A geostrophic empirical mode based on altimetric sea surface height

SCIENCE CHINA Earth Sciences

© Science China Press and Springer-Verlag Berlin Heidelberg 2012 earth.scichina.com www.springerlink.com

*Corresponding author (email: [email protected])

• RESEARCH PAPER • July 2012 Vol.55 No.7: 1193–1205

doi: 10.1007/s11430-011-4293-z

A geostrophic empirical mode based on altimetric sea surface height

ZHANG Lin & SUN Che*

Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China

Received November 16, 2010; accepted July 19, 2011; published online January 2, 2012

Recent discovery of low-dimensional coherent structure in oceanic currents along with a new merged altimeter product called Absolute Dynamic Topography (ADT) makes it possible to derive subsurface ocean information from satellite remote sensing data. An altimetric geostrophic empirical mode (-GEM) is developed in this study by projecting hydrographic transects onto the ADT sea surface height coordinate, based on which the four-dimensional thermohaline and velocity structures of oceanic currents are reconstructed from satellite surface observations. In the WOCE/SR3 area, the -GEM fields capture more than 95% of the total thermal variance. The GEM-derived flow has equivalent-barotropic structure and represents the velocity pro-file better than traditional dynamic modes. Comparison with mooring observations also demonstrates that the -GEM provides good estimates of the deep thermohaline fields.

-GEM, altimetry, SSH

Citation: Zhang L, Sun C. A geostrophic empirical mode based on altimetric sea surface height. Sci China Earth Sci, 2012, 55: 1193–1205, doi: 10.1007/s11430-011-4293-z

Satellite altimeter provides global-scale measurements of sea surface height (SSH) with high spatiotemporal resolu-tion and has been widely used in dynamical studies. Such remote sensing, however, only measures surface parameters and does not provide direct subsurface information of the ocean. Oceanic study of deep hydrographic structure has to rely on sparse and expensive in-situ observations. How to derive subsurface ocean information from satellite data therefore becomes an urgent question in marine sciences.

So far oceanographers have developed a variety of statis-tical methods to estimate subsurface fields from satellite measurements. Gilson et al. [1] and Willis et al. [2] used simple linear regression to infer temperature and transport from TOPEX/Poseidon data. Carnes et al. [3] and Gavart and De Mey [4] tried to derive temperature profiles from an empirical relationship between SSH and EOF amplitudes.

LaCasce and Mahadevan [5] and Isern-Fontanet et al. [6] developed a dynamical method for estimating subsurface fields from SSH or SST based on “surface quasi- geostrophic” (SQG) approximation. In fact, the oceanic modes assumed in these methods have large departures from the actual ocean. The relation between SSH and ther-mohaline fields is not a simple linear one. The vertical mode of the ocean varies spatially and differs from the con-stant mode in the EOF decomposition. Meanwhile the SQG method presumes that surface density is determined totally by the SST, which is not the case in reality.

Recent discovery of coherent thermohaline structure in oceanic currents opens an entirely new prospect. The hy-drographic analysis by Sun and Watts [7] reveals that the temperature and salinity fields in the Antarctic Circumpolar Current (ACC) exhibit a low-dimensional coherent structure if projected onto a baroclinic streamfunction coordinate such as sound travel time or dynamic height, which is called

1194 Zhang L, et al. Sci China Earth Sci July (2012) Vol.55 No.7

Geostrophic Empirical Mode (GEM). The GEM fields ena-ble us to study the water mass formation, mean structure, and low-frequency variability of the ACC in stream coordi-nate [8–10].

The stationary GEM structure essentially means that each baroclinic streamfunction value such as sound travel time or dynamic height corresponds to a fixed temperature or salin-ity profile. Based on the GEM fields, Watts et al. [11] esti-mated vertical profiles of temperature and salinity from In-verted Echo Sounder (IES) measured sound travel time in the WOCE/SR3 area. Similarly, these profiles could also be estimated given dynamic height measurements. Because dynamic height constitutes a major part of the SSH, techni-cally we may use the altimetric SSH as a proxy to infer subsurface thermohaline structures. This new approach to combining altimetry and GEM, however, is hampered by the lack of accurate geoid information in satellite altimetry.

