• Atlas, R., , S. C. Bloom, , R. N. Hoffman, , J. V. Ardizzone, , and G. Brin, 1991: Space-based surface wind vectors to aid understanding of air–sea interactions. Eos, Trans. Amer. Geophys. Union, 72 , 201208.

    • Search Google Scholar
    • Export Citation
  • Atlas, R., , R. N. Hoffman, , S. C. Bloom, , J. C. Jusem, , and J. Ardizzone, 1996: A multiyear global surface wind velocity dataset using SSM/I wind observations. Bull. Amer. Meteor. Soc., 77 , 869882.

    • Search Google Scholar
    • Export Citation
  • Busalacchi, A. J., , R. M. Atlas, , and E. C. Hackert, 1993: Comparison of Special Sensor Microwave Imager vector wind stress with model-derived and subjective products for the tropical Pacific. J. Geophys. Res., 98 , 69616977.

    • Search Google Scholar
    • Export Citation
  • Fissel, D. B., , S. Pond, , and M. Miyake, 1977: Computation of surface fluxes from climatological and synoptic data. Mon. Wea. Rev., 105 , 2636.

    • Search Google Scholar
    • Export Citation
  • Gulev, S. K., 1994: Influence of space–time averaging on the ocean–atmosphere exchange estimates in the North Atlantic midlatitudes. J. Phys. Oceanogr., 24 , 12361255.

    • Search Google Scholar
    • Export Citation
  • Hanawa, K., , and Y. Toba, 1987: Critical examination of long-term mean air–sea heat and momentum transfers. Ocean–Air Interact., 1 , 7993.

    • Search Google Scholar
    • Export Citation
  • Large, W. G., , and S. Pond, 1982: Sensible and latent heat flux measurements over the oceans. J. Phys. Oceanogr., 12 , 464482.

  • Ledvina, D. V., , G. S. Young, , R. A. Miller, , and C. W. Fairall, 1993: The effect of averaging on bulk estimates of heat and momentum fluxes for the tropical western Pacific Ocean. J. Geophys. Res., 98 , 2021120217.

    • Search Google Scholar
    • Export Citation
  • Peixoto, J. P., , and A. H. Oort, 1992: Physics of Climate. American Institute of Physics, 520 pp.

  • Ponte, R. M., , A. Mahadevan, , J. Rajamony, , and R. D. Rosen, 2003: Uncertainties in seasonal wind torques over the ocean. J. Climate, 16 , 715722.

    • Search Google Scholar
    • Export Citation
  • Rienecker, M. M., , R. Atlas, , S. D. Schubert, , and C. S. Willett, 1996: A comparison of surface wind products over the North Pacific Ocean. J. Geophys. Res., 101 , 10111023.

    • Search Google Scholar
    • Export Citation
  • Simmonds, I., , and K. Keay, 2002: Surface fluxes of momentum and mechanical energy over the North Pacific and North Atlantic Oceans. Meteor. Atmos. Phys., 80 , 118.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    (top) Annual mean values of stress 〈τ〉, (middle) respective contributions from nonlinear terms τ̃, and (bottom) τ̃s contributions from variability at periods of <6 days, calculated as explained in the text. (left) Zonal and (right) meridional stresses on the atmosphere are shown in units of 0.01 N m−2, with contour levels of 2.5 for 〈τ〉 and 0.5 for τ̃ and τ̃s. Shading denotes negative values

  • View in gallery

    Zonally averaged values of 〈τ〉 (thick solid), τ̃ (dashed), and τ̃s (thin solid) calculated by averaging fields in Fig. 1. The dotted curves represent contributions of periods shorter than 14 days to τ̃, for comparison with τ̃s representing periods shorter than 6 days. (left) Zonal and (right) meridional stress are shown in units of 0.01 N m−2

  • View in gallery

    As in Fig. 1 but for the DJF season. Values are anomalies with respect to the temporal means in Fig. 1, in units of 0.01 N m−2, with contour levels of 2.5 for 〈τ〉 and 0.5 for τ̃ and τ̃s

  • View in gallery

    As in Fig. 3 but for the JJA season

  • View in gallery

    Zonally averaged values of 〈τx〉 (thick solid), τ̃x (dashed), and τ̃sx (thin solid) for DJF and JJA stress anomalies in Figs. 3 and 4, respectively. Units are 0.01 N m−2

  • View in gallery

    Std dev of the difference between SSM/I and ECMWF winds for (a) u and (b) υ. Std dev of the difference between SSM/I and ECMWF winds containing only synoptic signals calculated as explained in the text for (c) u and (d) υ. Values are in m s−1. Fields in (c) and (d) divided by the std dev of the equivalent SSM/I wind fields are shown in (e) and (f), respectively. Contour levels are 0.3 in (a)–(d) and 0.1 in (e), (f)

  • View in gallery

    (top) Values of SSM/I minus ECMWF for annual mean stress and (bottom) respective contributions by differences in synoptic terms τ̃s in units of 0.01 N m−2. Contour level is 1 for Δ〈τx〉, 0.5 for Δ〈τy〉, and 0.2 for both Δτ̃sx and Δτ̃sy

