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AVAL POSTGRADUATE SC
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L
"T" 1
DEVELOPMENT OF
A MICROCOMPUTER COUPLED ATMOSPHERIC
AND
OCEANIC
BOUNDARY LAYER PRED]
by
Gary Lee Tarbet
December, 1983
XTION MODEL
Thesis
Advisor:
Kenneth Davidson
Approved for public release, distribution unlimited
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4. TITLE ( end Subtitle)
Development of a Microcomputer Coupled
Atmospheric and Oceanic Boundary Layer
Prediction Model
5. TYPE OF REPORT 4 PERIOD COVERED
Master's Thesis
December 1983
6. PERFORMING ORG. REPORT NUMBER
7. AUTHORS
Gary Lee Tarbet
8. CONTRACT OR GRANT NUM8ERC*;
» PERFORMING ORGANIZATION NAME ANO AOORESS
Naval Postgraduate School
Monterey, California 93943
10. PROGRAM ELEMENT. PROJECT, TASK
AREA 4 WORK UNIT NUMBERS
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Naval Postgraduate School
Monterey, California 93943
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12. REPORT DATE
December, 1983
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5;
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18. SUPPLEMENTARY NOTES
19. KEY WOROS (Continue on revert* etde It necaeeary end Identity by block number)
Marine Atmospheric Boundary Layer, MABL, Oceanic Boundary Layer, OBL
20. ABSTRACT (Continue on reveree
A coupled Marine Atmo
(OBL) model is develo
models respectively,
computer with emphasi
when feedback between
casts. The sensitivi
Light wind situations
predict is investigat
and wind. speed which
elde It necaeeary and Identity by block number)
spheric Boundary Layer (MABL) and Oceanic Boundary Layer
ped using the Naval Postgraduate School and Garwood
All coding is done on the Hewlett-Packard 9845 micro-
s on ease of use. The -model is used to explore cases
the boundary layers significantly influences model fore-
ty of the model to slight input variations is explored.
where stratus or fog formation is extremely difficult to !
ed . Cases covered include variations in mixed layer depth
produces significantly different forecasts from the
do ,;
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AN 73
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Approved for public release, distribution unlimited
Development of a Microcomputer Coupled Atmospheric and
Oceanic Boundary Layer Prediction Model
by
Gary Lee Tarbet
Lieutenant Commander, United States Navy
B.S., University of Utah, 1975
Submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY
from the
NAVAL POSTGRADUATE SCHOOL
December, 1983
ABSTRACT
A coupled Marine Atmospheric Boundary Layer (MABL) and
Oceanic Boundary Layer (OBL) model is developed using the
Naval Postgraduate School and Garwood models respectively.
All coding is done on the Hewlett-Packard 9845 microcomputer
with emphasis on ease of use. The model is used to explore
cases when feedback between the boundary layers significantly
influences model forecasts. The sensitivity of the model to
slight input variations is explored. Light wind situations
where stratus or fog formation is extremely difficult to
predict is investigated. Cases covered include variations in
mixed layer depth and wind speed which produces significantly
different forecasts from the initial input.
TABLE OF CONTENTS
I . INTRODUCTION 6
II. DESCRIPTION OF BOUNDARY LAYER FEATURES 10
III. MODELS 16
A. MARINE ATMOSPHERIC BOUNDARY LAYER (MABL)
MODEL 16
B. OCEANIC BOUNDARY LAYER (OBL) MODEL 23
C. COUPLED BOUNDARY LAYER MODEL 28
IV. DATA AND MODEL RESULTS 33
A. UNCOUPLED MODEL RESULTS 35
B. COUPLED MODEL RESULTS 37
C. COUPLED MODEL VARYING MIXED LAYER DEPTH
RESULTS 41
D. COUPLED MODEL VARYING WIND SPEED RESULTS 44
V. RESULTS AND CONCLUSIONS 48
LIST OF REFERENCES 5 0
INITIAL DISTRIBUTION LIST 52
LIST OF FIGURES
1. Simplified Atmospheric and Oceanic Boundary Layer
Temperature Profiles 11
2. Mechanical Energy Budget for the Ocean Mixed Layer . 13
3. Simplified Flow Diagram of the Boundary Layer Model
Showing Possible Configurations of Input Informa-
tion, Interrelation Between Atmospheric and Oceanic
Models, Model Outputs, and Tactical Models Which Use
These Outputs 14
4. Input and Flow Chart for MABL Prediction Model 18
5. Input and Flow Chart for OBL Prediction Model 29
6. Input and Flow Chart for Coupled OBL and MABL
Prediction Model 31
7. Data Set 34
8. Uncoupled Air Sea Boundary Layer Model 24-Hour
Forecast Using Fixed SST and MLD Values 36
9. OBL 24-Hour Forecast for Original Input Conditions . 38
10. Coupled Air Sea Boundary Layer 24-Hour Forecast
for Initial Input Conditions 39
11. OBL Forecast With Initial MLD Set at 10 Meters
All Other Input Values are Held Constant 42
12. Coupled Air Sea Boundary Layer 24-Hour Forecast
Varying Initial Sea Surface MLD to 10 Meters Vice
Initial Input of 2 Meters 43
13. OBL 24-Hour Forecast With Wind Speed Increasing
from 4 to 10 Knots in the Forecast Period 45
14. Coupled Air Sea Boundary Layer 24-Hour Forecast
Varying Wind Speed from 4 to 10 Knots in the
Forecast Period 47
I. INTRODUCTION
Military leaders, engineers, and scientists have become
aware of the environmental effects on electromagnetic (EM)
and elec trooptical (EO) signal propogation. Many of the
current weapons guidance systems, command and control
communications, and electronic countermeasures are critically
dependent upon environmental parameters. One extreme case
was recently brought to the attention of Pentagon officials
when a new missile guidance system became totally ineffective
in certain environmental conditions. The modern naval leader
must not only be aware of the environment but must also know
how to use the current environmental conditions to best
advantage. The deployment of resources, decision of
appropriate weapons systems, and overall tactics must include
a consideration of EM/EO propagation. The overall
effectiveness and the successful outcome of an operation
could be tied to this very knowledge.