To determine the geoid more accurately, a satellite mis-sion called GRACE (Gravity Recovery and Climate Ex-periment) was conducted, based on which the French Ar-chiving, Validation, and Interpolation of Satellite Oceano-graphic Data (AVISO) project produced a merged product of Absolute Dynamic Topography (ADT) by combining altimetry, hydrography and the latest geoid model [12]. In the Southern Ocean the effectiveness and accuracy of the ADT product have been verified by Sun et al. [13] with two years of mooring observations.

The advent of ADT data along with the GEM method enables us to derive four-dimensional oceanic structure from satellite altimetry. In this paper, GEM fields are con-structed based on ADT data and hydrographic transects at

the WOCE/SR3 line. The statistical properties of the new GEM fields are examined and compared with mooring ob-servations.

1 Data and methods

Two datasets are used in this study: CTD transects and ADT product from altimetry. Figure 1 shows the location of the WOCE/SR3 line with eight CTD transects completed along it during 1991–1997. Six of these transects are from WOCE cruises [14] and two of them are from SAFDE cruises [15]. The merged altimeter product of ADT from French AVISO project consists of a mean dynamic topography and the merged Sea Level Anomalies (SLA). The mean dynamic topography is estimated from the combination of a recent EIGEN-GRACE01S geoid model, altimetric mean sea sur-face heights and in situ measurements with an inverse tech-nique [12]. The SLA is derived from Topex/Poseidon, Ja-son-1 and ERS altimeter observations using the mapping method of Ducet et al. [16]. The data are interpolated onto a global grid of 1/4° resolution between 82°S and 82°N and are archived in weekly averaged frames (available from October 1992 to present). The tidal and sea level pressure corrections have been incorporated in the data. In addition, Inverted Echo Sounder (IES) and current meter measure-ments from SAFDE program are used in this study to vali-date the -GEM estimates (Figure 1).

The temperature and salinity sections from SR3-95/07 survey across the ACC are illustrated in Figure 2. They show four typical ACC water masses: the cold fresh Antarc-

Figure 1 Location of the WOCE SR3 line (thick line). Circles and triangles represent IES and current meter moorings from SAFDE program. Bottom topography from ETOPO5 is gray shaded every 500 m. Mean dynamic topography from AVISO is contoured.

Zhang L, et al. Sci China Earth Sci July (2012) Vol.55 No.7 1195

Figure 2 Temperature (°C) (a) and salinity (psu) (b) section for CTD-07/95 survey.

tic Surface Water (AASW) south of the Polar Front (PF); the warm salty Subantarctic Mode Water (SAMW) north of the Subantarctic Front (SAF); the Antarctic Intermediate Water (AAIW) descending across the SAF from 400 to about 1000 m; and the salty Circumpolar Deep Water (CDW) below 1500 m. Both temperature and salinity fields display a variety of frontal and water mass features and hence provide a good test bed for the -GEM technique.

GEM technique was developed by Sun and Watts [7] in the hydrographic analysis of the ACC. By projecting hy-drographic data onto a baroclinic streamfunction coordinate such as sound travel time or geopotential height, they found the ACC had a low-dimensional coherent structure, which meant that each baroclinic streamfunction value corre-sponded to a fixed temperature or salinity profile. The GEM fields capture more than 97% of the total thermohaline var-iance in the WOCE/SR3 area, and mechanism of the GEM dominance has been given in the context of geostrophic turbulence [17]. Based on the GEM technique, Watts et al. [11] estimated the vertical profile of temperature, salinity, and specific volume anomaly from IES measured sound travel time and further obtained the subsurface baroclinic currents with geostrophic relation. Comparisons showed that GEM estimates agreed well with independent moored temperature and current records.

2 Geostrophic empirical mode based on sea surface height (-GEM)

2.1 Construction of -GEM

Based on the GEM technique developed by Sun and Watts [7], we constructed GEM fields for temperature, salinity, and specific volume anomaly with SR3 hydrographic tran-sects, here we named it -GEM because the streamfunction parameter used is geopotential height

3000

300d ,p

where is specific volume anomaly. The surface geopoten-tial height relative to 300 dbar is removed because the near-surface water is subject to seasonally varying heat and freshwater flux.

