REGIONAL / LOCALWAVE MODELING

María Paula Etala

Naval Hydrographical Service

Naval Meteorological Service

Argentina

HIGH SEAS AND OFF-SHORE FORECASTS

-75 -70 -65 -60 -55 -50 -45 -40-70

-65

-60

-55

-50

-45

-40

-35

-30

zona Fin del Mundo

zona

Patagonia Sur

zona Golfo San Jorge

zona Valdéz

zona El Rincón

zona Mar del Plata

zona Río de la Plata

zona Río Grande

ZONA

OCEANICA zona

Islas

Malvinas

Combination of manual methods for swell propagation

Simple facilities: swell propagation and decay

Significant Wave Height

0 1

2 3

4 5

6 7

8

Hora local

Rawson

C. Rivadavia

Sta. Elena

Building total sea at a point

over time

Wave / Surge Model OperationsH - data

assimilationcycle

H

hincast period forecast period

rest

art

fro

mp

revi

ou

s ru

n

H + forecast period

Data assimilation cycle = analysed wind fields frequency

analysed winds forecasted winds

new

res

tart

Nivel inferior de viento

dU

dt

p

xfV

za

a

a

x 1 1

dV

dt

p

yfU

za

a

a

y 1 1

+ especification

0 and 1er order continuity

Planetary Boundary Layer

Surface Layer Uu

z zz z L( )*

( / )[ln( / ) ]

0

U(z) = A+ Bz

Boundary Layer Wind

Drag coefficient:

u*2 = CD (U)2

Cz

z

D

2

0

2

ln ( )

Iterative Method

Z0 htop

CD

u*

10 - m Wind Dependence of the Drag Coefficient

Field Experiments results vs. this numerical model

0

0.5

1

1.5

2

2.5

3

3 6 9 12 15 18 21 24

U(10) (m/s)

Cd

x10^

3Y&T

S&B

A1

H&R

W

L&P

A2

this approach

S

Conclusions:

This iterative approach is in accordance with field experiments results.

The convenience of using either empirical relationships or the numerical model to retrieve the surface stress over the sea depends on available data.

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0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

20.00

22.00

24.00

Local Effects: Atmospheric stability

Air – sea temperature contrast

General Conditions of Atmospheric Stability

Wind profile in the surface layer Uu

z zz z L( )*

( / )[ln( / ) ]

0

Lu

g wv

v

*' ' '

3

where

+ Businger et al. (1971) parameterization for

Obukhov length

v virtual potential temperature

L > 0 stableL=0 neutralL<0 unstable

Cz

z

D

2

0

2

ln ( )

make

= 0.35 ,

Drag coefficient CD as a function of 10 m wind and temperature

0

0.5

1

1.5

2

2.5

2.5 5 7.5 10 12.5 15 17.5 20

U (10) (m/s)

Cdx

10^3

0

0.5

1

1.5

2

2.5

2.5 5 7.5 10 12.5 15 17.5 20

U (10) (m/s)Cd

x10^

3

Ta-Tw=-6 Ta-Tw=-3 Ta-Tw=0

Ta-Tw=+3 Ta-Tw=+6

Hellerman and Rosenstein (1983)

This model

Atmospheric stability effect on the surface wind stress

Running Numerical ModelsThe approach for input wind / pressure fields

Real Time Data Flow / Operations

Dat

a A

ssim

ilat

ion

Tim

e H H + cut-off H + cut-off + NWP

Data

reception

Data assimilation

+ NWP run

Wave / Surge

Models run Pro

duct

s av

aila

ble

Pro

duct

s av

aila

ble

FTP

Wave / Surge

Models run

Numerical Models for Marine Forecasts

SMARA / WAM WAM ciclo 4.0 (Komen et al., 1994).

Nested versions:

Southeastern South Atlantic

1º x 1º Continental Shelf

1/4º x 1/4º Río de la Plata

1/20º x 1/20º

Depth averaged tide and surge model (Etala, 2000; 1996).

