Ocean Dynamics (2010) 60:933–955 DOI 10.1007/s10236-010-0296-0

Decadal long simulations of mesoscale structures in the northern North Sea/Skagerrak using two ocean models Jon Albretsen · Lars Petter Røed

Received: 10 January 2010 / Accepted: 28 April 2010 / Published online: 10 June 2010 © Springer-Verlag 2010

Abstract We consider results from two 27-year-long simulation pairs derived using two different ocean models. We focus on the Skagerrak/North Sea area. Each pair consists of the two terrain-following coordinate models ROMS and MIPOM. The first pair utilizes an eddy-permitting grid, that is, a grid in which the Rossby radius is barely resolved. The second pair utilizes an eddy-resolving grid in which the Rossby radius is truly resolved. The goal is to compare the quality of the two models and the two pairs. To this end we derive statistical properties such as probability density functions and compare them with similar statistics derived from observations. Thereby we obtain insight into whether a truly eddy-resolving model is required to realistically capture the mesoscale statistics. We find that eddy resolution is critical to get the mesoscale statistics correct, in particular, the strength of the current jets. Our results also indicate that the improvement gained by employing the eddy-resolving grid is mostly due to a better resolved topography. In particular, we find that this is the case in areas exhibiting prominent topographic features, such as the deep Norwegian Trench cutting into the heart of the northern North Sea/Skagerrak area. The results also highlight the advantage of first

Responsible Editor: John Grue J. Albretsen (B) Institute of Marine Research, P.O. Box 1870 Nordnes, 5817 Bergen, Norway e-mail: [email protected] J. Albretsen · L. P. Røed Norwegian Meteorological Institute, P.O. Box 43 Blindern, 0313 Oslo, Norway e-mail: [email protected]

performing quality assurance investigations when implementing a new model for a new area. Keywords Mesoscale circulation · ROMS · MIPOM · Model validation · North Sea · Skagerrak

1 Introduction We consider results derived using two ocean models and compare them with ocean observations from the northern North Sea/Skagerrak area. The aim is to get insight into the question of how high the resolution of an ocean model needs to be to realistically capture the statistical properties of the observations. As for instance observed by satellite imagery the sea surface temperature distribution in the North Sea/ Skagerrak area appears as a chaotic small scale pattern. The pattern is associated with the many mesoscale features in the area such as eddies, meanders, current filaments and jets. In turn these structures are manifestations of instabilities caused by the presence of two distinct water masses entering the area. One originates from the fresh Baltic Sea water that enters the area through the Kattegat. When it enters the Skagerrak it mixes with the in-flowing salty water of Atlantic origin entering the area along the western flank of the Norwegian Trench to form the low saline water in the Norwegian Coastal Current (NCC) (Rodhe 1987, 1996; Langenberg 1998; Røed and Fossum 2004; Rodhe et al. 2006; Fossum 2006; Winther and Johannessen 2006; Røed and Albretsen 2007). At the front separating these two water masses we observe a host of mesoscale structures including eddies, current jets and filaments. The pathways of any free floating substance such as cod

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fish eggs spawned in the free water masses of the North Sea therefore heavily depend on the actual pattern at the time of spawning. It is in fact conceivable that cod fish eggs spawned in the North Sea may end up in the Skagerrak rather than staying in the North Sea. The question then arises what exactly is the chance of North Sea spawned cod fish eggs to enter the Skagerrak at all? Our approach to possibly answer this question is to perform long term integrations using models of sufficiently high resolution to capture the statistics associated with the mesoscale structures, which in turn may be used to simulate pathways. The question then is what do we mean by a sufficient resolution? As is common we measure the models ability to support eddies in terms of the number, say N R , of grid cells per (internal) Rossby radius of deformation, that is, N R = L R /s where L R is the Rossby radius and s is a measure of the grid cell length. Commonly N R > 2 is required to be able to support eddies at all once generated. To amply resolve the Rossby radius the thumb of rule is that a number N R ≥ 10 is necessary. In the past we have employed models with mesh sizes of order 4 km. The Rossby radius in our area of interest is about 10– 15 km. Hence N R = 3 to 4, a number which, according to the thumb of rule, leaves us with a model categorized as an eddy-permitting model. The question then arises if a mesh size of 4 km is sufficient to capture the instability processes that generate the eddies? Earlier studies by for instance Fossum (2006) and Albretsen (2007) seems to indicate that this is the case. Given the somewhat limited capacity of today’s computers, the question may be rephrased. Is it possible that we may get away with employing an eddy-permitting model to capture the statistics of the mesoscale structures, or do we have to employ truly eddy-resolving model? The question asked is associated with statistics. Thus we do not intend to validate the deterministic skill of the models. Rather we aim at validating the statistics of the model results against observed statistics. We do this to unveil to which degree the model is able to mimic the observed statistics, and to investigate which of the two models might be better for the task. We focus on the North Sea/Skagerrak area since our long term goal is to investigate the pathways of cod fish eggs spawned in the eastern mid North Sea. Several earlier papers have studied the circulation pattern in areas partly overlapping ours. Perhaps the most relevant study is that of LaCasce et al. (2007) in which MIPOM and ROMS and a third model, the hybrid coordinate model HYCOM, were compared. The area they focused on was the northern North Atlantic and the North Sea, known as the Tampen area (see Fig. 1). The grid size they employed corresponds to

