CALIBRATION OF A TRANSPORT MODEL USING CALIBRATION OF A TRANSPORT MODEL USING DRIFTING BUOYS DEPLOYED DURING THE DRIFTING BUOYS DEPLOYED DURING THE

PRESTIGE ACCIDENTPRESTIGE ACCIDENT

S. CASTANEDO, A.J. ABASCAL, R. MEDINA and I.J. LOSADAS. CASTANEDO, A.J. ABASCAL, R. MEDINA and I.J. LOSADA

1. Introduction1. Introduction

2.2. DataData

3.3. MethodologyMethodology

4. Conclusions4. Conclusions

OUTLINE

1. Introduction1. Introduction

2.2. DataData

3.3. MethodologyMethodology

4. Conclusions4. Conclusions

OUTLINE

1. INTRODUCTION

• Along the Spanish coast several emergency spill response systems were built during the Prestige crisis (UC, AZTI, MeteoGalicia, IMEDEA,...). In these response systems one important task was to establish operational forecasting systems for developing proper response strategies

1. INTRODUCTION

• Generally, the structure of these predictions systems was composed by collection of observations including oil slicks, numerical modelling to provide forecasts of wind, waves, currents and oil trajectories and finally, data management and dissemination.

• The emergency spill response systems were considered to be important tools in addressing the Prestige crisis.

1. INTRODUCTION

- Daily cleaning-up of the beaches- Mechanical recovery from the water surface- Protection of estuaries by means of booms

Delegación del Gobierno en CantabriaConsejería de Medio Ambiente de Cantabria

1. INTRODUCTION

• Now, we can take advantage of the experience acquired during the Prestige accident and develop a Spanish operational oceanographic system (Project ESEOO:www.eseoo.org).

• One of the main objective of the ESEOO transport model is to be used by SASEMAR in sea rescue and response to pollution of marine water.

• The success of the system will be based on the accuracy of the different numerical models involved in trajectory forecasting.

1. INTRODUCTION

The aim of this study is to calibrate a Lagrangian particle-tracking trajectory algorithm and, at the same time, investigate about the relative importance that the different forcing (wind, wave, currents) have on the oil spill fate.

CD=0.02 CD=0.03

1. Introduction1. Introduction

2.2. DataData

3.3. MethodologyMethodology

4. Conclusions4. Conclusions

OUTLINE

2. DATA

WHAT DO WE NEED?WHAT DO WE NEED?

Trajectory Analysis handbook (NOAA)

WHAT DO WE NEED?WHAT DO WE NEED?

2. DATA

FORCINGS: Wind Currents Waves

BUOYS

NUMERICAL MODEL

2. DATA 2.1. Buoys

• Among the decisions made during the management of the Prestige accident, it was proposed to release lagrangian floats to both track the biggest oil slicks position and trajectory and to provide some feedback and/or validation for the numerical models of currents and oil dispersion forecast.

• The deployment of drifting floats was organised by the National Spanish Research Council (CSIC) and AZTI Foundation using available ARGOS buoys used for oceanographic studies (García-Ladona

et al., 2005).

Buoy number

TypeInitial

longitude Initial

latitudeInitial date Last date Owner

16291 PTR -5.868 45.311 15/01/2003 09/02/2003 AZTI

16651 PTR -3.518 44.278 27/12/2002 03/02/2003 AZTI

16735 PTR -6.593 45.175 29/12/2002 16/02/2003 AZTI

16751 SC40 -9.447 42.915 19/12/2002 31/01/2003 CSIC

16752 SC40 -9.356 43.155 19/12/2002 19/01/2003 CSIC

16753 SC40 -9.581 42.969 19/12/2002 30/01/2003 CSIC

16754 SC40 -9.604 42.688 19/12/2002 01/02/2003 CSIC

23249 SC40 -12.046 42.207 16/01/2003 19/02/2003 CSIC

23258 SC40 -9.58 42.662 11/01/2003 19/02/2003 CSIC

23259 SC40 -12.054 42.174 27/01/2003 19/02/2003 CSIC

23282 SC40 -3.350 45.249 02/01/2003 18/02/2003 CSIC

23289 SC40 -4.007 45.575 02/01/2003 18/02/2003 CSIC

23348 SC40 -9.416 42.861 11/01/2003 25/01/2003 CSIC

2. DATA 2.1. Buoys

December 2002 - February 2003

2. DATA 2.1. Buoys

WIND: HIRLAM model (INM) (www.inm.es)