  • View in gallery

    Zonal average of the absolute values of the difference in SSM/I and ECMWF annual means (heavy solid) and the respective differences in τ̃s (thin solid), calculated from fields in Fig. 7. The dashed curves correspond to similar calculations done on the difference in τ̃ terms. Units are 0.01 N m−2

  • View in gallery

    As in Fig. 7 but for DJF anomalies. Contour level is (top) 0.5 and (bottom) 0.2

  • View in gallery

    (top) As in Fig. 8 but for DJF anomalies. (bottom) Ratios of Δ〈τ〉/〈τ〉 (heavy solid), Δτ̃/Δ〈τ〉 (dashed), and Δτ̃s/Δ〈τ〉 (thin solid) computed from the values in (top) and zonal average of the absolute values of 〈τ

  • View in gallery

    As in Fig. 10 but for JJA anomalies

  • View in gallery

    (left) Annual amplitude and phase of SSM/I and ECMWF ocean torques, together with expected torque calculated from the time rate of change of AAM minus the torque over land with (R) and without (R*) gravity wave torque included. Latter values are reproduced from Ponte et al. (2003). Phase is plotted counterclockwise with 90° corresponding to vector pointing straight upward. A phase of 0° corresponds to max on 1 Jan. (right) Vectors corresponding to difference between SSM/I and ECMWF ocean torque values derived from 6-h winds and 3-day-averaged winds. Units are Hadleys (1 Hadley = 1018 kg m2 s−2)

  • View in gallery

    Zonal average of the absolute values of the difference in SSM/I and ECMWF wind stress curl (heavy solid) and the respective differences in the curl of τ̃ (dashed) and of τ̃s (thin solid), for DJF season. Units are 10−8 N m−3

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 94 94 5
PDF Downloads 10 10 3

Nonlinear Effects of Variable Winds on Ocean Stress Climatologies

View More View Less
  • 1 Atmospheric and Environmental Research, Inc., Lexington, Massachusetts
© Get Permissions
Full access

Abstract

Variability in surface winds at subseasonal time scales can affect the estimates of the mean and seasonal stress over the ocean, owing to the nonlinear dependence of stress on wind speed. A global ocean wind product that merges the European Centre for Medium-Range Weather Forecasts (ECMWF) fields with satellite and in situ data is used to assess the nonlinear effects of wind variability, in particular synoptic signals (taken here to include all periods of <6 days), on estimates of the mean and the seasonal cycle in zonal and meridional stress. Climatologies based on the period March 1988–February 1999 are considered. Synoptic effects are most pronounced at mid- and high latitudes, where they can amount up to 20% of the mean or seasonal stress. Uncertainties in stress values associated with synoptic wind errors are assessed by comparing estimates from merged-data winds to those from original ECMWF winds. Differences in synoptic winds contribute noticeably to the stress differences. Outside the Tropics, uncertainties related to synoptic wind terms can have amplitudes of more than 20% of the total estimated uncertainty for mean and seasonal zonal stress, with much higher values for the meridional stress. Implications of these findings for studies of the atmospheric and oceanic circulations are discussed. Results point to the importance of accurately determining wind variability at subweekly periods, thereby placing constraints on sampling strategies for observing winds over the ocean.

Corresponding author address: Dr. Rui M. Ponte, Atmospheric and Environmental Research, Inc., 131 Hartwell Avenue, Lexington, MA 02421-3126. Email: ponte@aer.com

Abstract

Variability in surface winds at subseasonal time scales can affect the estimates of the mean and seasonal stress over the ocean, owing to the nonlinear dependence of stress on wind speed. A global ocean wind product that merges the European Centre for Medium-Range Weather Forecasts (ECMWF) fields with satellite and in situ data is used to assess the nonlinear effects of wind variability, in particular synoptic signals (taken here to include all periods of <6 days), on estimates of the mean and the seasonal cycle in zonal and meridional stress. Climatologies based on the period March 1988–February 1999 are considered. Synoptic effects are most pronounced at mid- and high latitudes, where they can amount up to 20% of the mean or seasonal stress. Uncertainties in stress values associated with synoptic wind errors are assessed by comparing estimates from merged-data winds to those from original ECMWF winds. Differences in synoptic winds contribute noticeably to the stress differences. Outside the Tropics, uncertainties related to synoptic wind terms can have amplitudes of more than 20% of the total estimated uncertainty for mean and seasonal zonal stress, with much higher values for the meridional stress. Implications of these findings for studies of the atmospheric and oceanic circulations are discussed. Results point to the importance of accurately determining wind variability at subweekly periods, thereby placing constraints on sampling strategies for observing winds over the ocean.

Corresponding author address: Dr. Rui M. Ponte, Atmospheric and Environmental Research, Inc., 131 Hartwell Avenue, Lexington, MA 02421-3126. Email: ponte@aer.com

1. Introduction

Accurate knowledge of the mean and seasonal wind stress fields at the air–sea interface is important for understanding the behavior of the oceans and atmosphere in the climate system. The wind stress field largely controls the ocean general circulation, while the related stress torques on the atmosphere help shape its zonal circulation and angular momentum (e.g., Peixoto and Oort 1992). It is thus not surprising that an array of instruments and platforms, ranging from anemometers on buoys and ships to active and passive microwave sensors flying on satellites, is now gathering information on surface wind fields over the ocean, at a variety of temporal and spatial resolutions. Several global wind products, either based solely on data or involving complex modeling and assimilation efforts at national weather centers, have thus become available in recent years, and analyses of these fields are beginning to reveal their strengths and shortcomings.