In order to construct -GEM fields, the SSH (or ) from satellite altimetry is interpolated onto SR3 CTD stations. Meanwhile, the SSH is corrected by removing its regional- mean seasonal variation. The de-seasoned SSH versus is shown in Figure 3, exhibiting a tightly linear relationship with an rms of 4.8 cm. Based on this relation, we interpolate -GEM fields into SSH coordinate and obtain -GEM fields for temperature, salinity, and specific volume anoma-ly (Figure 4). Instead of constructing -GEM fields directly from SSH, we project -GEM into SSH coordinate here because the density structure of the currents is determined by the baroclinicity and hence is better in representing the vertical structure of the ocean compared to SSH. Moreover,

Figure 3 Correspondence between and SSH. Data are from CTD tran-sects at the SR3 line and the ADT product. Thick line represents the spline fit for the correspondence.


Figure 4 -GEM fields for temperature (°C) (a), salinity (psu) (b), and specific volume anomaly (107 m3 kg1) (c).

similar GEM fields make it easy to isolate the bias caused by SSH in reconstructing SR3 transects (see Section 2.3.2).

2.2 Characteristics of -GEM fields

The -GEM fields are look-up functions, based on which we can estimate the vertical profiles of temperature or salin-ity given a measurement of SSH. The vertical and lateral structure captured by the -GEM fields includes all of the frontal and water mass features identified in the original CTD data and does not smooth out persistent features with small vertical scales. For low SSH values, the temperature minimum layer and the large salinity gradient separating the AASW from the underlying CDW are well reproduced in the -GEM fields. For intermediate SSH values, the descent of the salinity minimum water beneath the SAMW is cap-tured by the -GEM salinity field. For high SSH values, -GEM field clearly shows the salinity minimum layer of the AAIW near 1000 dbar.

In order to test the -GEM fields, we show vertical cuts

through the -GEM temperature field at five different SSH values in Figure 5(a). CTD profiles are also shown with SSH values clustered within 2.5 cm of the respective five SSH values. The profiles in each group exhibit a similar structure below 300 dbar, confirming the effectiveness of SSH coordinate. Note that the vertical structure changes substantially between groupings. For high SSH value, the main thermocline is deep and overlain by a thermostad of mode water. For low SSH values, the thermocline is shal-low and there is a temperature minimum layer in the upper 500 dbar. Figure 5(b) illustrates the analogous SSH group-ing of salinity profiles and their respective -GEM curves. The profiles in each group agree well with -GEM curve. For high SSH values, all profiles exhibit the low salinity feature of the AAIW at 1000 dbar. For low SSH values, all profiles show the salty core of the CDW below 1500 dbar. These consistencies come about due to the “orderly” rela-tionship between thermohaline properties and SSH values.

Though CTD profiles coincide well with -GEM fields, there are still some differences between them, especially in the upper layer. Figure 6 shows the rms residuals of the -GEM fields from CTD measurements. For a given SSH value, the rms residuals indicate the uncertainty in estimat-ing the vertical profile of temperature and salinity with -GEM. The rms residuals for the temperature -GEM field decrease quickly with depth, and the rms contours appear to follow the sloping isopycnal surfaces. The rms residuals in the upper 500 dbar are between 0.5 and 1°C. Below the up-per layer of strong seasonal and atmospheric effects, the rms residuals decrease from 0.5°C to less than 0.2°C at 1000 dbar and to 0.05°C at 1500 dbar. The rms salinity residuals also decrease with depth. In the upper 500 dbar the rms are between 0.05 to 0.15 psu; below 500 dbar, through a slop-ing band extending to 500–1200 dbar, the rms salinity re-siduals are between 0.02 and 0.05 psu; below the intermedi-ate waters, the rms residuals decrease rapidly from 0.02 to 0.005 psu; in the CDW layer the rms residuals are less than 0.005 psu.

The rms residuals for near surface waters above 300 dbar have been reduced by subtracting a seasonal model for temperature and salinity, because the near surface waters are influenced strongly by seasonally varying heat and freshwater fluxes. The seasonal correction significantly im-proves the -GEM estimates in the surface mixed layer. After the correction, the rms residuals for the temperature estimates are reduced from 1°C down to 0.75°C for the sur-face layer. The salinity seasonal variation is not as strong as temperature, but the model still makes significant improve-ment. The seasonal models for temperature and salinity ob-tained here are similar to those in -GEM, and interpreta-tions for these models can be found in Watts et al. [11].