The atmospheric factors which effect EM/EO propogation
are the temperature, humidity, vertical gradient of pressure,
small scale inhomogene i t ies or turbulence, distribution of
aerosols, and concentration of water vapor. The refraction
of EM/EO signals is primarily affected by the first three
factors. Turbulence affects the index of refraction through
wave front distortions while the remaining factors cause
extinction and dispersion. All of these effects are
interlinked and they must be computed simultaneously.
Another problem comes in measuring each of these factors. No
known or planned system provides the accuracy required for
direct measurement. Indirect methods will have to be employed
by units in the operational arena for the foreseeable future.
An equally important problem is prediction of the mixed
layer depth and sea surface temperature in the ocean.
Research is underway to find the relationship between the
synoptic scale weather patterns and the sea surface
temperature. Naval operations generally take place in areas
where the marine atmospheric boundary layer (MABL) has been
extensively modified by contact with the ocean surface. The
effects of heat flux from the ocean to the atmosphere warming
the boundary layer, the subsequent increase in turbulence,
the transfer of water vapor to the air, and the effects of
salt and other aerosols being injected into the air by waves
are all important to Naval operations. These fluxes of heat
and water vapor can change the structure of the MABL to the
extent that clouds or fog are formed. Clouds and fog will
dramatically reduce the short wave solar radiation striking
the ocean surface thereby reducing the surface heating due to
radiation. The diurnal change in the sea surface temperature
and mixed layer depth will be decreased.
In determining the effect upon acoustic propagation, both
the depth and strength of the mixed layer gradient must be
considered. Skip zones and ducting are examples of oceanic
phenomena which must be considered in every naval operation.
Unusually strong or weak diurnal affects can significantly
alter these factors. To provide an optimum forecast of the
OBL, the effective shortwave radiation, internal mixing
forces, and atmospheric entrainment must be taken into
consideration.
It is obvious that any attempt at modeling the MABL and
OBL should be linked for optimum results. Microcomputer
programs developed at the Naval Postgraduate School for the
MABL (Davidson, et. al.) and for the OBL (Garwood) have been
linked to provide the necessary feedback. While both of
these models have been verified independently, the linking
should improve forecast accuracy.
Determining situations where the linking has significant
effects is the primary goal of this thesis. Sensitivity
studies were also conducted in an attempt to determine which
if any of the factors provide significant differences between
the coupled and uncoupled models. Additionally, since the
model is currently running on a Hewlett Packard 9836
microcomputer and the fleet units are and will be using
Hewlett Packard 9845's for several more years, it is
necessary to transfer the code to the latter unit. Since the
internal architecture of the two systems is significantly
different, changes in program structure will have to be
verified for accuracy and consistency with the original
model.
Having mixed layer forecasting capabilities onboard
should enable the operational fleet units to use the
environment to maximum advantage. Not only can forecasts be
updated rapidly as on-site conditions vary, but those "what
if questions can be answered quickly and accurately.
II. DESCRIPTION OF BOUNDARY LAYER FEATURES
The MABL extends from the surface through the capping
inversion which is typically .5-1.5 km above the surface.
The MABL is cooler andmore moist than the overlying air, and
it is capped by an inversion 50-100 meters thick.
Temperature increases and humidity decreases with height in
this inversion. The air-sea interface is bordered by oceanic
and atmospheric turbulent mixed layers which effectively
insulate the quasi-geostrophic regions above the inversion
and below the thermocline. The OBL or mixed layer in the
ocean typically spans the upper 10-100M of the ocean. Mean
velocity and density values tend to be vertically uniform in
this region. At the bottom of the mixed layer a transition
region exists called the thermocline. Turbulence in these
well mixed regions is created by bouyancy, flux and velocity
gradients that are a result of air-sea interactions. The
vertical homogeneity of these two mixed layers can be
attributed to the strong mixing by the turbulent motion.
Bouyancy driven energetic eddies fill the OBL and MABL.
In the atmosphere the eddies entrain warm, dry air with high
momentum from the free atmosphere into the boundary layer.
If this entrainment causes the MABL to extend above the
lifting condensation level, then clouds or fog will form. A
typical profile of the MABL and OBL is shown in Figure 1. As
10
Free Atmosphere
2
Inversion
Mixed Layer
4* Interface
Mixed Layer
± Thermocline
T
Free Ocean
Figure 1. Simplified Atmospheric and Oceanic Boundary Layer
Temperature Profiles
11
can be seen from Figure 2, the bouyancy driven fluctuations
have an even more direct role in the mechanical energy budget
for the OBL.
With the understanding of the importance of bouyantly
driven entrainment effects, the necessity to couple the near
surface prediction models is obvious. A cause and effect
relationship is developed through the interactions of the
ocean and atmospheric surfaces. Examples of this effect
include :
1. Surface bouyancy flux induced entrainment not only
increases the depth of the MABL, but it also changes its
effect on the ocean mixed layer.
2. Clouds in the MABL can be caused by a change in the
ocean surface temperature which in turn affects the
radiation budget.
The relatively complex models used to predict these
features have been tested in both the coupled and uncoupled
modes. While often little improvement is noted in the
output in the coupled versus uncoupled modes, under certain
circumstances the coupled mode is mandatory and produces
significantly better forecasts. It is the goal of current
research to determine exactly what factors have the strongest
influence on coupling and under what circumstances coupled
models must be utilized.
The purpose of this thesis is to show under what
circumstances the coupled approach is most useful. The
answers will hopefully be obtained through interpretive
12
T.U (o)
WORK OY
WHO STRESS
00
NET SURFACE BUOYANCY FLUX
PLUS ABSORPTION OF SOLAH RAOlATlOM
*#$$"
MEAN K.E.
{Pol (U2+\f^dZ
P.E. = RE.(tQ)
Pof jb^gz dt
to-h-S
A
SHEAR
PRODUCTION
INTERIOR
BUOYANCY FLUX
ENTRAPMENT *
BUOYANCY FLUX
0
REDISTRIBUTION
()
HORIZONTAL
TURB. K.E.
