences can be  significant and will have
to be included in any site evaluation.   Valleys  with local moisture sources
(ponds,  rivers,  lakes) will obviously increase the fogging potential.   On
the other hand,  tops  of hills  or raised areas with  greater  roughness will
disperse  the effluent  more efficiently.


5. 1     Site Evaluation

To facilitate further evaluation of the cooling tower modifications it will be
necessary to  derive  certain data as  statistics for given sites.   From the
modeling  concepts,  the following  meteorological parameters are  needed  for
site evaluation:

        (1)  Temperature measurements  from the surface to heights several
             hundred  meters in excess of the expected plume  penetration.

        (2)  Relative humidity as  a function of  height.

        (3)  Wind  speed and direction as  a function of height.

These  data which provide input conditions for use of the numerical  model,
are  generally  only available from standard radiosonde  stations,  and are only
taken every 12 hours.  Thus,  the standard  U.  S. Weather Bureau data  are
not totally  adequate for proper evaluation.   In  addition, observations on local
terrain effects  such  as valley winds,  sea breeze, lake effects, etc. ,  will
have to be  obtained.


5. 2     Specific Criteria

It would clearly be advantageous  to  have a quantitative set of criteria that
could be  utilized in evaluating potential  cooling tower  sites.   Unfortunately,
such criteria could not be derived  within the scope of  the present study.
Because the behavior of a tower  plume  depends on the interaction of several
tower characteristics (radius,  updraft, velocity,  and temperature) and the
ambient meteorological conditions through a depth of atmosphere, no simple
                                       37

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GO
00
           HIGH POTENTIAL


           MODERATE POTENTIAL


           SLIGHT  POTENTIAL
                      FIGURE 14.  GEOGRAPHICAL  DISTRIBUTION  OF POTENTIAL  ADVERSE EFFECTS FROM  COOLING TOWERS
                                    BASED ON FOG, LOW-LEVEL INVERSION AND LOW MIXING DEPTH FREQUENCY.

-------
direct parameter could be determined which effectively measured these
complex interactions.   Such a parameter could be derived  empirically by
making a large number of model runs.  However, far  more runs would
be needed than could be done in this preliminary study.

General geographic criteria  more  quantitative  than those  represented by
Figure  14 could be derived by processing historical weather data from
existing radiosonde stations.   Such an evaluation should determine,  from
actual atmospheric soundings:

         (a)  mean moisture  deficit,  surface to 2000 feet

         (b)  mean wind speed,  surface to 2000 feet

         (c)  potential temperature gradient,  surface to 2000  feet

The 2000 feet height  is somewhat  arbitrary, but  is  selected  on  the  basis that
if the plume  penetrates to at least that height, and  small moisture  deficits
do not  exist below that height,  there can be reasonable assurance that no
serious  adverse plume  effects will occur at the ground.

Given a sizeable statistical sample of soundings from a given radiosonde
station,  the frequency of  occurrence  of unfavorable  values  of these  three
quantities could be determined.

The recommended evaluation procedure for a  specific planned tower site  is
as follows:

         (a)  From local surface data and  upper-air  soundings,   determine
             the frequency of occurrence  of low-level inversions and lower
             atmosphere stability (potential temperature gradients).

         (b)  Determine the frequency distribution of  wind speed  and direction.

         (c)  Utilize  the numerical plume  model to calculate penetration
             heights  for the  most  common (and for potentially troublesome)
             wind  and stability conditions.   Actual tower  characteristics,
             or  a  range of planned characteristics should be used as  input.

         (d)  Evaluate the climatological  frequency of moisture deficits through
             the computed  plume  rise intervals.

         (e)  The magnitude and  relative frequency of moisture deficits in the
             plume layer  will be direct measures of the  potential for per-
             sistent  plume fogs.
                                       39

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(f)  The model should be further utilized to predict log extent
    and density in the most unfavorable situations.

(g)  Finally, consideration should be  given  to  any purely local
    small-scale factors  due to topography,   moisture sources,  etc.
    which would modify  the  fog potential indicated by the model.
                             40

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                               REFERENCES
Briggs, G.  A. ,  1968:  Momentum and Buoyancy Effects.   Meteorology
    and Atomic Energy,  1968, D.  H. Slade,  ed. , U.  S. Atomic Energy
    Commission,  July,  1968.  pg.  189-202.
Csanady,  G.  J. ,  1968:   Research  on Buoyant Plumes.   Annual  Report,
    1967,  Department of Mechanical Engineering, University of Waterloo.
    NYO-3685-13,  120 pgs.
Davis, L.  G. ,  1967:  Alteration of Buoyancy in  cumulus:   An investigation
    of dynamics and microphysics of clouds.   Report No.  10  and Final
    Report  to  National Science Foundation, NSF  GP-4743,  Dept.  of Met-
    eorology,  The Pennsylvania State University,  University Park, Pa.
Federal Water Pollution  Control  Administration,  1968:   Industrial Waste
    Guide  on Thermal Pollution.    U.  S.  Department of the Interior,  FWPCA,
    Northwest Region, Pacific Northwest Water Laboratory.,  Corvallis,
    Oregon, 112 pgs.
Kessler, E. A. ,  Newburg,  P. J.  Feteris, and G. C.  Wickham,  1962, 1963
    1964:   Relationship between tropical  circulations and kinematic cloud
    models.  Prog.  Repts. 1-5,   Travelers Research Center,  Inc. , Hartford,
    Conn. ,  Cont. DA 36-039  SC-89099.
Ledbetter,   1969:  Droplet  size distributions from model cooling tower  fogs.
    Paper presented at National  Meeting of Air Pollution  Control Association,
    New York,  June 24-26, 1969.
Malkus,  J. , 1952:  Quarterly Journal of the Royal Meteorological Society,
    7£, 530
Marshall,  J.  S. ,  and W.  McK.  Palmer,  1948:   The distribution of raindrops
    with size.   J. Meteor. ,  5,   165.
                                      41

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Pasquill,  F. ,  1961:   The estimation of the dispersion of windborne material.
    Meteor.  Mag. ,  90,  1063,  33-49.
Sutton,  O. G. ,  1953:  Micrometeorology,  New  York, McGraw-Hill.   333 pgs.
Turner,  D.  B. ,  1967,  1969  (revised):  Workbook of Atmospheric  Dispersion
    Estimates.   U.  S.  Department of Health,  Education, and  Welfare.
    Public Health Service, National Air Pollution Control Administration.
    84  pgs.
Weinstein, A.  I. ,  and L.  G. Davis,  1968:  A Parameterized  numerical
    model of cumulus convection.   NSF Kept.  No.  11,  NSF GA-777,  Dept.
    of Meteorology,  The Pennsylvania State Univ. ,  University Park,  Pa.
                                       42

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                            LIST OF FIGURES
Figure                          Title                              Page

   1       Natural Draft Wet  (Evaporative) Counterflow
           Tower From FWPCA  (1968)                               3

   2       Vertical Dispersion Coefficient as a Function of
           Downwind Distance from the  Source.   From Turner
           (1969)                                                   11

   3       Horizontal Dispersion Coefficient as a Function of
           Downwind Distance From  the Source.  From Turner
           (1969)                                                   12

   4       Droplet Size Distribution from Laboratory Experiments
           (Ledbetter,  et  al,  1969)                                  18

   5       Example of Numerical Model Result for  a Cooling
           Tower Plume.                                            22

   6       Effect of  Stack  Radius  on Penetration  Height              23

   7       Effect of  Stability on Penetration Height                   25
                                                               3
   8       Downwind Spread of Liquid-Water Content,  0. 05 g/m
           Contours  for Various  Values of Relative Humidity
           Expressed in %                                          26

   9       Pittsburgh Sounding,  February 28,  1968,  1200Z,
           ° Temperature,  ADewpoint                               28

  10       Vertical Profiles for Pittsburgh Case                     29

  11       Downwind Liquid-Water Content for  Pittsburgh Case
           Study, in g/m3                                           30

  12       Salem Sounding,  November  11,  1969,  1200Z,
           °Temperature,  ADewpoint                                31

  13       Downwind Liquid-Water Content for  Sale n Case
           Study, in g/m3                                           32
                                       43

