mathematical modeling of marine oil spills in the...

Research ArticleMathematical Modeling of Marine Oil Spills in the LuanjiakouDistrict near the Port of Yantai

Daming Li Xingchen Tang Yanqing Li XiaoWang and Hongqiang Zhang

State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University 135 Yaguan Rd N Jinnan DistrictTianjin 300350 China

Correspondence should be addressed to Xingchen Tang xingchentang1108yeahnet

Received 5 September 2017 Revised 21 November 2017 Accepted 19 December 2017 Published 17 January 2018

Academic Editor Seenith Sivasundaram

Copyright copy 2018 Daming Li et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents a simulation method for oil spills in a multi-island area The simulation considers three parts which consist of(1) the spreading of an oil slick on its edge as well as the diffusion and drift under dynamic actions (2) the evaporation and spreadingthickness of an oil slick in its interior and (3) the adsorption and emulsification near shorelines and islands The Euler-Lagrangemethod is adopted to track the spill location and particles positions on the edge of oil slicks A mathematical model of marine oilspills is established for the Luanjiakou District of the Port of Yantai The flow field verification shows that the BIAS of tidal levelflow velocity and flow direction is below plusmn10 cm 011ms and plusmn2∘ respectively and the oil spill verification captures satisfactoryresults Hence the proposed model could reproduce the oil spill process in this region Then we simulate oil spills under variousoperating conditions It is concluded that the transport of oil slicks is mainly influenced by floodebb currents whereas the windplays a major role in the drift and thickness of oil slicks The study provides an important reference to controlling and handling ofaccidental oil spills

1 Introduction

With the rapid development of modern industry humandemand for energy has grown The increasing energydemands have resulted in the increased exploitation of fossilenergy such as crude oil and gas [1ndash3] Consequently therisk of oil spill accidents has also increased Coupled withthe booming development of maritime transportation shipgrounding accidents collisions and capsized tankers havealso contributed to the frequent occurrence of oil spillpollution These accidents can result in severe damage tothe marine environment [4ndash6] Therefore in recent yearsgovernments worldwide have strengthened the overall man-agement of the water transportation of oil and have fosteredscientific research on the movement properties of oil in water[1ndash3 7]

Spreading is the horizontal expansion of an oil slickdue to gravity inertia viscosity and surface tension forceswhich plays an important role in the fate process of surfacespilled oil The transport and fate of spilled oil in water areprocesses affected by dynamic factors nondynamic factorsand variable oil properties [8] Dynamic factors include

the gravity inertia viscosity and surface tension forceswind tidal currents and randomness of the motion process[9 10] Nondynamic factors mainly consist of weatheringprocesses such as dissolution evaporation photooxidationemulsification biodegradation and other chemical changesThus to accurately simulate the transport process of anoil slick under the influence of these dynamic factors is asignificant component of oil spill modeling [11] At presentoil spill models chiefly consider the following four aspects(1) the spreading and drift of spilled oil on the sea (2) theevaporation and adsorption of spilled oil (3) the dispersion ofspilled oil in water and (4) the trajectories and fate of spilledoil [3]

Early researchers adopted various numerical methods tosimulate themovement of an oil slick based on the advection-diffusion equation In the mid-1990s an oil-particles modelwas developed by Johansen Elliot and Reed [12] Othercommercial models such as NOAA [13] OLIMAP [14]OSIS [15] and OSCAR [16] have been subsequently adoptedto simulate oil movement and distribution in water Inaddition the bio-optical forecasting (BioCast) system canbe used to forecast the oceanrsquos color optical environment

HindawiDiscrete Dynamics in Nature and SocietyVolume 2018 Article ID 2736102 22 pageshttpsdoiorg10115520182736102

2 Discrete Dynamics in Nature and Society

Stations for diurnal tideStations for tidal level

H1

H2

H3

U1

U8

U7

U6

U5U4

U3

U2

U9

Sang Island

Penglai City

Luanjiakou

Bohai Sea

Huanghai Sea

Miaodao Strait

Daheishan IslandMiaodao Islands

North Changshan Island

South Changshan Island

Artificial Islands

Longitude (E)

Latit

ude (

N)

37∘57

37∘53

37∘49

37∘45

120∘58

120

∘54

120

∘50

120

∘46

120

∘42

120

∘38

120

∘34

120

∘30

120

∘26

Figure 1 Map of the Luanjiakou District near the Port of Yantai and survey stations

and the nowcast-forecast studies of ocean color data streamsin physical circulation models [17] which have promotedthe further development of oil spill models What is moreRadarsat SAR technology is an effective way for marineoil spill detection which can identify and extract oil spillinformation on the sea surface quickly and accurately andprovide remote sensing image to calibrate themodeling resultand improve the forecast precision It is of great significancefor the protection of the marine environment and nearshoreecological environment [18 19]

In recent years there have been breakthroughs in termsof understanding the complex geometry for oil spill modelresearch Gjosteen [20] developed an oil-spreading modelbased on the conservation of volume and momentum whichis suitable for coupling with the discrete-element ice modeland other complex boundaries for oil spreading Dietrichet al [6] applied a coupled SWAN + ADCIRC model on ahigh-resolution computational mesh and the highly efficientLagrangian particle transport model to simulate the surfacetrajectories of the oil spill from the Macondo well northernGulf of Mexico during the spring of 2010 Wang and Shen[21 22] developed a three-dimensional integrated modelthat provides great flexibility for modeling oil spill accidentsin complex geometries such as tidal creeks barriers andislands Currently an unstructured grid is primarily usedto simulate the solid boundary for the study of oil spillsin complex terrains [6 21ndash28] Alves et al [1] proposed athree-step model to predict and assess shoreline and offshoresusceptibility to oil spills for confined basins with islandswhich comprises the leading edge in the study of oil spills incomplex terrains Then Alves et al [2] simulated a series ofoil spill accidents in the Eastern Mediterranean Sea whichincluded confined maritime basins Nevertheless furtherstudies need to be done in the problem of oil particles

penetrating the solid boundary such as a complex multi-island terrain or hydraulic structures

In this study an oil spill simulation method in a multi-island area is presented and the processingmodes for oil slicklongshore transport and its penetration-resistant boundariesare developed In addition a local search method that canspecify the search radius is proposed and adopted Whatis more the Euler-Lagrange method is adopted to trackthe spill location and the position of particles on the edgeof oil slicks which can easily calculate the oil slick areaBased on the Monte Carlo method a mathematical modelfor marine oil spills is established to simulate the movementof oil spills in the Luanjiakou District of the Port of Yantai(Figure 1)

2 Theories and Methods

The Euler-Lagrange systems are divided into two partsthat is Euler and Lagrange approaches The Euler approachdescribes the distributions of the variables in flow field atany time whose computational mesh is fixed in space whilethe Lagrange approach traces each particle from a certaintime and describes its trajectory whose computational meshis fixed on the centroid of the research object and canbe used to simulate the trajectory of an oil slick [29 30]Fundamentally the accuracy of the velocity information forthe hydrodynamic field established by the Eulerian approachhas a crucial role in the successful prediction of the oil spilltrajectory by adopting the Lagrange approach [25] Thusthe coupling approach can give full play to the advantagesof both approaches and avoid their defects which is thereason why it is widely used in solving two-dimensionalhydrodynamic problems by using finite element analysismethod

Discrete Dynamics in Nature and Society 3

21 HydrodynamicModule In the coastal area the horizontalmovement scale of the tidal current is much larger than thevertical movement scale and the hydraulic parameters areunconspicuous in the vertical direction so the flow fieldcan be expressed by the average flow quantities along thedirection of the water depth [31] If the three-dimensionalsimulation is adopted the calculation would be greatlyincreased and the simulation conditions would be morecomplex due to the impact of the vertical stratification onopen boundary conditions wind stress conditions bottomfriction forms and so on As said above the governingequations of hydrodynamic model are the two-dimensionaldepth-averaged shallow water circulation equations whichare discretized by the finite element method The continuityequation is given by120597119911120597119905 + 120597 (ℎ119906)120597119909 + 120597 (ℎV)120597119910 = 0 (1)

The equations for conservation of momentum are givenby 120597119906120597119905 + 119906120597119906120597119909 + V120597119906120597119910 + 119892120597119911120597119909

= minus119892radic1199062 + V21198882ℎ 119906 + 119891V + 120591119909119904120588ℎ + 119860ℎ (12059721199061205971199092 + 120597

21199061205971199102)120597V120597119905 + 119906 120597V120597119909 + V120597V120597119910 + 119892120597119911120597119910= minus119892radic1199062 + V21198882ℎ V minus 119891119906 + 120591119910119904120588ℎ + 119860ℎ (120597

2V1205971199092 + 1205972V1205971199102)

(2)

where 119906 and V are the component velocities of current in the119909 and 119910 directions respectively 119911 is the water level 119892 is thegravitational acceleration 119888 is Chezyrsquos friction coefficient ℎis the water depth 119891 is the Coriolis coefficient 119860ℎ is thehorizontal eddy viscosity coefficient 120588 is the density of waterand 120591119909119904 and 120591119910119904 are the wind stress components on the seasurface in the 119909 and 119910 directions respectively

Waves are generally induced by the wind on the seasurface According to the temporal and spatial variationthe waves can be divided into regular and irregular wavesRegular waves have constant amplitudes and wavelengthswhose waveforms do not vary with time and space It ispossible to form such waves only when the problem is two-dimensional the water depth is constant and the disturbancesource generating wave periodically varies with time Irreg-ular wave patterns are transient whose elements vary withtime and space The waves generated when the wind blowsover the sea surface are a common type of irregular wave [32]Thus the wind wave is just taken into account in the wavecalculation that is wind-induced shearing stresses on watersurfaces 120591119909119904 and 120591119910119904 which can be computed by the followingempirical formula

120591119909119904 = 0125119862119863119882119909 100381610038161003816100381610038161003816997888rarr119882100381610038161003816100381610038161003816120591119910119904 = 0125119862119863119882119910 100381610038161003816100381610038161003816997888rarr119882100381610038161003816100381610038161003816

(3)

where119882119909 and119882119910 are the component velocities of the windon the sea surface in the 119909 and 119910 directions respectively 997888rarr119882is the wind velocity vector and the wind drag coefficient 119862119863can be obtained from the following Heaps empirical formula

119862119863=

0564 times 10minus3 100381610038161003816100381610038161003816997888rarr119882100381610038161003816100381610038161003816 le 4917(minus012 + 013 100381610038161003816100381610038161003816997888rarr119882100381610038161003816100381610038161003816) times 10minus3 4917 lt 100381610038161003816100381610038161003816997888rarr119882100381610038161003816100381610038161003816 lt 192212513 times 10minus3 100381610038161003816100381610038161003816997888rarr119882100381610038161003816100381610038161003816 ge 19221(4)

22 Oil Spill Module

221 Spreading Fayrsquos [33] three-phase spreading theory isadopted to study the spreading of the oil slick on the still watersurface which is based on laboratory hydrostatic experiments[34]The spreading diameter of the oil slick in each phase canbe expressed by Fayrsquos empirical formulas

Gravity-inertia spreading phase

1198711 = 1198701 (119892119881Δ)14 11990512 (5)

