VALIDATION OF A REGIONAL WAVE MODEL WITH ENVISAT AND BUOY OBSERVATIONS

Transcription

1 VALIDATION OF A REGIONAL WAVE MODEL WITH ENVISAT AND BUOY OBSERVATIONS Jian-Guo Li, Martin Holt Met Office, FitzRoy Road, Exeter EX1 3PB, United Kingdom Jian-Guo.Li@metoffice.gov.uk, Martin.Holt@metoffice.gov.uk ABSTRACT A high resolution North Atlantic and European Wave (NAEW) model has been developed in the Met Office. It is framed in a rotated latitude-longitude grid with a space resolution of 12 km and based on the same physics as the Met Office global wave model except for a new 3 rd order positive-definite advection scheme and a new Sub-Range Wave Height (SRWH) output variable. The wind forcing comes from a regional atmospheric model of the same rotated grid and horizontal resolution and spectral boundary conditions from the global wave model. Four buoys and Envisat RA2 and ASAR ocean wave observations are used for model validation and they are in good agreement with the model. 1. INTRODUCTION Ocean wave forecasts are important for marine activities and there is a growing demand for coastal wave forecast due to increased offshore activities and flooding risks. A regional high resolution ocean wave model is recently developed in the Met Office to meet this requirement. It covers the Eastern part of the North Atlantic (East of Newfoundland) and European waters (including the Mediterranean, Black Sea, Baltic and White Sea) and is hence called the North Atlantic and European Wave (NAEW) model. The NAEW wave model is framed on a rotated latitudelongitude grid to avoid high-latitude grid distortion. The model formulation is similar to the Met Office global wave model except for a new 3 rd order positivedefinite advection scheme. Space resolution is about 12 km and spectral resolution is kept as the global wave model with 13 frequency bands and 16 direction bins, which represent waves with a range of periods between 3 and 25 seconds. It is driven by hourly winds at 10 m above mean sea-level from a Met Office atmospheric regional model. Boundary conditions are provided by the Met Office global wave model, which has a space resolution of about 60 km. Two-dimensional (2-D) ocean wave spectra measured by the Advanced Synthetic Aperture Radar (ASAR) and Significant Wave Height (SWH) by the Radar Altimeter (RA2) on board the European Space Agency Envisat satellite are used for validation of the NAEW model. SWHs from 4 UK buoys are also used for model validation. Sub-Range Wave Height (SRWH), defined in a similar way as the SWH but confined to a finite spectral range, is introduced as model output and used for analysis of the model wave spectral performance. 2. NAEW MODEL The Met Office NAEW model is built on the same formulation as used in the Met Office global wave model, which is developed in the 1970 s (Golding 1983) and continuously modified by subsequent development (eg Holt 1994 and Foreman et al. 1994). The formulation is based on the 2-D spectral wave energy balance equation given by E + ( Ecg ) + ( Ec g θ ) = S ( f, θ, t, x, y) (1) t θ where f = wave spectral frequency (Hz); = wave spectral direction (rad); x, y = horizontal space coordinates (m); i x + j y the horizontal gradient operator; t = time (s); E(f,,t,x,y) = wave spectral energy (m 2 Hz -1 rad -1 ); S(f,,t,x,y) = the source term; and c g = wave spectral group velocity (m s -1 ). The refraction term (3rd on l.h.s in Eq. 1) includes the great circle turning as well. The source term consists of an exponential wind sea generation term and a whitecapping dissipation term, similar to those in Tolman and Chalikov (1996). It also includes a parameterized term of the non-linear wave interactions. A new 3 rd order positive-definite advection scheme is used for the advection term (2nd on l.h.s. in Eq. 1). The old advection scheme (Gadd 1978) is not positivedefinite and resets any negative wave energy values to be zero, hence is not energy conservative. The new scheme is a flux-form adaptation of the Takacs (1985) 3 rd order scheme combined with a positive-definite upper-limit (Li 2003), and is conservative and positivedefinite. Comparison has showed that the new scheme is quicker in computation and better in agreement with RA2 and buoy observations than the old scheme. Proc. Envisat Symposium 2007, Montreux, Switzerland April 2007 (ESA SP-636, July 2007)