2.2. Wind and wave conditions

2. DATA

Wind at 10 meters above the MSL

x 0.2º x 0.2º (z 22 km)

t 6 hours

Data from re-analysis corresponding to the period November 2002-November 2003

x 0.25 x 0.25º (z 28km)

t 3 hours

WAVE: WAM model (PE) (www.puertos.es)

2.2. Wind and wave conditions

2. DATA

2.3. Currents

2. DATA

CURRENTS 1: NRLPOM model (USA) (http://www.aos.princeton.edu)

CURRENTS 2: MERCATOR model (FR) (http://www.mercator-ocean.fr/)

x z 7 km, t 3 hours

x z 7 km, t 24 hours

FORCING Período FUENTE

WINDRe-analysis data

Nov. 2002 -Nov. 2003HIRLAM

(INM)

WAVEDic. 2002 – Dic. 2003 WAM

(PE)

CURRENTS 1 Dic. 2002 - Dic. 2003NRLPOM

(USA)

CURRENTS 2 Nov. 2002 -Mar. 2003 MERCATOR (FR)

2. DATA

BUOYS Dic. 02 – Feb. 03

2.4. Summary

1. Introduction1. Introduction

2.2. DataData

3.3. MethodologyMethodology

4. Conclusions4. Conclusions

OUTLINE

We want to simulate the buoy trajectory by means of a numerical model: Lagrangian transport model

XXii(t+(t+t) = t) = XXii(t) + (t) + uu(t) (t) t + diffusiont + diffusion

u(t) = ucurrents+ CD* uwind + CW * uwave

CD: wind drag coefficient

CW : wave coefficient

Difussion: (García-Martínez y Flores-Tovar,

1999; Lonin, 1999)

k: diffusion coefficient

3. METHODOLOGY

6k

t

3. METHODOLOGY

US,V CD * UVUwind: Wind-induced current

CD: 3% (Sobey, 1992)

2.5%-4.4% (ASCE, 1996)

Uwave: Wave-induced Stokes drift , 8S H

gHU

C

(Sobey y Barker, 1997)

CW: 0.01- 0.1 (FLTQ, 2003)

3. METHODOLOGY

We need to determine the coefficients CD and Cw in order to obtain the best fit between the numerical result and the observed buoy trajectory

Owing to the great quantity of variables involved in the Owing to the great quantity of variables involved in the problem, aa problem, aa optimization algorithmoptimization algorithm is used in this study is used in this study as a as a preliminary preliminary tooltool

3. METHODOLOGY

1. Coefficients that minimize the error between numerical and actual buoy trajectory: optimization algorithm

PROCEDURE:

2. Introduction of these coefficients in the Lagrangian transport model

3. Analysis of the results/conclusions

3. METHODOLOGY

Global optimization algorithm: SCE-UA (shuffled complex SCE-UA (shuffled complex evolution method – University of Arizona) evolution method – University of Arizona) (Duan et al, 1994)(Duan et al, 1994)

3.1. Automatic calibration

N: number of buoys

UB: actual buoy velocity

UM: numerical buoy velocity (wind, wave and currents)

22

1

( , ) ( , , ) ( , ) ( , , )N

Bx Mx By Myt i

J U t U t U t U t

x x x x

( , , , , )H w w w Ca a

Objective function:Objective function:

The goal of calibration is to find those values for the coefficients that minimize J

f oB

x xU

t

( )

( )

Mx H wavex w windx c currentx

My H wavey w windy c currenty

U t a U a U a U

U t a U a U a U

aH: wave coefficient (Cw)aW: wind coefficient (CD) aC: current coefficient (indication of the error in the numerical current field)

