COMPARISON OF THE MET OFFICE GLOBAL SPECTRAL WAVE MODEL WITH ENVISAT SATELLITE AND BUOY OBSERVATIONS

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1 COMPARISON OF THE MET OFFICE GLOBAL SPECTRAL WAVE MODEL WITH ENVISAT SATELLITE AND BUOY OBSERVATIONS Jian-Guo Li, Martin Holt Met Office, FitzRoy Road, Exeter, EX1 3PB, UK Jian-Guo.Li / Martin.Holt@metoffice.gov.uk ABSTRACT The Met Office routinely runs a global spectral wave model providing analyses and forecasts of sea state on a grid spacing of approximately 60 km. The modelled two-dimensional wave energy spectra are compared with the Advanced Synthetic Aperture Radar (ASAR) Envisat satellite observations on a daily basis. Comparisons are also made with frequency ocean wave energy spectra observed by a moored buoy near Christmas Island (0.02S W) and with the wave height observed by the radar altimeter RA2 onboard the same satellite Envisat as the ASAR instrument. Comparison results indicate that Envisat ASAR level 2 energy spectra are systematically higher than the modelled spectra in the long periods (>16 s) or low frequency parts. There is a better agreement in the mid-periods of about 8-16 s for the integrated 1-D spectra. The variation of ASAR wave energy spectra is much larger than that of the modelled spectra. Comparison of the wave model and buoy 1-D wave spectra shows that the model spectra are in much better agreement with the buoy wave spectra than with the ASAR spectra. It also revealed that both the buoy and model spectra have similar variability while the ASAR spectra variations are much larger than them. The integrated model significant wave heights are also in good agreement with the along track RA2 altimeter data. 1. INTRODUCTION The Met Office runs a 2nd generation spectral wave model based on the wave model first developed by Golding [1] and continuously modified by subsequent development [2]. The operational global wave model provides analyses and forecasts of sea state on grid spacing of approximately 60 km, and nested regional models have resolution of 12 km. As standard the models operate with a spectral resolution of 13 frequency bins and 16 directional bins, which resolves waves with a range of periods between 25 and 3 seconds (deep-water wavelengths from about 10 to 1000 m). The wave model is forced by the wind field at 10m above mean sea-level generated in the Met Office atmospheric models, which include observations from satellite, ship and data buoy networks in their assimilation schemes. Based on the local wind speed and direction, energy is input to the waves through a parameterisation of the exponential growth of existing windsea energy. Parameterizations of the windsea spectral peakedness and peak frequency are used to select an appropriate member of the JONSWAP family of spectra to describe the growing wind-sea spectral distribution, and a cosine squared distribution about the mean windsea direction is applied. The frequency dependent rate of turn of wave energy responding to turning winds is also parameterised. As the waves grow, a balance is reached between the input, nonlinear transfer and dissipation parameterisations, ensuring that for a given wind speed, with sufficient fetch and duration, the limiting Pierson Moskowitz spectrum is reached. The general performance of this wave model is comparable to other operational wave models [3], such as the 3 rd generation WAM model [4]. The Advanced Synthetic Aperture Radar (ASAR) on board the European Space Agency (ESA) Envisat satellite is one of a few instruments which can measure the directional characteristics of the ocean wave field on a global scale and could be a very useful resource for ocean wave models [5]. Assessment of the ASAR data quality is, however, difficult due to lack of independent observations of similar temporal and spatial scales. The ocean wave heights measured by the radar altimeter instrument (RA2) onboard the same satellite as the ASAR can only be used for partial validation of the ASAR data as they do not have any spectral and directional information. Moored ocean data buoys are another independent observation and some of them offer wave spectral and directional information [6] though their spatial coverage is very limited. The major aim of this paper is for assessment of the Envisat ASAR level 2 ocean wave energy spectral products by comparisons with the Met Office wave model energy spectra and other independent observations. The Envisat ASAR level 2 products we used are the ASA_WVW_2P data set, obtained twice a day from the ESA ftp site. We also retrieve the Envisat RA2 altimeter ocean wave heights at the same time. Other observations we used are the moored buoy wave Proc. of the 2004 Envisat & ERS Symposium, Salzburg, Austria 6-10 September 2004 (ESA SP-572, April 2005)

