REGIONAL / LOCAL WAVE MODELING

1. REGIONAL / LOCALWAVE MODELING María Paula Etala Naval Hydrographical Service Naval Meteorological Service Argentina

2. zona Río Grande zona Río de la Plata zona Mar del Plata zona El Rincón zona Valdéz ZONA OCEANICA zona Golfo San Jorge zona Patagonia Sur zona Islas Malvinas zona Fin del Mundo HIGH SEAS AND OFF-SHORE FORECASTS

3. Combination of manual methods for swell propagation

4. Simple facilities: swell propagation and decay

5. Significant Wave Height 8 7 6 5 Rawson 4 C. Rivadavia 3 Sta. Elena 2 1 0 Hora local Building total sea at a point over time

7. Wave / Surge Model Operations H + forecast period H H - data assimilation cycle restart from previous run new restart hincast period forecast period analysed winds forecasted winds Data assimilation cycle = analysed wind fields frequency

8. Planetary Boundary Layer + t especification U(z) = A+ Bz 0 and 1er order continuity Surface Layer Boundary Layer Wind Nivel inferior de viento Drag coefficient: u*2 = CD (DU)2 Iterative Method Z0 htop CD u*

9. 3 2.5 Y&T S&B 2 A1 H&R 1.5 W Cdx10^3 L&P A2 1 this approach S 0.5 0 3 6 9 12 15 18 21 24 U(10) (m/s) 10 - m Wind Dependence of the Drag Coefficient Field Experiments results vs. this numerical model 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.

10. -34.00 -36.00 24.00 -38.00 22.00 20.00 -40.00 18.00 16.00 -42.00 14.00 -44.00 12.00 10.00 -46.00 8.00 6.00 -48.00 4.00 2.00 -50.00 0.00 -52.00 -54.00 -68.00 -66.00 -64.00 -62.00 -60.00 -58.00 -56.00 -54.00 -52.00 Local Effects: Atmospheric stability Air – sea temperature contrast

11. General Conditions of Atmospheric Stability Wind profile in the surface layer where Obukhov length virtual potential temperature make

12. Hellerman and Rosenstein (1983) This model Atmospheric stability effect on the surface wind stress Drag coefficient CD as a function of 10 m wind and temperature

13. H H + cut-off H + cut-off+ NWP Products available Data reception Data assimilation + NWP run Wave / Surge Models run Data Assimilation Time Wave / Surge Models run Products available FTP Running Numerical ModelsThe approach for input wind / pressure fields Real Time Data Flow / Operations

14. Wave Models Storm Surge Models • 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 Numerical Models for Marine Forecasts

15. a Charnock parameter ch Air – Sea Momentum Exchange • Over the waves, • totalsurfacestress • turbulentsurface wind stresswave induced stress • In classic theory, roughness length over the water is (Charnock, 1955) • 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)

16. Coupled System The May 2000 Storm Wind at the lowest sigma level of NCEP reanalisis 16 May 2000 12:00 Z. Isotachs every 2,5 m/s.

17. decoupled , • coupled, • friction velocity u* as calculated by WAM-4. 2 = u t r s a * Surface Stress in the Storm Surge Model

18. Normalized Wave Induced Stress Tn (%) 16 May 2000 12:00 Z Shelf SMARA / WAM Rio de la Plata SMARA / WAM

19. Normalized Wave Induced Stress Tn (%) and Significant Wave Height Hs(dm) At the outer Río de la Plata the minimum of Tn is associated to the maximum wave development. Off-shore the Uruguay maritime coast

20. The Shelf Sea Tide – Surge Model The Model Bathimetry The Model Grid

21. COUPLED DECOUPLED Storm Surge Water Level in Río de la Plata 16 May 2000 15Z

22. 3.5 3 2.5 2 nivel (m) 1.5 1 0.5 0 15/05/00 15/05/00 16/05/00 16/05/00 17/05/00 17/05/00 18/05/00 18/05/00 0:00 12:00 0:00 12:00 0:00 12:00 0:00 12:00 observada U10 (no acoplado) Usig (no acoplado) U10 (acoplado) Usig (acoplado) Observed water level and modeled values as from 10 - m wind (U10) and lowest sigma level (Usig) of the NCEP reanalyses. Coupled and decoupled runs. Storm Surge Water Level in Buenos Aires( Inner estuary )

