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Torsten Linders
and
Øyvind Saetra

Abstract

A unique dataset of atmospheric observations over the Nordic Seas has been analyzed to investigate the role of convective available potential energy (CAPE) for the energetics of polar lows. The observations were made during the flight campaign of the Norwegian International Polar Year (IPY) and The Observing System Research and Predictability Experiment (THORPEX) in February and March 2008, which specifically targeted polar lows. The data reveal virtually no conditional instability and very limited CAPE. It is suggested that the significance of CAPE values should be assessed by calculating the time scale t CAPE that is necessary for the heat fluxes from the ocean to transfer the corresponding amount of energy. Even the largest CAPE values have a t CAPE of less than 1 h. These CAPE values are associated with unconditional instability. It is concluded that the observed CAPE should be seen as a temporary stage in an energy flux rather than as an energy reservoir. Based on the findings in this investigation, it is proposed that significant reservoirs of CAPE over the marine Arctic atmosphere are impossible since CAPE production will automatically trigger convection and CAPE is consumed as it is produced.

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Günther Heinemann
and
Øyvind Saetra
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Arne Melsom
and
Øyvind SÆtra

Abstract

A theoretical model for the near-surface velocity profile in the presence of breaking waves is presented. Momentum is accumulated by growing waves and is released upon wave breaking. In effect, such a transition is a process involving a time-dependent surface stress acting on the mean current. In this paper, conventional theory for the Stokes drift is expanded to fourth-order accuracy in wave steepness. It is shown that the higher-order terms lead to an enhancement of the surface Stokes drift and a slight retardation of the Stokes volume flux. Furthermore, the results from the wave theory are used to obtain a bulk parameterization of momentum exchange during the process of wave breaking. The mean currents are then obtained by application of a variation of the “level 2.5” turbulence closure theory of Mellor and Yamada. When compared with the traditional approach of a constant surface stress, the mean Eulerian current exhibits a weak enhancement in the near-surface region, compensated by a negative shift deeper in the water column. However, it is found that the results of Craig and Banner and the results of Craig are not significantly affected by the present theory. Hence, this study helps to explain why the Craig and Banner model agrees well with observations when a realistic, time-varying surface stress acts on the drift currents.

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Arne Melsom
and
Øyvind SÆtra

Abstract

A theoretical model for the near-surface velocity profile in the presence of breaking waves is presented. Momentum is accumulated by growing waves and is released upon wave breaking. In effect, such a transition is a process involving a time-dependent surface stress acting on the mean current. In this paper, conventional theory for the Stokes drift is expanded to fourth-order accuracy in wave steepness. It is shown that the higher-order terms lead to an enhancement of the surface Stokes drift and a slight retardation of the Stokes volume flux. Furthermore, the results from the wave theory are used to obtain a bulk parameterization of momentum exchange during the process of wave breaking. The mean currents are then obtained by application of a variation of the “level 2.5” turbulence closure theory of Mellor and Yamada. When compared with the traditional approach of a constant surface stress, the mean Eulerian current exhibits a weak enhancement in the near-surface region, compensated by a negative shift deeper in the water column. However, it is found that the results of Craig and Banner and the results of Craig are not significantly affected by the present theory. Hence, this study helps to explain why the Craig and Banner model agrees well with observations when a realistic, time-varying surface stress acts on the drift currents.

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Øyvind Saetra
and
Jean-Raymond Bidlot

Abstract

The potential benefits of using the ECMWF Ensemble Prediction System (EPS) for waves and marine surface winds are demonstrated using buoy and platform data as well as altimeter data.

For forecasting purposes, the spread of the different forecasts in the ensemble may indeed be regarded as a measure of the uncertainties in the deterministic predictions. In order to demonstrate this point, a new method is presented in which the ensemble spread is divided into different classes. An upper bound for the model errors is established by calculating the corresponding percentiles of the errors for each separate class. Using this upper bound for the model errors, a strong correlation between the ensemble spread and the deterministic forecast skill is shown.

