by Nils Gunnar Kvamstø, Øyvind Sætra, Helge Drange, Harald Schyberg, Jan-Erik Haugen and Sigbjørn Grønås.
Objective
To strengthen the regional climate modelling activity under RegClim through intensified investigation of the exchange processes of momentum, heat and moisture across the air-sea boundary, and by coupling of an atmosphere and ocean model.
Background
In the present RegClim project (Iversen et al. 1997), it was planned to incorporate a quasi-coupling procedure between the atmosphere and the ocean model under Principal Task 4 (PT4). In the first step it was planned to use a global model of the atmosphere with stretched coordinates, where the resolution is focused in our region (AGCMS) and similarly an ORCM also with variable resolution. The ORCM model is currently under development within PT2 and PT7. The quasi-coupling approach has been subject to some controversy within RegClim. Since the interaction between the ocean and the atmosphere is continuous, and not intermittent, the quasi-coupling procedure is believed to have limitations when it comes to predicting climate variability. A more consistent method is to use a coupled atmosphere-ocean model, where the air-sea fluxes are calculated with regular time intervals. Here, the length of the time interval (e.g. less than a day) is determined such that the dynamics of the air-sea exchange process is resolved. On the global scale such models are already being used as the main tool in climate prediction. Also when it comes to predicting regional phenomena like the North Atlantic Oscillation (NAO) and variations in the Norwegian Atlantic Current (NAC), coupling between the atmosphere and the ocean model will probably be necessary.
The detailed processes which bring about air-sea interaction fluxes are not fully understood. Consequently, the way these processes are described in state-of-the-art climate models are highly parameterized. This leads to a drift away from the observed climate in the coupled ocean/atmosphere models. It has been demonstrated that a systematic error of 5 Wm-2 in heat flux, which is smaller than the local observational error, leads to a relatively large error in the annual average oceanic heat transport (Gleckler et al., 1994). Climate drift is therefore ameliorated by flux adjustment whereby the heat and fresh water fluxes (and possibly the surface stresses) are modified before being imposed on the ocean. The flux adjustment terms are calculated from the difference between the model surface fluxes and those required to keep the model close to the current climate. Corrections of this type are introduced in coupled models partly due to coarse resolution and partly due to insufficient parametrizations of physical processes in the atmosphere- and ocean models. On the other hand, there has been performed preliminary coupled simulations without flux corrections at a few modelling communities (a.o. CERFACS, GFDL and NCAR) (Gates et al., Table 5.1, Ch. 5, IPCC 1996). However, to our knowledge, characteristics of these experiments have not been documented in any publications yet.
To study variability on interannual time-scales and longer, coupled atmosphere-ocean models are required. Especially in the Labrador and the Nordic Seas, higher resolution than in most present AOGCMs is needed to resolve the relevant processes and geometry. When the resolution increases, physics on shorter space and time scale will be resolved in the models. Correct formulation of these processes therefore needs a better understanding of the air-sea interaction processes on short time and spatial scale. It is therefore of vital importance that the coupling between atmosphere and ocean models is carried out in connection with a detailed study of the air-sea interaction processes. This will give a better understanding of the physics at the air-sea boundary, and help to develop more sophisticated parametrizations to be used in high resolution regional climate models.
We propose to extend the present activities of PT4 with an investigation of air-sea fluxes and the development and validation of a coupled atmosphere-ocean model. This results in two new, and three redefined tasks in Iversen et al. (1997). The main objectives of PT4 will be kept unchanged. The amount of work is estimated to two man year for a period of three years. Since the quasi-coupling approach will be left out, approximately one half man year will be available from this activity. Totally, one and a half man year extra will then be necessary to carry out the suggested activities under PT4. Given this extension, the total number of man years in the period 1999-2001 adds up to 13. In the following the aim of the work is formulated and the details of the project extension are given. The main objectives of PT4 will be kept unchanged.
The air-sea interaction process study
The goal of this study is to evaluate the ocean surface flux parametrizations for momentum, heat and moisture in use in the HIRHAM model used in RegClim, to decide whether improved flux parametrizations are necessary, and if so, to suggest new formulations. The objective is to support the regional climate modelling activity in RegClim, and in particular high-resolution climate modelling in polar areas.
