Models for calculating oil spill damages to shores

Oil & Chemical Pollution 3 (1986/87) 69-81

Models for Calculating Oil Spill Damages to Shores

K n u t L. Seip, Kjell A r n e Brekke,* Kar i Kvese th t a n d H a r a l d I b r e k k

Central Institute for Industrial Research, Forsknings. 1, P.B. 350 Blindem, Oslo 3, Norway

ABSTRACT

A parametric calculation model and a regression model have been developed for estimating damage to a shoreline following an oil spill accident. The calculation model uses the amount of oil in nearshore waters, oil characteristics, littoral area and wave exposure of the different types of shoreline as the primary input parameters. It simulates, as a two stage process, the sequence of events often observed during an oil spill; oil strands on the shore and is then subsequently redistributed and inundates new areas. As output, the calculation model gives shoreline length contaminated, the amount of oil on the shore and the density of oil on different shoreline types at selected times after the initial impact. The model has been applied to a case study at Svalbard, Norway.

The regression model is based upon reports from 25 spills worldwide and gives the shorelength damaged S as a function of stranded oil X : S = 0.006 X + 70.6, r 2 = 0,58. There is no correlation between shorelength damaged and the amount of oil initially spilled. The calculation model seems to give better predictions of shoreline contaminated than the regression model. Verification of the model requires, however, data which are only recently being collected and reported.

1. I N T R O D U C T I O N

Dur ing oil spill accidents part of the oil may reach the coast and cause extensive damage to the shore ecology, and to the recreational and social utility of the shore. This damage is related to the length and type of shoreline con tamina ted and to the a m o u n t o f oil stranded. In format ion on

*Present address: Central Bureau of Statistics of Norway, Skippergt. 15, P.B. 8131, Dep 0033, Oslo 1, Norway. tPresent address: Royal Norwegian Council for Scientific and Industrial Research, Soqusvn. 72, P.B. 70, Teisen 0801, Oslo 8, Norway.

69 Oil & Chemical Pollution 0269-8579/86/$03.50 © Elsevier Applied Science Publishers Ltd, England, 1986. Printed in Ireland.

70 Knut L. Seip, Kjell Arne Brekke, Kari Kveseth, HaraM Ibrekk

probable shore damage is important, for example, when resources for oil combat preparedness are allocated, or when decisions are made on the extent and duration of shore cleaning operations.

We present two models for calculating shore damage: 1. A parametric calculation model which simulates the first impact and the subsequent redistribution of oil on the shore; and 2. An empirical regression model based on reports from 25 out of 70 oil spill accidents compiled by PFO (1983).

The first model may use the results from an oil slick movement model for oil on open water as part of its input data. The oil slick models usually give the overall nearshore distribution of oil as a function of seasonal wind and current records of the spill area, whereas the present (calculation) model emphasizes the nearshore sea condition and characteristics of the shoreline formation to give the amount and distribution ofoi l on different types of shores. The model has been used to evaluate probable damages on coastline sections of Svalbard from small oil spill accidents. Some results from this application of the model will be reported below.

The empirical model only uses oil discharged or oil stranded as an independent variable, and thus presents an average over a wide range of shoretypes. Results from the two models will be compared.

2. OUTLINE OF THE CALCULATION M O D E L

The calculation model is based on the description" of the Amoco Cadiz oil spill accident given by Finkelstein & Gundlach (1981). They describe the contaminat ion of the Brittany shores in France by the Amoco Cadiz oil as a two stage distribution. First, the initial impact damaged 123 km of shoreline at different places along a total shorelength of nearly 650 km. Over a period of about 20 days the oil spread and inundated a total of 375 km.

Figure 1 shows a generalized picture of the first impact process and the processes causing a reduction and redistribution of the oil on the shores. Data for Fig. l(c) and (d) are found by recalculating data from Finkel- stein & Gundlach (1981) for the distribution of oil on shore sections 0.250 km in length. It is seen that with time a lighter, but more widespread inundat ion of oil occurs on the coast.