Gravity-viscous spreading phase

1198712 = 1198702 [119892 (1 minus Δ) Δ]16 120592minus112119908 1199051411988114 (6)

Surface tension viscous spreading phase

1198713 = 1198703119892minus1412057512120588minus34119908 11990534 (7)

where Δ = 1 minus 1205880120588119908 where 1205880 and 120588119908 are the density of oilparticles and water respectively 119871 is the spreading diameterof the oil slick and the subscripts denote different phases 120575 =120575119908119886 minus 120575119886119900 minus 120575119900119908 where 120575119908119886 120575119886119900 and 120575119900119908 are the water-airoil slick-air and oil slick-water surface tension coefficientsrespectively 120592119908 is the kinematic viscosity of water1198701 = 1351198702 = 160 and 1198703 = 048 are experiment constants 119905 is theduration of the oil spill 119881 = sum119899119894=1 119876119894(119905)Δ119905[1 minus 119896(119905 minus 119894Δ119905)] isthe spill volume 119876 is the spill discharge 119896 is the syntheticattenuation coefficient and 119899 = 119905Δ119905 is the number of oil spilltimes

222 Drift andThickness The drift of the oil slick is a vectorsum of surface current and wind of which the velocity vectoris shown in Figure 2 The drift velocity 997888119906 119903 can be written as

997888119906 119903 = 119870119888997888rarr119906 119888 + 119870119908997888rarr119906119908 (8)

where 997888rarr119906 119888 is the surface current velocity 997888rarr119906119908 is the windvelocity at 10m above the water surface119870119888 = 1 is the currentfactor and 119870119908 = 0035 is the wind drift factor [35]

The spreading thickness ℎ can be determined from themass conservation equation as follows

120597 (119862ℎ)120597119905 + 120597 (119906119862ℎ)120597119909 + 120597 (V119862ℎ)120597119910 = minus (Φ119904 + Φ119887 + 119877) (9)


rarruw

rarru r

rarru c

Figure 2 Velocity vector of oil slick drift

where 119862 is the oil slick concentration Φ119904 and Φ119887 are thespill flux of the upper and lower surface of the oil slickrespectively and 119877 is the loss of the oil slick in the chemicaland physical processes

The spill flux is very similar to the mass transfer fluxin molecular diffusion so the spreading thickness ℎ can becomputed from Fickrsquos law

ℎ = 119881119890minus1198961199052120587120590119904120590119899 exp(minus 119904221205901199042 minus 119899221205901198992) (10)

where 119904 and 119899 are the natural coordinates in the oil slick driftdirection and the direction perpendicular to 119904 respectively 119896is the attenuation coefficient of oil and 120590119904 = 119886119904119905117 and 120590119899 =(1radic10)120590119899 are the standard deviation of the oil slick thicknessin the 119904 and 119899 directions respectively223 Particle MotionModel of Oil Slick Due to the influenceof various dynamic factors such as wind wave and currentthe diffusion of spilled oil on the sea surface has certainrandomness at any time which can be properly describedby the Monte Carlo method [36] It captures the multiplesampling data of the function based on the sampling of eachof the randomvariables and then calculates the function valueof each group from the independent sampling data so as todetermine the probability distribution of the function It isapplied to the problem of oil spill diffusion which is to obtainthe movement direction and displacement of oil particles bygiving each of the tracked particles a set of random numbersunder the premise of determining the disturbance intensityand time scale Namely the trajectories of oil particles arecaptured by adding a random term to the result obtained bythe Lagrange method The essence is to help supplement andrevise the Euler-Lagrange systems

The Monte Carlo method is adopted to calculate the oilmovement in the present study First the spill location andthe position of particles on the edge of oil slicks are trackedand recorded by using the Euler-Lagrange method Next thediffusion randomnumber is added to themodule As a resultthe action of the wave-guide and wind-induced currentson dispersion and fragmentation of oil slicks is taken intoaccount to describe the trajectory and irregular shape of thesesame spills

Assuming the sampling step Δ119905 gt 0 and119883119899 = 119883(119899Δ119905) wehave

119883119899 = 119883119899minus1 + 120590radicΔ119905119882119899 (120590 gt 0) (11)

where 119882119899 are independent random numbers on 119873(0 1)and the increment 119883119899 minus 119883119899minus119896 depends only on 119896 variables(119882119899minus119896+1 sdot sdot sdot119882119899) (119896 lt 119899) corresponding to (119899 minus 119896 119899) so 119883119899 minus119883119899minus119896 follows the normal distribution119873(0 120590radic119896Δ119905)

Specifically supposing that position coordinates of an oilparticle are 119877(119905119894) and 119877(119905119894+1) at times 119905119894 and 119905119894+1 respectivelyand 119877 is the movement distance of an oil particle under theactions of spreading drift and so on we will then have

997888rarr119877 (119905119894+1) = 997888rarr119877 (119905119894) + 997888rarr119877997888rarr119877 = 120574997888rarr119877 119904 + 997888rarr119877 119897 (12)

where 120574 is the random number ranging from 0 to 1 and997888rarr119877 119897 is the drift vector in the period of Δ119905 which can beobtained by integrating the Lagrange velocity as follows TheLagrange velocity can be approximately represented by theEuler velocity in the calculation

997888rarr119877 119897 = int119905119894+1119905119894

997888rarr119906 119903119889119905 (13)

997888rarr119877 119904 is the spreading vector in the period of Δ119905 which is givenby

997888rarr119877 119904 = 997888rarr119897 (119905119894+1) minus 997888rarr119897 (119905119894) (14)

The discrete form of transport distance of the labeled oilparticle can be obtained by

997888rarr119877 119905119894+1 = 997888rarr119877 119905119894 + Δ119905 sdot 997888rarr119906 119903 + 120574 (997888rarr119897 (119905119894+1) minus 997888rarr119897 (119905119894)) (15)

In addition 997888rarr119906 119903 can be obtained from (8) and997888rarr119897 (119905119894+1) and997888rarr119897 (119905119894) can be obtained from (5)ndash(7) As mentioned above

we can calculate the transport position of each of the oilparticles A large number of oil particles can reflect thebehavior processes of marine oil spills

224 Evaporation and Emulsification The evaporation rateis influenced by the temperature waves wind speed andoil slick areas among other factors Hence the evaporationamount of surface oil slick can be calculated by the followingdistillation formula [37]

119865V = ln [1 + (119861119879119866119879) 120579 exp (119860 minus 1198611198790119879)](119879119861119879119866) (16)

where 119865V is the volume fraction evaporated 119860 and 119861 arethe constants usually selected as 63 and 103 for crude oilsrespectively 119879119866 is the slope of distillation curve 119879 is thesurface temperature of the oil slick 1198790 = 5426minus30275API+1565API2 minus 003439API3 + 00002604API4 is the initial


Discrete node

Oil slick

Combination of particles and oil surface

Oil surfaceFigure 3 Description of the computing mode of the oil slick (thearea surrounded by the solid line represents the oil slick black pointsrepresent discrete nodes along the edge of the oil slick line betweendiscrete nodes represents oil surface and the area surrounded by thedashed line represents the combination of particles and oil surface)

boiling point [38] and API is the density of spilt oil followingthe classification of the American Petroleum Institute 120579 =00025(119906119908 + 1)078 times 2437ℎ is the exposure coefficient of oilslick and 119878(119905) is the area of the oil slick

When drifting on the sea surface under the influenceof wind and waves oil particles disperse to the aqueousphase and water particles also disperse to the oil phasecontinuously Subsequently an oily emulsion is generatedThe emulsification equation is given by [39 40]

119889119865119908119889119905 = 1198621 (119906119908 + 1199060)2 (1 minus 1198622119865119908) 119876 (119905) (17)

where 119865119908 is the emulsification fraction 1198621 is the absorptionrate usually selected as 2 times 10minus6 1198622 is the water contentusually adopted as 133 1199060 is the emulsification correctionfactor in the ocean environment and 119876(119905) is the emulsifyingamount of the oil slick

225 ComputationMode In this study a simulationmethodfor oil spills in a multi-island area is presented to simul-taneously observe and study the edge and centroid motionof an oil slick (see Figure 3) It is suggested that a numberof discrete nodes are distributed along the edge of the oilslick and there is a line along the edge of the oil slickbetween the nodes which is called the ldquooil surfacerdquo Thenumber of nodes can be increased or decreased appropriatelydepending on the degree of density so that the edge interfacecan be expressed by a continuous and smooth edge lineThe interface is referred to as ldquocombination of particles andoil surfacerdquo This way the motion quantities of the discretenodes can be calculated Therefore the model can entirelysimulate the motion process of the oil slick including thespreading of the oil slick on its edge the diffusion and driftunder the dynamic actions of wind waves and currentsthe evaporation and thickness of the oil slick in its interiorand the adsorption and emulsification of the oil slick nearshorelines and islands

Marine oil spill models usually cover large areas usingmany grids Furthermore in most calculations one does notonly need to determine the scope of the search unit but alsoneed to ascertain whether or not the search node is in thisunit In addition the centroid and edge of an oil slick are notnecessarily near the previous location because the transportof the oil slick with water movement may be very large overa short period However using the global search method(ie searching the entire study area) would lead to the huge

Search radius

Search node

Circle center

0 20 40 60 800

20

40

60

Figure 4 Schematic diagram of the local search method (redcircular area for the search range pink point for the circle centeryellow point for the search node yellow arrow for the search radiusblue solid line for the contour line of an oil slick in the previousmoment and blue dashed line for the contour line of an oil slickin the present moment)

calculationTherefore the local searchmethod is proposed inthis paper which specifies the search radius thereby reducingthe amount of computation (see Figure 4) As shown in thefigure the position of the node in the previous moment istaken as the circle center and the search radius is providedIn addition the unit number is arbitrary and its centroidcoordinate is provided This way we can determine whetheror not the unit is within the search range

During oil spills around multi-island areas coastal struc-tures such as breakwaters quays jetties wharfs and docksare likely obstacles to the spreading and transport of oil slicks[3 10] When transporting along these obstacles a portion ofthe oil slick would be adsorbed in the structures Note thatthe permanent absorption is taken into account in this studyHence the mode of the penetration-resistant boundary thatis the case where oil particles are transported along the coastand adsorbed on it and do not penetrate the solid boundaryis developed (see Figure 5(a)) In addition the mode canbe used for real-time detection of the solid boundary Thenthe adsorption unit and location of oil particles can beascertained using the unit information recorded by the localsearch method (see Figure 5(a)) This strategy is a good wayto avoid the unlikely case of oil particles penetrating the solidboundary when the current velocity is relatively large (seeFigure 5(b))

226 Oil Spill Verification

(1) Oil Spill on a Still Water Surface The spreading andextension of an oil slick are some of the main differencesbetween oil spill diffusion and concentration diffusion whichis reflected by the major and minor axes of the oil slickchanging with time Thus the scales of the major and minoraxes of the oil slick after an instantaneous oil spill are simu-lated under different oil volumes (Figure 6) A comparisonof the numerical results with the results obtained by Zhaoand Wu [41] shows good conformity in the majorminoraxes scales (see Tables 1 and 2) Moreover the numericalresults of the two studies convergewith increasing oil volumeThere is slightly larger discrepancy between simulated and


