Continental Shelf Research 64 (2013) 1–9

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Continental Shelf Research

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Research papers

Freshwater outflow of the Baltic Sea and transport in the Norwegiancurrent: A statistical correlation analysis based on anumerical experiment

Robinson Hordoir n,a, Christian Dieterich a, Chandan Basu b, Heiner Dietze c, H.E.M. Meier a

a SMHI, Folkborgsvägen 1, 601 76, Norrköping, Swedenb National Supercomputer Centre, Linköping University, SE-581 83 Linköping, Swedenc IFM-GEOMARWischhofstr. 1-324148 Kiel, Germany

a r t i c l e i n f o

Article history:Received 19 September 2012Received in revised form20 March 2013Accepted 12 May 2013Available online 23 May 2013

Keywords:Baltic SeaNorwegian coastal currentFreshwater fluxesNumerical modelStatistical reconstruction

43/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.csr.2013.05.006

esponding author. Tel.: +46 11 495 87 04.ail address: robinson.hordoir@smhi.se (R. Hor

a b s t r a c t

Based on the results of a numerical ocean model, we investigate statistical correlations between windforcing, surface salinity and freshwater transport out of the Baltic Sea on one hand, and Norwegiancoastal current freshwater transport on the other hand. These correlations can be explained in terms ofphysics and reveal how the two freshwater transports are linked with wind forcing, although thisinformation proves to be non-sufficient when it comes to the dynamics of the Norwegian coastal current.Based on statistical correlations, the Baltic Sea freshwater transport signal is reconstructed and shows agood correlation but a poor variability when compared with the measured signal, at least when datafiltered on a two-daily time scale is used. A better variability coherence is reached when data filtered on aweekly or monthly time scale is used. In the latest case, a high degree of precision is reached for thereconstructed signal. Using the same kind of methods for the case of the Norwegian coastal current, thenegative peaks of the freshwater transport signal can be reconstructed based on wind data only, but thepositive peaks are under-represented although some of them exist mostly because the meridional windforcing along the Norwegian coast is taken into account. Adding Norwegian coastal salinity data helpsimproving the reconstruction of the positive peaks, but a major improvement is reached when addingnon-linear terms in the statistical reconstruction. All coefficients used to re-construct both freshwatertransport signals are provided for use in European Shelf or climate modeling configurations.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Several operational or climate simulations require to have aknowledge of the input of freshwater that is provided by the BalticSea, and of the amount of freshwater that is carried by theNorwegian Coastal Current (NCC hereafter). Many methods useclimatological data considering the Baltic Sea as a river input(O'dea et al., 2012), and therefore that its freshwater delivery alongthe North Western European shelf is driven by the freshwater flowof all rivers flowing into the Baltic Sea. Recent studies (Hordoir andMeier, 2010) have showed this assumption to be biased as theBaltic Sea should be considered as a large estuary, and its fresh-water delivery is predominantly determined by wind blowing overthe Baltic Sea and by wind driven sea surface height variability inthe North Sea. This North Sea surface height variability is animportant factor driving exchanges between the North Sea and theBaltic Sea (Gustafsson and Andersson, 2001), and therefore ofmost of the volumic flow that can exit of the Baltic Sea. A

ll rights reserved.

doir).

numerical experiment measuring the NCC freshwater transporthas already been performed by Maslowski and Walczowski (2002),but with a configuration that lacked freshwater runoff into theBaltic Sea and had coarse Danish straight resolution. It is thereforerequired to have a numerical configuration with actual volumicand freshwater fluxes in order to find the right relations betweenfreshwater transport and forcing parameters.

In this article, we investigate with statistical methods theresults given by a high resolution numerical model of the Balticand North Sea, in order to provide a simple way to compute(1) the Baltic Sea freshwater output, and (2) the freshwatertransport in the Norwegian Coastal Current (NCC hereafter). Ourapproach is based on the known physical relations betweenwind forcing over the North Sea and the Baltic Sea, and theoccurency of an inflow or an outflow. Physics of barocliniccoastal currents is also used in order to estimate the freshwaterflux in the NCC.