The percent variance captured by the -GEM fields for temperature and salinity as a function of pressure is also calculated as Sun and Watts [7] did. For each of these two


Figure 5 (a) Five groups of SR3 CTD temperature profiles that have SSH values within 2.5 cm of the five central values, shifted to the right by 2°C. The bold dashed curves are the corresponding -GEM temperature profiles. (b) Same as in (a) but for salinity. The profile groups are offset 0.5 psu to the right.

Figure 6 The RMS residual map for SR3 -GEM temperature field (°C) (a) and salinity field (psu) (b).

variables, across each pressure level, the total variance among the full set of CTDs is 2

tot ( ).p The variance of

residuals of these CTDs from the -GEM fields is 2res ( ).p

The ratio 2 2res tot( ) / ( )r p p is the fraction variance not

captured by the -GEM fields, and (1r) is the fraction captured by the -GEM fields. The percent variances cap-tured by the -GEM fields for temperature and salinity are shown in Figure 7. In the depth range 300–3000 dbar, more than 95% of the variance in the observed temperature is captured by the -GEM field. For salinity, the -GEM field

captures more than 95% of the variance in the depth range 900–2000 dbar and more than 86% of the variance between 300 and 900 dbar. All these percent variances captured by -GEM fields are slightly less than those captured by -GEM fields.

2.3 Comparison between -GEM and -GEM

2.3.1 RMS residuals of GEM fields

To compare -GEM fields and -GEM fields, we calculate their rms residuals from CTD measurements and show their


Figure 7 Percent variance captured by the -GEM fields (solid) and -GEM fields (dashed), plotted for the temperature (a) and salinity (b) fields as a function of pressure.

differences in Figure 8. The rms temperature residuals of -GEM is larger than that of -GEM. Because the density structure of the ocean depends mainly on the baroclinicity, the baroclinic streamfunction =(s, t, p) therefore repre-sents the vertical structure of the ocean well [17]. If the al-timetric sea surface height and baroclinic streamfunction satisfy the linear relationship =F(), then these two GEM estimates TG (, p) and TG′(, p) are the same, TG′(, p)=TG′(F, p)=TG (, p). Affected by the barotropic and ageostrophic effects, the altimetric sea surface height ex-hibits some biases from the baroclinic streamfunction

=F()+(x, y, t),

which causes the relatively large error in the -GEM esti-mates.

( , ) ( ( ), ) ( , , ) ( , ) ( , , ).G G GT p T F p T x y t T p T x y t

Large differences between those two rms residual fields are located near the thermocline, and their distributions are correlated with the horizontal gradient of temperature GEM field (correlation is 0.81). The difference between those two GEM estimates is caused by the bias of SSH from , and the SSH bias produces large errors in the area where the hori-zontal gradient of GEM field is large, and therefore the dif-ference of rms residuals between those two GEM fields is tightly correlated with the horizontal gradient of the GEM field.

As shown in Figure 8, rms residual differences are main-ly located in two regions corresponding to SSH values of 115 and 140 cm. These two regions are also locations of two strong jets of the ACC. Further analysis in Section 2.3.2 shows this correspondence is due to barotropic effects. An-

other distinctive feature in the rms residuals is that the maximum difference does not appear in the surface layer but in the subsurface layer at 100 dbar, which is also related to the horizontal gradient of the GEM field. The mean rms residuals of -GEM and -GEM fields at different pressure levels are shown in Figure 9. We can also see that -GEM has larger rms residuals than -GEM. Their differences reach 0.2°C at 100 dbar and decrease to less than 0.05°C below 1000 dbar.

Similarly for the salinity, the rms residual difference is shown in Figure 8. The maximum difference is located in the upper 300 dbar. Moreover, large differences appear in a sloping band that decreases from 600 to 1500 dbar, corre-sponding to the boundary between AAIW and CDW. This pattern is also determined by the horizontal gradient of the GEM field. In those two regions corresponding to two jets of the ACC, there are also large differences produced by barotropic effects.