Unfortunately much of the information on the redistribution process is qualitative. However, the numerical data available indicate that characteristic values can be found for important processes. Thus, if the average decrease in oil with time on a shore area is described with first

Models for calculating oilspill damages to shores 71

FIRST TWO WEEKS

o,L T R . . . s P o R T

W , N D

~/" heavily oiled ~" / ~ j headl'a nd's.~ . . . . ,~i;;~ ~

Q

Number of coastline sections lEach 0.250 km long)

0il tons

7/.00 [ ~

o a i d [ ] o

C

AFTER ONE MONTH

F °"" I

Number of coastline sections (Each 0250 km tong)

o e [-71360 Oil tons

I 1

2 . ]

8 1

/ ' I 0 ~ i t 1 I

0 - 0 . 5 fl5-2 2-/. / ' -6 6 -8 B-1010-I2 |2-1 / . l t , -1616-18 18-20

Oil d e n s i t y . k g - m "2

d

Fig. 1. (a) and (b) Generalized oil coverage of the coastline after the first 2 weeks and after 1 month of theAmoco Cadiz spill. Initial dominant westerly winds transported large and heavy patches of oil onto the western shoreline sections. A shift in the winds after 2 weeks caused a lighter inundation ofoil along the entire coastline. (c) and (d) Number of coastline-sections contaminated with oil as a function ofoil density at 17 stations along the shore. (c) 1 study period March 19-April 2. (d) Study period April 10-April 28. The open quadrats indicate the relative amount of oil on shore within each density class.

Figures drawn on the basis of data from Finkelstein & Gundlach (1981).

order kinetics, i.e. the decrease is proportional to the instantaneous amount of oil on the shore, the parameter describing the loss of oil from a marsh area is significantly smaller than that of a rocky shore area, all other factors being equal.

When the model is applied, the user supplies characteristic data for the shoreline and for the wave conditions. We have found it convenient to run the model with several sets of data, for example one set assuming rough waves and one assuming smooth waves. The two wave types will


often correspond to low and high loading of oil on the shore. Wind and wave directions are given by, for example, an oil slick movement model.

The calculation model basically describes oil as stored in compart- ments corresponding to different shorelines and to the nearshore waters. Changes in the amount of oil in each compartment occur either as a transfer from one compartment to another, or as an exponential decay process. Details of the model are given in the Appendix. The output of the model is the amount and distribution of oil on different shoretypes, and also, by setting a limit below which the shore is no longer regarded as contaminated, the length of oiled shoreline. The data required to run the model and support for the values chosen are given below.

3. THE DATA

The data required to operate the calculation model consist of data describing the oil at the start, shoreline characteristics, oil densities and removal rates for oil on different shoretypes and under different environmental conditions.

The initial oil situation may be the output from an oilslick tracking model, giving the amount and distribution of nearshore oil. In the Svalbard case-study to be discussed below, we assume that the spill was close to the shore, wind blowing towards the shore and the initial spread- ing was very short, less than 1 km. Thus the saturating oil densities of the shores control the initial loading ofoiIon the shores. The model assumes that oil is discharged as a single event; however, the results of two or more discrete events may be superimposed. The model is not suitable for continual discharge. The shoretype characteristics consist of the average depth of such shorelines as sand beaches, rocks and mudflats and their average distribution in the area considered. The data may be obtained from detailed maps (cf. Senstad & Sindre, 1981), and knowledge of tides and tidal ranges. The model also allows for the assignment of different probabilities for hitting different shoretypes.

The oil density ranges quoted in the following are assumed to represent average values for areas of several hectares. The density estimates are based upon ITOPF (1983) technical papers, Finkelstein & Gundlach (1981), Gundlach et al. (1983), Owens et al. (1983) and several other sources giving qualitative assessments of the relative density on different shoretypes.

The shoreline can be divided into four main groups:

Rock slopes with smooth surfaces may be covered with a thin (about 1 mm) layer of oil, or oil-in-water emulsion. The density is of the order


0.01-0.30 kg m -2 (high value estimated after Finkelstein & Gundlach, 1981).

Boulders, defined as shore with particle size greater than 250 mm, may in the tidal region collect oil on rough and porous surfaces as well as in rock pools. Oil densities may range from 0.05 to 20 kg m -2.

Sand beaches and beaches of mixed sand, pebbles and cobbles <250 mm are affected by oil penetration characteristics also in the sub- surface sediments. However, oil penetration tends to increase with increasing stone size and typical densities may range from 0.10 to 10 kg m -2. Owens et al. (1983) found that during shoreline experiments actual loading that could be achieved was 0-5 to 0.9 cm 3 cm -2 (5-9 kg m -2) in spite of a design thickness of 1.0 cm of aged crude oil and 2.0 cm of emulsion. ITOPF (1983) quotes 8 kg m -2 (recalculated by the present authors) as severe contamination. The maximum value quoted by Finkelstein & Gundlach (1981) for this type of substrate was 48 kg m -2 over a 10 m 2 area during the A m o c o Cadiz spill.