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the “coarse,” eddy permitting mesh used in the present investigation (4 km mesh size). As pointed out by them only a portion of the inflowing Atlantic water in the so called slope current entering the Norwegian Sea west of Scotland between the Faeroe Islands and Shetland peels off to flow into the North Sea. The main portion actually continues northward across the Norwegian Trench opening in the Tampen area. We emphasize though that the portion flowing into the North Sea is important in that it is the main contributor to high salinities in the North Sea and Skagerrak and is a significant heat source during the winter season. Of the three models compared, LaCasce et al. (2007) concluded that only ROMS was able to reproduce the mean circulation pattern near Tampen in accord with observations. Furthermore, the study reported by LaCasce et al. (2007) also compared the three model statistics against in-situ current measurements at the Svinøy section further north off the Norwegian west coast (approximately 63◦ N, 4◦ E), a method also to be employed by us. Based on their statistics they found that the currents produced by ROMS were superior to those of the two other models and in particular that MIPOM produced too weak currents compared to the observed currents. On the other hand they found that in certain locations the ROMS velocities were too energetic. Finally they concluded that even though the observed near-bottom velocities along the slope had a poleward direction with the shelf to the right, MIPOM velocities were consistently equatorward at these depths. ROMS in contrast reproduced the observed velocities at all depths fairly well. They explained this by the fact that ROMS employs higher vertical resolution and more sophisticated numerics, e.g., third order upwind advection and a parabolic spline-based representation in the vertical. Earlier model studies focusing on our area include for instance Berntsen et al. (1996), Langenberg (1998), Berntsen and Svendsen (1999), Røed and Fossum (2004), Fossum (2006), Røed and Albretsen (2007), Albretsen (2007), and Hjøllo et al. (2009). For instance Røed and Fossum (2004), based on a two year integration employing a 4km grid found that MIPOM fairly well simulated the mean circulation. This finding is in line with the findings of Berntsen et al. (1996) and Berntsen and Svendsen (1999) using a slightly different model. Moreover, they also found that the mesoscale patterns produced by the model were qualitatively similar to that observed by satellite imagery. Fossum (2006), employing the fairly sophisticated energy and potential vorticity analyses developed by Fossum and Røed (2006), found that many of the mesoscale eddies, and in particular the recurrent eddy off the southern

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tip of Norway (denoted Lista in Fig. 1), was due to a combination of what was somewhat loosely referred to as barotropic and baroclinic instabilities, corroborating the findings of Langenberg (1998). This result was further strengthened and extended by Albretsen (2007) who maintained that the most important contributor to the instability was the vertical shear instability term, the contribution from the horizontal shear instability and other energy conversion terms being small in comparison. Directly relevant to the present study is Røed and Albretsen (2007) who performed a detailed valida-

tion of the MIPOM model for the northern North Sea/Skagerrak area based on a simulation covering the two years 1997 and 1998. They found that, in general, the model faithfully reproduced many of the observed hydrographic features. Furthermore, they found that the Baltic outflow is, by far, the most significant freshwater source in terms of its impact on the hydrography along the Norwegian coast, a result corroborating the earlier findings of Albretsen and Røed (2006). All of the earlier studies mentioned above base their result on a limited integration period and none of them employed the fine resolution grid of size 1.5km used

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Fig. 1 The regional model domains with bathymetry. The large domain shows the area for the 4 km models, and the small domain covering Skagerrak shows the area for the 1.5 km models

(darker grey colors). The Skagerrak section from where IMR hydrographical data are provided is indicated with a black thick line

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here. We argue that to possibly reproduce statistics we need to perform simulations that are several years long, or even decadal long. Accordingly we have performed four 27-year-long simulations covering the period from 1981 to 2007. Firstly, the two models were run on a 4 km (eddy permitting) grid for an area encompassing the North Sea and its surroundings (Fig. 1) employing the same atmospheric, tidal, freshwater and lateral boundary forcing. This enables us to compare the statistics of the two models, and to investigate to which degree their statistics is a fair reproduction of the observed ones. Next we run the same two models on a finer resolution grid (size of 1.5 km) for a smaller area which is simply nested into the 4 km grid. This enables us to investigate the effect of increasing the resolution to an eddy resolving level. To investigate the impact on the statistics we simply compare the statistics of the two models as well as comparing them to observed statistics. This allows us to draw conclusions regarding whether one model produces a better statistics than the other for the purpose at hand and whether increasing the resolution from eddy permitting to eddy resolving is helpful in improving the model statistics. We organize the paper by first giving a description of the two model systems and how they are implemented for the area in question (Section 2). Then we describe the data we use for validation (Section 3), the validation methods applied (Section 4) followed by a description of the model results (Section 5). We end by offering a summary and a discussion including some concluding remarks (Section 6).

2 Model systems The two model systems we employ are the Norwegian Meteorological Institute’s version of the Princeton Ocean Model, MIPOM (Blumberg and Mellor 1987; Engedahl 1995; Røed and Fossum 2004; Røed and Albretsen 2007) and the Regional Ocean Modeling System, ROMS (e.g., Shchepetkin and McWilliams 2005; Haidvogel et al. 2008). We have chosen to use these models simply because they are easily available to us. In particular we have almost 20 years experience in using MIPOM, a model which is at the core of the model based ocean nowcast/forecast system at Norwegian Meteorological Institute. Since the implementation of MIPOM at the Norwegian Meteorological Institute in the late 1980s it has become a well tuned and calibrated model that, despite the fact that it is becoming of age, gives fairly good results. In particular this is true regarding the circulation of the

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Northern Seas1 (e.g., Røed and Fossum 2004; LaCasce and Engedahl 2005; Røed and Albretsen 2007, and references therein). Other versions of the model are widely used in the international oceanographic community, and its user group is still active. ROMS on the other hand is a modern code and offers a large degree of flexibility with several builtin (higher order) advection schemes, vertical mixing schemes, open boundary schemes, etc. It should be emphasized that we use the ROMS version that includes the sea ice module, a version slightly modified also for ice free regions from the canonical version that can be downloaded from the ROMS web page2 . It is not previously thoroughly tested in Norwegian waters, although earlier studies indicate its potential to become the next generation ocean prediction model at met.no (LaCasce et al. 2007; Melsom et al. 2009). MIPOM and ROMS are free-surface, hydrostatic, primitive equation models, employing a terrainfollowing coordinate (σ -coordinate) in the vertical. We note, however, that ROMS employs a much more flexible and modified σ -coordinate due to Song and Haidvogel (1994). They are both finite difference models employing a time splitting between the fast external mode and the slower internal mode. The number of vertical levels and length of time steps employed are however different, and these are also changed when increasing the resolution as revealed in Table 1. We would like to emphasize that reduction in sigma-levels in the MIPOM configurations is due to numerical instabilities in the shallowest areas. ROMS has a more advanced built-in distribution of the spacing between the vertical levels, in particular near surface and bottom, and this prevents surface layers to be too thin in areas with the minimum depth of for instance 10 m. As horizontal advection scheme, we apply the standard second order centered scheme (leapfrog) in MIPOM, while we make use of the third order upwind scheme in ROMS. In the vertical the parabolic splinebased representation of Shchepetkin and McWilliams (2005) is used in ROMS, while MIPOM applies a first order (forward in time) upwind scheme. As nesting condition and open boundary condition we use the Flow Relaxation Scheme (FRS) in MIPOM as outlined in Martinsen and Engedahl (1987) for all dynamic variables. In ROMS, we chose to make use of the built in gradient condition in combination with a nudging condition.