The investigation will be based on the hypothesis that the wave age dependent momentum and heat flux may have a strong impact on the development, the life cycle and intensity of small scale atmospheric instabilities when there is a considerable temperature difference between the ocean and the atmosphere (polar lows etc.). for these phenomena, the growth of the instability is to a large extent governed by the heat and moisture flux from the ocean, and to a less extent by the baroclinic properties of the initial state. Earlier investigations have shown that parameters such as wind at 10 m height and sea state may be significantly influenced by taking this effect into account (Lionelli et. al. 1998, Janssen 1994). These parameters are considered being key climatic parameters (see Iversen et. al. 1997 p. 27).
We will focus on air-sea interaction processes which are important when modelling regional climate at high latitudes and on relatively high resolution. This area is among other things characterized by strong thermal difference between the ice-covered and the open ocean areas. This transition from a cold to a relatively warm underlaying surface have a significant impact on the atmospheric flow pattern. Here, we will focus our attention on studying the process of air-sea exchange in the case when there is large temperature differences between the atmosphere and the ocean. Specifically, we will study how phenomena which are governed by the heat flux from the ocean, may be affected by a wave age dependent sea-surface roughness. Such phenomena are related to shallow convection, as will be studied under PT 5, and in particular includes polar lows, which are strong small-scale vortices. The evolution of polar lows are strongly controlled by the air-sea heat- and moisture fluxes (see e.g. Økland and Schyberg, 1987), and has been thoroughly studied in a large international project at DNMI in the 1980s.
We will use the ocean surface flux formulations which are part of the atmosphere models used in RegClim, and those will be evaluated in such situations as discussed above, in particular the evolution of polar lows and arctic air outbreaks. We will address the effect of neglecting the wave-age dependence of momentum, heat and moisture fluxes to quantify the effect and its impact on climate simulations. If there turns out to be major deficiencies in the formulations, alternative formulations are necessary and we will address the necessity for coupling with an ocean wave model.
The flux parametrizations are not only important for the evolution of the weather phenomena mentioned above, but are also a part of the diagnostic relationships used for computing such climate parameters as surface temperature and 10 m wind, as well as the wave climate, which all are identified as key climate parameters in the RegClim project.
The total downward flux of momentum from the atmosphere to ocean current may be regarded as consisting of two contributions. One representing the flux from wind to ocean waves, and one representing the flux directly to ocean current. Because the wave amplitude is limited, the waves can only pertain a small part of the momentum. When the wave amplitude becomes too large the waves will break and the associated momentum will be transferred into ocean current. Consequently, the waves play an important role in transferring momentum across the air-sea boundary. Through the process of wave generation and subsequent wave breaking, followed by new wave growth and breaking e.t.c. the wave field act as an intermediate stage in the flux of atmospheric momentum to the ocean.
Traditionally, the fluxes at the air-sea interface are parameterized using a simple description like the Charnock's relation (Charnock 1955). This means that the sea-surface roughness can be calculated from the local wind speed at a prescribed height. For the ocean surface heat and moisture fluxes, relations similar to that for the stress or momentum flux are usually applied, although the physical mechanisms for the transfer are somewhat different. Also these fluxes depend on the surface shape and its roughness, and thus exhibit a sea state dependence.
From several field studies it has been demonstrated that the sea surface roughness is not only dependent on the local wind at a given moment, but may also be strongly dependent on the distribution of the wave spectrum, i.e. the history of the wave field. For young wind sea, the wave energy is concentrated in the high frequency part of the spectrum. Short waves act as roughness elements on the wind, and contribute effectively to the momentum transfer, whereas the air flows smoothly over longer swells (Doneland et.al. 1997). If the wind is blowing steady, the waves will become longer and the surface roughness decreases.
To be able to study the wave age dependent surface roughness, coupling between the atmospheric circulation and ocean wave model is necessary. Earlier investigations have been carried out using coupled atmosphere/wave models for studying both idealized cases (Lionelli et.al 1998) and for more realistic situations (Doyle 1994, Janssen 1994). In these studies, the horizontal grid resolution have been relatively coarse ( km), and they have mostly focused on the development of atmospheric lows in the mid-latitudes. Although there is some controversy on the importance of the effect, they all seems to agree on the following points:
The coupling has a significant effect on the development of the ocean wave field, wind at10 m height and the momentum transfer.
It has only a minor effect on the development of the atmospheric pressure and the life cycle of the mid latitude low pressure systems.