(a) (b)

Figure 5 Comparison of different movement conditions of oil particles (black point) when arriving at the solid boundary (solid line) ((a)represents themodes of the penetration-resistant boundary as well as the longshore transport and adsorption of the oil slick and (b) representsthe unlikely case of oil particles penetrating the solid boundary)

V-spill volume

0

10

20

30

40

50

60

70

Maj

or ax

is sc

ale (

km)

50 100 150 200 250 300 3500Time (h)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(a)

V-spill volume

50 100 150 200 250 300 3500Time (h)

0

5

10

15

20

25

30

35

Min

or ax

is sc

ale (

km)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(b)

Figure 6 The major (a) and minor (b) axes of the oil slick versus time

reference results for major axes as compared to minor axesThe reason for this is that the major axes of the oil slick aredeeply influenced by many factors such as wind waves andcurrents

(2) Oil Spill on a FlowingWater SurfaceThe oil slick diffusionand drift experiment were carried out in a flume 25 cmlong and 60 cm wide The flow section for experimentalobservation is 117m in which the flow is uniform andthe mean flow velocity is approximately 004ms The flumeexperiment and simulated results are shown in Figure 7in which (a) and (c) are the oil slick diffusion and drift atdifferent times in the flume and (b) is the simulated resultA comparison of the simulated and experimental results isshown in Table 3 which shows that the results are in goodagreement with each other

3 Model Setup and Verification

The Luanjiakou District is located in the western portion ofPenglai-Yantai City Shandong Peninsula The district faces

the Miaodao Islands whose eastern coastline extends in thedirection of Penglai City and the Yellow Sea and the westerncoastline extends in the direction of the Laizhou Gulf (seeFigure 1)

31 Study Area The model domain and its bathymetryare shown in Figure 8(a) The length of the domain isapproximately 100 km and its width is approximately 40 kmextending to deep water covering a sea area of approxi-mately 46 times 104 km2 There are three open sea boundariesaround that is the left right and upper straight boundariesTriangular grids covering this domain were generated bythe finite element method with a high grid resolution inthe harbor channel and artificial island regions with thefollowing total number of grids and nodes 47 and 244 and24 and 350 The maximum grid spacing is approximately2 km and the minimum is approximately 0025 km (seeFigure 8(b))

32 Boundary Condition To account for the lack of obser-vational data the astronomical tide we induced the tidal


(a)

= 004 ms

(b) (c)

Figure 7 Comparison of the flume experiment (a c) and the simulated result (b) of the spreading and drift of the oil slick

Table 1 Comparison of the major axes scales of the oil slick

Spill volume (m3) 102 103 104 105

Simulated values of this paper (km) 1533 2814 451 6483Simulated values of [41] (km) 1267 2591 4354 6549

Table 2 Comparison of the minor axes scales of the oil slick

Spill volume (m3) 102 103 104 105


Table 3 Comparison of the simulated and experimental results

Item Initial size (cm) Final size (cm) Movement distance (m) Movement time (s)Simulated results 15 21 117 30Experimental results 15 22 12 30

level condition at the three open boundaries Four main con-stituents in this domain are considered that is K1 M2 O1and S2 whose harmonic constants can be derived from theglobal ocean tide model from the United States Departmentof the Navy [42] so that the tidal levels processes can beobtained at the open sea boundariesMoreover observationaldata are used for the landward boundaries

33 Flow Field Verification According to historical data [43]the survey stations are shown in Figure 1 The data fromthree survey stations (H1 H2 and H3) from 000 on July 4to 1800 on July 7 2011 are adopted to validate tidal levelsThe data from nine survey stations (U1 U2 U3 U4 U5 U6U7 U8 and U9) of the diurnal tide from 1000 on July 5 to1400 on July 6 2011 are used to validate flow velocity anddirections

The validation results of the tidal level are shown in Fig-ure 9 which indicates that variations between the observedand the modeled results are in good agreement with eachother However the tidal range is slightly different betweenthe two At high tide the modeled values are smaller than

the observed values while at low tide the modeled values arelarger than the observed values This result could be relatedto datum selection prior to the modeling

There aremany diurnal tide survey stations (see Figure 1)Stations U1 U4 andU7 are used to illustrate our verificationsof the flow velocity and direction (see Figures 10 and 11)In Figures 10 and 11 the variations of the flow velocity anddirection between the observed and the modeled resultsare consistent at the three stations considered (U1 U4 andU7) except that there are deviations at individual timesThe reason for this discrepancy may be associated with theaccuracy of the observed data

In particular three criteria are adopted to assess themodel performance for tidal level flow velocity and flowdirection simulation including the mean absolute error(MAE) the root mean square error (RMSE) and bias (BIAS)[19] The equations for these three criteria are shown asfollows

MAE = 1119873119873sum119894=1

1003816100381610038161003816120578119898119894 minus 120578119900119894 1003816100381610038161003816


00

0

0

0

3

3

3

3

33

3

6

6

6

6

6

6

666

6

9

9

9

99

999

9

12

12

1212

12

12

12

15

15

15

1515

15

15

15

18

18

18

18

18

18

18

18

18 18

18

21

21

2121

21

21

21

21

21 21

21

24

24

24

2424

24

24

27

27

27

27

27 27

27

27

30

30

30

30

33

33

36

36

393942

260000 280000 300000 320000 340000 3600004160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

036912151821242730333639424548

Depth (m)Distance (m)

Dist

ance

(m)

N

E

S

W

(a)

Breakwater

Artificial islands

4160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

Dist

ance

(m)

280000 300000 320000 340000 360000260000Distance (m)

N

E

S

W

(b)

Figure 8 (a) Bathymetry and (b) unstructured grids for the model domain

ModeledObserved

H1

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

Tida

l lev

el (c

m)

H2

minus80

minus60

minus40

minus20

0

20

40

60

80

100Ti

dal l

evel

(cm

)

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved

H3

Tida

l lev

el (c

m)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved

Figure 9 Comparison of the tidal level between the modeled (solid line) and the observed (dots) results at three stations (H1 H2 and H3)


ModeledObserved

U1

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10Ve

loci

ty (m

s)

U4

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10

Velo

city

(ms

)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

Velo

city

(ms

)

ModeledObserved

Figure 10 Comparison of flow velocity between the modeled (solid line) and the observed (dots) results at three stations (U1 U4 and U7)

RMSE = radic 1119873119873sum119894=1

(120578119898119894 minus 120578119900119894 )2

BIAS = 1119873119899sum119894=1

(120578119898119894 minus 120578119900119894 ) (18)

where 120578119898119894 are the modeled results and 120578119900119894 are the observedresults The statistical errors for the differences between thesimulated and observed results can be found in Table 4 fromwhich it can be seen that for the tidal level the maximumRSME is 1210 cm at Station H3 and the BIAS is below plusmn10 cmat three stations (H1 H2 and H3) for the flow velocity themaximum RSME is 011ms at Station U1 and the BIAS isbelow plusmn010ms at three stations (U1 U4 and U7) and forthe flow direction the maximumRSME is 1763∘ at Station U1and the BIAS is below plusmn2∘ at three stations (U1 U4 and U7)

The distributions of the flow field at ebb and flood periodsare shown in Figure 12 The results indicate that during the

ebb period the velocities along the shoreline are much largerthan those near the islands because the water converges intothe deep areas During the flood period velocity differencesbetween the shoreline and the islands are less obvious At bothtimes the tendencies of the flow field were well reflected bythe model

In summary the hydrodynamic field can serve as the basisfor studying marine oil spills in our study area

34 Concentration Diffusion Verification In the concentra-tion diffusion verification of an oil slick the results of adyestuff tracing experiment carried out by South ChinaSea Institute of Oceanology Academia Sinica from 230 to530 on January 29 2002 were compared with the modeledresults as shown in Figure 13 The figure shows that thediffusion tendency and range of the oil slick are relativelyconsistent which provides the basis for the selection ofthe diffusion coefficient It is indicated that the model canbe adopted to reflect the actual oil slick movement in theregion


ModeledObserved

U1

0

50

100

150

200

250

300

350D

irect

ion

(deg

)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

U4

0

50

100

150

200

250

300

350

Dire

ctio

n (d

eg)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

0

50

100

150

200

250

300

Dire

ctio

n (d

eg)

ModeledObserved

Figure 11 Comparison of flow direction between the modeled (solid line) and the observed (dots) results at three stations (U1 U4 and U7)

260 270 280 290 300 310 320 330 340 350 3604160

4170

4180

4190

4200

4210

4220

4230

Distance (km)

Dist

ance

(km

)

10 msN

E

S

W

(a)

4160

4170

4180

4190

4200

4210

4220

4230

Dist

ance

(km

)

270 290280 300 310 320 330 340 350 360260Distance (km)

10 msN

E

S

W

(b)

Figure 12 Distributions of the flow field at the times of ebb (a) and flood (b)


Table4Statisticalerrorsattid

alsurvey

statio

nsform

odelverifi

catio

n

Station

Tidallevel

Station

Flow

velocity

Flow

direction

MAE(cm)

RSME(cm)

BIAS(cm)

MAE(m

s)

RSME(m

s)

BIAS(m

s)

MAE(deg)

RSME(deg)

BIAS(deg)

H1

918

1104

minus811

U1

009

011

006

1283

1763

163

H2

829

1032

minus683

U4

006

008

minus002

1055

1498

minus198

H3

1002

1210

minus913

U7

007

009

minus003

1172

1518

106


PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)

Figure 13 Comparison between the experimental result (a) and the modeled result (b) of the concentration diffusion of the oil slick

Table 5 Properties of the oil

Name Density (kgm3) Water content of emulsion () APICondensate oil 8305 74 38874Low sulfur fuel oil 972 80 1408

4 Results and Discussion

Theport has 10000-tonne tanker berths and the channel is animportant shipping route for oil tankers and ships Hence thesimulation assumes that spill locations are evenly distributedin the western middle and eastern portions of the portcovering the entire channel which are all the high-risk oilspill areas

According to the relevant specifications [44] the scenariosimulations of marine oil spills are assumed and carried outin two ways instantaneous and continuous The condensateoil is used for the instantaneous oil spill scenario andthe spill volume is approximately 8000 t For convenienceof comparison the low sulfur fuel oil is utilized for thecontinuous oil spill scenario whose spill volume is constantand the duration is 10 h The properties of the spilt oil areshown in Table 5

In this region the prevalent wind directions are SSW andS and the frequency is 1514 The static wind frequency is047The strong wind directions are N NW and NNE andthe instantaneous maximum wind speed is 28ms [43] Thewind rose diagram for Luanjiakou District in 2002ndash2006 isshown in Figure 14 Together with live telecast data the windconditions in themodel were set as shown inTable 6 inwhichWindDirection 1 predominates in the sea area and the islandsnear the Miaodao Strait Wind Direction 2 blows against theshoreline around the artificial islands and Wind Direction 3is unfavorable to the dock and harbor The simulation timestep was 60 s and the time length was 48 h To control the

c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420

Figure 14 Wind rose diagram for Luanjiakou District in 2002ndash2006

time the initial minimum distinguishable spacing was 15mand the maximum distinguishable spacing was set as 100m