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                     LIST OF FIGURES (CONTINUED)
Figure                             Title                            Page

  14       Geographical Distribution of Potential Adverse Effects
           from Cooling Towers,  Based on  Fog, Low-Level
           Inversion and Low Mixing Depth  Frequency.              38
                                     44

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                             LIST OF SYMBOLS
c            specific heat of air at constant pressure  (cal g    deg  )

c , c         Sutton  dispersion  parameters in the  horizontal and vertical
             directions  (mn  ,  where n is a  dimensionless constant)
             (n = 2p/l+p)

dz           (equation 2) height increment where  freezing  occurs  (m)
                                            _2
g            acceleration of  gravity   (m sec  )

K , K        Conversion coefficients  in  parameterized  cloud physics
             equations   (sec   )

L            Latent heat (cal g  ), L  evaporation, L   freezing,
             L   sublimation
               s

M           Mass of cloud (plume) air (g)

N            Number of  cloud  droplets of radius r per unit volume
 r
                                              _2
P            Atmospheric pressure (dynes cm  )

p            Power-law  wind profile exponent (dimensionless)

             Proportionality  constants  in  horizontal and vertical directions
             for linear  (shor
             (dimensionless)
V   Z
            for linear  (short-range) growth of plume  standard deviations
Q*           Source strength (release rate) of effluent from  tower (g sec  )

Q            Liquid water content of cloud (plume) (g of water per g of air),
             Q  cloud  liquid water, Q,  hydrometeor water.  (See  equations
             if and 12.)

q            Mixing ratio (total water,  vapor and liquid,  per unit mass of
             air)   (g water  per g air).   In the text,  q  is  sometimes used
             interchangeably with the  absolute humidity, qp  , the  mass  of
             water per unit volume of air.

q            mixing ratio in environment

q            saturation mixing ratio (a  function of temperature)
 S
                                      45

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qd           qs - qe


A q          additional mixing  ratio at a given point due to effect of

             cooling  tower.



R            Gas constant for air (erg g   deg   )   (eq. 2)



R            Radius of plume (m)



R            Radius of plume at  top of cooling tower  (m)
 s

                               _2
R            Total rainfall (g m   )



R            Rainfall rate  (mm  hr  )



r            Radius of cloud droplet (microns -u)



T            Absolute temperature  (deg K)



T            Air temperature in  environment of plume



T            Virtual  temperature   T  =  T (1 + g/e)/(l  +  g),  a ficticious

             temperature at  which  dry air would have the  density of actual

             moist air



T            Environmental  virtual temperature
 ve


t            Time (sec)



U, u         Horizontal wind speed (m sec  )



U            Horizontal wind speed in tower  plume



U            Horizontal wind speed in environment



U1           Horizontal wind speed in plume before mixing with environment



U            = U , Horizontal  wind speed in plume  after mixing
  i               P


u1           Horizontal wind speed at a reference height



V            Terminal fall speed of cloud droplets or precipitation particles

             (m  sec   )



w            Vertical velocity of air in plume (m sec  )
                                      46

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w            Calculated vertical velocity before wind  shear is taken into
             account  (value obtained from eqn  1)

x, y, z        Cortesian  space coordinates

X            Concentration  of material in plume (from diffusion equation)
             (g m-3)
                                     f\   — *^
Z            Radar reflectivity  (mm   m   )

z            Maximum  height of penetration  of  plume
 G

a            Angle between plume axis  and  the  outer edge of rising,
             spreading  plume (half-angle of plume spread)

0            Angle between the vertical and  the center-line (axis) of rising
             plume.  (Tilt  of plume due to  horizontal wind)

e            Ratio  of the molecular weights  of  water and dry air
                                 _3
p            Density  of air (g m  )

p            Density  of air in plume  environment

U            Entrainment parameter (eqn  3)   (m  )

T  , T        Standard deviations of the  spatial  distribution of material in
 v  z
             the plume in horizontal (y)  and vertical  (z) directions.    (m)
                                       47

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    APPENDIX A
COMPUTER PROGRAM
           48

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              MANUAL  FOR EG &G COOLING TOWER  MODEL

          (Adapted From Penn  State Cloud  Dynamics Model  MOD 2)
I.        Introduction

The  Steady State  Cumulus Dynamics model was  developed to  provide an
on-site evaluation of the  seedability of cumulus  clouds  in  the field.   The
model has steadily evolved to its present  state where it is now being used
by several  organizations  involved in  cloud physics  research.    The mod-
ification for cooling tower plumes was developed by EG &G under the
present  contract.

The  computer program is written in  Fortran IV.  A listing of  the  program
and  subroutines is  given  at the end.

II.       Model Structure

The  model  can be subdivided into four sections:  interpolation,  calculation,
diffusion,  and output.

In the interpolation section,  a standard  radiosonde  sounding is  broken down
into  a sounding at constant height increments.

The  calculation section of the program carries out the model calculations
producing profiles of vertical velocity, cloud temperature, temperature
excess,  cloud mixing ratio,  cloud and hydrometeor  liquid water content,
radar reflectivity factor,  and updraft  radius.

The  diffusion subroutine takes the calculated plume  properties  and computes
the spread  of water in  three  dimensions due to  atmospheric  diffusion.

The  last section outputs the profiles  in  tabular form and  prints a summary
table of total rainfall,   duration,  cloud top  height, and  cloud  top temperature
and  updraft  area for all  boundary conditions put into the  model.

III.      Input Parameters

The  model  requires,  as input data,  the  following:

         1)   A standard radiosonde sounding of pressure  (mb),   temperature
             (°C),  relative humidity  (%), and,  if  desired,  wind speed (m/sec)
             starting at the top of the cooling tower.
                                      49

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        2)   The vertical grid interval  desired.  (Meters)

        3)   The cooling tower  height (cloud base).  (KM)

        4)   The entrainment rate parameter (A in the relationship
             H = A/updraft radius)

        5)   The conversion  and collection rates for temperatures above
             and below the ice nucleation temperature.

        6)   The initial updraft radius.  (KM) (diameter of top of cooling tower)

        7)   The ice nucleation temperature.  (°A)

Several other input parameters are also required  as keys to the options of
the program.

IV.     Options

The model was originally constructed with maximum versatility in  mind.
For this reason there  are some extra input  parameters and several  extra
steps in the  program that  allow utilization of model options.   Several of these
are not relevant to the cooling  tower application,  but they will be briefly
described so that the complete  program can be understood.

In the interpolation section,  either  only the  initial sounding, or both the
initial and interpolated soundings may be printed  out.   The key for  this
option is  a paramete r, JN.   If  JN = 0, only the  input sounding is printed.

In the model calculation  section there are four options.

If desired, the  model  can  be run with or without a  correction of the vertical
velocity due  to  shear of  the  horizontal  wind.   The parameter  NS is the key
for this option.  If the calculations are desired without the wind shear
correction (as would be  the  case when  wind  data  are not available) the
parameter NS is set to the wore1 "No".   If the wind shear  correction is
desired, the parameter NS is lefl blank.

The original model calculation could be run  with  the updraft radius  varying
with height  as dictated by  continuity considerations (as the  vertical velocity
increases with  height,  the updraft decreases) or with the updraft radius
constant with height.   The parameter for this option is NCR (positive for
constant radius, zero  for variable radius).   For  the cooling tower program,
a  linear increase of radius with height  is  specified  in the program,  and the
variable radius option  should always be used.
                                      50

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In the energy equation used to determine the vertical velocity,  the source
term is,  of  course,  the cloud buoyancy.   This buoyancy,  however,  must
be reduced by the weight of  the  liquid water  being  carried aloft.   It is
still unclear how much liquid water  should be carried aloft.  An option is
allowed here.   If the parameter, LWC,  is set to zero,  the total liquid
water  (cloud water  and hydrometeor water) is used to retard the buoyancy.
If the  parameter, LWC, is set to 1, the buoyancy  is retarded  by the weight
of the cloud water only, whenever the terminal velocity of the  median volume
drop diameter of the hydrometeor water (assumed  distributed in a Marshall-
Palmer distribution) exceeds  the  vertical velocity in the cloud.    If the
terminal  velocity does not exceed the vertical velocity,  the total water is
again used to retard the buoyancy.

