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Sea State Assimilation . Ocean wave forecasting at ECMWF . Sea state assimilation Peter Janssen ECMWF <[email protected]> thanks to: Saleh Abdalla, Jean Bidlot and Hans Hersbach 1 . Ocean wave forecasting at ECMWF . INTRODUCTION Before we discuss the subject of assimilation of satellite observations in an ocean-wave forecasting system, first a brief introduction into the field of surface gravity waves and ocean wave forecasting is given. The programme of my talk is therefore as follows. WAVE FORECASTING The basic evolution equation of the wave spectrum: the energy balance equation Discuss a number of applications, in deterministic and ensemble prediction. ASSIMILATION OF ALTIMETER AND SAR Discuss observation principle, method and impact on analysis 2 . Ocean wave forecasting at ECMWF . USE OF ALTIMETER WINDS AS VALIDATION TOOL Although Altimeter wind speed data are not used in the analysis, they are extremely useful for validation purposes because they are really independent . SCATTEROMETER WIND OBSERVATIONS Obeys same observation principle as the SAR. Discuss the very recent introduction of ASCAT wind observations from Metop. 3 . Ocean wave forecasting at ECMWF . WAVE THEORY z U0(z) a Air(ρa) g x Water(ρw) λ Steepness s = ka =2πa/λ Figure 1: Schematic of the problem in two dimensions. For various reasons forecasting of individual ocean waves is not possible, hence we consider the evolution of average seastate: a spectral description! 4 . Ocean wave forecasting at ECMWF . 5 . Ocean wave forecasting at ECMWF . ENERGY BALANCE EQUATION Therefore concentrate on the prediction of the ensemble average of the action density £¥¤§¦ ¢ © ¡ spectrum ¨ . Action plays the role of a number density and is defined in such a £ ¢ © ¤§¦ way that energy spectrum ¨ is given as £ £ £ © © ¢ © ¢ ¢ ¤§¦ ¤ ¤§¦ ¡ ¨ ¨ which is the usual rule in wave mechanics. From first principles one finds the following evolution equation £ © ¢ ¢ © £ ! $#&% ¤ ¡ ¡ ¡ " ¦ £ £ ( ( ' £ ' ' £ ' ¤ ¤ where , ) , and the source functions represent the physics of wind-wave generation, dissipation by wave breaking and nonlinear four-wave interactions. 6 . Ocean wave forecasting at ECMWF . WAVE FORECASTING The energy balance equation (including nonlinear transfer) is solved by modern wave prediction systems, where the forcing of the waves is provided by surface winds from - +, weather prediction systems. For a large part ( * ) the quality of the wave forecast is determined by the accuracy of the surface wind field. An example of balance of source functions. Example of the forecast of wave height. Example of forecast wave spectra used as boundary condition for Irish limited area model. 7 . Ocean wave forecasting at ECMWF . 150 T = 2h T = 4h T = 8h T = 12h T = 24h 100 /Hz) 2 F(f) (m 50 0 0 0.2 0.4 f (Hz) Evolution in time of the one-dimensional frequency spectrum for a wind speed of . + m/s. 8 . Ocean wave forecasting at ECMWF . 0.010 Sin Snl Sds 0.005 0 S(f) 0.005 0.010 0 0.1 0.2 0.3 0.4 0.5 frequency (Hz) The plot shows the energy balance of wind-generated ocean waves for a duration of 3 hrs, and a wind speed of . + m/s. 9 . Ocean wave forecasting at ECMWF . Ocean wave forecasting at ECMWF is based on WAM cy4. Discuss global implementation only. GLOBAL MODEL (81 deg S to 81 deg N) coupled to atmospheric model [two-way interaction with feedback of ocean waves on ocean surface roughness (since June 29, 1998) thus giving a sea-state dependent momentum and heat flux] Deterministic forecasts : ¢ © / 0 3 1 , 2 ¦ has frequencies and directions 4 3 , runs on an irregular lat-lon grid, km. assimilation of ENVISAT& Jason Altimeter 576 and ENVISAT ASAR spectra. 10 day forecasts from 00Z and 12 Z. 4 8 9 . 