Based on the previous work, we know that there is acorrelation between the mean zonal Baltic Sea wind (Hordoirand Meier, 2010) and the freshwater outflow of the Baltic Sea:strong westerlies, typically occurring in winter drive an

R. Hordoir et al. / Continental Shelf Research 64 (2013) 1–92

accumulation of water in the Baltic Sea since the emergingpressure gradient blocks the drainage through the Danishstraights. Declining westerlies at spring fail to sustain thepressure gradient between the Baltic and the North Sea which,in turn, results in a freshwater discharge to the North Sea.Hence, the combined effect of strong westerlies followed byweak westerlies or easterlies drives strong freshwater pulses.In addition, the previous work implies that the inflows of saltwater into the Baltic Sea, which mean a reduction of the BalticSea freshwater outflows, are correlated with the mean zonalwind over the North Sea (Gustafsson and Andersson, 2001).

When it comes to the more complex structure of a freshwaterdriven baroclinic coastal current like the NCC, an extensiveliterature provides the driving mechanisms. Garvine (1999) andall the articles published by this author give an excellent source ofknowledge and show for example that the barolinic transport isrelated with the baroclinicity, and therefore with the salinityanomaly. Hordoir et al. (2008), Fong and Geyer (2002),Yankovsky and Chapman (1997) have also shown that freshwaterplumes are extremely sensitive to wind forcing as the near surfacehigh stratification imply contracts the Ekman depth over arestricted height. This results in a high ratio of wind energyprovided per mass above the halocline created by the freshwateranomaly, and therefore into a high sensitivity of the baroclinicstructure to wind forcing. Longshore wind heading towards thedirection of propagation of the Kelvin wave (downwelling) tendsto accelerate the freshwater transport, whereas upwelling windbrings most of the freshwater anomaly off the coast hencedispersing the freshwater anomaly, and requiring a new input offreshwater along the coast before the baroclinic transport can

Fig. 1. Bathymetry map for the BaltiX configuration used in the study. The open bouboundary, and between Scotland and Norway for the North Sea open boundary.

resume.In order to investigate the emergence of the Baltic Sea outflow

in the NCC, and statistical relations to freshwater transport,wind forcing and salinity anomalies, we use an ocean numericalconfiguration. The goal is to determine a simple statistical for-mulation which is a good predictor of the Baltic Sea freshwateroutflow, and the freshwater transport in the NCC.

In the first part of this article, we briefly present our numericalocean modeling configuration. In the second part, predictors basedon a priori knowledge of the physics of the system are alsopresented. In the third part of this article, we show how somestatistical relations can be obtained. The fourth part concludes thisarticle.

2. Configuration description

2.1. Domain and grid

We use the BaltiX configuration developed by SMHI (SwedishMeteorological and Hydrological Institute). BaltiX is a Baltic andNorth Sea configuration based on the NEMO (Madec, 2010) oceanengine and follows closely its development (Hordoir et al., 2013).

The computational domain covers the entire Baltic Sea, theEnglish Channel and the North Sea (Fig. 1), with open boundaryconditions between Cornwall and Brittany (meridional), andbetween Hebrides Islands and Norway (zonal). The model domainhas a horizontal resolution of approximately 2 nautical miles(3.7 km), and a basic vertical resolution of 3 m close to the surface,

ndaries are located between Cornwall and Brittany for the English Channel open

R. Hordoir et al. / Continental Shelf Research 64 (2013) 1–9 3

decreasing to 23 m at the bottom of the deepest part of thedomain that is the Norwegian trench.

A full description of the numerical aspects and physical para-meterizations used in the BaltiX configuration is described in thereference note available online (Hordoir et al., 2013).

2.2. Forcing data

The model is driven atmospheric forcing comes a downscalledrun of ERA40 reanalysis (used at the open boundaries) using RCA(Samuelsson et al., 2011) during 1961–2007. The resolution of the(atmospheric) RCA model is fairly high (50 km) but this is some-what misleading because of the dominant influence of theboundary conditions which are dominated by the ERA 40 modelwhich features a much coarser resolution.

The river runoff forcing is a composite based on which comesthe databases including ones already used by O'dea et al. (2012) forthe North Sea and Channel, and those used by Meier (2007). Thesalinity of runoff is set to 10−3 PSU which is enough to suppressnegative salinities caused by numerical dispersion in the vicinityof those grid cells which receive the river runoff.

