EINAL BEEQBI

to

The National Aeronatical and Space Administration

on

NASA Grant NAG 5-332

An Investigation of the

Marine Boundary Layer During Cold Air Outbreak

Principal Investigator:

Steven A. Stage

Department of Meteorology

Florida State University

Tallahassee, Florida 32306-3034

|%{NASA-CR-177287) AN IMVESI'IGATICN OF >3!HEN86-267;5 8

J3ARINE BCONDAEX LAYEfi DUfilNGi COLD Alfi

OUTBREAK Final Report (Florida Sta^e Dniv,)i

26 p HC AQ3/MI A01 CSCL/iOUB Dnclas

G3/47 43601 .

A — rt/»n *- ^ i-i<^- n, i\ ^ .-. t r\ i .• r/? UUX y A 3 O O
OUTLINE

1. Introduction.

2. A Method of Obtaining Surface Sensible and Latent Heat Fluxes

from Satellite Measurements.

2.1. Synopsis of the Method.

2.2. Discussion of the Method.

2.2.1. Applicability of the Method.

2.2.2. Accuracy of the Method.

3. A Method of Obtaining Surface Sensible and Latent Heat Fluxes

from an MABL Model and A Method Using Horizontal Transfer

Coefficients.

3.1. Synopsis of the Methods.

3.2. Discussion of the Methods.

3.2.1. The Model Used for the MABL.

3.2.2. The Method of Horizontal Transfer Coefficients.

3.2.3. The Analytic Solution for a Dry Case.

3.2.4. Generalization to a Cloudy Case.

3.3. Discussion of the Reliability of this MABL Model.

4. Summary, General Comments and Suggestions.

5. Thesis, Publications, and Papers Done Under this Grant.

6. Other References.
1. INTRODUCTION

The principal goals of this research have been to develop

and evaluate methods for use in the remote estimation of ocean

surface sensible and latent heat fluxes/ Three different

rffr°

i!CZ$SXi* ^ '

techniques have-^been developed for determining these fluxes. Ttve-

-f-i-rst rs~^dfscussed~.in section 2 and the other "two are discussed

«±.oge,ther i-n—sect-i-ort"~3^-: T.hen—sect-ion—4 summarizes the work and

g.i-ve,s—gene-r-a-l—comments—and -suggestions .

The details of the work performed under this grant have been

given in the thesis, publications, and papers listed below in

section 5 and will not be reproduced here. The purpose of this

report is to provide a summary of the most significant work and

results and to draw these together into a consolidated statement

of what has been learned about methods for remote estimation of

ocean surface heat and vapor fluxes.

2. A METHOD OF OBTAINING SURFACE SENSIBLE AND LATENT HEAT FLUXES

FROM SATELLITE MEASUREMENTS.

2.1. Sy.nop.sis of the Method.:

Satellite estimates can be obtained for the total integrated

water vapor in the atmosphere, qvx; the total integrated liquid

water, qn.; the cloud top temperature, TB~; the sea surface

temperature, T0; and either the surface wind speed, U, or the

surface friction velocity, Uw. Under the assumption that

equivalent potential temperature and total water vapor mixing

ratio are uniformly mixed throughout the MABL and making some

assumption about the profile of water vapor above the mixed layer
it-becomes possible to calculate values for the layer depth, ZB;

the mean mixed layer equivalent potential temperature, Q m- and

the mean mixed layer total water vapor mixing ratio, qT and then

to calculate the surface sensible and latent heat fluxes.

2.2. DiscussiSQ of the

This method is discussed in detail by Allison (1984) and

Allison and Stage (1986). Let ZB, ©'•/ and gx denote the mixed

layer depth, mixed layer mean equivalent potential temperature,

and mixed layer mean total water mixing ratio respectively.

