• Arbic, B. K., 2005: Atmospheric forcing of the oceanic semidiurnal tide. Geophys. Res. Lett., 32 , L02610. doi:10.1029/2004GL021668.

  • Cartwright, D. E., and R. D. Ray, 1991: Energetics of global ocean tides from Geosat altimetry. J. Geophys. Res., 96 , 1689716912.

  • Cartwright, D. E., and R. D. Ray, 1994: On the radiational anomaly in the global ocean tide with reference to satellite altimetry. Oceanol. Acta, 17 , 453459.

    • Search Google Scholar
    • Export Citation
  • Egbert, G. D., and R. D. Ray, 2000: Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature, 405 , 775778.

    • Search Google Scholar
    • Export Citation
  • Heimbach, P., R. M. Ponte, C. Evangelinos, G. Forget, M. Mazloff, D. Menemenlis, S. Vinogradov, and C. Wunsch, 2006: Combining altimetric and all other data with a general circulation model. Extended Abstracts, 15 Years of Progress in Radar Altimetry Symp., ESA Special Publication SP-614, Venice, Italy, ESA and CNES.

    • Search Google Scholar
    • Export Citation
  • Munk, W., and C. Wunsch, 1998: Abyssal recipes II: Energetics of tidal and wind mixing. Deep-Sea Res., 45 , 19772010.

  • Ponte, R. M., 1993: Variability in a homogeneous global ocean forced by barometric pressure. Dyn. Atmos. Oceans, 18 , 209234.

  • Ponte, R. M., and S. V. Vinogradov, 2007: Effects of stratification on the large-scale ocean response to barometric pressure. J. Phys. Oceanogr., 37 , 245258.

    • Search Google Scholar
    • Export Citation
  • Ray, R. D., and R. M. Ponte, 2003: Barometric tides from ECMWF operational analyses. Ann. Geophys., 21 , 18971910.

  • Ray, R. D., and G. D. Egbert, 2004: The global S1 tide. J. Phys. Oceanogr., 34 , 19221935.

  • Wang, W., and R. X. Huang, 2004a: Wind energy input to the surface waves. J. Phys. Oceanogr., 34 , 12761280.

  • Wang, W., and R. X. Huang, 2004b: Wind energy input to the Ekman layer. J. Phys. Oceanogr., 34 , 12671275.

  • Wang, W., C. Qian, and R. X. Huang, 2006: Mechanical energy input to the world oceans due to atmospheric loading. Chin. Sci. Bull., 51 , 327330. doi:10.1007/s11434-006-0327-x.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., 1998: The work done by the wind on the oceanic general circulation. J. Phys. Oceanogr., 28 , 23322340.

  • Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36 , 281314.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., and P. Heimbach, 2007: Practical global oceanic state estimation. Physica D, 230 , 197208. doi:10.1016/j.physd.2006.09.040.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., R. M. Ponte, and P. Heimbach, 2007: Decadal trends in sea level patterns: 1993–2004. J. Climate, 20 , 58805911.

  • View in gallery

    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.

  • View in gallery

    Rate of work done by mean S2 air tide on the equivalent (top left) radiational tide and (top right) gravitational tide. (bottom) Rate of work done by mean S1 air tide on the equivalent radiational tide. All values are given in 10−4 W. Note the different color bar ranges. The land mask in the model solutions used here is shown in white.

  • View in gallery

    As in Fig. 2, but for time-mean rate of work done by the pa continuum on ζ variability associated with the general circulation. Values are given in 10−4 W. Pressure-driven ζ signals are included in the left panel but not in the right panel.

  • View in gallery

    Time series of the rate of work done by pa on the ocean circulation for the period 1993–2004 obtained by integrating values of w over the global ocean. (top) Daily series and (bottom) monthly and annual-mean series are shown. Units are GW.

