Calculating wave parameters of specified return periods by using WAM4 model

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1 Calculating wave parameters of specified return periods by using WAM4 model Li Jie National Marine Environment Forecasting Centre, Beijing, ABSTRACT A new harbor is going to be built at Caofeidian ( E, N) in Bohai Sea. In order to obtain the design wave parameters for the engineer s use in designing the harbor structures, we need to understand the wave climate (including extreme waves) in the harbor waters, which requires long-term wave data series exceeding twenty years. We don t have such a long-term wave observation in the deep water out the harbor, so we use the wave model WAM4 and the reanalysis wind field provided by the European Centre for Medium-Range Weather Forecasts(ECMWF) to reproduce 21 year ( ) wave data. Also, wind observations at the coastal stations along Bohai Sea made every six hours are used to correct and validate the reanalysis wind field. In this presentation, description is given of the reproduction of the long-term hindcast wave data and the computation of design wave parameters. The results show that the approach is feasible and practical. Key word: reanalysis wind field, wave parameter, return period 1. INTRODUCTION A new harbor is going to be built at Caofeidian, its detailed geographic coordinate is E, N, in the west of Bohai Sea. To fulfill needs of designing docks, bulwarks and structure layout inside harbor, we must understand wave height distribution of various water depth in this sea area and calculate wave parameters of specified return periods that this engineering demands. According to Code of Hydrology for Sea Harbor by the Ministry of Communications, years of consecutive wave observation data must be not less than twenty years when we carry out the analysis of wave parameters of specified return periods (the more data samples, the more representative). Because there are no long-term wave observations in the vicinity of Caofeidian seaport, we adopt wave numerical model to calculate wave field of harbor area and provide bases for the engineering design. Printed on recycled paper 8-1

2 The computation of wave parameter we focus on is the calculating of offshore wave parameter. According to all kinds of available information about harbor waters, the engineering demands are to calculate design wave parameters of ENE, E, SE, S, SW, W directions with return periods of 50 year and 25 year at the appointed location. The design wave parameters include wave height and wave period of different accumulation probability H 1%, H 4%, H 13%. The calculating process involves selection of driving wind field, simulation of deep water wave and computation of wave parameters of specified return period. We take advantage of the reanalysis wind field derived from the European Centre for Medium-Range Weather Forecasts (ECMWF). Time period we selected is from 1981 to Wind observations made every six hour by China Meteorological Administration are used for validating and correcting the reanalysis wind data. The WAM4 model, driven by correction reanalysis wind field is adopted to calculate wave height and wave period. Before it is planning to build this harbor, there had been wave observing for two years outside the harbor. The wave model results are compared with these wave observations. Because the unusual big wave of E direction occurred in Bohai in 2003, we add hindcasts for 2002 and 2003 while calculating wave parameters of E and ENE direction. According to Code of Hydrology for Sea Harbor, we adopt Pierson extreme distribution theory of type III and the extreme wave height series to make the statistical analysis computation of design wave parameters of specified return periods. The whole computation flow is shown as figure Printed on recycled paper

3 year ECMWF reanal ysi s wi nd dat a correcti on year reanal ysi s wind data WAM4 model veri f i cat i on WAM4 model 21 year s hi ndcast resul t 21 years seri es of annual ext reme si gni f i cant wave hei ght wave paramet er of 50 and 25 year return peroi d Figure 1.1 the whole process flow Printed on recycled paper 8-3

4 2. DESCRIPTION AND CORRECTION OF WIND FIELD DATA The wind field is derived from the 40-years reanalysis data of The European Centre for Medium-Range Weather Forecasts (ECMWF), an independent international organization, supported by 25 European states. The new reanalysis project ERA-40 will cover the period from mid-1957 to 2001 including the earlier ECMWF reanalysis ERA-15, The aim of the reanalysis was to produce a dataset with no inhomogeneities as far as the technique of analysis is concerned, by reconstructing the 45 years of data using the same numerical model throughout, and to promote the use of global analyses of the state of the atmosphere, land and surface conditions over the period. The three dimensional variational technique is applied using the T159L60 version of the Integrated Forecasting System to produce the analyses every six hours. Analysis involves comprehensive use of satellite data, starting from the early Vertical Temperature Profile Radiometer data in 1972, then later including TOVS, SSM/I, ERS and ATOVS data. Cloud Motion Winds is used from 1979 onwards. ERA-40 products will also revitalize the use of data from past field experiments such as the 1974 Atlantic Tropical Experiment of the Global Atmospheric Research Program, GATE, 1979 FGGE, 1982 Alpine Experiment, ALPEX and more recent TOGA-COARE. The following observations were used: FGGE Level II-B data for 1978/79; COADS ship and buoy observations; ALPEX Level II-B data; ECMWF archive of observations received via the WMO GTS; additional TEMP and AIREP data from the Japan Meteorological Agency (JMA); Australian PAOB surface pressure pseudo-observations from Bureau of Meteorology (BoM), Melbourne; TOGA COARE data; TOVS Cloud Cleared Radiance data; Hadley Centre GISST and NCEP SST analyses. The ERA-40 data, considered as high-quality data by the field of meteorology, is widely used in many aspects of Europe and international climate research. It plays an important role in all meteorological service and scientific research. Though the reliability and accuracy of the ERA-40 wind field is widely accepted internationally, there is some limitation to the local region. The reason is: 1) The wind field of local region is frequently influenced by local circumstances (the distribution of 8-4 Printed on recycled paper