The  model was originally  constructed to be  run with  a series of different
updraft radii and ice nucleation  temperatures, to simulate natural and
artificially stimulated  clouds  of  different sizes.   Under  these conditions it
is unnecessary to carry out  the  calculations  starting  from cloud  base each
time.   If the program is run with two  successive initial conditions,  differ-
ing  only in the ice  nucleation temperature (to see the difference  between
a seeded and non-seeded cloud of the same  size), it  is  only  necessary to
start the calculations from cloud base for the seeded case (higher nucleation
temperature).   When the non-seeded case is  run,  the calculations need  only
start from the  level of ice nucleation in the  seeded case.   The profiles
below this level are the same for seeded  and non-seeded cases.   For the
cooling tower  application,  where tower parameters  or environment conditions
may be changed,  it  is necessary to  start  the  calculations  from cloud base
on every  calculation

The  model handles  this  choice of cloud base or ice nucleation level with
the  parameter NBS.   If NBS  is  set  to  1,  the  calculations  will  start at
cloud base.   If NBS is set to zero,  the calculations  start at the first level
below the ice nucleation level of the previous run.  The profiles  below this
level are taken from the previous run.

V.       Input  Formats

For  every run,  the  following input  cards  are  needed:

         1)  A  Sounding Identifier card

         2)  A  Ground Level Sounding  Card

         3)  One card for each level of the  input sounding

         4)  A  blank card
                                       51

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      5)    A  boundary conditions  card for  each different boundary
           condition

      6)    A  run termination card

The  formats for these cards are given below:

      1)    Sounding Identifier Card

           Columns 1-78  Any identifying information (alphabetic or
                 numeric.

           Columns 79-80   Key JN  (0  or blank  -  only input sounding
                 printed.  1  or -1 - input  and interpolated sounding
                 printed)

      2)    Ground Level Sounding Card (conditions at tower exit level)

           Columns 1-10     Pressure (mb)

           Columns 11-20    Temperature  (°C)

           Columns 21-30    Effluent Temperature (°C), EFT

           Columns 31-40    Relative Humidity  (100%)

           Columns 41-50    Height  (meters)

           Columns 51-60    Wind Speed at Cloud Base  (m/sec)

           Columns 71-80 Vertical grid increment (meters)

      3)    Input Sounding Cards (one for each level)

           Columns 1-10     Pressure (mb)

           Columns 11-20    Temperature  (°C)

           Columns 21-30    Blank

           Columns 31-40    Relative Humidity  (%)

           Columns 41-50    Wind Speed (m/sec)

-------
4)  Blank  card to  separate  input sounding from Boundary Condition
    Card.

5)  Boundary Condition Cards (up to 30)

    Column 1       Updraft  Radius option  (NCR)
                        Blank - variable updraft  radius
                        1 - Constant Updraft radius

    Column 2       Cloud Base Option  (NBS)
                        Blank - Calculations start from ice  nuclea-
                        tion level
                        1 - Calculations start from cloud base

    Column 3       Buoyancy Option (LWC)
                        Blank - Buoyancy decreased by  weight of
                        total water (cloud water and hydrometeor
                        water)  throughout cloud
                        1 - Buoyancy  decreased by weight of  cloud
                        water only when terminal  velocity s vertical
                        velocity

    Columns 4-7    Entrainment Rate parameter -  (Al)
                        Entrainment Rate  (u) = Al/Radius

    Columns 8-17   Conversion Rate below Ice  Nucleation Level (AK1)
                        Cloud water is converted to hydrometeor
                        water at a rate AK1 below ice nucleation
                        level

    Columns 18-27 Conversion Rate above Ice  Nucleation level (AKFl)
                        Cloud water is converted  to hydrometeor
                        water at a rate AKFl above ice  nucleation
                        level

    Columns 28-37 Collection Rate below  Ice Nucleation  level (AK2)
                        Hydrometeors  collect cloud water at a rate
                        AKF2 above ice nucleation level

    Columns 38-47 Collection Rate above  Ice Nucleation  level (AKF2)
                        Hydrometeors  collect cloud water at a rate
                        AKF2 above ice nucleation level

    Columns 48-57 Cooling tower (Initial  Updraft) Radius (CRAD)
                        Radius in km.

    Columns 58-67 Ice  Nucleation Temperature (TF)
                        Temperature in °A
                           53

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    Columns 68-69 Vertical Wind Shear  option (NS)
                       NO - No  correction  due  to vertical shear of
                       horizontal wind
                       Blank  - Invoke correction due  to vertical
                       shear  of horizontal wind

    Columns 70-73 Vertical Plume Velocity  (W)
                       Velocity in meters/sec.

6)   Run  Termination Card

    Column 2-1
                           54

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A  Sample set of input  cards  is  given below:

         1)   Sounding Identifier  Card
 Hypothetical  Sounding
 1
  0  1
787980
         2)   Ground Level Sounding Card
800.0 5.0 70.0 100.0 5.0 50.0
1 10 20 30 40 50 60 70








                                      55

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3)   Input Sounding Cards
608.0  -13.0          70.0   7.1                   \
    10    20     30     40    50     60      70   80
   554.0                70.0    7.8
      10     20     30     40    50      60     70    80
     200.0    -67.0         10.0  15.0                  \
         10     20      30     40     50     60      70    80^
        100.0   -67.0         10.0   20.0                  \
           10      20     30    40     50     60     70   80>
                            56

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   4)   Blank Card

   5)   Boundary Conditions Cards
III       .2   0.001    0.001  0.0052  0.0052  1.000     267.0  NO   05.0
                  I       23       45        667
 23       7       7      7       7       77        793
   I    I

   I  2 3
.2  0.001
0.001
   2
   7
0.0052
     3
     7
0.0052
     4
     7
1.000
   5
   7
248.0
    6
    7
NO
 6
 9
05.0
   7
   3
\
                  .2
       0.001
           I
          7
   0.001
       2
       7
    0.0052
         3
         7
   0.0052
        4
        7
    1.000
       5
       7
   248.0
       6
       7
    NO
     6
     9
   05.0
      7
      3
                     .2  0.001
          I  2 3
                 0.001
                     2
                     7
             0.0052
                 3
                 7
              0.0052
                   4
                   7
                1.000
                   5
                   7
               248.0
                   6
                   7
            NO
              6
              9
            05.0
               7
               3
                                    57

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The  four boundary conditions cards represent the common conditions of:

         1)   Cloud Buoyancy decreased by weight of cloud water only when
             terminal velocity  of hydrometeor is s  vertical velocity.

         2)   u = • 2/R

         3)   AK1  =  AKF1 =  0. 001

         4)   AK2  =  AKF2 =  0. 0052

         5)   CRAD  =  1.0 km (example  is for a cumulus cloud; for cooling
                              tower CRAD is tower radius)

         6)   No correction due to  vertical shear of the horizontal  wind.

         7)   Initial  vertical velocity (W) = 05. 0 mps

In addition,  the options  exercised  on  each card are as follows:

         Card  1 -   1)   Constant updraft radius

                    2)   Calculations start  from cloud  base

                    3)   The  ice nucleation temperature is -6°C (267°A)

         Card  2 -   1)   Constant Updraft  Radius

                    2)   Calculations start  at first  level below -6°C level.
                         Profiles below  this  level  are taken from previous runs.

                    3)   Ice nucleation temperature  is  -25°C  (248°A)

         Card  3 -   1)   Variable Updraft  radius

                    2)   Calculations start  from cloud  base

                    3)   Ice nucleation temperature  is  -6°C (267°A)

         Card  4  -  1)   Variable Updraft  radius

                    2)   Calculations start  at first  level below -6°C level

                    3)   Ice nucleation temperature  is  -25°C  (248°A)
                                     58

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VI.      Listing
A  listing of the program follows Table  Al.
Table Al contains a complete  description of the notation used in the listing.
Figures  Al and A2 show flow  diagrams for the interpolation  and calculation
portions  of the  program.