Mudflats, marshes and mangroves (particle size <0.1 mm) often have water-logged sediments which may reduce penetration of oil below the surface layer. Oil may, however, easily accumulate above the surface on such shores. At Ile Grande on the Brittany Coast of France, the A m o c o Cadiz oil reached an overall density of 19 kg m -E, but in restricted areas, densities as high as 380 kg m -2 (40 cm layer) occurred (J. E. Levasseur, pers. comm.). We assume that typical densities range from 0.5 to 20kgm -2

Background values for oil on the Brittany coast were 0.005-0.03 kg m -2 (recomputed from Gundlach et al., 1983). Owens et al. (1983) consider beaches with oil-in-sediment values of 90-500 mg kg -1 as clean, corresponding approximately to 0.007-0.04 kg m -2.

The removal rate (RR) of stranded oil depends upon shoreline exposure (fetch, F), oil type, O, and particle size, S, possibly in that order of importance. As a first approximation we may write:

R R = k l F + k 2 S + k30

However, Vandermeulen (1977) and Owens et al. (1983) pointed out that different processes may dominate at different times of the removal process. Also exposure and particle size often correlated (kl oc k2). This last relation is adopted in estimating the removal rates quoted below.

Based upon oil removal case histories we have estimated the exponential decay coefficients for rock slope, sand beaches and marsh areas to be 0.2, 0.12 and 0.04 d a y -1 respectively for the initial phase ofoil removal (cf. Finkelstein & Gundlach, 1981).

If the viscosity of the oil is either very low or very high the removal rates


could be modified according to oil type. For example, Owens et al. (1983) noted that experimental plots with aged crude oil were highly resistant to oil removal.

When oil is washed into the water, it is susceptible to surface currents, evaporation and to being mixed into the water column. From H~egh (1978) we have computed decay coefficients for oil on surface water as 0.04, 0.14 and 0.33 day -1 corresponding to wind speeds of 3.5 m s -1, 10 m s -] and 17 m s -1 respectively.

The time period T between the first impact and the time at which the oil distribution is calculated may be chosen at will. For the Amoco Cadiz study we chose T as the time between two observations, i.e. 2 weeks.

4. M O D E L CALCULATIONS

Verification of the model is difficult because most spill reports do not list the necessary data to run the model. However, some of the information required should be easily accessible, for example data on the distribution of shoretypes, average oil densities, etc.

We have applied the model on three sets of data.

First we have used data from theAmoco Cadiz spill. Since much of the data are derived from this spill, this application was only used to identify conceptual errors in the model. The simulation gave a damaged shore length of 325 km and with 154 heavily oiled (the observed data are 375 km and 162 km respectively).

The second data set was obtained from an oil spill scenario analysis to estimate the probable oil damages to selected locations at Svalbard from a 1000 tonnes spill of diesel oil. The relevant data used to make the calculations are given in the caption of Fig. 2. We have made two sets of calculations. One under conditions of consistently rough weather and one under conditions of consistently smooth weather. The results are shown in Fig. 2 for 7 and 21 days after the initial impact. The weather conditions have little influence on the length of shoreline contaminated after 7 days, but strongly affect it after 21 days when densities are becoming lower than what is defined as a 'clean' shore. In smooth weather the contaminated shoreline is slightly extended whereas rough weather reduces the length of shore having oil densities in the contaminated range (here greater than 0.1 kg m -2 for mudflats). The other bars in Fig. 2 show that oil removed from the shore increases and that the overall oil densities decrease with time. The model also gives detailed oil characteristics for each shoretype. This information was used, together with a safety factor, when it was recommended not to increase the oil spill preparedness on


Svalbard. The in format ion shou ld also be useful in deciding u p o n beach c leaning strategies. The detai led in format ion is now used in a beach cleaning mode l be ing deve loped for calculat ing cleaning resource requi rements (Danie lsen et aL, 1985).