Errors in wind speed estimates are a major factor contributing to uncertainties in mean and seasonal wind stress over the ocean. Aside from systematic errors, random errors at all frequencies can affect the mean and seasonal stress estimates, because of the nonlinear dependence of stress on wind speed. If nonlinear effects are important in contributing to uncertainty in annual and seasonal stress estimates, then reducing the errors at all time scales, including the synoptic and subsynoptic, may be required for better estimates of those stresses.

The importance of accounting for nonlinear effects in the calculation of mean and seasonal stresses, including the need to resolve synoptic and subsynotpic wind variability in particular, is well known (e.g., Fissel et al. 1977; Hanawa and Toba 1987; Gulev 1994; Simmonds and Keay 2002). Similar inferences are made by Ponte et al. (2003) in a study of the role of ocean stresses on the seasonal atmospheric angular momentum and torque balance, which provides the original motivation for the current study. The importance of nonlinear effects suggests that random errors at subseasonal frequencies could indeed contribute importantly to uncertainties in mean and seasonal stress estimates, depending on the covariance characteristics of errors in zonal and meridional wind components and wind magnitudes, but to our knowledge this possibility has not been addressed in any detail.

In this work, we explore the effects of nonlinearities in contributing to uncertainties in the mean and seasonal stresses over the oceans by examining two global wind products (Atlas et al. 1996; Ponte et al. 2003), available for an overlapping 11-yr period from March 1988 to February 1999. Differences in the two wind products are taken to represent a crude measure of the combined uncertainty in both wind fields (likely an underestimate because of common errors in the products used). The contributions of wind errors in the synoptic and subsynoptic bands are examined in detail. While addressing uncertainty issues, we also provide a detailed analysis of the nonlinear effects of variable winds on the mean and seasonal stresses, extending to a global domain earlier limited-area studies based on in situ wind records (Fissel et al. 1977; Hanawa and Toba 1987; Ledvina et al. 1993; Gulev 1994) and the recent Northern Hemisphere study of Simmonds and Keay (2002) based on a reanalysis wind product.

The wind fields and general methodology used in this study are described in section 2, followed by a discussion of nonlinear effects of variable winds on climatological estimates of mean and seasonal stresses in section 3. The possible impact of wind errors at subseasonal periods on inducing uncertainties in the stress climatologies is considered in section 4, with emphasis on the synoptic and subsynoptic signals at periods of <6 days. In section 5, some of the broader implications of our findings for studies of the atmospheric and oceanic circulations are addressed, followed by a summary and general discussion of results in section 6.

2. Data and methodology

Atlas et al. (1991, 1996) have created a multiyear wind dataset by merging the European Centre for Medium-Range Weather Forecasts (ECMWF) operational products with satellite observations from the Special Sensor Microwave Imager (SSM/I) and other in situ wind data using a variational method. Usefulness of these wind products for ocean studies has been shown (Busalacchi et al. 1993; Rienecker et al. 1996). In this work, we use the Atlas et al. satellite-enhanced winds (hereafter referred to as SSM/I for simplicity, but not to be confused with winds based on SSM/I data only) as our main wind product to first examine the nonlinear effects of variable winds on the calculation of mean and seasonal stresses. We then use differences in SSM/I and the original ECMWF wind products to assess the impact of potential uncertainties in subseasonal winds on the stress estimates. Specific focus is on the effects of winds at periods of <6 days, hereafter referred to simply as synoptic winds. Both SSM/I and ECMWF products represent 10-m winds and are available on a 1° × 1° grid at 6-h sampling for the period January 1988–June 1999. All analyses are based on the period March 1988–February 1999, to yield mean and seasonal climatologies based on a full 11 yr of data.

Surface wind stresses are calculated based on the bulk formula
τxτyρCdUu,υ
where ρ is the air density, Cd is the drag coefficient, u and υ are zonal and meridional wind speeds, respectively, U is the magnitude of the wind vector (u2 + υ2)1/2, and subscripts x and y refer to zonal and meridional stress, respectively. In evaluating (1), the formulation of Large and Pond (1982) is used for Cd, but only the dependence on wind speed is considered, with the effects of other parameters like the air–sea temperature difference and relative humidity neglected. In addition, ρ is taken as constant in (1).
We are interested in the time-averaged stress 〈τ〉 over a given period. For τx we have
τxτxτ̃x
where
τxρCdUu
is the contribution from the mean terms, and using the definition u = 〈u〉 + u′, etc.,
i1520-0442-17-6-1283-e4
All the covariance terms that incorporate the effects of nonlinearities in the stress relation are included in (4). Terms involving variability in ρ are neglected here. Substituting υ for u in (3) and (4) gives similar expressions for τy.