                                 TABLE Al
                   DESCRIPTION OF PROGRAM SYMBOLS
 SYMBOL
    AK1
    AKF1
    AK2
    AKF2
    AO.A1
    AREA
    CONG
    DA
    DEFX

    DEN
    DUR
    DZ, NDZ
    IDENT
    ILEVL
    INDOC
    IT
    ITOP
    JN
    LWC
                 DESCRIPTION
Conversion  coefficient  before  freezing.
Conversion  coefficient  after freezing.
Collection coefficient before freezing.
Collection coefficient after freezing
Entrainment parameter (it =   Al/Radius).
Updraft area.
Concentration of liquid water  (  g  m   ) from diffusion equation
Heat realized from freezing of  liquid water.
Difference between saturation and environmental moisture
concentration
Density of cloud air.
Duration of precipitation.
Vertical grid interval.
Characters  on Sounding Identifier Card.
Key  indicating if new input sounding level  has been read  in.
Grid interval desired in print out.
Key  to  indicate ice nucleation level has  been reached.
Cloud top height (height  at which  vertical  velocity goes to zero).
Key  to  indicate if  listing of interpolated sounding is desired.
Key  indicating if buoyancy should be  decreased by weight of
total water  or only cloud water.
                                      59

-------
TABLE Al  (Cont'd)
    NBS

    NCR
    NFRZ
    NTF,TF
    NS
    NUM
    P
    PE
    PRAD
    Q
    QCL, AQC
    QH, AQH
    RA, RO
    RH
    RHE
    RHO
    DBS

    SIZE, CRAD
    SIGY, SIGZ
    T, TC
     TE
     TEMPT
     TH
     THE, TTHE

     TVE
     U
     UE
Key  indicating if calculations should proceed from cloud base
or from previous ice nucleation  level.
Key  for  variable or  constant updraft radius.
Key  to indicate freezing level has  been reached.
Ice Nucleation temperature.
Key  for  correction due to  shear of horizontal wind.
Initial condition card number.
Pressure of initial input sounding.
Pressure of interpolated sounding.
Normalized updraft radius (UPRAD/CRAD).
Total liquid water  content.
Cloud liquid water content.
Hydrometeor  liquid water content.
Total rainfall.
Relative humidity of initial sounding.
Relative humidity of interpolated sounding  (environment R. H. ).
Density  of  environment air
Difference between saturated vapor pressure over water and
ice
Initial updraft radius.
Standard deviations of plume width in y and z  directions.
1)  Temperature of  initial input  sounding  in interpolation
    section.
2)  Cloud temperature in calculation and output sections.
Temperature  of interpolated sounding (environment temperature).
Cloud top temperature
Wind direction in initial sounding.
Wind direction in interpolated sounding (environment wind
direction)
Environment  virtual  temperature
Horizontal  wind speed in initial  sounding.
Horizontal  wind speed in interpolated sounding (environment
wind speed).
                                      60

-------
TABLE Al  (Cont'd)
    UPRAD
    W, AW
    X, AX
    XE

    XK1.XK2,
    XK3.XK4
    XL
    XMU.XMU1
    XS
    Z
    ZE
    ZFZC
Updraft radius.
Cloud  vertical velocity.
1)  Mixing ratio in initial  input  sounding in interpolated
    section.
2)  Cloud mixing  ratio in calculation and output sections.
Mixing ratio in  interpolated sounding  (environment mixing
ratio.
Constants  in equation to determine XS.
Latent Heat
Entrainment parameter.
Saturated mixing ratio.
Height in initial sounding.
Height in interpolated  sounding.
Radar Reflectivity factor.
                                       61

-------
    PR33RAM COOLTrf3( INPUT ,01'TH JT , TAPE 5^ I MP JT , TAPE6=OUTPUT )
    COOLING TDWER MODEL ADAPTED  FROM PENN STATE CUMULUS  MfDrL
    E^TRAINMENT WIND SPEED SOURCE .STREMGTH   4 DCT 70
    DI^E^SION P(2),T(2),X(2),Z(2),3<2),QCL(2),QH(2),T\/E{2),*«2),U(?),
   lTH(2),RH(2),DENm,PE(100).TEUOO),XE(100),ZE(lQO) ,UE(103),
   2THE(100')»RHE(100), AW( 100 ) , AQH ( 100 ) * AQC( 1 00 ) , TC< 103 ) , A X( I 00 ) ,
   3UP*AD(100) ,AO(30) ,RA(30) ,L>UR(30) ,ITOP(30),MTF(30),SIZE(33),
   4AREM30) , TEMPT130) , DES < 30) , 10ENIT( 78 > ,NS ( 2 ) , XS t 100 ) ,C DM: I 50, 7 , 50 ) , S
   5ISY(5D),SIGZ<50),DEFX(100),TTME(100),CDMC2< 50) , QE2L ( 1 03 )
    OAT A (OE S = 0.5 5, 1.02, 1. 41 , 1. 73, 2. 00, 2. 21, 2. 39, 2.5 1, 2.63 , ?. 66, 2 . 68 ,
   12.69,2.68,2.64,2.60,2.54,2.48,2.40,2.31,2.22,2. 13, 2. 04, 1 . 94, 1 .84,
   2 1.75, .1.65.1.5S, 1.47,1.38,1.29)
100 READ (5,110)  (IDENTU )t 1 = 1,78), JN
110 FORMAT (7RA1.I2 >
    NSR=14N
                                   *****
    WRITE  (6,120) UDENT( I),I=1,
    FORMAT (1H1.79A1)
    *****   PAUT i  INTERPOLATI0^4
    WRITE  (6,130)
    FORMAT (1H , 40X , 16HIN IT I AL  SOUNDING)
    H-2
    WRITE  (6,140)
    FORMAT (* PRESSURE*, 3X, *HEIGHT*, 3X,*TEHPE^AT JRE*, 3X,
   l,3X,*WIND SPEEO*,3X,*WINO DI RECT IOM*// )
    READ 15,150) P( 1),T( 1 > , RH( 1 ) , Z( 1 ) ,U( l),TH(l),OZ
150 FORMAT (2F10.0, 10X , 4F10.0, F 10.0 )
    NOZ=DZ
    INDOC=50/NDZ
    TE(l), = T(l)+273,3
    PE(1)=.P(1)/10.0
120
130
140
                                                           E. 4 TI VE  HUM*
    RHE(1)=RH(1)/100
    ZE(1)=Z(1 )
160
170
190
200
    THE(l)=TH(l)
    ILEVL=0
    READ (5,170) P( Z ) ,T (2 ) , RH( 2 ) , U( 2 ) ,TH< 2 )
    FORMAT (2F10.0, IOX,3F10.0)
    WRITE (6,180) P(l),Z(l)TT(ntRH(l).UE< J-l )*EXP(-9.87*DZ/(287.04*TE( J-l) ) »
    CJPa*LO&(PE(J)/PE(J-l))
    T£(J1=TE( J-1)«-(DTDP*DP)
    RHE(J)=RHE( J-l)*(DRHDP*DP)
    UE(J).=UE( J-1)+(OUDP*DP)
    THE( J)=THE(J-1)+(OTHDP*DP>
    GO TO 220
    P(1) = P( D/10.0
    PE( J) =P(l)*eX?{-9.87*
-------
220

>30
240
260
270
280
290
300
310
ZE(2)=.ZE( 1J + DZ
IF (ZE(2)-Z(2))  230,230,250
ZE(1)=ZE(2)
CONTINUE
Z(1)=Z(2)
P(1)=P(2>
T(l)»T(2)
UMMLH2)
TH(l)=TH(2)
RH(1)=RH( 2)
N=J
ILEVL=1
GO TO 160
IF 
FORMAT(*1MU=*,F5.3,*/RUP*,2X,*^UP = *,F6.3,*  KM*, 4X , *K I =* , F !>. 3 , 2X
320