20

10

shoreline a) contaminated ( km )

' L H

H

7 21

oit washed ~ b) off shore lO~'tons

1.5

I.O

--~ 1.5

0 7 21 Days after impact 1.

oit density c) k g / m 2

7 21

Fig. 2. Model calculations for a 1000 tonnes diesel oil spill at a partly protected location on the western coast of Svalbard (fetch less than 2 km). (a) Shoreline contaminated, (b) oil washed offshore, (c) average oil density, all shoretypes. H, L indicate rough and smooth weather conditions respectively. The spill is assumed to occur close to the shore. There are three shoretypes defined for this spill: rock, sand and mud/clay. The widths of the shoretypes are 3-5, 10-20 and 100-200 m respectively; average values used. The relative distribution of the shores are 35:50:15. Oil erosion coefficients for rough (high value) and smooth weather conditions are 0" 10-0-20; 0" 05-0" 10 and 0"005-0' 03 respectively. The corresponding values for nearshore waters are 0.1-0.3. Saturating densities for oil

have been set to 0"30, 10 and 20 kg m -3 respectively.

The last data set consists o f a selection of data f rom 70 ma jo r oil spills wor ldwide (PFO, 1983). O f the 44 spills repor ted to have caused shorel ine damage, we have tried to make est imates of (a ) oil spilled, (b) oil repor ted on shore and (c) oil recovered on shore. The quanti t ies (a) and (c) should consti tute uppe r and lower limits for oil on shore respectively. In calculat ing oil recovered on shore, however, we occas iona l ly had to make assumpt ions on oil-in-water contents and oil- in-debris contents.

Seventeen spills had a fair descr ipt ion o f shore characterist ics and weather condi t ions dur ing the spill sufficient to be used in the model . The results are shown in Fig. 3 as open circles, and will be d iscussed below.

5. R E G R E S S I O N M O D E L S

The mode l calculat ions descr ibed above have been c o m p a r e d to regression models relating shore length d a m a g e d to oil vo lume spilled,

76 Knut L. Seip, Kjell Arne Brekke, Kari Kveseth, Harald Ibrekk

400

300

200

100

2q 1•

• 2& / Shoretength 19 . o /

• observatton 24 / 2..6 damaged (km) o calculated • / 0

/

23

~o

17 20 o o /

"~6 22 o ~,:~.o~ o 7 I0 18 0 9 "11 h5 / 22

5 8 10 ~ 14. Regression )3 06 • ~12 O • 15

0 £ 11 }3 • , 0.0061.X+70.6

16 ~8 r 2 : 0 . 5 7 o 08 i • i

100 ]000 10.000 Oil on shore ( tonnes) 100.000

Fig. 3. Shoreline damaged as a function of oil reported to be stranded. Closed circles show observations, open circles show results from the calculation model. Full line shows linear regression. Not all observed spills were described in enough detail to allow the calculation model to be applied (1, 14, 19, 21). Oil densities for the 26 spills depicted range from 0"74 tonnes km -l to 596 tonnes km -1.

The problem is exacerbated by the unknown or unreported oil spill clean up taking place while redistribution of the oil is in progress.

The spills are: 1, Olympic Alliance; 2,Erawan; 3, Golden Robin; 4, GlobaI Hope; 5, Christos Bitas; 6, Burmah Agate; 7, Betelgeuse; 8, Esso Bayway; 9, Wafra; 10, Ethel H; 11, Hellenic Carrier; 12, Esso Bernicia; 13, Universe Leader; 14, Jacob Mae;'sk 15, Peck Slip Barge; 16, Oregon Standard,17,Antonio Gramsci; 18, Zoe Colocotroni; 19,Ixtoc I Well; 20, Tanio; 21, Globe Asimi; 22, Santa Barbara Well; 23, Urquiola; 24, Torrey Canyon; 25,Metula; 26,Amoco

Cadiz. Details can be found in PFO (1983).

oil on shore and oil recovered from the shore. The 44 spills, or subselections of these spills, have been regressed against shore length damaged. Subselections have been made according to the type of data available in the spill descriptions. We have tried three prototype regression equations: linear, power curve and logarithmic equations. The results are shown in Table 1. It is seen that the best result is obtained for the linear regression between oil reported stranded on shore and shorelength damaged. The coefficient of determination, r 2 = 0.58 is, for example, in the same range as those often reported for predictions between phosphorus concentrations and algal biomasses in lakes, see Canfield & Bachmann (1981) (eqn 4). It is also seen that there is no correlation between oil spilled and shorelength damaged (r 2 = 0.01 << 1.0).

