ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 29, NO. 4, 2012, 823–837

Altimetric Data Assimilation by EnOI and 3DVAR

in a Tropical Pacific Model: Impact on

the Simulation of Variability

FU Weiwei∗1,2 (符伟伟)

1Center for Ocean and Ice, Danish Meteorological Institute, Copenhagen, 2100, Denmark

2ICCES, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

(Received 25 February 2011; revised 27 June 2011)

ABSTRACT

When altimetric data is assimilated, 3DVAR and Ensemble Optimal Interpolation (EnOI) have differentways of projecting the surface information downward. In 3DVAR, it is achieved by minimizing a cost functionrelating the temperature, salinity, and sea level. In EnOI, however, the surface information is propagatedto other variables via a stationary ensemble. In this study, the differences between the two methods werecompared and their impacts on the simulated variability were evaluated in a tropical Pacific model.

Sea level anomalies (SLA) from the TOPEX/Poseidon were assimilated using both methods on datafrom 1997 to 2001 in a coarse resolution model. Results show that the standard deviation of sea level wasimproved by both methods, but the EnOI was more effective in the central/eastern Pacific. Meanwhile,the SLA evolution was better reproduced with EnOI than with 3DVAR. Correlations of temperature withthe reanalysis data increased with EnOI by 0.1–0.2 above 200 m. In the eastern Pacific below 200 m,the correlations also increased by 0.2. However, the correlations decreased with 3DVAR in many areas.Correlations with the independent TAO profiles were also compared at two locations. While the correlationsincreased by up to 0.2 at some depths with EnOI, 3DVAR generally reduced the correlations by 0.1–0.3.Though both methods were able to reduce the model–data difference in climatological sense, 3DVAR appearsto have degraded the simulated variability, especially during El Nino–Southern Oscillation events. Forsalinity, similar results were found from the correlations. This tendency should be considered in future SLAassimilations, though the comparisons may vary among different model implementations.

Key words: EnOI, 3DVAR, SLA assimilation, Tropical Pacific, variability

Citation: Fu, W. W., 2012: Altimetric data assimilation by EnOI and 3DVAR in a Tropical Pacific model:Impact on the simulation of variability. Adv. Atmos. Sci., 29(4), 823–837, doi: 10.1007/s00376-011-1022-7.

1. Introduction

Satellite data allows spatial and temporal resolu-tion that is hard to attain using other platforms. Italso provides a quasi-synoptic view of the ocean sur-face and benefits the study of large-scale low-frequencyvariations of the tropical oceans. As a result, satel-lite altimeter data has been widely used in assimila-tion studies to improve the temperature simulationsin the tropical Pacific. Some previous studies foundthat assimilation of the altimetric sea level data canhelp to resolve major features of the seasonal cycle(Carton et al., 1996) and has the potential to improve

the El Nino–Southern Oscillation (ENSO) predictionskills (Fischer et al., 1997; Ji et al., 2000).

In Tropical Pacific Ocean models, simulated vari-ability can serve as an important indicator of perfor-mance. While assimilating temperature profiles canimprove the simulated variability of the temperature,it is more complicated in the case of the altimetric dataassimilation. There are two problems to be carefullyaddressed. First, the downward projection of the sur-face information to subsurface layers must be consid-ered; second, impacts on both subsurface temperatureand salinity should be addressed simultaneously. Theassimilation of sea level observations places an integral

∗Corresponding author: FU Weiwei, weiweifu@mail.iap.ac.cn

© China National Committee for International Association of Meteorology and Atmospheric Sciences (IAMAS), Institute of AtmosphericPhysics (IAP) and Science Press and Springer-Verlag Berlin Heidelberg 2012

824 SIMULATION OF VARIABILITY ALTERED BY ENOI AND 3DVAR VOL. 29

constraint on the density, but not on the vertical struc-ture of density. Therefore, if the assimilation schemeis not suitably applied, the assimilation may worsenthe salinity variability while improving the simulatedvariability of temperature. In fact, some studies showthat to use sea surface height data properly, a bivariateassimilation scheme should be used to correct salinityas well as temperature (Behringer et al., 1998; Ji et al.,2000). When the temperature is changed in the assim-ilation by 3DVAR or optimal interpolation (OI), salin-ity should be adjusted either by a temperature-salinity(T -S) relation (Troccoli and Haines, 1999; Vossepoelet al., 1999; Maes and Behringer, 2000) or by verticalshifts of the T -S profiles (Cooper and Haines, 1996;Alves et al., 2001). For instance, Yan et al. (2004) pro-posed a method for 3DVAR to assimilate the surfacedynamic height data. This method takes into consid-eration vertical correlations for both temperature andsalinity background errors and the nonlinear T -S re-lation. In addition to the 3DVAR, EnOI and otherreduced forms of the ensemble Kalman filter (EnKF)such as Singular Evolutive extended Kalman (SEEK)filter, are also applied to assimilate sea level data inOGCMs (Testut et al., 2003; Parent et al., 2003; Birolet al., 2005; Oke et al., 2008; Counillon and Bertino,2009). The ensemble-based methods present a rela-tively straightforward method in altimetric data as-similation by utilizing the inherent multivariate re-lation. Fu et al. (2009a) compared two multivariateschemes, a modified form of 3DVAR (cf. Yan et al.,2007) and the EnOI in the context of sea level data as-similation. Both methods have positive impacts on thetemperature and salinity fields from the surface downto 300 m in terms of climatology. However, their im-pacts on the simulated variability were not examined.Simulation of the variability is important in the Trop-ical Pacific, which is closely associated with ENSO.Therefore, we aimed to extract some useful informa-tion from the sea level data to improve the simulationof temperature and salinity variability at subsurfacelayers.

