BCCS TECHNICAL REPORT

Transcription

1 BCCS TECHNICAL REPORT LOfoten and VEsterålen CURrents (LOVECUR) REQUEST NO. 2010/00311 Avlesen, H, Torsvik, T, and Thiem, Ø November 27, 2010 Deliverance to Statoil. Contract number UNI Research the University of Bergen research company BERGEN, NORWAY

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3 1 Introduction The Norwegian Deepwater Programme (NDP) formed the LOVECUR- project to validate hindcast currents for the Lofoten and Vesterålen Area, in order to prepare for eventual oil and gas exploration. Meteorological and oceanographic parameters (metocean parameters) such as winds, waves and currents must be understood and estimated in order to design structures that are both safe and cost efficient. Currents are usually assumed to have less significant year to year variations than wind and waves, although long-term current measurements in the Svinøy section show considerable annual variability. Currents do however have larger variations from one location to another than wind and waves often due to topographic features. Numerical current models can describe this variability, however to be able to predict the variability it is important to have high resolution, which is not within the scope of this project. Regional current modeling is often applied by oil companies in an early phase of a field development. Current hindcasts generated by a suitable model can provide indications of extreme values for design of facilities, operating conditions, and local variations of currents in a field. Current hindcast data will also be useful as input for environmental impact studies such as oil drift studies. Model data is also useful during the planning of measurement campaigns. In general, it is recommended that a shorter time series (at minimum one year) of site specific current measurements are available before finalizing the design of structures. The combination of the site specific current measurements and long term current hindcasts at regional scale is usually considered sufficient for final design. Regional models will typically have a grid and time resolution that does not allow for the variability measured in the timeseries caused by smaller scale physics due to lack of resolution. To include this physics demand very high resolution both of the model but also of the forcing and boundary condition, especially the bottom topography. Typically a small model area (that allow for high resolution) close to the point of interest will depend on the larger scale forcing. Examples are low pressures or the thermohaline inflow which can have scales of maybe several 100 km, and can set up currents on smaller scale (like down to meter scale) when internal waves or spun off eddies are modified or breaks along the topography. To resolve these processes in idealized experiments are challenging in itself and might be impossible in region scale models with the computer power that we have available today. One of problems modellers meet when setting up a regional model is the fundamental lack of good initial data. Bottom data from the 4 km Meteorological Institute model or the International Bathymetric Chart of the Arctic Ocean (IBCAO) will not be able to generate the variability in the Lofoten Vesterålen area. Further it can be questioned if the smooth salinity and temperature profiles that are generated by coarse models and nested into higher resolution models will be able to force the variability that are of interest for the developers of the oil and gas fields. In this project a regional model are set up with the data that are freely available. The model tool that are used is the newest version of Bergen Ocean Model which has been continuously developed at the University of Bergen and Uni Research. The model has well documented non-hydrostatic capabilities [Berntsen et al., 2006, 2009, Thiem and Berntsen, 2009], however, with a resolution of 4 km these effects can be neglected. 2 Methods 2.1 The numerical model The model used in this study is the Bergen Ocean Model (BOM). The equations that are solved is the continuity equation for an incompressible fluid, the Reynolds averaged hydrostatic momentum equations, conservation equations for temperature and salinity and the 1