2.3. Diagnostics

Fig. 2 shows a schematic vision of the Baltic Sea, and its outflowregion located between Denmark and Sweden, the Kattegat andSkaggerak regions located between Sweden and Norway, and thewestern Norwegian coast. During the entire simulation, and forevery time step of it, several parameters are sampled alongsidewith the Baltic Sea freshwater outflow and the NCC freshwatertransport:

�

The mean zonal wind over the Baltic Sea (Area 1), which ishighly correlated with the Baltic Sea inflow and outflowperiods (Hordoir and Meier, 2010).

�

The mean zonal wind over the Kattegat/Skaggerak area (Area2). Strong westerlies over the North Sea and over this areaaccumulate North Sea water between Denmark and Sweden,and lower the Baltic Sea outflow (Gustafsson and Andersson,2001). Lower westerlies or easterlies in this area on the

SEA

Baltic Sea outflow cross section

NCC flow cross section

LAND

AREA 3 : Western Norwegian Coast

Fig. 2. Schematic view of the pathway of freshwater between th

contrary result in a lower mean North Sea sea surface heightwhich allows a stronger Baltic Sea outflow.

�

As the main source of freshwater for the NCC is the Baltic Sea,the NCC freshwater transport should be related with the twoparameters described above. However, wind has also a directinfluence on the behavior of the NCC: a positive Kattegat andSkaggerak wind drives as an upwelling wind in the region ofthe NCC that has not yet reached the Norwegian coast (Fongand Geyer, 2002), and can spread the NCC freshwater off thecoast of Norway thus lowering the speed of the baroclinictransport. A positive meridional wind along the WesternNorwegian coast is on the contrary accelerate the speed ofthe river plume by compressing it along the Norwegian coast.Hence in addition to the Kattegat and Skarrerak mean wind, weexpect that the wind (both magnitude and direction) along theNorwegian coast might contain information essential for theconstruction of a statistical predictor and we also add a thirdwind sampling area along the Norwegian coast both for zonaland meridional components (Area 3).

�

Although not an atmospheric parameter, surface salinity issampled along the western Norwegian coast. Its variability isrelated with the cross-shore density gradient, and thereforewith the baroclinic transport of the NCC (Area 3).

The locations of the sampling cross-sections for the Baltic Seaoutflow and the NCC transport are also described in Fig. 2. Thelength of the cross-sections includes the entire width of thestraight for the Baltic Sea outflow, and almost half of the NorthSea zonal cross-section when it comes to the NCC freshwatertransport. All flux computations are integrated from surface tobottom. For all freshwater fluxes computation, the freshwaterconcentration Cfresh is computed using the simple formula

Cfresh ¼ 1−SSref

ð1Þ

in which Sref is a reference salinity taken equal to 35 PSU. Thefreshwater flow Fr for a given cross-section S can therefore bedefined as

FrSðtÞ ¼∬SCfreshðX; tÞU!ðX; tÞ dS

�!ðX; tÞ ð2Þ

e exit from the Baltic Sea and the Norwegian coast.

R. Hordoir et al. / Continental Shelf Research 64 (2013) 1–94

with local velocities U!

and surface vectors dS�!

at location X andtime t. Local surface vectors depend on time as the configurationuses free-surface following coordinates.

3. Results

3.1. Validation in the framework of this survey

The Baltic Sea is the main provider of freshwater both for toDanish Straights and the Norwegian current. It is important thatthe model features a realistic variability of the Baltic Sea volume,which, in turn is known to be closely related with the freshwaterexport out of the Baltic. An efficient and simple measure of theBaltic Sea volume (and associated freshwater export across theDanish Straights) is the sea surface height at Landsort, a tide gaugelocated at the Southern tip of the Stockholm Archipelago.

Fig. 3 shows the SSH at Landsort for the year 2005. Althoughvery little tuning has been done, and the forcing dataset is basedon a reanalysis which gives a free range to the model within itsdomain (i.e. the assimilation comes only from the open boundaryconditions, which means that within the model domain thatcovers North Western Europe, the path of depressions is not asprecise as it would have been provided by a configuration thatdoes data assimilation all over the place), the correlation betweenthe model and hourly SSH measurements reaches almost 80%.Errors in the representation of the SSH mostly come in this case ofbiases in baroclinic effects (temperature and salinity biases) whichplay an important role in the Baltic Sea. However, these errors areall relative if one considers that the simulation has been runningsince 1961, which is 45 years, when it reaches year 2005.