5 local mountains, the undulation of topographic form, the types of vegetation and so on), but with running model to calculate the ERA-40 data, much influence of local environment might be smoothed; 2) For large scale, the resolution of the ERA-40 data, degree, is fine enough, but for local small region, the wind field of this resolution could not reflect the particular structure of the wind field of local region. As for Bohai Sea and its adjacent waters we concerned, there are a lot of data of many observation stations along coast and at islands, these materials were not utilized in recalculating the ERA wind field of ECMWF. So with making use of much valuable material, we could verify and correct the ERA data to improve its exactness. The detailed method is as follow: So far, meteorological station observations are considered the most reliable wind observation. We selected nine locations along the coast, mainly in the area we concerned. Nine meteorological stations, as showed in figure 2.1, are Tanggu(54623), Laoting(54539), Suizhong(54454), Dalian(54662), Longkou(54753), Yangjiaogou(54736), Chengshantou(54776), Qingdao(54857) and Shengsi(58472). From 1981 to 2001, wind observations made every six hour by China Meteorological Administration are available. There are also two more years wind speed observations at operation spot Caofeidian. Due to their high quality they will be used here to validate and correct the ERA data. In comparison with observations of nine meteorological stations and CFD, we could see the ERA data could reproduce historical strong weather system. But in Bohai Bay, especially close to operation spot, the ERA wind speed is much smaller than observations, and these cases in Summer are much more prominent than those in Winter. While we corrected the ERA wind data, we found out those wind speed observations over 7m/s and the corresponding ERA wind data and obtained their ratios. Then for two situations, in Summer and in Winter, we averaged twenty-one years ratios and got the correction coefficients respectively. Figures of the ERA data in comparison with observations of operation spot and nine meteorological stations are showed as follows. Printed on recycled paper 8-5

6 45 40 TG LT CFD SZH DL YJG LK CHSHT Latitude( o N) QD SHS Longitude( o E) Figure 2.1 locations of operation spot and nine meteorological stations 25 Observed Reanalysis 20 Wind Speed*2(m/s) Time(h) Figure 2.2 wind speed comparison of Caofeidian in Aug, 1997 Figure 2.3 wind speed comparison of Tanggu meteorological station in Aug, Printed on recycled paper

7 Figure 2.4 wind speed comparison of Laoting meteorological station in Aug, 1997 Figure 2.5 wind speed comparison of Suizhong meteorological station in Aug, 1997 Figure 2.6 wind speed comparison of Longkou meteorological station in Aug, 1997 Figure 2.7 wind speed comparison of Chengshantou meteorological station in Aug, 1997 Figure 2.8 wind speed comparison of Figure 2.9 wind speed comparison of Printed on recycled paper 8-7

8 Qingdao meteorological station in Aug, 1997 Shengsi meteorological station in Aug, WAM MODEL WAM is a third-generation wave model, which calculates the evolution of the wave energy spectrum by an explicit method, without any prior assumptions about its shape. It represents the physics of wave evolution in accordance with present day knowledge for the full set of degrees of freedom of the two-dimensional surface wave spectrum. It solves the action density balance equation, expressed in terms of wave energy, for the case of steady depths and currents. In deep water, the energy balance equation reads F ρ F + vg ρ = S t x (1) F( f, θ ) where w is the wave spectrum described by the frequency f w and the v ρ g wave direction θ, is the group velocity, and S is the source term given by S = S + S + S + S in nl ds bf, (2) where the terms on the right hand side represent the physics of wind input, wave-wave interaction, dissipation due to whitecapping and bottom friction, respectively. The WAM4 model has a certain number of advantages over earlier cycles of the WAM model. First of all, the latest cycle allows the surface stress to be determined, including the dependence on the sea state through the wave-induced stress. This was accomplished by introducing a parametrized version of the quasi-linear theory of wind-wave generation into the WAM model (Janssen, 1989; Jassen, 1991) which treats both the generation of waves and the slowing down of air flow because of the air-sea momentum transfer. As a consequence, the sea state dependence on the surface stress may be determined (which shows good agreement with Hexos observations). The resulting growth rates of ocean waves by wind turn out to be slightly larger than previous cycles, which were based on the Snyder et al parametrization of the wind input S source function in. Secondly, the high-frequency part of the wave spectrum shows more realistic levels when compared to observations. By introducing a somewhat stronger wave dissipation at high-frequencies (Janssen 1991; Komen et al., 1994) more realistic high-frequency levels were obtained. Thirdly, WAM4 model shows reduces dissipation of swell. The reason for the reduced swell attenuation in the WAM4 model is directly related to the afore-mentioned reduced level of the high-frequency part of the wave spectrum, and the dependence of the dissipation source function on a measure of the mean square slope. The steeper the waves the larger the wave dissipation so the reduced level of the high-frequency waves may therefore give rise to a reduction of 8-8 Printed on recycled paper