The reliability of the probability forecasts as derived from the EPS for wind and waves is found to be good. However, the reliability diagrams indicate a small tendency for overconfidence in the wave probability forecasts for waves above 6 and 8 m. This is most pronounced in the Southern Hemisphere, whereas the reliability for the Northern Hemisphere is relatively good.

The impact of using of the wave EPS in decision making is studied by a cost–loss model for the relative economic value. For comparison, poor-man's ensembles (PMEs) are also created by adding normally distributed noise to the control forecasts. This study reveals that the real EPS performs better than both the PME and the control forecasts in terms of relative economic value. When more complex forecasting parameters are considered, such as the joint probability of wave height and period, benefits of using the EPS become even more pronounced.

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Øyvind Saetra
,
Trygve Halsne
,
Ana Carrasco
,
Øyvind Breivik
,
Torstein Pedersen
, and
Kai Håkon Christensen

Abstract

The Lofoten Maelstrom has been known for centuries as one of the strongest open-ocean tidal currents in the world, estimated to reach 3 m s−1, and by some estimates as much as 5 m s−1. The strong current gives rise to choppy seas when waves enter the Moskenes Sound, making the area extremely difficult to navigate. Despite its reputation, few studies of its strength exist, and no stationary in situ measurements for longer time periods have been made due to the challenging conditions. By deploying for the first time in situ wave and current instruments, we confirm some previous estimates of the strength of the current. We also show that its strength is strongly connected with wave breaking. From a consideration of specific forcing terms in the dynamical energy balance equation for waves on a variable current, we assess the impact of the underlying current using a convenient metric formulated as a function of the horizontal current gradients. We find that the horizontal gradients are a likely explanation for the observed enhanced wave breaking during strong currents at a rising tide.

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Øyvind Breivik
,
Ole Johan Aarnes
,
Jean-Raymond Bidlot
,
Ana Carrasco
, and
Øyvind Saetra

Abstract

A method for estimating return values from ensembles of forecasts at advanced lead times is presented. Return values of significant wave height in the northeast Atlantic, the Norwegian Sea, and the North Sea are computed from archived +240-h forecasts of the ECMWF Ensemble Prediction System (EPS) from 1999 to 2009. Three assumptions are made: First, each forecast is representative of a 6-h interval and collectively the dataset is then comparable to a time period of 226 years. Second, the model climate matches the observed distribution, which is confirmed by comparing with buoy data. Third, the ensemble members are sufficiently uncorrelated to be considered independent realizations of the model climate. Anomaly correlations of 0.20 are found, but peak events (>P 97) are entirely uncorrelated. By comparing return values from individual members with return values of subsamples of the dataset it is also found that the estimates follow the same distribution and appear unaffected by correlations in the ensemble. The annual mean and variance over the 11-yr archived period exhibit no significant departures from stationarity compared with a recent reforecast; that is, there is no spurious trend because of model upgrades. The EPS yields significantly higher return values than the 40-yr ECMWF Re-Analysis (ERA-40) and ECMWF Interim Re-Analysis (ERA-Interim) and is in good agreement with the high-resolution 10-km Norwegian Reanalyses (NORA10) hindcast, except in the lee of unresolved islands where EPS overestimates and in enclosed seas where it has low bias. Confidence intervals are half the width of those found for ERA-Interim because of the magnitude of the dataset.

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Øyvind Saetra
,
Hans Hersbach
,
Jean-Raymond Bidlot
, and
David S. Richardson