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

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  • 1 Atmospheric and Environmental Research, Inc., Lexington, Massachusetts
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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 1° × 1° 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 −60 GW, respectively, mostly occurring at low latitudes. The net extraction of energy at a rate of −46 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 possibility, however.

Corresponding author address: Rui M. Ponte, Atmospheric and Environmental Research, Inc., 131 Hartwell Avenue, Lexington, MA 02421. Email: rponte@aer.com

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 1° × 1° 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 −60 GW, respectively, mostly occurring at low latitudes. The net extraction of energy at a rate of −46 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 possibility, however.

Corresponding author address: Rui M. Ponte, Atmospheric and Environmental Research, Inc., 131 Hartwell Avenue, Lexington, MA 02421. Email: rponte@aer.com

1. Introduction

Understanding what maintains the large-scale ocean circulation involves detailed knowledge of the energy sources and sinks and the pathways and mechanisms involved in the source-to-sink energy fluxes over the global ocean. Over the years, a detailed picture of the energy sources has emerged, with wind and gravitational tidal forcing supplying most of the mechanical energy to the ocean (Munk and Wunsch 1998). Quoting typical time-mean, globally integrated values, wind energy input into surface waves can be quite large at ∼6 × 1013 W, or 60 TW (Wang and Huang 2004a), and total input into the Ekman layer is ∼3 TW (Wang and Huang 2004b). Such input is, however, thought to be mostly dissipated by turbulent processes very near the surface, and thus its importance to the energetics of the large-scale circulation remains unclear (Wang and Huang 2004a). More relevant in this regard is the rate of work done by the winds on the large-scale geostrophic circulation, estimated at ∼1 TW by Wunsch (1998). The power input by the gravitational potential is ∼3.5 TW (Munk and Wunsch 1998), but only up to 1 TW is believed to be involved in large-scale mixing over the deep ocean (Egbert and Ray 2000), again with the rest being dissipated over shallow shelves.

As the dominant wind and gravity terms become better known, for a quantitative analysis of the energetics one needs to consider other contributions, such as the work done by atmospheric pressure pa on the general circulation. Our unpublished preliminary estimates of ∼10 GW, quoted in the review by Wunsch and Ferrari (2004), were based on short test runs of both barotropic and baroclinic models forced by realistic atmospheric fields including pa, but excluding the effects of barometric air tides. More recently, Wang et al. (2006) used altimeter measurements from Ocean Topography Experiment (TOPEX)/Poseidon at crossover points and daily mean pa values from the National Centers for Environmental 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 mid- and high latitudes.

As acknowledged by Wang et al. (2006), one difficulty in using altimeter data is the relatively sparse sampling in time. In addition, the work done by pa on the ocean tides, in particular the semidiurnal S2 tide, which has a nonnegligible contribution forced by the corresponding barometric air tide (Cartwright and Ray 1994), has not been discussed in the literature (R. Ray 2007, personal communication). In this note, we revisit the calculation of the work rates associated with pa, using the model results of Ponte and Vinogradov (2007) and the near-global ocean-state estimates produced as part of the Estimating the Circulation and Climate of the Ocean–Global Ocean Data Assimilation Experiment (ECCO–GODAE) project (Wunsch and Heimbach 2007).

2. Calculating pa work rates

Atmospheric pressure pa exerts a normal force on the ocean surface, with the power input or rate of work done per unit area w being simply given by
i1520-0485-39-2-458-e1
where the velocity in the direction of the pa force is approximated by the time derivative of the sea surface height ζ. (In our sign convention, decreases in ζ correspond to positive work done on the ocean.) All temporal variability in ζ, including that forced by the gravitational potential, surface winds, and heat fluxes, as well as pa, can contribute to w. For analysis of steady energy balances, one can average (1) in time to obtain
i1520-0485-39-2-458-e2
where the overbar denotes time-mean quantities and prime variables represent anomalies from the mean. The term pat tends to be small if trends in time are weak compared to the overall variability in ζ. Temporal correlations between pa and ζ are important in determining the values of w. In the case of periodic signals of the form cos(ωt + ϕ), such as those involved with tides, integrating (1) over a full cycle gives
i1520-0485-39-2-458-e3
where ζ and pa now denote amplitudes, and ϕζ and ϕpa are the respective phases. Maximum work rates occur for pa and ζ signals that are 90° out of phase. Given time series of pa and ζ, one can use (1)(3) to estimate the pa work rates on the ocean.