The effect is stronger for smaller scale atmospheric structures which appear when the horizontal grid resolution increases. However,
Since we indent to investigate this effect on small scale atmospheric phenomena, like polar lows, a horizontal resolution of about km is necessary. To our knowledge, this has never been done before. Lionelli et. al. (1998) studied the effect of coupling on the development of an idealized mid-latitude baroclinic instability. They found that the increased surface roughness at the early stages of the process, lead to a significantly larger heat flux from the ocean to the atmosphere. However, this increased heat flux did only have a minor effect on the development of the atmospheric low. They argue that the reason for this is that the life cycle and intensity of a mid-latitude low is strongly dominated by the baroclinic instability of the basic flow.
On this background we suggest that the changes in surface roughness due to wave age dependent stress may significantly alter life cycle of instabilities which has the heat flux from the ocean as its main driving force.
Model tools and observations
The atmospheric model to be used in this part of the study, is the HIRHAM-model (which is the HIRLAM - High Resolution Limited Area Model described in Källén 1996 with a modified physics package). This is the same model which is used in PT1 for dynamic downscaling. As ocean wave model we will use the third generation wave model WAM (Wave Modelling), developed by an international group of scientists (The WAMDI Group, 1988). At The Norwegian Meteorological Institute versions of both models have been developed for MPP-computers (Massive Parallel Processing), and are now being used for operational weather- and wave forecasting. They are set up to be run on identical grid.
For the coupling we will apply the OASIS software which is described in the chapter `Coupled atmosphere-ocean modelling'.
Since very few observations of stress or surface fluxes are available, the surface flux parameterization must be evaluated indirectly using other observations. An important tool in this connection will be the ability to use satellite observation in a coupled objective analysis system for ocean surface wind and sea state. In this system we will assimilate satellite altimeter observations of wind speed and wave height from ERS and ENVISAT satellite radar altimeters. Possibly also other surface observations could be used. DNMI has a large database of ERS altimeter and scatterometer observations back to 1992 (see Breivik and Reistad, 1994) and we aim at processing observations from ENVISAT from 2000.
The analysis system is a further development of the currently operational altimeter wave data assimilation system at DNMI, and by using a coupled system which lets observations simultaneously affect both wind field and wave field the observations will be utilized in a more optimal way.
The optimal surface analyses produced this way can be used as an initial state of wind field and sea state for model runs of interesting cases with different formulations for the surface stresses. The prognoses using the various surface flux parameterizations can then be evaluated against satellite observations in the area.
Coupled atmosphere-ocean modelling
The ARPEGE-IFS climate model (Courtier et al., 1991; Déqué et al., 1994) is already chosen as the atmospheric model under PT4. In RegClim the model is used with variable resolution (Courtier and Geleyn 1988, Deque and Piedelievre 1995, Deque et al., 1998). ARPEGE has been adapted to different Norwegian super-computer platforms (Cray J90, SGI-Cray Origin 2000) and several climate simulations with prescribed sea-surface temperatures (SST) have been performed (Kvamstø, pers. comm.).
We choose to couple ARPEGE with the ocean model MICOM used in PT2. The MICOM model was originally developed by Rainer Bleck and co-workers at the University of Miami (Bleck et al., 1992). In RegClim MICOM is used both as a global and a limited area model with variable resolution. It has been used at NERSC as a modelling tool to study such diverse problems as the carbon cycle in the North Atlantic (Drange 1994, 1997) and the stratified circulation over abrupt topography on the Norwegian continental shelf (Budgell et al., 1994). An important aspect of MICOM, which is particularly important for climate studies, is its ability to conserve water masses. This property is linked to the isopycnal nature of the model. MICOM is now being adapted for use in Arctic areas and coupled to a sea ice model. Several inherent parameterizations relevant for the Arctic Ocean are being tested in PT2.
We propose to do the coupling between ARPEGE and MICOM in the frame of the software package OASIS developed by Dr. Terray at National Centre for climate modelling and global change, Toulouse, France (CERFACS). OASIS is well recognised and today widely used at many climate centres (e.g ECMWF, Max Planck Institute and CERFACS) (http://www..).