Under the assumption that the equivalent potential temperature

and total water vapor mixing ratio are uniformly mixed throughout

the MABL and making an assumption for the profile of water vapor

above the top of the mixed layer, the thermodynamical equations

dictate that there is an explicit set of equations which gives

TB-, qvi, and qiaL as functions of ZB, ©•, and qT • This set of

equations can be not be explicitly inverted but can be implicitly

inverted using standard mathematical techniques. One simple

technique for doing so is given by Allison (1984) and Allison and

Stage (1986). The satellite measurements can, therefore, be used

to determine ZB, 0 •, and qT. The satellite values of T0 and

either U or Uw can them be used along with any standard bulk

transfer relationship to obtain estimates for the surface

sensible and latent heat fluxes. Allison uses a bulk transfer

method which combines the method proposed by Stage and Businger

(1981a) and the widely accepted method of Liu, et al_. (1979).

The beauty of this method lies in the fact that the only

physical assumptions used are that the MABL is well-mixed, that
one- can find a suitable profi-le. to use for water vapor above the

mixed layer, and that the bulk transfer relationship used is

appropriate. Another advantage of this method is that

instantaneous fluxes can be computed rather than the weekly or

monthly average fluxes which are computed by previously existing

methods (e.g. Prabhakara et al±, 1982). It must be emphasized

that this method in no way relies on any assumption about the

rate of entrainment into the MABL. The accuracy of this method

is determined by how well the actual MABL structure matches the

assumed structure and by the accuracy of the data used in the

computation.

2.2.1. Ap.ElicabiIity. of the Method.:. Data from cold air outbreak

episodes such that obtained during as the International Field

Year for the Great Lakes (IFYGL, Stage and Businger, 1981a) and

from the MASEX experiment show that the MABL is such cases has

well mixed equivalent potential temperature and total water

mixing ratio. This is because large amounts of vertical mixing

are generated by the large surface buoyancy fluxes associated

with cold air outbreak.

Data taken in stratus-topped mixed layers along the

California coast (Neiburger et aIA/ 1961) indicate that the MABL

is often well-mixed there. In that case the ocean and air

temperatures are close to each other and surface buoyancy fluxes

are small; mixing is mostly generated by infrared radiative

cooling of the cloud top. Davidson et al... (1983) noted that the

water vapor mixing ratio values in coastal MABL profiles often

decreased slightly with height and found that it was necessary to

include that decrease in the MABL model of Stage and Businger
(1981a) in order to simulate the coastal MABL evolution. The

vertical changes in mixing ratio which they observed were,

however, small enough that they are not a serious source of error

in flux computation by the method described here.

Nichols and Leighton (1986) show MABL profiles of cloudtopped boundary layers taken around the United Kingdom. In

several of their cases there was not uniform mixing of potential

temperature or mixing ratio between the surface and the cloud

top. A marked example is shown in their figure 1. In that case

this method would not work well. It should, however, be noted

that the cases studied by Nichols and Leighton had near-surface

air temperatures which were close to the sea surface temperatures

and therefore had small surface sensible heat flux. In fact, the

reason these layers were not well mixed from surface to cloud top

is that the infrared cooling of the cloud top generated mixing in

the cloud layer, but the associated buoyancy flux was mostly

offset by absorption of solar radiation in the cloud layer thus

giving only very small buoyancy flux in the lower boundary layer.

We therefore conclude that the method described here can be

applied to cold air outbreak episodes and to cases which have air

which is sufficiently colder than the water surface to give

mixing by the surface buoyancy flux. Since these cases provide a

large fraction of the air-sea energy exchange, the technique is

useful for obtaining fluxes during the most significant episodes.

The technique can also be used when air-sea temperature

differences are more moderate including cases of coastal stratustopped layers.
2.2.2. Assyrasv. Sf tb§ M.gtbsd.1 Allison (1984) and Allison and

Stage (1986) study the sensitivity of this method to errors in

the data and determine the size of errors which would be expected

when measurements are made using currently available technology.

The cloud top temperature may be found with an accuracy of +/-2°C

and the accuracies of the sea surface temperature, the 10 m

neutral wind speed, and the friction velocity are +/-1.5°C, +/-2

m/s or 20%, and +/-20%, respectively (Allan, 1983, using SEASAT

and NIMBUS 7 data). According to Chang and Wilheit, 1979) the

expected retrieval errors of the integrated liquid water and

water vapor contents for the SMMR package on NIMBUS 5 are +/-

0.65 m and +/-1.50 m. Table 1 summarizes the uncertainties in

surface heat and vapor fluxes which are caused by each of these

measurement errors and the expected overall R. M. S. errors in

the fluxes. If the needed satellite parameters are measured

simultaneously each set of measurements produces a flux estimate.