{PqJ u2 + v2 dZ
-h-8
=0
c
DISSIPATION
VERTICAL
TURB. K.E.
j /°o/°W2dZ
-h-8
Figure 2. Mechanical Energy Budget for the Ocean Mixed Layer
efforts using the power of the computer. By varying the
angle of radiation (latitude), amount of radiation (month),
and start time for the program, each set of output will be
compared and analyzed for consistency. A typical case will
then be selected and further studies will be conducted. The
effects of coupled versus uncoupled oceanic mixed layer depth
variations and wind speed variations will be examined.
The magnitude and usefulness of this effort is
illustrated in Figure 3. Outputs from the coupled model can
13
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14
be used tactically in forecasts shown in the righthand column
of Figure 3. The models to be used for the forecast include
the Garwood Model and the Naval Postgraduate School Marine
Atmospheric Boundary Layer Model. A detailed description of
each model and the approach taken in coupling the outputs
will be discussed. While this understanding is not necessary
in the utilization of the output, it may provide useful
information in obtaining maximum benefit from the program.
15
III. MODELS
A. MARINE ATMOSPHERIC BOUNDARY LAYER (MABL) MODEL
The NPS MABL model is a zero-order, two layer, integrated
mixed layer model. The model assumes the atmosphere consists
of two layers; a well mixed, turbulent boundary layer, and
the relatively non-turbulent free atmosphere above. The
model is based on radiative transfers described by Davidson,
et. al. (1983) and entrainment energetics formulated by Stage
and Businger (1981).
The two zones are separated by an inversion layer or
transition zone. The zero-order model assumes this
transition zone to be infinitely thin; therefore, a jump or
discontinuity occurs at this point in the profiles of all
conservative parameters.
The current model requires the following inputs:
1. An initial atmospheric sounding.
2. The geostrophic wind.
3. The surface temperature.
In an operational scenario the boundary layer winds can
be estimated from standard meteorological charts. During
this evaluation the actual hourly winds were input for
initialization purposes. In the uncoupled version, sea
surface temperature (SST) remains unchanged; however, when
coupled, the SST does change with time and is predicted by
16
the OBL model. The humidity and temperature in the well
mixed MABL are predicted. Inputs of the surface wind and
wind shear at the inversion are required by the MABL model.
The large scale subsidence normally obtained from synoptic
scale NWP products must also be prescribed for the model
period.
The model is very sensitive to subsidence values;
therefore, care should be taken in selecting this value for
proper results. Three methods can be used to compute the
subsidence (large scale vertical velocity) from single
station observations. These three methods are the kinematic
method, adiabatic method, and integration of the moisture
budget equation (Q-method) which are all well described by
Gleason (1982). Gleason's study showed the Q-method
displayed the most merit as a single-station assessment of
subsidence. Computation of the solar zenith angle, which is
used to compute effective short wave flux, uses the latitude,
Julian day and start time which are initial input values.
As shown in Figure 4 the atmospheric model has a 30-
minute time step. During each cycle, the program predicts
the mixed layer temperature, humidity, and the jump of these
values at the inversion. When clouds or fog are formed, the
cloud top cooling and entrainment computations are important
in the physical processes.
17
Prescribed inputs:
Aeos trophic wind speed
Sea surface temp.
Subsidence
Advection
-J/
Required profiles:
Temperature
Humidity
(Surface to 3 Km)
V
'
Compute:
Surface fluxes
Condensation levels
30 min.
time
step
Compute:
Entrainment
Compute:
Entrainment
Cloud top cooling
I
J
Compute updated:
Mixed layer depth
Mixed layer temperature
Mixed layer humidity
Jump strengths
EM ducts
Optical turbulence and extinction
Dispersion
Figure 4. Input and Flow Chart for MABL Prediction Model
18
The conservative quantities and their jump at the
inversion is predicted by using the standard integrated rate
equations (Tennekes, et.al., 1981). The equations are:
h(Dx/Dt) = (w'x'Jq - (w'x')h + source (1)
h(DAx/Dt) = hrx(3h/at) - (w'x')o + (w'x')h " source (2)
r = Lapse Rate
Source =y-(Fnh - Fnn)/pCp for x = temperature
(_0 for x = humidity
Fn = Net Radiative Heat Flux
The subscripts "h" and "0" refer to inversion height and
surface values respectively.
To close this system of equations and to compute the
variation in the inversion height (Stage, et.al., 1981)
entrainment velocity parameterization is used. One
additional assumption is used to close the system and that is
that the dissipation rate of turbulent kinetic energy (TKE)
is a fraction (1-A) of the production rate. The entrainment
coefficient (A) is taken as .2 for the formulation.
The bulk aerodynamic formulas are used for surface fluxes
of momentum, sensible heat, and latent heat.
u* = Cd1/2U10 (3a)
T* = C^/2(eo _ Q) (3b)
<5* = c//2(q0 - q) (3c)
These fluxes are given by:
19
u'w1 = u*^ (momentum) (4a)
T'w1 = u*T* (sensible heat) (4b)
q'w1 = u*q* (latent heat) (4c)
C3 and c^ = ten meter stability dependent drag
coefficient
<j> = potential temperature
q = specific humidity
The subscript 0 denotes surface values.
In the MABL model, extensive work has been done on the
radiation portion because of its significance to the OBL
model and the sampling of the two models. The short wave
radiative flux is computed through use of the delta-Edington
Method. An excellent review of the delta-Edington Method
including all parameters, atmospheric factors, and equations
has been published by Fairall (1981). This portion of the
model was added to account for the heating of the mixed layer
by solar radiation.
In the boundary layer, short wave extinction is dominated
by scattering vice absorption. This second short wave
radiative component is usually referred to as diffuse solar
radiation. Atmospheric particles such as cloud droplets and
sea-salt aerosols are the primary scattering nuclei in the
MABL. The current MABL model computes both direct and
diffuse radiation components to determine a total short wave
radiation flux value at the surface. In addition, the
20
fraction of reflected short wave radiation, Ag, from the sea
surface is prescribed as .1 in the MABL model.