Tasks
The objective of the extension is to implement and test a coupled atmospheric/ocean model for air/sea interaction in the North Atlantic. There are presently six tasks in PT4. Three of these (4.3, 4.4 and 4.6) deal with application of the quasi-coupling procedure (QCP) on both present day and future climate simulations. A straight-forward replacement of the QCP experiment originally planned, would be to integrate the AOGCM over the same time interval with same spatial resolution in both model components as originally planned in the QCP experiment. However, in a fully coupled system, an integration interval of 10-15 years may be too short due to the fact that any drift in the mean (model) ocean state or misrepresentation of interdecadal coupled oscillations may disturb the signal of interest. We therefore suggest a different setup with longer integration time in order to get a representative variability spectrum of the model and in this way quantify any of the above mentioned ``error'' sources. For our purposes an integration interval of at least 50 years should be sufficient in order to obtain representative characteristics of the variability spectrum, up to decadal variations, of the coupled system (Sutton 1997, Hurrell 1995). Longer integrations will be made if computer resources are available. The coupled configuration may consist of MICOM with variable resolution that gives sufficient description of the dynamics and thermodynamics in the target area and ARPEGE in with regular horizontal resolution of T42. Following studies like Huck et al (1997), Delworth et al. (1994) and Frakignoul et al. (1992), it seems that with a T42 (2.8 degrees) resolution, the atmospheric forcing (on the variably resolved ocean) should be represented in sufficient detail. At this resolution, the relevant atmospheric phenomena are resolved and the computer requirements will be met by the national resources. To interpret the simulated atmospheric state in better detail, chosen time-slices of 5 years in the coupled simulation can be run with the ARCM, HIRHAM, possibly coupled with a slab-ocean model.
Task 4.1: (IDENTICAL TO ORIGINAL TASK 4.1)
Task 4.2: (IDENTICAL TO ORIGINAL TASK 4.2)
Task 4.3: (REPLACES ORIGINAL TASK 4.3)
Technical Coupling of ARPEGE/MICOM and initialisation
The coupling will be done with the OASIS software mentioned earlier. This is a technical task which will be made with help from Dr. Terray at CERFACS. Test for smaller time periods will be made to ensure that the coupling works satisfactory.
It is a complicated task to initialise a coupled model so that unrealistic climate drift is prevented. The main problem is to spin up the ocean model and long integrations are here usually needed to ensure the needed balance. In a RegClim setting, slice experiments with initial conditions from an AOGCM should be made. This means that the AORCM must be started from states predicted by a AOGCM. However, for the ocean part this will be a major task since the resolution in the regional version is considerably higher. The main steps of the initialisation procedure we will employ are as follows: i) A first initial state may be obtained from an ongoing experiment with MICOM, where the model will be run for at least 300 years with climatological atmospheric forcing (repeated annual cycle of monthly means). ii) Use the preliminary initial state and run MICOM with forcing fluxes from a selected year in the AOGCM experiment (from MPI) until a quasi equilibrium state is achieved (probably not more that 100 years of simulation). Again the atmospheric forcing will be monthly mean fluxes applied in a repeated annual cycle. At this stage the initial conditions of MICOM should correspond to the ocean state of the AOGCM at the beginning of the selected time-slice. One may note here that simulating 100 years with MICOM takes about 1 month (wall-clock time) on the SGI-Cray Origin 2000 computer.
Task 4.4: (REPLACES ORIGINAL TASK 4.4)
Control run with AORCMS on present climate
Internationally, atmospheric climate models are often tested on present climate in so-called AMIP runs (Gates, 1992). The test period is usually 10 years. Coupled models are now also being tested in similar so-called CMIP1 runs (http://www-pcmdi.llnl.gov/covey/cmip/cmiphome.html), where external forcing terms (CO2, solar luminosity, etc.) are kept constant. The ARPEGE model is being tested in a AMIP-type of run for 10 years (task 4.1). Similarly, the MICOM model is being tested in a longer run which also cover the same 10 years (task 2.2). We propose to make a kind of a CMIP1 run with AORCMS as described above. The length of the integration period should be up to 50 years. Subsequently, selected time-slices of 5 years should be run with HIRHAM, possibly coupled with a slab-ocean model.
The results will be evaluated for both atmosphere and ocean and compared with the results of the stand-alone simulations in task 4.1 and task 2.2 and with available observations of the atmosphere and ocean.
Task 4.5: (IDENTICAL TO ORIGINAL TASK 4.5)
Task 4.6: (REPLACES ORIGINAL TASK 4.6)
Future climate simulations with coupling
We here propose a similar run as under 4.4, with the difference that the initial conditions will be taken from a simulated future state of the atmospheric/oceanic system by an AOGCM.