2 The NAEW model domain is shown in Fig.1. The dashed lines represent the standard latitude and longitude at 5 intervals. The stars indicate the positions of 4 buoys used for the model validation. The model grid is a rotated latitude and longitude grid mesh with the new North Pole located at p = 37.5 N and p = E and the new Equator crossing mid England. The rotated latitude and longitude are related to the standard latitude and longitude by sinψ = cosψ cosψ cosγ + sinψ sinψ cosψ sin λ = cosψ sinγ p where = p The model domain consists of 588x348 grid points with a grid spacing of 0.11 in both rotated latitude and longitude directions. The average grid length is about 12 km. Time step is set to be multiple of 300 s for the advection scheme and 1800 s for other source terms. The NAEW wave model is driven by the hourly averaged surface (10 m) wind fields from an atmospheric model on the same rotated grid in the Met Office unified weather prediction system. The wave energy spectra have 16 directions and 13 frequency bands with their centres between 0.04 and Hz. Boundary conditions are provided by the Met Office global wave model which has the same spectral resolution, but grid spacing at about 60 km. The global model 2D wave spectra are rotated by the same angle as from the rotated north to the standard north directions before interpolated on the NAEW boundary points. Table 1. Sub-ranges used for SRWH integration. SRWH bin Frequency f (Hz) Period T=1/f (s) 1 < > > 0.2 < 5 p (2) 1/12 Hz or wave periods greater than 12 s, that is, H 12 = H s (0, 1/12). Four sub-range bins are used in the NAEW model and their bounds are listed in Tab. 1. The wave spectrum is extended beyond the high-frequency end of the model bands with an inverse fifth power of frequency tail in the last SRWH integration. The wave spectrum below the lowest model frequency band is set to be zero in the first SRWH integration. 3. MODEL VALIDATION Ocean wave data from the Envisat satellite and 4 moored buoys are used for the NAEW model validation. The Envisat satellite data include the SWHs from the Envisat RA2 altimeter and 2D ocean wave spectra from Envisat ASAR level-2 products. The fast delivery Envisat data are retrieved twice a day from the European Space Agency (ESA) ftp site. Model 2D spectra at the nearest grid point and time step to each ASAR entry are saved in model hind-cast run and compared with the ASAR spectra. A few tens of ASAR entries pass the QC filters on average for each 12-hour run. Envisat RA2 SWH is paired with model SWH which is interpolated to the RA2 SWH position and time. Typical half-day Envisat tracks crossing the NAEW domain are illustrated in Fig.1. It contains 4 descending and 1 ascending RA2 tracks and 1 ASAR track. The RA2 data density is high (~ 7 km) so the data points form nearly solid lines. The ASAR points, however, are about 120 km apart and are represented by the isolated + marks. The background colour contours represent the model SWH field at 1200Z model time on 18 March Buoy data are collected once a month. Unfortunately no spectral buoy data are available in this domain so only SWH data from the 4 UK buoys (marked by the stars) are used in this validation study. The SRWH is defined similar to the SWH except that SRWH is integrated over a finite frequency range. The relationship between the SRWH, H s (f 1, f 2 ), and the 2D ocean wave energy spectrum, E(f, ), within a given frequency range from f 1 to f 2 is defined by s ( ) (, ) 4 f2 2π 1 2 = θ (, θ ) f (3) 0 H f f df d E f This definition is similar to the narrow-band wave height used by Voorrips et al. (2001), which has a constant interval of 2 s in wave period. The acronym, SRWH, is chosen because of its resemblance to SWH so its relationship with SWH is reflected by the name. In fact, SWH is equal to SRWH over the whole frequency range, that is, H s (0, ), or simply H s. Besides, the lowfrequency wave height, H12, also used by Voorrips et al. (2001) is equivalent to the SRWH of frequency up to Figure 1. NAEW SWH (1200 hr) with Envisat ASAR (+ symbols) and RA2 (solid line) tracks on 18 March 2007 and 4 UK buoys (stars). Comparison of the RA2 and model SWH along the RA hr track (the longest track in Fig.1) is shown in Fig.2. The model SWH (red) is interpolated within one