As mentioned, the T -S relation is usually derivedfrom the time averaged variability at a fixed position(Vossepoel and Behringer, 2000; Ricci et al., 2005; Yanet al., 2007). Some efforts have also been made to in-clude seasonal variations in the correlation coefficientsbetween temperature and sea level anomalies (Masinaet al., 2001). However, it is difficult to include morevariations of the salinity in the statistically derivedschemes due to the scarcity of salinity observations.On the other hand, ensemble-based methods allowmore variation in the T -S relation by taking advantageof the long-term model simulations. However, the T -Srelation can suffer from the model errors in tempera-

ture and salinity. As a result, two questions arise here.First, does the climatological T -S relation have nega-tive effect on the simulated variability in the tropicalPacific? Second, is the modeled T -S relation in EnOIbeneficial in improving variability when sea level datais assimilated? Huang et al. (2008) found that thesynthetic salinity constructed from temperature and alocal T -S climatology has the advantage in improvingthe climatological salinity analysis but that it seriouslyunderestimates salinity variability on the intraseasonaland interannual time scales. In addition, Huang et al.(2008) found that replacing the synthetic salinity withthe Argo salinity obviously improved the salinity anal-ysis, which in turn contributed to improved surfacecurrent and sea surface height analyses. The secondquestion has received less attention in recent studies.In particular, the coarse resolution of the model usedin this study is inadequate to resolve the equatorialKelvin waves, which may cause problems in the simu-lated variability. It is of primary interest to examinewhether the assimilation of sea level data can alleviatesuch a problem. This is the second topic we want toaddress in this paper.

The rest of the paper is organized as follows. Sec-tion 2 describes the equatorial tropical Pacific model.The assimilated sea level anomaly (SLA) data anddata used for validation are introduced in section 3.The implementation of the two assimilation schemes isintroduced in section 4. Experimental setup is intro-duced and results from 5-yr assimilation experimentsare compared with various datasets in section 5. Asummary is presented in section 6.

2. Model configurations

The tropical Pacific General Circulation Model(GSM) used in this study was first developed by Zhangand Endoh (1992). It is a free surface model in a σ-coordinate framework. The dynamics of the modelare governed by the primitive equations under the hy-drostatic and Boussinesq approximations. The modeldomain extends from 120◦E to 69◦W and from 30.5◦Nto 30.5◦S in the tropical Pacific Ocean. The flat-bottom ocean is 4000 m deep. In the vertical, 14unevenly distributed levels lie at 10 m, 30 m, 50 m,75 m, 105 m, 135 m, 165 m, 195 m, 225 m, 270m, 330 m, 420 m, 670 m, and 2390 m, respectively.The model is mainly purported to simulate the up-per tropical Pacific Ocean. The horizontal resolutionused in this study was 2◦ (lon) by 1◦ (lat). Themodel introduces a standard stratification and con-tains a convective adjustment procedure when hydro-statical instability takes place. The lateral boundariesare assumed to be “non-slip” and insulated, but at

NO. 4 FU 825

the northern and southern boundaries the relaxationterms γ(T ∗−T ) and γ(S∗−S) were added to the T -Sequations, where T and S are temperature and salinityrespectively, γ is the Newton cooling coefficient, whichequals (60 d)−1，and T* and S∗ are climatologies ofLevitus (1982).

The initial ocean state for the start of the assimi-lation run should not be far from observed conditions.This could be achieved by using a strong relaxationon sea surface temperature combined with a weakersubsurface restoration to climatological temperatureand salinity at northern/southern lateral boundaries.The model was spun up with climatological fluxes ofmomentum, heat and freshwater data from a previ-ous study by Levitus (1982), starting from the mon-tionless ocean. The model was integrated until theupper-ocean reached a quasi-equilibrium state. Thenthe model was forced with time-varying fluxes from1982 to 2002. The wind stress was obtained from theproduct of Florida State University (FSU; Bourassaet al., 2001) and was processed to fit the model grid.The heat flux was calculated by restoring sea surfacetemperature to Reynolds SST (Reynolds and Smith,1994) with a time scale of 50 days. The freshwaterflux was calculated from the monthly mean values ofsurface marine data (SMD94) described by da Silva etal. (1994).

3. Data

3.1 TOPEX/Poseidon sea level anomaly(SLA) data

The satellite altimetry data used in this studyare the merged product provided by the Jet Propul-sion Laboratory (JPL) of the National Aeronauticsand Space Administration (NASA). The gridded datacover all latitudes between 66◦N and 66◦S. The val-ues at each bin represent the difference between theaverage sea level measured in that space–time bin andthe 9-year average (1993–2001) of the measurements inthat spatial bin. This is necessary in order to removeresidual geoid signals, because errors in the geoid mod-els exceed dynamical topographic signals over much ofthe ocean, and removing a time mean is more accuratethan removing the GDR mean sea surface. Therefore,all the data are sea level residuals above the 9-yearmean. Their estimated accuracy is better than 4 cmat each bin. The temporal resolution of the griddeddata is 5 days, while the horizontal resolution is 1◦×1◦.

3.2 Validation data

The independent observations provide an ideal toolto verify the model and the reanalysis data. For ex-ample, some temperature and salinity profiles from

Tropical Atmosphere Ocean (TAO) moored array data(McPhaden et al., 1998) were used. The TOPEX/Po-seidon sea level anomalies were also used to calculatethe standard deviation and compared with that of themodel.

Independent observations are not adequate topresent a full picture of the simulated variability be-cause there are spatial and temporal gaps in thesedata. An alternative is the reanalysis product thataffords very good spatial and temporal coverage es-pecially below the surface. It should be noted thatthe reanalysis product is not error-free and has itsown weakness. For instance, reanalysis data maybe not independent because of model configurationand external forcing. Nevertheless, reanalysis datais a good surrogate to the observations because itcombines all of the available observations. In thisstudy, the reanalysis data were produced by the OceanVariational Analysis System (OVALS), which synthe-size many currently available observed data includingTAO, Expendable Bathythermographs (XBT’s), satel-lite sea surface height (SSH), Argo, etc. (Zhu et al.,2006). The reanalysis data were used to validate modeland assimilation results (Yan et al., 2007; Fu et al.,2009a). The data agreed well with other known re-analysis data (e.g., NCEP reanalysis in the TropicalPacific) and some independent observations, partic-ularly for the temperature field. Because OVALS isbased on the same dynamical model used in this pa-per, the errors due to interpolation between differentmodel grids were avoided.

