Rate of Work Done by Atmospheric Pressure on the Ocean General Circulation and Tides

458 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 39

RUI M. PONTE Atmospheric and Environmental Research, Inc., Lexington, Massachusetts

(Manuscript received 22 April 2008, in ﬁnal form 27 August 2008)

ABSTRACT

Quantitative analysis of the energetics of the ocean is crucial for understanding its circulation and mixing.

The power input by ﬂuctuations in atmospheric pressure pa resulting from the S1 and S2 air tides and the stochastic continuum is analyzed here, with a focus on globally integrated, time-mean values. Results are based on available 18318 near-global pa and sea level ﬁelds and are intended as mainly order-of-magnitude estimates. The rate of work done on the radiational and gravitational components of the S2 ocean tide is estimated at 14 and 260 GW, respectively, mostly occurring at low latitudes. The net extraction of energy at

arateof246 GW is about 10% of available estimates of the work rates by gravity on the S2 tide. For the mainly radiational S1 tide, the power input by pa is much weaker (0.25 GW). Based on daily mean quantities, the stochastic pa continuum contributes ;3 GW to the nontidal circulation, with substantial power input being associated with the pa-driven dynamic response in the Southern Ocean at submonthly time scales. Missing contributions from nontidal variability at the shortest periods (# 2 days) may be substantial, but the rate of work done by pa on the general circulation is likely to remain , 1% of the available wind input estimates. The importance of pa effects when considering local, time-variable energetics remains a possi- bility, however.

1. Introduction mated at ;1 TW by Wunsch (1998). The power input by the gravitational potential is ;3.5 TW (Munk and Understanding what maintains the large-scale ocean Wunsch 1998), but only up to 1 TW is believed to be circulation involves detailed knowledge of the energy involved in large-scale mixing over the deep ocean sources and sinks and the pathways and mechanisms in- (Egbert and Ray 2000), again with the rest being dissi- volved in the source-to-sink energy fluxes over the global pated over shallow shelves. ocean. Over the years, a detailed picture of the energy As the dominant wind and gravity terms become sources has emerged, with wind and gravitational tidal better known, for a quantitative analysis of the ener- forcing supplying most of the mechanical energy to the getics one needs to consider other contributions, such as ocean (Munk and Wunsch 1998). Quoting typical time- the work done by atmospheric pressure p on the gen- mean, globally integrated values, wind energy input into a eral circulation. Our unpublished preliminary estimates surface waves can be quite large at ;6 3 1013 W, or 60 TW of ;10 GW, quoted in the review by Wunsch and Ferrari (Wang and Huang 2004a), and total input into the (2004), were based on short test runs of both barotropic Ekman layer is ;3 TW (Wang and Huang 2004b). Such and baroclinic models forced by realistic atmospheric input is, however, thought to be mostly dissipated by fields including p , but excluding the effects of baro- turbulent processes very near the surface, and thus its a metric air tides. More recently, Wang et al. (2006) used importance to the energetics of the large-scale circula- altimeter measurements from Ocean Topography Ex- tion remains unclear (Wang and Huang 2004a). More periment (TOPEX)/Poseidon at crossover points and relevant in this regard is the rate of work done by the daily mean p values from the National Centers for En- winds on the large-scale geostrophic circulation, esti- a vironmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis to arrive at a value of ;40 GW, with most of the power input occurring at Corresponding author address: Rui M. Ponte, Atmospheric and Environmental Research, Inc., 131 Hartwell Avenue, Lexington, mid- and high latitudes. MA 02421. As acknowledged by Wang et al. (2006), one difficulty E-mail: [email protected] in using altimeter data is the relatively sparse sampling

DOI: 10.1175/2008JPO4034.1

Ó 2009 American Meteorological Society Unauthenticated | Downloaded 09/27/21 09:50 AM UTC FEBRUARY 2009 N O T E S A N D C O R R E S P O N D E N C E 459

r r in time. In addition, the work done by pa on the ocean radiational S2 and S1 tides in the ocean (Cartwright and tides, in particular the semidiurnal S2 tide, which has a Ray 1994; Ray and Egbert 2004). Ponte and Vinogradov nonnegligible contribution forced by the corresponding (2007) have calculated the radiational tides associated barometric air tide (Cartwright and Ray 1994), has not with forcing by the mean climatological barometric tides been discussed in the literature (R. Ray 2007, personal S1,2, with results very similar to other studies (Ray and communication). In this note, we revisit the calculation Egbert 2004; Arbic 2005). The barometric tides used by of the work rates associated with pa, using the model Ponte and Vinogradov (2007) are the well-resolved in- results of Ponte and Vinogradov (2007) and the near- terpolated solutions from Ray and Ponte (2003) derived global ocean-state estimates produced as part of the from the 6-hourly operational analyses of the European Estimating the Circulation and Climate of the Ocean– Centre for Medium-Range Weather Forecasts. Their esti-