The R. M. S. errors shown in the table are for each such flux

estimate. When several such estimates are averaged together

errors become smaller. For instance if twice daily values are

averaged for one week and the errors assumed to be random, the

expected R. M. S. errors of the weekly average will be 6% and 22%

respectively for heat and vapor. Non-random errors could be

removed through calibration.

The largest source of error is from the uncertainty in the

total integrated water vapor (the vapor flux error would be

reduced from 84% to 32% if the error in ql± could be eliminated).

In most situations nearly all of the water vapor is in the mixed
Table 1 Individual Exp«ct»d Errors du« to Each

Batvllit* Parameter and Total Exp«ct«d

Mod»l Error

PARAMETER SATELLITE RMS ERRORS HEAT MOISTURE

u,- 20X 20X 20X

ion

2.O -C BX 9X

1.9 -C 4.3X 6.73X

650 m g/kg 1.6X 22.75X

qyt 1SOO m g/kg 9X 7SX

Total Exp«ct»d R.M.8. Errorat 24X 82X
layer" and very little above. If one assumes that the water vapor

above the mixed layer can be approximated from the water vapor

profile above the mixed layer in some nearby radiosonde sounding,

or uses a water vapor profile appropriate for that particular

meteorological situation, or even uses a profile suitable for

that location and month; then the uncertainties associated with

the amount of integrated water vapor which is above the MABL will

be negligible compared to the errors in measuring qii using

current technigues.

There are also errors in the heat and vapor fluxes which are

associated with use of bulk transfer relationships. These errors

would be present even in computations of these fluxes using in

Situ measurements of air sea temperature and humidity differences

and wind speed in bulk transfer formulae.

3. A METHOD OF OBTAINING SURFACE SENSIBLE AND LATENT HEAT FLUXES

FROM AN MABL MODEL AND A METHOD USING HORIZONTAL TRANSFER

COEFFICIENTS.

3.1. Sy.D2Es.is gf the Methods!

There are two related methods which can be used to calculate

heat and vapor fluxes during cold air outbreak situations, which

we have evaluated, and which need to be discussed together.

Assuming that the near-surface air temperature and humidity are

known at the shore and that the sea surface temperature and the

wind speed are also known; one either knows or makes educated

guesses for the lapse rates of temperature and humidity at the

shore, for the divergence of the MABL, and for the radiative sky

temperature. In the first method a computer model is then run
which calculates the rates of change of ZB, © ./ and gT as the

air moves off the coast and which gives values for the surface

heat and vapor fluxes, for the total radiative cooling, and for

the rate of entrainment of inversion layer air into the mixed

layer. The fluxes which are computed by the model are not very

sensitive to the accuracy of the measured or guessed quantities

and the model is computationaly simple enough to be economically

run on a small computer.

In the second method the need to make a run of a computer

model is replaced by use of horizontal transfer coefficients.

Based on the mathematics of the MABL equations and the inspection

of model results, it has been found that the heat flux per unit

travel between the shore and any given fetch is nearly

proportional to the difference between the near-surface air

temperature and the water temperature with a constant of

proportionality known as the horizontal transfer coefficient.

The latent heat flux per unit travel can also be expressed as the

product of a horizontal transfer coefficient and the air-sea

humidity difference. The sensible and latent heat horizontal

transfer coefficients are functions of nondimensional fetch which

can be specified graphically or in tables. The computations

required to find the fluxes then become simple enough to be made

with a hand-held calculator or even by hand.

3.2. Discussion of the Methods!

The two methods are closely intertwined and will be

discussed together. More complete explanations and discussions
of these -techniques are given by Chang (1986) and Chang and Stage

(1986).