4. Assimilation algorithms

4.1 EnOI

EnOI is a simplified form of EnKF (Evensen, 2003).The computational cost is much lower than EnKF be-cause only one model integration is needed. In EnKF,random errors for the model forecast (ε) and the mea-surements (γ) can be introduced as

d = Hψt + γ , (1)

andψf = ψt + ε , (2)

where d denotes the measurements, ψf is the modelforecast, ψt is the true state, and H is the measure-ment operator relating the prognostic model state tothe measurements. By assuming that the distributionof stochastic errors are Gaussian and nonbiased, it ispossible to calculate a least-square estimate ψa, whichminimizes the distance to ψt.

Different from the EnKF, the model covariance ma-trix of EnOI is stationary and computed from a his-

826 SIMULATION OF VARIABILITY ALTERED BY ENOI AND 3DVAR VOL. 29

torical ensemble using

εεT ≈ α

N − 1A′A′T , (3)

where A′ is the centered historical ensemble (i.e. A′ =A−A), and A is the historical ensemble composed ofmodel states. The superscript T denotes the transposeof matrix. Here, the overbar denotes ensemble aver-aging or expected value. N is the ensemble size. α isa scaling factor. In addition, the measurement errorcovariance Re can be constructed using

Re =γγT

N − 1. (4)

By the above definitions and some manipulation, theEnOI analysis is computed by solving the followingequation:

ψa =ψ+αA′A′T(αHA′A′THT+γγT)−1(d−Hψ) . (5)

The analysis is calculated in the space spanned by astationary ensemble of model states, which is sampledfrom long time integration. This is the key differ-ence with the EnKF. The stationary ensemble sam-pled over a long time period tends to have a large sea-sonal/interannual variance, which is not able to repre-sent the instantaneous forecast error variance. There-fore, a scaling factor α ∈ (0, 1] is introduced.

4.2 3DVAR

For the 3DVAR, the SLA is assimilated in twosteps. First, the temperature and salinity profiles areestimated by solving a cost function as follows:

J =12(T − Tb)TE−1

T (T − Tb) +12[S − g(T )]TE−1

S ×

[S − g(T )] +1

2σ2[h(T ,S)− h0]2 ,

(6)

where T and S are the column vectors containingthe state variables of temperature and salinity, respec-tively, Tb and Sb are the corresponding backgroundvectors, ET and ES are the background error covari-ance matrices with the vertical correlation of back-ground errors for temperature and salinity, and g(T )represents a nonlinear T -S relation. More details canbe found in Yan et al. (2004). The empirical functionsused by Behringer et al. (1998) are adopted to deter-mine the variances of background errors. The vari-ance of temperature background error at the depth zis given by:

αvT(dT/dz)1/2

[(dT/dz)1/2]max, (7)

where the constant avT is determined empirically bytuning the analysis; we set avT = 1.2. For the salin-ity, the definition of the background error covariance

is analogous to temperature, but the correspondingconstant avS is set to 0.7. The function h denotes anobservation operator that transforms T , S to surfacedynamic height (SDH); h0 is the observed value of seasurface height. Observation error of sea surface heightis σ which is set to 4 cm. The definition of h is asfollows:

h(T, S) = −∫ zm

0

ρ(T, S, p)− ρ0(p)ρ0(p)

dz (8)

where ρ(T, S, p) is the state equation for density calcu-lation; ρ0(p) = ρ(0, 35, p) is the reference density, zm

is the reference depth, z denotes the vertical coordi-nate, and p denotes pressure. In this study, we choosea depth of 630 m as the reference depth. For each SLAobservation, a T (S) profile can be derived.

Second, temperature and salinity profiles obtainedin the first step are taken as observations. The T , S as-similation scheme are based on a cost function similarto Derber and Rosati (1989) defined by

J =12xT A−1x+

12(D(x)−x0)T F−1(D(x)−x0) , (9)

where X = [T1,T2, · · · ,TM ,S1,S2, · · · ,SM ] is thestate vector denoting a correction to the first-guesstemperature and salinity fields, A is the first-guesserror covariance matrix, X0 is the vector containingthe difference between the observations and the inter-polated first-guess temperature and salinity fields, Dis bilinear interpolation operator from the grid to theobservation locations, and F is the observation errorcovariance matrix.

4.3 Implementations and experiments

Estimation of the background and the observa-tion error is of critical importance for both EnOI and3DVAR. For EnOI, the background error covarianceis approximated by the stationary ensemble. In thisstudy, the stationary ensemble was sampled from themonthly forecasts during the period from 1985 to 2000.A large ensemble (N = 180) was chosen, but the SVDwas then used to reduce its size. The ensemble wasnormalized prior to performing the SVD to ensure thatthe variances of all variables were preserved (Fu etal., 2009b). The first 70 dominant components ex-plained ∼90% of the total variance. The dominantcomponents were converted into the physical space andserved as our final stationary ensemble. Backgrounderror covariance estimated in this way exhibited somefeatures of the local flow pattern. This can be illustr-

NO. 4 FU 827

Fig. 1. The ensemble-based cross-correlation of sea sur-face temperature at (a) 0◦, 148◦E and (b) 0◦, 152◦W.The cross-correlations were computed at the two loca-tions and their surrounding areas. The contour intervalis 0.2.

ated in Fig. 1 by the ensemble-based spatial correla-tions at (0, 148◦E) and (0, 152◦W). The correlationsfor (0, 148◦E) declined more rapidly in the zonal di-rection (<0.3 west of 165◦E). The contours were morestretched in the meriodional direction and squeezedclose to the boundary area. On the other hand, thede-correlation scales at (0, 152◦W) were much largerin the zonal direction than in the meridional direc-tion, which is consistent with the dominant equatorialcurrent directions in this area. The background errorvariance was approximated from a long-term variabil-ity in the stationary ensemble. Parameter α in Eq. (5)was empirically set to be 0.7 for this study by assum-ing that the long-term variability was stronger thanthe instantaneous forecast error variance. It should benoted that increasing the scaling factor α was equiv-alent to reducing the observation error. Because thesatellite data are given as SLA, the modeled SLA wascalculated by subtracting mean SSH field (Haugen andEvensen, 2002).