2 energy spectra from the (American) National Data Buoy Center (NDBC) web site ( Currently we selected 11 buoys which measure hourly averaged wave energy spectra for comparison with the wave model. But only one near the Christmas Island (Buoy ID at 0.02 S W as indicated in Fig.1) is used in this comparison work. The reason for selecting this buoy is that it is located in the middle of ocean where the wave model is under less influence of coastal effects (reflections, shallow water, tide, etc) than the other buoy sites. Both the ASAR and model output are two-dimensional (2-D) wave energy spectra, which are integrated for comparison with the altimeter wave heights or the buoy one-dimensional wave energy spectra. The relationship between the 2-D ocean wave energy spectrum E(f, ) (here f is the frequency and is the direction) and the significant wave height (SWH) in a given frequency range (f 1, f 2 ) is defined by f2 ( ) = ( ) H s f2 f1 4 df E f (1) f1 where E(f) is the one-dimensional (1-D) spectrum, defined by 2π ( ) = θ (, θ ) E f d E f (2) 0 The total SWH, denoted as H s, is then equal H 0. Instead of frequency, we also use the to ( ) s wave period T, which is the reciprocal of the given frequency, T=1/f. Apart from the comparison of total SWH as in other validation study [3], we also calculate the SWH in 4 frequency sub-ranges for comparison. This spectral breakdown of ocean wave energy shed some light on the spectral characteristics of the wave model and the observations. The boundaries of these 4 spectral bins (4-bin) at periods of second are approximately 23, 16, 11, 8, 5 s. Envisat satellite tracks are extracted from the ASAR data set twice a day and a typical half day track plot is showed in Fig.1. The colour background is the model SWH at 0600 hr on the chosen day (15 June 2004) and the red asterisk symbols indicate where the ASAR 2-D wave energy spectra are available. The model 2-D wave energy spectra at (grid point closest to) the Envisat data sites are saved from hindcast runs in half hour time steps. These model data are then used for comparison with the ASAR observations. Two-D energy spectra at selected buoy sites are also saved in the hindcast runs along with global SWHs for RA2 altimeter comparison. Fig.1 Global significant wave weights from the Met Office ocean model and overlaying Envisat tracks on 15 June The buoy (ID 51028) site is indicated by the yellow spot and text CI. 2. COMPARISION OF SWHs 2.1 Comparison with buoy SWHs Measured ocean wave energy spectra from the moored CI buoy at 0.02 S W over the first 6 month of 2004 are used for this comparison. A total of 3447 hourly wave energy spectra from the buoy are collated with the model wave energy spectra. These wave energy spectra are integrated over all frequencies and over the 4 sub-ranges to produce total and 4-bin SWHs, respectively. Fig.2a is a scatter plot of the model and buoy total SWHs. Each pair of model and buoy SWHs are plotted as a point in the diagram with its x- coordinate equal to the buoy SWH and the y- coordinate to be the model SWH. The contours indicate the data density and the diagonal line runs through the perfect matching positions. The large plus sign marks the model and buoy mean SWHs and its width and height indicate the standard deviations of buoy and model SWHs, respectively. As shown in Fig.2a, the mean value of the modelled total SWHs (2.17 m) at the buoy site is slightly higher than the average of the buoy measured SWHs (2.01 m) over the first 6 months of The standard deviations (SDs) for the model and buoy SWH are 0.32 m and 0.27 m, respectively. The SD or root-mean-square (rms) of the model and buoy SWH difference is 0.37 m. These results are comparable to those of another validation work [3]. Fig.2b shows the comparison of model and buoy s 4- bin SWHs. The wave model slightly overestimated the wave energy in the period range of s as indicated by top-right plot in Fig.1b. The model and buoy mean SWHs are 1.15 and 0.83 m, respectively. Model SD (0.36 m) is also higher than the buoy SD (0.29 m) in this sub-range. The rms value of the subrange SWH difference is 0.33 m. In the other 3 subranges, the modelled SWHs are in general agreement with the buoy observations as showed in Fig.2b. The statistics of the buoy and model comparison in these