Global Ocean Data Assimilation Experiment (ECCO– mates of the amplitudes and phases of pa,andtherespec- GODAE) project (Wunsch and Heimbach 2007). tive z solutions in Fig. 2 of Ponte and Vinogradov (2007), are used in (3) to calculate w for the periodic air tides. 2. Calculating p work rates Another tidal issue to consider is the presence of a g gravitationally forced ocean tides S1;2 at the same exact Atmospheric pressure p exerts a normal force on the a periods of the radiational tides. For the case of S1, the ocean surface, with the power input or rate of work barometric tide is the primary driver, and thus the ef- done per unit area w being simply given by fects of gravity on z can be neglected (Ray and Egbert 2004). For S , however, forcing by the S air tide is much w 5 pazt; ð1Þ 2 2 weaker than that by gravity, and the gravitational ocean where the velocity in the direction of the pa force is tide is not only considerably larger but also quite similar approximated by the time derivative of the sea surface to and correlated with the radiational component height z. (In our sign convention, decreases in z corre- (Cartwright and Ray 1994; Arbic 2005). Thus, the work g spond to positive work done on the ocean.) All tem- done by the S2 air pressure tide on S2 is likely to be poral variability in z, including that forced by the important and is also considered here. For an estimate g gravitational potential, surface winds, and heat ﬂuxes, as of amplitudes and phases of z associated with S2, well as pa, can contribute to w. For analysis of steady we take the radiational tide calculated by Ponte and energy balances, one can average (1) in time to obtain Vinogradov (2007), and, using the conversion factors ÀÁ derived by Arbic (2005), simply scale the amplitudes by w 5 pazt 1 p9az9t ; ð2Þ 6.81 and subtract 109.48 from the phase values.

The power input by the pa variability continuum is where the overbar denotes time-mean quantities and calculated using pa fields from the NCEP–NCAR re- prime variables represent anomalies from the mean. analysis and z fields from the optimized ECCO– The term pazt tends to be small if trends in time are GODAE solutions. The latter are produced in an iter- weak compared to the overall variability in z. Temporal ative optimization procedure, described in Heimbach correlations between pa and z are important in deter- et al. (2006) and Wunsch and Heimbach (2007), that fits, mining the values of w. In the case of periodic signals of in a least squares sense, a general circulation model to the form cos(vt 1 f), such as those involved with tides, most available datasets, including all altimetric and integrating (1) over a full cycle gives hydrographic observations, within expected model and 1 data uncertainties. The basic solution used here is from w 5 vzpa sinðfz fp Þ; ð3Þ version 2, iteration 216 (v2.216), analyzed in detail by 2 a Wunsch et al. (2007) in the context of decadal sea level where z and p now denote amplitudes, and f and f trends. The model configuration (grids, topography, and a z pa are the respective phases. Maximum work rates occur frictional parameters) is the same as in the air tide ex- for pa and z signals that are 908 out of phase. Given time periments of Ponte and Vinogradov (2007). To the series of pa and z, one can use (1)–(3) to estimate the pa nominal forcing by surface fluxes of momentum, heat, work rates on the ocean. and freshwater, we have added pa, for comparison with Power in pa series is characterized by red spectra with results that do not include pa driving. The solution with marked periodicity at 12 and 24 h, associated with the pa forcing will be denoted as v2.2161pa. The analysis barometric expression of the S2 and S1 air tides (Ray is focused on the 12-yr period from 1993 to 2004. In and Ponte 2003; Ponte and Vinogradov 2007). The peaks addition, because the 6-hourly NCEP–NCAR pa fields at 12- and 24-h periods dominate variability at daily give only a crude representation of the air tides and time scales and give rise, respectively, to the so-called other near-daily variability (e.g., Ray and Ponte 2003),

Unauthenticated | Downloaded 09/27/21 09:50 AM UTC 460 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 39

