frequency barotropic response of the ocean to ... - Wiley Online Library

JOURNAL

OF GEOPHYSICAL

RESEARCH,

VOL. 106, NO. C12, PAGES 30,987-30,995, DECEMBER,

2001

Modeling the high-frequency barotropic response of the ocean to atmospheric disturbances' Sensitivity to forcing, topography, and friction Naoki Hirose, • Ichiro Fukumori, and Victor Zlotnicki Jet PropulsionLaboratory,California Institute of Technology,Pasadena,California, USA

Rui M. Ponte Atmosphericand EnvironmentalResearch,Inc., Lexington,Massachusetts, USA

Abstract. This studyexamineshigh-frequencysea level variationsforced by changesin surfaceatmosphericpressureand wind and their sensitivityto different forcing mechanisms,bottom topographyresolution,and amount of friction in a barotropicocean model. Optimal model performance,defined in terms of the explainedvariancein satellite altimeter and bottom pressuredata, is found when usingrelatively strongfriction, equivalentto a dampingtimescaleof only a few daysover the deep ocean,and topography with minimal smoothing.Spatialvariationsof the optimal friction parameter seemto reflect the roughnessof bottom topography.The model demonstratesskill in simulating the wind-drivenresponseas well as the nonequilibriumresponseto atmosphericpressure variations.

1.

from lower-frequencyvariabilityin the altimeter data. The HF signalincludesthree distinctcomponents:

Introduction

High-frequency(HF) sea level signalsat periods shorter than several weeks have been the focus of recent

hHF: h•B+ hp+ h.,

studies. Fu-

kumori et al. [1998] noted that sea level variability associated with wind-driven barotropic motion could be aliased in altimeter observationsat high latitudeson the basisof their model and datacomparisons. Fukttmoriet al. [1998]alsoreportedthat the HF variabilityis not uniform in spacebut can be enhanced in some semienclosedregions.Stammeret al. [2000] showed that a wind-driven ocean general circulation model can successfullysimulatea significantpart of the HF sealevel signals measuredby TOPEX/Poseidon(T/P). Besideswind forcing, air pressurevariationscan also drive HF signals.Ponte [1993] simulatedthe barotropic ocean responseto realisticpressureforcingand found large deviations from a static(or invertedbarometer,lB) responseat periods shorter than a few daysand at large spatial scales.Ponte and Gaspar [1999] and more recently Mathers and Woodworth [2001]showedthat the larger deviationsfrom lB in the tropics seen in the T/P data are indeed related to a dynamic ocean responseto pressure.Tierneyet al. [2000]useda pressure-and wind-drivenoceangeneralcirculationmodel to predict HF sea level signalsand for periods between 5 and 20 days found better consistency with T/P datawhenusingpressurepluswind forcingrather than wind forcing alone. The HF variability is clearlypresentand of detectableamplitude in the altimeter observations,but the satellite'ssampling pattern will alias it in a complicatedway into longer periods. Thus one cannot easily distinguishthe HF signals

(1)

where h is the sea level, subscriptsHF, lB, and p and w indicate high-frequency, inverted barometer, and pressureand wind-driven dynamic components,respectively.The IB signal(h •B)will be estimatedfrom local air pressureminusthe averagepressureover the globaloceanasby Ponte[1993].This

studyaimsat estimating hw and hp, particularlytheir HF signals,using a barotropic ocean model. Successful estimation

of HF sea level variations

will contrib-

ute to dealiasingsignalsat frequencieshigher than the Nyquist frequencyin altimetry(e.g.,T/P, Jason-l,ERS-2, and Envisat) or gravity missions(e.g., the Gravity Recovery and Climate Experiment(GRACE)). The conceptis similar to the treatment of tidal aliasing.A relativelysimple,shallowwater model is chosenfor this study. Previousstudiesconcludedthat the densitystratificationdoes not make much difference in modeling sea level HF signalsbecausethe responseis essentially barotropic[e.g., Tierneyet al., 2000]. This study examinesthe sensitivityof the barotropic model to severalimportant factors.How much variance of the HF signalsis explainedby the wind and/or pressureforcing?Does