As for 3DVAR, the estimated temperature andsalinity profiles were assimilated using Eq. (9). Fora fair comparison, the background error covariance of3DVAR was also estimated from the stationary ensem-ble used in EnOI. Therefore, the spatial de-correlationstructure was the same as in the EnOI as illustrated inFig. 1. For example, the influence radius of the two lo-cations was determined accordingly (Fig. 1). Becausethe SLA data itself has errors and the cost functionin Eq. (6) is not perfect, the temperature and salin-ity profiles retrieved from the SLA data may have hadlarger errors than the direct observations (Argo). Byreferring to the errors of Argo data, the observation er-

ror covariances were empirically set to 0.7◦C and 0.15psu for temperature and salinity, respectively.

The TOPEX/Poseidon SLA data was assimilatedevery 5 days from January 1997 to December 2001 withboth methods. The experiment without assimilation ishereafter referred to as exp CNT. The assimilation runusing 3DVAR is denoted as exp 3DVAR. The secondassimilation run was the same as exp 3DVAR exceptthat the assimilation scheme was replaced with EnOI.This run is denoted as exp EnOI.

5. Results

In this section, the impacts of SLA assimilation onthe modeled variability are reported. Both the reanal-ysis and TAO data were used in the comparisons. Ourmajor concern was whether or to what extent the mod-eled variability was improved by EnOI and 3DVARespecially at subsurface.

5.1 Sea level elevation

The temporal evolution of the SLA along the equa-tor is presented in Fig. 2. The SLA was computedrelative to the climatology over the 5-yr period. Onenoticeable feature during 1997–2001 is the evolutionof ENSO events. A strong El Nino event occurredin 1997–1998, followed by a strong La Nina event in1999. In the eastern Pacific, the observation showsthat the sea level was anomalously high (>30 cm inthe peak phase) during the strong El Nino in 1997–1998. The strong positive anomalies above 10 cm arecentered at ∼125◦W, spanning the second half-yearof 1997. For the exp CNT, however, the onset of thepositive anomalies was several months later. In ad-dition, two separate maxima were found in the east-ern Pacific at ∼140◦W and 90◦W. The two maximaof the positive anomalies were further displaced in theexp 3DVAR. In the western Pacific, the observed nega-tive anomalies of ∼26 cm propagating eastward acrossthe basin were not captured in both assimilation runs.The negative anomalies disappeared west of 150◦Win March of 1998. Relatively, the negative anomaliesin the exp EnOI were closer to the observations, withanomalies of approximately −20 cm appearing in themiddle of 1998. Moreover, the pattern of the anomalyin the exp EnOI agreed better with the observation inthe central/eastern Pacific in terms of position, start-ing time and extending domain compared with theexp 3DVAR. For instance, evolution of the negativeanomalies was more improved in the central Pacific.

Standard deviations of the sea surface height areshown in Fig. 3. From the observation data, largevariabilities appear to have agreement with the maincurrent systems in the equatorial Pacific. For example,

828 SIMULATION OF VARIABILITY ALTERED BY ENOI AND 3DVAR VOL. 29

Fig. 2. The evolution of sea level anomalies on the longitude-time section along theequator for (a) exp CNT, (b) exp 3DVAR, (c) exp EnOI, and (d) observations fromTOPEX/Poseidon. Contours are drawn every 4 cm.

large variabilities are seen along the latitude of 10◦S,12◦N in the eastern Pacific and 3◦–7◦N in the cen-tral Pacific, which corresponds to the south equatorialcurrent (SEC), north equatorial current (NEC), andthe north equatorial counter current (NECC), respec-tively. In these regions, the variability in the exp CNTwas severely underestimated by 64 cm. Standard de-viation was improved by both schemes in terms of thespatial pattern and magnitude. Relatively, 3DVARperformed better in the western Pacific than EnOI.The structure of standard deviation >10 cm was closerto the observation data, while this was overadjustedin the exp EnOI, especially in the southern Pacificaround 10◦S. However, EnOI was more effective in thecentral and eastern Pacific. The standard deviation

in a band-shape area between 8◦S–10◦N increased by62 cm and agreed better with the observations. Vari-ability in this area is usually underestimated and nar-rowly confined to the equator due to the deficiency ofsimulating the strong upwelling of cold water. Theexp 3DVAR even deteriorates the standard deviationhere by restricting the large variability (>8 cm) fur-ther toward the equator.

Compared to the 3DVAR, EnOI seems to be moreeffective in improving the simulated variability. Onereason is that the EnOI produces more dynamicallybalanced adjustments to the temperature and salinitythan the 3DVAR, which in turn has sizable impact onthe simulated sea level. Another reason is that therelation between SLA and temperature/salinity in the

NO. 4 FU 829

Fig. 3. The standard deviation of sea level elevation from(a) exp CNT, (b) exp 3DVAR, (c) exp EnOI and (d) theobservations of TOPEX/Poseidon. The contour intervalis 2 cm.

EnOI has spatial variation. The spatial variation is notfully accounted for in the 3DVAR. Figure 4 displaysthe ensemble-based cross-correlations between the sealevel and temperature/salinity along the equator. Fortemperature, the vertical correlations in the westernPacific are large (60.9 at 100 m), while the correla-tions decline to −0.8 in the eastern Pacific. The cross-correlations are ∼0.1–0.2 in the central Pacific. Itshould be noted that the cross-correlations for salinityare quite different from those of temperature. Thesespatial variations help to distribute the surface infor-mation downward to different areas.