Nested versions:

Continental Shelf :

1/3º x 1/3º Río de la Plata:

1/20º x 1/20º Bahía Blanca

1/180º x 1/120º

Wave Models Storm Surge Models

� Currently, it is accepted that roughness length is a function of wave age (Johnson et al., 1998).

�WAM-4 introduces dependence for Charnock parameter (Janssen, 1989)

� Over the waves,

total surface stress

turbulent surface wind stress wave induced stress

� In classic theory, roughness length over the water is (Charnock, 1955)

zu

gch ch *2

Air – Sea Momentum Exchange

ch

w1

turb w

w

turb

ch Charnock parameter

w

Coupled SystemThe May 2000 Storm

285 290 295 300 305 310 315 320 325 330 335 340-60

-55

-50

-45

-40

-35

-30

0.0m /s

2.5m /s

5.0m /s

7.5m /s

10.0m /s

12.5m /s

15.0m /s

17.5m /s

20.0m /s

22.5m /s

25.0m /s

27.5m /s

30.0m /s

Wind at the lowest sigma level of NCEP reanalisis16 May 2000 12:00 Z.

Isotachs every 2,5 m/s.

Surface Stress in the Storm Surge Model

� decoupled ,

� coupled,

friction velocity u* as calculated by WAM-4.

s =

au

*

2

s a DC W W | |

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-32.00

0 %

1 0 %

2 0 %

3 0 %

4 0 %

5 0 %

6 0 %

7 0 %

8 0 %

9 0 %

1 0 0 %

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Normalized Wave Induced StressTn (%) 16 May 2000 12:00 Z

Normalized Wave Induced StressTn (%) 16 May 2000 12:00 Z

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-36.00

-35.50

-35.00

-34.50

-34.00

Shelf SMARA / WAM Rio de la Plata SMARA / WAM

Normalized Wave Induced Stress Tn (%) and Significant Wave Height Hs(dm)

Normalized Wave Induced Stress Tn (%) and Significant Wave Height Hs(dm)

Off-shore the Uruguay maritime coast

Off-shore the Uruguay maritime coast

0

10

20

30

40

50

60

70

13/05/0012:00

14/05/0012:00

15/05/0012:00

16/05/0012:00

17/05/0012:00

Fecha / Hora

Hs

(dm

)

01020

30405060

708090

Tn

(%

)

Hs Tn

0

5

10

15

20

25

30

35

13/05/0012:00

14/05/0012:00

15/05/0012:00

16/05/0012:00

17/05/0012:00

Fecha / Hora

Hs

(dm

)

01020

30405060

708090

Tn

(%

)

Hs Tn

At the outer Río de la Plata the minimum of Tn is associated to

the maximum wave development.

At the outer Río de la Plata the minimum of Tn is associated to

the maximum wave development.

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-36.00

-34.00

Bahía Samborombón

Rincón de BahíaBlanca

Golfo San Matías

Península de ValdézGolfo Nuevo

Golfo San Jorge

Bahía Grande Islas Malvinas

Estrecho de MagallanesBahía San Sebastián

The Model Bathimetry

The Shelf Sea Tide – Surge Model

The Model Grid

-58.00 -57.50 -57.00 -56.50 -56.00 -55.50 -55.00

-36.00

-35.50

-35.00

-34.50

-3.00m

-2.60m

-2.20m

-1.80m

-1.40m

-1.00m

-0.60m

-0.20m

0.20m

0.60m

1.00m

1.40m

1.80m

2.20m

2.60m

3.00m

COUPLED

Storm Surge Water Level in Río de la Plata

16 May 2000 15Z

Storm Surge Water Level in Río de la Plata

16 May 2000 15Z

-58.00 -57.50 -57.00 -56.50 -56.00 -55.50 -55.00

-36.00

-35.50

-35.00

-34.50

-3.00m

-2.60m

-2.20m

-1.80m

-1.40m

-1.00m

-0.60m

-0.20m

0.20m

0.60m

1.00m

1.40m

1.80m

2.20m

2.60m

3.00m

DECOUPLED

Storm Surge Water Level in Buenos Aires( Inner estuary )