3 sub-ranges are listed in Table 1 and they will be discussed further in next section when compared with the ASAR spectral performance. as indicated in Fig.3a. The ASAR mean SWH (2.08 m) is quite close to the model mean (2.09 m) but the SD is much larger in the ASAR data (1.30 m) than in the modelled SWHs (0.37 m), which have similar variations as the modelled SWHs at the buoy site in Fig.2a (SD of 0.32 m). The rms of model and ASAR SWH difference is 1.34 m, much larger than the rms for the buoy (0.37 m). Fig.2a Comparison of buoy (51028) and wave model total SWH over the first 6 months of Fig.3a Comparison of model and ASAR total SWHs within 15 latitude and longitude from CI at 0.02 S W in June Fig.2b Comparison of buoy (51028) and wave model 4-bin SWH over the fist 6 months of Comparison with ASAR SWHs For comparison of the wave model with the Envisat ASAR level 2 ocean wave energy spectra, a sub-set of ASAR 2-D spectra within 15 degree latitude and longitude distance from the CI buoy site (0.02 S W) in June 2004 are first selected to calculate the total and 4-bin SWHs in a similar way to those for the buoy comparison in the previous section. This will allow an indirect comparison of the Envisat ASAR and the CI buoy performance by referring to the same wave model. ASAR energy spectra with land flag on are excluded from the selection for quality control. The corresponding model spectra along the ASAR tracks are paired with the ASAR observations and total and 4-bin SWHs scatter plots are presented in Fig.3a and 3b. The ASAR total SWHs have large variations Fig.3b Comparison of model and ASAR 4-bin SWHs near CI in June The mean sub-range ASAR SWHs are also quite close to the modelled ones but ASAR SWHs have larger variations than the modelled SWHs as illustrated in Fig.3b. The most prominent difference is in the first sub-range or the long wave range (periods of s) where the modelled values are much smaller (0.08 m on average) than the ASAR ones (mean SWH 0.47 m). The ASAR standard deviation is as high as 0.34 m while the model standard deviation is only 0.08 m. The rms of difference between the model and ASAR SWHs in this long wave bin is 0.34 m, which is higher than the rms of model and buoy difference in the same