5.2 Temperature

In Fig. 5, correlations of temperature with theOVALS reanalysis data are compared on the longitu-de-depth section along the equator. Higher correla-tions imply that the simulated variability was closer

Fig. 4. The ensemble-based cross correlations betweensea level and (a) temperature and (b) salinity on thelongitude-depth section of along the equator. The con-tour interval is 0.1.

to the reanalysis data. In the exp CNT, it is clearthat the corrections >0.6 mainly existed above 200m. The correlations were <0.4 in most parts of thewestern Pacific below 200 m. In the exp 3DVAR, thecorrelations were reduced by 0.2 nearly for the wholelayer especially in the western Pacific. In addition, thecorrelations were clearly reduced across the section be-tween 50 m and 150 m. The only exception appearedbelow 200 m from 150◦W to 120◦W. Comparatively,

830 SIMULATION OF VARIABILITY ALTERED BY ENOI AND 3DVAR VOL. 29

Fig. 5. The correlations of temperature between (a) exp CNT, (b) exp 3DVAR, (c)exp EnOI and OVALS reanalysis data on the longitude-depth section along the equa-tor. The contour interval is 0.1.

EnOI exhibited positive impact except below 200 min the western Pacific. In particular, the correlationsincreased by ∼0.2 for the whole layer in the easternPacific. The correlations on the longitude-depth sec-tion give a clear message that assimilation of the SLAis effective in improving the simulated variability ofthe subsurface ocean.

In addition to the reanalysis data, some indepen-dent observations from TAO profiles were also usedto further verify the effects of the two methods. Attwo locations (0◦, 165◦E and 0◦, 155◦W), the differ-ences between model runs and TAO observations werecalculated for the uppermost 400 m. Differences onthe depth-time sections are presented in Figs. 6 and

7. At (0◦, 165◦E) large temperature differences up to4◦C were found below 200 m from 1997 to 1999. Forthe top 200 m, the temperature of the control run wasgenerally 1◦C lower than the observations, except atthe end of 1997, where positive difference of ∼1.0◦Cwas seen from 50 m to 200 m. The differences were re-duced to varying extent in both the exp 3DVAR andexp EnOI below 200 m. Comparatively, the reductionwas more significant in the exp EnOI where magni-tudes of the differences were reduced to <1.0◦C overmost of the section. In the exp 3DVAR, the differenceof temperature was also reduced by 0.5◦C below 200m. However, it is noted that the differences with TAOin exp 3DVAR were larger than the exp CNT above

NO. 4 FU 831

Fig. 6. The difference of temperature on the depth-time section between (a) exp CNT, (b) exp 3DVAR, and(c) exp EnOI and TAO independent observation at (0◦,165◦E). The contour interval is 0.5◦C.

200 m from 1998 to the middle of 1999. The negativedifferences of approximately −3.5◦C were found ex-tending from the beginning of 1998 at 50-m depth tothe depth of 150 m in the middle of 1999, which wereabsent in the exp CNT. The differences were slightlyreduced for the rest of this period. It suggests theassimilated temperature and salinity profiles retrievedfrom sea level caused more errors during ENSO events.This can be partly explained because the nonlinearT -S relation in Eq. (6) is constructed from the cli-matological observations. Though the retrieved pro-files helped to improve the simulated temperature, thestrong variability of temperature during ENSO events

Fig. 7. The difference of temperature on the depth-time section between (a) exp CNT, (b) exp 3DVAR, and(c) exp EnOI and TAO independent observation at (0◦,155◦W). The contour interval is 0.5◦C.

were largely smoothed. In the exp EnOI, the differ-ences were generally reduced with respect to the con-trol run. More importantly, the differences were notamplified as in the exp 3DVAR during ENSO eventsfrom 1998 to 1999. In theory, the analysis of the EnOIcan be regarded as a combination of the state vector inthe stationary ensemble. The combination varies withtime and is modulated by the instantaneous observa-tions. Therefore, the strong variability during ENSOevents can to some extent be taken into account.

At (0◦, 155◦W), the differences of temperaturebetween the exp CNT and TAO data show distinctchanges across the thermocline (at thedepthof 130 m).

832 SIMULATION OF VARIABILITY ALTERED BY ENOI AND 3DVAR VOL. 29

The negative differences are found above 150 m overthe 5-year period, except the strong El Nino at the endof 1997. The large values of approximately −3.0◦C ap-peared during the second half-year of 1999 when the LaNina occurred. Below 150 m, however, the exp CNTshowed uniformly positive differences. The largest dif-ference was seen during 1998–1999 when the strong ElNino occurred. Below 250 m, some improvements werefound in both assimilation experiments. However, thedifferences were even larger in the exp 3DVAR from1997 to 1998, especially between 50 m and 150 m. Forexample, the positive difference of ∼3.5◦C was foundat the end of 1997. The difference reached −4.0◦C atthe end of 1999. The large differences during 1997–1999 suggest a destroyed vertical stratification. Dif-ferent from 3DVAR, the differences were noticeablyreduced in most parts of the section in the exp EnOI.The differences were reduced to <1◦C below 100 m.In the mixing layer above 100 m, the differences werealso reduced (but not significantly).

In addition to the correlations calculated with theOVALS reanalysis, correlations between the modelruns and the independent TAO profiles were also cal-culated at the above two positions. The TAO pro-files were first interpolated to the model depths byspline interpolation, the correlation at each depth wasthen calculated with the two time series. Figure 8gives the correlation coefficients at each depth for theexp CNT, exp 3DVAR, exp EnOI, respectively. The

correlations dropped with depth for all the three ex-periments. Large correlations appeared mainly above200 m, which is in good agreement with the result ob-tained from the OVALS analysis (Fig. 5). From thesetwo locations, it is clear that EnOI is more effectivein increasing the correlations with independent TAOobservations than 3DVAR nearly at every depth. At(0◦, 165◦E), the correlation coefficients were reducedby 0.2 with 3DVAR. Moreover, the correlation coeffi-cients declined further below 150 m and were even neg-ative below 250 m. This indicates that the variabilityof temperature at subsurface is severely impaired af-ter the SLA assimilation with 3DVAR. Relatively, thecorrelations increased with EnOI nearly at every depthcompared to the exp CNT. The impact was more sig-nificant below 150 m. At (0◦, 155◦W), the correla-tions exhibited similar features. One difference from(0◦, 165◦E) is that the improvements were more sig-nificant above 250 m.