A particular problem is that the 'observed' data for oil on shore often

Models for cal..ulating oilspill damages to shores 77

TABLE 1 Regression Equations Between Shoreline Damaged, (km) S and (a) Oil Spilled (tonnes), (b) Oil Reported on Shore (tonnes) and (c) Oil Recovered on Shore (tonnes). (n = number of samples,

r 2 = coefficient of determination)

No. Equation n r 2 Oil range (tonnes)

X = oil spilled 120-224-000 (1) S = 0"008 X - 142 44 0"01

X = oil on shore 48-62.000 (2) S = 34"4 l n X - 150'5 25 0"45 (3) S = 6"3X °'31 25 0"26 (4) S = ff006X+ 70"6 25 0.58 (5) S = 0"008X 25 0-58

X = oil recovered 102-4000 (6) S = 0"06 X + 26 11 0.49

m a y be measu red indirect ly by calculat ing it as the overall densi ty o f oil x shore area con tamina ted . There seems to be a need for total mass ba lance calculat ions in which s t randed oil is es t imated independent ly .

In Table 1 eqns (4) a n d (5) represent two forms o f the l inear regression. One (eqn (5)) forces the line to go through zero, which seems sensible. However, spills causing small damages to the shore m a y be under- reported, thus for m e d i u m and large spills the full l inear regression (eqn (4)) m a y be the best choice.

6. D I S C U S S I O N

We have demons t r a t ed f rom actual spill data that there is no correlat ion between initial spill vo lume a n d the length o f shorel ine affected. How- ever, there is a correla t ion be tween the a m o u n t o f oil actual ly s t randed on a shorel ine and the length o f the shorel ine contamina ted . The correla t ion is only fair. However, the model represent ing it m a y never- theless be useful for oil comba t p l ann ing purposes if only spilled oil volume, the oil which will d isappear offshore and the oil which is potent ial ly recoverable, is known.

Visual inspect ion in Fig. 3 o f the cor respondence between observed and calcula ted results shows that the calcula t ion model gives reasonable est imates for about 2/3 of the 26 spills. Since m a n y of the data used for the spill descr ipt ion had to be extracted f rom semiquant i ta t ive statements, we believe that improved report ing could have e n h a n c e d the correla t ion

78 Knut L. Seip, Kjell Arne Brekke, Kari Kveseth, HaraM 1-brekk

for some spills. Also, clean-up operations, during redistribution of oil, may for some spills have led to less damage than our calculation model predicted.

The application of the calculation model to the Svalbard scenario seems to give reasonable results. The length of shoreline contaminated, about 18 km, is however, more than twice as long as the 8 km which is predicted by the regression eqn (5) for small spills.

We now have three sets of data available for a subset of the PFO spills (cf. the curve and circles of Fig. 3): (a) the observations, (b) the linear regression results of eqn (4) and (c) the model calculations. We have estimated the relative errors by summing the absolute differences (a)-(b) and (a)-(c) (the average shore length damaged is set equal for all three sets of data). The results show that the error sum is 30% less for the model calculations than for the regression equations.

Since data are scarce, verification of either model is difficult; however, the results indicate that the calculation model will give the best estimates. The regression equations are derived directly from observed data. The calculation model includes the description of oil processes and depends upon the choices of many parameters. Since all the parameters depend upon uncertain estimates, this model may potentially give results which are far from the observed values.

In spite of the shortcomings described, we believe that the results presented show that the calculation model will be a better predictor of shore length damaged than regression models and other types of assessments presently used. Furthermore, by using the model it may be meaningful to compare spill results from widely different coasts and thus accumulate and utilize spill damage experiences more effectively. The model may also be improved as more data become available.

ACKNOWLEDGEMENT

We would like to thank the Oil Pollution--Research and Development Program (PFO) for financial support of this project. We would also like to thank the referee for helpful advice and comments.

REFERENCES

Canfield, D.E. & Bachmann, R.W. (1981). Prediction of total phosphorus concentrations, chlorophyll, and secci depths in natural and artificial lakes. Can. J. Fish Aquat. Sci. 38, 414-23.


Danielsen, A., Klokk, T., Sandvik, J., Scholten, B. & Seip, IC L. (1985). Beach cleaning after an oil spill. A calculation model for estimating cleaning resources, cleaning operation time and oil remains for a cleaning operation. SI report 84 0706. Center for Industrial Research, Oslo, 54 pp. (in Norwegian).

Finkelstein, IC & Gundlach, E.R. (1981). Method for estimating spilled oil quantity on the shoreline. Environmental Science and Technology 15, 545-9.

Gundlach, E. R., Boehm, P. D., Marchand, M., Atlas, R. M., Ward, D.M. & Wolfe, D. A. (1983). The fate of Amoco Cadiz oil. Science 221, 122-9.