41 Spill Trajectories The trajectories of instantaneous oilspills from the western portion of the channel under fivewind conditions are shown in Figure 15 In the figure it


Table 6 Wind conditions of the model

Wind direction No wind Southwest wind (SW) South wind (S) Northwest wind (NW) Northeast wind (NE)Wind speed (ms) 0 49 20 34 27Note Maximum wind direction Wind Direction 1 Wind Direction 2 Wind Direction 3

No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)

Figure 15 Trajectories of instantaneous oil spills (red line) from the western portion of the channel (black star symbol for the western spilllocation) under five wind conditions ((a) represents oil spill trajectory in the case of no wind (b) represents oil spill trajectory under theinfluence of southwest winds (c) represents oil spill trajectory under the influence of south winds (d) represents oil spill trajectory under theinfluence of northwest winds and (e) represents oil spill trajectory under the influence of northeast winds)


24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

Figure 16 Transport processes of instantaneous oil spills (red area) from thewestern portion of the channel (black star symbol for the westernspill location) in the case of no wind

can be seen that in the case of no wind (Figure 15(a))the oil slick migrated with floodebb currents and the areatrajectory radiated towards the surrounding areas from thespill location because the ebb and flood velocities wereroughly the same When the oil spread to the narrowwaterway of the Miaodao Strait the ebb velocity increasedand an oil slick zone protruding into the open sea appearedUnder the influence of southwest winds (Figure 15(b)) theoil slick after spill migrated towards the ebb because thebreakwater had little effect on the migration of the oil slickalong the wind and floodebb directions When removingthe preventive area of the breakwater the oil slick quicklyspread to the Miaodao Islands and the scope swept by thearea trajectories was relatively large Under the influenceof south winds (Figure 15(c)) the oil slick approached thebreakwater and then migrated towards the ebb due to theresistance of the breakwater When removing the preventivearea of the breakwater the oil slick insufficiently spreadso the scope swept by the area trajectories was relativelysmall Under the influence of northwest winds (Figure 15(d))most of the oil slick after spill entered the Luanjiakou Portbecause the tidal current velocity was relatively small Underthe influence of northeast winds (Figure 15(e)) after driftingsome distance with the ebb current the oil slick movedto the southwest through passenger ferry berths and theport due to the combined effect of the wind and the floodcurrent Finally part of the oil slick reached the westernshoreline

42 Movement Process of Oil Slicks Figures 16 and 17show the transport processes of instantaneous oil spills thatoccurred in the western portion of the channel in the caseof no wind and the eastern portion of the channel under theinfluence of south winds respectively The figures show thatoil slicks after spill migrated with the tidal current and windand they spread by themselves

Figures 18 and 19 show the transport processes of con-tinuous oil spills that appeared in the western portion of thechannel in the case of no wind and the eastern portion ofthe channel under the influence of south winds respectivelyThe figures indicate that oil slicks after spill mixed with eachother and that a narrow oil slick was formed Then oil slicksmigrated with tidal current and wind and they spread bythemselves

From Section 222 it can be seen that the transportvelocity of oil slicks is related to the local current velocity andthe wind speed and that the spreading velocity is influencedby the spill volume the density of the oil and the surroundingterrain Therefore the instantaneously spilled oil drifted inthe shape of the approximate ellipse After bursting anirregular multilayer ring was formed (see Figures 16 and 17)Conversely the continuously spilled oil drifted in the shape ofa narrow strip and an irregular single-layer ring was finallyformed (see Figures 18 and 19)

43 Area of Oil Slicks versus Time Figures 20ndash24 show therelationship of the slick area of instantaneous and continuous


Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

Figure 17 Transport processes of instantaneous oil spills (red area) from the eastern portion of the channel (red star symbol for the easternspill location) under the influence of south winds

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)

Figure 18 Transport processes of continuous oil spills (red area) from the western portion of the channel (black star symbol for the westernspill location) in the case of no wind


4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

Figure 19 Transport processes of continuous oil spills (red area) from the eastern portion of the channel (red star symbol for the eastern spilllocation) under the influence of south winds

WesternMiddleEastern

0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)

Figure 20 Area of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spilllocation blue line for the middle spill location and red line for the eastern spill location) in the case of no wind

oil spills versus time The results show that in the case ofno wind (Figure 20) the spreading area of instantaneousand continuous oil spills reached the maximums within48 h Under the influence of southwest winds (Figure 21)the maximum spreading area appeared in the eastern spilllocation Under the influence of south winds (Figure 22)

the maximum spreading area appeared in the middle spilllocation Under the influence of northwest winds (Figure 23)the maximum spreading area of an instantaneous oil spillappeared in the western spill location and the maximumspreading area of a continuous oil spill appeared in themiddle spill location Under the influence of northeast winds



0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)

Figure 21 Area of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spilllocation blue line for the middle spill location and red line for the eastern spill location) under the influence of southwest winds


0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)

Figure 22 Area of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spilllocation blue line for the middle spill location and red line for the eastern spill location) under the influence of south winds

(Figure 24) the maximum spreading area of the instanta-neous oil spill appeared in the western spill location and themaximum spreading area of the continuous oil spill appearedin the eastern spill location

From Figures 20ndash24 it can be concluded that the max-imum spreading area of oil slicks occurred in the easternlocation which spilled quickly under the influence of south-west winds and reached 109385 km2 after 48 hTheminimumarea occurred in the western and middle locations andreached 0823 km2 which was continuously spilling underthe influence of northwest and northeast winds respectively

44 Thickness of Oil Slicks versus Time Figures 25 and 26show the relationship of the slick thickness of instantaneousand continuous oil spills versus time under different con-ditions It can be observed that the thickness of oil slicks

was relatively large in the beginning and gradually decreasedwith spreading and drift When obstructed by the shorelineoil slicks accumulated and the thickness suddenly increasedor remained constant After spilling for 48 h the maximumthickness of oil slicks was approximately 9998mm whichmainly occurred under the influence of northwest andnortheast winds Due to the small current velocity near theshoreline harbors and islands the wind squeezed oil slicksand limited the spreading and drift of them forming a thickeroil slick area in the vicinity

45 Fate Process of Oil Volume In the present study the oilfate mainly includes the oil on the sea surface evaporatedemulsified and adsorbed near the shoreline after comingashore Figure 27 shows the fate processes of the instanta-neous oil spills where the following can be observed the



0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)

Figure 23 Area of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spilllocation blue line for the middle spill location and red line for the eastern spill location) under the influence of northwest winds


0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)

Figure 24 Area of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spilllocation blue line for the middle spill location and red line for the eastern spill location) under the influence of northeast winds

initial oil volume on the sea surface is relatively large andthen decreased slowly after the 48 hours due to evaporationemulsification and adsorption evaporated and emulsified oilvolume relate to the wind speed on the sea surface whosetendencies are gradually increasing and then tend to be stablethe oil slick would be adsorbed when coming ashore so thecorresponding oil volume is also increasing

Figure 28 shows the fate processes of the continuous oilspills where it can be observed that the oil volume on the seasurface gradually increases during the initial 10 h and thenthe tendency is basically consistent with the instantaneous oilspill And the other fate processes are in agreement with theinstantaneous oil spill

46 Future Work The scenario simulations of marine oilspills in this study were preliminary using a two-dimensionaloil spill model which is actually a large-scale simulation in

large areas Further work remains to be done to improvethe model performance such as the multiscale simulationFor instance the vertical diffusion of spilled oil in the watercolumn can be carried out by the advanced SPH (SmoothedParticle Hydrodynamics) method that is the mesh-freeparticle method which describes the transport of an oil slickwith a series of particles and is more in coincidence withthe idea of ldquooil-particlesrdquo model In addition the acquisitionand usage of remote sensing information are essential tosimulate and predict the marine oil spills in the near futuredue to its wide area coverage and the all-weather and all-daycapabilities

5 Conclusions

In this paper a simulation method for the spreading anddrift of an oil slick in a multi-island area and the mode of



10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)

Figure 25 Slick thickness of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the westernspill location blue line for the middle spill location and red line for the eastern spill location) in the case of no wind


10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)

Figure 26 Slick thickness of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the westernspill location blue line for the middle spill location and red line for the eastern spill location) under the influence of northeast winds

the penetration-resistant solid boundary are presented Toimprove the computation efficiency a local search methodthat can specify the search radius is adopted The Euler-Lagrange method is adopted to track the spill location andthe position of particles on the edge of oil slicks in orderto calculate the slick area easily Based on the Monte Carlomethod a mathematical model for marine oil spills wasestablished for the Luanjiakou District near the Port ofYantai A series of verifications of the tidal current field andthe movement of an oil slick show that the model can reflectthe actual oil slick movement

The model has been applied to simulate the movement ofoil slicks including the trajectory transport area thicknessand fate processes It was concluded that the scope of spill

trajectories was the largest under the influence of southwestwinds and it was the smallest under the influence of north-west winds the transport of oil slicks was mainly affectedby floodebb currents and oil slicks could reciprocate withfloodebb currents the spreading area of instantaneouslyspilled oil reached the maximum in the eastern spill locationunder southwest winds after spilling for 48 h The minimumoil area appeared in the western and middle spill locationswhich continuously spilled oil under the influence of north-west and northeast winds respectively the wind had a signif-icant influence on drift and thickness of oil slicks especiallywhen the flow velocity was relatively smallThe fate processesof oil volume on the sea surface gradually increase duringthe initial 10 h and subsequently the variation tendency is


000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)

Oil on sea surfaceOil evaporated

Oil emulsifiedOil coming ashore

(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)

Figure 27 Fate processes of the instantaneous oil spill that occurred in the west of the channel in the case without wind (a) and in the eastof the channel under the action of northwest wind (b)

20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)

Figure 28 Fate processes of the continuous oil spill that occurred in the west of the channel in the case without wind (a) and in the east ofthe channel under the action of northwest wind (b)

basically consistent with the instantaneous oil spill The fateprocesses of evaporated emulsified and adsorbed oil volumeof two types of oil spills are basically the same

Overall the proposed model provides a reasonablemethod for the study of marine oil spills Moreover thesimulation results will be helpful for controlling and handlingof accidental oil spills efficiently

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was financially supported by the Opening Foun-dation of Key Laboratory of Marine Spill Oil Identificationand Damage Assessment Technology State Oceanic Admin-istration (SOA)The authors greatly appreciate the assistancefrom Dr Yangyang Li for subject research

References

[1] T M Alves E Kokinou and G Zodiatis ldquoA three-step modelto assess shoreline and offshore susceptibility to oil spills thesouth aegean (crete) as an analogue for confinedmarine basinsrdquoMarine Pollution Bulletin vol 86 no 1-2 pp 443ndash457 2014


[2] T M Alves E Kokinou G Zodiatis R Lardner C Panagio-takis andHRadhakrishnan ldquoModelling of oil spills in confinedmaritime basins the case for early response in the EasternMediterranean Seardquo Environmental Pollution vol 206 articleno 8069 pp 390ndash399 2015

[3] T M Alves E Kokinou G Zodiatis H RadhakrishnanC Panagiotakis and R Lardner ldquoMultidisciplinary oil spillmodeling to protect coastal communities and the environmentof the Eastern Mediterranean Seardquo Scientific Reports vol 6Article ID 36882 2016