1 The Northern Seas encompass the Norwegian, Greenland and Iceland Seas and the adjacent Arctic and Barents Seas 2 http://myroms.org

Ocean Dynamics (2010) 60:933–955 Table 1 Configuration of the model simulations

Item

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No. of vertical levels Long (internal) time step Short (external) time step Horizontal dissipation Vertical mixing Horizontal advection scheme

26 21 150 s 60 s 5s 1.5 s Smagorinsky Mellor-Yamada 2.5 level 2nd order centered

Regarding vertical mixing we use the Generic Length-Scale second order turbulence closure of Umlauf and Burchard (2003) in ROMS, while we use the traditional Mellor-Yamada Level 2.5 (Mellor and Yamada 1982) in MIPOM. Furthermore, in MIPOM we parameterize the horizontal eddy viscosity in accord with Smagorinsky (1963). No explicit horizontal eddy viscosity term is activated in ROMS, but there is some weak numerical, horizontal momentum diffusion left due to the application of the third order upwind advection scheme. To keep things as similar as possible we run both model systems on exactly the same geographical domains. As displayed in Fig. 1 the 4km domain covers the entire North Sea and Skagerrak area. At the open boundaries of this domain we use the Simple Ocean Data Assimilation (SODA) as reported in Carton et al. (2000b,a) as input. Compared to other reanalysis ocean products SODA is one of the better in capturing water masses (Gemmel et al. 2009). Since the SODA data base covers the period until 2004 only, we extend the database using the monthly climatological values from the EKASC archive of Engedahl et al. (1998) for the last three years. The 1.5 km domains on the other hand cover a smaller area encompassing Skagerrak only (Fig. 1). The domain is nested into the 4km domain. Hence results from the coarser model are used as input at its open boundaries. The bathymetry is based on an improved version of the ETOPO-2 database from the National Geophysical Data Centre (NGDC). Note that the bathymetry in the MIPOM and ROMS simulations is smoothed. The MIPOM bathymetry is smoothed applying a simple filter to avoid too much 2x noise to be generated which in turn must be damped by excessive eddy viscosity. In ROMS the bathymetry is smoothed to fulfill the common restriction in ROMS on the r-factor3 and to avoid model instability and/or spurious deep currents. The region along the Norwegian coast in Skagerrak, in particular, the Norwegian Trench, has steep bottom slopes, and using terrain following coordinate models = |h(i − 1) − h(i)|/|h(i − 1) + h(i)| where h is the topography and the indices i indicate a model grid point.

3r

937 MIPOM 1.5 km

ROMS 4 km

ROMS 1.5 km

32 32 120 s 90 s 4s 3s No explicit diffusion GLS mixing scheme 3rd order upwind

may cause false velocities due to internal pressure errors. Fossum (2006) investigated the response of internal pressure errors in a MIPOM 4km configuration encompassing the northern North Sea and Skagerrak, and she found that these velocities were less than 0.05 m/s. We then assume that this conclusion holds for our MIPOM simulations, and that velocities associated with internal pressure errors can be neglected. Berntsen and Thiem (2007) state that the internal pressure error decreases as the bathymetry is smoothed, and we assume that this holds for the ROMS simulations as well. In addition, problems with such errors have been avoided by using more generalized topography following coordinate systems (Song and Haidvogel 1994) and more advanced numerical techniques. The smoothing of the bathymetry, however, will create an additional source of errors (Di Lorenzo et al. 2006), but we ignore them in our simulations. Eight dominant tidal constituents are included. Four of them are semi-diurnal (M2 , S2 , N2 and K2 ) and four are diurnal (K1 , O1 , P1 and Q1 ). The amplitude and phase information for these constituents are obtained from the numerical simulations of Flather (1981) and Gjevik et al. (1990). To eliminate most of the tidal motion in the model results, all model fields used in the validation and verification are averaged over 24 h. Røed and Fossum (2004) investigated the spectral properties of currents at three locations in this area and were able to define mesoscale (eddy) motion with periods of 2–10 days. Applying daily means in our analysis should then capture current events associated with mesoscale motion. As atmospheric input we mainly use the ERA-40 re-analysis (1.125∗ 1.125 degrees resolution) data base developed by the European Centre for Medium-Range Weather Forecasts (ECMWF) with forcing fields every sixth hour. This data base ends 2001, and hence to get atmospheric input for the remaining integration period we extended this data base with the analysis from the operational ECMWF model for the years 2002–2007. The riverine freshwater fluxes encompass the discharges from all the major rivers in the area, and monthly climatological values are used. Note that we use 1980 as a spin up year and that no data assimilation is applied in any of the simulations.

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Finally, we emphasize that the two models employ similar parameterizations of the ocean-atmosphere fluxes at the free surface. Regarding MIPOM we calculate the fluxes in a separate module as detailed in Røed and Debernard (2004). In ROMS we use the bulk flux calculations that come with the sea ice version.