The modeling of radiative flux transfer has been
accomplished in numerous ways; however, even the simple
models are extremely complex compared to other
par ameter izat ions used in the model. Even though long and
short wave radiative fluxes are computed separately, there
are numerous sources of error in these calculations. Some of
these sources include:
1. Concentrations or lack of absorbing gases such as
carbon dioxide, ozone, or water vapor in the
atmosphere.
2. The uncertainty of quantity, size and distribution of
background aerosols.
3. The size of various cloud droplets and their
distribution.
Since this model primarily intended for use over ocean
areas non-black stratus clouds were permitted by introducing
cloud emissivity (ec) into the long wave radiative flux
calculation. Cloud emissivity is a function cf total cloud
liquid content, w. Cloud liquid content profiles are
approximately linear with height (Davidson, et.al., 1983)
Cloud water content and emissivity are given by equations 5
and 6.
w = 0.5 Pa (h-Zc) qh (5)
e c = 1 - exp(-aw) (6)
21
pa = air density (1.25 x 10~3 gm cm~^)
h = height of the mixed layer (cloud top)
Zc = lifting condensation level (cloud bottom)
a = 0.158 (Slingo, et.al., 1981)
q^ = liquid water content at cloud top
Using the Stefan Boltzman Law, the net long wave cloud
top radiation flux, Ln^/ can be calculated from the cloud top
temperature, Th. The cloud bottom temperature, Tc, and the
sea surface temperature, Ts, are used to calculate the flux,
Lnc, at the bottom of the cloud. These fluxes are given by:
Lnh = eca (Th4 - Tsky4) (7)
Lnc = ec° (Ts4 " Tc4) (8)
o = Stefan's Constant (4.61 x 10-11
ec = obtained from equation (4)
The net long wave radiation at the surface, F]_ong, becomes:
Flong = (Ts4 " =CT4 " d " ^C)Tsky4) (9)
T = average cloud temperature
For the cloud free case, the net fluxes are calculated at
Z = h and Z = 0 by integrating the flux emissivity profile
(Fleagle, et.al., 1978). The net long wave flux at the
surface for the clear sky case is given by:
22
Flong = Fu - Fd (10)
Fu = upward radiative flux
F^ = downward radiative flux
B. OCEANIC BOUNDARY LAYER (OBL) MODEL
A mixed layer model for the ocean using the continuity
equation for an incompressible fluid, the first law of
thermodynamics (heat equation), the conservation of salt
equation, the Navier-S tokes equation of motion with the
geostrophic component eliminated, an analytical equation of
state, and a two-component vertically integrated turbulent
kinetic energy budget was developed by Garwood (1977).
An understanding of the dynamics of the entrainment
process is a key factor in predicting the variable changes in
the mixed layer. The turbulence of the overlying mixed layer
provides the energy needed to destabilize and erode the
underlying stable water mass (Garwood, 1977). The turbulent
kinetic energy equation is the basis for the entrainment. A
closed system of equations is obtained by using the bulk
buoyancy and momentum equations with the mean turbulent field
modeling of the vertically integrated equations for the
individual turbulent kinetic energy (TKE) components.
To better define the mixing process, separate horizontal
and vertical TKE equations are used. Energy for vertical
mixing is provided by both buoyancy flux and shear
23
production. The buoyancy equation is derived from the heat
and salt equations coupled with the equation of state as
shown in equation (11).
7 = P0 [1 - a(§- e0) + b(s - s0)] (11)
Bouyancy is given by:
6 = g (pq - p)/po (12)
9 = temperature
s = salinity
p = density
g = gravity
a = expansion coefficient for heat
B = density coefficient for salt
Note: The tilde represents instantaneous values and the
subscript 0 represents an arbitrary, but representa-
tive, constant value.
The effect of the salinity on the short-term density profile
evaluation is generally found to be insignificant except at
higher latitudes. Temperature is usually the dominating
factor in the density profile. However, by using buoyancy
instead of only temperature permits the model to be applied
in situations where evaporation and precipitation contribute
significantly to the surface bouyancy flux.
For extended forecasts, the Ekman wind-driven horizontal
current profiles as well as the temperature and salinity
24
profiles must be provided with initial values. The mixed
layer depth, "h", as defined by the Garwood OBL model, is the
shallowest depth at which the observed density value, ofcf is
.02 at units greater than the observed surface density value.
Additional ocean parameters which must be prescribed include
the radiation extinction coefficient, the fraction of short
wave radiation absorbed in the upper meter of the ocean, and
the critical Richardson number which defines a stability
adjustment at the bottom of the mixed layer. Surface
boundary conditions required for the OBL model include air
temperature (dry bulb), dew point temperature, wind speed and
direction, the rate of evaporation (E) and precipitation (P) ,
and the incident solar radiation.
Using the bulk aerodynamics formulas, the turbulent
fluxes of sensible heat, Qhr and latent heat, Q6' can be
computed as follows:
Qe = Cd (.98 Es - Ea)U10 (13a)
Qh ■ Cd (Ts - Ta)Ui0 (13b)
The net back radiation is estimated from the empirical
equation (Husby, 1978).
Qb=1.14xl0"7(273.16+Ts)4(.39-.5Ea1/2) (1-.6C2) (13c)
Es = saturated vapor pressure (.98 corrects for salt
defects)
Ea = vapor pressure of air based on dew point temperature
T= = air temperature
25
Ts = sea surface temperature
C = fractional cloud cover
The upward heat flux, Qu, is then given by:
Qu = Qe + Qh + Qb (14)
The solar radiation, Qs, is given by:
Qs = (1 - a b) (1 - .66C3)Q0 (15)
The constants "a" and "b" are adopted from Tabata (1964) and
the cubic cloud cover correction from Laevestu (1960). Qq is
the clear sky radiation given by Seckel and Beauday (1973) :
Q0 = An + A1 COS4, + 3j_ sin<j) + A2 cos2 <j> + B2 sin2<j> (16)
The coefficients Ao , Ai» etc. are calculated by harmonic
representation of the values predicted in the Smithsonian
Meteorological Tables with
4> = (2V365) (t-21) (17)
where t is the Julian day of the year (O'Loughlin, 1982).