4 UNESCO-equation of state. BOM uses a terrain following coordinate system, where coordinates are given as (x, y, σ, t), x and y are the horizontal coordinates, σ the vertical coordinate, and t is the time. The vertical coordinate is given by the standard σ-transformation, σ = z η H + η, (1) where z is the vertical Cartesian coordinate, η the surface elevation, and H the bottom depth. The variables are discretized on a staggered grid. The model is thoroughly described in Berntsen [2000] and available from The model is mode split in a barotropic mode, resolving the fast moving surface signals, and a baroclinic mode resolving the slower (interior signals). Such a mode splitting saves computational time since the full equations are not solved as often as the barotropic equations. In the presence of steep topography, the dynamic pressure (non-hydrostatic) component may become significant, thereby violating the hydrostatic approximation. However, for the effect of non-hydrostatic pressure to be included high resolution is needed, which is not the case for this study. The hydrostatic approximation assume a primary balance in the vertical between the gravitational force and the vertical pressure gradient. For more information about the non-hydrostatic methods used, see [Berntsen and Furnes, 2005]. Synoptic forcing fields of wind are used to force the model. The wind speeds 10 m above the sea level wsu and wsv in the x- and y-directions respectively are used to calculate the wind stress (wfu, wfv). The wind stress are given as quadratic functions of the wind speed for wind speeds less than 11 ms 1, where α = , see Equation 2 and Equation 3. For larger wind speeds the wind stress increase cubically with α = ws. (wfu, wfv) = ρ a ρ 0 αws(wsu, wsv), (2) ws = wsu 2 + wsv 2. (3) Here ρ 0 is a reference density and ρ a is the density of the air. The gradients of the atmospheric pressure is used to compute velocities due to the atmospheric pressure. An explicit method is used to propagate the velocities forward in time. d(u, V ) dt = 1 ρ 0 dp atm (dx, dy) Here P atm is the atmospheric pressure. If the gradients in the atmospheric pressure are along the open boundaries the changes in the water level are estimated. The bottom layer is parametrized through the bottom stress τ b (x, y, t) specified by τ b (x, y, t) = ρ 0 C D ub2 u b (x, y, t). (5) Here ρ 0 is the reference density, u b (x, y, t) is the velocity in the nearest bottom grid cell, in the x- and y-direction. The drag coefficient C D is given by C D = max[0.0025, (4) κ 2 (ln(z b /z 0 )) 2 ], (6) where z b is the distance of the nearest grid point to the bottom and z 0 the bottom roughness parameter, see Blumberg and Mellor [1987]. The von Karman constant κ is 0.4. For additional information about numerical methods used in BOM, consult Berntsen [2000]. 2

5 (a) Map of model area (b) Detailed map of Lofoten area Figure 1: Bathymetry maps of the model area. 2.2 Model setup The model area covers the Norwegian Sea basin, see Figure 1. The horizontal grid size is 4 km. In the vertical 30 σ-layers are applied and these are distributed according to a formula given in Lynch et al. [1995]. Their formula distribute the layers symmetrically about the midpoint in the vertical with a gradually finer resolution towards the surface and the bottom. The model is run for 378 days with an internal 3-D time step of 180 s. There are 40 2-D time steps per 3-D step. The bottom matrix is based on the 4 km bottom resolution used by the forecast model of the Meteorological Institute ( and data from the International Barometric Chart of the Arctic Ocean (IBCAO) 1. At the present time Uni Research has not access to higher resolution data from the Lofoten-Vesterålen area and therefore higher resolution model runs are not performed. At the lateral open boundaries, flow relaxation schemes (FRS) are implemented [Martinsen and Engedahl, 1987]. The FRS-zones are 10 grid-cells wide. In addition to the initial values for water elevation (η), velocity (u and v), temperature (T ) and salinity (S) four tidal constituents (M 2, S 2, K 1, N 2 ), are used to specify the lateral boundary conditions The Baltic Sea The boundary towards the Baltic Sea has been closed off in the model domain, and the influence of the Baltic Sea discharge is included in a similar manner as river discharge through three outlets representing Lillebælt, Storebælt and Öresund (Table 1). Seasonal variability is obtained by monthly means of water discharge, with realistic salinity and temperature for the Baltic Sea. This method does not allow actual water exchange with the Baltic Sea region, but allows realistic seasonal variation of temperature and salinity in the southern part of Kattegat. Outlet Longitude Latitude Discharge (m 3 /s) Lillebælt Storebælt Öresund Table 1: Outlets - Baltic Sea. Longitude and latitude values are poitive east of Greenwich and north of equator. Discharge is the mean anual flux in m 3 /s

6 2.2.2 Rivers Fresh water runoff from 35 rivers around the North Sea and Norwegian coast is included (Tables 2, 3, and 4). The data originates from the Institute of Marine Research and is the monthly mean over a longer time period. All rivers contribute water masses with zero salinity and water temperature constant at 10 C. This temperature is probably too high as an annual mean for most of the rivers, and does not reflect any seasonal variability, but we were not able to obtain such data for the river water temperature. For experiments over longer periods this forcing will affect strongly the coastal circulation and the Norwegian Coastal Current. River Longitude Latitude Discharge (m 3 /s) Bjerkreimsvassdraget Drammenselva Glomma Kvina Lynga Mandalselva Namsen Nidelva (Aust-Agder) Numedalslågen Otra Orklaelva Sira (Åna-Sira) Skiensvassdraget Suldalslågen Tovdalselva Vefsna Table 2: River outlets - Norway. Longitude and latitude values are poitive east of Greenwich and north of equator. Discharge is the mean anual flux in m 3 /s. River Longitude Latitude Discharge (m 3 /s) Ätran Göta Älv Lagan Nissan Viskan Table 3: River outlets - Sweden. Longitude and latitude values are poitive east of Greenwich and north of equator. Discharge is the mean anual flux in m 3 /s Temperature and salinity Water elevation and velocities are spun up from zero. Initial values of temperature and salinity are taken from the MERSEA model setup 2 and interpolated into the model grid. The model are then forced by data from the MERSEA model setup at the open boundaries. The MERSEA model data is freely available, but the resolution is very coarse which means that the representation close to the bottom needed to be extrapolated. 2 laurentb/ecrits/mersea-wp05-nersc-tecn a.pdf 4