4 sub-range (0.22 m). In the short wave bin (periods of 8-6 s) the ASAR data have the largest variations (SD of 0.88 m) among the 4 bins though its mean SWH (1.25 m) is close to the modelled one (1.05 m). For comparison of the ASAR and the buoy performance, all statistics in Fig.2 and Fig.3 are listed in Table 1. The rms values listed in Table 1 indicate that the ASAR SWHs have larger errors than the buoy data in all spectral ranges though the mean values are comparable to each other. Table 1. Comparison of ASAR and buoy spectral performance with the wave model. All values are in unit of m. CI buoy Model at buoy Model near buoy Mean SWH SWH SD RMS SWH Diff s SWH s SD s RMS s SWH s SD s RMS s SWH s SD s RMS /6 s SWH /6 s SD /6 s RMS ASAR near buoy m) is higher than the model mean (2.67 m), which is similar to the altimeter but ASAR SWHs show much larger variations than the altimeter values. The ASAR SD (2.62 m) is more than double of the model SD (1.23 m) and the rms value of the model and ASAR SWH difference is 2.64 m, much higher than the altimeter one (0.78 m). Fig.4 Comparison of model and RA2 altimeter SWHs in June 2004 along the Envisat tracks. 2.3 Comparison with altimeter SWHs Fig.4 compares the modelled SWHs with the RA2 altimeter data along the Envisat tracks in June A total of pairs of data are plotted here. Altimeter data at rain points are excluded as the data are less reliable at those points. Any pair of model and altimeter collocation, in which either the model or the altimeter part is zero, are also removed. The model mean SWH (2.67 m) is slightly lower than the altimeter mean (3.05 m). Both the model and altimeter SWHs have similar variations (SD of 1.23 and 1.48 m, respectively) as the data scatters along the diagonal line. So the model and RA2 altimeter SWHs are generally in agreement with an overall rms value of 0.78 m. Fig.5 is the plot for ASAR level 2 SWHs along the same Envisat tracks as for the altimeter data in Fig.4. The model mean SWH (2.67 m) and SD (1.28 m) are similar as those in Fig.4. This is expected as both plots used the model spectra along the same satellite tracks except that fewer model data are used for ASAR than RA2 because ASAR data points are more scarce than altimeter ones. For ASAR data comparison, the total number of pairs is 26980, about 36% of the number for altimeter data (74923). The ASAR mean SWH (3.00 Fig.5 Comparison of model and ASAR level 2 SWHs in June 2004 along the Envisat tracks. For further illustration of the ASAR and RA2 altimeter data difference, the Envisat track on 15 June 2004 cross the CI buoy site and the Hawaii island as showed in Fig.1 is selected for the along track SWH plots in Fig.6. Fig.6a shows the altimeter (cross symbols) and model (plus symbols) SWHs along the Envisat track and Fig.6b show the ASAR (crosses) and model (pluses) SWHs along the same satellite track. The ASAR data have obviously much larger oscillations along the track than either the model or the altimeter

5 values, indicating large errors of the ASAR level 2 data. Note the large difference around 20 N, which is most probably caused by the Hawaii Island underneath the satellite track. We will discuss this further in the next section. is slightly to the south of the ASAR point, the model 1- D spectra at these two sites are very similar in shape and magnitude. The buoy 1-D spectrum (solid line with cross symbols) is better in agreement with the model spectrum than the ASAR spectrum, especially in the two ends of the spectrum. The model hardly resolves the double peaks which appear in both the ASAR and buoy spectra. The relatively coarse spectral resolution of the wave model is most likely to be blamed for this. Fig.6a Comparison of model and RA2 altimeter SWHs along one Envisat track on 15 June Fig.7a Comparison of ASAR and model 2-D wave energy spectra at 0.2N 154.1W 2006 hr 23 June Fig.6b Comparison of model and ASAR level 2 SWHs along the same Envisat track as in Fig.6a. 3 COMPARISON OF WAVE ENERGY SPECTRA Validation of 2-D wave energy spectra is still a difficult job due to lack of observations. The ASAR level 2 wave energy spectra are the only available observations we have at present with global coverage. Comparison of the ASAR 2-D spectra with the wave model has revealed large differences in both frequency distribution and travelling directions. Fig.7a shows one example at a point close to the CI buoy site on 23 June The 2-D wave energy spectra, E(f, ), is represented by the contour lines in a polar plane with the frequency increases radially from f=0 at the centre. The two spectra look completely unrelated and have no overlapping area at all. It is difficult to judge which is closer to the reality. Fig.7b compares the corresponding 1-D spectra integrated from the 2-D spectra in Fig.7a over all directions. The ASAR frequency distribution is relatively close to the model one if the directional information is ignored. Note the low frequency part, where the ASAR spectra are usually higher than the model ones as indicated by the 4-bin scatter plot (Fig.3b). Fig.7c shows the nearby CI buoy 1-D spectra and the model spectra at the buoy site. Although the buoy site Fig.7b Comparison of ASAR and model 1-D wave energy spectra integrated from the 2-D spectra showed in Fig.7a. Fig.7c Comparison of CI buoy and model 1-D spectra at 2000 hr on 23 June One possible cause of the large variations of ASAR 2- D spectra is caused by small islands, which are not filtered out by the quality control procedure. For instance, the large variation showed in Fig.6b is related