Note that the BaltiX configuration is assessed in the BaltiXreport (Hordoir et al., 2013). The results show that the Baltic Seadeep salinity stays stable over the simulation period, although themixed layer depth is under estimated. Concerning the Kattegat/Skaggerak area, results show that the very close to surface salinityis under estimated due to too-high stratification, but that thevertical profiles are consistent with observation as soon as onelooks slightly deeper.

3.2. Baltic Sea freshwater outflow and Norwegian current seasonalvariability

Fig. 4 shows the climatological surface salinity of the Kattegat,Skaggerak and Western Norwegian coast region for spring, sum-mer, autumn and winter seasons. One can observe the variability

Sea

Surf

ace

Hei

ght (

m)

Fig. 3. Measured SSH (in meters) at Landsort for the year 2005, model (red) against obsethe reader is referred to the web version of this article.)

of the extension of the NCC freshwater anomaly and Baltic Seafreshwater outflow according to seasons which fits basically withthe observations made by Hordoir and Meier (2010), Eilola andStigebrandt (1998). During spring and summer time, the extensionof the Baltic Sea freshwater outflow is maximum but the NCCsalinity anomaly is maximum only during summer time whichindicates that the salinity anomaly needs a long time to travel fromthe Kattegat area to the Western Norwegian coast region. Thisfeature, if salinity can be used as a tracer, shows that the progressof the salinity anomaly against prevailing winds is difficult, hencethe slow progression.

3.3. Baltic Sea freshwater outflow correlation analysis

All the analysis work presented in this article is based on the entiresimulation. Based on the data sampled from the simulation, weperform a linear regression analysis in order to find the relationsbetween wind forcing, local salinity and freshwater transport at givencross-sections. For each case, we investigate a physical explanation tounderstand the correlation or the lack of it. Then we assume that alinear expression of the freshwater flow can be obtained as a linearcombination of each term to which a proper time lag is applied. Timelag that is obtained through the correlation analysis.

Fig. 5 shows pronounced cross-correlations between the Baltic Seafreshwater outflow and the mean zonal wind over the Baltic Sea andthe Skaggerak areas. The two curves are very similar and exhibit aminimum value for delays of 4 h and 12 h, respectively. From thisresults, it appears that strong westerlies over the Baltic Sea block theoutflow faster than strong westerlies over Skaggerak (although bothcome one after the other), but that the pilling up of water in Skaggerakcomes slightly after but is more efficient to block the Baltic Seaoutflow.

Faint and diffuse positive correlations can be observed muchlater and are logical in the sense that a strong westerly event doesnot last more than a few days, and lower westerlies after a strongwesterly event will result into a flushing effect of the Baltic Sea,hence increasing the outflow. Based on the minimum and max-imum correlation values, we write the following linear relation:

FrBalticðtÞ ¼ α0þαBaltic1UBalticðt−τBaltic1 Þ þ αBaltic2UBalticðt−τBaltic2 ÞþαKattgt1UKattgtðt−τKattgt1 Þ þ αKattgt2UKattgtðt−τKattgt2 Þ ð3Þ

in which UBaltic and UKattgt are zonal wind normalized statisticalestimators for the Baltic Sea and the Kattegat/Skaggerak area, andτBaltic1 ¼ 4 h, τBaltic2 ¼ 12 h, τKattgt1 ¼ 6 days and τKattgt2 ¼ 6 days. Bylinear regression, we find values for the coefficients α0, αBaltic1 ,

rvations (black). (For interpretation of the references to colour in this figure caption,