A very small percentage of the incoming solar radiation
penetrates the ocean mixed layer. Approximately 50 percent
is absorbed in the first meter of the ocean in most parts of
the open ocean. The portion absorbed varies from region to
region and is highly dependent upon such things as suspended
26
particulate matter and phytoplankton. More radiation will be
absorbed in coastal regions than the open ocean because of
the increased amount of suspended particulates. This portion
of the absorbed radiation is considered to be part of the
upward heat flux because very little of this heat is
entrained into the deep ocean. Most of this energy is
transferred upward out of the ocean and back into the
atmosphere. The remainder of the short wave radiation does
penetrate the mixed layer; however, an exponential
attenuation does take place which is highly dependent upon
water turbidity. With the fraction of solar radiation
absorbed in the first meter, RF, the net heat at the surface
is given by:
Qnet ■ Qu + (RF) Qs ~ Qs (18)
From the equations discussed above, the momentum and
surface fluxes of buoyancy (heat and salt) can be computed.
The mixed layer temperature, salinity, bouyancy and velocity
fluxes are given by:
(T'w1) = Qnet/ Cp (19a)
(S'w1) = (P - E) S0 (19b)
(b1"^) = g[a(Trwnr) - b (s^w"1") ] (19c)
(uV") = U*2 (19d)
Subscript 0 refers to surface value. The friction velocity
in air, U*, is given by:
27
U* = (ts/pa)1/2 (20)
where ts = pa Cd Uio2 (21)
ts = surface stress (dynes cm" )
A positive surface buoyancy flux results when Qnet < 0 an<3
E > P. During daytime periods, the solar heating at the sur-
face dominates giving a negative buoyancy flux. At night the
combination of long wave radiation and the upward turbulent
fluxes of heat and moisture produce a positive buoyancy flux.
The ocean model, as shown in Figure 5, details the inputs
discussed above. At each one-hour interval, new mixed layer
depth, temperature, salinity, and wind-driven current
profiles are predicted.
C. COUPLED BOUNDARY LAYER MODEL
The advantage of linking the two models described in the
previous two sections is obvious when examining the inputs to
each of the models. Allowing feedback of current input
parameters to occur between the models at each time step can
potentially produce significantly better forecasts.
O'Loughlin (1982) accomplished the initial coupling on a
Hewlett-Packard 9836 microcomputer taking care not to alter
the physical process in each of the models and insuring all
variable units were passed uniformly. The MABL model only
requires the SST from the OBL model. The correct SST is
extremely important to the MABL model and affects the entire
output package as discussed in the next section.
Prescribed Inputs:
Surface wind speed and direction
Incident Radiation
Precipitation - Evaporation
Surface (lm) Radiation Absorption
Critical Richardson Number
N/
Required Profiles:
Temperature
Salinity
Velocity
Compute:
Surface Fluxes
Stability Parameters
Retreat
Mode
Compute Updated:
Mixed layer depth
Well mixed temperature (SST)
Well mixed salinity
Figure 5. Input and Flow Chart for CBL Prediction Model
29
The initial coupling problems overcome by O'Loughlin
[Ref. 13] included:
1. The atmospheric model uses a 30-minute timestep
while the ocean model uses a 1-hour timestep. The coupled
model calls the ocean model on every other timestep to
overcome this problem.
2. The atmospheric model requires only wind speed
and not direction. The ocean model requires wind direction
to compute the horizontal ocean turbulent velocity flux,
Uy*^ , for the momentum budget equation. A subroutine was
added to compute the horizontal wind components from speed
and direction input during the initialization.
A complete flow diagram of the steps in the coupled model's
prediction computation is shown in Figure 6.
In 1982 and 1983 the Naval Oceanography Command purchased
and distributed Hewlett-Packard 9845 microcomputers to all
aviation support ships and selected detachments. These units
were designated as interim TESS (Tactical Environmental
Support System) units until the TESS system is deployed. The
9845 has proven itself as a structurally strong computer.
Many application packages have been written for the unit and
more are being distributed by The Naval Environmental
Prediction Research Facility (NEPER)F all the time.
The original formulation of a coupled model was done on a
Hewlett-Packard (HP) 9836 computer. Transferring this
working code from the 9836 to the 9845 would, on the surface,
appear to be a trivial matter. On the contrary, the 9836 is
a 16 bit computer system based on the Motorola 68000 micro-
processor capable of addressing one megabyte of memory.
30
Prescribed inputs:
Aecstrophic wind speed
SST (Initial)
Subsidence
Advecticn
Required profiles:
Temperature
Humidity
T
Compute:
Surface fluxes
Condensation levels
Conpute:
Ehtrainment
Compute:
Ehtrainment
Cloud top cooling
1,
Call ocean model:
Compute updated:
Sea surface temp
Mixed layer depth
Compute updated:
Mixed layer depth
Mixed layer temperature
Mixed layer humidity
Jump strengths
EM ducts
Optical turbulence and extinction
Dispersion
Figure 6. Input and Flow Chart for Coupled OBL and MABL Pre-
diction Model
31
Having 16 bit accuracy and the large memory addressing
capability allowed the relatively easy coupling of the
initial model. The 9845 is advertised by HP to be a 16 bit
computer with a proprietary processor to HP. The processor
has the limited capabilities of an 8 bit processor in
addressable memory (64K). This required extensive changes in
the structure of the coupled model. In addition, while the
company claims 16 bit accuracy with the 9845, the extensive
changes in code require verification that model physics and
output have not been modified by the lack of precision or
round off error within the computer system. Another factor
in preparing the program was to reduce its overall size so as
to use only one tape for the program and one tape for data to
eliminate the confusing practice of continually swapping
tapes during program execution. Transfer of information from
or to tape units is slow and must be limited. Making the
program as user friendly as possible is an additional
consideration.