999

330

340
350
 10
360
   14.1.2A1,*  SHEAR CORRECTION*)
    RAD1=1000.0*C3AD
    XMU1=AO(MUM) /RA01
    WRITE  (6,370)
370 FORMAT  ( *0*, 2X, *HEI C,HT*, 4X, *HE I GHT*, 3X, *PXESSURE*, 2X
   13X,.*CtOUD*,6X,*TEMP.*.4X,*MIXING*,4X,*CLOJn*,'5X,*H'.r
   28X,*UPDRAFT*)
    WRITE  (6,380)
380 FORMAT(* *,31X, *VELOC ITY*, 3X, *T EMP. *, 5X, *5XCESS*, 4X,
   l*WATEH*,5X,*WATKR*,1JX,*FACTOR*,5Xt*RAni JS*)
    mirr  (6,390*
>90 FORMAT  (*  *. IX, *(Mr.TKKS) *,3X, *( f K I: F ) * , 5 X , >( M3)*,ryX,*
   i«-«n». :'.  A >*,4 x ,<•( HFC. r.)*,?x,*i ,>VKr, )*, ^,\, *•( v-i/\r, > *, 3X,
   .-'*( "1M6/M .1 ) *,4X, * ( METFRS ) * »
    WlUTt  (6,400)
400 FORMAT  (1HO)
    *****   [-JJ TI ALI / ATI UN  *****
    IF (NBS) 420,420,410                63
,  >
 r)*,
                                                          ^ T!
                                                          7X,
                                                                 CAL* ,
                                                                 *Z*,
                                                          * *\ T 1 0*, 5X,
                                                                   , 3 x
                                                                            00067
                                                                            00058
                                                                            00069
                                                                            00070
                                                                            00071
                                                                            0007?
                                                                            00073
                                                                            00074
                                                                            00075

                                                                            000/7
                                                                            00078
                                                                            00079
                                                                            OOOHO
                                                                            00081
                                                                            00082
                                                                            00083
                                                                            00084
                                                                            00065
                                                                            00086
                                                                            00087
                                                                            OOOK8
                                                                            00389
                                                                            00090
                                                                            00093
                                                                            00094
                                                                            00098
                                                                            OOD99
                                                                            00100
                                                                            00101
                                                                            00108
                                                                            00109
                                                                            001 10'
                                                                            00111
                                                                            001 12
                                                                            00113
                                                                            00114
                                                                            00115
                                                                            00116
                                                                            00117
                                                                            00118
                                                                            00119
                                                                            OOK'O
                                                                            00 I?. I
                                                                            001??
                                                                            001?4

-------
410 J=l
    NFRZ=0
    TH(1)=THE(1)
    U(1)=UE(1)
    TU)=305.0
    TC< L)=305.0
    XU)=XE(l)/RHE(1)
    QH(1)=0.0
    AQH(l)=0.0
    QCL(1)=0.0
    AW(1)=W(1>
    IHT=IHT1
    RO^O.P
    RAD=RAD1
    UPRADI1 ) = 1.0
    DTMAX=0.0
    SDTMX=0.0
    JOTMX=0
    JSOTM=0
    GO TO  440
    *****   INITIALIZATION AT PREVIOUS  FRFFZIN3 LEVEL  *****               00145
420 J=ITOB                                                                  O01'f6
    OTMAX = SOTMX                                                             001^.7
    JDTMX = JSOTM                                                             OOl'trt
    T(1)=TC(ITOB)                                                           00149
    xm^Axuros)                                                           ooiso
    OCL{1)=AQC(ITDB)                                                        00151
    QH(1)=AQH(IT03)/1000.0                                                 001S2
    W«l)=AW(I FOB)                                                           00153
    RAO=UPRAO(IT03)*RAD1                                                   00154
    RO=ROD                                                                 00155
    TH(1)=THTH                                                              00156
    U<1)=UU                                                                 00157
    IHT=IHT1                                                                00158
    IST=I^DUO1                                                             00159
    DO 430 I=ISTtITll8tINDOC                                                00160
    IHT=IHT-»-NDZ*INDOC                                                       00161
    IHTT='IHT*325/100                                                        OOU,?
    A=TC(I)-TE(U                                                           00163
    PRAD=UP^AD(I)*RAD1                                                     00164
    BQH=AQH(11/1000.0                                                       00165
    C=.U4000.0*RGH>**1.136                                                 00166
    ZFZC=200.0*(C**1.6)                                                    00167
430 WRITE  (6,790)IHTt IHTT,PE( M tAW( I ),TCII) t A,AX( I ) ,A3r,( I )t 33H.ZFZC,      0016«
   1PRAD                                                                    00169
440 TVE(l)=T(l)*(1.0*.6l*X(l))                                             00170
    Q(1)-QCL<1)+QH{1)                                                       00171
    0&N(l)=PE(J)/(2«7.04*TF(J))                                            00172
    INDIC=0                                                                 30173
    XL=2500000.0                                                            00174
    DA=0.0                                                                 00175
    XK1=22.5518                                                             00176
    XK2=2937.4                                                              00177
    XK3=4.93                                                                00178
    XK4=15.39                                                               001 t'i
    AKA=AK2                                                                 00160
    AK = AK1                                                                  001 PI
    UBASE=UE(1)                                                             0018?
    THBSE=THE(l)                                                            00183
    IT=0                                                                    00184
450 J=J+1                                                                   001^5
    IF (N-J)  330,460,460                                                   OOU'6
460 IHT=.HT + NDZ
         RAnU(0- 12* ( IHT-IHT1 ) )

-------
470
480
       VIOIST  OR  ICE ADIABATIC ASCENT   *****
A=-0.009H3*DZ
B=l.O+( (X( 1)*XL )/( 287.0't*T ( 1 ) ) )
C=1.0+.622*XL*XL*X< 1 ) / I 1 004, 0*2 B7 . 04 *T ( 1 ) *T ( 1 ) )
T(2)=*T( 1 )+(A*B+UA)/C
*****  MIXING  AT  CONSTANT PRESSURE   *****
ES=,(10.0**( (XK1*T(2)-XK2)/T(2)))/(T(2)**X<3)
X(2) = < .622*ES)/ (PE( J)-ES)
A={XMU*DZ*XL/1004.0 )*(X(2)-XE(JM
8=(XMJ*D7 )*(T(2)-TE(J) )
C=1.0«-(.622*XL*XL*X(2))/( I 004 . 0*2 87 . 04* T ( ?)*T(2) )
T(2)=T(2)-(A+B)/C
ESM10.0**((XK1*T(2>-XK2)/T<2)))/(T(2)**X<3)
X(2)=(.622*ES)/ -XK4*QH( 1 ) **0. 1 2 5 ) ) *DZ
QCL(2)=QCLm-(X<2)-X(l) )-A
IF (QCH2M  500,510,510
QCL(2)=0.0
GH12)=QH< 1)
GO TO 550
QECH J) = (X(2)-Xt(J)+QCL( 1) )*UZ*XMU
QCL(2)=QCL(2 ) -XMU*D7.* (X ( 2 ) -XF ! J ) +QCL ( I) )
IF (QCL<21)  520,530,530
QCL(2)=0.0
OH(2)=QH(1 )*A
IF (QH( 2) )  540, 550,550
QH<2)=0.0
IF (LWC)  5f>0,560,570
a{2)=QCL(2)+QH(2 )
500
510
520
530

540
550
560
    GO TO 590
570 IF (W<1)-4.5*3H(I)**.125) 580,580,560

    WATER=QCL(2)
590 ES=.T(2)*( UQ + .61*X(2) )
    TVE(2)=TE< J)*(1.0+.61*XE< JM
    *****  VERTICAL  VELOCITY COMPUTATION   *****
    A=ES-TVE(2)
    D=,(TVE(2)*-TVE(1 ) )*.5
    B=,9.87*DZ*( (A/U)-WATER)
    A=(l.3-2.0*XMU*DZ)*W( I ) *H ( 1 ) +2. 0*8
    *****  CORRECTION  DUE TO SHEAR OF THE  HORIZONTAL WTO  *****
    IF(NSR.EQ.NS(1))  GO TO  600
    ALPHA=U<1)/(1.0+XMU*DZ)
    BETA=((XMU*DZ)/(1.0+XMU*DZ))*UE(J)
    GAM=2.0*ALPHA*BETA*(COS(THE(J))*COS(TH(1))*SIN(THE(J))
   l*SIN(TH(1) ))
    EPSLN = 2.0*ALPHA*UBASE*(CGSUH<1) )*COSUHBSF)*-SIN(TH(l))*
   ISIN(THBSE))
    ZETA=.2.0*BETA*UBASE*(COS(THt'( J) ) *COS ( THBSF: ) +!>! n ( THE( J ) )«
   1SIN)
    OVEL = ALPHA*AL?)HA4UE T A*BE T A* JO AS E *UB ASE + 3 A^- bHSL N-/ F T A
    A=A-OVEL
    ALPHA=(1.0/(1.0+XMU*OZ))**2.
    BETA=XMU*OZ
    GAM = :nS(TH(l))*COS(THE(J))4-SIN(TH(U)*SIN(THl;IJ))
    U( 1 ) = I\LI'H A*( BET A'-^ETA*UE ( J ) ^iJEt J )-H.H 1 )* J ( I ) *-2.0*BETA*(i7 ( J ) - J ( 1 ) *
   1C.AM)                               65
                                                                            00190
                                                                            00191
                                                                            00192
                                                                            00193
                                                                            001 94
                                                                            00195
                                                                            00196
                                                                            00197