In this study, we examine both the mean and seasonal stress climatologies. The mean analysis is based on the whole 11-yr period of data. Seasonal analyses use 3-month averages for December–January–February (DJF, hereafter all 3-month periods are denoted by an acronym consisting of the first letter of each respective month), MAM, JJA, and SON. By calculating 〈τ〉 based on 6-h values of u, υ, U, and Cd and on averaged values over different periods and then comparing results, one can quantify the importance of τ̃ on the seasonal and mean stress values as a function of temporal resolution. Similarly, using the difference in ECMWF and SSM/I winds as a crude proxy for error, one can compare respective τ values to assess the effects of uncertainties in winds at different time scales. Here we typically estimate 〈τ〉 and τ values and obtain τ̃ as 〈τ〉 − τ. No attempt is made at separating out the contribution of each term in (4) to τ̃. Previous studies (Hanawa and Toba 1987; Ledvina et al. 1993) have, however, shown that the major contribution to τ̃ comes from 〈Cd〉〈Uu′〉, with other terms in (4) being much smaller. For this same reason, the potential effects of static stability on Cd, which are neglected here, should not be important for the purposes of estimating τ̃.

3. Contribution of τ̃ to stress climatologies

a. Mean SSM/I climatology

Figure 1 shows values of 〈τx〉 and 〈τy〉 based on 6-h quantities, with the averaging period being the full 11 yr of data, together with the respective contributions from τ̃. Values of τ̃ are small but not negligible, with typical amplitudes between 10% and 20% of 〈τ〉 values. For both τ̃x and τ̃y, largest signals are observed in mid- and high latitudes such as the northern North Atlantic and Southern Ocean, and also in the Arabian Sea, where the seasonal monsoon circulation seems to add considerably to the strength of 〈τ〉. Over these regions, values of τ̃ can be more than 30% of 〈τ〉. In general, 〈τ〉 and τ̃ have the same sign, and thus if τ̃ contributions are neglected weaker 〈τ〉 amplitudes ensue. The effects of synoptic variability τ̃s, calculated by differencing τ̃ values based on 6-h winds and 3-day-averaged winds also shown in Fig. 1, can amount to a substantial part of τ̃. The largest values of τ̃s coincide with storm track regions (e.g., the western North Atlantic and North Pacific Oceans), where amplitudes can be more than 20% of 〈τ〉 values.

Easier quantitative inferences about the relative size of τ̃ and τ̃s can be made by examining the zonally averaged fields in Fig. 2. Largest values of τ̃ and τ̃s are found near 55°S and 45°N for τx and 70°N for τy. Values of τ̃x amount to between 10% and 30% of 〈τx〉, and about one-third to one-half of its amplitude is due to τ̃sx. Similar results are seen for τ̃y, and synoptic contributions are particularly important in northern mid- and high latitudes. Figure 2 also shows curves calculated by differencing τ̃ values based on 6-h and 7-day-averaged quantities, to compare effects of periods shorter than 14 versus 6 days on τ̃. Differences in the 7- and 3-day (synoptic) curves are not large relative to τ̃. Results inferred for the synoptic band are thus not sensitive to an increase in the period chosen to define that band. Similar findings apply for all the remaining analyses here, and thus only synoptic results based on 3-day-average quantities are presented in the rest of the paper.

b. Seasonal SSM/I climatology

To examine effects of τ̃ on the seasonal cycle, Figs. 3 and 4 show the same fields in Fig. 1 but for the DJF and JJA seasons, respectively. Maximum effects of τ̃ are expected during these boreal and austral winter seasons. Anomalies from the overall means in Fig. 1 are shown. The presence of the annual cycle is evident from the opposite signs of the DJF and JJA anomaly fields. As in the mean climatology, τ̃ has the same sign as 〈τ〉, and neglecting it would lead to a noticeably weaker seasonal cycle in 〈τ〉.

Largest τ̃x values tend to occur in northern mid-and high latitudes, even during the JJA season. Over large portions of the northern North Atlantic and North Pacific, τ̃x values are more than 30% of 〈τx〉, for both seasons. Contributions by τ̃sx are not small and can amount to 50% of τ̃x. Similar results are found for 〈τy〉, but large τ̃y signals can also occur in some tropical regions (e.g., the Indian Ocean, western tropical Pacific) and also around the boundaries in general, where large values of 〈τy〉 are found. Synoptic effects contribute importantly to 〈τy〉 especially in mid- and high latitudes.

Zonally averaged fields for τx are also shown in Fig. 5. Apart from differences ∼60°S, curves for DJF and JJA are similar in shape and of opposite sign, reflecting the dominance of the annual cycle. The size of τ̃x ranges from ∼10% of 〈τx〉 in the Tropics to ∼30% of 〈τx〉 in extratropical regions with a clear seasonal cycle. Contributions by τ̃sx amount to between 25% and 50% of τ̃x for DJF and are somewhat larger for JJA.