Abstract

The effects of observation errors on rank histograms and reliability diagrams are investigated using a perfect model approach. The three-variable Lorenz-63 model was used to simulate an idealized ensemble prediction system (EPS) with 50 perturbed ensemble members and one control forecast. Observation errors at verification time were introduced by adding normally distributed noise to the true state at verification time. Besides these simulations, a theoretical analysis was also performed. One of the major findings was that rank histograms are very sensitive to the presence of observation errors, leading to overpopulated upper- and lowermost ranks. This sensitivity was shown to grow for larger ensemble sizes. Reliability diagrams were far less sensitive in this respect. The resulting u-shaped rank histograms can easily be misinterpreted as indicating too little spread in the ensemble prediction system. To account for this effect when real observations are used to assess an ensemble prediction system, normally distributed noise based on the verifying observation error can be added to the ensemble members before the statistics are calculated. The method has been tested for the ECMWF ensemble forecasts of ocean waves and forecasts of the geopotential at 500 hPa. The EPS waves were compared with buoy observations from the Global Telecommunication System (GTS) for a period of almost 3 yr. When the buoy observations were taken as the true value, more than 25% of the observations appeared in the two extreme ranks for the day 3 forecast range. This number was reduced to less than 10% when observation errors were added to the ensemble members. Ensemble forecasts of the 500-hPa geopotential were verified against the ECMWF analysis. When analysis errors were neglected, the maximum number of outliers was more than 10% for most areas except for Europe, where the analysis errors are relatively smaller. Introducing noise to the ensemble members, based on estimates of analysis errors, reduced the number of outliers, particularly in the short range, where a peak around day 1 more or less vanished.

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Øyvind Saetra
,
Jon Albretsen
, and
Peter A. E. M. Janssen

Abstract

The impact of wave-dependent surface stress on the ocean circulation has been studied using surface stresses calculated from a numerical wave model. The main questions to be investigated were what the effect would be on the Ekman currents in the upper ocean and what the impact would be on storm surge predictions. To answer the first question, the response of wave-dependent forcing on an Ekman type of model was studied. Here, the wave forcing was provided by a one-gridpoint version of the wave model. Second, the impact of the waves was studied with a three-dimensional ocean circulation model for the North Sea. Three different experiments were performed for a period of 1 yr. To test the effect on the storm surge signal, the results have been compared with sea level observations from 22 stations along the Norwegian and Dutch coasts. One of the main findings is that calculating stresses in the wave model, thereby introducing sea-state-dependent momentum fluxes, has a strong positive impact on the storm surge modeling compared with applying a traditional parameterization of surface stresses from the 10-m wind speed. When all cases with sea level deviation from the mean of less than 0.5 m were removed, the root-mean-square error for 1 yr averaged over all stations was reduced by approximately 6 cm. Splitting the momentum budget into an Eulerian and a wave part (Stokes drift) has only a negligible effect on the modeling of the sea surface elevation but increases the angular turning of the Eulerian surface drift to the right of the wind direction with an angle of about 4°.

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Jan Erik H. Weber
,
Göran Broström
, and
Øyvind Saetra

Abstract

It is demonstrated that the Eulerian and the Lagrangian descriptions of fluid motion yield the same form for the mean wave-induced volume fluxes in the surface layer of a viscous rotating ocean. In the Eulerian case, the volume fluxes are obtained in the familiar way by integrating the horizontal components of the Navier–Stokes equation in the vertical direction, as seen, for example, in the book by Phillips. In the direct Lagrangian approach, the perturbation equations for the second-order mean drift are integrated in the vertical direction. This yields the advantage that the form drag, which is a source term for the wave-induced transports, can be related to the virtual wave stress that acts to transfer dissipated mean wave momentum into mean currents. In particular, for waves that are periodic in space and time, comparisons between empirical and theoretical relations for the form drag yield an estimate for the wave-induced bulk turbulent eddy viscosity in the surface layer. A simplistic approach extends this analysis to account for wave breaking. By a generalization from a wave component to a wave spectrum, a set of equations for the wave-induced transport in the surface layer is derived for a fully developed sea. Solutions are discussed for an idealized spectral formulation. The problem is formulated such that a numerical wave prediction model can be used to generate the wave-forcing terms in a numerical barotropic ocean surge model. Results from the numerical simulations with a wave-influenced surge model are discussed and compared with similar results from forcing the surge model only by the traditional mean horizontal wind stress computed from the 10-m wind speed. For the simulations presented here, the wave-induced stress constitutes about 50% of the total atmospheric stress for moderate to strong winds.

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