3 Validation data Within the context of studying pathways in the ocean, the most rationale validation data are currents. However, we note that long time series of currents in the ocean are in general scarce. This is also true for the Skagerrak/North Sea area. In fact we have only been able to get hold of one time series located at the flank of the shelf along the southeastern coast of Norway, displayed as Torungen in Fig. 1. The series is about five months long starting October 27, 1992 and ending April 4, 1993. It consists of measurements of the horizontal current component at standard depths every 10 min. In contrast hydrographic data are more plentiful, and more easily available. A particular valuable data set consists of temperature and salinity measurements originating from the Institute of Marine Research monthly cruises across the Skagerrak between Norway and Denmark, along the so called Torungen-Hirtshals section (Fig. 1). It contains, with only a few exceptions, data from each month during the entire simulation period and the collection counts 293 data sets from January 1981 through December 2007. Each data set in turn consists of 12 individual CTD casts across the transect. The data set is especially valuable as it covers both the inflow of high saline water from the North Sea of Atlantic origin and the outflow of fresher water along the Norwegian coast known as the Norwegian Coastal Current4 . The transects are typically completed in less than a day (∼ 12–18 h). In addition to the Torungen-Hirtshals section data we have also extracted hydrographic data from the data base at the International Council for the Exploration of the Sea (ICES)5 . These data consist of publically available hydrographic measurements, mostly CTD casts, distributed irregularly in space and time, and they cover the entire simulation period. We note that most of the hydrographic data consist of CTD casts. Each measurement is therefore as a rule one single depth profile of salinity and temperature at a 4 As

noted by Røed and Albretsen (2007) the most important fresh water source for the Norwegian Coastal Current is water originating from the Baltic Sea.

5 http://ices.dk

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particular geographical location per day. Furthermore the observed current data consist of 10 min averaged measurements at fixed, standard depths. This is in contrast to the model results which are simply stored as daily averages. To facilitate a meaningful comparison of model results and observations we have therefore averaged the 10 min measured current data over one day (24 h) to produce data compatible with the model result. With regard to the hydrographic data we assume that the single day profile is representative of the daily average for the day in question. This assumption is certainly true regarding the salinity measurements, and also concerning the temperature at depths. However, the assumption is questionable when related to the temperature in the upper water masses, where the temperature is affected by the incoming solar (shortwave) radiation in the daytime and outgoing long-wave radiation during nighttime.

4 Validation methods The validation methods we use range from comparison of time mean horizontal fields, comparison of vertical sections, in particular the Torungen-Hirtshals section, comparison through production of scatter diagrams and probability density functions (PDF). Since our purpose is to investigate the skill of the various models with respect to its ability to reproduce the statistical properties of the observed currents, our focus is on the PDFs, and in particular PDFs of currents. We underline that in general a perfect PDF distribution is not a measure of the model’s forecast skill. A scatter diagram may still show very low correlation coefficients and the root mean square error (RMSE) may still be high. Reproduction of the observed PDFs, however, indicates that the model is useful as a “climate” model, and hence is useful for our purposes. To produce horizontal mean fields based on the hydrographic data we have first mapped the model results onto the observations’ location and time (day) and then gridded both measurements and model results onto a regular geographical grid with 20km horizontal resolution. As this may result in more than one CTD cast within one grid cell at the same day we average them to obtain a single grid profile (daily average). Finally we average them in time over the entire 27year simulation period. In grid cells where there are too few measurements within the simulation period to produce a meaningful mean, somewhat arbitrary set at fewer than 20 observations, the grid cell will appear blank. We also separate between measurements pertaining to the “mixed layer,” corresponding to measure-

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ments in the upper 20 m, and those pertaining to the deeper water masses, corresponding to measurements below 50 m depth. Time mean vertical sections are produced in a similar manner, but then data solely from the Torungen-Hirtshals section are used, i.e., the IMR hydrographical data. To facilitate a meaningful comparison the model results are handled exactly the same way. Thus model results are first mapped onto the observations by extracting model results corresponding to the same time, geographical position and depth as the CTD cast. Thereafter the model results are gridded and then finally time averaged to form the simulated mean field. To produce the scatter diagrams and PDFs of currents relating to the one single, 5 months long, current profile available to us, we have mapped the model results onto the observational depths and dates. Since we have model results not only for the “winter” season when the measurements where taken, we have also extracted model results for all 26 winter seasons (from November 1981 to March 2007), resulting in what may be viewed as 26 independent realizations of the same time series. In a statistical sense they may therefore be looked upon as 26 members of an ensemble. As a diagnostic tool to illustrate the spread of the ensemble for each model we have chosen the rank histogram. The underlying assumption for a rank histogram is to distribute the predicted variable from each model’s ensemble members in bins or ranges such that the probability of occurrence of the measured variable within each bin is equal. Rank histograms are prepared by determining which of the ranked bins the observation falls into for each case, and then plotting a simple histogram of the total occurrences in each bin. We have chosen current speed in our diagnose of each model’s ability to reproduce the statistical properties of the observed currents. Since our purpose is to validate the statistical properties of the model currents, it would be useful to make use of the hydrographic data base. To this end we first note that currents consist of two components or modes; a barotropic component and a baroclinic component. The barotropic component (or external mode) refers to that part of the current which is forced by the pressure forcing disregarding the stratification. It is therefore in general depth independent, except in relatively thin frictional layers close to the surface and bottom (relates to deep seas with low tidal velocities). In contrast the baroclinic current component (or internal mode) owes its very existence to the presence of a density stratification. A common method whereby the baroclinic current component may be estimated from hydrographic data alone is to assume that the

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motion satisfies the hydrostatic approximation and is in geostrophic balance, i.e., satisfies the thermal wind relation. Under these circumstances the baroclinic current component is proportional to the density gradients which in turn may be estimated from hydrographic data. The resulting current is commonly referred to as the geostrophic current component. We emphasize that the accuracy of this estimate of the baroclinic current component depends on the degree to which the current satisfies the thermal wind balance. We can therefore, to a certain extent, utilize the hydrographic data to validate model currents. In particular this is true in areas where the currents are in an approximate geostrophic balance. This is for instance the case along the Norwegian coast where the so called Norwegian Coastal Current is in essence a density driven current. Finally we note that since the geostrophic currents depend on the gradients only, the currents may validate well even though the absolute values of the temperature and salinity differ from the observed ones.

