National weather Digest

A TECHNIQUE FOR FORECASTING SPILLED OIL TRANSPORT IN BAYS

Kurt W. He.. (1)Technique Oevelopment Laboratory

Office of Sy.tem. OevelopmentNltlonll Weather Service. NOAA

Sliver Sprtng, Maryland 20910

ABSTRACT

An AFOS-based computer model for predicting themotion of oil is described and applied to a histor­ical spill. In this model, a surface oil slick issimulated by a set of drifting particles. Eachdrifter moves at a velocity which is the sum of awind drift, a tidal current, and a random currentthat simulates diffusion. The wind drift is down­..... ind at 3% of the wind speed. Drifters .....ill beachwhen they cross a shoreline, and may re-enter the.....ater if the winds are offshore. The program re­quires the location of the spill, a wind forecast,and some delta on the tidal currents. The outputis a series of maps showing the positions of float­ing and beached oil.

A hindcast was made of the spill of 1.1 milliongallons of crude oil in San Francisco Bay in1971. Data on the oil distribution and currentsin the bay are readily available. Several computerruns .....ere made, and the oil behavior during thefirst 26 hours is discussed. In general, changesin the pos i tion of the main mass of pe trol eum onthe .....ater .....ere correctly forecasted. However, themodel under forecasted the intensity of oil beach­ing, even when the model was modified to increasebeaching by enhanced diffusion. The author con­cludes that gravi tational spreading, which is notincluded in the modeL may have been important.

1. INTRODUCTION

In the early hours of January 18. 1971 twofully-loaded oil tankers. the ArizonaStandard and the Oregon Standard collidedin heavy fog under the Golden Gate Bridge(2, 3). The oil spill which followed, theworst in San Francisco history. contamina­ted miles of shoreline. including parts ofSausalito and the beaches of the Presidio.and eventually triggered a Congressionalinvestigation.

In situations such as this. National Weath­er Service forecasters may be called uponto supply projections of winds or oil be­havior. especially in the short term beforea distantly-located response team can beactivated. A computer simUlation model.OILSPILL (4). has been written in the Tech­niques Development Laboratory to assistforecasters. This Automation of Field Ob­servations and Services (APOS) applicationsprogram tracks the motion of oil on theopen sea or inside bays where winds. andoften tidal currents. are primarily respon­sible for transporting the oil.

26

We have used the OILSPILL program to simu­late the behavior of oil during the SanFrancisco event to demonstrate the method'sapplication and to reveal problems and in­sights in oil spill forecasting. The SanFrancisco spill had many features usuallynot encountered. making it both very diffi­cult to predict and very instructive tosimulate. Some of these features are theimportance of tidal currents. the presenceof islands and complex geography. the rapidrelease of a large amount of petroleum. themotion of the oil source point. and thedifficulty of forecasting winds inside abay. Data on the local tidal currents andobservations of the areas of oil coveragewere quite good. Wind information is notso complete. however, and its shortcomingsdemonstrate the importance of having bothsite-specific forecasts and observations bytrained meteorologists.

Many of OILSPILL's features will be de­scribed in the following sections. but thereader is referred to (4) for more details.This technique is also quite differentfrom that used by the Composite oil SpillModel for Operational Services (COSMOS)program (5). In COSMOS. the two-dimen­sional. vertically averaged fluid equationsare solved by a finite-difference method toget oil motion over the continental shelfarea. A separate numerical model for thewind- and tidally-driven currents is alsoincluded. The computer code. designed torun on NOAA's IBM 360/195. proved to bemuch too large and complicated to run onthe AFOS computer. OILSPILL employs great­ly simplified physics and requires lesscore and running time.

2. OUTLINE OF THE SIMULATION MODEL

OILSPILL was designed to run on the AFOSData General S/230 computer with a fore­caster providing input data such as windforecasts and water current data. The dy­namics of oil motion. which are in factquite complex. are simplified here in thetrajectory method so they can be run onthe 5/230. The resulting equations cannotbe expected to simulate oil behavior per­fectly. but rather to show general oil mo­tion tendencies. The output of the compu­ter program is a series of maps which in­clude a coastline for reference and showthe areas of oil coverage. This output isproduced on the APOS paper plotter.

Volume 9 Number 2

where M is the number of walks. or steps,per unit time.