4. Assessing effects of uncertainties

Given the importance of τ̃ in the determination of mean and seasonal stresses over many regions, we assess the effects of possible time-dependent wind errors in introducing uncertainty in those stresses. Our focus is on synoptic effects, and our approach is to form differences between the various τ fields shown in Figs. 15 for SSM/I winds and their counterparts based on ECMWF winds. These differences are taken here to represent the uncertainty in the mean and seasonal τ estimates due to inaccuracies in the wind fields. Uncertainty is meant here to represent the combined effects of errors in both wind fields. However, SSM/I winds are derived from ECMWF winds, and thus the two products likely contain common errors. Hence, the difference fields should be interpreted as representing a lower bound on the true uncertainty. To set the stage for the stress comparisons, we first provide a quantitative assessment of the differences in wind fields.

a. Wind differences

The standard deviation of the series formed by differencing SSM/I and ECMWF winds is shown in Figs. 6a,b. Typical values range from 1 to 2 m s−1 for Δu and similar but smaller values for Δυ, with largest differences found in the tropical Pacific and the Southern Ocean. The tropical Pacific differences show a clear sign of the influence of the Tropical Atmosphere Ocean (TAO) buoy wind data on the variational analyses (Atlas et al. 1996), while differences in the Southern Ocean are expected due to relatively sparse data coverage in the typical ECMWF analysis.

Atlas et al. (1996) note the large differences between instantaneous SSM/I and ECMWF wind fields associated with differences in synoptic signals. By subtracting the variance values based on 3-day-averaged difference series from those based on 6-h series and taking the square root, as done in Figs. 6c,d, one gets a measure of how much of the variability in Figs. 6a,b is associated with differences in SSM/I and ECMWF winds at synoptic periods. The synoptic contributions are indeed large and can amount to more than half of the total variability in Figs. 6a,b, for both u and υ, over most regions.

In absolute terms, differences in synoptic winds are more than 10% of the total signal variability in the SSM;clI series over most of the oceans (Figs. 6e,f), and are thus a significant source of noise in the wind fields. Whether this synoptic wind noise translates into substantial uncertainties in mean and seasonal stresses depends on how the errors in u′, U′, etc., correlate and contribute to the various terms in (4). These issues are explored next.

b. Uncertainties in mean stress

Synoptic effects on annual mean τ estimates are assessed in Fig. 7. Differences Δ〈τx〉 between SSM/I and ECMWF are typically in the range of ±0.01 N m−2, or about 10% of the mean values in Fig. 1 but are larger in regions such as the Southern Ocean, the tropical Pacific, and the south Indian Ocean. The amplitude pattern for Δ〈τx〉 is similar to that of 〈τx〉 in Fig. 1, indicating that uncertainties are generally proportional to the amplitude of 〈τx〉. Deviations from this pattern can be seen in the northern mid-and high latitudes, however, indicating relatively better determined 〈τx〉 values in those regions compared to the Tropics and southern latitudes. Amplitudes of SSM/I 〈τx〉 are stronger over most regions.

Differences in synoptic terms Δτ̃sx are an order of magnitude smaller than those in Δ〈τx〉, with amplitudes in the range ±0.002 N m−2 over most regions. The impact of τ̃sx seems most important in the Southern Ocean and the northern North Atlantic. The sign pattern of Δτ̃sx values is similar to Δ〈τx〉 and thus adds to the uncertainty.

Uncertainties in 〈τy〉, also shown in Fig. 7, are largest in the Southern Ocean, near the intertropical convergence zone (ITCZ) in the eastern tropical Pacific, and in several regions near the continental boundaries, where stronger τy are also present (Fig. 1). Values are mostly in the range ±0.005 N m−2, compared to ±0.025 N m−2 for 〈τy〉 values (Fig. 1), suggesting typical uncertainties of about 20%. The contribution of Δτ̃sy to Δ〈τy〉 is comparatively larger than for the case of τx, particularly in the Southern Ocean (amplitudes of Δτ̃sy ∼ 0.002 N m−2, cf. Δ〈τy〉 ∼ 0.005 N m−2).

For easier quantitative comparisons, Fig. 8 shows zonal averages of the absolute values of the fields in Fig. 7, together with similar averages for Δτ̃. (Absolute values are used to better represent the magnitudes of the fields examined, given the presence of both positive and negative values at the same latitude.) Maximum amplitudes seem to coincide with maxima in stress fields in Fig. 2, but the relative amplitudes differ. In particular, uncertainties in 〈τx〉 seem larger in the Tropics than in the Southern Ocean when normalized by the zonally averaged values in Fig. 2, while the same is true for high-latitude uncertainties in 〈τy〉.

At latitudes of maximum Δ〈τx〉, the amplitude of Δτ̃x is typically ∼25% of Δ〈τx〉, with that of Δτ̃sx being ∼10% of Δ〈τx〉. Larger contributions are observed in northern mid-and high latitudes, but uncertainties are smaller there. For τy, uncertainties in τ̃y are generally more important: amplitudes of Δτ̃y are more than 50% of Δ〈τy〉 at both southern and northern high latitudes, with Δτ̃sy being close to 30%.

c. Uncertainties in the seasonal cycle

Differences in τ anomalies for the DJF season, shown in Fig. 9, reveal largest uncertainties in the northern North Atlantic and also at low latitudes, particularly in zonal bands approximately along the ITCZ and in the western Indian Ocean. Strongest values of Δτ̃s are seen in the northern North Atlantic. The similarity in sign patterns of Δ〈τ〉 and Δτ̃s imply that the latter add to the estimated uncertainty.