Power in pa series is characterized by red spectra with marked periodicity at 12 and 24 h, associated with the barometric expression of the S2 and S1 air tides (Ray and Ponte 2003; Ponte and Vinogradov 2007). The peaks at 12- and 24-h periods dominate variability at daily time scales and give rise, respectively, to the so-called radiational S2r and S1r tides in the ocean (Cartwright and Ray 1994; Ray and Egbert 2004). Ponte and Vinogradov (2007) have calculated the radiational tides associated with forcing by the mean climatological barometric tides S1,2, with results very similar to other studies (Ray and Egbert 2004; Arbic 2005). The barometric tides used by Ponte and Vinogradov (2007) are the well-resolved interpolated solutions from Ray and Ponte (2003) derived from the 6-hourly operational analyses of the European Centre for Medium-Range Weather Forecasts. Their estimates of the amplitudes and phases of pa, and the respective ζ solutions in Fig. 2 of Ponte and Vinogradov (2007), are used in (3) to calculate w for the periodic air tides.

Another tidal issue to consider is the presence of gravitationally forced ocean tides S1,2g at the same exact periods of the radiational tides. For the case of S1, the barometric tide is the primary driver, and thus the effects of gravity on ζ can be neglected (Ray and Egbert 2004). For S2, however, forcing by the S2 air tide is much weaker than that by gravity, and the gravitational ocean tide is not only considerably larger but also quite similar to and correlated with the radiational component (Cartwright and Ray 1994; Arbic 2005). Thus, the work done by the S2 air pressure tide on S2g is likely to be important and is also considered here. For an estimate of amplitudes and phases of ζ associated with S2g, we take the radiational tide calculated by Ponte and Vinogradov (2007), and, using the conversion factors derived by Arbic (2005), simply scale the amplitudes by 6.81 and subtract 109.4° from the phase values.

The power input by the pa variability continuum is calculated using pa fields from the NCEP–NCAR reanalysis and ζ fields from the optimized ECCO–GODAE solutions. The latter are produced in an iterative optimization procedure, described in Heimbach et al. (2006) and Wunsch and Heimbach (2007), that fits, in a least squares sense, a general circulation model to most available datasets, including all altimetric and hydrographic observations, within expected model and data uncertainties. The basic solution used here is from version 2, iteration 216 (v2.216), analyzed in detail by Wunsch et al. (2007) in the context of decadal sea level trends. The model configuration (grids, topography, and frictional parameters) is the same as in the air tide experiments of Ponte and Vinogradov (2007). To the nominal forcing by surface fluxes of momentum, heat, and freshwater, we have added pa, for comparison with results that do not include pa driving. The solution with pa forcing will be denoted as v2.216 + pa. The analysis is focused on the 12-yr period from 1993 to 2004. In addition, because the 6-hourly NCEP–NCAR pa fields give only a crude representation of the air tides and other near-daily variability (e.g., Ray and Ponte 2003), the pa continuum analysis is based for the most part on daily mean pa and ζ fields. Effects from variability at periods ≤ 2 days are thus not included in the main results, but are briefly discussed in the final section of the paper.