5 Results 5.1 Salinity We start by comparing the salinities of the two 4 km models against each other and against the ICES data. We repeat that the ICES data are assumed to represent the daily average at the day the CTD cast was made. We have averaged model errors (defined as mod − ob s) within gridded regions for the whole simulation period to quantify the models’ salinity bias. The salinity bias for MIPOM and ROMS for the mixed layer (all measurements above 20 m depth) is shown in Fig. 2 (upper panels). The salinity in MIPOM validates well in the North Sea, but has a positive bias along the British and Norwegian coast on the order of 0.5–1 psu. The salinity bias in the mixed layer in ROMS is less positive than in MIPOM, and ROMS scores well in the whole North Sea except for the near shore regions off the Norwegian coast. The positive salinity biases in both MIPOM and ROMS in the Norwegian Coastal Current area indicate that there are persistent problems with the discharge of brackish water from the Baltic Sea and/or fresh water from rivers. The salinity bias for all depths below 50m is shown in Fig. 2 (lower panels). ROMS validates better than MIPOM, but both models display a positive salinity bias in the middle of the North Sea. A more detailed validation of salinity with depths across the Skagerrak is accomplished using the IMR measurements from the Hirtshals (Denmark) -

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MIPOM.4KM Innov_salt_hordistribution 0m 3.5 4 3 3.5 2.5 3 2 2.5 1.5 2 1 1.5 0.5 1 0 0.5 0.5 0 1 0.5 1.5 1 2 1.5 2.5 2 3 2.5 3.5 3 4 3.5

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d.

Fig. 2 The salinity bias between ICES data and model results (from the 4-km models) for all depths above 20-m depth (upper panels) and below 50-m depth (lower panels) averaged over the years 1981 to 2007. Biases from MIPOM are shown in a and c, and from ROMS in b and d. The contour interval is 0.5 psu for

the surface layer salinity and 0.1 psu for the bottom salinity. Red colors indicate that the model has a positive salinity bias, i.e., too salt. The grey areas indicate that fewer than 20 observations where available

Torungen (Norway) section. We show salinity biases for the 4km models only (Fig. 3), because the statistical hydrographical properties are comparable for both resolutions. The model error in salinity at all stations for all depths are averaged in time for the whole simulation period. The biases in salinity are mostly positive in both

MIPOM and ROMS near the surface, and in particular near the Norwegian coast, but ROMS validates better near the Danish coast. The salinity bias in the Norwegian Coastal Current is approximately equal in both models, and we suggest that this is caused by erroneous external forcing.

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Fig. 3 The salinity bias between IMR data from the Skagerrak section (Denmark to the left) and model results as an average from 1981 to 2007. Bias from the MIPOM 4 km run is shown in a and ROMS 4 km in b. The colors follow the values along the

colorbar with irregular equidistance. Non-blue colors indicate in which area and depths the model is too salt. Note that the vertical axis (depth in meters) is stretched for the upper 100 m

The same salinity observations from IMR across the Skagerrak transect along with the corresponding model values are presented as PDFs in Fig. 4. By sorting the

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Fig. 4 Probability density functions of salinity based on IMR data from the Skagerrak transect and corresponding model results from the same location and time. The PDFs are based on values for the years 1981 to 2007 and they are divided into two

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depth regimes, i.e., above (a) and below (b) 100-m depth. The black line denotes observations, the blue and red line are from the MIPOM and ROMS results, respectively. Salinities are in psu

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Fig. 5 Surface salinity values off Torungen along the Norwegian coast in Skagerrak from both measurements and models are displayed as a time series with a 10-year moving average and as b scatter plot displaying the models’ abilities to reproduce the surface salinity within the Norwegian Coastal Current. The measurements come from the monthly cruises across Skagerrak between Norway and Denmark and corresponding model results are retrieved from MIPOM 4 km (red color) and ROMS 4 km (blue color). The horizontal axis in the upper panel denotes the time in years, and the vertical axis denotes the salinity value. The observed SSS is displayed as black pentagrams. The horizontal axis in the scatter plot denotes the modelled values while the vertical axis denotes the observations from the same date. The dense shaded areas correspond to the 10-year moving averages of the measurements vs the MIPOM (red) and ROMS (blue) results

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i.e., the extremes. The values are divided into two categories, measurements above 100 m depth and below. For the upper 100 m values, both models reproduce the statistical distribution in salinity well. The MIPOM

and ROMS salinities are slightly displaced to lower values, and this is caused by a underestimation of the highest salinities, i.e., related to the water masses off Denmark and in the central Skagerrak. The represen-

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tation of the near surface salinities is overestimated. For the salinities below 100 m depth both models have too much variance in their distributions and have little resemblance to the observations. The IMR measurements across the Skagerrak section are the most consistent data set available and provide a tool for investigation of potential trends in

MIPOM.4KM Innov_temp_hordistribution 0m 3.5 4 3 3.5 2.5 3 2 2.5 1.5 2 1 1.5 0.5 1 0 0.5 0.5 0 1 0.5 1.5 1 2 1.5 2.5 2 3 2.5 3.5 3 4 3.5

ROMS.4KM Innov_temp_hordistribution 0m

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the systems. We picked the station located approximately 10 km off the Norwegian coast (off Torungen) within the Norwegian Coastal Current to see how the sea surface salinity (SSS) evolves from 1981 to 2007 in both the observations and the two models (Fig. 5, upper panel). The fluctuations in SSS between each cruise are much larger in the observations than in the

c.