0

0.5

1

1.5

2

2.5

3

3.5

15/05/00

0:00

15/05/00

12:00

16/05/00

0:00

16/05/00

12:00

17/05/00

0:00

17/05/00

12:00

18/05/00

0:00

18/05/00

12:00

niv

el

(m)

observada U10 (no acoplado) Usig (no acoplado)

U10 (acoplado) Usig (acoplado)

Observed water level and modeled values as from 10 - m wind (U10) andlowest sigma level (Usig) of the NCEP reanalyses. Coupled and decoupledruns.

� The wave induced stress acts in the scale of wave development, which is similar to the storm surge scale.� At the initial stage of the event, the wave induced stress may be the same order of the turbulent stress.� The wave induced stress action has direct consequences on the storm surge forecast, BUT ....� The benefit introduced by the coupling may be still of less magnitude than the error introduced by surface wind uncertainty. � The Rio de la Plata is a large estuary where wave growth may be important and this interaction has got enough time to develop its effects.� Depending on local and regional features, the consideration of other types of interactions can be more relevant in determining total water level.

Remarks

STORM SURGE / TIDAL MODEL

A SIMPLE INTERACTIVE SCHEMEA SIMPLE INTERACTIVE SCHEME

ATMOSPHERIC MODEL

WAVE MODEL

surface wind stress

sea level pressure

wave stress

tidal and surge currents water level

total surface stress

The Bahía Blanca estuary

The Model Bathimetry

The Model Grid

M2

Bahia Blanca M2 Tide

PIW - Puerto Ing. White (Canal Principal)

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1 1.5

u (m/s)

v (

m/s

)

APB - Acceso a Pto. Belgrano

-1.5

-1

-0.5

0

0.5

1

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

u (m/s)

v (

m/s

)

BCP - Boca Canal Principal (Torre Ocean.)

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

u (m/s)

v (

m/s

)

IBI - Isla Bermejo Interior

-0.5

0

0.5

1

-0.5 0 0.5

u (m/s)

v (

m/s

)

Modeled hourly currents during 30

days

Du(i,t+t) > dmin flooded grid point

whereDu

(i,t+t) = Hu(i) + (h(i,t+t) + h(i+1,t+t)) / 2

andD(i,t+t) > dmin y D(i+1,t+t) > dmin

orD(i,t+t) > dmin y D(i+1,t+t) dmin pero h(i,t+t) - h(i+1,t+t) >

orD(i,t+t) dmin y D(i+1,t+t) > dmin pero h(i+1,t+t) - h(i,t+t) >

from Flather and Heaps (1975)

Flooding and Drying Algorithm

dmin

h = 0

i i + 1

hh

i + ½i i + 1

hh

i + ½Flooded Point

i i + 1

h h

i + ½

Dry Point

i i + 1

h h

i + ½

h = 0dmin

The Tide / Surge Model Equations

where:H mean water levelh water level perturbation over the meanu,v components of depth averaged currentFs,Gs components of the surface wind stressFB,GB components of the bottom stressp atmospheric pressureD=H+h total water depthr constant water densityR radius of the EarthA horizontal diffusion parameter

h

t+

1

R[

(Du)+

(Dvcos )] = 0

cos

u

t+

u

Rcos

u+

v

R

u-

uvtg

R- fv = -

g

Rcos

h-

1

Rcos

p+

1

D( F - F ) A us B

2

v

t+

u

Rcos

v+

v

R

v+ u

R+ fu =

g

R

h-

1

R

p+

1

D( G - G ) A v

2

s Btg

_ 2

|W|Wc=T sas

|q|qc=T BB

Surface Stress

a = air density

W = surface windcs = drag coefficient

Bottom Stress

q = depth averaged currentcB = drag coefficient

In the scale of the tide ...

