Topographic effects on current variability in the Caspian Sea

P. Ghaffari,1 P. E. Isachsen,2 and J. H. LaCasce1

Received 22 May 2013; revised 22 October 2013; accepted 28 November 2013; published 26 December 2013.

[1] Satellite-derived surface height fields reveal that variability in the central and southernbasins of the Caspian Sea is correlated with topography. Consistently, empirical orthogonalfunctions from current meter data from the southern basin are aligned with the isobaths. Inaddition, the gravest mode, which accounts for over 80% of the variance, has an equivalentbarotropic structure in the vertical. To what extent this variability can be modeled using alinear analytical model is examined. The latter assumes equivalent barotropic flow alignedwith the geostrophic contours, which in turn are dominated by the topography. WithECMWF winds and ETOPO2 topography, the model yields surface height deviations whichare significantly correlated with satellite-derived estimates on seasonal and longer timescales in the central basin. The model is somewhat less successful in the southern basin,where the stratification is stronger. Nevertheless, the results are encouraging, given theextreme simplicity of the model.

Citation: Ghaffari, P., P. E. Isachsen, and J. H. LaCasce (2013), Topographic effects on current variability in the Caspian Sea, J.Geophys. Res. Oceans, 118, 7107–7116, doi:10.1002/2013JC009128.

1. Introduction

[2] The Caspian Sea (CS) is the largest inland waterbody of the world in both area (379,000 km2) and volume(78,000 km3). The CS is located between 36�N and 47�Nin a region with complex bathymetric features [Ismailova,2004]. There are three distinguished basins: the northern,central, and southern basins. The southern and the centralbasins have maximum depths of 1025 and 788 m, respec-tively, and a sill with a maximum depth of approximately170 m separates two [Peeters et al., 2000]. The northernbasin is a shallow extension with maximum depth of 20 m.The CS is classified as a deep inland sea, due to its thermo-haline structure and water circulation [Lebedev and Kostia-noy, 2006].

[3] The CS is enclosed and tides are fairly weak.Density-driven and wave-driven flows do occur [Bondar-enko, 1993; Ghaffari and Chegini, 2010; Ibrayev et al.,2010; Terziev et al., 1992], but the currents are primarilyforced by the winds. Due to the strongly variable topogra-phy, the resulting flows are often spatially and temporallyvariable, with an active mesoscale eddy field [Terzievet al., 1992; Trukhchev et al., 1995].

[4] Diverse observations with floats and hydrography,and the results of numerical models simple hydrodynamicinterpretations [Bondarenko, 1993; Terziev et al., 1992],

suggest that the circulation in all three basins is predomi-nantly cyclonic. The circulation is thus associated with apredominantly southward flow along the western coast andnorthward flow along the eastern coast. Recent observa-tions in the shallow coastal area (�100 m depth or less)likewise indicate cyclonic flow, but also reveal exceptions.In particular, the flow near the eastern coast has beenobserved to reverse episodically [Ibrayev et al., 2010], ashas the flow near the southern boundary [Ghaffari and Che-gini, 2010]. Further information about the hydrographicstructure and general circulation of the CS is given by Kos-tianoy [2005].

[5] Although the region has been studied extensively, acomprehensive picture of the circulation is lacking. In par-ticular, we do not have a first-order model explaining theresponse to wind forcing and, more generally, an explana-tion for the predominantly cyclonic flow. The goal of thepresent study is to propose such a model.

[6] Our model is relevant in regions where the ambientpotential vorticity contours (PV), or geostrophic contours,are closed. For unstratified regions these are the f/H con-tours, where f is the Coriolis parameter and H is the waterdepth. Such models have been used before to investigatewind-driven variability [see Kamenkovich, 1962; Hassel-mann, 1982; Isachsen et al., 2003]. The main assumptionof such models is that the primary component of the flow isparallel to the f/H contours. The flow is then forced by con-vergence or divergence in the surface Ekman layer and bal-anced by divergence or convergence in the frictionalEkman layer at the bottom (details are given below).