3 model grid length (~ 12 km) and output time step (30 min) to the RA2 data point (blue). The plot indicates that the NAEW model SWH is in good agreement with the RA2 observation along this track. The lower panel in Fig.2 compares the model wind speed (red) with the RA2 value (blue). They are in good agreement as well except for wind speed over 21 m s -1, when the RA2 wind speed is no longer valid. The RA2 SWH showed fluctuations in the high wind part, indicating that the data are less reliable than those of moderate wind speed. The NAEW wave model validation runs started in late March 2006 and satellite data comparison commenced later after some initial tuning. It was suspended in December 2006 for technical reasons and restarted in March Eight-month data from April to November 2006 are used here for statistical analysis. Fig.4 shows the SWH scatter plots of model vs. RA2 data during the 8 months with a total number of 432,239 pairs of data. RA2 data affected by rain are excluded using the rainflag in the RA2 data header. Land affected RA2 data are partially filtered out by removing SWH values of 5 m higher than model ones. RA2 data with wind speed greater than 21 m s -1 are also excluded. The model and RA2 mean SWH are very close to 2.13 m and are marked by the large cross in Fig.4. The size of the larger cross represents their standard deviations (SD) and they are 1.34 and 1.30 m, respectively. The rms difference between the model and RA2 SWH is m and their correlation coefficient is 0.880, implying very good agreement between the RA2 and model SWHs. Figure 2. Comparison of Envisat RA2 SWH (upper) and wind speed (lower) with NAE model along the 1203 hr RA2 track on 18 Mar The ASAR may also not work in high wind (> 16 m s -1 ) conditions. This restriction is reflected by the gap in the ASAR track in Fig.1 in the high wind area. ASAR data are also subject to coastal land influence and most ASAR data near coastlines are simply excluded by QC. In fact, not a single ASAR point passed the QC along the Envisat tracks in Fig.1 except the 1203 hr one. Comparison of the model and ASAR SWH along this ASAR track is shown in Fig.3. The model SWH is from the closest model grid and time, which may differ from the ASAR point by 6 km in space and 15 min in time at the most. As shown in Fig.3 the ASAR SWH difference from the model is larger than the RA2 one. Figure 4. Comparison of NAEW model and Envisat RA2 SWH from April to December Figure 3. Comparison of ASAR SWH with NAEW model along one ASAR track on 18 Mar Figure 5. Comparison of model and RA2 wind speed from April to December 2006.

4 The corresponding model and RA2 wind speed at the same points as in Fig.4 are compared in Fig.5. The mean model forcing wind speed (7.03 m s -1 ) is also close to the RA2 mean wind speed (7.15 m s -1 ). Their SD values are 3.54 and 3.66 m s -1, respectively. The rms difference between model and RA2 wind speeds is 1.81 m s -1 and their correlation Note that the RA2 wind speed range is confined between 1.20 and 21.0 m s -1. Model minimum wind speed is 0.5 m s -1. The overall performance of the NAEW model is satisfactory in comparison with the RA2 observations. One reason for the large ASAR difference is due to poor resolution of wind-sea wave spectra by the ASAR instrument, which could not resolve any waves of wavelength shorter than the so called azimuthal cut-off wavelength (about 300 m) in the satellite travelling or azimuthal direction. As a result, the ASAR spectrum is not complete especially when the wind direction is along the satellite travelling direction. Figure 7. Comparison of NAEW and ASAR SWH during