Increases or disminishes the storm surge.

Factors affecting the nature of the interaction:

• Large VELOCITIES enhance FRICTION interaction. • Large AMPLITUDES enhance SHALLOW WATER interaction (either for

local permanent factors or transitory astronomical factors)• Small depth enhances both.• Interaction is favoured when the tidal and surge waves travel together for a

long distance.

Tide / Surge Interaction

In the storm surge scale...• Changes the phase of the tidal wave.• It may modify the tidal amplitude if it is close to resonance.• Reverses the frictional interaction effect in the scale of the tidal wave, according to its increasing or decreasing stage.

q

q

D

h ss 2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

1 13 25

hora

nivel (m)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

1 13 25

hora

nivel (m)

-2

-1

0

1

2

3

4

1 13 25

hora

nivel (m)

marea

total

onda de tormenta

V = 5 m/s V = 10 m/s

V = 20 m/s

If friccional interaction prevails.

Constant Wind Simulation (Bahia Blanca Estuary)

¿ Which is the main cause of interaction ?

15/6/97 0:00 Z

Surface Pressure. Isobars every 3 hpa. NCEP 10-m wind. Isotachs every 2,5 m/s.

Case Study: 14 - 15 june 1997

The surge on the shelf

interval 0.20 m

Torre Oceanográfica

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

analizada 1.09 0.17 0.15 0.20 0.17

modelada 1.08 0.16 0.15 0.20 0.16

M2 S2 N2 K1 O1

Torre Oceanográfica

0

50

100

150

200

250

300

350

analizada 233 356 19 85 159

modelada 234 358 16 88 160

M2 S2 N2 K1 O1

Puerto Belgrano

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

analizada 1.44 0.24 0.16 0.22 0.19

modelada 1.43 0.20 0.15 0.22 0.20

M2 S2 N2 K1 O1

Puerto Belgrano

0

50

100

150

200

250

300

350

analizada 259 38 36 98 169

modelada 266 44 31 107 202

M2 S2 N2 K1 O1

Ingeniero White

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

analizada 1.63 0.22 0.13 0.19 0.24

modelada 1.55 0.22 0.14 0.22 0.21

M2 S2 N2 K1 O1

Ingeniero White

0

50

100

150

200

250

300

350

analizada 271 48 43 110 172

modelada 276 59 39 115 215

M2 S2 N2 K1 O1

Tidal Constants in the Bahia Blanca Estuary

Amplitude Phase

Water level at Bahia Falsa. An anticipation of the combined wave with respect to the tide is observed, due to the shallow water interaction.

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

13/6/97 21:0014/6/97 9:0014/6/97 21:0015/6/97 9:0015/6/97 21:00

nivel (m)

total

tide

surge

Shallow water Interaction

0.00

0.50

1.00

1.50

2.00

2.50

13/6/97 21:00 14/6/97 9:00 14/6/97 21:00 15/6/97 9:00 15/6/97 21:00

nivel (m)

Torre Oceanografica

Puerto Belgrano

Ingeniero White

Modeled Storm Surge Water Level at three points along the Main Channel

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

13/6/97 21:00 14/6/97 9:00 14/6/97 21:00 15/6/97 9:00 15/6/97 21:00

nivel (m)

Observado

Modelado (referencia)

Nivel total observado

Observed and Modeled Storm Surge Water Level and Total Water Level

Puerto Belgrano

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

13/6/97 21:00 14/6/97 9:00 14/6/97 21:00 15/6/97 9:00 15/6/97 21:00

nivel (m)

no tideReference run

Puerto Belgrano

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

13/6/97 21:00 14/6/97 9:00 14/6/97 21:00 15/6/97 9:00 15/6/97 21:00

nivel (m)

Total level (lineal)

Total level(combined)

interaction

Effect on water Level

Is the surge / tide interaction responsible for the modulations ?