[4] H A Espedal and T Wahl ldquoSatellite SAR oil spill detec-tion using wind history informationrdquo International Journal ofRemote Sensing vol 20 no 1 pp 49ndash65 1999

[5] C Brekke and A H S Solberg ldquoOil spill detection by satelliteremote sensingrdquo Remote Sensing of Environment vol 95 no 1pp 1ndash13 2005

[6] J C Dietrich C J Trahan M T Howard et al ldquoSurfacetrajectories of oil transport along the Northern Coastline of theGulf of Mexicordquo Continental Shelf Research vol 41 pp 17ndash472012

[7] H Yang B Hong and S Chen ldquoResearch and applicationprocess of marine oil spill modelsrdquo Transactions of Oceanologyand Limnology vol 2 pp 156ndash163 2007 (Chinese)

[8] X Lou and S G Liu ldquoReview in theory and study of oil spillmodelsrdquo Environmental Science and Management vol 33 no10 article 61 pp 33ndash37 2008 (Chinese)

[9] G Coppini M De Dominicis G Zodiatis et al ldquoHindcastof oil-spill pollution during the Lebanon crisis in the EasternMediterranean July-August 2006rdquo Marine Pollution Bulletinvol 62 no 1 pp 140ndash153 2011

[10] G Zodiatis M De Dominicis L Perivoliotis et al ldquoThemediterranean decision support system for marine safety dedi-cated to oil slicks predictionsrdquoDeep-Sea Research Part II-TopicalStudies in Oceanography vol 133 pp 4ndash20 2016

[11] W J GuoNumerical simulation of oil spill based onPOM DalianUniversity of Technology 2007 (Chinese)

[12] American Society of Civil Engineers ldquoState-of-the-art review ofmodelling transport and fate of oil spillsrdquo Journal of HydraulicEngineering vol 122 no 11 pp 594ndash609 1996

[13] J A Galt G Y Watabayashi D L Payton and J C PetersenldquoTrajectory analysis for the Exxon Valdez hindcast studyrdquo inProceedings of the 1991 Oil Spill Conference vol 1991 pp 629ndash634 Washington DC Wash USA

[14] E Howlett K Jayko and M L Spaulding ldquoInterfacing real-time informationwithOILMAPrdquo in Proceeding of the 16th Arcticand Marine Oil Spill Program Technical Seminar pp 517ndash527Ottawa Canada 1993

[15] M Leech M Walker M Wiltshire et al ldquoOSISmdasha windows-3 oil spill information-systemrdquo in Proceedings of the 16th Arcticand Marine Oil Spill Program (AMOP) Technical Seminar pp549ndash572 Calgary Canada

[16] O M Aamo M Reed and K Downing ldquoOil spill contingencyand response (oscar) model system sensitivity studiesrdquo inProceedings of the 1997 International Oil Spill ConferencemdashImproving Environmental Protection vol 1997 pp 429ndash438 FTLauderdale FL USA

[17] J K Jolliff S Ladner R Crout et al ldquoForecasting the oceanrsquosoptical environment using the BioCast systemrdquo Oceanographyvol 27 no 3 pp 68ndash79 2014

[18] M Skedsmo R Ayasse N Soleng and M Indregard ldquoOilspill detection and response using satellite imagery insight

to technology and regulatory contextrdquo in Proceedings of theSPE International Conference and Exhibition on Health SafetySecurity Environment and Social Responsibility 2016 April 2016

[19] MMarghany ldquoAutomaticDetection ofOil Spill Disasters AlongGulf of Mexico Using RADARSAT-2 SAR Datardquo Journal of theIndian Society of Remote Sensing vol 45 no 3 pp 503ndash511 2017

[20] J K O Gjosteen ldquoOil spreading in cold waters - A modelsuitable for broken icerdquo in Proceedings of the 11th InternationalOffshore and Polar Engineering Conference (ISOPE rsquo01) Sta-vanger Norway 2001

[21] J H Wang and Y M Shen ldquoDevelopment of an integratedmodel system to simulate transport and fate of oil spills in seasrdquoScience China Technological Sciences vol 53 no 9 pp 2423ndash2434 2010

[22] J H Wang and Y M Shen ldquoOil spill simulation system forcomplex terrainrdquo Scientia Sinica (Technologica) vol 40 no 11pp 1367ndash1377 2010 (Chinese)

[23] J Wang and Y Shen ldquoModeling oil spills transportation in seasbased on unstructured grid finite-volume wave-ocean modelrdquoOcean Modelling vol 35 no 4 pp 332ndash344 2010

[24] J-HWang and J-S Zhang ldquoSpecification of turbulent diffusionby random walk method for oil dispersion modelingrdquo AppliedMechanics and Materials vol 212-213 pp 1161ndash1167 2012

[25] M De Dominicis N Pinardi G Zodiatis and R ArchettildquoMEDSLIK-II a Lagrangian marine surface oil spill modelfor short-term forecasting-Part 2 numerical simulations andvalidationsrdquo Geoscientific Model Development vol 6 no 6 pp1871ndash1888 2013

[26] Z Deng T Yu X Jiang et al ldquoBohai Sea oil spill model anumerical case studyrdquoMarine Geophysical Research vol 34 no2 pp 115ndash125 2013

[27] Y Lu X Li Q Tian et al ldquoProgress in marine oil spill opticalremote sensing detected targets spectral response characteris-tics and theoriesrdquoMarine Geodesy vol 36 no 3 pp 334ndash3462013

[28] M De Dominicis S Falchetti F Trotta et al ldquoA relocatableocean model in support of environmental emergenciesrdquo OceanDynamics vol 64 no 5 pp 667ndash688 2014

[29] Y C Zeng J P Yang and C W Yu ldquoMixed Euler-Lagrangeapproach to modeling fiber motion in high speed air flowrdquoApplied Mathematical Modelling vol 29 no 3 pp 253ndash2612005

[30] E Capo A Orfila J M Sayol et al ldquoAssessment of operationalmodels in the Balearic Sea during aMEDESS-4MS experimentrdquoDeep-Sea Research Part II Topical Studies in Oceanography vol133 pp 118ndash131 2016

[31] W Y Tan Computational ShallowWater Dynamics Applicationof Finite Volume Method Tsinghua University Press BeijingChina 1998

[32] Y F Xu Numerical Simulation of Wave and Analysis of Its FlowField Structure [Master Thesis] Harbin Institute of Technology2013

[33] J A Fay The Spread of Oil Slicks on a Calm SeaOil on the SeaSpringer 1969

[34] H M Li Numerical Simulation of the Spread-Diffusion Processof Oil Released from Seabed in Penglai 19-3 Oilfield Area [PhDThesis] Ocean University of China 2013 (Chinese)

[35] L X Huang G X Zhang and Z Z Wan ldquoThe spread of oil inthe seardquo Chinese Journal of Environmental Engineering vol 3no 1 pp 7ndash11 1982


[36] F Yu J Li S Cui Y Zhao Q Feng and G Chen ldquoA hindcastmethod to simulate oil spill trajectories for the Bohai SeaNortheast Chinardquo Ocean Engineering vol 124 pp 363ndash3702016

[37] W Stiver and D MacKay ldquoEvaporation rate of spills of hydro-carbons and petroleum mixturesrdquo Environmental Science ampTechnology vol 18 no 11 pp 834ndash840 1984

[38] H T Shen and P D Yapa ldquoOil slick transport in eiversrdquo Journalof Hydraulic Engineering vol 114 no 5 pp 529ndash543 1988

[39] D A Mackay A Mathematical Model of Oil Spill BehaviourOttawa ontario Canada 1980

[40] D A Mackay and I Buist AMascarenhas R Patersons Oil SpillProcessed and Models Ottawa Ontario Canada 1980

[41] W Q Zhao and Z H Wu ldquoDetermination of the dimension ofan oil film by instantaneous oil slick on the sea surfacerdquo Journalof Chengdu University of Science and Technology vol 41 no 5pp 63ndash72 1988 (Chinese)

[42] RD Ray ldquoA global ocean tidemodel fromTOPEXPOSEIDONaltimetry GOT99 2rdquo Tech Rep 209478 NASA TechnicalMemorandum 1999

[43] TSDIWTE Hydrometry Test Analysis Report of Tourism Con-struction Project in the Western Penglai Coast Tianjin ResearchInstitute for Water Transport Engineering Ministry of Trans-portation 2011

[44] State Standard of the Peoplersquos Republic of China ldquoSpecificationsfor identification system of spilled oils on the sea (GBT 21247-2007)rdquo Tech Rep 21247 Standards Press of China BeijingChina 2007 (Chinese)

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


Stations for diurnal tideStations for tidal level

H1

H2

H3

U1

U8

U7

U6

U5U4

U3

U2

U9

Sang Island

Penglai City

Luanjiakou

Bohai Sea

Huanghai Sea

Miaodao Strait

Daheishan IslandMiaodao Islands

North Changshan Island

South Changshan Island

Artificial Islands

Longitude (E)

Latit

ude (

N)

37∘57

37∘53

37∘49

37∘45

120∘58

120

∘54

120

∘50

120

∘46

120

∘42

120

∘38

120

∘34

120

∘30

120

∘26

Figure 1 Map of the Luanjiakou District near the Port of Yantai and survey stations

and the nowcast-forecast studies of ocean color data streamsin physical circulation models [17] which have promotedthe further development of oil spill models What is moreRadarsat SAR technology is an effective way for marineoil spill detection which can identify and extract oil spillinformation on the sea surface quickly and accurately andprovide remote sensing image to calibrate themodeling resultand improve the forecast precision It is of great significancefor the protection of the marine environment and nearshoreecological environment [18 19]

In recent years there have been breakthroughs in termsof understanding the complex geometry for oil spill modelresearch Gjosteen [20] developed an oil-spreading modelbased on the conservation of volume and momentum whichis suitable for coupling with the discrete-element ice modeland other complex boundaries for oil spreading Dietrichet al [6] applied a coupled SWAN + ADCIRC model on ahigh-resolution computational mesh and the highly efficientLagrangian particle transport model to simulate the surfacetrajectories of the oil spill from the Macondo well northernGulf of Mexico during the spring of 2010 Wang and Shen[21 22] developed a three-dimensional integrated modelthat provides great flexibility for modeling oil spill accidentsin complex geometries such as tidal creeks barriers andislands Currently an unstructured grid is primarily usedto simulate the solid boundary for the study of oil spillsin complex terrains [6 21ndash28] Alves et al [1] proposed athree-step model to predict and assess shoreline and offshoresusceptibility to oil spills for confined basins with islandswhich comprises the leading edge in the study of oil spills incomplex terrains Then Alves et al [2] simulated a series ofoil spill accidents in the Eastern Mediterranean Sea whichincluded confined maritime basins Nevertheless furtherstudies need to be done in the problem of oil particles

penetrating the solid boundary such as a complex multi-island terrain or hydraulic structures