Full ζ variability includes a large inverted barometer component, but it is easily shown that this term yields w ∼ −(2)−1 (pa2)t, which can be neglected in a time-mean sense. For our calculations, the relevant parameter is dynamic ζ (i.e., full ζ minus the inverted barometer signal). The standard deviation of the daily averaged dynamic ζ values (Fig. 1) ranges from a few centimeters over most of the deep ocean to more than 10 cm in some western boundary regions and more than 20 cm in shallow coastal areas. Note that our ζ estimates attempt to represent only the large-scale variability. Contributions by the eddy field to ζ, which can be quite large near strong currents (western boundaries and the Southern Ocean), are not considered, but given the mismatch in oceanic eddy scales compared to those of synoptic atmospheric weather systems, their effects on w are expected to be small.

An estimate of the effects of pa driving on dynamic ζ, evaluated by differencing solutions with and without pressure forcing, also shown in Fig. 1, reveals patterns and amplitudes very similar to earlier calculations by Ponte (1993) and Ponte and Vinogradov (2007). Standard deviations range from < 1 cm over most of the ocean, 1–3 cm in several Southern Ocean regions, and considerably larger values in shallow or semienclosed areas. Most of this variability is at submonthly periods (e.g., Ponte and Vinogradov 2007). Although weak compared to the full ζ variability, the pa-driven signals are expected to be well correlated with pa and thus important in the energetics.

3. Results

a. Work by mean air tides

Values of w corresponding to the rate of work done by the climatological air tides S1 and S2 on the respective radiational ocean tides are displayed in Fig. 2. Largest values of ∼ ±0.5 mW tend to occur at low latitudes, where the air tides have their strongest signatures (Ray and Ponte 2003). The spatial patterns of w reproduce mostly those of the largest amplitudes of the radiational tides, with a string of maxima along equatorial latitudes for S2 (Arbic 2005; Ponte and Vinogradov 2007) and maxima in the western Indian Ocean, the Indonesian seas, and the Gulf of Mexico for S1 (Ray and Egbert 2004; Ponte and Vinogradov 2007). These patterns are themselves related to the particular resonances associated with the oceanic response to the air tides. Compared to S1, S2 is far more resonant and also more strongly forced, as the air tide amplitudes estimated by Ray and Ponte (2003) suggest. Thus, w values for S2 are larger than those for S1.

The rate of work done by the S2 air tide on the much more vigorous gravitational ocean tide S2g is also shown in Fig. 2. Results are not a simple linear scaling of w values for the radiational tide, because there is a phase shift (∼110°) between pa and ζ. This phase shift causes a dominance of negative values of w at low latitudes, in contrast with S2r results. The much larger amplitudes of S2g yield stronger w, extending farther from the low latitudes.

Globally integrated values of w, hereafter denoted W, are given in Table 1. As inferred from the w values in Fig. 2, the rate of work done on the S1r tide is negligible (∼l/4 GW) compared to that done on S2r (14 GW). The largest values of W are found for the case of S2g at about −60 GW. The combined power input for the S2 ocean tide is −46 GW, or about 10% of the estimated rate of work done by the gravitational potential (Cartwright and Ray 1991). The negative values are consistent with an S2 air tide that acts to reduce the energy in the ocean tide, given its phase relation with the gravitational forcing.

Superposed on the climatological air tides, there is stochastic variability at both diurnal and semidiurnal periods, but the associated variance is about an order of magnitude smaller than that of the mean air tides (Ponte and Vinogradov 2007, cf. their Fig. 5). Thus, assuming an approximately linear oceanic response, such stochastic variability is expected to introduce small perturbations on the estimates of w and W discussed here.

b. Work by pa continuum

As explained in section 2, here we use daily mean pa and ζ fields, excluding poorly resolved near-daily variability from the analysis. Values of w were calculated from (1), where ζt is approximated as a centered difference.1 Figure 3 shows values of w based on the v2.216 + pa estimates of ζ, representing large-scale variability associated with full atmospheric forcing including pa. Regions of the largest (> 0) values tend to occur in shallow areas (e.g., Patagonian shelf, South Australian Bight, and Hudson Bay) where strongest ζ variability is seen in Fig. 1. Over the deep ocean, the strongest positive work rates are found in a number of Southern Ocean regions, where the dynamic response to pa is relatively enhanced (Fig. 1; Ponte and Vinogradov 2007). The importance of pa-driven dynamic effects to the energetics can be seen by comparing these results to those obtained without including pa in the forcing fields, also shown in Fig. 3. Although patterns are fairly similar in both cases, when pa forcing is excluded there is a general decrease in positive values of w clearly seen at mid- and high latitudes, particularly in the Southern Ocean.