[7] As shown in Figure 1, the f/H contours in the CaspianSea are indeed closed in both the central and southernbasins. We will, therefore, investigate the use of such amodel here. However, as there is significant stratification inthe CS, it is not certain that a barotropic model is sufficient.

1Department of Geosciences, University of Oslo, Oslo, Norway.2Research and Development Department, Norwegian Meteorological

Institute, Oslo, Norway.

Corresponding author: P. Ghaffari, Department of Geosciences, Univer-sity of Oslo, Oslo 0315, Norway. (peygham.ghaffari@geo.uio.no)

©2013. American Geophysical Union. All Rights Reserved.2169-9275/13/10.1002/2013JC009128

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JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 118, 7107–7116, doi:10.1002/2013JC009128, 2013

So we extend the existing model to allow for vertical shear.As seen below, observations from the southern basin showthat current fluctuations are approximately equivalent baro-tropic, and taking that into account is straightforward.

[8] The manuscript is organized as follows: relevantobservations are described in section 2. In section 3, theequivalent barotropic model is derived. In section 4, themodel solutions are presented and discussed and conclud-ing remarks are given in section 5.

2. Observations

2.1. Satellite Observations

[9] Satellite observations provide the most comprehen-sive information about basin-scale variability in the sea.Weekly updated gridded maps of sea level anomalies(SLA) for the region and covering the period January 1992to December 2011 are available (online at http://www.aviso.oceanobs.com). We used these fields to conduct anEOF analysis of the variability.

[10] The leading EOF, which accounts for 92% of thetotal variance, is remarkably similar to the f/H field in thecentral basin (Figure 2). This implies the sea surface isoscillating coherently across the basin. A similar result wasfound in the Norwegian, Lofoten, and Greenland basins byIsachsen et al. [2003].

[11] The response in the southern basin is less clear. Thefirst mode does have a positive lobe that approximatelytraces out the f/H contours in the western portion of thebasin, but the other lobes do not bear an obvious relation to

Central basin

Southern basin

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ude

(deg

rees

)

Iran

Azerbaijan

Russia Kazakhstan

Turkmenistan

Kara Bogaz Gol

Northern basin

Dep

th (

m)

Study area

Figure 1. The bathymetric field of the CS (shown as gray shading), and potential vorticity field (con-tours) in the Caspian Sea. While the f/H contours have semicircular shapes in the central basin, the south-ern basin encompass relatively complicated feature.

46 48 50 52 54 5636

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Jul92 Jan95 Jul97 Jan00 Jul02 Jan05 Jul07 Jan10 Jul12-5

0

5PC1

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ude

(deg

rees

)

Figure 2. Principal component analysis of sea levelanomalies (SLA) for the CS. (top) Leading EOF mode andf/H contours, and (bottom) associated PC time series, whichaccounts for 92% of the total variance in the field.

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the contours. EOF1 also exhibits distinct variability in thenorth-west region. Here the depth is 5–6 m and the flowmoreover is heavily influenced by the Volga River.

[12] The remaining EOFs account for only 8% of thevariance. These structures (not shown) are dominated byhigher-wave number features that give little dynamicalinsight. So we will focus on the first EOF hereafter.

2.2. Current Meter Observations

[13] Three current meter moorings were deployed in aline perpendicular to the coastline off the south-westernshelf of the CS, from November 2004 to early May 2005(Figure 3). The moorings were located over the 20, 50, and230 m isobaths at (37.505�N; 49.865�E), (37.531�N;49.866�E), (37.553�N; 49.864�E), respectively.

[14] Recording Current Meters (RCM 9) were deployednear the surface, at middepths (for the 230 m mooring), andnear the bottom, to provide measurements throughout thewater column. The sampling frequency was 3 cph, but theanalysis presented here is based on daily averagedvelocities.