7 River Longitude Latitude Discharge (m 3 /s) Elbe Ems Firth of Forth Seine Somme Tay Thames Tweed Weser The Rhine-Meuse-Scheldt delta Haringvliet sluices Maassluis Scheldt North Holland IJsselmeer North Sea Canal Table 4: River outlets - Europe. Longitude and latitude values are poitive east of Greenwich and north of equator. Discharge is the mean anual flux in m 3 /s Tidal forcing Tidal forcing is obtained by using four tidal constituents; M 2, S 2, K 1, and N 2. Figures 2 and 3 show a comparison between the simulated free surface elevation and the calculated and measured tidal signal downloaded from the vannstand.no web page from Statens Kartverk 3, for the two locations Andenes and Bergen, respectively. The graphs are shown for tidal variation over a week, starting from midnight at 15/06/2009. The figures show that BOM is capturing the phase of the tidal signal and the amplitude is of the same order. The discrepancy in the amplitude is expected to be due to differences in the location where the measurement and model result are taken. Figure 2: Tidal signal comparison: Andenes. Figure 3: Tidal signal comparison: Bergen Wind and atmospheric forcing The wind fields are and taken from the re-analyzed NAPE2 data. These data has a coarse spatial resolution, however the resolution in time is very good and the wind statistics are good. Wind forcing is updated at intervals of 4 simulated hours. Figure 4 show the wind field for the entire computational domain on the date 13 Oct Wind at a single point (C1: N, E) over the entire time of the 3 5

8 Figure 4: Wind field for the entire computational domain on 13 Oct simulation is shown in Fig. 5 for wind speed and Fig. 6 for wind direction. Detailed plots for a 5 day period (September 25 30) are shown in Figs. 7 and 8. Figure 5: Wind speed over a year Figure 6: Wind direction over a year The simulation does not include forcing due to atmospheric pressure variation. The reason is that we were only able to obtain coarse resolution pressure data which did not include sufficient details of the pressure field, especially in coastal areas. An erroneous pressure field may easily lead to artificial upwelling or downwelling events. Some realistic upwelling and downwelling events are likely to be lost when simulating without atmospheric pressure variation, but we reduce the risk of interpreting artifacts as real events as in the simulations. 3 Results A one year hindcast from the period July 1, 2009 to July 1, 2010 is performed. An example of surface temperature and salinity at 13 October 2009 is given in Figure 10. The effect of the fresh water runoff from 35 rivers is clearly seen in the salinity, Figure 10 a) and is important for the Norwegian Coastal Current. The temperature, Figure 10 b), shows the splitting of the Atlantic Inflow north of Vesterålen where one branch is the Spitsbergen Current and the other branch intrudes into the Barents Sea. The figures also show that meso-scale features are generated along the Norwegian shelf. 6

9 Figure 7: Wind speed over 5 days. Figure 8: Wind direction over 5 days. (a) Salinity (b) Temperature Figure 9: Surface salinity and temperature 13 October

10 (a) Current direction (b) Speed (c) Salinity (d) Temperature Figure 10: Timeseries 13 October 2009 at 10 m depth. The timeseries of current speeds, direction, temperature, salinity, and surface elevation taken at the locations given in Table 5 has been studied. Location Longitude Latitude Depth (m) C E N 130 C E N 120 C E N 135 C E N 112 C E N 120 C E N 150 C E N 100 C E N 228 C E N 80 Table 5: Locations of time series By inspection of graphs for current speeds, we find a general tendency that results for the stations C1-C6 display similar trends both in terms of the magnitude of the current and variability for strong current events. The currents at the three stations C7-C9 seem to vary more independently, both from each other and from the group of stations C1-C6. A general trend was difficult to find for the temperature and salinity. It was for instance found that the temperature had oscillations close to one degree at 50 m depth, but the variations in salinity was very small and did not oscillate corresponding to the temperature. The tidal range in the Vesterålen-Lofoten area was found to be within -0.7 m and 1.0 m in the simulation. It was found that the numerical model had smaller tidal amplitudes than what was found in measurements from the area. Tide was estimated for a point on the 8