Integrating w in Fig. 3 over the global ocean yields W ∼ 2.8 and −2.9 GW for the cases with and without pa forcing, respectively (Table 1). The impact of the dynamic response to pa, which is confined mostly to the shortest time scales (e.g., Ponte 1993; Ponte and Vinogradov 2007), is thus quite important and amounts to a difference of 5.7 GW. From the values in Table 1, about 60% of this difference comes from the Southern Ocean (latitudes poleward of 40°S), where the large-scale dynamic response to pa is strongest (Fig. 1); contributions from tropical latitudes (±20°) are the same (∼0.6 GW) with or without full forcing, as expected from the weak pa effects at low latitudes (Fig. 1). In addition, of the estimated total power input, contributions from shallow regions (depth < 200 m) are very substantial, amounting to ∼1.1 and 0.6 GW for the cases with and without pa forcing, respectively. Combined with the results in Table 1, one infers that the dynamic response to pa over the deep ocean contributes more than 5 GW to W, and that correlations of that response with wind and other forcing effects reduces total contributions to W over the deep ocean to ∼1.8 GW.

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 land–ocean mask used in our calculations. Thus, these estimates are only shown to give an idea of the range of temporal variability in W. Daily variability (±40 GW) is quite large compared to the W values in Table 1. Averaged monthly variability ranges over a few gigawatts about the mean. Means for each year are, however, fairly stable.

The impact of the ECCO–GODAE data fitting and optimization procedures in determining our nontidal estimates of W can be assessed by calculating W based on the first-guess, nonoptimized ECCO–GODAE solution, which is not constrained by observations (values under version 2, iteration 0 listed in Table 1). The difference of ∼2 GW between v2.216 and v2.0 results is considerable and comes mostly from changes in the variability of the Southern Ocean. These differences mainly reflect corrections in the wind stress fields and the consequent changes in the barotropic response of the Southern Ocean, which are effected by the optimization. In the absence of formal errors, the difference between v2.216 and v2.0 values can be taken also as a crude measure of uncertainty in W values provided here.

4. Summary and discussion

Local and global estimates of the rate of work done by pa on the ocean tides and general circulation have been derived from the radiational tides of Ponte and Vinogradov (2007) and the ECCO–GODAE state estimates (Wunsch and Heimbach 2007). From the globally integrated, time-mean results summarized in Table 1, the largest values of W are related to the S2 tide, with work being done at a rate of −46 GW on the combined radiational + gravitational ocean tide, and primarily in the tropics. Power input associated with the mainly radiational S1 tide is much weaker. Values of W for nontidal variability are only a few gigawatts, with a substantial contribution from shallow regions. The nontidal pa-driven dynamic response is found to be very important, particularly in the Southern Ocean. From the known characteristics of such response (Ponte 1993; Ponte and Vinogradov 2007), one can conclude that most of the power input by pa is associated with submonthly variability at scales longer than a few hundred kilometers and with typical velocities < 1 cm s−1.

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). Because 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.