4E 6E 8E 10E 12E53N

54N

55N

56N

57N

58N

59N

6.008.0010.0012.0014.0016.0018.0020.0022.0024.0026.0028.0030.0032.0034.00

4E 6E 8E 10E 12E53N

54N

55N

56N

57N

58N

59N

8.0010.00

12.00

14.00

16.00

18.00

20.00

22.00

24.00

26.00

28.00

30.00

32.00

34.00

4E 6E 8E 10E 12E53N

54N

55N

56N

57N

58N

59N

8.0010.00

12.00

14.00

16.00

18.00

20.00

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24.00

26.00

28.00

30.00

32.00

34.00

4E 6E 8E 10E 12E53N

54N

55N

56N

57N

58N

59N

6.008.0010.0012.0014.0016.0018.0020.0022.0024.0026.0028.0030.0032.0034.00

Fig. 4. From left to right and up to down, mean climatological simulated surface salinities (in PSU) for the months of April (Spring), July (Summer), October (Autumn) andJanuary (Winter), respectively. Climatology based on monthly mean values for the period 1980–2000.

R. Hordoir et al. / Continental Shelf Research 64 (2013) 1–9 5

αBaltic2 , αKattgt1 and αKattgt2 . These coefficients are provided inAppendix A, α0 ¼ 15 596 m3 s−1 which is a value that fits withthe mean Baltic Sea outflow value. Using this linear regressionprovides a correlation of 70%. Not taking into account the twostatistical estimators (wind over the Baltic and over Kattegat),

and their two respective time shiftings provides a lowercorrelation.

However, the variability of the reconstructed signal appears tobe lower than that of the sampled signal, 33 683 m3 s−1 for thereconstruction against 48 033 m3 s−1 the measured signal. This

Cor

rela

tion

Time Lag (days)Positive correlation between zonal wind over the Baltic Sea and Kattegat,and Baltic Sea freshwater outflow. Delays of about 6 days.

Negative correlation between zonal wind over the Baltic Sea and Kattegat,and Baltic Sea freshwater outflow. Delays of 4 and 12 hours respectively.

Fig. 5. Cross-correlation (ordinate) between the Baltic Sea freshwater outflow and,the mean Baltic Sea zonal wind (plain line), the mean Skaggerak zonal wind(dashed) line. The abscissa represents the number of hours of shift between thetwo signals.

Cor

rela

tion

Time Lag (days)

Fig. 6. Cross-correlation (ordinate) between the Baltic Sea freshwater outflow andthe NCC freshwater transport. The abscissa represents the number of hours of shiftbetween the two signals.

Fig. 7. Freshwater flow (in m3 s−1) in the Norwegian current as represented in theBaltiX configuration (black curve), and as reconstructed using a linear correlationbased on four wind statistical indicators (yellow curve) for the year 2000. Althoughthe reconstruction is presented for a specific year, the coefficients have beencalculated for the entire time period of simulation. (For interpretation of thereferences to colour in this figure caption, the reader is referred to the web versionof this article.)

R. Hordoir et al. / Continental Shelf Research 64 (2013) 1–96

difference of variability becomes lower if one filters wind andmeasured signals on lower frequencies, with 31 571 m3 s−1 and41 108 m3 s−1 for reconstructed and measured on a weekly timescale, and with 15 281 m3 s−1 and 18 776 m3 s−1 on a monthly timescale. In this latest case, the correlation reaches more than 80%.

3.4. A reconstruction of the Norwegian current freshwater transportvariability

A similar analysis is done for the Norwegian current freshwatertransport, although the analysis in this case is more complex. Wefirst check the correlation between the Baltic Sea freshwateroutflow and the freshwater transport in the NCC. Fig. 6 showsthe correlation between the Baltic Sea freshwater outflow and theNCC freshwater transport. There is a distinct maximum at about50 h, which is the time it takes for a baroclinic wave travelingapproximately at 2 m s−1 a distance of 360 km. This distanceappears to be too small for the distance between the Baltic Seaoutflow cross-section and the one located along the westernNorwegian coast. This means that this correlation is a correlationbetween two negative signals: the NCC flow becomes negative aswesterlies increase along the Norwegian coast, and the Baltic Seaoutflow becomes negative some hours later with a highestnegative peak 50 h later, as an atmospheric depression travelsfrom west towards east. This means it is actually very difficult tocorrelate the positive freshwater flux from the Baltic Sea outflowtowards the NCC freshwater transport using only wind data, which

is consistent with the results already shown in Fig. 4 and thatshow a slow progression from east towards west of the salinityanomaly. One does not observe any correlation on longer timescales, which suggests that using only wind data will be efficient torepresent negative NCC freshwater transport but can be harder torepresent positive one.