Task 4.7: (NEW)
Technical Coupling of HIRHAM and WAM.
The coupling between the atmosphere model HIRHAM and the wave model WAM will be carried out using the OASIS software. The model will be set up to run in parallel mode on the Cray T3E computer at NTNU. In this task the model domain will be an idealized zonal channel with cyclic boundary conditions.
Various formulations for the air-sea fluxes will be implemented. In particular, we will study the existing models for calculation of the wave induced stress from the ocean wave spectrum.
Task 4.8: (NEW)
Air-Sea Interaction Case studies
Weather charts and literature will be examined and a suitable situation will be selected for a case study. Here, we will focus our attention on situations with strong thermal differences across the marginal ice zone, and the subsequent formation of atmospheric instabilities (polar lows etc.).
The case studies will be carried out using the coupled atmosphere/wave model and the coupled system for data assimilation. The prognoses using the various surface flux parameterizations can then be evaluated against satellite observations in the area.
The models for air-sea fluxes will be evaluated if possible we will suggest improvements of these models.
Relations to other Principal Tasks
PT1: Results from PT4 will be evaluated with the aim of improving process descriptions in the models applied in PT1. Possible impovements of the parameterization of air-sea interaction processes will be implementet in the HIRHAM model.
PT2: PT2 will provide the ocean model to be used in PT4. Tasks 4.7 and 4.8 will provide the model tools for Task 2.3 under PT2.
PT5: Task 4.8 will be coordinated with the investigations of shallow convection under task 5.8.
PT7: As before.
PT8: As before.
Milestones
Institutions and personnel
Task 4.1-4.4 and 4.6: The work 4.1 -4.2 is to be carried out at GfI-UiB by Dr. N. G. Kvamstø. It is planned that Kvamstø will fill one full position. Tore Furevik, who will defend his doctor thesis in summer 1998, will be working full time on 4.3-4.4, 4.6 together with Drs. Drange and Kvamstø. His working time will be evenly shared between GfI-UiB and NERSC.
Task 4.5-4.6: The work will be organized as a collaboration between scientists in Bergen and Oslo. In Bergen the work will be performed at NERSC and IMR, and in Oslo by DNMI. At NERSC the work will be headed by Dr. Helge Drange (PI for PT2), and will involve Dr. K. Simonsen and the modelling team affiliated with the recently established G. C. Rieber Climate Institute within NERSC. The work at IMR will be headed by Dr. Bjørn Ådlandsvik who will work together with Dr. Paul Budgell. The work at DNMI will be headed by Bruce Hackett who will work in close collaboration with Drs. H. Engedahl, Ø. Sætra and L. P. Røed (PI PT7). Also the remaining modelling team at DNMI will be involved in several of the roposed tasks.
Task 4.7-4.8: The work will be carried out at DNMI in Oslo by Dr. Ø. Sætra, Dr. J.E. Haugen, H. Schyberg and L.A. Breivik.
Budget for PT4
The following numbers give contributions to the different intitutions in units of Person-years. Earlier funds granted (or applied for earlier for 2000 and 2001) from NFR ro RegClim are given in brackets. New funds applied for are given in bold types.
DNMI's activity on quasi-coupling, originally under task 4.6, has been transferred to the new tasks 4.7 and 4.8, and are given in brackets here.
References
Bleck, R., C. Rooth, D. Hu and L.T. Smith, 1992: Salinity-driven thermocline transients in a wind- and thermohaline-forced isopycnic coordinate model of the North Atlantic. J. Phys. Oceanogr, 22, 1486-1505.
Breivik, L.A. and Reistad, M. (1994): Assimilation of ERS-1 Altimeter Wave Heights in an Operational Numerical Wave Model. Weather and Forecasting, 9. No. 3.
Budgell, W.P., B. Hackett, L.P. Røed and P.E. Bjerke, 1994: A numerical investigation of stratified circulation over abrupt topography on the Norwegian continental shelf. In Proceedings of the 4th International Symposium on Stratified Flows, Grenoble, 29 June - 2 July, 1994.
Charnock, H. (1955): Wind stress on a water surface. Quart. J. Roy. Meteor. Sol., 81, 639-640.