[15] Figure 4 shows the variance ellipses for the dailyaveraged currents for the three moorings. These have higheccentricities and the principal axes of the variability areclosely aligned with the f/H contours, at all three moorings.

[16] The alignment and magnitude of the ellipses sug-gests the currents are fairly barotropic. To quantify this, wecalculated the fraction of energy in the barotropic mode:

R5Hhu2i= Hhu2i1XN

n51

u0ð Þ2dz

* +" #; (1)

where N is the total number of the depth layers, u and u0

are depth-averaged and depth-varying velocities, respec-tively. The angle brackets in (1) are time averages and H isthe depth at the mooring. The depth-averaged velocityaccounts for 92%, 79%, and 83% of the total variance inthe moorings from the south to the north, respectively. Thisis consistent with previous results which suggested the flow

field in the eastern part of the southern basin is nearly baro-tropic [Ghaffari and Chegini, 2010; Zaker et al., 2011].

[17] The deepest mooring has current meters at 3.5, 65,and 112 m. Thus, the upper two are in the seasonal thermo-cline (which spans the upper �30 m in summer) and thelower one is well below it (Figure 3, right). The very highfrequency fluctuations are not well correlated between theupper two and the lower one. But the squared coherencesbetween the three time series are 0.6–0.8 at periods longerthan 3 days. So the low frequency fluctuations have a rea-sonably large vertical coherence. As this mooring yieldsthe best information about the flow in the basin interior, weuse its currents for the subsequent analysis.

[18] The velocity ellipses suggest that the velocities atthe deepest current meter at the third mooring are weakerthan at the surface instruments, but also aligned (or coun-ter-aligned) with them (Figure 4). To examine the vertical

0 8 24

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rees

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The Caspian Sea

Moorings

Anzali Port

IRAN

CTD stations

Anzali lagoon

Figure 3. (left) The study area and the location of three moorings along the Iranian coast in the south-western part of the southern basin (shown with stars). (right) Summer structures of the potential tempera-ture, and the potential density isolines across the water column in the study area. The first two mooringsare located over the continental shelf, and the third mooring is located on the continental slope.

49.80 49.85 49.90 49.95 50.00 50.05

37.45

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f/H contours

37.40

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49.75

Longitude (degrees)

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(deg

rees

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0.2 ms-1

510 55

65 75

9098

90

65

55

20

10

5

75

Figure 4. The current ellipses for surface (black line),bottom (light gray line) currents, and depth-averaged cur-rents (dashed line). The dark gray ellipse in the third moor-ing represents middepth observation.

GHAFFARI ET AL.: CASPIAN SEA VARIABILITY

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structure, we calculated complex EOFs for the threeinstruments [Kaihatu et al., 1998]. The first mode,which accounts for over 80% of the variance, is shown in

Figure 5. This mode has the largest velocities at the surfaceand decays with depth, but the velocities are approximatelyparallel throughout the water column. So the velocities areapproximately equivalent barotropic (EB). The e-foldingscale, determined by nonlinear least squares, is about 350m. The velocities are also aligned with the topography,consistent with the conclusions from the satellite data thatvariability is so-aligned.

[19] Of course stratification can cause current fluctua-tions, as those observed here, to decay with depth. Figure 3(right) shows the potential density and temperature struc-tures in summer (2008), along a transect extending fromthe coast toward the offshore region, in the study area. Itreveals a strong seasonal thermocline located at �30 mdepth, which is a typical seasonal thermocline depth insummer for almost whole basin [see Kostianoy, 2005].Ghaffari et al. [2010] using hydrographic data (the sametransect) showed that during the unprecedented severe win-ter (2008), the seasonal thermocline reached almost 100 m,where the water mass was still stratified. In fact, the CS haslow salinity and the density stratification largely deter-mined by temperature [Terziev et al., 1992]. Therefore, thedensity stratification mimics the temperature structure, i.e.,the stratification is weaker but does not vanish in winter[Kosarev, 1975]. Figure 6 provides a large-scale picture ofthe stratification in the CS. Basin-wide potential densityprofiles reveal that the southern basin is more stratified thanthe central basin. In the southern basin, the surface den-sities are significantly less, producing larger near-surfacegradients. Correspondingly, estimates of the Burger num-ber, Bu5 Ld

L

� �2, where Ld is the internal deformation radius

and L is the scale of motion, are 0.057 and 0.027 for thesouthern and central basins, respectively (assuming alength scale as 50 km).