23. Remarks • 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.

24. ATMOSPHERIC MODEL WAVE MODEL A SIMPLE INTERACTIVE SCHEME surface wind stress sea level pressure wave stress total surface stress STORM SURGE / TIDAL MODEL tidal and surge currents water level

25. The Bahía Blanca estuary

26. The Model Grid The Model Bathimetry

27. M2 Bahia Blanca M2 Tide

28. Modeled hourly currents during 30 days

29. i + ½ i + 1 i h h Flooding and Drying Algorithm • Du(i,t+Dt) > dmin flooded grid point • where • Du(i,t+Dt) = Hu(i) + (h(i,t+Dt) + h(i+1,t+Dt)) / 2 • and • D(i,t+Dt) > dmin y D(i+1,t+Dt) > dmin • or • D(i,t+Dt) > dmin y D(i+1,t+Dt)£ dmin pero h(i,t+Dt) - h(i+1,t+Dt) > e • or • D(i,t+Dt)£ dmin y D(i+1,t+Dt) > dmin pero h(i+1,t+Dt) - h(i,t+Dt)> e • from Flather and Heaps (1975) Flooded Point i + ½ i + 1 i h = 0 h h dmin Dry Point i + ½ i + 1 i + ½ i + 1 i i h = 0 h h h h dmin

30. The Tide / Surge Model Equations where: H mean water level h water level perturbation over the mean u,v components of depth averaged current Fs,Gs components of the surface wind stress FB,GB components of the bottom stress p atmospheric pressure D=H+h total water depth r constant water density R radius of the Earth A horizontal diffusion parameter

31. Surface Stress ra = air density W = surface wind cs = drag coefficient Bottom Stress q = depth averaged current cB = drag coefficient

32. 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. 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.

33. ¿ Which is the main cause of interaction ? If friccional interaction prevails. Constant Wind Simulation (Bahia Blanca Estuary) V = 5 m/s V = 10 m/s V = 20 m/s

34. Surface Pressure. Isobars every 3 hpa. NCEP 10-m wind. Isotachs every 2,5 m/s. Case Study: 14 - 15 june 1997 15/6/97 0:00 Z

35. The surge on the shelf interval 0.20 m

36. Tidal Constants in the Bahia Blanca Estuary Amplitude Phase

37. Shallow water Interaction nivel (m) 3 2.5 2 1.5 total 1 tide 0.5 surge 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 Water level at Bahia Falsa. An anticipation of the combined wave with respect to the tide is observed, due to the shallow water interaction.

38. Modeled Storm Surge Water Level at three points along the Main Channel Observed and Modeled Storm Surge Water Level and Total Water Level Puerto Belgrano

39. Is the surge / tide interaction responsible for the modulations ? nivel (m) 1.8 1.6 1.4 1.2 no tide 1 Reference run 0.8 0.6 0.4 0.2 0 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) 3.00 2.50 2.00 1.50 Total level(lineal) 1.00 Total level(combined) 0.50 interaction 0.00 -0.50 -1.00 -1.50 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 Puerto Belgrano Frictional Interaction Effect on water Level

40. speed (m/s) level (m) 1.5 3.00 2.50 1 2.00 tide 1.50 0.5 surge, no tide 1.00 0 0.50 total combined 0.00 interaction -0.5 -0.50 Total level (combined wave) -1.00 -1 -1.50 -1.5 -2.00 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 Analisis of Modeled Currents Puerto Belgrano where Fi = Ft+s - Ft - Fs is interaction on variable F positive sign towards the mouth of the estuary (ebb) negative sign towards the head (flood)

41. Storm Surge Ebb Tide Water Level (m) and Currents 14/6/97 8 Z Tidal Wave Combined Wave

42. Storm Surge Flood Tide Water Level (m) and Currents 14/6/97 14 Z Tidal Wave Combined Wave

43. Storm Surge High Tide Water Level (m) and Currents 14/6/97 17 Z Tidal Wave Combined Wave

44. The Tide and Surge relative Phase Currents produced by the tide / surge interaction when modifying the relative phase of the waves. Evolution of the surge level near high tide when varying its phase with respect to the tide.

45. Scenario of Strong Tidal CurrentsImplications for waves and surge M2 Tidal Constants and Tidal Current Ellipses

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

47. Stations used for tidal model verification

48. Verification of Tidal Constants in the Shelf Sea (M2)

49. Wave Height Verification Vs. Topex - Poseidon

50. Wind Speed Verification Vs. Topex - Poseidon