the pressure-driven component (hp) reallyhelpin explaining

the altimeter observations?How is the simulationimprovedby the use of finer resolutiontopography?What is the optimal friction parameter for the barotropicmodel?While addressing these questions,we seek model solutionsthat maximize the explained variance in T/P and bottom pressure records (BPRs). A more accurate formulation to incorporate steep bottom topographyis also suggestedand used in this study. •Nowat Dynamics Simulations Research Center,Research Institute

for Applied Mechanics,KyushuUniversity,Kasuga,Japan. Copyright2001 by the American GeophysicalUnion.

2.

Paper number 2000JC000763.

The barotropic,shallowwater model of Ponte[1993] is used in this study.The model is forced by 12-hourly surfacewind

0148-0227/01/2000JC000763509.00

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HIROSE ET AL.' BAROTROPIC

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Longitude Figure 1. Bottom pressuregaugelocationsusedin this study.

stressand/orpressurefrom the National Centersfor Environmental Prediction (NCEP) operational analysis.The 10-m wind speedsare convertedto stresses usingthe bulk methodof Kondo [1975].The simulationis performedfrom July 1992 to December 1995 to overlapwith the first few yearsof the T/P mission.

The horizontalviscousterms have a Laplacianform with a

coefficient of 108cm2/s.No-slipboundary conditions are refined to incorporatethe subsurfaceside topographyeffect, as derivedin AppendixA. The refinementmakesthe model numerically more robust and allows more accuraterepresentation of the complexbottom relief, e.g., lesssmoothingof the topographyis required to maintain numericalstabilityof the

gaugesare located at depthsdeeper than 1000 m. Measurement intervals of T/P and BPRs are 9.9 days and 1 hour, respectively. Oceanictides are correctedusing the University of Texas (CSR3.0) model [Eanesand Bettadpur,1996]for both T/P and BPRs.Residualvariabilitiesat tidal frequenciesand trendsare furtherremovedfrom the BPRsby a leastsquaresfit. The T/P data are corrected