2 : : ¨ coupled to 10 m winds from " ATM model every timestep min. 10 . Ocean wave forecasting at ECMWF . Tuesd2a0°yE 14 M40a°Erch 20600°E6 00U80T°EC EC10M0°EWF 1 2F0o°Ereca1s40t° Et+361 6V0°TE : We1d80n° esd1a60y° W15 M14a0°rWch 201200°6W 12U10T0°CW Su8r0fa°Wce: s6i0g°Wnifica4n0t° Wwave2 0h°Weight 10.29 70°N 70°N 9.75 60°N 60°N 50°N 50°N 9 40°N 40°N 8.25 30°N 30°N 7.5 20°N 20°N 6.75 10°N 10°N 6 0° 0° 5.25 10°S 10°S 4.5 20°S 20°S 3.75 30°S 30°S 3 40°S 40°S 2.25 50°S 50°S 1.5 60°S 60°S 0.75 70°S 70°S 0 20°E 40°E 60°E 80°E 100°E 120°E 140°E 160°E 180° 160°W 140°W 120°W 100°W 80°W 60°W 40°W 20°W 11 . Ocean wave forecasting at ECMWF . Sunday 25 January 2004 12UTC ECMWF Forecast t+24 VT: Monday 26 January 2004 12UTC Surface: 2-d wave spectrum EXP: 0001 16.5°W 15°W 13.5°W 12°W 10.5°W 9°W 7.5°W 6°W 4.5°W 3°W 1.5°W 0° 1.5°E 4 2.5 4.5 3 57°N 57°N 2 4 55.5°N 55.5°N 5 1.5 5 54°N 4 54°N 4.5 52.5°N 52.5°N 3 4 3.5 3 51°N 51°N 2 2.5 2.5 49.5°N 49.5°N 48°N SWH [m] 48°N 3 2 2.5 3 3.5 4 4.5 5 16.5°W 15°W 13.5°W 12°W 10.5°W 9°W 7.5°W 6°W 4.5°W 3°W 1.5°W 0° 1.5°E MAGICS 6.7 icarus - waa Mon Jan 26 03:42:49 2004 Bjorn Hansen 12 . Ocean wave forecasting at ECMWF . Probabilistic Forecasts : ;=< ;=< . (50+1) > > 10-day wave ensemble forecasts coupled to the 10 m winds 8 1 : : from the " ATM model. Potential use: Probability of high sea state and Ship Routing. For example, error in forecast ship route may be obtained from the 50 shiproutes generated by the winds and waves of the 50 member ensemble. 13 . Ocean wave forecasting at ECMWF . Brest -> New York 20031215 12 Det. fc. 20031222 00 80°W 60°W 40°W 20°W 0° 70°N 70°N 60°N 60°N 50°N 50°N 40°N 40°N 30°N 30°N 80°W 60°W 40°W 20°W 0° MAGICS 6.8 leda - was Tue Dec 16 01:27:09 2003 14 . Ocean wave forecasting at ECMWF . MAXIMUM WAVE HEIGHT Although wave forecasting is about the mean sea state in a grid box one can also make statements about deviations from the mean: e.g. maximum wave height. Example is the recent extreme event at La Reunion.´ 15 . Ocean wave forecasting at ECMWF . Large swell reaching la Réunion: the m odel A new parameter is being developed. Namely the maximum wave height that can be expected within a certain time window (here 3 hours). It will be introduced in operations soon. New parameter: Maximum wave height on May 12, 18UTC Saint Pierre buoy averaged observed H1/3 model Hs averaged observed Hmax model Hmax (30min) 10 9 8 ) 7 m ( t 6 h g i e 5 h e v 4 a W 3 2 1 0 12/05/2007 12/05/2007 12/05/2007 12/05/2007 13/05/2007 13/05/2007 13/05/2007 13/05/2007 14/05/2007 00:00 06:00 12:00 18:00 00:00 06:00 12:00 18:00 00:00 Slide 16 . Ocean wave forecasting at ECMWF . ALTIMETER DATA MEASUREMENT PRINCIPLE The altimeter is a radar (usually operating at Ku-band) that transmits a pulse towards the sea surface at nadir. Significant wave height is then determined from the slope of the return pulse (the wave form), while wind speed follows from the total backscatter. For a random sea the return pulse also depends on the probability distribution of the ocean waves. In good approximation this is a Gaussian, but nonlinear effects, giving sharper crests and wider throughs, result in a skewed distribution. As a consequence, the waveform is retarded, as illustrated in the next figure, and therefore an Altimeter - 5@6 ? measures a slightly longer Range (of the order of ) than the actual distance between satellite and mean ocean surface. The difference between the two is called the sea-state bias and is directly related to properties of ocean waves such as the mean square slope and wave age (Melville et al, 2004; Kumar et al, 2003). 17 . Ocean wave forecasting at ECMWF . Waveform versus normalised time black: Gaussian; red non−Gaussian 1.5 1.0 W 0.5 0.0 −5.0 −4.0 −3.0 −2.0 −1.0 0.0 1.0 2.0 3.0 4.0 5.0 τ 18 . Ocean wave forecasting at ECMWF . ANALYSIS METHOD Two problems in wave height analysis: 3 1, 2 The wave spectrum has degrees of freedom while we only provide observed information on an integral of the wave spectrum A too many degrees of freedom ! Windsea is strongly coupled to the generating winds, hence a change in wave height implies, to be consistent, a change in local wind. The many degrees of freedom problem is solved by using our knowledge on the evolution of ocean waves. Analysed spectrum is obtained by scaling the first-guess B spectrum, where the scaling constants and C depend on first-guess and observed parameters © ¢ © ¢ 4 B 0 / 0 / 0 ED @FHG C ¦ ¦ ¦ 4 0 where FHG is rotated by an amount if this information is available (e.g.
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