3.2.1. Tfae Model Used fgr the MABLj. This work uses a model for

the evolution of an MABL during cold air outbreak which was

developed by Stage and Businger (1981a). It predicts the rates

of change of mean mixed layer equivalent potential temperature,

total water mixing ratio and mixed layer depth following a column

of air as it moves across the water. The effects of surface

fluxes, infrared radiation, divergence, and entrainment at the

layer top are included. Stage and Businger studied a cold air

outbreak episode over Lake Ontario and found that the model was

able to accurately match changes in temperature and dewpoint

experienced by mixed layer air as it crossed the lake. Good

agreement was also obtained between profiles observed at the

south shore of the lake and those predicted by the model. As

discussed by Stage and Businger (1981b) this model uses a

relationship for the rate of entrainment of air into the mixed

layer which appears to be more logically based on the energetics

of the layer than previous models for stratocumulus cloud-topped

marine mixed layers and is thus expected to be more accurate.

3.2.2. The Metfegd. of Hor.izon.tal Transfer Coefficientsi Atlas et

ali (1981) and Chou and Atlas (1982) considered the Stage and

Businger model and found that it held promise for the

determination of sea-surface heat and vapor fluxes from satellite

measurements. By empirically studying the behavior of the model

for several profiles based on a cold-air outbreak episode off New
York on February 17, 1979, Chou and Atlas (1982) found that in

the area between the shore and the edge of the cloud (the cloudfree region) the sensible and latent heat flux per unit travel at

a particular distance from shore are not very sensitive to

divergence or to the lapse rates of the temperature and dewpoint

soundings at the shoreline. They therefore suggested that the

sensible heat flux could be approximately modeled by the product

of a transfer coefficient and the potential temperature

difference between the air at the shore and the sea surface

temperature. Similarly, the latent heat flux could be modeled by

the product of a transfer coefficient and the difference between

the mixing ratio of the air at the shore and the saturation

mixing ratio corresponding to the SST. They called these

coefficients horizontal transfer coefficients because they

connect the fluxes to horizontal differences between shore air

properties and water properties rather than the vertical

differences usually used in bulk transfer formulae.

3.2.3. The Analytic Solution for a Dry. Casei Stage (1983)

studied the model equations as they apply to the cloud-free

region. By assuming that potential temperature and humidity

profiles at the shore may be treated as linear, he was able to

obtain analytic solutions which give the mixed layer potential

temperature, mixing ratio, dewpoint, and layer depth as functions

of fetch; which can be solved numerically to find the location of

the edge of the cloud; and which allow calculation of heat and

vapor fluxes. Stage (1983) examined the form of these solutions

and found that to completely specify a particular cold-air
outbreak episode requires the measurement of more parameters than

can be obtained using data which is currently available from

space. He then investigated the use of the horizontal transfer

coefficients as proposed by Chou and Atlas (1982). He found that

it is possible to nondimensionalize the MABL equations and to

determine the horizontal transfer coefficients, g± and ga, for

virtual temperature and latent heat respectively as universal

functions of the nondimensional fetch. He found that the

functions gj. and ga depend only very weakly on divergence and was

able to show that even very crude estimates of the lapse rates of

potential temperature and mixing ratio at the shore allow

accurate estimates to be made for the heat fluxes in the cloudfree region. He was thereby able to demonstrate that the

findings of Chou and Atlas (1982) can be generalized to any coldair outbreak episode and provide a method for the simple

computation of heat fluxes in the cloud-free region.

3.2.4. Generalization to a Cloudy. Case! Stage (1983) showed

that the dry case can be nondimensionalized so that plots of the

transfer coefficients, g* and ga, as functions of the

nondimensional fetch, X, give universal curves. Once a cloud

forms in the boundary layer, latent heat release and radiation

become important; the equations increase in complexity; and it is

no longer possible to find an analytic solution. Nonetheless,

Chang (1986) and Chang and Stage (1986) have run the computer

model in cloudy cases and inspected the results using the drycase nondimensionalization. The reader is referred to Chang and