2.3.2 Reconstruction of SR3 transect

A -GEM-estimated transect corresponding to the directly measured CTD-07/95 section is shown in Figure 10. SSH is interpolated for each CTD cast and the corresponding tem-perature and salinity profiles are estimated with -GEM fields. These -GEM estimates are then contoured using the geographical position just as for the original CTD section. The -GEM estimates match well with the CTD observa-tion, including the thermostad of the SAMW and the low salinity tongue of the AAIW. However, the -GEM esti-mates are somewhat smoother with less small-scale struc-ture than the CTD measured sections. The differences be-tween CTD and -GEM estimates are also contoured. Sta-tions between 50°S and 47°S have slightly warmer and sal-


Figure 8 Difference of RMS residuals between -GEM and -GEM temperature fields (°C) ((a), (b)) and horizontal gradient of -GEM temperature field (°C) ((c), (d)). (b), (d) Same as (a), (c) but for salinity (psu).

Figure 9 (a) RMS residuals of -GEM and -GEM temperature fields as a function of pressure; (b) same as in (a) but for salinity.

tier water above 1000 dbar. South of 53°S, there is slightly colder and fresher water between 300 and 1000 dbar, com-pensated by warmer and saltier water near the surface.

SR3-07/95 temperature sections estimated with -GEM are compared with that from -GEM, and their differences are shown in Figure 11. Though the magnitude of the dif-

ference varies with depth, its sign does not change in the vertical. Figure 12 shows the SSH and geopotential height along SR3-07/95 transect. It is obvious that positive tem-perature difference corresponds to anomalous high SSH relative to and negative temperature difference corre-sponds to anomalous low SSH. These consistencies confirm


Figure 10 -GEM produced SR3-07/95 temperature section (°C) ((a), (b)) and its difference from the measured CTD section (°C) ((c), (d)). (b), (d) Same as (a), (c) but for salinity (psu).

Figure 11 Difference between the -GEM and -GEM produced SR3-07/95 temperature fields (°C).

that the difference between -GEM and -GEM estimates is produced by the SSH bias from .

As shown in Figure 13, geostrophic currents consist of barotropic component and baroclinic component. SSH con-tains information of both barotropic and baroclinic compo-nents, but contains baroclinic component only, and there-fore barotropic effect is the main physical process that ac-counts for the difference between SSH and . In strong cur-rent regions, the barotropic currents are relatively strong, and therefore SSH deviates more from , which results in large differences between two GEM estimates. This ex-plains why the maximum difference of rms residuals be-tween the two GEM fields corresponds to the strong jet in the ACC (Figure 8). The accuracy of the altimeter data is

Figure 12 Geopotential height derived from the SR3-07/95 transects and the coinstantaneous SSH from the ADT data.

around 3 cm/s, and the rms difference between SSH and is 4.8 cm; hence the SSH bias from can also be ascribed to the altimeter data error partially. Though -GEM fields exhibit relatively larger errors in estimating SR3 transects compared with -GEM, they are still very useful in oceanic studies owing to their abilities to reconstruct subsurface thermohaline structures with the continuous measurements from satellite altimetry.

3 Velocity structure

Through theoretical analysis, Sun and Watts [7] found that


Figure 13 Schematic map for geostrophic flow. In this study the ba-rotropic component is defined as the near-bottom geostrophic flow.

-GEM-estimated currents had equivalent-barotropic struc-ture, which meant the current direction did not change with depth. But their works considered only baroclinic currents since they chose a deep reference level. In this study, we extend their results by choosing the sea surface as the ref-erence level. It enables us to estimate subsurface currents from satellite altimetry, including barotropic component.

Based on the obtained -GEM specific volume anomaly field, the -GEM geopotential height field is calculated through vertically integrating, and then the baroclinic cur-rents are calculated as the horizontal gradient of geopoten-tial height. At a particular geographic location, the -GEM geopotential height field is

( , ) ( , )d ,r

p

Gp

p p p

where G is the -GEM specific volume anomaly field, is the streamfunction-SSH, and the reference level is the sea surface with Pr=0.

The geostrophic relation in isobaric coordinates becomes

bc

( , ) ( , )( , ) ( , ) ,

p pfu p E p

y y y

bc

( , ) ( , )( , ) ( , ) ,

p pfv p E p

x x x

where ubc and vbc are baroclinic currents, E (p, ) represents the derivative of the -GEM geopotential height field,

( , )

( , ) ,p

E p

then

bc s

bc s

( , ) ( ),

( , ) ( )

u p u

v p v

where us () and vs () are surface currents derived from altimetry.