[20] So both current meter observations and hydrographysuggest that the vertical stratification may be important, at

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Figure 5. EOF1 for the currents at the deepest mooringin the southern basin. The arrows are from the EOF, at thedepths corresponding to the current records. The topo-graphic contours are indicated at the bottom, and an expo-nential function with an e-folding scale of 350 m is shownfor comparison.

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Figure 6. The potential density profiles in the central (gray lines) and southern (black lines) basins.The data were collected during the cruise on the CS (organized and conducted by the InternationalAtomic Energy Agency) in September 1995 [IAEA, 1996]. (left) Vertical distributions of the potentialdensity in the southern and central basins. (right) Overlay of the potential density profiles.

GHAFFARI ET AL.: CASPIAN SEA VARIABILITY

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least in the southern basin. An equivalent barotropicdescription of currents seems appropriate, and a simplifiedmodel of wind-driven variability should thus assume EBcurrents. Having such depth-decaying currents is significantbecause topography will then exert a weaker influence thanin a purely barotropic flow. EB models have been studiedpreviously in the context of the Southern Ocean [Ivchenkoet al., 1999; Krupitsky et al., 1996; LaCasce and Isachsen,2010]. Below, we develop such a model in the context ofclosed-PV contours.

3. Theoretical Model

[21] The dynamics of flows with closed-PV contours dif-fer from those with blocked contours. With blocked con-tours, forcing is required to support a steady circulation, aswith the Sverdrup circulation. With closed contours, steadyflows parallel to the PV contours can exist in the absence offorcing and dissipation [Kamenkovich, 1962; Killworth,1992; Hasselmann, 1982; Greenspan, 1990; Young, 1981].Such flows can be very strong and can be excited by windforcing.

[22] Isachsen et al. [2003] derived a linear, barotropicmodel to study such flows. In the model (described below),an imbalance between the net transport in the surface andbottom Ekman layers results in a change in the geostrophiccirculation within the closed contour region. The modelwas used to study wind-driven fluctuations in the NordicSeas and was reasonably successful at reproducing variabil-ity observed from satellite and in a GCM. The success ofsuch a model at high latitudes is aided by having relativelyweak stratification. Whether such a model could work atlower latitudes, as in the Caspian Sea, remains to be seen.

[23] As the current fluctuations in the Caspian have anapproximately EB structure, we recast the barotropic solu-tion of Isachsen et al. [2003] for an EB flow. This involvesmostly slight modifications, and the barotropic solution isrecovered as a limiting case.

[24] As noted, the variables (e.g., pressure and velocity)vary with depth, but the direction of flow does not. So wecan write

uðx; y; z; tÞ5usðx; y; tÞPðzÞ; (2)

and

pðx; y; z; tÞ5psðx; y; tÞPðzÞ; (3)

where u and p are the horizontal velocity vector and pres-sure, us and ps are the corresponding surface values, andP(z) is a vertical structure function. Following Isachsenet al. [2003], we assume a linear bottom drag, so that thebottom stress is:

sb5Ruð2HÞ5reus; (4)

where R is the bottom friction coefficient, Hðx; yÞ is depth,and re5RPð2HÞ is a modified drag coefficient. Similarequations were derived previously by Krupitsky et al.[1996] and LaCasce and Isachsen [2010]. Substitutingthese into the linear horizontal momentum equation andintegrating over the fluid depth yields:

@us

@t1f k3us52grg1

ss

q0F2

reus

F

� �: (5)

where q0 is a constant density, g the acceleration due togravity, and k is the unit vector in the vertical direction.Furthermore, ss is the surface stress vector, g is the sea sur-face height, and Fðx; yÞ is the vertical integral of the profilefunction:

F �ð0

2HPðzÞdz: (6)

[25] Substituting (2) into the continuity equation andintegrating vertically yields:

@

@xFusð Þ1 @

@yFvsð Þ50; (7)

where us and vs are eastward and northward velocity compo-nents. Thus, we may define a transport stream function as:

Fus52wy; Fvs5wx: (8)

[26] Taking the curl of (5) and using (8), we obtain theequivalent barotropic potential vorticity equation:

@

@tr3us1J w;

f

F

� �5r3

ss

q0F2r3

reus

F; (9)

where the Jacobian term Jðw; f =FÞ5Fus � rf =F is theadvection of PV by the flow. According to (9), a steadyflow must be parallel to the f/F contours in the absence offorcing. These are the geostrophic contours in the EBmodel.

[27] As in Krupitsky et al. [1996], Ivchenko et al. [1999],and LaCasce and Isachsen [2010], we take P(z) to be anexponential function

PðzÞ5expz

h0

� �; (10)

so that :

F5h0 12exp 2H

h0

� �� �: (11)

[28] We see that F, and hence the PV contours, areaffected by vertical shear. For strongly sheared flows, i.e.,for h0 � H , F is approximately constant and the PV gradi-ent is dominated by planetary beta. For deeper currents,i.e., for h0 � H , F ! H and the barotropic model is recov-ered. So the PV contours are intermediate between latitudelines and f/H contours, depending on the e-folding scale.Note too that the shear affects the effective bottom drag, asthe latter is proportional to the bottom velocity. In deeperwaters, where the depth is much greater than the e-foldingscale, the drag is weak.

[29] The solution then follows that of Isachsen et al.[2003]. Assuming the forcing and friction are weak, andthat the variations occur on long times scales, the dominantbalance in (9) is:

GHAFFARI ET AL.: CASPIAN SEA VARIABILITY

7111

J w;f

F

� �50: (12)

[30] This implies that the first-order flow follows the f/Fcontours (which we assume are closed). The model thus fil-ters out, for example, topographic waves, which entailcross-contour motion. So:

w5Gf

F

� �; (13)

where G is some function. The surface velocity is thengiven by:

us51

Fk3rG5

1

FG0k3r f

F

� �; (14)

where G0 is the derivative of G with respect to its argument,f =F.

[31] To determines G, we integrate equation (9) over aregion bounded by an f/F contour. This eliminates the Jaco-bian term, after invoking the continuity equation, and yields:

@

@t

þus � dl5

þss

q0F� dl2

þreus

F� dl; (15)

after applying Stokes’ theorem. The first term on the RHSis the net transport into the surface Ekman layer and thelast is the net transport in the bottom layer. An imbalancebetween these two results in a change in the circulationaround the contour.

[32] We solve (15) by Fourier transforming the variablesin time:

ss x; y; tð Þ5X

x

~ss x; y;xð Þeixt; us x; y; tð Þ5X

x

~us x; y;xð Þeixt:

[33] With this, (15) is:

þix1

re

F

� ~us � dl5

þ~ss

q0F� dl: (16)

[34] The surface circulation depends on the bottom fric-tion and the forcing frequency. At low frequencies(x� re=F), the circulation is in phase with the winds andhas an amplitude which is inversely proportional to themodified bottom friction coefficient. At high frequencies,the circulation lags the wind by 90� and is independent offriction.

[35] Finally, inserting (14) into (16) gives:

G05

þ~ss= q0Fð Þ � dlþ

ix=F1re=F2ð Þr f =Fð Þ � n̂dl; (17)

which is the EB equivalent to equation (8) in Isachsenet al. [2003]. They also discussed the equivalent barotropicmodel, but neglected that baroclinicity alters the PV con-tours. Assuming the flow is zero outside the region ofclosed contours, (14) can be integrated sequentially inward,

yielding G and hence the stream function (applying theinverse Fourier transform). Furthermore, since the streamfunction is proportional to the surface pressure, i.e., G5Fðg=f Þg the result can also be used to find sea surface heightdeviations between the inner and outer contours.