6 to the Hawaii Island. Fig.8 shows 4 Envisat track positions around 20 N 157 W. The contour lines illustrate the Hawaii Islands derived from a 2 nautical mile bathymetry dataset. One of the Envisat track point is right above one of the small islands but all the four ASAR spectra did not flag any land surface. The spectra at these 4 positions are showed in Fig.9 in increasing time sequence or ascending track sequence. but the directions change in the ASAR spectra while the model spectra retain a relatively fixed direction. In the first two diagrams, the ASAR spectra are almost in the opposite direction from the model spectra. While in the subsequent two diagrams the ASAR spectra nearly overlap with the model spectra. Change of wave energy direction in such a short distance and time looks unreal though there is not sufficient evidence to make the final verdict. Reasons for this discrepancy are not clear and further investigations are required. 4 SUMMARY AND CONCLUSIONS The Envisat ASAR 2-D wave energy spectra are assessed by comparisons with the Met Office global spectral wave model and other observations, including the 1-D ocean wave energy spectra observed by a moored buoy near Christmas Island (0.02S W) and the significant wave heights observed by the RA2 radar altimeter onboard the same satellite, Envisat, as the ASAR instrument. Fig.8 Four consecutive Envisat track positions (asterisk symbols) around 20 N 157 W on 15 June 2004, from the same track showed in Fig.6a. The first (top) and the last (lowest) diagrams in Fig. 9 show the ASAR and model spectra are of similar order in magnitude though they have spectral and directional differences. The ASAR wave energy in the other two intervening diagrams, however, increased dramatically while the model wave energy remains almost unchanged. This large increase of ASAR wave energy is clearly unrealistic and related to the Hawaii Island, which might distort the ASAR radar signal substantially due to the strong contrast of land and sea surfaces as seen by the ASAR. Notice that the model spectra are selected from the nearest model points and do not match exactly the satellite track positions. The ASAR level 2 product has land flag of zero over all the four track positions as indicated by the variable land_flag (last line below each plot) in Fig.9, indicating that the islands were missed in the ASAR data processing. The directional differences between the ASAR and model 2-D spectra are more baffling than the magnitude discrepancies. Fig.10 shows one example of the directional difference between the ASAR and model spectra. The 4 diagrams are selected from one ascending track on 30 June 2004 in the Southern Ocean, about 1.5 apart in latitude or 30 s in time. In this case, the bathymetry shows no land present. As showed in the last column in Fig.10, the 1-D spectra are almost in agreement at the 4 selected nearby points Comparison results indicate that Envisat ASAR level 2 energy spectra are systematically higher in the long periods (>16 s) or low frequency parts than the modelled spectra. There is a better agreement in the mid-periods of about 8-16 s for the integrated 1-D spectra. The variations of ASAR spectra are much larger than for modelled spectra. Comparison of one-dimensional wave spectra from the buoy shows much better agreement with the wave model spectra and both the buoy and model spectra have similar variability. The integrated model SWHs are also in good agreement with the along track RA2 altimeter data. One possible reason for the large variability of the ASAR wave energy is identified to be measurements over small islands which are not filtered out by the ASAR data quality control. Ocean wave directional information extracted from the Envisat ASAR 2-D spectra is not reliable based on this limited comparison study. Further investigations are required to identify the cause (or causes) of this problem. 5 ACKNOWLEDGEMENT We are very grateful to Dr Jim Gunson (Met Office) for providing programs for retrieval and processing of the ASAR and RA2 data and Dr Gary Fullerton (Met Office) for assistance in the wave model transfer to our new computer system. We would also like to thank Dr Jean Bidlot (ECMWF) for his suggestions about the NDBC buoy data.

7 Fig.9 Comparison of ASAR and model wave energy spectra along an Envisat track at 4 consecutive positions around 20 N 154 W on 15 June 2004.

8 Fig.10 Comparison of ASAR and model wave energy spectra at 4 ever other consecutive points along an Envisat track on 30 June 2004, illustrating the directional difference.

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