32
IV. DATA AND MODEL RESULTS
The data set used for this analysis of the model is a
modified set from the Cooperative Experiment on West Coast
Oceanography and Meteorology (CEWCOM-76) shown in Figure 7.
The data set was modified to maximize the effects on the
program output. Care has been taken to ensure the input is
reasonable and representative of the area to be discussed.
The primary goal of this application is to show the
sensitivity of the program to variations in input.
Additionally, these model results could easily form a
scenario for a fleet application showing the utility of the
program.
The problem to be posed for this analysis is "will clouds
form within the next 24 hour period?" This problem could be
quite significant if perhaps the forecaster was on a vessel
with only the local observations. The availability of good
facsimile and satellite products have greatly reduced the
burden on present day forecasters. The other problem
associated with forecasting for an afloat unit, especially
any U.S. Navy ship, is that these forecast officers transfer
positions. The forecaster does not have the opportunity to
gain the expertise of an individual permanently assigned to
one forecast office. Therefore, it is of paramount
importance that adequate tools be made available to the
33
ATMOSPHERIC DATA SET
Date 21 June
Latitude 30° N
Surface Temperature 19° C
Temperature Jump at Inversion 3.5° C
Lifting Condensation Level 567m
Inversion Level 607m
Winds Average ~ 3.5 knots
Mixed Layer Specific Humidity 10.2 g/kg
Jump Strength -2.4 g/kg
OCEAN DATA SET
Sea Surface Temperature 21.07° C
Mixed Layer Depth (initial) 2.0 m
Jump Strength 2.0° C
Figure 7. Data Set
forecaster. This program is just such a tool. Using onboard
HP9845 assets, the fleet geophysics officer can input local
observations and receive a 24-hour forecast for the OBL and
MABL. In addition this program allows the forecaster to
answer those nagging and sometimes critical "what if"
questions such as:
34
1. What if the wind speed varies?
2. What if the mixed layer depth changes?
3. What if the subsidence rate varies?
To examine the coupled and uncoupled models and their
interactions, the models were initialized using the following
conditions. The overall synoptic situation is very stable.
A large high pressure system is dominating the synoptic
pattern in the region. Light winds averaging approximately 3
knots with the strong subsidence of the high pressure system
has resulted in clear summer days. No change in the general
synoptic pattern is forecast for the region by the numerical
weather prediction (NWP) products produced from Fleet
Numerical Oceanography Center (FNOC). The air temperature
has remained around 19° C. The long periods of sunlight have
caused a strong, shallow mixed layer to form on the surface
of the ocean approximately 2.0 meters deep with a 2° C
temperature jump at the boundary. Two soundings and hourly
meteorological observations have been taken in the last 24
hours and are available for use. The date is June 21st and
all data assumes a latitude of 30° N. Start time for each
forecast is 1900.
A. UNCOUPLED MODEL RESULTS
The first output to be examined is that of an uncoupled
(atmospheric model only) model. As seen in Figure 8, the
mixed layer depth (MLD) is held fixed at the original value.
35
-BOO
on
C3
Ui
Q_
on
4 -
2-
£ -H
Q_
UJ
-2
INV(LJNE)
LCLIDP.SH)
RIR TEMP (LINE)
SEfl TEMP(DflSH)
SPEC HUM
WIND SPEED
12
MIXED LAYER DEPTH
8 12 16
HOURS PETER START
20
21
Figure 8.
Uncoupled Air Sea Boundary Layer Model 24-Hour
Forecast Using Fixed SST and MLD Values
36
Winds for this run were forecast to remain light and variable
and generally out of the north. The specific humidity shows
an almost linear rise throughout the forecast period as heat
and moisture is transferred from the ocean surface into the
MABL. Evidence of this heating can also be found in the plot
for the MABL temperature. The plot shows an almost linear
increase toward the sea surface temperature (SST) during the
first 20 hours. Looking closely, a slight steepening of the
gradient does occur with the rising of the sun, and the
gradient decreases sharply late in the period as the solar
altitude decreases and the strong temperature difference has
been removed. The difference in height of the lifting
condensation level (LCL) and the inversion decreases early in
the period and then becomes parallel. Looking at this
forecast, no clouds will form, however, the LCL and inversion
height are very close together and asking a couple of the
"what if" questions listed above would seem appropriate.
B. COUPLED MODEL RESULTS
In Figures 9 and 10 the differences in the coupled model
output can be examined. As discussed earlier, many cause and
effect relationships exist between the ocean and atmosphere.
The changes in SST and mixed layer depth are input at each
time step into the atmospheric model. Changes in air tempe-
rature and winds are fed back to the ocean model. It would
37
TEMPERATURE TETPERRTURE TEMPERATURE
18 19 20 21 22 18 19 2D 2) 22 18 18 20 2) 23
a-r
2303
4C0
TEMPERBTliRE TEMPERATURE
18 18 20 21 Z2 IS 18 20 21
0 I I |
X
s -
soo
T-
1400
TEMPERATURE
22 18 '.9 20 2)
i \r i
1900
Figure 9. OBL 24-Hour Forecast for Original Input Conditi
ons
38
1000
INVILINEZ)
LCLIDR5H)
AIR TEKPILINE)
SEP TEMP(DRSH)
SPEC HUM
WIND SPEED
MIXED LfiYER DEPTH
8 12 16
HOURS RPTER S7RRT
20
24
Figure 10,
Coupled Air Sea Boundary Layer 24-Hour Forecast
for Initial Input Conditions
39
seem logical that the coupled model should produce a better
forecast since many of these factors are taken into account.
The strong gradient near the surface is evident in Figure
9. Note that a small decrease in temperature at the surface
has a marked effect on the depth of the mixed layer. Through-
out the early period heat is being transferred into the
atmosphere with no replenishment. This trend is reversed
later in the day when short wave radiation absorbed by the
sea surface is converted into heat, re-establishing the
shallow mixed layer. Changes in the mixed layer are also
traced in the lower plot of Figure 10. The wind speed has
been prescribed and is the same as for the previous case.