April-December Figure 6. Comparison of NAEW model and 4 UK buoys SWH during April to December Buoy wave measurements are also useful for model validation as Bidlot et al. (2002) have demonstrated. Four UK moored buoys (K1-K4) are selected for the NAEW model validation (ref Fig.1). The buoy SWH is at every 6 hours and all the 4 buoys give 6853 entries in total over the 8 months. As shown in the Fig.6, the model mean SWH (2.98 m) is slightly higher than the buoy one (2.87 m) and their SD are very close (1.47 and 1.46 m, respectively). The rms difference is m and correlation 0.915, even better than the RA2 values (0.646 m and 0.880). These results confirm that the NAEW model SWH agrees well with both RA2 and buoy observations. Fig.7 compares the model and ASAR SWH during the same period of April-November 2006, as for the RA2 and buoy comparison. There are 9022 entries of ASAR data selected within the NAEW model domain during the 8 months. The ASAR mean SWH (2.20 m) is lower than the model mean (2.69 m) and their SDs are and 1.18 m, respectively. The rms difference between the ASAR and model SWH (0.992 m) is higher than those of RA2 (0.646 m) and buoys (0.605 m). The ASAR correlation (0.579) is smaller than the RA2 (0.880) and buoy (0.915) ones. The cross-comparison among RA2, buoy and ASAR statistics reveals that ASAR SWH has larger errors than RA2 and buoys ones. This azimuthal cut-off effect is illustrated by the ASAR 2-D spectrum in Fig.8 (left panel). The ASAR 2-D wave spectrum is selected from one of the points along the ASAR track in Fig.1. The middle panel is the model 2-D spectrum at the nearest grid point and time. The radial scale is frequency in Hz, increasing outward logarithmically. The inner (0.04 Hz) and outmost (0.4 Hz) solid circles mark the frequency range of the wave model and the 0.1 Hz dotted circle represents wavelength about 156 m in deep water and may be considered as a guideline for the azimuthal cut-off wave-length. Along the satellite moving direction as indicated by the array in the ASAR spectrum panel, there is no wave energy beyond the 0.1 Hz circle in the ASAR spectrum. While in the model 2-D spectrum wave energy (middle panel) is non-zero in this part. To tackle this missing spectral part, some users simply remove all the spectral energy below the cut-off wavelength for all directions and use the ASAR as swell energy only (Abdella 2006). The obvious drawback of this approach is that the wind-sea resolved by ASAR in the range direction is wasted. Another problem associated with the level 2 ASAR spectrum is its long-wavelength or low-frequency energy (the part close to the 0.04 Hz circle in the ASAR spectrum). The ASAR spectrum usually contains too much energy in this low-frequency end. This is easy to see in the integrated 1-D plot in the right panel where the ASAR spectral density is higher than the model one in the low-frequency end. The erroneously large ASAR

5 long-wave energy has been confirmed by comparing the ASAR spectra with buoy spectra (Li and Holt 2006) and other wave model spectra (Aouf et al 2006). Also note that the ASAR spectral density is lower than the model value in the high-frequency part due to its loss of windsea energy along the azimuthal directions. Figure 8. Comparison of model and ASAR 2-D spectra at one point on 18 March Figure 9. Comparison of 4 SRWH between NAEW model and ASAR wave spectra during April-December The corresponding sub-range in wave period (s) is indicated at the beginning of the title line on each panel. The spectral features of the ASAR wave data can be quantified using the 4-bin SRWH as shown in Fig.9. These are calculated from each wave spectrum used in integration of SWH for Fig.7. The corresponding sub-