The background current is taken to be con­stant over the area of interest. and isused to simulate semi-permanent featuressuch as the Gulf Stream. The wave driftis usually small. and since it is not wellunderstood. is neglected here.

(3)

(4)02 t 3 -1/2)1/6

g u '

s - s(w a

Sw1. 45R

R

Beside oil advection, there are severalother features of OILSPILL worth noting.Coastal geography is included in the datapackage: the program automatically drawsthe shoreline and islands. This geography

where 9 is the gravitational accelerationand u. the kinematic viscosity of water.The third regime. dominated by surface ten­sion. predicts even faster expansion.Table 1 shows representative values of theradius predicted by each formula for vari­ous oil volumes and times. For the rangeof values chosen. Fay's equation predictsradii an order of magnitude larger thanBlokkerls.

The first regime involves inertial forces.and its duration is short. During the sec­ond. gravity is the dominant force. and theradius can be expressed as

where Sw and So are the specific grav­ities of water and oil. respectively; K. aconstant depending on oil type; Q. the oilvolume: and t. the time after the oil en­ters the water. Fay (10) performed a di­mensional analysis of the forces involvedin the spreading and postulated the exist­ence of three regimes.

For an actual spill. the most importantforecast is where the oil will come ashore.OILSPILL predicts this when it advects theoil toward the coastline. When currentscarry the oil into the shoreline. a checkis performed and the oil is Ilbeached il(1. e., stopped from motion) if the sum ofwind drift and the random current (withoutwater currents) is sufficient to carry itonto the shore. Beached oil is checkedevery hour. and the oil will refloat. underfavorable winds, with a probabi 1 i ty basedon the residence time half-life. The half­life is defined as the time interval overwhich half the beached drifters will re­float. given that the winds are continuallyoffshore.

Forecasters frequently want to know hoWlarge an area wi 11 be covered by a givenvolume of oil. Any finite amount of oilwill tend to spread out more or less uni­formly over a calm water surface under theforce of gravity. Since our model simu­lates drifting point masses. we don't ex­plicitly include oil spreading. Severalequations from the literature. however.will help to estimate the area which apoint mass may cover. By assuming a circu­lar oil mass of constant thickness. Blokker(9) formulated the slick radius. R. as

(2 )

(1)

-l 22M q ,D

Basically. the motion of oil is simulatedas the downstream advection of driftingparticles or drifters. Each drifter rep­resents a finite volume of oil resultingfrom an (assumed) uniform rate of releaseat the spill site. The drifters move at avelocity which equals the sum of the localwind drift and other currents. and has thegeneral form

OILSPILL uses data on the tidal flood cur­rent direction. speed. and time of maximumstrength at the spill site and at otherstations. if available. This type of datais available for San Francisco Bay fromboth the National Ocean Service's (NOS'S)Tidal Current Tables (6) and from the TidalCurrent Charts (7). When one or mo~e extratidal current stations are added. OILSPILLcreates a two-dimensional field of currentvectors by interpolating values betweendata points. It uses a weighted mean ofthe north and east components of the floodcurrent. with the weighting function depen­dent on the inverse-square of the distanceto the data point.

The random current accounts for the effectsof atmospheric and oceanic turbulent diffu­sion. and is idealized as a small velocityof constant magni tude. q. and a variabledirection. Random walk theory (8) showsthat q is related to the two-dimensionaldiffusion coefficient. D. in the followingway:

where U is the oil velocity. and the termson the right side are (in general order ofimportancs) the wind drift (cVI, 1he tidalcurrent (W

t). the random current (W ). the

backgro~nd current (Wb ), and the wavedrift (i/w)'

The wind drift is taken to be a simplefraction (c) of the wind velocity. V. andto be in the same direction. Data on thedrift fraction are scarce and show a lotof scatter (Fig. I), but a value of 0.030was chosen for this study. Observationsshow that the oil tends to drift slightlyto the right of the wind direction by asmall angle (5°_10°). but we shall ignorethis small deviation for this study.

27

National Weather Digest

is needed for calculating the beaching ofoil. The weathering of oil is simulatedby randomly removing a fraction of alldrifters; the probability of removal isbased on the petroleum type and its half­life. The oil spill source point is al­lowed to move. simulating drifting withthe currents or cruising at a predeterminedheading.