As in the case of the mean, zonally averaged absolute values are shown in Fig. 10, together with the ratios Δ〈τ〉/〈τ〉, Δτ̃/Δ〈τ〉, and Δτ̃s/Δ〈τ〉. Typical uncertainties in 〈τ〉 are below 0.005 N m−2 or between 10% and 20% of the estimated SSM/I values. Values of 30% occur near 60°S for τy. (Values above 40% near 30°S for τx occur at a latitude of weak stress in general.) A significant part of these uncertainties can be associated with Δτ̃ terms. Largest amplitudes for Δτ̃ are found outside the Tropics, where they can range from 40% to 80% of the Δ〈τ〉 amplitudes. Synoptic uncertainties are clearly important in mid and high latitudes. Magnitudes of Δτ̃s/Δ〈τ〉 in these regions can be higher than 0.4 for τy and are near 0.2 for τx. In general, the impact of Δτ̃ and Δτ̃s is larger for τy than for τx.

Results for JJA are similar in general, indicating no large seasonality in the analyzed uncertainties. Only zonally averaged absolute values are shown in Fig. 11. Largest amplitudes of Δ〈τ〉 are again found at low latitudes. Amplitudes in high southern (northern) latitudes tend to be somewhat larger (smaller) than for DJF (Fig. 10), consistent with the expected seasonality. As with DJF, the importance of Δτ̃ and Δτ̃s is clear in extratropical latitudes, particularly for τy.

5. Broader implications

As noted in the introduction, knowledge of τ fields is important for studies of the atmospheric and oceanic circulations. It is useful to explore, in this broader context, the implications of the uncertainty analysis in the previous section. A brief discussion of the ocean stress torque in relation to the seasonal cycle in atmospheric angular momentum (AAM) and of wind stress curl fields relevant to ocean dynamics serves to illustrate some of those implications.

Ponte et al. (2003) discuss the large discrepancies observed in the seasonal balance between the time rate of change of AAM and the sum of the torques on the atmosphere and the possible role of uncertainties in the stress torque over the ocean To on that imbalance. (To is the integral over the ocean surface of r cosϕ τx, with r being the radius of earth and ϕ the latitude.) They noted the importance of including synoptic wind variability in the calculation of To (cf. their Fig. 5).

The AAM and torque balance for the annual cycle is revisited in Fig. 12, to check how uncertainties in τ̃s can affect the estimates of To. The difference in the SSM/I- and ECMWF-based To is ∼1 Hadley in amplitude (1 Hadley = 1018 kg m2 s−2), with little difference in phase. The amplitude difference is about 15% of that of To but, as noted before, likely an underestimate of the uncertainty in the annual cycle (cf. Fig. 7 in Ponte et al. 2003). The effects of differences in synoptic winds on ΔTo are assessed in Fig. 12 by comparing ΔTo value based on 6-h winds with that based on 3-day-averaged winds. The latter is smaller in amplitude by ∼0.5 Hadleys and also shows some phase shifting. Hence, a large part of the uncertainty in the annual cycle of To as estimated here can be due to noisy synoptic wind estimates.

To cast these results in the context of uncertainties in other components of the AAM and torque budget, Fig. 12 also shows the expected values of To calculated from the time rate of change of AAM minus the torque over land with or without gravity wave torque included; see Ponte et al. (2003) for more details. The potential uncertainty in the treatment of gravity wave effects is quite large and a major hampering factor in closing the AAM and torque budget, in addition to the discussed uncertainties in To.

For studies of the ocean circulation, wind stress curl rather than stress is the relevant forcing field. Using simple centered differences, we have calculated the curl of Δ〈τ〉, Δτ̃, and Δτ̃s fields to assess the uncertainties deriving from the nonlinear terms. Figure 13 shows the absolute values of those fields zonally averaged for the DJF season. Comparing the estimates of the curl of Δτ̃ and Δτ̃s to those of Δ〈τ〉 reveals the importance of nonlinear effects, and in particular of synoptic effects, in contributing to differences in the curl fields. Over northern mid- and high latitudes, where largest differences in the curl are found, amplitudes of nonlinear effects are around 50% of the total differences, with synoptic terms being around 25%.

The two examples described above illustrate the importance of having accurate knowledge of synoptic winds, even if one is only interested in climatological studies of mean and seasonal properties of the climate system. Note that the impact of uncertainties in synoptic winds can be substantial even for spatially averaged or integrated quantities such as the ones considered in Figs. 12 and 13. For processes dependent on local τ fields or on τ values for an individual season, the effects of synoptic wind errors could well be larger.