Chang and Stage for mathematical details of their analysis. In
the cloudy case the curves obtained .for gi^and ga depend to wind

speed, shoreline near-surface temperature and humidity, shoreline

lapse rates of temperature and humidity, boundary layer

divergence, radiative sky temperature, and SST. The papers cited

examine the curves obtained for gi and ga when each of these

parameters are varied over the range which would be encountered

during cold air outbreak. Figure 1 shows the plot which they

obtained by varying T»*y, the radiative sky temperature, between

-80 and 0°C. As expected, the curves reproduce the dry case

analytic curves for fetches in the cloud-free region. After

cloud formation the curves depend on T.^y, but the separation is

not great. Table 2 shows the ranges of gi and ga associated

with this range of T.xy for selected fetches. Even with the

large range chosen the percentage change in gi and therefore in

the heat flux remains less than +/-25%. The range for ga and

latent heat flux remains less than +/-5.2%. It will nearly

always be possible to obtain a value of T.ny with a much smaller

range than that even if seasonal averages are used. The

variation of gt and ga with each of the other parameters which is

important in the cloudy case has been determined. Table 3 is a

summary of the variations in the horizontal transfer coefficients

when each of the parameters of the problem varies over a wide

range of values. None of the flux variations is large. Errors

in each of these parameters will be smaller than these ranges

thus heat and vapor flux errors will be quite small.

A few words on the significance of the Chang (1986) and

Chang and Stage (1986) work are in order. First of all, the main

significance of this work is that it shows that if one begins
J2.0

1.5

11..

0.5

l(f5 ID'4

10~3 10~2

X

ID'1 10° 101

- 0

Figure 1: gi and ga as functions of X for various radiative sky

temperatures, T.*y from -80 to 0 in increments of 20

"C.
Table 2

The changes of g± and ga caused by TBKY. TEKY' 0 to -80 C,

in increments of -20 C.

Log X x Range of Range of Percent Change in

TBKY g± ga g± gz

(km) (°C) (gi±^9i) Cga+Ag2) (2Ag1/g'1) (2Aga/g-2)

-1.0 193 -20 to -80 1.43+0.03 1.80±0.02 4.4% 1.8%

-0.5 611 -20 to -80 1.03+0.07 1.72+0.04 13.8% 4.6%

0.0 1932 -20 to -80 0.51+0.06 1.53+0.04 25.0% 5.2%
Table 3

The uncertainties of gA and ga caused by the errors of the

external parameters at fetch equal to 600 km (The

measurement errors are allowed to be up to 50%).

external data tolerance range of

(w/ standard of data parameters

sounding

values

resulting errors

(fetch = 600km)

( g"3±Ag2 )

) (2Ag2/g-3)

Initial sounding ( changes of )

sounding data

9=1 (6C) 11.5,

gx± (g/kg) 3.4,

c ( C/km) 3.8,

: (——3 ) -0.75,

kw

11.5 to 13.5

3.4 to 4.4 1.07+0.01 1.59+0.05

( 1.9%) ( 6.3%)

3.0 to 3.8

-0.75 to 0.0
Table 3 (continued)

external data tolerance range of resulting errors

(w/ standard of data parameters (fetch = 600km)

sounding ("gi + Agj.) ("ga+^ga)

values (2Agi/g~i) (2Ag2/g~2)

U (m/sec) 16, 50% 8 to 24 1.01+0.02 1.73+0.02

( 3.9%) ( 2.3%)

Di (10-°/sec) 4, 50% 2 to 6 0.96+0.06 1.58+0.06

(12.5%) ( 7.6%)

Da (10-°/sec) 4, 50% 2 to 6 0.84+0.03 1.41+0.10

( 7.1%) (13.5%)

To ( C) 12, 8 to 16 1.03+0.11 1.72+0.03

(21.4%) ( 3.5%)

TSKV( C) -40, -20 to -60 1.00+0.04 1.72+0.02

( 8.0%) ( 2.9%)

RB (mK/sec) 0.1, 50% .05 to .15 1.01+0.05 1.72+0.03

( 9.9%) ( 3.5%)

.RHX(%) 40, 50% 20 to 60 1.03+0.03 1.55+0.08

( 6.1%) (10.7%)
with available measurements or best estimates of the needed

parameters and uses the MABL model to compute heat and vapor

fluxes per unit travel, the computed answers will not be very

sensitive to errors or uncertainties in the input parameters.