Frictional Interaction

Analisis of Modeled Currents

Puerto Belgrano

where i = t+s - t - s is interaction on variable

positive sign towards the mouth of the estuary (ebb) negative sign towards the head (flood)

-1.5

-1

-0.5

0

0.5

1

1.5

13/6/97 21:00 14/6/97 9:00 14/6/97 21:00 15/6/97 9:00 15/6/97 21:00

speed (m/s)

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

level (m)

tide

surge, no tide

total combined

interaction

Total level (combined wave)

Ebb Tide

Water Level (m) and Currents 14/6/97 8 Z

Storm Surge

Tidal Wave

Combined Wave

Flood Tide

Water Level (m) and Currents 14/6/97 14 Z

Storm Surge

Tidal Wave

Combined Wave

Water Level (m) and Currents

14/6/97 17 Z

High TideStorm Surge

Tidal Wave

Combined Wave

The Tide and Surge relative Phase

-1

-0.5

0

0.5

1

1.5

14/6/97 9:00 14/6/97 21:00 15/6/97 9:00

intensidad (m/s)

viento horario

t + 2 horas

t - 1 hora

t - 2 hs

Currents produced by the tide / surge interaction when modifying the relative phase of the waves.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

14/6/97 9:00 14/6/97 21:00 15/6/97 9:00

nivel (m)

viento horario

t + 2 hs

t - 1 h

t - 2 hs

Evolution of the surge level near high tide when varying its phase with respect to the tide.

M2 Tidal Constants and Tidal Current Ellipses

Scenario of Strong Tidal CurrentsImplications for waves and surge

M2 Tidal Currents Ellipses __ after Rivas (1997) __ this model

Stations used for tidal model verification

B U E N O S A I R E S

R I O N E G R O

C H U B U T

S A N T A C R U Z

T I E R R A . D E L F U E G O

Verification of Tidal Constants in the Shelf Sea (M2)

0

0.5

1

1.5

2

2.5

3

3.5

4

Punt

a de

l Est

e

San

Clem

ente

Mar

de

Ajó

Pina

mar

Mar

del

Pla

ta

Puer

to Q

uequ

én

Torre

Oce

anog

ráfic

a

San

Blas

San

Anto

nio

Punt

a Co

lora

da

Puer

to M

adry

n

Raws

on

Sant

a El

ena

Com

odor

o Ri

vada

via

Puer

to D

esea

do

San

Juliá

n

Punt

a Qu

illa

Punt

a Lo

yola

San

Seba

stiá

n

Río

Gran

de

Bahí

a Th

etis

Puer

to A

rgen

tino

FS1

AMPLITUD (m)

modelada analizada

-30

0

30

60

90

120

150

180

210

240

270

300

330

360

Punt

a de

l Est

e

San

Clem

ente

Mar

de

Ajó

Pina

mar

Mar

del

Pla

ta

Puer

to Q

uequ

én

Torre

Oce

anog

ráfic

a

San

Blas

San

Anto

nio

Punt

a Co

lora

da

Puer

to M

adry

n

Raws

on

Sant

a El

ena

Com

odor

o Ri

vada

via

Puer

to D

esea

do

San

Juliá

n

Punt

a Qu

illa

Punt

a Lo

yola

San

Seba

stiá

n

Río

Gran

de

Bahí

a Th

etis

Puer

to A

rgen

tino

FS1

FASE (º)

Wave Height Verification Vs. Topex - Poseidon

Wind Speed Verification Vs. Topex - Poseidon

Concluding Remarks

• Local / regional applications main challenge is to be accurate while practicable, that is, to keep in mind the final objective that useful forecasts reach the public in a timely fashion.

• Each developer identifies local or regional fenomena features and consequently chooses the approach and tools that better represent them, always fitting real capabilities for achieving sustained services.

• International cooperation, data and models availability provide a favourable scenario for the development of such applications. At the same time, they provide a frame for local products quality, that forecasters currently know they can obtain.