6 ranges are indicated by periods T > 16 s, s, 10-5s and T < 5 s, respectively, on the title line of each SRWH panel. As the ASAR azimuthal cut-off wavelength is about 300 m or near 13 s in period, the two SRWHs over period range 10-5 s and < 5 s may be treated as beyond ASAR resolution. The other two SRWHs over s and T > 16 s periods are usually covered by the ASAR. However, only the s ASAR SRWH matches well with the model one with mean values close to 1.3 m for both ASAR and model. The erroneous large long-wave energy in the ASAR spectrum has rendered the first SRWH for period > 16 s un-reliable. So it is not a surprise that the s SRWH shows the best agreement between model and ASAR among the 4 SRWHs in Fig.9 with the highest correlation of The first ASAR SRWH has a mean value of m, over 2 times large as the model one (0.263 m). The last two ASAR mean SRWHs (1.49 and m) are lower than the corresponding model values (1.95 and 1.04 m), indicating that model spectra have more wind-sea energy than ASAR spectra. Because of these spectral restrictions, Envisat ASAR 2-D spectra could not completely fulfill the model spectral validation. Other 2-D spectral observations are required to take this job forward. Unfortunately, there are no alternative 2-D wave spectra available in the NAEW model domain. 4. CONCLUSIONS A high-resolution ocean wave (NAEW) model has been developed in the Met Office. The model has similar formulations as the Met Office global wave model except that it is framed on a rotated grid and uses a new 3 rd order positive-definite advection scheme. The NAEW model is validated with buoys and Envisat RA2 and ASAR wave observations over 8 months from April to December Comparison results indicate that the wave model generally performs well and its total wave energy or SWH is in good agreement with RA2 and buoy values. Partial wave energy or SRWH is also in good agreement with ASAR ones within the valid ASAR spectral ranges. Differences between the model and ASAR 2-D spectra are relatively larger towards the low- and highfrequency ends than in the central part. The underestimation of high-frequency wave energy by the ASAR is the result of a technical restriction (azimuthal cut-off) of the ASAR instrument. The large ASAR energy in the low-frequency end is probably erroneous and requires further examinations. Other independent 2-D ocean wave spectra are needed for validations of both the NAEW model and the ASAR wave product. 5. REFERENCES Abdalla, S. 2006: Global validation of ENVISAT wind, wave and water products from RA-2, MWR, ASAR and MERIS. ECMWF, ESA Contract Report, 75pp. Aouf, L., Lefevre, J. M., Hauser, D., Chapron, B. and Collard, G. 2006: The impact of using the upgrade processing of ASAR level 2 wave products in the assimilation system. Proc. of SEASAR 2006 Workshop, ESA-ESRIN, Frascati, Italy, Jan 2006, 6pp. Bidlot, J. R., Holmes, D. J., Wittmann, P. A., Lalbeharry, R and Chen, H. S. 2002: Intercomparison of the performance of operational ocean wave forecasting systems with buoy data. Weather and Forecasting, 17, Foreman, S. J., Holt, M. W. and Kelsall, S. 1994: Preliminary assessment and use of ERS-1 altimeter wave data, J. Atmos. Oceanic Techn., 11, Gadd, A. J. 1978: A numerical advection scheme with small phase speed errors. Q. J. R. Meteor. Soc., 104, Golding, B. W. 1983: A wave prediction system for real-time sea state forecasting. Q J Roy Met Soc, 109, Holt, M. 1994: Improvement to UKMO wave model swell dissipation and performance in light winds. Met Office Forecasting Research Division Tech. Rep. 119, 12pp. Li, J. G. 2003: A multiple-cell flat-level model for atmospheric tracer dispersion over complex terrain. Boundary-Layer Meteor., 107, Li, J. G. and Holt, M. 2006: Comparison of ENVISAT ASAR ocean wave spectra with buoys and altimeter observations via a wave model. Proceedings of SEASAR 2006 Workshop, ESA- ESRIN, Frascati, Italy, Jan 2006, 6 pp. Takacs, L. L. 1985: A two-step scheme for the advection equation with minimised dissipation and dispersion errors. Mon. Wea. Rev., 113, Tolman, H. L. and Chalikov, D. 1996: Source terms in a third-generation wind-wave model. J. Phys. Oceanography, 26, Voorrips, A. C., Mastenbroek, C. and Hansen, B. 2001: Validation of two algorithms to retrieve ocean wave spectra from ERS synthetic aperture radar. J. Geophys. Res., 106, C8, WAMDI group 1988: The WAM model - a third generation ocean wave prediction model. J. Phys. Oceanogr. 18,