We establish the highest correlation shifts using the samemethod as that of Section 3.3 that was used for the Baltic Sea,using statistical estimators representing, respectively, the meanBaltic Sea zonal wind, the mean Skaggerak zonal wind, the meanNorwegian coast zonal wind, for which negative correlations withthe NCC freshwater transport only can be established. A fourthestimator is added, the mean Norwegian coast meridional windfor which a positive correlation with the NCC freshwater transportis found, which is in agreement with the usual dynamics ofcoastally trapped baroclinic currents: positive meridional windalong the Norwegian coast compresses the baroclinic wave alongthe coast, increases the velocity in the direction of propagation ofthe Kelvin wave and hence the NCC freshwater transport.

3.4.1. Reconstruction based on wind data onlyUsing the wind data statistical estimators, we write the

following linear relation:

FrNorwgðtÞ ¼ α0 þ αBaltic1UBalticðt−τBaltic1 Þ þ αKattgt1UKattgtðt−τKattgt1 ÞþαNorweg1UNorwegðt−τNorweg1 Þ þ αNorweg2VNorwegðt−τNorweg2 Þ

ð4Þin which FrNorwg(t) is the freshwater transport in the Norwegiancurrent at time t. αBaltic1 , αKattgt1 , αNorweg1 and αNorweg2 are coeffi-cients whose values are given in Appendix B. UNorweg and VNorweg

are the statistical estimators for the zonal and meridional wind forthe Norwegian coast, respectively. τBaltic1 ; τKattgt1 ; τNorweg1 andτNorweg2 are time shifts obtained using maximum correlationvalues. These time shifts are of course different from thoseobtained for the Baltic Sea outflow, and are displayed inAppendix B.

Fig. 7 shows the measured and reconstructed signals for theyear 2000. The correlation reaches 60%, with a standard deviationof 12 330 m3 s−1 against 20 240 m3 s−1 for the measured signal ifthe entire period 1962–2007 is taken into account. One can noticeon the reconstruction that the negative peaks of freshwatertransports are well represented but the positive peaks are totallyunder estimated which is in agreement with the difficulties ofmaking positive correlations between NCC freshwater transportand wind input, except for the meridional wind along the

Fig. 8. Freshwater flow (in m3 s−1) in the Norwegian current as represented in theBaltiX configuration (black curve), and as reconstructed using a linear correlationbased on four wind statistical indicators plus another estimator representing thesurface salinity anomaly along the Norwegian coast (yellow curve) for the year2000. Although the reconstruction is presented for a specific year, the coefficientshave been calculated for the entire time period of simulation. (For interpretation ofthe references to colour in this figure caption, the reader is referred to the webversion of this article.)

Fig. 9. Freshwater flow (in m3 s−1) in the Norwegian current as represented in theBaltiX configuration (black curve), and as reconstructed using a linear correlationbased on four wind statistical indicators plus one estimator representing thesurface salinity anomaly along the Norwegian coast, and two non-linear statisticalestimators (yellow curve) for year 2000. Although the reconstruction is presentedfor a specific year, the coefficients have been calculated for the entire time period ofsimulation. (For interpretation of the references to colour in this figure caption, thereader is referred to the web version of this article.)

R. Hordoir et al. / Continental Shelf Research 64 (2013) 1–9 7

Norwegian coast. The distance between the NCC cross-section onwhich the measurements are made and the freshwater input is toolarge which makes it impossible to assess the salinity along theNorwegian coast using only wind data. Finding this salinity basedonly on this data would require that the entire system has a simplealmost linear Kelvin wave structure, with a high degree ofsimilarity both in time and space frames. This appears to beimpossible considering the time it takes for the salinity anomalyto reach the Norwegian coast: there is no clear correlation from asalinity anomaly point of view between the NCC baroclinicity andthe Baltic Sea outflow, which is the main source of baroclinicity, ifone uses only wind data.