9 wave attenuation of 50%. It is emphasized that dissipation of swell energy is only important when the ocean waves are just leaving the storm track. Because of the white cap dissipation the ocean waves experience a considerable reduction of their mean square slope (giving a considerable reduction of the attenuation rate)and for the rest of their life time the swells propagate virtually undamped, in agreement with the findings of Snodgrass et al. (1966). Figure 3.1 oversea wave calculated region (red point is the location of Caofeidian harbor) The calculated region of offshore wave is E, 30-42N, and the resolution is 0.25 x The water depth, derived from ETOP5, is revised by the newest sea chart of Bohai area. The driving wind field is obtained from ECMWF s reanalysis wind field that is corrected and interpolated. The wind force is updated every six hours. The wave model is numerically solved by integrating the source term and advection term with the time steps of 10 and 20 minutes, respectively. The wave spectrum has 25 frequencies and 12 directions at each gridpoint. The time period is from 1981 to For ENE and E direction, we make a supplement to calculate the extreme wave process in 2002 and The calculated model results are compared with wave observations of Caofeidian, showed as figure 3.2. We could see that the wave model can reproduce big wave out Printed on recycled paper 8-9

10 Caofeidian harbor well. 3.5 Observed Reanalysis Wave height(m) Time(hour) Figure 3.2 comparison of wave model result and observation of CFD on Aug, 1997 In Bohai sea on Oct 11, 2003, a simulated case caused by a very strong cold air is shown as figure 3.3. We also output every hour wave height out Caofeidian harbor, shown as figure 3.4 Figure 3.3 significant wave height distribution of calculation region on 18UTC October 11, Printed on recycled paper

11 4 Significant wave height output at Caofeidian from Oct 8, Wave height(m) Time(hour) Figure 3.4 calculated significant wave height from 20UTC October 8 to 02UTC October 14, CALCULATING OFFSHORE WAVE PARAMETERS OF SPECIFIED RETURN PERIOD H As example of 1/ 100 wave height of ENE direction,it is shown as table 4.1 that the series of annual extreme wave height from out Caofeidian harbor. From this, we calculate the average annual extreme wave height H = 4.07m, C 0.26 v =. We get the best fitting curve of P-Ⅲ type by adjusting Cs / C v, shown as figure 4.1. From this curve of P-Ⅲ type,wave heights of all kinds of specified return period could be obtained. The method is completely same for wave height of other directions and accumulation probability. There are some cases from figure 4.2 to figure 4.6. Table 4.1 the series of annual extreme wave height from out Caofeidian harbor year 13% H H 4% H 1% H 1/ Printed on recycled paper 8-11

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13 Figure 4.1 the P-Ⅲ type fitting curve of H 1/100 wave height(ene) Figure 4.2 the P-Ⅲ type fitting curve of H 1/100 wave height(e) Figure 4.3 the P-Ⅲ type fitting curve of H 1/100 wave height(s) Figure 4.4 the P-Ⅲ type fitting curve of H 1/100 wave height(se) Printed on recycled paper 8-13

14 Figure 4.5 the P-Ⅲ type fitting curve of H 1/100 wave height(sw) Figure 4.6 the P-Ⅲ type fitting curve of H 1/100 wave height(w) 5. CONCLUSION We use the reanalysis wind field and wave model WAM4 to reproduce long-term wave data series. From discussion above, we could see the approach is feasible and practical. REFERENCES Janssen P. A. E. M., (1991) Quasi-linear theory of wind wave generation applied to wave forecasting. J. Phys. Oceanogr., 21, 1631~1642 Janssen P. A. E. M., (1989) Wave-induced strees and the drag of air flow over sea waves. J. Phys. Oceanogr., 19, 745~754 Komen G. J., L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann, P.A.E.M.Janssen, (1994) Dynamics and modelling of ocean waves. Cambridge Uniersity Press. Snodgrass F.E., G.W. Groves, K. Hasselmann, G. R. Miller, W. H. Munk, W. H. Powers, (1966) Propagation of ocean swell across the Pacific. Philos Trans Roy Soc, London, A249, Printed on recycled paper