FIG. 1. Standard deviation of dynamic sea level (i.e., deviations from an inverted barometer; cm) for the case of (left) full forcing and (right) pa forcing, calculated as described in the text. Note the different color bar range in the two panels.

the pa continuum analysis is based for the most part on compared to the full z variability, the pa-driven signals daily mean pa and z fields. Effects from variability at are expected to be well correlated with pa and thus periods # 2 days are thus not included in the main important in the energetics. results, but are briefly discussed in the final section of the paper. 3. Results Full z variability includes a large inverted barometer a. Work by mean air tides component, butÀÁ it is easily shown that this term yields 1 2 w ; ðÞ2gr pa t, which can be neglected in a time- Values of w corresponding to the rate of work done mean sense. For our calculations, the relevant parame- by the climatological air tides S1 and S2 on the respec- ter is dynamic z (i.e., full z minus the inverted barometer tive radiational ocean tides are displayed in Fig. 2. signal). The standard deviation of the daily averaged Largest values of ;60.5 mW tend to occur at low lat- dynamic z values (Fig. 1) ranges from a few centimeters itudes, where the air tides have their strongest signa- over most of the deep ocean to more than 10 cm in some tures (Ray and Ponte 2003). The spatial patterns of w western boundary regions and more than 20 cm in reproduce mostly those of the largest amplitudes of the shallow coastal areas. Note that our z estimates attempt radiational tides, with a string of maxima along equato- to represent only the large-scale variability. Contribu- rial latitudes for S2 (Arbic 2005; Ponte and Vinogradov tions by the eddy field to z, which can be quite large near 2007) and maxima in the western Indian Ocean, the strong currents (western boundaries and the Southern Indonesian seas, and the Gulf of Mexico for S1 (Ray and Ocean), are not considered, but given the mismatch in Egbert 2004; Ponte and Vinogradov 2007). These pat- oceanic eddy scales compared to those of synoptic at- terns are themselves related to the particular reso- mospheric weather systems, their effects on w are ex- nances associated with the oceanic response to the air pected to be small. tides. Compared to S1,S2 is far more resonant and also An estimate of the effects of pa driving on dynamic z, more strongly forced, as the air tide amplitudes esti- evaluated by differencing solutions with and without mated by Ray and Ponte (2003) suggest. Thus, w values pressure forcing, also shown in Fig. 1, reveals patterns for S2 are larger than those for S1. and amplitudes very similar to earlier calculations by The rate of work done by the S2 air tide on the much g Ponte (1993) and Ponte and Vinogradov (2007). Stan- more vigorous gravitational ocean tide S2 is also shown in dard deviations range from , 1 cm over most of the Fig. 2. Results are not a simple linear scaling of w values ocean, 1–3 cm in several Southern Ocean regions, and for the radiational tide, because there is a phase shift considerably larger values in shallow or semienclosed (;1108) between pa and z. This phase shift causes a areas. Most of this variability is at submonthly periods dominance of negative values of w at low latitudes, in r (e.g., Ponte and Vinogradov 2007). Although weak contrast with S2 results. The much larger amplitudes

Unauthenticated | Downloaded 09/27/21 09:50 AM UTC FEBRUARY 2009 N O T E S A N D C O R R E S P O N D E N C E 461

FIG. 2. Rate of work done by mean S2 air tide on the equivalent (top left) radiational tide and (top right) gravitational tide. (bottom) 24 Rate of work done by mean S1 air tide on the equivalent radiational tide. All values are given in 10 W. Note the different color bar ranges. The land mask in the model solutions used here is shown in white.

g of S2 yield stronger w, extending farther from the low approximately linear oceanic response, such stochastic latitudes. variability is expected to introduce small perturbations Globally integrated values of w, hereafter denoted W, on the estimates of w and W discussed here. are given in Table 1. As inferred from the w values in r b. Work by pa continuum Fig. 2, the rate of work done on the S1 tide is negligible r (;l/4 GW) compared to that done on S2 (14 GW). The As explained in section 2, here we use daily mean pa and g largest values of W are found for the case of S2 at about z ﬁelds, excluding poorly resolved near-daily variability 260 GW. The combined power input for the S2 ocean tide is 246 GW, or about 10% of the estimated rate of TABLE 1. Globally integrated work rates for various different work done by the gravitational potential (Cartwright terms; W200 and WSO columns denote values for depths , 200 m and Ray 1991). The negative values are consistent with and for the Southern Ocean (latitudes poleward of 408S). Units are GW. an S2 air tide that acts to reduce the energy in the ocean tide, given its phase relation with the gravitational W W200 WSO forcing. r S2 14 ;11 Superposed on the climatological air tides, there is g S2 260 ;13 r stochastic variability at both diurnal and semidiurnal S1 0.25 periods, but the associated variance is about an order of v2.2161pa 2.8 1.1 0.4 magnitude smaller than that of the mean air tides (Ponte v2.216 22.9 0.6 23.0 and Vinogradov 2007, cf. their Fig. 5). Thus, assuming an v2.0 24.9 0.2 24.8