Our W estimates for nontidal ζ variability are approximately an order of magnitude lower than those by Wang et al. (2006), who estimated W ∼40 GW from analyses of altimeter crossover data. The reasons for such discrepancy remain unclear. Comparing Fig. 3 to Wang et al.’s Fig. 1 reveals considerably different spatial patterns. In particular, w values in Wang et al. are always > 0 and seem to follow the patterns of variability in pa closely. We note that, in our calculations, if we use full ζ as in Wang et al., instead of dynamic ζ, the results are very sensitive to the method of defining ζt, because one can introduce small phase shifts between pa and ζt.2 Thus, it is possible that in the presence of the large inverted barometer variability at rapid time scales, the results of Wang et al. may have been affected by any small time shifts between pa and ζ series. There is less sensitivity to the formulation of time derivatives, or any other issues affecting the phasing of pa and ζ series, if dynamic ζ is used. Given that, as discussed in section 2, the inverted barometer signals should not be important in determining w, working in terms of dynamic ζ is preferable.

Although based on our current best estimates of ζ and pa, the results in Table 1 should be taken as tentative. Estimates are not truly global, because much of the Arctic region is missing, and the resolution of coastal shallow areas is very coarse. Apart from these domain issues, if one is interested in the energetics of the deep ocean and the topic of oceanic mixing, one nontidal missing contribution to W is probably more relevant. Given the importance of pa-driven dynamic signals, and their primary high-frequency nature (Ponte and Vinogradov 2007), the effects of motion at periods of 2 days and shorter are likely to be sizable. Although the shortest periods are poorly determined, tentative estimates based on 6-hourly pa and ζ fields for the period of 2002–03 yielded values of W a factor of 2 higher than using daily fields. Thus, nontidal contributions 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 pa on the full ocean tides at diurnal and semidiurnal periods here. In addition to the largest M2 tide, there are several other ocean tides at these periods with energy comparable to S2g, but the power in pa fields across these other tidal lines is much weaker than at 12- and 24-h periods. Poor spatial and temporal coherence between pa variability and ocean tides other than for S1,2 is also expected, which should lead to comparatively weak contributions to w. A thorough examination of this issue would require global pa fields of at least hourly resolution, as well as a global model of tidal heights, and should be tried in the future.

As a final point, we recall that changes in global-mean ζ are not explicitly treated in the current ECCO–GODAE solutions (Wunsch et al. 2007). Thus, those effects have not been included in our calculations. Although locally a 1 mm yr−1 of sea level rise yields w ∼ −3 × 10−6 W, which is weak compared to values in Fig. 3, it amounts to more than 1 GW when integrated over the global oceans. Similarly, peak-to-peak annual changes of ∼1 cm in the global-mean ζ associated with seasonal warming and cooling imply an annual cycle in pa work rates on the order of 10 GW. The pa power input associated with these global-mean ζ patterns does not involve, however, any ocean dynamics and is thus irrelevant as a source of mechanical energy for mixing.

Acknowledgments

This work was motivated by inquiries from Carl Wunsch (MIT) about the role of pa in ocean energetics. The author is much indebted to Patrick Heimbach (MIT) for providing the various ECCO–GODAE output. Financial support from the National Oceanographic Partnership Program (NASA, NOAA) and from the NASA Jason-1 Project (Contract 1206432 with JPL) is gratefully acknowledged. Most ECCO-GODAE estimates were calculated using the computer resources of the Geophysical Fluid Dynamics Laboratory/NOAA.

REFERENCES

  • Arbic, B. K., 2005: Atmospheric forcing of the oceanic semidiurnal tide. Geophys. Res. Lett., 32 , L02610. doi:10.1029/2004GL021668.

  • Cartwright, D. E., and R. D. Ray, 1991: Energetics of global ocean tides from Geosat altimetry. J. Geophys. Res., 96 , 1689716912.

  • Cartwright, D. E., and R. D. Ray, 1994: On the radiational anomaly in the global ocean tide with reference to satellite altimetry. Oceanol. Acta, 17 , 453459.

    • Search Google Scholar
    • Export Citation
  • Egbert, G. D., and R. D. Ray, 2000: Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature, 405 , 775778.

    • Search Google Scholar
    • Export Citation
  • Heimbach, P., R. M. Ponte, C. Evangelinos, G. Forget, M. Mazloff, D. Menemenlis, S. Vinogradov, and C. Wunsch, 2006: Combining altimetric and all other data with a general circulation model. Extended Abstracts, 15 Years of Progress in Radar Altimetry Symp., ESA Special Publication SP-614, Venice, Italy, ESA and CNES.