These comparisons show that EnOI outperforms3DVAR in reproducing the variability of temperatureafter SLA assimilation. In addition, the impact of3DVAR was unsatisfactory during an ENSO event, es-pecially near the thermocline depth (Fig. 7). The rea-son can be traced back to the implementation of thetwo methods. As stated previously, 3DVAR projectsthe surface information downward with Eq. (6) thatinvolves a climatological T -S relation. Furthermore,the variance of background error would be αvT ac-

Fig. 8. The correlations between the time series of temperature from exp CNT,exp 3DVAR, exp EnOI, and TAO observations on the model depth at the locationof (a) 0◦, 165◦E and (b) 0◦, 155◦W. TAO profiles are first interpolated to the modellevels.

NO. 4 FU 833

cording to Eq. (7) at the thermocline depth becausethe thermocline has the largest temperature gradi-ent. Therefore, the larger background error varianceat thermocline depth tends to cause more errors inderived T -S profiles than at other depths. Notably,the parameter αvT remained constant and failed toaccount for the spatial and temporal variations of thebackground error. The parameter αvT that is appro-priate in the eastern Pacific may misrepresent the vari-ation in the western Pacific. This problem is exacer-

bated during the ENSO events. That is why large er-rors appear in 1998 and 1998 at the depth of 100–150m. Therefore, the T -S relation should be addressedwith more efforts in future applications of 3DVARwhen sea level data are assimilated. Different from3DVAR, the temperature is adjusted in EnOI throughthe cross-correlations that are spatially varying (Fig.4). Moreover the stationary ensemble is also beneficialto reproduce the temperature variability during ENSOevents.

Fig. 9. The correlation of salinity between (a) exp CNT, (b) exp 3DVAR, (c) exp EnOI, andOVALS reanalysis on the longitude-depth section along the equator. The contour interval is 0.1.

834 SIMULATION OF VARIABILITY ALTERED BY ENOI AND 3DVAR VOL. 29

5.3 Salinity

Compared to the temperature, salinity is not onlya tracer of the interannual variability in the tropicalPacific but could play an active role in determining thedensity structure. Horizontal gradients of salinity con-tribute to horizontal pressure gradients, and thus tothe mean state and variability of the currents. Salinityalso modulates vertical stratification and can thus fa-vor or inhibit vertical mixing (Godfrey and Lindstrom,1989).

Similar to the temperature, correlations of salin-ity between the model runs and OVALS reanalysis areshown in Fig. 9. From the exp CNT, large correlations(up to 0.6) were mainly located in the eastern Pacificat the depth of 100 m–200 m. At other places, thecorrelations were generally <0.5. The correlations de-creased with 3DVAR, especially in the eastern Pacific,where correlations >0.4 were largely reduced. As forEnOI, the spatial distribution of the correlations wasquite similar to the exp CNT. Some small improve-ments were found in the eastern Pacific at the depthof 150 m and the western Pacific below 300 m. Asfar as the correlation is concerned, EnOI and 3DVARbehaved similarly for salinity and temperature.

Some TAO salinity profiles were also used to verifythe model runs. Two stations at (0◦, 156◦E) and (2◦S,156◦E) were chosen because relatively complete datarecords were available. The model-observation differ-ence was calculated on the depth-time section relativeto TAO observations (Fig. 10). At (0◦, 156◦E), theexp CNT showed large differences above 75 m, wherea negative difference of ∼0.6 psu was found. Positivedifferences of ∼about 0.1 psu appeared mainly below150 m. The differences in the upper 50 m were largelyreduced by the 3DVAR. The large negative differencesdecreased by 0.2 psu after March of 2000. However,the differences between 100 m and 250 m were largerthan the exp CNT, where the differences were reducedto be negative. With respect to the EnOI, it was lesseffective than the 3DVAR in the upper 50 m. Thenegative differences were even bigger than those seenin exp CNT, especially at the end of year 2000. The3DVAR also produced bigger differences at this time.For EnOI, small improvements (<0.15 psu) appearedbetween 100 m and 250 m, which is consistent withthe large vertical cross-correlation between sea leveland subsurface salinity (Fig. 4b). The comparison atthe location (2◦S, 156◦E) showed similar results (figurenot given).

Correlations between time series of the TAO pro-files and model runs are shown at (0◦, 156◦E) and(2◦S, 156◦E) in Fig. 11. Correlations >0.5 in the con-trol run mainly appeared in the upper 50 m and atdepths of 150–250 m. 3DVAR generated worse results

Fig. 10. The difference of salinity on the depth-timesection between (a) exp CNT, (b) exp 3DVAR, and(c) exp EnOI and TAO independent observation at 0◦,156◦E. The contour interval is 0.1 psu.

than the control run. The correlations were reducedfrom positive to negative at some depths for bothstations. The correlations in the exp 3DVAR dif-fered greatly with the exp CNT below 100 m for (2◦S,156◦E) and above 100 m for (0◦, 156◦E). However,EnOI yielded general improvements on the correla-tions at nearly every depth. There was general im-provement at (0◦, 156◦E) between 100 m and 250 m,where the cross-correlation between SLA and salinityalso had the largest values. This comparison with in-dependent TAO data agrees well with the comparisonrelative to the OVALS reanalysis. From these compar-isons, we conclude that 3DVAR tends to worsen thevariability of subsurface salinity, though it reduces themodel–observation differences of salinity in the upper

NO. 4 FU 835

Fig. 11. The correlations between the time series of salinity from exp CNT,exp 3DVAR, exp EnOI, and TAO observations on the model depth at (a) the lo-cation 2◦S, 156◦E and (b) 0◦, 156◦E. TAO profiles were first interpolated to themodel levels.

layers.