Unauthenticated | Downloaded 09/27/21 09:50 AM UTC 462 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 39

FIG. 3. As in Fig. 2, but for time-mean rate of work done by the pa continuum on z variability associated with the general circulation. Values are given in 1024 W. Pressure-driven z signals are included in the left panel but not in the right panel. from the analysis. Values of w were calculated from (1), forcing, respectively (Table 1). The impact of the dy- 1 where zt is approximated as a centered difference. Fig- namic response to pa, which is conﬁned mostly to the ure 3 shows values of w based on the v2.2161pa estimates shortest time scales (e.g., Ponte 1993; Ponte and of z, representing large-scale variability associated with Vinogradov 2007), is thus quite important and amounts full atmospheric forcing including pa. Regions of the to a difference of 5.7 GW. From the values in Table 1, largest (. 0) values tend to occur in shallow areas (e.g., about 60% of this difference comes from the Southern Patagonian shelf, South Australian Bight, and Hudson Ocean (latitudes poleward of 408S), where the large-

Bay) where strongest z variability is seen in Fig. 1. Over scale dynamic response to pa is strongest (Fig. 1); con- the deep ocean, the strongest positive work rates are tributions from tropical latitudes (6208) are the same found in a number of Southern Ocean regions, where (;0.6 GW) with or without full forcing, as expected the dynamic response to pa is relatively enhanced (Fig. from the weak pa effects at low latitudes (Fig. 1). In 1; Ponte and Vinogradov 2007). The importance of addition, of the estimated total power input, contribu- pa-driven dynamic effects to the energetics can be seen tions from shallow regions (depth , 200 m) are very by comparing these results to those obtained without substantial, amounting to ;1.1 and 0.6 GW for the cases including pa in the forcing ﬁelds, also shown in Fig. 3. with and without pa forcing, respectively. Combined Although patterns are fairly similar in both cases, when with the results in Table 1, one infers that the dynamic pa forcing is excluded there is a general decrease in response to pa over the deep ocean contributes more positive values of w clearly seen at mid- and high lati- than 5 GW to W, and that correlations of that response tudes, particularly in the Southern Ocean. with wind and other forcing effects reduces total con- Integrating w in Fig. 3 over the global ocean yields tributions to W over the deep ocean to ;1.8 GW.

W;2:8 and 22.9 GW for the cases with and without pa Spatially integrated values of w yield the time series shown in Fig. 4. The detailed behavior of this time series is likely sensitive to many uncertain factors, like the 1 We use land–ocean mask used in our calculations. Thus, these zðt 1 dtÞzðt dtÞ estimates are only shown to give an idea of the range of p ðtÞ ; a 2dt temporal variability in W. Daily variability (640 GW) is quite large compared to the W values in Table 1. Av- with dt 5 1 day, but other formulations with potentially better eraged monthly variability ranges over a few gigawatts resolution of the time derivative zt, such as about the mean. Means for each year are, however, p ðtÞ 1 p ðt dtÞ zðtÞzðt dtÞ a a ; fairly stable. 2 dt The impact of the ECCO–GODAE data ﬁtting and yielded essentially the same results. optimization procedures in determining our nontidal

Unauthenticated | Downloaded 09/27/21 09:50 AM UTC FEBRUARY 2009 N O T E S A N D C O R R E S P O N D E N C E 463

When globally averaged, the mean power input by pa is ;10% of the gravitational effects on the S2 tide (Cartwright and Ray 1991) and less than 1% of the wind effects on the general circulation (Wunsch 1998). Be- cause the work done by winds is dominated by contributions from the time-mean circulation in the Southern

Ocean, pa effects can be relatively larger for local nontidal energetics away from the latitudes of the Antarctic Circumpolar Current (cf. Fig. 3 and Fig. 2 in Wunsch 1998). In addition, day-to-day ﬂuctuations in Fig. 4 can be an order of magnitude larger than the value of W.