4. Results

[36] First, we compare the model prediction against sealevel anomaly (SLA) measurements from the satellite. Todo this, we estimated time series of SLA differences acrossboth the central and southern basins, between an ‘‘inner’’f/F contour in the deep basin and an ‘‘outer’’ contour nearland. This SLA difference is proportional to the geostrophictransport between the two contours. The satellite-basedestimate was calculated as the difference between SLAaveraged over the two contours while the model estimatewas calculated by integrating g05f =ðgFÞG0 over a set ofclosely spaced contours between the inner and outer ones.

[37] The 0.125� 3 0.125�-resolution European Centrefor Medium-Range Weather Forecasts (ECMWF) opera-tional analysis (available online at http://www.ecmwf.int)was used as wind forcing for the model. Topographic datawere obtained from the ETOPO2 0�20 3 0�20 data set(available at http://www.ngdc.noaa.gov). The raw topo-graphic data were smoothed to �10 km, a scale which iscomparable to the internal deformation radius here [seealso Isachsen et al., 2003; LaCasce, 2000; Krupitsky et al.,1996].

[38] The model’s free parameters are the bottom frictioncoefficient R and the e-folding scale of the vertical shear,h0. We set the bottom friction coefficient, R55:031024 ms21, following Gill [1982] and Isachsen et al. [2003]. Wetested a range of values for h0 for both basins.

4.1. Central Basin

[39] To do this, we calculated the correlation betweenthe observed and modeled sea level differences, betweenan inner and an outer f/F contour, as a function of h0; theresult for the central basin is shown in Figure 7. The corre-lations are low at small values, confirming that topographyis important for the response (recall that with small valuesof h0, the PV contours are essentially latitude lines). As h0

is increased, the correlations grow and they are constantabove h05800. The correlation coefficients are 0.68,implying reasonably good agreement.

[40] The latter is confirmed by comparing the two timeseries (Figure 8). Both are dominated by the seasonal sig-nal, with negative values (SLA lower on inner contour thanon outer contour) during winter months, indicating anoma-lous cyclonic circulation. The ratio of the model’s RMSvalue to the observed value is 1.1, so the model capturesboth the variability and the amplitude of the signal.

[41] The fact that the correlations do not decrease as h0

gets large suggests that a model based on f/H would doequally well as the equivalent barotropic model here. Weconfirmed this. This in turn implies topography exerts acontrolling effect in the central basin, regardless of thestratification.

4.2. Southern Basin

[42] Figures 9 and 10 show the corresponding results forthe southern basin. As in the central basin, the model-data

GHAFFARI ET AL.: CASPIAN SEA VARIABILITY

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correlations are lowest with small values of h0 and they arelarger and approximately constant for large values. Butthey are also slightly higher at an intermediate decay scale,around h05500. So it would seem the EB model is slightlybetter than a barotropic f/H model here. The correlationsnevertheless are somewhat lower than in the central basin,reaching a maximum value of about 0.58.

[43] The time series from the satellite and the model,with h05500, are shown in Figure 10. The seasonal cycleis less pronounced than in the central basin, in both timeseries. But the two series are less similar than in the centralbasin. Moreover, the ratio of the RMS amplitudes is 0.7; sothe model somewhat under-predicts the amplitude of theresponse.