Because of model simplicity and computerstorage limitations. a number of importanteffects cannot be simulated. The biggestdrawback results from the representation ofa two-dimensional continuum of oil on thesea surface as an ensemble of driftingpoints. Oil spreading due to gravity andsurface tension effects is therefore pre­vented. and diffusion and weathering canonly be roughly approximated. Also. thewind field is assumed to be constant overthe area of simulation. so the channelingeffects of land features are not inclUded.And finally. the tidal current phase is. byassumption. constant at all locations--anextreme simplification of actual tidalflow.

The computer program has been developedover several years and has been tested withdata from several large oil spill events.The events. chosen because they had suffi­cient data. are the Torrey Canyon tankergrounding oil near the southwest coast ofEngland in 1967; the Chevron oil drillingplatform fire and spill off the MississippiDelta in 1970; the Argo Merchant tankergrounding and breakup near Nantucket Islandin 1976: the Amoco Cadiz tanker groundingoff the Brittany coast of France in 1978:and the Burmah Agate tanker collision nearGalveston. Texas in 1979.

Hindcasts of oil motion with OILSPILL showthat useful results can be obtained inspite of the modells simplifications. Wenow proceed to a case study of the SanFrancisco spill of 1971.

3. THE SAN FRANCISCO BAY SPILL

At approximately 0141 PST on January 18.1971. the outbound oil tanker Oregon Stand­ard was struck ports ide by the incomingtanker Arizona Standard. and the two ves­sels. locked together. drifted on the floodtide toward Angel Island. The OregonStandard began leaking its cargo of nearly4.3 million gallons of heavy bunker fuelalmost immediately. and within a few hoursapproximately 1.1 million gallons hadspilled out (2). The drifting ships even­tually came to rest a thousand yards offthe south shore of Angel Island. Duringthis time the winds were light. and visi­bility was extremely low due to the fog.which lifted at approximately 1030 PST (3).All leaking had stopped by the late after­noon.

28

One reason this spill was chosen was thatthe data are fairly complete. especiallywinds. tidal currents. and areas of oilcoverage. Maps showing the location ofoil. based on ship reports and u.S. CoastGuard overflights. are given in (3) forthree times on January 18 and once each dayon the following three days. We have usedobserved winds from an offshore ship at 30 0

45' N. 122 0 41 t W; winds from the CoastGuard base on Verba Buena Island (3) arealso known. Strengths and times of occur­rence of tidal flood and ebb currents forthe Golden Gate are found in the NOS TidalCurrent Tables. Values for January 18 and19. 1971 are given in Table 2.

The local current pattern is depicted onthe NOS Tidal Current Chart for San Fran­cisco Bay (7). A copy of the chart forflood conditions at the Golden Gate appearsin Fig. 2.

About 30 computer simulations of the SanFrancisco spill were made. In general.results improved markedly as more tidaldata stations were added. Several simula­tions were carried out to test for the in­fluence of specific variables on oil beach­ing. which. for this event. is somewhat un­derpredicted by our model. As a result. wemodified the beaching routine by adding arandom current to the wind drift whenbringing oil ashore. rather than using winddrift alone. This mOdification increasedthe beaching frequency somewhat. but not asmuch as did an increased diffusion coeffi­cient.

The diffusion coefficient employed was lar­ger than that used in previous studies.For previous oil spills. we got satisfac­tory results with 0 = 100 ft 2 /s. Herethe use of D 500 ft 2 /s improved thesimulation of the beaching of oil as itexited the bay on the first ebb tide.Gravity-induced spreading was neglected inthis model, and it's likely that high dif­fusion was necessary to compensate for itsabsence. Spreading by gravity forces ismost likely to be important during thefirst few hours of a spill when the oil isthickest.

Most of the other input values were fairlystandard. We assumed a drift fraction of0.030 and the type of petroleum to be con­servative. i.e .• it would not lose any massby weathering. The beach residence timehalf-life was taken to be 15 hours.

The source motion used during the study re­quires further explanation. After the twoships collided. they drifted under the ac­tion of wind and current toward Angel Is­land. Tests of the drifting algorithm,with the source moving at 100~ of the tidalcurrent plus either O~ or 3~ of the wind.showed the source moving. unrealistically.up into Richardson Bay. The probable rea-

Volume 9 Number 2

son is that some of the details of thetidal current field have not been retainedin our simplified model. The source mo­tion was therefore modeled as a poweredmove with two segments: first the shipsheaded 52° (true) at 2.0 kt for 54 minutes.then headed 52° (true) at 1.0 kt for 54minutes.