Thus, contributions from pa may be important when considering time variable nontidal energetics. FIG. 4. Time series of the rate of work done by pa on the ocean Our W estimates for nontidal z variability are ap- circulation for the period 1993–2004 obtained by integrating values of w over the global ocean. (top) Daily series and (bottom) proximately an order of magnitude lower than those by monthly and annual-mean series are shown. Units are GW. Wang et al. (2006), who estimated W;40 GW from analyses of altimeter crossover data. The reasons for such estimates of W can be assessed by calculating W based discrepancy remain unclear. Comparing Fig. 3 to Wang on the first-guess, nonoptimized ECCO–GODAE so- et al.’s Fig. 1 reveals considerably different spatial pat- lution, which is not constrained by observations (values terns. In particular, w values in Wang et al. are always under version 2, iteration 0 listed in Table 1). The dif- . 0 and seem to follow the patterns of variability in pa ference of ;2 GW between v2.216 and v2.0 results is closely. We note that, in our calculations, if we use full z considerable and comes mostly from changes in the as in Wang et al., instead of dynamic z, the results are variability of the Southern Ocean. These differences very sensitive to the method of defining zt, because one 2 mainly reflect corrections in the wind stress fields and can introduce small phase shifts between pa and zt. Thus, the consequent changes in the barotropic response of it is possible that in the presence of the large inverted the Southern Ocean, which are effected by the optimi- barometer variability at rapid time scales, the results of zation. In the absence of formal errors, the difference Wang et al. may have been affected by any small time between v2.216 and v2.0 values can be taken also as a shifts between pa and z series. There is less sensitivity to crude measure of uncertainty in W values provided here. the formulation of time derivatives, or any other issues affecting the phasing of pa and z series, if dynamic z is used. Given that, as discussed in section 2, the inverted 4. Summary and discussion barometer signals should not be important in determin- Local and global estimates of the rate of work done by ing w, working in terms of dynamic z is preferable. pa on the ocean tides and general circulation have been Although based on our current best estimates of z and derived from the radiational tides of Ponte and Vinogradov pa, the results in Table 1 should be taken as tentative. (2007) and the ECCO–GODAE state estimates (Wunsch Estimates are not truly global, because much of the and Heimbach 2007). From the globally integrated, time- Arctic region is missing, and the resolution of coastal mean results summarized in Table 1, the largest values shallow areas is very coarse. Apart from these domain of W are related to the S2 tide, with work being done issues, if one is interested in the energetics of the deep at a rate of 246 GW on the combined radiational 1 ocean and the topic of oceanic mixing, one nontidal gravitational ocean tide, and primarily in the tropics. missing contribution to W is probably more relevant.

Power input associated with the mainly radiational S1 Given the importance of pa-driven dynamic signals, tide is much weaker. Values of W for nontidal variability and their primary high-frequency nature (Ponte and are only a few gigawatts, with a substantial contribution Vinogradov 2007), the effects of motion at periods of from shallow regions. The nontidal pa-driven dynamic 2 days and shorter are likely to be sizable. Although response is found to be very important, particularly in the shortest periods are poorly determined, tentative the Southern Ocean. From the known characteristics estimates based on 6-hourly pa and z ﬁelds for the of such response (Ponte 1993; Ponte and Vinogradov 2007), one can conclude that most of the power input by 2 In fact, using a backward (instead of centered) differencing pa is associated with submonthly variability at scales scheme, which introduces a small half-day lag, leads to spatial longer than a few hundred kilometers and with typical patterns and values of W much closer to those in Wang et al. 2 velocities , 1cms 1. (2006).