The specific humidity curve is markedly different. While the
early results show the same increase approximately 14 hours
into the forecast, a strong decrease is noted in the specific
humidity. This change is associated with the formation of
clouds in the MABL and reduction of the moisture flux as the
atmosphere becomes warmer than the SST. The temperature pro-
files are also markedly different. Allowing the SST to vary
at each time step allows the atmosphere and sea surface tem-
peratures to come together very rapidly. The sea surface
continues to cool until short wave radiation inputs reverse
the trend. Early in the period the LCL and inversion heights
are similar to the uncoupled case; however, the feedback
process does allow the two levels to intersect, predicting
40
the formation of a thin cloud deck. In time this cools the
atmosphere by cloud top radiation, allowing the stratus deck
to thicken as the inversion and LCL heights diverge. This
case is obviously quite different from the uncoupled case,
and it would result in a markedly different forecast.
C. COUPLED MODEL VARYING MIXED LAYER DEPTH RESULTS
As noted earlier, this model is useful in that it not
only provides a 24-hour local forecast but conditions can be
varied and examined for their effect on the output. A couple
of "what if" circumstances will be examined for the current
problem. First, "what if during local maneuvers of the task
force an ocean front is crossed and the mixed layer is
suddenly 10 meters deep rather than the current 2 meters?"
Will this affect the model output? Examining Figure 11, the
new MLD is evident with the same strong temperature gradient
as in the previous case. Changes in surface temperature no
longer have the strong effect on MLD previously noted. This
is correct as the heat capacity of a 10 meter mixed layer is
much greater than that of a 2 meter mixed layer. The near
surface heating which took place in the previous case late in
the period is also repeated in this case. A time variance of
the surface MLD is shown graphically in the lower panel of
Figure 12. The same wind speed profile as used in the two
previous cases is evident. Of interest is the large variance
in the specific humidity profile.
41
TCrrCRflTDRE TEMPCRPTURE TEflPERRTURE
IS IS 20 22 18 18 20 22 IS IS 20 22
0 I I 'II I I I
19G0
2X0
•ICO
TT^lRPTURE TEfiPERHTURC TEW»D»flTURE
IS 18 20 2i IS IB 20 22 IS IS 20 23
3 I i i i m i
900
MOO
1900
Figure 11.
OBL Forecast With Initial MLD Set at 10 Meters,
All Other Input Values are Held Constant
42
800
en
o
LJ
en
4 -
2-
E -5-»
X
fc-1
& -io
25 +
0
8 12 16
HOURS AFTER STRRT
20
INVIL1NE)
LCLlDASH)
RIR TEMP(LINE)
SEfl TEMP (DASH J
SPEC HUM
NINO SPEED
MIXED LAYER CEPTH
2A
Figure 12.
Coupled Air Sea Boundary Layer 24-Hour Forecast
Varying Initial Sea Surface MLD to 10 Meters
Vice Initial Input of 2 Meters
43
This case looks identical to the uncoupled case with no
humidity decrease as in the previous case. The air
temperature profile also matches the uncoupled case while the
SST has the same trends as in the coupled case. The
amplitude of variance is much less in this case, and the SST
and air temperature are never equal. As discussed before,
heat and moisture are being transferred into the atmosphere.
However, prior to the two temperatures becoming equal, the
effects of solar radiation upon the SST cause the two
temperatures to diverge again. The LCL and inversion plots
also have the same general characteristics of the uncoupled
model. The only difference is the slight divergence of the
two heights late in the period which results in no clouds
being formed during the period.
D. COUPLED MODEL VARYING WIND SPEED RESULTS
The second "what if" case to be examined is one in which
the wind speed is varied. What if the winds increased from
the current conditions to 10 knots late in the period? As
shown in Figure 13, the extra mixing reduces the SST rapidly
and drives the MLD down much more rapidly than in the pre-
vious cases. The early temperature reduction is much stronger
than in previous cases. There is no near surface heating
late in the period which occurred in both of the coupled
cases examined previously. The rapid decrease in MLD is again
44
TEMPEPflTURE TEMPERATURE TEMPERRTURf
IS t7.S SO 22.5 IS 17.5 20 22. SIS 17.5 20 22. S
1900
2300
400
TEMPERATURE TEWERfflURE TEMPERATURE
15 17.5 20 22.S IS 17. 5 2D 22.5 IS 17. S 20 22.5
0 I III
Figure 13.
OBL 24-Hour Forecast With Wind Speed Increasing
from 4 to 10 Knots in the Forecast Period
45
shown graphically in the lower panel of Figure 14. The slow
increase in wind speed is depicted in the next panel.
The specific humidity has the same general trends shown
in Figure 10; however, the gradients are much steeper early
in the period and fall off rapidly when clouds begin to form.
The increased wind speed allows the heat and moisture to be
transferred into the atmosphere much faster than in the
previous cases. This increased mixing is also apparent in
the rapid convergence of the sea surface and air tempera-
tures. Also, the SST shows a continual decrease throughout
the period as heat is transferred out of the water creating
convective turbulence in the upper ocean. However, the early
formation of clouds effectively reduces the incoming short
wave radiation which would heat the sea surface.
Cloud top cooling affects the MABL temperature between 6
and 10 hours into the forecast period. However, this effect
is negated by the trapping of heat in the boundary layer
between the stratus deck and the sea surface. This effect is
apparent during the latter half of the model run. The inver-
sion height moves above the LCL almost immediately after the
first increase in wind speed. As the wind increases, the
depth of the stratus layer also increases. While the initial
cloud top cooling does lower the LCL slightly, the surface
heating quickly overcomes this effect. This causes the LCL
to rise late in the period and affects cloud base height.
46
1500
INV(LINE)
LCLlDflSH)
AIR TEMP (LINE J
SCR TEMP(DBSH)
SPEC HUM
WIND SPEED
MIXED LAYER DEPTH
HOURS RFTER START
Figure 14.