[44] The preceding results suggest perhaps that theagreement is superior in the central basin because the sea-sonal signal is more pronounced there. This is partly true.Shown in Figure 11 are the coherences as functions of fre-quency. Results are shown both for the EB model and thebarotropic (large h0) version of the model. The coherencesare insignificant on time scales less than about 5 months, in

both basins. In the central basin, the coherence peaks ataround 10 months, or roughly one year; this is consistentwith the model capturing the seasonal cycle. It decays atlonger time scales. And the barotropic model performsequally well as the EB model, as noted before. In the south-ern basin the response is similar, but the coherences arealso lower. They are largest at around 1 year too, but thedifference is less marked from the lower frequencies. Fur-thermore, the barotropic model produces consistently lowercoherences than the EB model.

[45] The fact that the coherences are low on the shorttime scales is to be expected from the model. With H� 1000 m and R5531024 m, the barotropic decay timescale, Td � H=R, is on the order of a month. The time scalein the EB model is longer because the velocity shearreduces the bottom velocities; with h05500 m, it is roughlyfive times longer. The model assumes that time variationsin the circulation are equally long (otherwise the first-orderflow would not be along f/F contours). So it is not surpris-ing we capture only time scales exceeding a few months.

[46] That the coherences also decrease for the long timescales is consistent with the results found by Isachsen et al.[2003]. At these scales, baroclinic effects presumably comeinto play, effects which cannot be captured in an equivalentbarotropic model. So the model is most effective on theintermediate time scales, particularly at the seasonalfrequency.

4.3. Comparison With Current Meter Observations

[47] Lastly we revisit the mooring data from the southernbasin and compare the along- f/F velocities at the deepestmooring with the model predictions. The model velocitieswere calculated from (14) and (17). As before, we use adrag coefficient of R55:031024 m s21 and an e-foldingscale of h05500 m.

[48] The observed and modeled velocity time series (Fig-ure 12) show some similarities. The correlation coefficient,0.48, is slightly lower than that obtained with the SLA datain the southern basin. This is to be expected, as the entirecurrent meter record is just over six months long. From thepreceding discussion, the model is better at capturing themonth-to-month variations than those on shorter timescales. The ratio of the RMS velocities is �0.8, so the pre-dicted amplitude is also reasonable.

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0.35

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Figure 7. The correlation coefficient ðRcÞ between thesatellite observations and the EB model as a function ofe-folding scale ðH0Þ for the central basin.

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c

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11

Figure 8. Time series of the relative sea level displacements between the rim and inner qe contours inthe central basin where H05800. The thin and thick lines indicate weekly time series of the sea levelanomalies based on the satellite observations and the EB model predictions, respectively.

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[49] Note that the assumed e-folding scale of 500 m issomewhat larger than the e-folding scale deduced from thefirst EOF from the current meter, which was 350 m. Usingh05350 m yields a slightly lower correlation �0.4 and alsoa lower amplitude ratio �0.6. Nevertheless, this is fairlyinconclusive, given the short record length.

[50] Interestingly, the observed fluctuations lag the EBmodel prediction, by roughly 1 week. Accordingly, addinga 5 day lag to the model time series raises the correlationcoefficient from 0.48 to 0.64, and most of the increase isdue to a better match at shorter time scales. But it is clearthat such comparisons should be done with a longer timeseries before any speculation is made.

5. Summary and Conclusions

[51] We have used a linear analytic model to study cur-rent fluctuations in the central and southern portions of theCaspian Sea. The model assumes the flow is wind drivenand that dissipation is entirely by bottom drag. Motivated

by current meter satellite altimeter observations, the veloc-ities are assumed to be equivalent barotropic (EB) andaligned with EB PV contours, the f/F contours (where F isa modified function of depth which takes the vertical decayof the velocities into account). These contours close onthemselves in both the central and southern basins of theCaspian Sea and allow us to estimate the flow variabilityfrom a simplified expression. A barotropic version of themodel was used previously to study the response in theNordic Seas and Arctic Ocean [Isachsen et al., 2003]. Themodification to EB flow and the application to the midlati-tude Caspian Sea is new.

[52] The model was reasonably successful at simulatingcurrent variability on time scales exceeding a few months.