Courtier, Ph., Freydier, C., Geleyn, J.F., Rabier, F., and Rochas, M. 1991: The ARPEGE project at METEO-FRANCE. In: Proc ECMWF Workshop on Numerical Methods in Atmospheric Modelling, 9-13 Sept. 1991, vol. 2, 193-231. ECMWF, Shinfield Park, Reading, UK.
Courtier, P., and Geleyn, J.F., 1988: A global numerical weather prediction model with variable resolution: application to shallow water equations. Q J R Meteor Soc, 114: 1321-1346.
Delworth, T.L., S. Manabe, R.J. Stouffer, 1993: Interdecadal Variations of the thermohaline
Déqué, M., A. Dreveton, A. Braun, and D. Cariolle, 1994: The ARPEGE/IFS atmosphere model: a contribution to the French community climate modelling. Climate Dynamics, 10, 249-266.
Déqué, M. and J. Ph. Piedelievre, 1995: High resolution climate simulation over Europe. Clim. Dyn.,7: 321-339.
Déqué, M. , P. Marquet and R. G. Jones, 1998: Simulation of climate change over Europe using a global variable resolution model. Clim. Dyn.,14, 173 - 189.
Donelan, M.A., Drenen, W.M. and Katsaros, K.B. (1997): The Air-Sea Momentum Flux in Conditions of Wind Sea and Swell. Journ. Phys. Oceanography. 27. 2087-2099.
Doyle, J.D. (1994): Air-Sea Interaction During Marine Cyclogenesis. In symposium proc.: The Life Cycles of Extratropical Cyclones (ed. S. Grønås and M.A. Shapiro), pp. 61-66. University of Bergen, Norway.
Drange, H., 1994: An Isopycnic Coordinate Carbon cycle Model for the North Atlantic; and the Possibility of Disposing Fossil Fuels CO2 in the Ocean. PhD Thesis Nansen Environm. Remote Sensing Centr. and Dep. of Math. Univ. of Bergen, Norway (286pp).
Drange, H., 1997: An isopycnin coorinate model of the seasonal cycling of carbon and nitrogen in the Atlantic Ocean, Physics and Chemistry of the Earth.
Frankignoul, C., P. Muller, and E. Zorita, 1996: A simple model of the decadal response of the ocean to stochastic wind forcing. J. Phys. Oceanogr.
Gleckler, P.J., D.A. Randall, G. Boer, R. Colman, M. Dix, V. Galin, M. Helfand, J.Kiehl, A. Kitoh, W. Lau, X.-Z. Liang, V. Lykossov, B. McAvaney, K. Miyakoda and S. Planton 1994: Cloud-radiative effects on implied oceanic energy transports as simulated by atmospheric general circulation models. Report No. 15, PCMDI, Lawrence Livermore National Laboratory, Livermore, CA, 13 pp.
Huck, T., A.C. Verdiere, A.J. Weaver, 1997: Decadal variability of the thermohaline circulation in ocean models. Submitted to Journal of Physical Oceanography: June 25, 1997
Hurrell, J., 1995: Decadal trends in the North Atlantic Oscillation: Regional Temperatures and Precipitation, Science, vol 269, 676-679.
Janssen, P.A.E.M. (1994): Results with a coupled wind wave model. ECMWF technical report No. 71.
IPCC, 1996. Climate Change 1995. Cambridge University Press.
Iversen, T., E.J. Førland, L.P. Røed and F. Stordal 1997: RegClim - Regional Climate development under global warming. Project description. DNMI, Pb 43 Blindern, N-0313 Oslo.
Källén, E., 1996: HIRLAM Documentation Manual, System 2.5. SMHI, Norrkoping, Sweden, 1996.
Lionello, P., Malguzzi, P. and Buzzi, A. (1998): Coupling between Atmospheric Circulation and the Ocean Wave Field: An Idealized Case. Journ. Phys. Oceanography. 28. 161-177.
Nordeng, T.E. (1991): On the wave age dependent drag coefficient and roughnes of length at sea. J. Geophys. Res., 96, 7167-7174.
Sutton, R. T., and Allen, M.R. (1997) Decedal predictability of North Atlantic sea
surface temperature and climate. Nature, 388, 563-567.
The WAMDI Group (1988): The WAM Model - A Third Generation Ocean Wave Prediction Model. Journ. Phys. Oceanography. 18. 1775-1810.
Økland, H. and Schyberg, H. (1987): On the contrasting influence of organized moist convection and surface heat flux on a barotropic vortex. Tellus, 39A, 385-389.