Therefore the model is a promising tool for flux computation.

Secondly, it is possible to make plots of the horizontal

transfer coefficients, g± and ga, as functions of nondimensional

fetch, X, using typical values of the parameters; e.g. typical

conditions for cold air outbreak off New York during December.

These plots may then be used to make estimates of the heat and

vapor fluxes for a particular case. Use of the MABL model wil l

have the smallest errors and is therefore preferred whenever

sufficient computational power is available (The model can be run

on a PC class microcomputer.) Because of the large number of

parameters affecting gx and ga it is not practical to plot or

tabulate values for all possible combinations of parameters.

However, since the curves do not change very much as these

parameters change, it is possible to use g* and ga values from a

few typical cases. Because of this simplification, use of

horizontal transfer coefficient plots has larger errors than a

model run based on parameter values which fit a particular case,

but has the advantage of enabling computations to be made with a

hand-held calculator or even by hand.

3.3. Discussion of the Re liability, of this MABL Model.!

There has been much discussion in the literature which

compares the MABL model of Stage and Businger (1981a) with those

used by other authors. Most discussion has relied on heuristic
grounds rather than measurements because data sets with

sufficient detail to evaluate the models are rare, however

Davidson et al.. (1983) have used this model (with minor changes)

to obtain good simulations of the structure and diurnal cycle of

the stratocumulus-topped MABL. Nichols (1984), Nichols and

Leighton (1986), and Nichols and Turton (1986) studied flux

profiles from near the UK and found that the mixed layer model

from Stage and Businger underestimated the rate of entrainment.

Those profiles had air temperatures which were close the seasurface temperatures so that surface heat fluxes were small and

were primarily mixed by infrared cooling of the cloud top.

Furthermore, the IR cooling was nearly balanced by solar warming

in the cloud layer, thus turbulent fluxes were small below the

cloud base and there was often a layer near the surface which was

not well-mixed with the cloud layer. Since this does not satisfy

the MABL structure assumed by Stage and Businger, it is not

surprising that the observed flux profiles do not agree with

those computed by the model.

The good simulation of IFYGL data obtained by Stage and

Businger (1981a), has verified their model for use in cold air

outbreak situations. Nonetheless, a test was done by Chang and

Stage (1986) to determine the importance of the entrainment rate

on the above-listed conclusions about flux calculations. Figure

2 shows the curves obtained for gi and ga when the entrainment

coefficient, A, changes from its usual value of 0.2 to 0.0, 0.4,

0.6, and 0.8. The changes in gt are extremely small, just barely

visible. ga has somewhat larger changes, however the range of
ORIGINAL -IS

OF POOR QUALfTTY

2.0

I

 1>5

1.0

0.0

10

-3 to"2 10"

X

10'

Figure 2: gi and ga as functions of X for various values of the

entrainment coefficient, A from 0.0 to 0.8 in

increments of 0.2.
values remains less than 10% for all fetches. Furthermore, if

the plots of gi and ga for variations of the cold air outbreak

parameters were redone using one of these different values of A,

then the curves would be shifted slightly, but the conclusions

about the usefulness of the model would not be changed.

Similarly, if an entirely different closure where used for the

entrainment rate (e.g. the closure used by Deardorff, 1972 or

Kraus and Schaller, 1978) were used, the curves would be slightly

shifted, but the conclusions of the usefulness of the horizontal

transfer coefficients would not be changed. In short, the values

computed for heat flux per unit travel are not very dependent on

the entrainment closure used in the model.