Fig. 6 The temperature bias between ICES data and model results (from the 4-km models) for all depths above 20-m depth (upper panels) and below 50-m depth (lower panels) averaged over the years 1981 to 2007. Biases from MIPOM are shown

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in a and c, and from ROMS in b and d. The contour interval is 0.5◦ C in all panels. Red colors indicate that the model has a positive temperature bias, i.e., too warm. The grey areas indicate that fewer than 20 observations where available

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model results, in particular in the low salinity range. The overall salinity properties in this region are highly dependent on advection of low salinity water from the European continental rivers, the Baltic Sea and the Norwegian rivers east of this location (Albretsen and Røed 2006). However, the lowest SSS values (below 25 psu) are probably caused by advection of the near-shore surface water that is highly influenced by freshwater supply from local (Norwegian) rivers. The 10 year moving average displays that the measured SSS increased from 1981 to 1994 followed by a decrease, but a linear regression shows no drift over the 27 year period. The maximum in the 10-year average is mainly due to less low SSS observations in the early 1990s, and we assume that this is due to the sporadic cruises that accidentally are not able to capture all low salinity events. Linear regression of the time series shows that none of the models have a drift in SSS at this location. However, both models have a positive bias in SSS, and none of them are able to reproduce the low salinity events. The models’ poor ability to reproduce the low salinity events are shown more clearly in Fig. 5 (lower panel), where the same SSS values are displayed in a scatter plot. We relate some of this to the fact that the model set ups do not include realistic riverine freshwater fluxes, and therein are not able to capture

5.2 Temperature The averaged model errors in temperature are shown in Fig. 6. As this is based on a 27-year simulation it is clearly seen that MIPOM is too warm while ROMS scores remarkably well for the upper 20 m without any large biased areas at all. However, ROMS has a larger warm bias than MIPOM below 50 m depth. The main contribution to the warm biases in MIPOM is the summer heating. Temperature is well reproduced during winter seasons, but the modelled summer temperatures are exaggerated, as revealed by time series of sea surface temperature (SST) off Torungen (Fig. 7). The time series are based on SST values from the IMR monthly cruises and corresponding model results from MIPOM

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Fig. 7 Surface temperature off Torungen along the Norwegian coast in Skagerrak. The time series are based on measurements from the monthly cruises across Skagerrak between Norway and Denmark (black lines) and corresponding model results from MIPOM 4 km (red lines) and ROMS 4 km (blue lines). The thin lines show the monthly values while the thick lines show the 10-year moving average. The horizontal axis denotes the time period from 1981 to 2007, and the vertical axis shows the temperature (in ◦ C)

relatively wet/dry periods with large/small discharges. The lowest observed SSS value is around 17 psu, while the lowest modelled value is 24 psu in both models. We find the center of gravity for modelled vs. observed SSS to support the result that both models have a positive bias in salinity with comparable sizes. This is in line with the mean mixed layer salinity shown in Fig. 2 (upper panels). We also find the correlation between observed and modelled SSS to be 0.45 and 0.54 for MIPOM and ROMS, respectively.

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and ROMS. We see that MIPOM overestimates the SST during summer while ROMS underestimates the SST, and we see a warm and cold bias in MIPOM and ROMS, respectively, for this single location. The 10 year moving average from the observations displays an increase in SST of about 1◦ C/decade, and both models reproduce this heating of Skagerrak. The permanent warm bias in SST for this location between 1981 and 2007 in MIPOM is about 0.5◦ C and the corresponding cold bias in ROMS is 0.3◦ C. Although we find biases, the correlation between observed and modelled SST is 0.98 for both models. PDFs based on the IMR temperature data along the Skagerrak transect and the corresponding model values (Fig. 8) show that both models reproduce the temperature values fairly well. For the upper 100 m, the highest temperatures in MIPOM (10–20◦ C) are overrepresented, the lowest (0–5◦ C) match well and the intermediate (5–10◦ C) temperatures have a too low representation. In other words, the main problem with the MIPOM temperatures is the overestimating of the summer heating. The values below 100m are recognized by a small cold bias in the MIPOM results. We link this to production of false values from the second-order centered advection scheme applied in MIPOM. The temperatures in the upper 100 m from ROMS show a similar pattern, but the highest (summer) temperatures (above 16◦ C) are under-represented. The shape of the PDF for temperature values below 100m depth is well reproduced in ROMS compared with the observations.

5.3 Circulation The 27-year averages in currents at 50 m depth from MIPOM and ROMS in the Tampen area are shown in Fig. 9. The northward flow of Atlantic water west of Shetland is recognized in both models, in accord with observations (Orvik and Niller 2002), but the currents are stronger in MIPOM. The average maximum current speed at 50 m depth between The Faeroe Islands and Shetland is about 0.7 and 0.5 m/s in MIPOM and ROMS, respectively. Similar model comparison of currents at 50m is performed by LaCasce et al. (2007). Their results were based on two and a half year long simulations only. We note with satisfaction that our results based on 27-year-long simulations using slightly different versions of ROMS and MIPOM corroborate their findings regarding the circulation pattern in the Tampen area. From our model results we find that only a minor portion of the northward flow in ROMS peels off into the North Sea from the Tampen area. This portion is exaggerated in the MIPOM results, in accordance with LaCasce et al. (2007). In contrast to the relatively high current speed in the Tampen area in MIPOM, ROMS produces the strongest velocities in the cyclonic circulation in Skagerrak. However, within the Norwegian Coastal Current off the Norwegian west coast, both models have comparable average maximum speeds. Having the validation results from the Tampen area of LaCasce et al. (2007) in mind and assuming that the

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depth regimes, i.e., above (a) and below (b) 100-m depth. The black line denotes observations, the blue and red line are from the MIPOM and ROMS results, respectively. Temperatures are in ◦ C

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a. 0.2m/s

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Fig. 9 Long term average (1981–2007) current direction (arrows) and speed (shading) at 50 m depth from the MIPOM 4 km (a) and ROMS 4 km (b) simulations. The area shown is a sub domain

west of Norway and north of Scotland. The contour interval for the current speed is 0.1 m/s, and the areas with more intense currents are displayed with darker grey shading

same conclusions hold for our model simulations, we will compare in-situ current measurements from Skagerrak with MIPOM and ROMS velocities from both the 4km and 1.5 km models. Increasing the model’s

effective resolution, should imply an increase in the eddy activity and the likelihood of capturing more high current events. Validation of the mean speed for the semi-annual time series off the Norwegian southwest

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coast (Fig. 10, upper panel) shows that the 4 km models score well near the surface, but the 1.5 km models have less error than their respective 4 km model closer to the sloping bottom (below 50 m). Note that the bathymetry used in the 1.5 km applications is more realistic around this location. While the measured depth is 120 m, the equilibrium depth in the 1.5 and 4 km models is 163 and 233 m, respectively. The standard deviations from the speed averages based on the same time series (Fig. 10, lower panel) show that the MIPOM runs have too

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Fig. 10 Comparisons between measured and modelled currents off Torungen near the Norwegian coast in Skagerrak (for location see Fig. 1). Mean current speed and standard deviation are shown in a and b, respectively. The speed is denoted in meters per second and the vertical axis shows depth in meters

large variation in near-surface velocities, while this is considerably improved near the bottom when the resolution is increased. We also see an overestimated variation in current speed in the ROMS models, and that the improvement due to better spatial resolution is approximately constant with depth. The current measurements from 13 and 75 m depth and their corresponding model velocities are then picked out and presented as probability density functions (PDFs) split into direction and speed (Fig. 11).