In this study an oil spill simulation method in a multi-island area is presented and the processingmodes for oil slicklongshore transport and its penetration-resistant boundariesare developed In addition a local search method that canspecify the search radius is proposed and adopted Whatis more the Euler-Lagrange method is adopted to trackthe spill location and the position of particles on the edgeof oil slicks which can easily calculate the oil slick areaBased on the Monte Carlo method a mathematical modelfor marine oil spills is established to simulate the movementof oil spills in the Luanjiakou District of the Port of Yantai(Figure 1)

2 Theories and Methods

The Euler-Lagrange systems are divided into two partsthat is Euler and Lagrange approaches The Euler approachdescribes the distributions of the variables in flow field atany time whose computational mesh is fixed in space whilethe Lagrange approach traces each particle from a certaintime and describes its trajectory whose computational meshis fixed on the centroid of the research object and canbe used to simulate the trajectory of an oil slick [29 30]Fundamentally the accuracy of the velocity information forthe hydrodynamic field established by the Eulerian approachhas a crucial role in the successful prediction of the oil spilltrajectory by adopting the Lagrange approach [25] Thusthe coupling approach can give full play to the advantagesof both approaches and avoid their defects which is thereason why it is widely used in solving two-dimensionalhydrodynamic problems by using finite element analysismethod






2V1205971199092 + 1205972V1205971199102)

(2)



120591119909119904 = 0125119862119863119882119909 100381610038161003816100381610038161003816997888rarr119882100381610038161003816100381610038161003816120591119910119904 = 0125119862119863119882119910 100381610038161003816100381610038161003816997888rarr119882100381610038161003816100381610038161003816

(3)


119862119863=


22 Oil Spill Module



1198711 = 1198701 (119892119881Δ)14 11990512 (5)


1198712 = 1198702 [119892 (1 minus Δ) Δ]16 120592minus112119908 1199051411988114 (6)


1198713 = 1198703119892minus1412057512120588minus34119908 11990534 (7)



997888119906 119903 = 119870119888997888rarr119906 119888 + 119870119908997888rarr119906119908 (8)



120597 (119862ℎ)120597119905 + 120597 (119906119862ℎ)120597119909 + 120597 (V119862ℎ)120597119910 = minus (Φ119904 + Φ119887 + 119877) (9)


rarruw

rarru r

rarru c








119883119899 = 119883119899minus1 + 120590radicΔ119905119882119899 (120590 gt 0) (11)





997888rarr119877 119897 = int119905119894+1119905119894

997888rarr119906 119903119889119905 (13)








119865V = ln [1 + (119861119879119866119879) 120579 exp (119860 minus 1198611198790119879)](119879119861119879119866) (16)



Discrete node

Oil slick





119889119865119908119889119905 = 1198621 (119906119908 + 1199060)2 (1 minus 1198622119865119908) 119876 (119905) (17)




Search radius

Search node

Circle center

0 20 40 60 800

20

40

60







(a) (b)


V-spill volume

0

10

20

30

40

50

60

70

Maj

or ax

is sc

ale (

km)

50 100 150 200 250 300 3500Time (h)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(a)

V-spill volume

50 100 150 200 250 300 3500Time (h)

0

5

10

15

20

25

30

35

Min

or ax

is sc

ale (

km)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(b)










(a)

= 004 ms

(b) (c)



Spill volume (m3) 102 103 104 105



Spill volume (m3) 102 103 104 105










MAE = 1119873119873sum119894=1

1003816100381610038161003816120578119898119894 minus 120578119900119894 1003816100381610038161003816


00

0

0

0

3

3

3

3

33

3

6

6

6

6

6

6

666

6

9

9

9

99

999

9

12

12

1212

12

12

12

15

15

15

1515

15

15

15

18

18

18

18

18

18

18

18

18 18

18

21

21

2121

21

21

21

21

21 21

21

24

24

24

2424

24

24

27

27

27

27

27 27

27

27

30

30

30

30

33

33

36

36

393942

260000 280000 300000 320000 340000 3600004160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

036912151821242730333639424548


Dist

ance

(m)

N

E

S

W

(a)

Breakwater

Artificial islands

4160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

Dist

ance

(m)

280000 300000 320000 340000 360000260000Distance (m)

N

E

S

W

(b)


ModeledObserved

H1

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

Tida

l lev

el (c

m)

H2

minus80

minus60

minus40

minus20

0

20

40

60

80

100Ti

dal l

evel

(cm

)

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved

H3

Tida

l lev

el (c

m)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved



ModeledObserved

U1

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10Ve

loci

ty (m

s)

U4

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10

Velo

city

(ms

)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

Velo

city

(ms

)

ModeledObserved


RMSE = radic 1119873119873sum119894=1

(120578119898119894 minus 120578119900119894 )2

BIAS = 1119873119899sum119894=1

(120578119898119894 minus 120578119900119894 ) (18)







ModeledObserved

U1

0

50

100

150

200

250

300

350D

irect

ion

(deg

)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

U4

0

50

100

150

200

250

300

350

Dire

ctio

n (d

eg)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

0

50

100

150

200

250

300

Dire

ctio

n (d

eg)

ModeledObserved


260 270 280 290 300 310 320 330 340 350 3604160

4170

4180

4190

4200

4210

4220

4230

Distance (km)

Dist

ance

(km

)

10 msN

E

S

W

(a)

4160

4170

4180

4190

4200

4210

4220

4230

Dist

ance

(km

)

270 290280 300 310 320 330 340 350 360260Distance (km)

10 msN

E

S

W

(b)




alsurvey

statio

nsform

odelverifi

catio

n

Station

Tidallevel

Station

Flow

velocity

Flow

direction

MAE(cm)

RSME(cm)

BIAS(cm)

MAE(m

s)

RSME(m

s)

BIAS(m

s)

MAE(deg)

RSME(deg)

BIAS(deg)

H1

918

1104

minus811

U1

009

011

006

1283

1763

163

H2

829

1032

minus683

U4

006

008

minus002

1055

1498

minus198

H3

1002

1210

minus913

U7

007

009

minus003

1172

1518

106


PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)








c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420







No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018













2V1205971199092 + 1205972V1205971199102)

(2)



120591119909119904 = 0125119862119863119882119909 100381610038161003816100381610038161003816997888rarr119882100381610038161003816100381610038161003816120591119910119904 = 0125119862119863119882119910 100381610038161003816100381610038161003816997888rarr119882100381610038161003816100381610038161003816

(3)


119862119863=


22 Oil Spill Module



1198711 = 1198701 (119892119881Δ)14 11990512 (5)


1198712 = 1198702 [119892 (1 minus Δ) Δ]16 120592minus112119908 1199051411988114 (6)


1198713 = 1198703119892minus1412057512120588minus34119908 11990534 (7)



997888119906 119903 = 119870119888997888rarr119906 119888 + 119870119908997888rarr119906119908 (8)



120597 (119862ℎ)120597119905 + 120597 (119906119862ℎ)120597119909 + 120597 (V119862ℎ)120597119910 = minus (Φ119904 + Φ119887 + 119877) (9)


rarruw

rarru r

rarru c








119883119899 = 119883119899minus1 + 120590radicΔ119905119882119899 (120590 gt 0) (11)





997888rarr119877 119897 = int119905119894+1119905119894

997888rarr119906 119903119889119905 (13)








119865V = ln [1 + (119861119879119866119879) 120579 exp (119860 minus 1198611198790119879)](119879119861119879119866) (16)



Discrete node

Oil slick





119889119865119908119889119905 = 1198621 (119906119908 + 1199060)2 (1 minus 1198622119865119908) 119876 (119905) (17)




Search radius

Search node

Circle center

0 20 40 60 800

20

40

60







(a) (b)


V-spill volume

0

10

20

30

40

50

60

70

Maj

or ax

is sc

ale (

km)

50 100 150 200 250 300 3500Time (h)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(a)

V-spill volume

50 100 150 200 250 300 3500Time (h)

0

5

10

15

20

25

30

35

Min

or ax

is sc

ale (

km)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(b)










(a)

= 004 ms

(b) (c)



Spill volume (m3) 102 103 104 105



Spill volume (m3) 102 103 104 105










MAE = 1119873119873sum119894=1

1003816100381610038161003816120578119898119894 minus 120578119900119894 1003816100381610038161003816


00

0

0

0

3

3

3

3

33

3

6

6

6

6

6

6

666

6

9

9

9

99

999

9

12

12

1212

12

12

12

15

15

15

1515

15

15

15

18

18

18

18

18

18

18

18

18 18

18

21

21

2121

21

21

21

21

21 21

21

24

24

24

2424

24

24

27

27

27

27

27 27

27

27

30

30

30

30

33

33

36

36

393942

260000 280000 300000 320000 340000 3600004160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

036912151821242730333639424548


Dist

ance

(m)

N

E

S

W

(a)

Breakwater

Artificial islands

4160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

Dist

ance

(m)

280000 300000 320000 340000 360000260000Distance (m)

N

E

S

W

(b)


ModeledObserved

H1

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

Tida

l lev

el (c

m)

H2

minus80

minus60

minus40

minus20

0

20

40

60

80

100Ti

dal l

evel

(cm

)

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved

H3

Tida

l lev

el (c

m)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved



ModeledObserved

U1

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10Ve

loci

ty (m

s)

U4

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10

Velo

city

(ms

)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

Velo

city

(ms

)

ModeledObserved


RMSE = radic 1119873119873sum119894=1

(120578119898119894 minus 120578119900119894 )2

BIAS = 1119873119899sum119894=1

(120578119898119894 minus 120578119900119894 ) (18)







ModeledObserved

U1

0

50

100

150

200

250

300

350D

irect

ion

(deg

)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

U4

0

50

100

150

200

250

300

350

Dire

ctio

n (d

eg)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

0

50

100

150

200

250

300

Dire

ctio

n (d

eg)

ModeledObserved


260 270 280 290 300 310 320 330 340 350 3604160

4170

4180

4190

4200

4210

4220

4230

Distance (km)

Dist

ance

(km

)

10 msN

E

S

W

(a)

4160

4170

4180

4190

4200

4210

4220

4230

Dist

ance

(km

)

270 290280 300 310 320 330 340 350 360260Distance (km)

10 msN

E

S

W

(b)




alsurvey

statio

nsform

odelverifi

catio

n

Station

Tidallevel

Station

Flow

velocity

Flow

direction

MAE(cm)

RSME(cm)

BIAS(cm)

MAE(m

s)

RSME(m

s)

BIAS(m

s)

MAE(deg)

RSME(deg)

BIAS(deg)

H1

918

1104

minus811

U1

009

011

006

1283

1763

163

H2

829

1032

minus683

U4

006

008

minus002

1055

1498

minus198

H3

1002

1210

minus913

U7

007

009

minus003

1172

1518

106


PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)








c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420







No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









rarruw

rarru r

rarru c








119883119899 = 119883119899minus1 + 120590radicΔ119905119882119899 (120590 gt 0) (11)





997888rarr119877 119897 = int119905119894+1119905119894

997888rarr119906 119903119889119905 (13)








119865V = ln [1 + (119861119879119866119879) 120579 exp (119860 minus 1198611198790119879)](119879119861119879119866) (16)



Discrete node

Oil slick





119889119865119908119889119905 = 1198621 (119906119908 + 1199060)2 (1 minus 1198622119865119908) 119876 (119905) (17)