The base map drawn for the spill is shownin Fig. 3. The cOllision site appears nearthe center of the rectangular area. and thegrounding site is denoted by a '$'. Loca­tions of additional tidal current stationsare denoted by the symbol 'X', In othermaps (Figs. 4-6). positions of floating oilare denoted by a number (' 0'. •1'. 12'.etc.). The number 0 means that from 1 to 3drifters occupy the grid. the number 1means that from 4 to 6 drifters occupy thegrid. and so on. The symbol '@' indicatesthat one or more drifters are beached inthe qrid.

The time period we simulated began on 0000GMT on January 18. and proceeded for 26hours. Data on oil coverage for January19-21 are less detailed so that period wasnot simulated. Oi 1 release was begun athour 10 (0200 PST) and discontinued after5 hours. The computer run. which simulatesthe motion of 165 drifters. took about 12minutes. Descriptions of oil coverage andmodel results for three different times isdiscussed below.

Hour 0600: By 0600 on January 18. the oilhad been leaking from the Oregon Standardfor 4 hours. Passing ships reported alarge area of oil contamination in thewaters from the Marin Peninsula out to An­qel Island (Fiqs. 4a and 4b). The oriqinalCoast Guard drawings (3) do not distinguishbetween areas of heavy and light coverage.but the model results show the thickest oilto be around the site of the leakinq ship.Our model shows beached oil on Alcatraz Is­land and at Sausalito. The Coast Guard.while not specifically reporting any oil atthese sites. mentions the presence of oiloffshore of San Francisco's piers south ofAlcatraz (3). While modeled and observeddistributions are similar. it should be re­membered that finding oil must have beendifficult. to say the least. during thosepredawn hours in heavy fog.

Fort Point. but not the extensive contami­nated area that was observed. The computermap also shows more beached oil on theMarin Peninsula. close the the areas actu­ally hit. The Coast Guard reported anortherly breeze springing up at 1030 PSTand concluded that this breeze was respon­sible for beaching oil at Fort Point.

The Coast Guard observed three separatestreaks of oil. each aligned roughly paral­lel to the ebb current direction. just out­side the bay's mouth. Streaking usuallyoccurs because of winds. but here the tidalcurrents apparently created them. Ourmodeled output for hour 10 shows a singlelarge diffuse patch of oil located offshorewith no evidence of the streaky distribu­tion. The fact that the patch lies furtheroffshore than the streaks is probably dueto the tidal current in the model being toostrong in that region.

Three patches of oil were sighted veryclose to the location of the anchored ship.indicating that the Oregon Standard wasstill leaking some oil at this time. Thetwo streaks to the north and west of theanchored ship seem to have come from pointson the shore where oil had previouslybeached.

Our model has oil beaching on the north tipof Alcatraz Island. A large patch of oilis situated nearby (Fiq. 5b). althouqh wecouldn't find reference to any beachingthere.

Hour 1700: A late afternoon survey. towardthe end of the flood tide. showed a contin­ued presence of oil near the mouth of thebay. with large concentrations at BakerBeach and Fort Point (Fiq. 6al. Our compu­ter simUlation also shows a large mass ofoil near the bay entrance. especially theBaker Beach area. Our simulation alsoshows renewed oil beaching on the MarinPeninSUla. although no heavy concentrationswere reported at that time. Again. thesimulation does not show the streakinessthat was observed. Other areas where oilwas sited. such as around Alcatraz. in theRacoon Straights. and near Sausalito. alsohave oil in the simulation.

4. CONCLUSIONS OF THIS STUDY

Simulations of the 1971 San Francisco Bayoil spill have shown that the model can beapplied in a real situation and how it canbe useful to a forecaster. The model's re­sults are highly dependent upon the accur­acy of the input data. but most of thesedata should be easily obtainable during anactual spill.

Hour 1200: Shortly past noon the CoastGuard had finished its first overflightand reported oil coverage as shown in Fig.Sa. The time of the flight nearly coin­cides with the time of slack water afterthe ebb. The most prominent features ofthe oil distribution are the oil masses onthe north and south shores of the GoldenGate. each with tails extending westwardout to sea. Some oi 1 apparently beachedas it flowed past with the ebb tide. Thecomputer map (Fig. 5b) shows an area ofbeached oil on the San Francisco shore at

The importance of goodnot be overstated. Inwinds were used. and

windthiseven

forecasts can­case. 3-hourlymore frequent

29

National Weather Digest

wind data may be necessary at times whenoil passes a vulnerable location.