6. Summary and final remarks

Eleven years of satellite-enhanced ocean surface winds from Atlas et al. (1991, 1996) for the period March 1988–February 1999 were used to study the effects of variable winds and the nonlinear dependence of τ on wind speed on estimates of the mean and seasonal τ climatologies and their uncertainties. Emphasis was on the effects of synoptic wind signals at periods shorter than 6 days. The synoptic variability was found to measurably affect the mean and seasonal cycle of τ, amounting to 20% of their amplitudes in several mid- and high-latitude regions. These findings are in agreement with previous studies based on in situ data. The pattern of strong nonlinear effects in the North Atlantic and the North Pacific also coincides with those identified by Simmonds and Keay (2002) in their study of the Northern Hemisphere. Our results provide a first look at the importance of nonlinear effects and, in particular, those related to synoptic signals over the global ocean.

The differences in τ fields based on the Atlas et al. winds and the original background winds from ECMWF were analyzed to explore how random errors in synoptic winds could affect the mean and seasonal τ climatologies. In mid- and high-latitude regions, differences in synoptic winds were found to lead to marked differences in the climatological τ values. Synoptic effects can amount to more than 20% of the total differences in 〈τx〉 and to more than 40% for 〈τy〉. Uncertainties in τ climatologies can thus contain a substantial contribution from synoptic wind errors due to the nonlinear dependence of τ on wind speed.

Differences between SSM/I and ECMWF products found here are in general agreement with those described in Busalacchi et al. (1993) for the tropical Pacific and Rienecker et al. (1993) for the North Pacific. One noticeable difference is the higher impact of the TAO buoy data (especially in the eastern Pacific) in our results, which are based on merged SSM/I winds that make full use of the TAO array (Atlas et al. 1996). For the earlier merged winds used by Busalacchi et al. (1993) and Rienecker et al. (1993), TAO data were withheld from the variational analysis for verification purposes.

In any case and as acknowledged before, SSM/I and ECMWF fields used here may contain common errors, and thus their differences may likely underestimate the uncertainties in the wind fields. Busalacchi et al. (1993) show that differences between SSM/I and ECMWF are indeed small compared to those among other wind stress products. Our discussion of results have thus emphasized the relative size of the synoptic contributions to uncertainty rather than absolute amplitudes. We note also that differences between ECMWF and SSM/I products might underestimate the uncertainty at the highest frequencies, because satellite data coverage at the shortest sampling intervals considered (6 h) may be less than global. For more quantitative inference, similar analyses should be performed using different wind products, including data products based on scatterometers and other instruments. Using different wind products would also be useful because the errors arising from nonlinear terms should depend on the specific error covariance properties of u, υ, and U.

If our uncertainty analysis withstands further scrutiny, one implication is that for better estimates of mean and seasonal τ, besides having to sample the wind fields with sufficient frequency to resolve the synoptic scales, one may need to further reduce the uncertainties of those winds. This may involve the need to increase the sampling rate above what would be strictly necessary to resolve the synoptic scales. That is, if one needs to observe daily wind variability, then 6-hourly or higher sampling may be required to average out random errors in the needed daily estimates. The time scale that needs to be estimated accurately depends itself on the τ values under consideration. For the seasonal or annual averages considered here, present and previous findings suggest that good daily wind estimates are required. For monthly or shorter averages, good subdaily wind estimates might be required, implying the need for very high sampling rates and putting a strong burden on observational and modeling systems.

Acknowledgments

We are grateful to R. Atlas, J. C. Jusem, and J. Ardizzone for the wind data. P. Nelson helped with data analysis and figures. This research is based upon work supported by the National Science Foundation under Grant ATM-0002688.

REFERENCES

  • Atlas, R., , S. C. Bloom, , R. N. Hoffman, , J. V. Ardizzone, , and G. Brin, 1991: Space-based surface wind vectors to aid understanding of air–sea interactions. Eos, Trans. Amer. Geophys. Union, 72 , 201208.

    • Search Google Scholar
    • Export Citation
  • Atlas, R., , R. N. Hoffman, , S. C. Bloom, , J. C. Jusem, , and J. Ardizzone, 1996: A multiyear global surface wind velocity dataset using SSM/I wind observations. Bull. Amer. Meteor. Soc., 77 , 869882.

    • Search Google Scholar
    • Export Citation
  • Busalacchi, A. J., , R. M. Atlas, , and E. C. Hackert, 1993: Comparison of Special Sensor Microwave Imager vector wind stress with model-derived and subjective products for the tropical Pacific. J. Geophys. Res., 98 , 69616977.

    • Search Google Scholar
    • Export Citation
  • Fissel, D. B., , S. Pond, , and M. Miyake, 1977: Computation of surface fluxes from climatological and synoptic data. Mon. Wea. Rev., 105 , 2636.

    • Search Google Scholar
    • Export Citation
  • Gulev, S. K., 1994: Influence of space–time averaging on the ocean–atmosphere exchange estimates in the North Atlantic midlatitudes. J. Phys. Oceanogr., 24 , 12361255.

    • Search Google Scholar
    • Export Citation
  • Hanawa, K., , and Y. Toba, 1987: Critical examination of long-term mean air–sea heat and momentum transfers. Ocean–Air Interact., 1 , 7993.

    • Search Google Scholar
    • Export Citation
  • Large, W. G., , and S. Pond, 1982: Sensible and latent heat flux measurements over the oceans. J. Phys. Oceanogr., 12 , 464482.