                                                                            00 199
                                                                            00200
                                                                            OOP.O?
                                                                            00203
00206
00?07
00208
002^9
00210
00213
00214

00216
0021 T
00218
00219
00220
00222
00223
00224
00225
00276
00227
0022H
00229
00230
002 51
00232
00233
00234
00235
00236
00237
00238
C0239
00240
00241
0024?
00? 43
00244
00245
00246
0024 1
0024U
00249
00250
no 2 SI
002 52
OOP53
00254
00255
O025'>
     1

-------
      U(1)='J( U**.5
      TTH=(U( l)*SIN(TH(l) )+BETA*UE( J)*SIM(THE( J) ) )/UJ< 1 ) *C J S( T H < 1 ) )
     1+BETA*UE(J)*CDS(THE(J)))
      TH(1)=ATAN(TTH)
  600 IF (A) 610,670,.670
  610 IF (T<2)-TF)  630,630,620
  620 NFRZ=*1
      GO TO 810
  630 IF (IT) 640,640,810
  640 DEN(2)=PE(J)/(287.04*TE( J»
      *00=RO+(QH(2)+QH(1) )*(DEN(2)*DEM(1))*.25*DZ
      IT08=J-l
      IF (JDTKX-IT03)  650,650,660
  650 SDTMX-DTMAX
      JSDTM=JDTHX
  660 UU=.UU)
      THTH=TH(1)
      GO TO 810
  670 H(2)=*A**.5
Q     *****  FREEZING   *****
      IF (IT) 680,680,720
  680 IF (H2)-TF1  690,690,720
  690 ITaIT+1
      XL=2800000.0
      XK1=9.5553
      XK2=2667.0
      XK3=0.0
      XK4=11.58
      AK=AKF1

      DA = 330.0*m2)<-(UES(MT)*0.622*2.8E6/(PE( J ) *1 004 . OE2 ) )
      ITOB=J-1
      IF (JDTMX-ITOB)  700,700,710
  700 SDTMX=DTMAX
      JSDTM=JOTMX
  710 UU=U(1)
      THTH=TH(I)
      ROD=RO
      GO TO 460
  720 DA=0.0
C     *****  UP3RAFT  RADIUS  *****
      DEN(2)=PE(J)/(287.04*TE( J) )
      IF (NCR) 730,730,740
  730 RAD=RAD1+(0.11*(IHT-IHTl))
C     *****  TOTAL  PRECIPITATION  *****
  740 RO = *OMQH(2)«-QH( 1 ) ) *(DEN<2) +DE^( 1) )*.25*DZ
Q     *****  RADAR  REFLECTIVITY  FACTOR   *****
      C=(14000.0*QH(2))**(!.136)
      ZFZC=200.0*(C**1.6)
C     *****  UPDRAFT  AREA   *****
      IF (T(2)-TE(J)-T(1)*TE(J-l)) 750,770,770
  750 IF (DTMAX-TI l) + TE(J-l) )  760,770,770
  760 HT*IHT-IHT1-NDZ
      DTMAX=T(1)-TE4
    OOL'66
    00267
    00? 68
    002f>9
    00?7C
    00271
    00? 72
    00273
    00274
    00? 75
    00276
    002 77
    00?78
    0027?
    00280
    00? HI
    002H2
    00283
    002P4
    00285
    00?«6
    00287
    00288
    002 a 9
    D0290
    002^)1
    00292
    00293
    00294
    00275
    00296
    00297
    00   9
    00300

    00302
    00.304
    00305
    00306
    003T7
    00308
    00309
    00310
    00311
    00312
    00313
    00314
    0031r>
    00316
    00317
       1°
66
    00319
    00320
    00321

-------
800
    *****  STOKE PKuf-lLbS  FOR  GRAPHICAL OUTPUT  *****
    ITAB*J
    AW( ITAB)=W(2)
    TCUTAB)=T(2)
    AQH(ITAfl)=QH(2)*1000.0
    AX(ITA8)=X<2)
    AQCUTAB)=QCL(2)
    UPRAD(ITAB)=RAD/RAD1
    *****  PREPARE FOR  NEXT
    Q(l)=Q(2?
    TVE(1)=TVE<2)
    Ttl)=T<2)
    X(1)*X<2)
    QCL(1)=QCL(2)
    QH(1)=QH( 2)
                             GRID STEP  *****
                                       *****
      W<1)=W(2)
      GO TO 450
C     *****  TOTAL PRECIPITATION   *****
  BIO RA(NUM)=RO*39.37
      *****  DURATION OF  PRECIPITATION
      A=IHT-IHTl
      WRirE(6,40)  QH(2),XK4
   40 FORMAT(* *,5X,*wH2 = *,E15.5,5X,*XK4 = *.El 5.5)
       IF(QH(21) 35,45,35
35      CONTINUE
      OUR(NUM)=2*(A/(XK4*QH(2)**.125))/60.0
       GO TO 55
45      DUR(NUM)=0.0
55      CONTINUE
      *****  CLOUD TOP HEIGHT   *****
      ITOP(NUM)=IHT
c     *****  FREEZING TEMPERATURE  (OEG C)  *****
      NTF(NUM)=-NT
      WRITE(6,30) NTF(NUM)
      FORMAT(* *,5X,*NTF=*,E15.5)
      *****  CLOUD TOP TEMPERATURE (DEG C)  *****
      TEMPT(NUM)=T(2)-273.3
      WRITE (6,820) RA ( NUM ) ,DUR( NUM ) , I TOP ( NUM ) , <\REA { NUM )
      FORMAT(* TOTAL RAIN  =*,F10.4,*  INCHES  PER  CLOUD*,5X,* ^AIN
     l,F10.2f* MINUTES*,5X,*CLOUO  TOP = *,I5,*METEKS*,3X,*UPOrU-T t
     2F6.4//)
      INDX5=1
      IF
-------
 824  CONTINUE
 832  CONTINUE
 833  FORMATdH  .17F7.4)
 835  FORMATdH  ,16F7.4!
     INDX5=INDX5+1
     IF(INDX5.LE.0)821,830
             IF  TOP  DOES  NOT REACH  WARMEST FREEZING LEVEL,   *****           00355
             PROCEED TO NEXT BOUNDARY  CONDITION CARD   *****                 00356
 830  READ (5,340) NCR,NBS,LWC,A 1,AK1,AKF1,AK2,\)           00383
     IF(NSR.EQ.NSd) ) GO TO 930                                              00384
     NUM=.l                                                                    003 R5
     IF (CRAD)  330,940,330                                                   003"6
 930  IF (CRAD)  100,940,100                                                   003«7
40   GO TO 100
     END                                                                      00389
     SUBROUTINE  DIFFZ(XS,XE,TE,W,PE,GCL,RAO,JE,.),IHT,CT^C,rFHE,DEFX,OEC
    1L, IHT1)
     DIMENSION  DFFX( 100) ,TTH£(100) ,C3:NC( 5 0, 7, 50 ) , UE ( I 0^ ) , JC. ( ? ) , P r ( 1 00 )
    l,W(2),TEdOO),XE(100),XS(100),SIGY(bO),SI3Z(-iO),X(100),:3r>j:2(50)fG
    2ECH100)
     nT=50.0/W(2)
        = 3480.0*( (PE( J-1)+PE( J-2) 1/2.0) /( ( TE( J-l ) «• T E ( J - 2 ) ) /?.3)
        = 50.0*UE( J)*OT*RAl/*2.0
     WGT=RHO*VOL
     Q=WGT*OECL(J)/OT
     IF(Q.LE.O.O)GO TU 60
12
  13
  14
  16
  I r
     DX=0.2
     DO 15  1=2,50
     XU)=X( I-1
     SIGYl I ) =0.010*1 ALOG10(X( I ) ) )+1.839
     SIGY( I »=10.0**SIGY( I )
     I F ( X I I) . L E . 1 . 0 ) 1 3 , 1 4
   SIGZU )=n
   SIGZI I )=10.0**SIGZ( I )
   GO TO  15
   IF(X(M.LF.10.0)U>,17
   SIGZ(I)=0.(>37*( .\LUG10(X( I ) )
   Sir,/( I ) =10.0**S !G/ ( I )
   r.n vo  i '-
   \ ic- / ( i ) - r1- s.'.i*( u i;r. ioi x ( i ) ) ) •»- 1. 62
   sl>;/ ( ! ) --i c>.o**s 1 1,/ i i )
                                                68