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Fig. 11 Probability density functions of current direction and speed at 13- and 75-m depth for in-situ observations and model velocities. PDFs of current direction from 13 and 75 m are shown in a and b, respectively, and PDFs of speed from 13 and 75 m are shown in c and d, respectively. The horizontal axis denote

direction (in ◦ from northward direction) or speed (in m/s), and the vertical axis denotes the relative frequency. Note that currents following the local isobaths at this location have value 225◦ from the convention that currents from the north and east have an angle of 180◦ and 270◦ , respectively

We see that all models reproduce the main direction of their surface currents in parallel to the local isobaths. While the direction of the currents at 13 m depth from the 1.5 km models coincide well with the observations, these currents in ROMS 4 km are too confined to the local isobaths. The currents at 13 m in MIPOM 4 km are recognized with too many occasions with onshore direction. The latter is seen more clearly at 75 m depth. Increasing MIPOM’s resolution from 4 to 1.5 km improves this weakness considerably, and we see a remarkably good resemblance with observations for this model. At 75 m depth the currents in ROMS are too confined to the isobaths and they miss the small variation in observed current direction. The PDFs from current speed (Fig. 11, bottom panels) are hard to

interpret, but the overall impression is that representations of speed are improved when model resolution is increased. Due to the limited access of current measurements in our validation, we have performed a model ensemble approach to investigate each model’s ability to reproduce the observed current statistics off Torungen. The observed current was valid for five months only (November 1992 to March 1993), but model results from the same location were available for 26 “winter” seasons from November 1981 to March 2007. We then assume that each model has simulated the observed time series of currents off Torungen 26 times independently, and present rank histogram for each model (Fig. 12). We have chosen current speed at 13 m to

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MIPOM 1.5 km in c and from ROMS 1.5 km in d. The size of each ensemble is equal to the number of days within each “winter” period. The horizontal and vertical axes denote the bin number and the relative frequency of occurrence in each bin, respectively

illustrate characteristic differences between the models. Keeping the assumption underlying the rank histogram in mind, that the probability the measured current speed will fall in each bin is equal, we see that ROMS 1.5 km scores well. Its distribution is nearly flat between the bins, and we see only small variations about the “expected” frequency value (0.037). We may then conclude that on the average, the spread of simulated “winter” current speed values off Torungen in ROMS 1.5 km is an approximate representation of the uncertainty of each winter’s modelled state. For MIPOM 4km the observed current speeds occur too frequently in the highest-valued bins, and we can conclude that this model underestimate the current speed. This is improved in MIPOM 1.5 km, but this model also seems

to have a small bias toward underestimation of current speed. For ROMS 4 km the observed current speed tend to occur too often toward the center of the distribution and not frequently enough toward the extremes. This indicates that ROMS 4 km current speed values are over-dispersed on average, i.e., the model values have too large a spread. As a supplement to the averaged current fields (Fig. 9) showing the differences in the cyclonic circulation pattern in Skagerrak between MIPOM and ROMS, we display the mean and eddy kinetic energy fields in the same region. The energy terms are found according to Fossum and Røed (2006) and Albretsen (2007). The higher frequency motions are filtered out by using 24-h block averages of modelled currents.

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Røed and Fossum (2004) showed that the temporal scale of the (eddy) mesoscale motion in the Skagerrak is about 2–10 days. To capture these phenomena in our analysis, we then define the mean motion as a 30day average and the eddy motion as the 24-h average’s deviations from the 30-day mean. The 27-year averaged mean kinetic energy (MKE) for both models applying both horizontal resolutions is shown in Fig. 13. As we corroborated by investigating mean currents in 50 m depth, we see that ROMS is more energetic than MIPOM in both the inflow of Atlantic water along Denmark and within the Norwegian Coastal Current. Increasing the resolution from 4 to 1.5 km also increases

the energetic level in both models. In addition, the MKE patterns in all four realizations are comparable. To get an impression of the variability we have also computed the corresponding 27 year averaged eddy kinetic energy (EKE) for both models and horizontal resolutions as shown in Fig. 14. The EKE increases when resolution is increased, and as for the MKE, ROMS has higher values than MIPOM. We relate most of this to the higher order advection scheme applied in ROMS which increases the theoretical resolution compared with MIPOM. In addition, extra numerical diffusion (from the Asselin filter following the horizontal advection scheme in addition to enhanced vertical

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Fig. 13 Depth averaged mean kinetic energy calculated from the four experiments with focus on Skagerrak. The values are averaged from 1981 to 2007 and the contour interval is 1,500 J/m2 .

The panels show the mean kinetic energy level from a MIPOM 4 km, b ROMS 4 km, c MIPOM 1.5 km and d ROMS 1.5 km

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Fig. 14 Depth averaged eddy kinetic energy calculated from the four experiments with focus on Skagerrak. The values are averaged from 1981 to 2007 and the contour interval is 500 J/m2 .

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mixing near the surface) is used in MIPOM to suppress numerical instabilities, and this may dissipate gradients that could add to the mesoscale motion. In contrast to the MKE patterns, the EKE patterns are not comparable when resolution is increased. We find broad high values in all of the Norwegian Trench in the 1.5 km models with a maximum in the deepest and inner part of the Trench. In the 4 km models the extremes are mostly limited to the coastal and shallower areas, although the ROMS 4 km results indicate an extension of the maximum EKE into the inner part of the Trench. The explanation is therefore due to an increase in the eddy activity when the resolution is increased.