Actual buoy velocity

Numerical buoy velocity

3. METHODOLOGY 3.1. Automatic calibration

3.2. Experiment with all buoys

3. METHODOLOGY

Numero Boya

Fecha inicial

Fecha final

Número de horas

16291 15/01/2003 09/02/2003 107

16651 27/12/2002 03/02/2003 215

16735 29/12/2002 16/02/2003 240

16751 19/12/2002 31/01/2003 234

16752 19/12/2002 19/01/2003 143

16753 19/12/2002 30/01/2003 234

16754 19/12/2002 01/02/2003 235

23249 16/01/2003 19/02/2003 80

23258 11/01/2003 19/02/2003 155

23259 27/01/2003 19/02/2003 33

23282 02/01/2003 18/02/2003 301

23289 02/01/2003 18/02/2003 157

23348 11/01/2003 25/01/2003 45

• Hipothesis:1.- Linear expression of the wind coefficient aW =w + w|uwind|

2.- Swell ( ), 8S H

gHU

C

3.2. Experiment with all buoys

3. METHODOLOGY

Correlation coefficient < 50%

Next step: We need to delimitate the problem

Calibration for each buoy

3.2. Experiment with all buoys

3. METHODOLOGY

Boya aH w w ac Rx Ry

16291 0.10085 0.022426 0.000478 0.10444 0.5818 0.6521

16651 -0.13077 0.026448 0.000384 0.01123 0.6854 0.5972

16735 0.03162 0.020349 0.000845 0.06369 0.5919 0.4331

23249 0.05341 0.031110 0.000769 0.16435 0.4812 0.5012

23258 0.05797 0.024382 -0.000186 0.38309 0.5487 0.4948

23259 -0.16932 0.024124 -0.000371 -0.02391 0.7645 0.4155

23282 0.03702 0.021286 0.000226 0.04080 0.5084 0.2750

23289 0.03398 0.029249 -0.000489 -0.27240 0.4212 0.2726

16751 0.09023 0.025523 -0.000676 0.47468 0.2193 0.1955

16752 0.39433 0.015369 0.000513 0.54086 0.3856 0.2220

16753 0.21031 0.012407 0.000902 0.17193 0.4022 0.4244

16754 0.04053 0.029186 -0.000566 0.46913 0.4392 0.3780

23348 -0.04004 0.018670 -0.000627 0.19433 0.0002 0.1553

3.3. Experiment with each buoy

3. METHODOLOGY

Boya aH w w ac Rx Ry

16291 0.10085 0.022426 0.000478 0.10444 0.5818 0.6521

16651 -0.13077 0.026448 0.000384 0.01123 0.6854 0.5972

16735 0.03162 0.020349 0.000845 0.06369 0.5919 0.4331

23249 0.05341 0.031110 0.000769 0.16435 0.4812 0.5012

23258 0.05797 0.024382 -0.000186 0.38309 0.5487 0.4948

23259 -0.16932 0.024124 -0.000371 -0.02391 0.7645 0.4155

23282 0.03702 0.021286 0.000226 0.04080 0.5084 0.2750

23289 0.03398 0.029249 -0.000489 -0.27240 0.4212 0.2726

16751 0.09023 0.025523 -0.000676 0.47468 0.2193 0.1955

16752 0.39433 0.015369 0.000513 0.54086 0.3856 0.2220

16753 0.21031 0.012407 0.000902 0.17193 0.4022 0.4244

16754 0.04053 0.029186 -0.000566 0.46913 0.4392 0.3780

23348 -0.04004 0.018670 -0.000627 0.19433 0.0002 0.1553

3.3. Experiment with each buoy

3. METHODOLOGY

Boya ac Rx Ry

16291 0.10444 0.5818 0.6521

16651 0.01123 0.6854 0.5972

16735 0.06369 0.5919 0.4331

23249 0.16435 0.4812 0.5012

23258 0.38309 0.5487 0.4948

23259 -0.02391 0.7645 0.4155

Best fit buoys

Small current coefficient

Dominant forcing : wind

3.3. Experiment with each buoy

3. METHODOLOGY

Boya ac Rx Ry

23282 0.04080 0.5084 0.2750

23289 -0.27240 0.4212 0.2726

16751 0.47468 0.2193 0.1955

16752 0.54086 0.3856 0.2220

16753 0.17193 0.4022 0.4244

16754 0.46913 0.4392 0.3780

23348 0.19433 0.0002 0.1553

Worse fit buoys

Dominant forcing : wind and current

3.3. Experiment with each buoy

3. METHODOLOGY

We obtain the best fit when wind is the dominant forcing

When currents are important (continental slope and near

the coast) the agreement between observed and numerical

trajectories is worse

The numerical current field must be improved

3.3. Experiment with each buoy

3. METHODOLOGY

3. METHODOLOGY

PROCEDURE:

1. We select the buoys located outside of the continental slope (mainly affected by wind)

• Hipothesis:In these buoys the effect of the currents is negligible

2. We obtain CD and CW with these outer buoys

3. With all buoys and with CD and CW obtained in 2., the current coefficient is carried out

Numero

BoyaFecha inicial

Fecha finalNúmero de

horas

16291 15/01/2003 20/01/2003 37

16651 14/01/2002 21/01/2003 59

16735 29/12/2002 18/01/2003 100

23282 14/01/2003 18/02/2003 37

23289 01/02/2003 16/01/2003 51

23259 28/01/2003 03/02/2003 31

23289 01/02/2003 16/01/2003 51

3.4. Outer buoys

3. METHODOLOGY

1. We select the buoys located outside of the continental slope (mainly affected by wind)

• Hipothesis:In these buoys the effect of the currents is negligible

2

2

N Bx H wavex w w wind windx

t i iBy H wavey w w wind windy

U a U U UJ

U a U U U

2. We obtain CD and CW with these outer buoys

3.4. Outer buoys

3. METHODOLOGY

( ) M H wave w windU t a U a U

aW =w + w|uwind|

3.4. Outer buoys

3. METHODOLOGY

Current fields

POM MERCATOR

0.0526 (0.0178 0.00079 ) M wind C currentawave windU U + U U U

3.5. Current coefficient

3. METHODOLOGY

3. With all buoys and with CD and CW obtained in 2., the current coefficient is carried out

2 2

0.0526 0.0178 0.00079 0.0526 0.0178 0.00079

N

Bx oleajex viento vientox c corrx By oleajey viento vientoy c corryt i i

J U U U U a U U U U U a U

POM

3.5. Current coefficient

3. METHODOLOGY

MERCATOR

3.5. Current coefficient

3. METHODOLOGY

2 2

0.0526 0.0178 0.00079 0.0526 0.0178 0.00079

N

Bx oleajex viento vientox c corrx By oleajey viento vientoy c corryt i i

J U U U U a U U U U U a U

XXii(t+(t+t) = t) = XXii(t) + (t) + uu(t) (t) t + diffusiont + diffusion

Introduction of the calculated coefficients (CD, Cw, ac) in the Lagrangian transport model

3.6. Lagrangian model

3. METHODOLOGY

u(t) =0.10312* ucurrent +(0.0178+0.000798*| uwind |)* uwind+ 0.0526* uwave

x=7.27 km, y=6.77 km, t=60 s

2

0

1 T

m b mi

RMSE x xT

RMSE: CD, Cw and ac coefficients calculated by the SCE_UA method Numerical simulation with all buoys

3.6. Lagrangian model

3. METHODOLOGY

2

0

1 T

m b mi

RMSE x xT

3.6. Lagrangian model

3. METHODOLOGY

RMSE: CD and Cw coefficients calculated by the SCA_UA method and ac=1 Numerical simulation with all buoys

Period: 15-01-2003 al 23-01-2003

3.6. Lagrangian model

3. METHODOLOGY

Numerical simulation with 5 buoys (3 outside of continental slope)

21

3

4

5

8 days

1

2

3

4

5

48 hour steps

3.6. Lagrangian model

3. METHODOLOGY

FechaRMSEm (km)

Boya 1

RMSEm (km)

Boya 2

RMSEm (km)

Boya 3

RMSEm (km)

Boya 4

RMSEm

(km) Boya 5

15/01/200317/01/2003

30.29 15.49 4.57 4.67 8.20

17/01/200319/01/2003

25.62 16.02 5.47 5.94 2.78

19/01/200321/01/2003

21.73 55.38 12.75 3.17

21/01/200323/01/2003

43.94 49.92 15.27

FechaRMSEm (km)

Boya 1

RMSEm (km)