3.4.2. Reconstruction based on wind and salinity dataIn order to correct the flaws of the wind only based statistical

reconstruction, we add another statistical estimator based on thesurface salinity anomaly of the Norwegian current followingformulation:

αNorweg3SaNorwegðt−τNorweg3 Þ ð5ÞThe results are shown in Fig. 8 for the year 2000, and present

now a correlation of 70% with the measured flow, and a variabilityof 14 100 m3 s−1 against 20 240 m3 s−1 for the measured signal. Inthe plot, one can hardly notice a better representation of positivefreshwater transport in the NCC, and the positive transport peaksare still under represented although the correlation has signifi-cantly increased as well as the variability.

3.4.3. Addition of extra-non linear termsDuring downwelling conditions, which are most likely related

with NCC freshwater transport peaks, the power provided by windto coastally trapped baroclinic wave can be approximated as theproduct of the mean baroclinic current velocity with the meanwind stress in the direction of propagation of the Kelvin wave(Hordoir et al., 2008). Based on simple Ekman layer dynamics andassuming a linear drag at the atmosphere/ocean interface as a firstapproximation, we can estimate that the baroclinic current velo-city Uc is linearly related with the meridional wind velocity. Alsobased on simple geostrophic dynamics, one can estimate thecurrent velocity Uc as linearly related with the density gradient,which in the NCC is predominantly determined by salinity andtherefore write the following equation:

Uc∝VNorweg

Uc∝δρ ð6Þin which ρ is the surface density (or density anomaly) along theNorwegian coast. The power Pw provided to baroclinic currentpeaks can therefore be estimated as

Pw∝VNorweg � VNorweg ð7Þor

Pw∝VNorweg � δρ ð8ÞBased on the fact that the power provided by wind can be

linearly related with the flux (Hordoir et al., 2008) (Eq. (13), (14)and (16)), we therefore add two statistical estimators N1 and N2.This last addition, which does not require any extra data, permitsto achieve a higher representation of the reconstruction of the NCCfreshwater transport (Fig. 9) with a correlation coefficient thatnow reaches more than 76%, and a higher standard deviation of15 500 m3 s−1 for the reconstruction against 20 240 m3 s−1 for themeasured signal

N1 ¼ αNorweg2VNorwegðt−τNorweg2 Þ � αNorweg2VNorwegðt−τNorweg2 ÞN2 ¼ αNorweg2VNorwegðt−τNorweg2 Þ � αNorweg3SaNorwegðt−τNorweg3 Þ ð9Þ

4. Conclusion

Results from our numerical ocean circulation model suggestthat the Baltic Sea freshwater outflow can be predicted with anacceptable accuracy (70%) by using wind data only. However, thevariability of this flow is too small in comparison with the BalticSea freshwater outflow sampled in the numerical configuration,meaning that the standard deviation of the reconstructed signal istoo weak in comparison with that of the sampled freshwateroutflow.

Considering the semi-closed shallow area of the Baltic Sea andKattegat, one can imagine that a lot of reflexion of locallygenerated barotropic waves can occur. This may well generatehigher frequencies than that of the wind input which makes ithard to reproduce the Baltic Sea freshwater outflow. Whenfiltering both wind and measured signals on larger time scales (aweek to a month), a much better agreement in terms of variabilitybetween reconstructed and measured signals is obtained with acorrelation that reaches 80%.

If the Baltic Sea is considered as a lateral boundary condition, itis always more precise from a variability point of view to create aboundary condition based on weekly or monthly time scales. In

R. Hordoir et al. / Continental Shelf Research 64 (2013) 1–98

any case, this method is always more precise than considering theBaltic Sea as a river input from climatological perspective.

Concerning the NCC freshwater transport, the variability basedon wind data only turns out to be closer to the measured NCCfreshwater transport. However, wind based data does not permitto reproduce the amplitude of positive NCC transport peaks. Therelation between the salinity anomaly of the NCC and the BalticSea freshwater outflow cannot be traced using wind data only: theentire baroclinic structure from Kattegat towards the westernNorwegian coast does not behave like a single baroclinic wavefrom a statistical perspective.