Search radius

Search node

Circle center

0 20 40 60 800

20

40

60







(a) (b)


V-spill volume

0

10

20

30

40

50

60

70

Maj

or ax

is sc

ale (

km)

50 100 150 200 250 300 3500Time (h)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(a)

V-spill volume

50 100 150 200 250 300 3500Time (h)

0

5

10

15

20

25

30

35

Min

or ax

is sc

ale (

km)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(b)










(a)

= 004 ms

(b) (c)



Spill volume (m3) 102 103 104 105



Spill volume (m3) 102 103 104 105










MAE = 1119873119873sum119894=1

1003816100381610038161003816120578119898119894 minus 120578119900119894 1003816100381610038161003816


00

0

0

0

3

3

3

3

33

3

6

6

6

6

6

6

666

6

9

9

9

99

999

9

12

12

1212

12

12

12

15

15

15

1515

15

15

15

18

18

18

18

18

18

18

18

18 18

18

21

21

2121

21

21

21

21

21 21

21

24

24

24

2424

24

24

27

27

27

27

27 27

27

27

30

30

30

30

33

33

36

36

393942

260000 280000 300000 320000 340000 3600004160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

036912151821242730333639424548


Dist

ance

(m)

N

E

S

W

(a)

Breakwater

Artificial islands

4160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

Dist

ance

(m)

280000 300000 320000 340000 360000260000Distance (m)

N

E

S

W

(b)


ModeledObserved

H1

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

Tida

l lev

el (c

m)

H2

minus80

minus60

minus40

minus20

0

20

40

60

80

100Ti

dal l

evel

(cm

)

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved

H3

Tida

l lev

el (c

m)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved



ModeledObserved

U1

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10Ve

loci

ty (m

s)

U4

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10

Velo

city

(ms

)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

Velo

city

(ms

)

ModeledObserved


RMSE = radic 1119873119873sum119894=1

(120578119898119894 minus 120578119900119894 )2

BIAS = 1119873119899sum119894=1

(120578119898119894 minus 120578119900119894 ) (18)







ModeledObserved

U1

0

50

100

150

200

250

300

350D

irect

ion

(deg

)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

U4

0

50

100

150

200

250

300

350

Dire

ctio

n (d

eg)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

0

50

100

150

200

250

300

Dire

ctio

n (d

eg)

ModeledObserved


260 270 280 290 300 310 320 330 340 350 3604160

4170

4180

4190

4200

4210

4220

4230

Distance (km)

Dist

ance

(km

)

10 msN

E

S

W

(a)

4160

4170

4180

4190

4200

4210

4220

4230

Dist

ance

(km

)

270 290280 300 310 320 330 340 350 360260Distance (km)

10 msN

E

S

W

(b)




alsurvey

statio

nsform

odelverifi

catio

n

Station

Tidallevel

Station

Flow

velocity

Flow

direction

MAE(cm)

RSME(cm)

BIAS(cm)

MAE(m

s)

RSME(m

s)

BIAS(m

s)

MAE(deg)

RSME(deg)

BIAS(deg)

H1

918

1104

minus811

U1

009

011

006

1283

1763

163

H2

829

1032

minus683

U4

006

008

minus002

1055

1498

minus198

H3

1002

1210

minus913

U7

007

009

minus003

1172

1518

106


PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)








c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420







No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









Discrete node

Oil slick





119889119865119908119889119905 = 1198621 (119906119908 + 1199060)2 (1 minus 1198622119865119908) 119876 (119905) (17)




Search radius

Search node

Circle center

0 20 40 60 800

20

40

60







(a) (b)


V-spill volume

0

10

20

30

40

50

60

70

Maj

or ax

is sc

ale (

km)

50 100 150 200 250 300 3500Time (h)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(a)

V-spill volume

50 100 150 200 250 300 3500Time (h)

0

5

10

15

20

25

30

35

Min

or ax

is sc

ale (

km)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(b)










(a)

= 004 ms

(b) (c)



Spill volume (m3) 102 103 104 105



Spill volume (m3) 102 103 104 105










MAE = 1119873119873sum119894=1

1003816100381610038161003816120578119898119894 minus 120578119900119894 1003816100381610038161003816


00

0

0

0

3

3

3

3

33

3

6

6

6

6

6

6

666

6

9

9

9

99

999

9

12

12

1212

12

12

12

15

15

15

1515

15

15

15

18

18

18

18

18

18

18

18

18 18

18

21

21

2121

21

21

21

21

21 21

21

24

24

24

2424

24

24

27

27

27

27

27 27

27

27

30

30

30

30

33

33

36

36

393942

260000 280000 300000 320000 340000 3600004160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

036912151821242730333639424548


Dist

ance

(m)

N

E

S

W

(a)

Breakwater

Artificial islands

4160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

Dist

ance

(m)

280000 300000 320000 340000 360000260000Distance (m)

N

E

S

W

(b)


ModeledObserved

H1

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

Tida

l lev

el (c

m)

H2

minus80

minus60

minus40

minus20

0

20

40

60

80

100Ti

dal l

evel

(cm

)

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved

H3

Tida

l lev

el (c

m)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved



ModeledObserved

U1

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10Ve

loci

ty (m

s)

U4

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10

Velo

city

(ms

)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

Velo

city

(ms

)

ModeledObserved


RMSE = radic 1119873119873sum119894=1

(120578119898119894 minus 120578119900119894 )2

BIAS = 1119873119899sum119894=1

(120578119898119894 minus 120578119900119894 ) (18)







ModeledObserved

U1

0

50

100

150

200

250

300

350D

irect

ion

(deg

)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

U4

0

50

100

150

200

250

300

350

Dire

ctio

n (d

eg)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

0

50

100

150

200

250

300

Dire

ctio

n (d

eg)

ModeledObserved


260 270 280 290 300 310 320 330 340 350 3604160

4170

4180

4190

4200

4210

4220

4230

Distance (km)

Dist

ance

(km

)

10 msN

E

S

W

(a)

4160

4170

4180

4190

4200

4210

4220

4230

Dist

ance

(km

)

270 290280 300 310 320 330 340 350 360260Distance (km)

10 msN

E

S

W

(b)




alsurvey

statio

nsform

odelverifi

catio

n

Station

Tidallevel

Station

Flow

velocity

Flow

direction

MAE(cm)

RSME(cm)

BIAS(cm)

MAE(m

s)

RSME(m

s)

BIAS(m

s)

MAE(deg)

RSME(deg)

BIAS(deg)

H1

918

1104

minus811

U1

009

011

006

1283

1763

163

H2

829

1032

minus683

U4

006

008

minus002

1055

1498

minus198

H3

1002

1210

minus913

U7

007

009

minus003

1172

1518

106


PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)








c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420







No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b)


V-spill volume

0

10

20

30

40

50

60

70

Maj

or ax

is sc

ale (

km)

50 100 150 200 250 300 3500Time (h)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(a)

V-spill volume

50 100 150 200 250 300 3500Time (h)

0

5

10

15

20

25

30

35

Min

or ax

is sc

ale (

km)

V = 105Ｇ

3

V = 104Ｇ

3

V = 103Ｇ

3

V = 102Ｇ

3

(b)










(a)

= 004 ms

(b) (c)



Spill volume (m3) 102 103 104 105



Spill volume (m3) 102 103 104 105










MAE = 1119873119873sum119894=1

1003816100381610038161003816120578119898119894 minus 120578119900119894 1003816100381610038161003816


00

0

0

0

3

3

3

3

33

3

6

6

6

6

6

6

666

6

9

9

9

99

999

9

12

12

1212

12

12

12

15

15

15

1515

15

15

15

18

18

18

18

18

18

18

18

18 18

18

21

21

2121

21

21

21

21

21 21

21

24

24

24

2424

24

24

27

27

27

27

27 27

27

27

30

30

30

30

33

33

36

36

393942

260000 280000 300000 320000 340000 3600004160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

036912151821242730333639424548


Dist

ance

(m)

N

E

S

W

(a)

Breakwater

Artificial islands

4160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

Dist

ance

(m)

280000 300000 320000 340000 360000260000Distance (m)

N

E

S

W

(b)


ModeledObserved

H1

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

Tida

l lev

el (c

m)

H2

minus80

minus60

minus40

minus20

0

20

40

60

80

100Ti

dal l

evel

(cm

)

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved

H3

Tida

l lev

el (c

m)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved



ModeledObserved

U1

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10Ve

loci

ty (m

s)

U4

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10

Velo

city

(ms

)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

Velo

city

(ms

)

ModeledObserved


RMSE = radic 1119873119873sum119894=1

(120578119898119894 minus 120578119900119894 )2

BIAS = 1119873119899sum119894=1

(120578119898119894 minus 120578119900119894 ) (18)







ModeledObserved

U1

0

50

100

150

200

250

300

350D

irect

ion

(deg

)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

U4

0

50

100

150

200

250

300

350

Dire

ctio

n (d

eg)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

0

50

100

150

200

250

300

Dire

ctio

n (d

eg)

ModeledObserved


260 270 280 290 300 310 320 330 340 350 3604160

4170

4180

4190

4200

4210

4220

4230

Distance (km)

Dist

ance

(km

)

10 msN

E

S

W

(a)

4160

4170

4180

4190

4200

4210

4220

4230

Dist

ance

(km

)

270 290280 300 310 320 330 340 350 360260Distance (km)

10 msN

E

S

W

(b)




alsurvey

statio

nsform

odelverifi

catio

n

Station

Tidallevel

Station

Flow

velocity

Flow

direction

MAE(cm)

RSME(cm)

BIAS(cm)

MAE(m

s)

RSME(m

s)

BIAS(m

s)

MAE(deg)

RSME(deg)

BIAS(deg)

H1

918

1104

minus811

U1

009

011

006

1283

1763

163

H2

829

1032

minus683

U4

006

008

minus002

1055

1498

minus198

H3

1002

1210

minus913

U7

007

009

minus003

1172

1518

106


PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)








c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420







No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









(a)

= 004 ms

(b) (c)



Spill volume (m3) 102 103 104 105



Spill volume (m3) 102 103 104 105










MAE = 1119873119873sum119894=1

1003816100381610038161003816120578119898119894 minus 120578119900119894 1003816100381610038161003816


00

0

0

0

3

3

3

3

33

3

6

6

6

6

6

6

666

6

9

9

9

99

999

9

12

12

1212

12

12

12

15

15

15

1515

15

15

15

18

18

18

18

18

18

18

18

18 18

18

21

21

2121

21

21

21

21

21 21

21

24

24

24

2424

24

24

27

27

27

27

27 27

27

27

30

30

30

30

33

33

36

36

393942

260000 280000 300000 320000 340000 3600004160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

036912151821242730333639424548


Dist

ance

(m)

N

E

S

W

(a)

Breakwater

Artificial islands

4160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

Dist

ance

(m)

280000 300000 320000 340000 360000260000Distance (m)

N

E

S

W

(b)


ModeledObserved

H1

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

Tida

l lev

el (c

m)

H2

minus80

minus60

minus40

minus20

0

20

40

60

80

100Ti

dal l

evel

(cm

)

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved

H3

Tida

l lev

el (c

m)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved



ModeledObserved

U1

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10Ve

loci

ty (m

s)