6. Summary

The main purpose of this study was to comparethe different impacts of the 3DVAR and EnOI on sim-ulated variability in a Tropical Pacific model in thecontext of sea level data assimilation. The verifica-tions were based on two assimilation experiments withEnOI and 3DVAR. A series of quantitative and quali-tative results comparing the results from 1997 to 2001with various observations are presented. Results showthat the two schemes have quite different impacts onthe simulated variability of the sea level, temperatureand salinity.

For sea level, both methods improved the spa-tial standard deviation to some extent. 3DVAR wasmore effective in the western Pacific while EnOI pro-duced more improvements in the central/eastern Pa-cific. Standard deviation was significantly increased byEnOI in the eastern Pacific and became much closerto the reanalysis data. The evolution of SLA alongthe equator shows that EnOI was more effective than3DVAR in improving the spatial-temporal pattern ofthe SLA during this period. However, the strong pos-itive anomalies during the El Nino in 1998 were stillunderestimated by 10 cm.

The impacts of the two methods on simulated vari-ability at subsurface were major concerns of this study.We calculated the spatial correlations between themodel runs and reanalysis data to investigate the vari-ability on the longitude-depth section. Results show

that EnOI can increase the correlations with reanalysisdata by 0.2 for temperatures above 200 m. Compar-atively, 3DVAR exhibited a negative impact on thevariability as the correlations with the OVALS analy-sis above 200 m were even reduced. This problem isfurther corroborated by the comparison with the inde-pendent TAO profiles. The correlations with TAO pro-files at (0◦, 165◦E) and (0◦, 155◦W) show that 3DVARhad a negative impact at most depths, indicating adeteriorated simulation of variability. One reason isthat the cross-correlation between sea level and tem-perature (and salinity) varies spatially in the EnOIwhile the climatological T -S relation is utilized in the3DVAR. Another reason may be that the empiricalparameters in the 3DVAR scheme fail to capture thespatial-temporal variations. Although these parame-ters of 3DVAR helped to reduce the root mean squaredifference of temperature (and salinity) as shown inFu et al. (2009a), but the simulation of variability wasdegraded.

The comparisons of salinity were quite similar tothose of temperature. Correlations between assimila-tion runs and the observations also reveal that 3DVARplayed a negative role in the simulated variability,though it helped to reduce the model-observation dif-ferences in the upper levels (above 50 m, comparedto the TAO profiles). Comparatively, EnOI presentssome improvements on the simulated variability ofsalinity, especially in the eastern Pacific. Verificationsagainst the independent TAO salinity also demon-strated that 3DVAR tends to worsen the variabilityof salinity at some depths. For instance, the correla-

836 SIMULATION OF VARIABILITY ALTERED BY ENOI AND 3DVAR VOL. 29

tion was negative from the surface to 100 m at (0◦,165◦E). It was similar at the location (2◦S, 165◦E).

Sea level assimilation leads to changes in thesubsurface temperature and salinity, which result inchanges in the vertical density structure. The changedvertical density structure in turn has a direct impacton the simulation of sea level. Some studies haveshown that the sea level data assimilation helps to im-prove model’s climatology (Parent et al., 2003; Birol etal., 2005; Fu et al., 2009a). Comparisons in this studyshow that the SLA assimilation was also helpful for im-proving the variability of the subsurface temperatureand salinity, provided that the assimilation methodis appropriately used. Compared with EnOI, the re-lation between sea level and temperature/salinity inthe 3DVAR involves the climatological data that can-not capture the strong anomalies during the ENSOevents. Therefore, the model–observation differencesbecame even larger during those periods.

For sea level data assimilation, some problems re-main to be addressed, even when the multivariateschemes are applied. For instance, the climatologicalT -S relation in 3DVAR had some detrimental impacton the simulated variability, which agreed with someprevious studies such as Huang et al. (2008). More-over, the assimilation of SLA by the two methods couldnot correct the model deficiencies such as diffuse ther-mocline and the poor simulation of salinity. This prob-lem could be expected to be better resolved with thecombined assimilation of more subsurface temperatureand salinity observations from Argo and other in-situdata. It should be noted that the comparisons may de-pend on different implementations of and assumptionsregarding the two schemes. Nevertheless, our compar-isons reveal that special care should be taken in assim-ilating the SLA data because the assimilation methodscould negatively impact the simulation of variability,even though the root mean square errors (RMSE) be-tween model and observations might be reduced.

Acknowledgements. This work is jointly supported

by National Natural Science Foundation of China (Grant

Nos. 41176014 and 41075064) and the Key Technologies

R&D Program of China (Grant No. 2011BAC03B02). The

author wishes to thank the two anonymous reviewers for

their comments and constructive suggestions which help to

improve the manuscript.

REFERENCES

Alves, J. O. S., D. L. T. Anderson, and K. Haines, 2001:Sea level assimilation experiments in the tropical Pa-cific. J. Phys. Oceanogr., 31, 305–323.

Behringer, D. W., M. Ji, and A. Leetmaa, 1998: An im-proved coupled model for ENSO prediction and im-

plications for ocean initialization. Part I: The oceandata assimilation system. Mon. Wea. Rev., 126,1013–1021.

Birol, F., J. M. Brankart, J. M. Lemoine, P. Brasseur,and J. Verron, 2005: Assimilation of satellite al-timetry referenced to the new GRACE geoid es-timate. Geophys. Res. Lett., 32(6), L06601, doi:10.1029/2004GL021329

Bourassa, M. A., S. R. Smith, and J. J. O’Brien, 2001: Anew FSU winds and flux climatology. 11th Confer-ence on Interactions of the Sea and Atmosphere, SanDiego, CA, Amer. Meteor. Soc., 912.

Carton, J. A., B. S. Giese, X. Cao, and L. Miller,1996: Impact of altimeter, thermistor and expend-able bathythermograph data on retrospective analy-ses of the tropical Pacific Ocean. J. Geophys. Res.,101, 14147–14159.