-15

-10

-5

0

5

10

15

Southern Basin, R = 5E-4, H0 = 500

R = 0.58, rms_sat = 3.8, rms_mod = 2.7, ratio = 0.7

δSLA

(cm

)

92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11Date (yr)

c

Figure 10. Time series of the relative sea level displacements between the rim and inner qe contours inthe southern basin where H05500. The thin and thick lines indicate weekly time series of the sea levelanomalies based on the satellite observations and the EB model predictions, respectively.

0 200 400 600 800 1000 1200 1400 1600

0.35

0.40

0.45

0.50

0.55

0.60

e-folding scale (m)

Cor

rela

tion

coef

ficie

nt

Figure 9. The correlation coefficient ðRcÞ between thesatellite observations and the EB model as a function ofe-folding scale ðH0Þ for the southern basin.

0.2

0.4

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0.8

Coh

eren

ce m

agni

tude

10-2 10 -110

0

0.2

0.4

0.6

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Frequency (cpm)

1

1

0

0

Central Basin

Southern Basin

Figure 11. Coherence estimates between the models andthe satellite measurements as functions of the frequency for(top) the central and (bottom) the southern basins. The darkand light lines represent the coherence between the EBmodel and observation and the barotropic model and obser-vation, respectively. The dashed line shows 95% confi-dence level.

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In the central basin, where the stratification is weaker, the f/F model and the barotropic f/H limit yield comparableresults. Both agree with the satellite observations of lowfrequency (seasonal to annual time scales) sea surfaceheight variability. In the southern basin, the stratification isstronger. As such, the EB model is more successful thanthe barotropic model. We find reasonable correlations withboth the satellite data and with the current meter data, againprimarily on time scales of seasons to a few years.

[53] The coherences here are also somewhat less thanthose obtained in the Nordic Seas. In some cases there, thecorrelation coefficients exceeded 0.8. This is likely due tohaving weaker stratification at those latitudes. Neverthe-less, the dependence of the coherences on frequency wassimilar. The (barotropic) model was most successful atintermediate frequencies, capturing primarily seasonalvariations.

[54] It should be emphasized what the analytical modelleaves out. The assumption that the flow is dominated by acomponent which is purely along the PV contours removesall dynamics with cross-contour flow. This includes topo-graphic and internal Kelvin waves. The associated timescales are on the order of several days in the Caspian Sea(J. E. H. Weber and P. Ghaffari, Mass transport in internalcoastal Kelvin waves, submitted to European Journal ofMechanics B, 2013.) The assumption of barotropic orquasi-barotropic motion neglects baroclinic effects, andthis evidently decreases coherences on interannual timescales. To take such effects into account will require addi-tional assumptions about the density field. As suggested bythe findings of Nöst and Isachsen [2003] and Aaboe andNöst [2008], a time-mean solution may then be found inwhich the connection between the top and bottom Ekmanlayers is modified by the divergence of the meridional ther-mal wind transport.

[55] Nevertheless, the model is appealing for its extremesimplicity. A first-order assessment of intermonthly vari-ability can be estimated using a single equation and a sim-ple Matlab routine. The model moreover should beapplicable in other regions, and possibly in large inlandlakes.

[56] Further assessments in the Caspian Sea wouldclearly benefit from more observations, particularly fromlonger-term current measurements in both basins. Studiesusing primitive equation models would also help unravelthe possible role of nonlinearities and eddy momentumtransport, processes that have been ignored here.

[57] Acknowledgments. We thank Andrey Trebler and Paula P�erezBrunius for helpful comments.

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Dec04 Jan05 Feb05 Mar05 Apr05 May05-0. 2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

U|| (

ms

-1)

Observation: along f/F current, 1 cpd

EB model: along f/F current, 1 cpd

Nov04

R = 5E-4 ms-1

R ~ 0.48c

Figure 12. The depth-averaged along-f/F currents. Thethin solid line; the weighted depth-averaged recordedvelocities from the third mooring. The thick line; the EBmodel prediction.

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