H~egh, T. (1978). Characterization of an oil blow at Ecofisk and a tanker accident at Risvika. IKU, Trondheim, 20 pp. (in Norwegian).

ITOPF (1983). Technical information papers 1-7 from The International Tanker Owners Pollution Federation Ltd, London.

Owens, E. H., Harper, J. R. Foget, C. R. & Robson, W. (1983). Shoreline experiments and the persistence of oil on arctic beaches. In: Proceedings of 1983 Oil Spill Conference. American Petroleum Institute, Washington, DC, pp. 261-8.

PFO (1983). Oil Pollution Control Research and Development Program. Abstracts of 70 major oil spills worldwide. Vol. I, p. 365.

Senstad, E. & Sindre, E. (1981). Physiological coastal zone mapping to combat oil pollution. SFTA 81046. SINTEF, Trondheim, 62 pp. + 31 plates.

Vandermeulen, I. (1977). The Chedabucto Bay spill m Arrow 1970. Oceanus 20, 31-9.

A P P E N D I X

DETAILS OF T H E C A L C U L A T I O N M O D E L

The equat ions describing the oil distr ibution processes in the model are presented below.

At the first stage of calculat ion we assume that an a m o u n t ofoi l Q with an offshore front L reaches the shore. The shorelines inunda ted are loaded either to a point where oil starts to run off, i.e. to a saturat ion density 6 s, or are loaded to a certain fraction F i of the offshore l inear density Qo/L outside of each shoretype. I f the resulting density is below a cutoff density 6 0 we substitute by 60 and assume that some of the shore is so little con tamina ted that it can be regarded as non-polluted. We then calculate the average density 6 which can be loaded on a uni t of mixed shoretypes characteristic for the coastline considered. For each shore segment L; with width 14z~, a density 6 i is first calculated:

S~ = max (So, FiQ/(LiW,.)) (1)

Si = min (S~, Ss, i) (2)

8 0 Knut L. Seip, Kjell Arne Brekke, Karl Kveseth, Harald Ibrekk

Then

6 = E S ~ L , / E L ~ (3) i i

The length of the contaminated shore at first impact is then

S1 = Qoh5 (4)

We have found it convenient at this stage to choose values for the parameters in eqns (1)-(4) so that $1 gives, with high probability, a lower limit for the predicted length of shoreline contaminated. In the subsequent calculation we chose values so that we get an upper limit.

At the second stage we calculate the effect of natural processes removing and redistributing the oil during the time period T between the first impact and a second period after the initial stranding of the oil. The rate of removal depends upon shoretype, wave energy levels at the shoreline, the nature of the stranded oil, etc. We assume that this removal can be formulated as an exponential decay process and that the amount of oil left on shore Q ss is given by:

Oss(t) = E O o , i e-kit (5)

where Q0, ; is the oil initially stranded on shoretype i, k; is the rate of natural oil removal from shoretype i and t is time (days).

At time t oil is removed from the shore i and transported back into the nearshore waters at a rate qu, i

qu, i(t) = Qo, iki e'-kit (6)

A fraction qn, ~(t) is mixed into the water column in the period (t, T):

qN, i(t) = qu, i(t) (1 -- e -kw(r-t)) (7)

Where kw is the rate of removal ofoil from the water column. Oil originat- ing from an oil covered shore and mixed into the water column in time T may be calculated as:

for kw 4: ki

T

Qw, i = fJN, i(t)dt = Q0,i[1 - (kw e-k`T- kie-kwr)!(kw - ki)] (8)

or for kw = ki

Qw, i = Q0, i [ 1 -- e -k ,T - T k i e-kwT] (9)

Qw = (lO)


The oil Qs(T) left on the water surface and available for redistribution is:

Qs(T) = Qo - Qs~(T) - Q,v(T) (11)

The quantity Qs (average for the period T) can now be redistributed on the shore, and we find the second impact length $2 by repeating the calculations (1) to (4). At this second stage we have found it convenient to choose parameter values for the equations so that $2 most probably gives an upper limit to the predicted length of shore contaminated by the redistribution process.

To calculate the total shoreline contaminated with oil, we now add the shoreline lengths SI and $2. This tends to give a high value for the shoreline contaminated because oil, during the redistribution phase, to some degree will hit shoreline sections already contaminated (cf. the Amoco Cadiz case).

Documents

Models for calculating oil spill damages to shores