5.4 Geostrophic currents The continuous time series of hydrographic profiles between Denmark and Norway is a valuable data set also for use in estimating the baroclinic component of the geostrophic velocity. We find this analysis useful as it will give information on how well the models reproduce the density gradients independent on the absolute values of salinity and temperature. We apply the standard thermohaline equation to find the baroclinic component of the geostrophic current from each single density field, and by assuming zero velocity at the bottom, the 27-year average is shown in

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Fig. 15. From the estimated baroclinic velocities based on observations and model results we are not able to identify the inflow from the North Sea with Atlantic water masses or the West-Jutland current with the relative light water masses. These flows into Skagerrak are clearly seen in the total current field from the model results, but its fluctuations in the baroclinic field may be smoothed out due to the long term averaging. On the other hand we see clearly that the highest resolution models are able to build up a realistic southwestward current off the Norwegian coast although

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in agreement with our explanation of the difference between eddy-permitting and eddy-resolving models as outlined in Section 1.

6 Summary and discussion We have run two different ocean model systems, MIPOM and ROMS, for 27 years (1981–2007) using similar configurations and identical external forcing. Effects of data assimilation are excluded. Both model systems are run on an eddy-permitting resolution for the North Sea and Skagerrak (4 km) and an eddyresolving resolution for the Skagerrak (1.5 km). Well validated, long hindcast runs are important to be able to understand the behavior of the ocean model in our regional domains. It is also vital to be able to estimate the quality of the modelled current fields when these are applied in particle drift simulations. The circulation pattern in the North Sea/ Skagerrak area appears to consist of randomly distributed mesoscale structures. When we want to ask what is the chance that cod fish eggs spawned in the North Sea enter Skagerrak, we must revert to numerical simulations. It is then crucial that the model is able to reproduce the actual mesoscale pattern, at least statistically. The ocean forecast system at the Norwegian Meteorological Institute has been based on MIPOM for the last two decades. The model has been tested and tuned to behave satisfactory in Norwegian waters, but we have also discovered its weaknesses and limitations. More modern ocean models with more advanced numerics are available from different communities. Based on results from several long, validated model runs, in particular LaCasce et al. (2007), the Institute has decided to replace MIPOM with ROMS. In this study we find that the models confirm many of the conclusions from LaCasce et al. (2007), particularly the current structure in the Tampen area. We find that both MIPOM and ROMS scores well on currents off the Norwegian coast in Skagerrak. The accuracy is improved in both models when the horizontal resolution is increased from 4 to 1.5 km. We experience MIPOM’s remarkable improvements in currents below the mixed layer when the resolution is increased indicating that there is a relation to a more precise representation of the topography. We find that ROMS validates better than MIPOM against surface currents, a result also supported by diagnosing the validation results in an ensemble approach. We have shown that ROMS is more energetic than MIPOM, in particular in the cyclonic circulation in Skagerrak. This result is supported by estimations of kinetic energy. The validation of cur-

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rents below the mixed layer in Skagerrak indicates that ROMS is too energetic in those intermediate layers. As opposed to the comparable patterns in the MKE in Skagerrak between the 4- and 1.5-km models, the EKE have fundamental differences in both size and horizontal distribution. As expected, the EKE values are increased when the model resolution is increased. However, the maximum in EKE in the deepest and inner part of the Norwegian Trench in the 1.5-km models is not seen in the 4-km models. This may indicate that it is necessary to have as high horizontal resolution as 1– 2 km to be able to capture the mesoscale activity properly in this region. A resolution of 4 km is apparently too coarse, and we conclude that a truly eddy resolving model is preferred to capture the statistics associated with the mesoscale structures in Skagerrak, which in turn may be used to simulate pathways, e.g., for cod eggs spawned in the eastern part of the North Sea. In supplement to the model comparison and validation of circulation in Skagerrak, we have performed analysis of the modelled hydrography. The baroclinic currents contribute strongly to the total circulation in this area, and hydrographic measurements are in solid majority compared with the number of current observations. Using the hydrographic measurements and corresponding model results along the transect between Denmark and Norway to find the baroclinic component of the geostrophic current, we show that the 1.5 km resolution models only are able to reproduce a realistic flow along with the Norwegian Coastal Current. The coarser 4km models underestimate the strength of this baroclinic flow by a factor of about two. However, we have not shown that 1.5 km is sufficient to resolve the flow field completely, but leave refinements of the modelling to further studies. When we analyze the hydrography in MIPOM and ROMS and compare the results with measurements from a variety of sources, we find that ROMS in most regions and depths behaves more satisfactory than MIPOM. We note that the version of ROMS used in the present study is slightly modified compared with the canonical version so that surface fluxes of salt and heat are handled in a fashion similar to that done in MIPOM and as described in Røed and Debernard (2004). Results from these exploratory experiments, in which the two ROMS versions are compared, using the 4-km version only, are presented in Albretsen (2009). The main finding of Albretsen (2009) is that the canonical ROMS with its inherent surface heat and salinity fluxes introduces too large positive biases in temperature and salinity all over the domain and in all depths. Improving the representation of the surface fluxes introduces significant, positive impacts on model

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hydrography while only small changes in current properties are experienced. Acknowledgements The Torungen-Hirtshals section data was kindly made available to us by Lars Johan Naustvoll at the Institute of Marine Research Flødevigen, Arendal, Norway. Other hydrographic profile data used was made available to us through the International Council for the Exploration of the Sea (ICES) Oceanographic database. The current measurements were provided by the Norwegian Marine Data Centre, Institute of Marine Research, Bergen, Norway. We would hereby like to thank all the various contributors to these databases for allowing us to use their data. We would also like to thank two anonymous reviewers for comments that helped to improve the readability. This research was supported by the Research Council of Norway through the SKAGCOD Project No. 178322/S40 and the Norwegian Meteorological Institute. Computer time on the IBM p575+ (njord) and the Sun X2200 (titan) at the Norwegian Metacenter for Computational Science was granted by the Research Council of Norway.

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