    • Search Google Scholar
    • Export Citation
  • Munk, W., and C. Wunsch, 1998: Abyssal recipes II: Energetics of tidal and wind mixing. Deep-Sea Res., 45 , 19772010.

  • Ponte, R. M., 1993: Variability in a homogeneous global ocean forced by barometric pressure. Dyn. Atmos. Oceans, 18 , 209234.

  • Ponte, R. M., and S. V. Vinogradov, 2007: Effects of stratification on the large-scale ocean response to barometric pressure. J. Phys. Oceanogr., 37 , 245258.

    • Search Google Scholar
    • Export Citation
  • Ray, R. D., and R. M. Ponte, 2003: Barometric tides from ECMWF operational analyses. Ann. Geophys., 21 , 18971910.

  • Ray, R. D., and G. D. Egbert, 2004: The global S1 tide. J. Phys. Oceanogr., 34 , 19221935.

  • Wang, W., and R. X. Huang, 2004a: Wind energy input to the surface waves. J. Phys. Oceanogr., 34 , 12761280.

  • Wang, W., and R. X. Huang, 2004b: Wind energy input to the Ekman layer. J. Phys. Oceanogr., 34 , 12671275.

  • Wang, W., C. Qian, and R. X. Huang, 2006: Mechanical energy input to the world oceans due to atmospheric loading. Chin. Sci. Bull., 51 , 327330. doi:10.1007/s11434-006-0327-x.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., 1998: The work done by the wind on the oceanic general circulation. J. Phys. Oceanogr., 28 , 23322340.

  • Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36 , 281314.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., and P. Heimbach, 2007: Practical global oceanic state estimation. Physica D, 230 , 197208. doi:10.1016/j.physd.2006.09.040.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., R. M. Ponte, and P. Heimbach, 2007: Decadal trends in sea level patterns: 1993–2004. J. Climate, 20 , 58805911.

Fig. 1.
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.

Citation: Journal of Physical Oceanography 39, 2; 10.1175/2008JPO4034.1

Fig. 2.
Fig. 2.

Rate of work done by mean S2 air tide on the equivalent (top left) radiational tide and (top right) gravitational tide. (bottom) Rate of work done by mean S1 air tide on the equivalent radiational tide. All values are given in 10−4 W. Note the different color bar ranges. The land mask in the model solutions used here is shown in white.

Citation: Journal of Physical Oceanography 39, 2; 10.1175/2008JPO4034.1

Fig. 3.
Fig. 3.

As in Fig. 2, but for time-mean rate of work done by the pa continuum on ζ variability associated with the general circulation. Values are given in 10−4 W. Pressure-driven ζ signals are included in the left panel but not in the right panel.

Citation: Journal of Physical Oceanography 39, 2; 10.1175/2008JPO4034.1

Fig. 4.
Fig. 4.

Time series of the rate of work done by pa on the ocean circulation for the period 1993–2004 obtained by integrating values of w over the global ocean. (top) Daily series and (bottom) monthly and annual-mean series are shown. Units are GW.

Citation: Journal of Physical Oceanography 39, 2; 10.1175/2008JPO4034.1

Table 1.

Globally integrated work rates for various different terms; W200 and WSO columns denote values for depths < 200 m and for the Southern Ocean (latitudes poleward of 40°S). Units are GW.

Table 1.

1
We use
i1520-0485-39-2-458-eq1
with δt = 1 day, but other formulations with potentially better resolution of the time derivative ζt, such as
i1520-0485-39-2-458-eq2
yielded essentially the same results.
2

In fact, using a backward (instead of centered) differencing scheme, which introduces a small half-day lag, leads to spatial patterns and values of W much closer to those in Wang et al. (2006).

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