-------
   15 CONTINUE
      HT=IHT+50.C-IHT1
      UAVG=UE< J)
      DO 30 1=2,50
      A=Q/(6.28*SIGY( I )*S IGZ ( I )*UAVG)
      Z = 0.0
      DO 20 K=l,50
      B=-(0.5*< «Z-HT)/SIGZ(I ) »*( (Z-HT)/SIGZ( I )) ) )
      C=-(0.5*< ( (Z*HT)/S!&Z( I ) )*( (Z+HT)/SIGZ( MM)
      CONC1=A*< EXP(B)^FXP(C) )
      CONCt I, 1,K)=CONC( I, 1,K)>COMC1
      COMC2(K)=CONCL
      Z=Z-i-50.0
   20 CONTINUF
      DY=0. 0
      00 25 M=2,2
      D=-( 0.5*1 (DY*34.95*X( I ) ) /S IGY( I ) )*( ( DY* 54.95*X ( I ) ) /S I '1Y ( [ ) ) )
      DO 25 K = l ,50
      CONC(l,M,K) = CONC( I,M,K M-CONC2
-------
   START
   Compute
  Height of
   L2 Data
     (Z2)
      /Print
    Headings
  Read Soundings at
  Cloud  Base (L2),
Cloud  Base Ht.  (Z2),
 Grid  Interval (DZ)
    Initialize
  (First Level
Interpolated (11) =
Cloud Base (LI))
    Read
  Sounding
Next Level
    (L2)
   Compute
   Vertical
   Gradient
(L2-L1)/(Z2-Z1)
                                                       Interpolate
                                                        Sounding
                                                          at DZ
                                                       Intervals
                       No
                                                             Yes
 Drop LI  Data
  Replace by
    L2 Data
                                                          List
                                                         Inter.
                                                        ounding
                                                        Print
                                                        Inter.
                                                       Sounding
                                                       Compute
                                                     Interpolated
                                                        Mixing
                                                         Ratio
   TO MODEL
CALCULATIONS
    SECTION
      Figure Al.  Flow diagram for interpolation section of steady-state cumulus model.

-------
                   Collection
     From
  Interpolation
    Section
                                                                                            GO    TO
                                                       More
                                                    Soundings
                                                       Summary
                                                       Table
                                                                                            START
                                      Vertical
                                    Velocity (W)
                  Conversion
                                                        More
                                                      Boundary
                                                    Conditions
Read Boundary
  Conditions
(K , K ,  etc.)
  J.
                                     Correction
                                                        Plot
                                                      Profiles
                                      Adjust
                                     Vertical
                                     Velocity
 Initialization
     W=W
                     Mixing

                     Ratio
                                 Precipitation
                                    Duration
                                      Area
                                                                             Compute
                                                                          Heat released
                                                                            by freezing
  Lift Parcel
One  Grid Int.
(Include  heat
of freezing  if
 appropriate)
Mix  Parcel
    at
 Constant
I                                                        Print
                                                       Drofile
                                                        this
                                                        level
 Pressure
         Figure A2.  Flow diagram for calculation section of steady-state cumulus model.

-------
VII.      Output

Examples of the output from the  program follow.   The  first portion of the
output gives the input  atmospheric  sounding and the interpolated  sounding.
These are clearly labeled and self-explanatory.   Units  are  pressure-mb,    ,
height-m,  temperature-deg C, relative humidity-%,  and wind speed-m sec

The  second portion of the output  lists parameters of the cooling tower plume
itself as computed by  the  cloud physics and dynamics portion of the model.
These parameters are also  clearly labeled and show the cloud properties
at 200m vertical  intervals.   Above the table are given  the values of input
parameters and constants  used in the  run.   The  conversion factors (A)K1,
K1F, K2,  and K2F,  and the  ice  nucleation temperature  (TF) are always
given the values shown in the example.   These have proven to be appropriate
in our computer runs  both for natural  clouds  and cooling  tower plumes.   The
initial updraft radius (RUP) and updraft velocity  (Wl)  should be taken to
match the  characteristics  of the  tower being modeled.   The  entrainment
rate ii(MU) has been taken as 0. 2/ updraft radiiis,  and  this relationship has
proven to be  appropriate  for cooling  tower plumes  as well as can be judged
from presently available data.  As shown in the  program,  we  have used
R =  R0  +  0. 12Z for the variation of  updraft radius  with height (R = Radius,
Ro = initial radius,  Z - height).   Further  experience may indicate  a modifi-
cation of the  factor  0. 12,  or a variation of the proportionality parameter
with meteorological  conditions, but for the present the  program  is  written
for the value  0. 12,  and the relationship ^  - 0. 2/R is recommended.

The  final portion of the output gives  the  concentration of cloud water (excess
of available plume water  over that required to saturate  the  atmosphere)  in
g m~^ as  a function of height,  downwind distance from  the  tower, and hori-
zontal angle measured from the mean wind  direction.    Azimuth Angle 1
refers to the  centerline of the plume,  i. e. , the  mean, wind  direction.   Angle
2 is a direction 2 deg on  either  side of the wind direction.
The example shown  includes  only  a  portion of the output cloud water  field.
The horizontal  axis  is height; columns are for height s at 59m. intervals.
The vertical axis is downwind distance; each row is  for  a separate distance
and in this  example the  grid spacing is lOOrn in the  horizontal.   The com-
plete output continues  this table to include heights  arid distances beyond those
shown in the sample.   Then  similar tables are  given for Azimuth Angle 2.

Normally, the model computes  water  concentration directly  from,  downwind
transport of plume  water only at 50m vertical increments (the same heights
for which plume properties are  computed).  Concentrations  at  intermediate
heights are  obtained by  assuming  all  material to be  released at .the  200n.i
g..'-ui points.
                                        72

-------
and letting  diffusion spread it vertically thereafter.  Thus for example,
the sample  shown indicates a water concentration of 41. 78  g m    at  a
height of 900m (above sea level) and a distance of 0. 3km   downwind  (entry
in 3rd row,  5th column from the  right).   At this height,  the concentration
decreases to  a value of 0. 08  g  m~  at a  distance  of 1. 5km (15th  row).
The  adjacent  columns  (for 850 and 950m height)  show  lower concentrations
resulting from  vertical diffusion.   A more realistic  vertical distribution  of
water  is  obtained if the tabular values are averaged or smoothed  in the
vertical.