4. SUMMARY, GENERAL COMMENTS AND SUGGESTIONS

The work done under this grant has developed and tested

techniques for the remote estimation of ocean surface heat and

vapor fluxes. Thes ^e techniques are not very sensitive to errors

in the data and therefore appear to hold promise of producing

useful answers. However, questions still remain about how

closely the structure of the real atmosphere agrees with the

assumptions made for each of these techniques, and, therefore

about how well these techniques can perform in actual use. It

is, unfortunately, a difficult problem to satisfactorily verify

any of the three techniques. Full verification of the techniques

requires analysis of a large number of cases in which the needed

input data exists along with surface truth measurements of the
fluxes. The value of these techniques is that they promise to

provide methods for the determiniation of fluxes over regions

where very few traditional measurements exist. The irony is that

the absence of such traditional methods makes verification of

these methods difficult. These techniques have now been shown to

be theoretically sound. Further work is needed to demonstrate

that they are practically usable.
5. THESIS, PUBLICATIONS AND PAPERS DONE UNDER THIS GRANT.

Allison, D. E., 1984: A Model for the Estimation of the Surface

Fluxes of Momentum, Heat, and Moisture of the Cloud Topped

Marine Atmospheric Boundary Layer From Satellite Measurable

Parameters. M.S. Thesis, Florida State University,

Tallahassee, Fl, 66 pp.

Allison, D. E., and S. A. Stage, 1986: A Technique for

Determination of Ocean Surface Heat and Vapor Fluxes from

Satellite Measurements. Paper in preparation.

Chang, V. Y-W., 1986: Sensitivity Analysis of Horizontal Heat

and Vapor Transfer Coefficients for a Cloud-Topped Marine

Boundary Layer During Cold-Air Outbreaks. M. S. Thesis,

Florida State University, Tallahassee, Fl, 104 pp.

Chang, V. Y-W. and S. A. Stage, 1986: Methods for Determining

Ocean Surface Heat and Vapor Fluxes during Cold Air

Outbreak. Paper in preparation.

Stage, S. A., 1983: PBL Modeling and MASEX Data. Paper

presented at the MASEX Workshop, NASA Goddard Space Flight

Center, Greenbelt, MD, November 3-4, 1983.

Stage, S. A., 1984: An Evaluation of a Boundary Layer Model by

Comparison with MASEX Data. Paper presented at the Fifth

Conference on Air-Sea Interaction of the American

Meteorological Society, January 10-13, 1984, Miami, Florida.

Stage, S. A., 1984: Progress Report on An Investigation of the

Marine Boundary Layer During Cold Air Outbreak. Presented

at the NASA Global Scale Atmospheric Processes Program

Review, NASA Goddard Space Flight Center, Greenbelt, MD,

August 8-9, 1984.

Stage, S. A., 1985: Progress Report on An Investigation of the

Marine Boundary Layer During Cold Air Outbreak. Presented

at the Panel Review of Data Analysis, Modeling and

Theoretical Research in the NASA Global Scale Atmospheric

Processes Program Review, Columbia, MD, July 8-12, 1985.
6. OTHER REFERENCES.

Allan, T. D. ed.,1983. Satellite Microwave Remote Sensing..

Halstead Press, New York, 526 pp.

Atlas, D., S.H. Chou, , and P. Hwang, 1981: Estimating Heat

Transport over Coastal Waters from Cloud Street Signatures.

Er.Sc.. of a WorksJiSE QQ AEEiication of Existing Sa.tel.iite

Data £° the Study. Qf Ocean Surface Energetics, November 19-

21, 1980, Report NASW-57380, February 1981, University of

Wisonsin Press, 49-60.

Atlas, D. and S. H. Chou, 1983: The Influence of Coastal Shape

on Winter Mesoscale Air-Sea Interaction. Mon.. Wea.. Re v.. ,

ill, 245-252.

Chang, A.T.C., and T. Wilheit, 1979: Remote Sensing of

Atmospheric Water Vapor, Liquid Water, and Wind Speed of the

Ocean Surface by Passive Microwave Techniques from the

NIMBUS 5 Satellite. Radio Sci.., 14, 793-802.

Chou, S. H., and D. Atlas, 1982: Satellite Estimates of OceanAir Heat Fluxes During Cold Air Outbreaks. Mon.. Wea.. Rev..,

110, 1434-1450.

Deardorff, J. W., 1976: On the Entrainment Rate of a

Stratocumulus-Topped Mixed Layer. Quart... J... Roy.... Met... Soc...,

102, 563-582.

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