Then, geostrophic currents ug (p, ) and vg (p, ) at dif-ferent pressure levels satisfy

g s bc s

g s bc s

( , ) ( ) ( , ) ( ).

( , ) ( ) ( , ) ( )

u p u u p u

v p v v p v

It indicates that -GEM-estimated currents also have an equivalent-barotropic structure. The estimated current di-rection depends on streamfunction only and does not change with depth. The surface speed may change with the varying SSH pattern, but the normalized velocity profile is prede-termined by the time-invariant -GEM field.

bc bc

s s

( , ) ( , )( , ).

( ) ( )

u p v pE p

u v

This result is similar to Sun and Watts [7]. Furthermore, the normalized geostrophic currents satisfy

g g

s s

( , ) ( , )( , ) 1,

( ) ( )

u p v pE p

u v

showing that normalized currents g s( , ) / ( )u p u and

g s( , ) / ( )v p v have the same vertical structure, and its

profile varies with SSH value (Figure 14(a)). Based on the normalized velocity field, we estimated the currents at dif-ferent depth from the surface currents derived from altime-try, and the currents exhibited equivalent-barotropic struc-ture (Figure 14(b)). The mean velocity field of the Fine Resolution Antarctic Model (FRAM) also exhibits a strong consistency in the vertical [18], and the -GEM analysis provides strong observational evidence for this model sim-ulation. Moreover, the -GEM estimation needs no deep reference level and can estimate the barotropic currents at depth. Comparisons with current meter measurements at 3200 dbar confirm this point (Figure 14(b)).

The -GEM velocity mode is also compared with tradi-tional dynamic mode. Since the decomposition of normal modes only applies to a region with horizontally uniform stratification [19], it is questionable to apply it in a strong baroclinic current. Recent studies also show that the first baroclinic mode is insufficient to represent the vertical mode of the currents [20, 21]. The -GEM velocity mode is in SSH coordinate, and its vertical profile depends on the SSH derivative of the geopotential height -GEM field. Figure 15 shows the -GEM velocity profile for SSH value of 120 cm and the corresponding profile derived from the first baroclinic mode. The -GEM mode clearly implies much deeper velocity shear and exhibits a realistic subsur-face velocity maximum. Moreover, the -GEM velocity is relatively smaller above 1000 dbar and larger below 1000 dbar compared with traditional dynamic mode. To compare


Figure 14 (a) Normalized velocity structure across the ACC determined by the SR3 -GEM filed. The velocity has been multiplied by the mean surface velocity in SSH coordinate from altimetry. (b) Zonal currents at the SR3 line on September 4, 1996 estimated from -GEM. Red triangles indicate the posi-tion of the southern and central current meter moorings at 3200 dbar. The current meter measurements at these two moorings are 2.1 and 3.5 cm/s respec-tively.

Figure 15 Normalized velocity profiles corresponding to SSH value of 120 cm derived from -GEM (solid) and the first baroclinic mode (dashed). Current meter measurements from the southern and eastern moorings are marked with circles and squares respectively.

these two modes, we calculated the velocity mode of the ACC from current meter measurements in the SR3 area. The results show that -GEM velocity mode represents the vertical structure of the ACC better (Figure 15).

4 Comparison with hydrographic measurements

4.1 Time series of temperature

-GEM estimates are compared with independent meas-urements made by current meters moored within the IES array. The most extensive comparison available is from the southern current meter and the temperature records at this site are at depths of 300, 600, 1000, and 2000 dbar. Figure 16 shows the comparison of the directly measured tempera-ture time series with the -GEM estimates. The agreement

between them is noteworthy: the rms differences are 0.79, 0.69, 0.28, and 0.09°C at depths of 300, 600, 1000, and 2000 dbar respectively.