11 continental shelf, but some distance from the shore, which may have contributed to the reduced tidal amplitude when compared with measurements. 4 Discussion Bergen Ocean Model has been set up for the Norwegian Sea and a hindcast study for the period July 1, 2009 to July 1, 2010 has been carried out. The model result show that the model is able to generate the meso-scale eddies that are measured by satellite along the Norwegian coast, and also the path of the Atlantic Inflow corresponds to what is known from measurements and the literature. Sigma-coordinate models or z-coordinate models are often used for regional modeling. Both these models has weaknesses when it comes to steep areas like the Lofoten-Vesterålen area. For sigma-coordinate models it is the internal pressure errors that may be significant. How large the artificial currents due to this errors are has not been studied in this work, and this should have been within the scope of the work assignment. Higher resolution will decrease the internal pressure error in these models, however, like mentioned in the Introduction, in studies where large scale forcing forces small scale physics there will be a computational limitation on how high resolution that are possible to achieve. For the z- coordinate model the stair case grid will generate artificial mixing that will affect the thermohaline circulation along the Norwegian coast in general and in the Lofoten-Vesterålen area in particular. Timeseries of salinity, temperature, speed, and speed angle were modeled for nine different locations in the Lofoten-Vesterålen area. The hight of the water column varied for the different locations and the model data was sampled for every 10 m depth. The data has not been validated due to lack of measurements for this area. The simulated data of salinity, temperature, speed, and speed angle will be used by internal and/or external experts to evaluate the model s skill in hindcasting currents. It has to be raised a critical voice about the setup and planning of the LoveCur project. How the model s skill can be evaluated within the frames of this project is questionable since the model input like tide, wind, velocities, salinity, temperature, and bottom topography,from different participants will be different which means that it is not the model s skill that will be assessed, but who has the best model setup at the time the project were performed. In short the LoveCur project will be good for finding the one that has the best model setup, which most likely will be the one that has a model setup up and running, but will fail to find the best model tool due to the large difference in initial forcing and boundary conditions. The time frame of the project has been short since the code had to be set up on a new area. However, to participate in the LoveCur project has been very interesting and challenging. Getting good forcing fields and input data was the first obstacle that had to be mastered. Then a lot of new routines for parallel computing had to be developed like for instance the framework for dumping 500 time series for one year. The code was run on 512 processors on the supercomputer hexagon that are maintained by Uni Research, and we are proud to present the numerical results to Statoil. Acknowledgement This research has received support from Statoil through the LoveCur project, contract number

12 References J. Berntsen. USERS GUIDE for a modesplit σ-coordinate numerical ocean model. Technical Report 135, Dept. of Applied Mathematics, University of Bergen, Johs. Bruns gt. 12, N-5008 Bergen, Norway, p. 48. J. Berntsen and G. Furnes. Internal pressure errors in sigma-coordinate ocean modelssensitivity of the growth of the flow to the time stepping method and possible nonhydrostatic effects. Cont. Shelf Res., 25: , J. Berntsen, J. Xing, and G. Alendal. Assessment of non-hydrostatic ocean models using laboratory scale problems. Cont. Shelf Res., 26: , J. Berntsen, J. Xing, and AM. Davies. Numerical studies of flow over a sill: sensitivity of the non-hydrostatic effects to the grid size. Ocean Dynamics, 59(6): , A.F. Blumberg and G.L. Mellor. A description of a three-dimensional coastal ocean circulation model. In N.S. Heaps, editor, Three-Dimensional Coastal Ocean Models, volume 4 of Coastal and Estuarine Series, page 208. American Geophysical Union, ISBN D.R. Lynch, J.T.C. Ip, C.E. Naimie, and F.E. Werner. Convergence studies of tidallyrectified circulation on Georges Bank. In D.R. Lynch and A.M. Davies, editors, Quantitative Skill Assessment for Coastal Ocean Models. American Geophysical Union, E.A. Martinsen and H. Engedahl. Implementation and testing of a lateral boundary scheme as an open boundary condition in a barotropic ocean model. Coastal Engineering, 11: , Ø Thiem and J. Berntsen. Numerical studies of large-amplitude internal waves shoaling and breaking at shelf slopes. Ocean Dyn., 59: ,