Several methods were tried to find a better estimation of thepositive transport and not discussed in the present article, includ-ing trying to relate the NCC freshwater transport with the Dutchand German river runoff which is carried along the Jutlandcurrent. This freshwater flux contributes for about 20% to thefreshwater input to the NCC in the BaltiX configuration, as the NCCmean freshwater transport measured in the configuration reachesmore than 20 000 m3 s−1 although the mean Baltic Sea freshwateroutflow has a mean value of more than 15 000 m3 s−1. But the onlymethod that appeared to work is to include a coastal salinitystatistical estimator based on the measured western Norwegiancoastal salinity.

Using this latest estimator, and adding the interaction betweenbaroclinicity and wind power input allows to represent the positivepeaks. This permits to achieve an accuracy of more than 76% in thereconstruction with a variability that is naturally better representedusing two-daily filtered data. Of course, one could argue that thedependency of this latest reconstruction with a local ocean para-meter such as the salinity is a major drawback of the method.Salinity can however be rather easily measured, and although this

Appendix A. Set of coefficients for the Baltic Sea freshwater outflo

The coefficients that were applied for the present study are provnumerical configuration or based on actual measurements. BS windSkagerrak zonal wind.

Mean value BS wind

4 h 25 min. time lag 6 daTwo daily filtering 15 596 −11 855.3 4744

no time lag 6 daWeekly filtering 15 596 −7430 2509

no time lag 10 dMonthly filtering 15 596 −4988 −87

Appendix B. Set of coefficients for the NCC freshwater transport

A similar set of coefficients is provided for the NCC freshwater trastands for mean Skagerrak zonal wind, NC ZWind stands for Norwmeridional wind, NC Salt stands for Norwegian coast surface salinity a

Mean value BS wind, 1.8 daystime lag

Two dailyfiltering

20 670 −3644

NC salt, 4 h time lagTwo daily filtering 7013

does not allow to make future projections easily, reconstructing thevariability of the NCC freshwater transport for long past time seriesappears consistent. In the case of future projections, one canhowever use the method by using, for example a climatologicalsalinity, which allows to explore the sensitivity to the other para-meters such as the wind variability.

One can notice a difference of behavior in terms of variabilitybetween the two reconstructions: the NCC freshwater transportreconstruction reaches an acceptable variability using two-dailyfiltered input data, whereas this variability is hardly reached forthe Baltic Sea freshwater outflow reconstruction using the samerange of frequency for the input data. This emphasizes thedifference of behavior of a coastal shallow semi-enclosed basin(The Baltic Sea), with that of an open and deeper basin (The NorthSea). In both cases, the ocean shifts some energy to frequenciesthat are higher than those inherent to the atmospheric forcingbecause of low depth barotropic waves and reflexions. But in thefirst case, the ocean recreates higher frequencies than that of theatmospheric forcing because of the local effect explained by thelow barotropic wave velocities and the reflexions. In the secondcase, that of North Sea, such high frequencies are easier to rebuildbased on wind data because of the higher depths (especially alongthe Norwegian coast) and because of a more opened basin thatallows high frequency waves in the ocean to travel out.

Acknowledgements

This research work was funded by the KASK (Hav möter Land)project and SMHI. The NEMO-BaltiX model simulations were partlyperformed on the climate computing resources ‘Ekman’ and ‘Vagn’

w

ided in the following array for anyone to experiment them in astands for mean Baltic Sea zonal wind, Sk. wind stands for mean

Sk. wind

ys time lag 12 h 45 min. time lag 6.4 days time lag.5 −23 522 9212ys time lag 6 h 25 min. time lag 6.2 days time lag

−24 194 14 565ays time lag no time lag 10 days time lag(can be set to 0.) −13 974 12 522

nsport. BS wind stands for mean Baltic Sea zonal wind, Sk. windegian coast zonal wind, NC MWind stands for Norwegian coastnomaly.

Sk. wind, 3htime lag

NC ZWind,no time lag

NC MWind,no time lag

−2660 −4042 8725

N1 N2

5242 2430

R. Hordoir et al. / Continental Shelf Research 64 (2013) 1–9 9

jointly operated by the Centre for High Performance Computing(PDC) at the Royal Institute of Technology (KTH) in Stockholm andthe National Supercomputer Centre (NSC) at Linkoping University.‘Ekman’ and ‘Vagn’ are funded by a grant from the Knut and AliceWallenberg foundation. We wish to thank the two anonymousreviewers for their work that helped to improve this manuscript.

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