For example. we ran a test case with a 13kt north wind at hour 1800 GMT. replacingthe previously-used 13 kt ENE wind. As aresult of this change. more oil was simula­ted to beach along the San Francisco shore.

Tidal currents were very important duringthis spill and reasonably good data wereavailable on their characteristics. Im­proved results were obtained when addition­al data locations were used because thetwo-dimensional flow pattern was more accu­rately portrayed.

The fact that a relatively large diffusioncoefficient was necessary indicates thatgravity spreading should be explicitly in­cluded in future versions of this model.There are ways of estimating oil thicknessper drifter. and since drifter separationis known. an estimate of the spreading ac-

celeration. based on the thickness gradi­ent. could be made. High values for thediffusion coefficient would most likely berequired during the early hours of a spill.and should become less necessary as theevent continues.

In the model OILSPILL. even one drifterbeaching is sufficient to be denoted on themap. In several cases for this spilL onesimulated location of beached oil corres­ponded to a rather long stretch of actuallycontaminated coastline. This is becausethe model deals with drifting points. eachof which has a lower probability of impact­ing a coastal segment than does the oil.distributed over a finite area. that itrepresents.

For this study. the oi 1 was taken to beconservative. or non-weathering. Thisgives a larger area of oil coverage than islikely to occur. but the model is less aptto miss areas of beached oil that may actu­ally be present.

Method

Blokker

Fay

Time Oil Volume(Hours) (Thousands of gallons)

1 5 10 20 SO

1 0.1 0.1 0.1 0.1 0.22 0.1 0.1 0.1 0.2 0.25 0.1 0.1 0.2 0.2 0.3

10 0.1 0.2 0.2 0.3 0.420 0.1 0.2 0.3 0.4 0.5SO 0.2 0.3 0.4 0.5 0.6

100 0.2 0.4 0.5 0.6 0.8200 0.3 0.5 0.6 0.8 1.0

1 0.2 0.4 0.5 0.6 0.92 0.3 0.6 0.7 0.9 1.25 0.5 0.9 1.1 1.4 2.0

10 0.7 1.3 1.6 2.0 2.820 1.1 1.8 2.3 2.9 3.9SO 1.7 2.9 3.6 4.5 6.2

100 2.4 4.1 5.1 6.4 8.7200 3.4 5.7 7.2 9.1 12.3

Table 1. Radii in nautical miles of a circular oil slick of con­stant thickness calculated from the equations of Blokter (8) andFay (9). The Blokker method. Eq. (5), is applied with the follow­ing values: Sw=I.02. 50 =0.90. and K=3xl0 4 min-I. TheFay method. Eg. (6). uses the same specific gravities. plusg=9,81 m2 /s and u=1.0xl0- 6 m2 /s.

Date

18

19

Time of Maximum(hour, minute)

02350841152120550321093216292152

CUrrent Speed (kt)(F=flood. Ezebb)

2.3 F2.9 E1.7F2.0 E2.0 F3.1 E1.8 F1. 6 E

Table 2. Tidal current floods and ebbs at the Golden Gate forJanuary 18-19. 1971. Flood direction is given as 65°. ebb direc­tion as 245°. Time is Pacific Standard.

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Volume 9 Number '}

enz0 3f-«

2>lL a:0 w 1en0 lDZ 0 0

0 1 2 3 4 5

Figure 1. Frequency of observation for va­rious values of the wind drift fraction.

6

WIND DRIFT FRACTION (%)

Figure 2. Flood cur rent vectors for theSan Francisco Bay entrance for averagetidal conditions (7). Speeds are in knots .

.,

PACIFIC OCEAN

, ,

. ;~ RACCOON STR.

UANGEL 1.'0'

$----2 x GROUNDING

12 x Al~TRAZ I. ~~;~:~3 'X . .

."".,..,.,....~.'""... -":~'~'.: , ..~-".-r g X

':- BAKER BEACH~;

Figure 3. Base map for the San FranciscoBay spill. The symbol 'X' preceded by anumber represents one of the 12 additionaltidal current stations.