for the IB effect estimated

from the NCEP

pressuredata. No IB correctionis applied to the BPRs since that effect on bottom pressureshouldbe negligible. Another dominantsignal,stericheightchange,is alsonot of interest to this study.To focuson the barotropicsignals,the stericeffect is removedfrom the T/P data usingNCEP surface model. heat fluxes.Mixed layertemperaturechangesare computedat The model coversmost of the global oceansfrom 65øNto each grid point by integratingthe surfaceheat flux. Initial 75øS. Excluded from the model domain are the Mediterranean depth of the mixed layer is determinedfrom Levitus[1982] Sea, other marginalseas,aswell as large shallowregionssuch climatology.Density(or volume) changesare then computed as the Patagonian Shelf and Hudson Bay; thus the results from the temperaturechangesassumingthat salinityremains generallyreflectbehaviorin deepwaters.Bottom topography unchanged.The stericheight correctionreducesthe sea level is given by ETOPO5 from the National GeophysicalData variance by 2.46cm2 on a globalaverage. Center. The original 1/12ømeshdata are simplyaveragedover every 1.125ø box accordingto the model grid resolution.The land-oceandistributionof Ponte [1993] is usedbut with mini- 4. Sensitivity Experiments mum depth set at 50 m; with the subsurfaceno-slipcondition in AppendixA, largegradientsin depth,asoften seennear the 4.1. Topography and Friction Bottomtopographyis often smoothedto preventnumerical coast,canbe representedin the model.The maximumdepthis limited to 6000 m to keep the model time step as long as instabilityin oceanmodels.This sectionexaminesthe effectsof possible(1 min); the time step is usuallydeterminedby the smoothingby comparingsolutionswith two differenttopography fields. The "fine" topographyis obtainedby averaging fastestgravitywave speed. Dissipationis given by a linear drag form with coefficient ETOPO5 on the model'sresolution(1.125ø) as explainedin b/H, where b is constantand H is depth. A number of simu- section2. The fine topographyis then smoothedby a Gaussian lations are carried out with variousvaluesof the friction pa- functionwith a 250-km e-folding scaleto create the "smooth" rameter b, rangingfrom 0.25 to 16 cm/s,to find an optimal topography.Plate 1 comparesthe two topographiesin horivalue that minimizes the residual variance in the observations zontal and vertical views.Small-scalefeaturesare clearlyfiltered out in the smoothtopography. after subtractingmodel solutions. Several numerical experimentsare carried out with these topographiesand differentfriction coefficients.Plate 2 shows 3. Data the T/P sealevelvarianceaccountedfor (or explained)by the Sea level data from T/P [JetPropulsionLaboratory,1997, model,whichis definedas{d2} - {(d - m)2}, whered and available at http://podaac.jpl.nasa.gov] and BPRs are used in m representdata and model,respectively,and the anglebrackthis study.The former coversthe entire global oceansexcept ets indicateaverages.The model is forcedby surfacepressure the regionsshallowerthan 1000 m or affectedby sea ice, and and wind, and the friction parameterb is set to 2 cm/sfor the the latter is locatedin the SouthernOcean as shownby Figure caseshown.The IB componentis subtractedfrom both the 1. Althougha few more BPR recordsexist(availableat http:// altimeter data and the model sea level using the 12-hourly www'pøl'ac'uk/psmslh/gløup/gløup'html) than the onesusedin NCEP data. The modelwith the fine topographyexplainsthe better in mostregionsof the SouthernOcean this study,at the time thesewere the only oneswe had access T/P observations to for the time period of interest.Most of the bottom pressure and of the northern Atlantic and Pacific Oceans. The smooth

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topographyworks slightlybetter in someequatorialand subtropicalregionsthan the fine topography,as evidencedby the negativevaluesin Plate 2c. However, thesedifferencesat lower latitudesare insignificant as neitherfine nor smoothtopography resultsaccountfor much of the T/P data within 20ø from the equator. Figure 2 showsthe globally averagedmodel sea level and explainedvariancesas a functionof b. The model usingfine topographyexplains more T/P variance than that with the smoothone for friction parameterb smallerthan 4 cm/s.The

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Plate 2. Varianceaccountedfor by the pressure-andwinddrivenmodelwith mediumfriction(b - 2 cm/s)for (a) fine and(b) smoothtopography,respectively. Numbersshownon the top left (over Asia) are the globalaverages.(c) Differencebetweenthe explainedvariancesof the two simulations (Plate 2a minusPlate 2b).

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Plate 3. Difference in the explainedvarianceby model runs with variousvaluesof b. (a) Run with b = 1 cm/sminusrun with b = 2 cm/s,and (b) run with b = 4 cm/sminusrun with b = 2 cm/s.

30,990

HIROSE ET AL.: BAROTROPIC RESPONSE TO ATMOSPHERIC FORCING

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optimalfrictionparameterseemsto fall between1 and4 cm/s with either fine or smooth topography,with the maximum explainedvariancefound at b --- 2 cm/s.The dependenceof modelperformanceon b is further examinedin section4.2. The BPRs and model sealevel (equivalentto bottompressurein our barotropicocean)are alsocomparedat the positions shownin Figure 1. Table 1 givesdata, model, and explainedvariancesaswell as correlationbetweenthe data and the model usingb = 2 cm/s. As evidencedby positiveexplainedvariances andsignificant correlations, themodelisable to simulatepart of the variability observedby the bottom pressure

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Figure 3 showsthe dependenceof the modeland explained variancesaveragedoverthe 18 pressuregauges.The simulated bottom pressurevariance increaseswith smaller friction. Small-scale (