Note  also that the origin of  the vertical scale is arbitrary,  depending on  the
choice of sounding  and tower  heights.   The first primary cloud water column
in the output  corresponds to  the first  height  in the plume properties  table for
which  a  value  of  cloud water  is obtained,  in this  case 900m.
                                     73

-------
 PIT  290CT69  1 L

PRESSURE   HEIGHT
KEYSTONE COOLING TOWER CASE
                    INITIAL SOUNDING
TEMPERATURE   RELATIVE HUM   WIND SPEED
WIND DIRECTION
969.00
962.00
V05.00
850.00
777.00
700.00
500. 00
PPESSIRE
989.00
964.25
940.54
917.21
8S4.25
B71.94
850.19
828.97
808. 3J
788.24
768.75
749.68
731.02
712.76
694.78
677.30
060.19
643.43
027.01
610.94
595.20
5/9.79
564.70
t>49.93
535.48
521.32
b07.48
493.92
500.00
719.77
1205.44
1701.70
2*14.92
3241.H8
5b03.01
HEIGHT
500.00
700.00
900.00
1100.00
1300.00
IbOO.OO
1700.00
1900.00
2100.00
2300.00
2bOO.OO
2700.00
2VQO.OO
3100. 00
3300.00
3bOO.OO
3^00.00
3900.00
4100.00
4300.00
4SOO.OO
4700. 00
4900.00
5100.00
5300.00
5500.00
5700.00
5900.00
-1.90
1.40
-1.10
-1.10
.80
-2.90
-20.00

TEMPERATURE
271.40
274.42
273.78
272. 7b
272.20
272. 2U
272, 2u
272.73
273.20
273.80
273.72
272.83
271.94
271.04
270.02
268.72
267.42
266.12
264.80
263. 4b
262.10
260.82
259.48
258.14
256.78
255.42
254. Ob
252.68
86.0
73.0
60.0
?2.0
20.0
21. n
10.0
INTERPOLATED -
RELATIVE HUM WliMD
86.000
74.009
68.198
62.852
52.766
37.448
22.135
21.442
20.880
20.320
20.102
20.343
20.585
20.827
20.755
19.922
19.086
18.245
17.400
16.551
15.698
14.840
13.978
13.112
12.24]
11.365
1«.485
9.600
6.00
11.00
9.00
11.00
13.00
20.00
30.00
'OUNDU
SPEED
6.00
10.58
10.26
9.44
9.38
10.19
10.99
11.56
12.12
12.68
13.72
15.40
17.09
18.79
20,22
2o.98
21.74
22.50
23. ?7
24.Q4
24.82
25.60
26. 3H
27.17
27.96
28.76
29,56
30.36
                                                                          -0
                                                                          -0
                                                                          -0
                                                                          -0
                                                                          -0
                                                                          -0
                                                                          -0

                                                              WIND DIRECTION
                                                                          -0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           0
                                                                           n
                                                                           0
                                                                           n
                                                                           o
                                                                           o
                                                                           o
                                                                           0
                                       74

-------
MU= ,200/RUP RUF=
HEIGHT

(METERS)
700
900
1100
1300
1500
HEIGHT

(FEET)
2275
2925
3575
42c5
4875
.030 KM
PRESSURE

(MB)
9b4.?543
940.54Q2
V17,?087
8V*. ,537
B71.9435
Kl= .001
VEHTICAL
VELOCITY
IMPS)
IS. 12982
11.26220
10.15187
0.59639
5.98962
KlFa .001 K2= .0052 K2Fo .
CLOUD
TEMP.
(REG A)
29n.384n
28?. 7493
27R.0140
274.73ln
272.2292
TEMP.
EXCESS
(UEO C)
15.9631
8.9727
5.2655
2.5310
.0292
MIXTMG
RATIO
(GM/KG)
I2.95m97
8.010377
5.920146
4.B05571
4.107319
0052 TF



0
2
?
1
1
CLOUD
WATER
(3M/KG)
.000000
.323961
.148326
.673263
.160076
* 24H.O Wl* 5. own SHEAR CORRECTTON
HYDRO
W&TER
(GM/KG)
0.000000
O.OoOoOO
.032391
.0*3676
.K.2880
7
FACTOR
(MM6/M3)
0.
0.
4.75F. + 01
2.A7E*02
8.95E*n2
UPDRAFT
RADIUS
(METERS)
52.no
74.no
96.00
118.00
140.00
TOTAL RAIN
                  XK4
 -o.
=     .0018 IMCHES PER CLOUD
1«53900F_*01

        RAIN LASTS
                                                              6.74 MINUTES
                                                                    CI.OUD  TOP=  1700MFTERS   UPORAFT AREA-il .000
AZIMUTH ANGLE =  i
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-------
BIBLIOGRAPHIC:  E G § G, Inc., Environmental Services
Operation, "Potential Environmental Modifications
Produced by Large Evaporative Cooling Towers,"  FWQA
Publication No. 16130—-01/71.

ABSTRACT:  The objective of the study was to develop
techniques for evaluating the extent of plumes from
large evaporative cooling towers.  Analytical techniques
were used to describe the dynamics of the wet cooling
tower plume and its interaction with the environment.
Primary emphasis was placed on predicting the height
of the plume.   Classical atmosphere diffusion theory
was used to determine the downwind spread.

The study showed that the saturation deficit of the
atmosphere clearly controls the downwind spread of
the ejected liquid water.  Except for cases where the
relative humidity approaches 100%, downwind propagation
is limited to periods when the air temperature falls
below the freezing point.  For a given set of atmos-
pheric conditions, increases in the tower radius, the
saturation temperature, and the intial vertical velocity
of the plume contribute to increasing the final plume
height.

The potential for adverse atmospheric effects due to
cooling towers was analyzed on a national basis and is
presented in the form of a map of the United States.

A computer program was developed to perform the neces-
sary calculations.  The Appendix contains a description
of the program, including input specifications.

This report was submitted in fulfillment of contract
number 14-12-542 under the sponsorship of the Water
Quality Office of the Environmental Protection Agency.
(Tichenor-EPA)
ACCESSION NO.
KEY WORDS

Cooling Tower Plumes
Atmospheric Diffusion
Cooling Towers
Meteorology
Weather Modification
Fog

-------
1

5
Acce.ss/on Number
n Subject Field & Group
05C
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization
    Title
     "Potential  Environmental  Modifications Produced by Large Evaporative  Cooling
      Towers"
1Q Authors)
E G & G, Inc.
Environmental
Services Operation
16

21
Project Designation
FWQA Contract No.
14-12-542
Note
 22
    Citation
    Report No. 16130 DNIQ1/71,  Water Pollution Control Research Series, Water  Quality
    Office, EPA,  1971,  75  p.
 23
    Descriptors (Starred First)
    *Cooling towers,   *Meteorology,  *Weather modification, *Fog, Cloud physics,
    Thermal pollution, thermal  power plants, air pollution, evaporation, mathematical
    models, computer programs,  cloud seeding
 25
    Identifiers (Starred First)
    *Cooling tower plumes, *Atmospheric diffusion
 27
     Abstract The objective of the  study was  to develop techniques for evaluating the extent  of
     plumes from large evaporative  cooling  towers.   Analytical techniques were used to
describe the dynamics of the wet cooling tower plume and its interaction with the environment.
Primary emphasis was placed on predicting the height of the plume.  Classical atmosphere
diffusion theory was used to determine  the downwind  spread.
    The study showed that the saturation deficit of the atmosphere clearly controls the  down-
wind spread of the ejected liquid  water.   Except for cases where the relative humidity
approaches 100%, downwind propagation is limited to  periods when the air temperature falls
below the freezing point.  For a given  set of atmospheric conditions, increases in the tower
radius, the saturation temperature,  and the  initial  vertical velocity of the plume contribute
to  increasing the final plume height.
    The potential for adverse atmospheric effects due to cooling towers was analyzed on  a
national basis and is presented in the  form  of a map of the United States.
    A computer program was developed to perform the necessary calculations.  The Appendix
contains a description of the program,  including input specifications.
    This report was submitted in  fulfillment of contract number 14-12-542 under the sponsor-
snip of the Water Quality Office of  the Environmental  Protection Agency. (Tichenor-EPA)
Abstractor
Jruce A. Tichenor
                                'A'-"wffiJ-PNWL-Nationa1  Thermal Pollution Research  Program
 WR;102 (REV JULY 1969)
 WRSIC
                                               SEND TO: WATER RESOURCES SCIENTIFIC INFORMATION CENTER
                                                      U.S. DEPARTMENT OF THE INTERIOR
                                                      WASHINGTON. D. C. 20240


                                                                               * GPO: 1969-359-339

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