Unauthenticated | Downloaded 09/27/21 09:50 AM UTC 464 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 39 period of 2002–03 yielded values of W a factor of 2 mates were calculated using the computer resources of the higher than using daily fields. Thus, nontidal contribu- Geophysical Fluid Dynamics Laboratory/NOAA. tions to W from periods # 2 days are potentially of the same order as those from periods . 2 days. In addition, we have not considered the work done by REFERENCES pa on the full ocean tides at diurnal and semidiurnal Arbic, B. K., 2005: Atmospheric forcing of the oceanic semidiurnal periods here. In addition to the largest M2 tide, there are tide. Geophys. Res. Lett., 32, L02610, doi:10.1029/2004GL021668. several other ocean tides at these periods with energy Cartwright, D. E., and R. D. Ray, 1991: Energetics of global ocean comparable to Sg, but the power in p fields across these tides from Geosat altimetry. J. Geophys. Res., 96, 16 897–16 912. 2 a ——, and ——, 1994: On the radiational anomaly in the global other tidal lines is much weaker than at 12- and 24-h ocean tide with reference to satellite altimetry. Oceanol. Acta, periods. Poor spatial and temporal coherence between 17, 453–459. pa variability and ocean tides other than for S1,2 is also Egbert, G. D., and R. D. Ray, 2000: Significant dissipation of tidal expected, which should lead to comparatively weak energy in the deep ocean inferred from satellite altimeter contributions to w. A thorough examination of this issue data. Nature, 405, 775–778. Heimbach, P., R. M. Ponte, C. Evangelinos, G. Forget, M. Mazloff, would require global pa fields of at least hourly resolu- D. Menemenlis, S. Vinogradov, and C. Wunsch, 2006: Com- tion, as well as a global model of tidal heights, and bining altimetric and all other data with a general circulation should be tried in the future. model. Extended Abstracts, 15 Years of Progress in Radar As a final point, we recall that changes in global-mean Altimetry Symp., ESA Special Publication SP-614, Venice, z are not explicitly treated in the current ECCO– Italy, ESA and CNES. Munk, W., and C. Wunsch, 1998: Abyssal recipes II: Energetics of GODAE solutions (Wunsch et al. 2007). Thus, those tidal and wind mixing. Deep-Sea Res., 45, 1977–2010. effects have not been included in our calculations. Al- Ponte, R. M., 1993: Variability in a homogeneous global ocean though locally a 1 mm yr21 of sea level rise yields forced by barometric pressure. Dyn. Atmos. Oceans, 18, 209–234. w ; 3 3 106 W, which is weak compared to values in ——, and S. V. Vinogradov, 2007: Effects of stratification on the Fig. 3, it amounts to more than 1 GW when integrated large-scale ocean response to barometric pressure. J. Phys. Oceanogr., 37, 245–258. over the global oceans. Similarly, peak-to-peak annual Ray, R. D., and R. M. Ponte, 2003: Barometric tides from ECMWF changes of ;1 cm in the global-mean z associated with operational analyses. Ann. Geophys., 21, 1897–1910. seasonal warming and cooling imply an annual cycle in ——, and G. D. Egbert, 2004: The global S1 tide. J. Phys. Ocean- ogr., 34, 1922–1935. pa work rates on the order of 10 GW. The pa power input associated with these global-mean z patterns does Wang, W., and R. X. Huang, 2004a: Wind energy input to the surface waves. J. Phys. Oceanogr., 34, 1276–1280. not involve, however, any ocean dynamics and is thus ——, and ——, 2004b: Wind energy input to the Ekman layer. irrelevant as a source of mechanical energy for mixing. J. Phys. Oceanogr., 34, 1267–1275. ——, C. Qian, and R. X. Huang, 2006: Mechanical energy input to the world oceans due to atmospheric loading. Chin. Sci. Bull., Acknowledgments. This work was motivated by inqui- 51, 327–330, doi:10.1007/s11434-006-0327-x. ries from Carl Wunsch (MIT) about the role of pa in ocean Wunsch, C., 1998: The work done by the wind on the oceanic energetics. The author is much indebted to Patrick Heim- general circulation. J. Phys. Oceanogr., 28, 2332–2340. bach (MIT) for providing the various ECCO–GODAE ——, and R. Ferrari, 2004: Vertical mixing, energy, and the general output. Financial support from the National Oceano- circulation of the oceans. Annu. Rev. Fluid Mech., 36, 281–314. ——, and P. Heimbach, 2007: Practical global oceanic state estimation. graphic Partnership Program (NASA, NOAA) and from Physica D, 230, 197–208, doi:10.1016/j.physd.2006.09.040. the NASA Jason-1 Project (Contract 1206432 with JPL) ——, R. M. Ponte, and P. Heimbach, 2007: Decadal trends in sea is gratefully acknowledged. Most ECCO-GODAE esti- level patterns: 1993–2004. J. Climate, 20, 5880–5911.

Unauthenticated | Downloaded 09/27/21 09:50 AM UTC