  • Ledvina, D. V., , G. S. Young, , R. A. Miller, , and C. W. Fairall, 1993: The effect of averaging on bulk estimates of heat and momentum fluxes for the tropical western Pacific Ocean. J. Geophys. Res., 98 , 2021120217.

    • Search Google Scholar
    • Export Citation
  • Peixoto, J. P., , and A. H. Oort, 1992: Physics of Climate. American Institute of Physics, 520 pp.

  • Ponte, R. M., , A. Mahadevan, , J. Rajamony, , and R. D. Rosen, 2003: Uncertainties in seasonal wind torques over the ocean. J. Climate, 16 , 715722.

    • Search Google Scholar
    • Export Citation
  • Rienecker, M. M., , R. Atlas, , S. D. Schubert, , and C. S. Willett, 1996: A comparison of surface wind products over the North Pacific Ocean. J. Geophys. Res., 101 , 10111023.

    • Search Google Scholar
    • Export Citation
  • Simmonds, I., , and K. Keay, 2002: Surface fluxes of momentum and mechanical energy over the North Pacific and North Atlantic Oceans. Meteor. Atmos. Phys., 80 , 118.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

(top) Annual mean values of stress 〈τ〉, (middle) respective contributions from nonlinear terms τ̃, and (bottom) τ̃s contributions from variability at periods of <6 days, calculated as explained in the text. (left) Zonal and (right) meridional stresses on the atmosphere are shown in units of 0.01 N m−2, with contour levels of 2.5 for 〈τ〉 and 0.5 for τ̃ and τ̃s. Shading denotes negative values

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 2.
Fig. 2.

Zonally averaged values of 〈τ〉 (thick solid), τ̃ (dashed), and τ̃s (thin solid) calculated by averaging fields in Fig. 1. The dotted curves represent contributions of periods shorter than 14 days to τ̃, for comparison with τ̃s representing periods shorter than 6 days. (left) Zonal and (right) meridional stress are shown in units of 0.01 N m−2

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 3.
Fig. 3.

As in Fig. 1 but for the DJF season. Values are anomalies with respect to the temporal means in Fig. 1, in units of 0.01 N m−2, with contour levels of 2.5 for 〈τ〉 and 0.5 for τ̃ and τ̃s

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 4.
Fig. 4.

As in Fig. 3 but for the JJA season

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 5.
Fig. 5.

Zonally averaged values of 〈τx〉 (thick solid), τ̃x (dashed), and τ̃sx (thin solid) for DJF and JJA stress anomalies in Figs. 3 and 4, respectively. Units are 0.01 N m−2

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 6.
Fig. 6.

Std dev of the difference between SSM/I and ECMWF winds for (a) u and (b) υ. Std dev of the difference between SSM/I and ECMWF winds containing only synoptic signals calculated as explained in the text for (c) u and (d) υ. Values are in m s−1. Fields in (c) and (d) divided by the std dev of the equivalent SSM/I wind fields are shown in (e) and (f), respectively. Contour levels are 0.3 in (a)–(d) and 0.1 in (e), (f)

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 7.
Fig. 7.

(top) Values of SSM/I minus ECMWF for annual mean stress and (bottom) respective contributions by differences in synoptic terms τ̃s in units of 0.01 N m−2. Contour level is 1 for Δ〈τx〉, 0.5 for Δ〈τy〉, and 0.2 for both Δτ̃sx and Δτ̃sy

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 8.
Fig. 8.

Zonal average of the absolute values of the difference in SSM/I and ECMWF annual means (heavy solid) and the respective differences in τ̃s (thin solid), calculated from fields in Fig. 7. The dashed curves correspond to similar calculations done on the difference in τ̃ terms. Units are 0.01 N m−2

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 9.
Fig. 9.

As in Fig. 7 but for DJF anomalies. Contour level is (top) 0.5 and (bottom) 0.2

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 10.
Fig. 10.

(top) As in Fig. 8 but for DJF anomalies. (bottom) Ratios of Δ〈τ〉/〈τ〉 (heavy solid), Δτ̃/Δ〈τ〉 (dashed), and Δτ̃s/Δ〈τ〉 (thin solid) computed from the values in (top) and zonal average of the absolute values of 〈τ

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 11.
Fig. 11.

As in Fig. 10 but for JJA anomalies

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 12.
Fig. 12.

(left) Annual amplitude and phase of SSM/I and ECMWF ocean torques, together with expected torque calculated from the time rate of change of AAM minus the torque over land with (R) and without (R*) gravity wave torque included. Latter values are reproduced from Ponte et al. (2003). Phase is plotted counterclockwise with 90° corresponding to vector pointing straight upward. A phase of 0° corresponds to max on 1 Jan. (right) Vectors corresponding to difference between SSM/I and ECMWF ocean torque values derived from 6-h winds and 3-day-averaged winds. Units are Hadleys (1 Hadley = 1018 kg m2 s−2)

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Fig. 13.
Fig. 13.

Zonal average of the absolute values of the difference in SSM/I and ECMWF wind stress curl (heavy solid) and the respective differences in the curl of τ̃ (dashed) and of τ̃s (thin solid), for DJF season. Units are 10−8 N m−3

Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1283:NEOVWO>2.0.CO;2

Save