Cooper, M., and K. Haines, 1996: Altimetric assimilationwith water property conservation. J. Geophys. Res.,101, 1059–1077.

Counillon, F., and L. Bertino, 2009: Ensemble optimalinterpolation: Multivariate properties in the Gulf ofMexico. Tellus-A, 61, 296–308.

da Silva, A.M., C. C. Young-Molling, and S. Levitus,1994: Algorithms and procedures. Vol. 1, Atlas ofSurface Marine Data 1994, Tech. Rep. 6, U.S. De-partment of Commerce, NOAA, NESDIS, 83pp.

Derber, J., and A. Rosati, 1989: A global oceanic dataassimilation system. J. Phys. Oceanogr., 19, 1333–1347.

Evensen, G., 2003: The Ensemble Kalman Filter: The-oretical formulation and practical implementation.Ocean Dyn., 53, 343–367.

Fischer, M., M. Flugel, M. Ji, and M. Latif, 1997: The im-pact of data assimilation on ENSO simulations andpredictions. Mon. Wea. Rev., 125, 819–829.

Fu, W., J. Zhu, and C. Yan, 2009a: A comparison be-tween 3DVAR and EnOI techniques for satellite al-timetry data assimilation. Ocean Modelling, 26, 206–216.

Fu, W., J. Zhu, C. Yan, and H. Liu, 2009b: Toward aglobal ocean data assimilation system based on En-semble Optimum Interpolation: Altimetry data as-similation experiment. Ocean Dyn., 59, 587–602.

Godfrey, J. S., and E. J. Lindstrom, 1989: The heat bud-get of the equatorial western Pacific surface mixedlayer. J. Geophys Res, 94, 8007–8017.

Huang, B., Y. Xue, and D. W. Behringer, 2008: Im-pacts of Argo salinity in NCEP Global OceanData Assimilation System: The tropical IndianOcean. J. Geophys. Res., 113, C08002, doi:10.1029/2007JC004388.

Haugen, V. E. J., and G. Evensen, 2002: Assimilationof SLA and SST data into an OGCM fort he IndianOcean. Ocean Dyn., 52, 133–151.

Ji, M., R. W. Reynolds, and D. W. Behringer, 2000: Useof TOPEX/ POSEIDON sea level data for oceananalyses and ENSO prediction: Some early results.J. Climate, 13, 216–231.

NO. 4 FU 837

Levitus, S., 1982: Climatological Atlas of the WorldOcean. NOAA/ERL GFDL Professional Paper No.13, Princeton, N.J., 173pp.

Maes, C., and D. Behringer, 2000: Using satellite-derivedsea level and temperature profiles for determiningthe salinity variability: A new approach. J. Geophys.Res., 104, 8537–8547.

Masina, S., N. Pinardi, and A. Navarra, 2001: A globalocean temperature and altimeter data assimilationsystem for studies of climate variability. ClimateDyn., 17, 687–700.

McPhaden, M. J., and Coauthors, 1998: The TropicalOcean-Global Atmosphere (TOGA) observing sys-tem: A decade of progress. J. Geophys. Res., 103,14169–14240.

Oke, P. R., G. B. Brassington, D. A. Griffin, and A.Schiller, 2008: The Bluelink ocean data assimilationsystem (BODAS). Ocean Modelling, 21, 46–70.

Parent, L., C. E. Testut, J. M. Brankart, J. Verron,P. Brasseur, and L. Gourdeau, 2003: Comparativeassimilation of Topex/Poseidon and ERS altimetricdata and of TAO temperature data in the tropicalPacific Ocean during 1994–1998, and the mean sea-surface height issue. J. Mar. Syst., 40–41, 381–401.

Reynolds, R.W., and T. M. Smith, 1994: Improved globalsea surface temperature analysis. J. Climate, 6, 929–948.

Ricci, S., A. T. Weaver, J. Vialard, and P. Rogel, 2005:Incorporating state-dependent temperature-salinityconstraints in the background error covariance ofvariational ocean data assimilation. Mon. Wea. Rev.,133, 317–338.

Testut, C. E., P. Brasseur, J. M. Brankart, and J. Ver-

ron, 2003: Assimilation of sea-surface temperatureand altimetric observations during 1992–1993 intoan eddy-permitting primitive equation model of theNorth Atlantic Ocean. J. Mar. Syst., 40–41, 291–316.

Troccoli, A., and K. Haines, 1999: Use of T -S relationin a data assimilation context. J. Atmos. Oceanic.Technol., 16, 2011–2025.

Vossepoel, F., R. W. Reynolds, and L. Miller, 1999: Useof sea level observations to estimate salinity variabil-ity in the tropical Pacific. J. Atmos. Oceanic Tech-nol., 16, 1400–1414.

Vossepoel, F., and D. W. Behringer, 2000: Impact of sealevel assimilation on salinity variability in the west-ern equatorial Pacific. J. Phys. Oceanogr., 30, 1706–1721.

Yan, C., J. Zhu, R. Li, and G. Zhou, 2004: Roles of ver-tical correlations of background error and T-S rela-tions in estimation of temperature and salinity pro-files from sea surface dynamic height. J. Geophys.Res., 109, C08010, doi: 10.1029/2003JC002224.

Yan, C., J. Zhu, and G. Zhou, 2007: Impact of XBT,TAO, altimetry and Argo observations on the Tropi-cal Pacific Ocean data assimilation. Adv. Atmos. Sci.24(3), 383–398, doi: 10.1007/s00376-007-0383-4.

Zhang, R. H., and M. Endoh, 1992: A free surface gen-eral circulation model for the tropical Pacific Ocean.J. Geophys. Res., 97(C7), 11237–11255.

Zhu, J., G. Zhou, C. Yan, W. Fu, and X. You, 2006:A three-dimensional variational ocean data assimila-tion system: Scheme and preliminary results. Sciencein China (D), 49(11), 1212–1222.