Coupled Air Sea Boundary Layer 24-Hour Forecast
Varying Wind Speed from 4 to 10 Knots in the
Forecast Period
47
V. RESULTS AND CONCLUSIONS
While no verification data exist to indicate which of the
above forecasts was most correct, the primary goal of showing
the utilization of the model has been demonstrated. As with
any computer generated product, the forecast generated is a
direct reflection of the quality of the initialization data.
The finest computer model will generate poor output given
poor input. The requirement for more man-machine cooperation
with this model is such that, with the use of a little common
sense and some meteorological theory, the program should
prove useful to the naval geophysic is t. Operating in data
space regions and often adverse communications areas the
ability to use local conditions as inputs to a locally
generated forecast should improve forecaster performance.
In the numerous runs which have been completed the
performance of the model has proven to be at least a good
predictor of trends. While often little difference exists
between the coupled and uncoupled model outputs it is those
cases which are critical to naval operations that the
difference is appreciable. Regions of fog and stratus
formation is one of these circumstances. The formation of
fog can be critical to the ability of naval aircraft being
able to accomplish their mission.
48
EM/EO propogation is strongly affected by changes in the
temperature and/or humidity profiles. The ability for a task
force screen to properly guard a carrier or for a task force
to remain hidden from enemy radar lies in its ability to
properly use the environment. Changes in the MLD and the
subsequent focusing or ducting of sound can be used to find
enemy targets as well as to hide convoy noise from these same
forces.
Improvements in model input techniques and coupling of
output from this model to IREPS would provide an improved
package. Making inputs as straight forward and non-
subjective as possible will aid the fleet operator in
obtaining a useful product for presentation purposes. Having
an onboard capability to produce short range single station
forecasts should help the environmentalists in better serving
fleet operations. Through proper use of the Air-Sea Boundary
Layer Model and other environmental data, the trust in
forecasts presented should improve, and the readiness of
other fleet units will improve by the efforts of the entire
geophysics community.
49
LIST OF REFERENCES
1. Davidson, K. L., Fairall, C. W., Boyle, P.J. and
Schacher, G. E., "Verification of an Atmospheric Mixed-
Layer Model for a Coastal Region", submitted, CA, 39
pp., Journal of Applied Meteorology, 1983, 28 pp.
2. Fleagle, R. G. and Businger, J. A., An Introduction to
Atmospheric Physics, New York, New York: Academic Press,
1978.
3. Garwood, R. W. , Jr., "An Ocean Mixed Layer Model Capable
of Simulating Cyclic States", Journal of Physical
Oceanography, 1977, 7_, 455-468.
4. Gleason, J. P., S_i ng_l.e__2S _ta t__io_H Assessments o_f the
S_Yno£t^c-Sca l^e For_£_ing_ on the Marine A__tlH2:2.p_he _r ic
Boundary Layer , Master's Thesis, Naval Postgraduate
School, Monterey, CA, 1982.
5. Laevastu, T. , "Factors Affecting the Temperature of
Surface Layer of the Ocean", Soc. Scient. , Femica.
Comment-Physico.-Mathem. , 1960, 25_(1) , 1-136.
6. Naval Postgraduate School Report 63-81-004, A Review and
Evaluation of Integrated Atmospher ic Boundary-Layer
Mode_ls_, by Fairall, C. W., Davidson, K. L., and
Schacher, G. E., 1981.
7. NOAA Technical Report NMFS SSRF-696, Large Scale Air-Sea
Interactions at Ocean Station V, by Husby, D. M. and
Seckel, G. R. , 1978.
8. O'Loughlin, Michael Charles, Formulation of a Prototype
Coupled Atmospher ic and Oceanic Boundary Layer Model,
Master's Thesis, Naval Postgraduate School, Monterey,
CA, 1982.
9. Seckel, G. R. and Beaudry, F. H., "The Radiation from
Sun and Sky Over the North Pacific Ocean", EOS, Trans.
Am. Geophys. Union, 1973, 5_4, 1114.
10. Slingo, A., Nichols, S. and Wrench, C. L., "A Field
Study of Nocturnal Stratocumulus: III. High Resolution
Radiative and Microphysical Observations", Quart. J. R.
Met. Soc, 1981, 108, 145-166.
50
11. Stage, S. A. and Businger, J. A., "A Model for
Entrainment into a Cloud-Topped Marine Boundary Layer —
Part I: Model Description and Application to a Cold Air
Outbreak Episode", Journal of Atmospheric Science, 1981,
3J3, 2230-2242.
12. Tabata, S., A Study_ of the MajLn Phy_s_!£a_i Z££tor_s_
Governing the Oceanographic Conditions of Station P in
the Northwest Pacific Ocean, Ph.D. Thesis, University of
Tokyo, Tokyo, Japan,- 1964.
13. Tennekes, H. and Dreidonks, A. G. M., "Basic Entrainment
Equations for the Atmospheric Boundary Layer", Boundary
Layer Meteorology, 1981, 20_, 515-531.
51
INITIAL DISTRIBUTION LIST
No . Copies
1. Defense Technical Information Center 2
Cameron Station
Alexandria, VA 22314
2. Library, Code 0142 2
Naval Postgraduate School
Monterey, CA 93943
3. Professor R. J. Renard, Code 63Rd 1
Naval Postgraduate School
Monterey, CA 93943
4. Professor C.N.K.. Mooers, Code 68Mr 1
Naval Postgraduate School
Monterey, CA 93943
5. Professor K. L. Davidson, Code 63Ds 4
Naval Postgraduate School
Monterey, CA 93943
6. Professor R. W. Garwood, Code 68Gd 4
Naval Postgraduate School
Monterey, CA 93943
7. LCDR Gary L. Tarbet 4
113 Gallant Fox Road
Virginia Beach, VA 23462
Thesis
T1383
c.l
Target
Development of a
microcomputer coupled
Atmospheric and Oceanic
Boundary Layer predic-
tion model.
21 U
c:7
Thesis
T1383
c.i
Tarbet
Development of a
microcomputer coupled
Atmospheric and Oceanic
Boundary Layer predic-
tion model.
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