31

National Weather Digest

..... 11111111111111II

.31.~0­

I111IIIIIIII1,II

.H'''5­IIII1

u

u "Uo .....".....

a 011S002212000

o 00112UOOOOUO 00 0,

111111,11",111111

._---.-----------------------.----------------------.-----------------.• • ••• Jl. :.:.-

122,25122,30

37,45

Figure 4. Spilled oil distribution for 18January, hour 0600 PST. The left panelshows the observed oil distribution (cross­hatched area) and the grounding positionof the tankers (' $'), The right panel

shows the simulated distributionface oil for the same time (10 1 •etc. denote floating oil. I@Ibeached oil).

of sur-Ill. 121.

denotes

-.:..

••• Jl.:lo~-

••••• 11I111IIIIIIII1I

.37.50­IIII11IIIII11I11

Jl.11:;'_

IIII,

,"

122.2:lo

a ..•

,.

u

,

iil ••

.,......'"

1111111I,,,1I1I1I1

•IIII10 U ou1 0!I)OOU100 0 0100 OU 010 lUO 01010 0 U1000 uoLU ouu1 0I1

.----.-----------------------+----------------------.-----------------.

.----.-----------------------.----------------------.-----------------.

\1",.'.,:,-

:.••..

122,25,

/~Q'

122,30

'".

~~' ,;BY

A""

":

37,55

37,50

37,45

Figure 5.1200 PST.

Same as Fig. 4. but for hour

32

Volume 9 Number 2

•..

••........••..

o•

•... .o ."'••••o 0 0

o u uuu u00 0 00 •••

000 U 00o 0 u OUU •••

00 0 a ••uu au

o 0 Uol.

o

o

o

o

IIII11I11 ••1111III

+----+-------_.--------------+--------------.-------.-----------------+... "1.~~-..... 1

111IIIIII1II1II

."7.50·1111III111111111

"7, "5­I111

12o!.,,~ lo!l,jO lotl,2~ 1

+----+-----------------------+----------------------+-----------------+122,25

.."1,

U"'-·':. "

, -Q

\~ G1~d

122,30

";',..~

37,55

37,50 '~.

37,45'

\

Figure 6.1700 PST.

Same as Fig. 4. but for hour

REFERENCES AND FOOTNOTES

(1) Dr. Hess earned his B.S. at the University ofCalifornia, his M.S. at Columbia University, andhis Ph. D. at the University of Rhode Island. Heis presently a Physical Scientist in the MarineTechniques Branch of the Techniques DevelopmentLaboratory. His career interest and work have beenin tides and tidal current prediction and in numer­ical modeling of coastal and estuarine circulationand storms surges.

(5) Barrientos, C. S., and K. W. Hess, 1983:Ocean Oil Spill Concentration and Trajectory Fore­cast Project. Final Report to the EnvironmentalProtection Agency under Interagency Agreement EPA­lAG-0693 (available from NTIS as PB84-114453).

(6) National Ocean Survey, 1983: "Tidal CurrentTables 1984, Pacific Coast of North America andAsia, It National Oceanic and Atmospheric Administra­tion, U. S. Department of Commerce, 260 pp.

(7) 1973: "Tidal Current Charts -- SanFrancisco Bay." National Oceanic and AtmosphericAdministration, U.S. Department of Commerce, 12 pp.

(9) Blakker, P. C., 1964: "Spreading and evapora­

tion of petroleum products on water," ProceedingsFourth International Harbour Conference, Antwerp,Belgium, pp. 911-919.

(10) Pay, J.A., 1971: "Physical processes in thespread of oil on a water surface," Proceedings

Joint Conference on Prevention and Control of OilSpills, Washington, D. C., American Petroleum Insti­tute, pp. 463-467.

(2) Conauos, T. J., 1975: "Movement of spilledoil as predicted by estuarine nontida1 drift."LimnologY and Oceanography, v. 20 (2), pp. 159-173.

(3) U. S. Congress, 1971: "San Francisco OilSpill," Hearings before a special subcolMlittee ofthe Committee on Merchant Marine and Fisheries,House of Representatives, Serial No. 92-3, 533 pp.

(4) Hess, K. W., 1983: "Simulation of SpilledOil Behavior in Bays and Coastal Waters." NOAATechniques Development Laboratory Computer ProgramTDL CP 83-2, National Weather Service, NOAA, U.S.

Department of Canmerce, 21 pp.

(8) Csanady, G. T., 1972:the Environment." Reidel,

"Turbulent Diffusion inBoston, pp. 248.

33