4.2 Time series of currents

Based on the -GEM velocity mode described in Section 2, we calculated the currents at depths from the surface cur-rents derived from altimetry and compared them with cur-rent meter measurements (Figure 17). The rms differences for zonal currents at depths of 300, 600, 1000, and 2000 dbar are 9.9, 7.0, 4.5, and 2.5 cm/s respectively, and rms for meridional currents are 14.2, 9.8, 6.6, and 4.1 cm/s. The estimated currents are calculated directly from surface flow derived from altimetry and need no deep reference level. It is more consistent with current meter measurements com-pared with baroclinic currents derived from specific volume anomaly while the rms residuals are reduced by 0.15 cm/s. This improvement is because -GEM velocity mode con-tains the barotropic component that is parallel to the baro-clinic currents. The relationship between and is

( ) ( , , ),F x y t

then

( ) ( , , ),F x y t

( ( ) ) ( , , ),F x y t

s ng bc bt bt .u u u u

According to the above formulas, geostrophic currents ug consist of baroclinic currents ubc and barotropic currents ubt, and barotropic currents ubt can be divided into two parts:

sbtu which is parallel to ubc and n

btu which is perpendicular


Figure 16 -GEM derived temperature (°C) (solid) and current meter measurements (dotted) at the southern mooring.

Figure 17 (a)–(d) -GEM derived zonal currents (solid) and current meter measurements (dotted) at the eastern mooring; (e)–(h) same as in (a)–(d) but for meridional currents.

to ubc. Traditional methods calculate only baroclinic cur-rents ubc from specific volume anomaly, but -GEM esti-mate ( )F contains barotropic component s

btu besides

baroclinic currents ubc, and therefore -GEM estimates are more consistent with in situ measurements.

Besides sbtu , the barotropic currents ubt also contain n

btu

which is perpendicular to ubc. We calculated the part of sea surface height missed by -GEM estimates (x, y, t) with baroclinic geopotential height 0/3000 from IES and ADT data from altimetry (Figure 18). The results show that (x, y, t) is orthogonal to the baroclinic field 0/3000 and consistent with the current meter measurements at 3200 dbar. That


Figure 18 Flow field in the IES area on September 27, 1995 (a) and February 26, 1997 (b). Contours show baroclinic geopotential 0/3000 derived from IES measurements. Color map shows the residual of absolute dynamic topography from the baroclinic geopotential. Vectors indicate current meter measurements at 3200 dbar.

implies (x, y, t) represents the barotropic component nbtu

which is perpendicular to the baroclinic currents ubc. Though -GEM estimates coincide well with current

meter measurements, they are still relatively smooth and exhibit less meso-scale fluctuations (Figure 17). There are two possible reasons for these differences. First, the current meter data are point-measurement and contain various age-ostrophic noises, while -GEM estimates are based on geo-strophic velocity determined from neighboring geopotential heights and therefore represent the mean currents within a cell. Second, the current meter data used here are daily measurements, whereas the SSH data are weekly and miss many high frequency signals.

5 Summary

Based on the geostrophic empirical mode (-GEM) devel-oped by Sun and Watts [7], we constructed a -GEM with hydrographic transects and satellite altimeter measurements. The vertical and lateral structure captured by the -GEM field includes all of the frontal and water mass features identified in the original CTD data. In the WOCE/SR3 area, more than 95% of the variance in the observed temperature is captured by the -GEM field. Compared with -GEM, -GEM fields exhibit relatively larger rms residuals from CTD measurements, which is caused mainly by the SSH bias from due to barotropic and ageostrophic effects.

The -GEM velocity mode is also derived in this study. The subsurface currents estimated with -GEM contain barotropic component and exhibit equivalent-barotropic

structure. Compared with traditional dynamic mode, the -GEM velocity mode is more consistent with current meter measurements in the WOCE/SR3 area and represents the vertical structure of the currents better.

Time series of currents and temperatures estimated with -GEM is compared with mooring observations in the SR3 area. The -GEM estimates agree well with in situ meas-urements. At depths of 300, 600, 1000, and 2000 dbar, the rms residuals of estimated zonal currents are 9.9, 7.0, 4.5, and 2.5 cm/s, and the rms residuals of estimated tempera-tures are 0.79, 0.69, 0.28, and 0.09°C respectively.

Comparisons with mooring measurements demonstrate that -GEM technique can accurately estimate the profiles of temperature, salinity, and velocity from the altimetric sea surface height. It provides us a powerful means to recon-struct the subsurface structure of the ocean from the con-tinuous measurements of the satellite altimeter. It is also very useful in assimilating altimeter data into numerical models.

This work was supported by National Basic Research Program of China (Grant Nos. 2007CB411804 and 2012CB417401), Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KZCX2-YW- Q11-02) and National Natural Science Foundation of China (Grant No. 41006114).

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A geostrophic empirical mode based on altimetric sea surface height