Boya 2

RMSEm (km)

Boya 3

RMSEm (km)

Boya 4

RMSEm

(km) Boya 5

15/01/200323/01/2003

95.51 83.19 26.31 22.77 19.37

RMSE (48 HOUR STEPS)

RMSE (8 DAYS SIMULATION)

3.6. Lagrangian model

3. METHODOLOGY

FechaRMSEm (km)

Boya 1

RMSEm (km)

Boya 2

RMSEm (km)

Boya 3

RMSEm (km)

Boya 4

RMSEm

(km) Boya 5

15/01/200317/01/2003

30.29 15.49 4.57 4.67 8.20

17/01/200319/01/2003

25.62 16.02 5.47 5.94 2.78

19/01/200321/01/2003

21.73 55.38 12.75 3.17

21/01/200323/01/2003

43.94 49.92 15.27

FechaRMSEm (km)

Boya 1

RMSEm (km)

Boya 2

RMSEm (km)

Boya 3

RMSEm (km)

Boya 4

RMSEm

(km) Boya 5

15/01/200323/01/2003

95.51 83.19 26.31 22.77 19.37

3.6. Lagrangian model

3. METHODOLOGY

RMSE (48 HOUR STEPS)

RMSE (8 DAYS SIMULATION)

FechaRMSEm (km)

Boya 1

RMSEm (km)

Boya 2

RMSEm (km)

Boya 3

RMSEm (km)

Boya 4

RMSEm

(km) Boya 5

15/01/200317/01/2003

30.29 15.49 4.57 4.67 8.20

17/01/200319/01/2003

25.62 16.02 5.47 5.94 2.78

19/01/200321/01/2003

21.73 55.38 12.75 3.17

21/01/200323/01/2003

43.94 49.92 15.27

FechaRMSEm (km)

Boya 1

RMSEm (km)

Boya 2

RMSEm (km)

Boya 3

RMSEm (km)

Boya 4

RMSEm

(km) Boya 5

15/01/200323/01/2003

95.51 83.19 26.31 22.77 19.37

3.6. Lagrangian model

3. METHODOLOGY

RMSE (8 DAYS SIMULATION)

RMSE (48 HOUR STEPS)

1. Introduction1. Introduction

2.2. DataData

3.3. MethodologyMethodology

4. Conclusions4. Conclusions

OUTLINE

A global optimization method (SCE-UA), developed for calibrating A global optimization method (SCE-UA), developed for calibrating

watershed models, has been used in this study. The goal of this watershed models, has been used in this study. The goal of this

method was to find the optimal forcing coefficients to be applied in method was to find the optimal forcing coefficients to be applied in

a numerical transport model. a numerical transport model.

The forcing coefficients that minimize the error between the The forcing coefficients that minimize the error between the

numerical and the observed buoy trayectories were obtained. numerical and the observed buoy trayectories were obtained.

A linear relation between wind velocity and wind drag coefficient A linear relation between wind velocity and wind drag coefficient

was found.was found.

4. CONCLUSIONS

Regarding the wave action, the separation of the sea and swell Regarding the wave action, the separation of the sea and swell

effect on the buoy trajectory provided the best result.effect on the buoy trajectory provided the best result.

We obtained the best solution when the wind was the dominant

forcing.

When it is not possible to neglect the currents (continental slope When it is not possible to neglect the currents (continental slope

and near the coast) the agreement between actual and numerical and near the coast) the agreement between actual and numerical

trajectories was worsetrajectories was worse The numerical current fields were no correct to simulate the buoy The numerical current fields were no correct to simulate the buoy

trajectories. Further research in this area is needed. trajectories. Further research in this area is needed.

4. CONCLUSIONS

CALIBRATION OF A TRANSPORT MODEL USING CALIBRATION OF A TRANSPORT MODEL USING DRIFTING BUOYS DEPLOYED DURING THE DRIFTING BUOYS DEPLOYED DURING THE

PRESTIGE ACCIDENTPRESTIGE ACCIDENT

S. CASTANEDO, A.J. ABASCAL, R. MEDINA and I.J. LOSADAS. CASTANEDO, A.J. ABASCAL, R. MEDINA and I.J. LOSADA