U4

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10

Velo

city

(ms

)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

Velo

city

(ms

)

ModeledObserved


RMSE = radic 1119873119873sum119894=1

(120578119898119894 minus 120578119900119894 )2

BIAS = 1119873119899sum119894=1

(120578119898119894 minus 120578119900119894 ) (18)







ModeledObserved

U1

0

50

100

150

200

250

300

350D

irect

ion

(deg

)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

U4

0

50

100

150

200

250

300

350

Dire

ctio

n (d

eg)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

0

50

100

150

200

250

300

Dire

ctio

n (d

eg)

ModeledObserved


260 270 280 290 300 310 320 330 340 350 3604160

4170

4180

4190

4200

4210

4220

4230

Distance (km)

Dist

ance

(km

)

10 msN

E

S

W

(a)

4160

4170

4180

4190

4200

4210

4220

4230

Dist

ance

(km

)

270 290280 300 310 320 330 340 350 360260Distance (km)

10 msN

E

S

W

(b)




alsurvey

statio

nsform

odelverifi

catio

n

Station

Tidallevel

Station

Flow

velocity

Flow

direction

MAE(cm)

RSME(cm)

BIAS(cm)

MAE(m

s)

RSME(m

s)

BIAS(m

s)

MAE(deg)

RSME(deg)

BIAS(deg)

H1

918

1104

minus811

U1

009

011

006

1283

1763

163

H2

829

1032

minus683

U4

006

008

minus002

1055

1498

minus198

H3

1002

1210

minus913

U7

007

009

minus003

1172

1518

106


PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)








c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420







No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









00

0

0

0

3

3

3

3

33

3

6

6

6

6

6

6

666

6

9

9

9

99

999

9

12

12

1212

12

12

12

15

15

15

1515

15

15

15

18

18

18

18

18

18

18

18

18 18

18

21

21

2121

21

21

21

21

21 21

21

24

24

24

2424

24

24

27

27

27

27

27 27

27

27

30

30

30

30

33

33

36

36

393942

260000 280000 300000 320000 340000 3600004160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

036912151821242730333639424548


Dist

ance

(m)

N

E

S

W

(a)

Breakwater

Artificial islands

4160000

4170000

4180000

4190000

4200000

4210000

4220000

4230000

Dist

ance

(m)

280000 300000 320000 340000 360000260000Distance (m)

N

E

S

W

(b)


ModeledObserved

H1

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

Tida

l lev

el (c

m)

H2

minus80

minus60

minus40

minus20

0

20

40

60

80

100Ti

dal l

evel

(cm

)

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved

H3

Tida

l lev

el (c

m)

minus80

minus60

minus40

minus20

0

20

40

60

80

100

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 911Time (h)

ModeledObserved



ModeledObserved

U1

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10Ve

loci

ty (m

s)

U4

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10

Velo

city

(ms

)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

Velo

city

(ms

)

ModeledObserved


RMSE = radic 1119873119873sum119894=1

(120578119898119894 minus 120578119900119894 )2

BIAS = 1119873119899sum119894=1

(120578119898119894 minus 120578119900119894 ) (18)







ModeledObserved

U1

0

50

100

150

200

250

300

350D

irect

ion

(deg

)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

U4

0

50

100

150

200

250

300

350

Dire

ctio

n (d

eg)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

0

50

100

150

200

250

300

Dire

ctio

n (d

eg)

ModeledObserved


260 270 280 290 300 310 320 330 340 350 3604160

4170

4180

4190

4200

4210

4220

4230

Distance (km)

Dist

ance

(km

)

10 msN

E

S

W

(a)

4160

4170

4180

4190

4200

4210

4220

4230

Dist

ance

(km

)

270 290280 300 310 320 330 340 350 360260Distance (km)

10 msN

E

S

W

(b)




alsurvey

statio

nsform

odelverifi

catio

n

Station

Tidallevel

Station

Flow

velocity

Flow

direction

MAE(cm)

RSME(cm)

BIAS(cm)

MAE(m

s)

RSME(m

s)

BIAS(m

s)

MAE(deg)

RSME(deg)

BIAS(deg)

H1

918

1104

minus811

U1

009

011

006

1283

1763

163

H2

829

1032

minus683

U4

006

008

minus002

1055

1498

minus198

H3

1002

1210

minus913

U7

007

009

minus003

1172

1518

106


PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)








c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420







No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









ModeledObserved

U1

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10Ve

loci

ty (m

s)

U4

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

09

10

Velo

city

(ms

)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

00

01

02

03

04

05

06

07

08

Velo

city

(ms

)

ModeledObserved


RMSE = radic 1119873119873sum119894=1

(120578119898119894 minus 120578119900119894 )2

BIAS = 1119873119899sum119894=1

(120578119898119894 minus 120578119900119894 ) (18)







ModeledObserved

U1

0

50

100

150

200

250

300

350D

irect

ion

(deg

)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

U4

0

50

100

150

200

250

300

350

Dire

ctio

n (d

eg)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

0

50

100

150

200

250

300

Dire

ctio

n (d

eg)

ModeledObserved


260 270 280 290 300 310 320 330 340 350 3604160

4170

4180

4190

4200

4210

4220

4230

Distance (km)

Dist

ance

(km

)

10 msN

E

S

W

(a)

4160

4170

4180

4190

4200

4210

4220

4230

Dist

ance

(km

)

270 290280 300 310 320 330 340 350 360260Distance (km)

10 msN

E

S

W

(b)




alsurvey

statio

nsform

odelverifi

catio

n

Station

Tidallevel

Station

Flow

velocity

Flow

direction

MAE(cm)

RSME(cm)

BIAS(cm)

MAE(m

s)

RSME(m

s)

BIAS(m

s)

MAE(deg)

RSME(deg)

BIAS(deg)

H1

918

1104

minus811

U1

009

011

006

1283

1763

163

H2

829

1032

minus683

U4

006

008

minus002

1055

1498

minus198

H3

1002

1210

minus913

U7

007

009

minus003

1172

1518

106


PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)








c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420







No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









ModeledObserved

U1

0

50

100

150

200

250

300

350D

irect

ion

(deg

)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

U4

0

50

100

150

200

250

300

350

Dire

ctio

n (d

eg)

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

ModeledObserved

U7

3 5 7 9 11 13 15 17 19 21 23 25 27 291Time (h)

0

50

100

150

200

250

300

Dire

ctio

n (d

eg)

ModeledObserved


260 270 280 290 300 310 320 330 340 350 3604160

4170

4180

4190

4200

4210

4220

4230

Distance (km)

Dist

ance

(km

)

10 msN

E

S

W

(a)

4160

4170

4180

4190

4200

4210

4220

4230

Dist

ance

(km

)

270 290280 300 310 320 330 340 350 360260Distance (km)

10 msN

E

S

W

(b)




alsurvey

statio

nsform

odelverifi

catio

n

Station

Tidallevel

Station

Flow

velocity

Flow

direction

MAE(cm)

RSME(cm)

BIAS(cm)

MAE(m

s)

RSME(m

s)

BIAS(m

s)

MAE(deg)

RSME(deg)

BIAS(deg)

H1

918

1104

minus811

U1

009

011

006

1283

1763

163

H2

829

1032

minus683

U4

006

008

minus002

1055

1498

minus198

H3

1002

1210

minus913

U7

007

009

minus003

1172

1518

106


PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)








c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420







No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018










alsurvey

statio

nsform

odelverifi

catio

n

Station

Tidallevel

Station

Flow

velocity

Flow

direction

MAE(cm)

RSME(cm)

BIAS(cm)

MAE(m

s)

RSME(m

s)

BIAS(m

s)

MAE(deg)

RSME(deg)

BIAS(deg)

H1

918

1104

minus811

U1

009

011

006

1283

1763

163

H2

829

1032

minus683

U4

006

008

minus002

1055

1498

minus198

H3

1002

1210

minus913

U7

007

009

minus003

1172

1518

106


PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)








c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420







No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(a)

PPB0ndash22ndash6

6ndash9gt9

200 400 600 800

0

400

800

1200

1600

2000

(b)








c = 047

Frequency ()

Wind speed (ms)le54

55~107

108~138

ge139

N

420







No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018











No wind

4180

4185

4190

4195

4200

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

N

E

S

W

(a)

Wind direction SW

4180

4190

4200

4210

Dist

ance

(km

)285 290 295 300 305 310 315280

Distance (km)

Wind speed 49 ms

N

E

S

W

(b)

Wind direction S

4180

4185

4190

4195

4200

4205

Dist

ance

(km

)

285 290 295 300 305 310 315280Distance (km)

Wind speed 20 ms

N

E

S

W

(c)

Wind direction NW

4182

4184

4186

4188

4190

Dist

ance

(km

)

289 291 293 295 297 299287Distance (km)

Wind speed 34 msN

E

S

W

(d)

Wind direction NE

4180

4182

4184

4186

4188

4190

Dist

ance

(km

)

280 285 290 295 300 305 310275Distance (km)

Wind speed 27 msN

E

S

W

(e)



24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









24 h

4180

4185

4190

4195D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

300295290 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)








Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









Dist

ance

(km

)

4185

4190

4195

4200

4205

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W


290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

4180

4185

4190

4195

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W

290 295 300 305 310285Distance (km)



4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









4185

4190

4195

4200D

istan

ce (k

m)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

290 295 300 305 310285Distance (km)

4185

4190

4195

4200

4205

Dist

ance

(km

)

4185

4190

4195

4200

Dist

ance

(km

)

290 295 300 305 310285Distance (km)

24 h12 h

36 h 48 h

N

E

S

W

N

E

S

W

N

E

S

W

N

E

S

W



0

20

40

60

80

100

120

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)

0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)






0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018










0

20

40

60

80

100

120

140A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)

0

10

20

30

40

50

60

70

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)


(b)



0

10

20

30

40

50

60

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

10

20

30

40

50

60

70A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)









0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018










0

02

04

06

08

1

12

14A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6

7

8

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(b)



0

5

10

15

20

25

30

Are

a (kＧ

2)

10 20 30 40 50 600Time (h)

(a)


0

1

2

3

4

5

6A

rea (

kＧ2)

10 20 30 40 50 600Time (h)

(b)






5 Conclusions




10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018










10 20 30 40 50 600Time (h)

001

01

1

10

100

1000

10000Th

ickn

ess o

f oil

slick

[log

(m)]

(a)


10 20 30 40 50 600Time (h)

001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

(b)



10 20 30 40 50 600Time (h)

01

1

10

100

1000

10000

Thic

knes

s of o

il sli

ck [l

og(m

)]

(a)


001

01

1

10

100

Thic

knes

s of o

il sli

ck [l

og(m

)]

10 20 30 40 50 600Time (h)

(b)






000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018









000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(a)

20 40 600Time (h)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]



(b)


20 40 600Time (h)



000001

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

(a)

00001

0001

001

01

1

10

100

1000

10000

100000

Oil

volu

me [

log(Ｇ

3)]

20 40 600Time (h)



(b)






Acknowledgments


References























































Journal of












Journal of







Volume 2018






Volume 2018





























































Journal of












Journal of







Volume 2018






Volume 2018








mathematical modeling of marine oil spills in the...

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