1. Introduction
Studies examining the torques responsible for the seasonal cycle in M date back to White (1949) and Widger (1949) but have been relatively rare, in part due to the lack of appropriate observations (see review by Rosen 1993). More recent attempts include the model studies by Boer (1990) and Lejenäs et al. (1997) and the analyses based on observations by Wahr and Oort (1984), Ponte and Rosen (1993, 2001) and Huang et al. (1999). These studies clarify the importance of the friction torque, in particular its ocean component TO, in explaining the seasonal cycle in M. Yet, establishing a balance between the torques and Ṁ, as required by (1), has proved difficult with observations. Huang et al. (1999) found large discrepancies in the Ṁ and torque balance at seasonal timescales when they used 29 yr of the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data (see also Ponte and Rosen 2001).
Problems with the Ṁ and torque balance computed with the NCEP–NCAR dataset are largely attributed to errors in the estimated torques, including possible problems with Tgw (Huang et al. 1999). The discrepancies in the seasonal budget are far larger than expected errors in Ṁ (Ponte and Rosen 2001). In contrast, torques are inherently uncertain owing to the many parameterizations of surface processes needed to calculate them. Estimates of TO, which depend on knowledge of surface zonal winds, may be particularly prone to large error (e.g., Bryan 1997) because wind observations are very sparse over the ocean. Given the importance of TO for the seasonal M budget, an assessment of its uncertainties thus seems in order.
Ponte and Rosen (1993) demonstrated that estimates of TO were significantly altered by the use of surface wind data derived from the Special Sensor Microwave Imager (SSM/I) satellite instruments over the 1987–89 period. Similar results were obtained by Xu (1997) and Salstein et al. (1996) with wind scatterometer data from the first European Remote Sensing satellite (ERS-1). Using other torque and M data from NCEP operational analysis and NCEP–NCAR reanalysis, they were also able to show slight improvements in the M balance when using the scatterometer-based TO values. Since these studies, significantly longer SSM/I and scatterometer datasets have been created. Here we make use of these longer datasets and the NCEP–NCAR torque dataset of Huang et al. (1999) to reexamine the seasonal Ṁ and torque balance. Our goals are to assess the uncertainty in TO on seasonal timescales, to identify where the largest errors in TO lie, and to determine whether the uncertainty in TO is a significant hurdle toward attaining a closed seasonal M budget. The various TO products and their calculation, as well as other ancillary torque and M data used, are discussed in section 2, followed by a detailed comparison of the TO estimates and discussion of their differences in section 3. In section 4, the various TO estimates are assessed in the context of the seasonal M budget before a summary and final remarks are presented in section 5.
2. Torque and ancillary datasets
a. NCEP–NCAR reanalysis
Motivation for the present work stems partly from the availability of the comprehensive NCEP–NCAR reanalysis torque and M dataset described by Huang et al. (1999) and Ponte and Rosen (1999). In brief, the data include 6-hourly gridded values of zonal wind on pressure levels up to 10 hPa, surface pressure, and the various torques (Tf, Tm, Tgw) on the atmosphere for the period 1958 to the present. Daily values of M, Ṁ, TL, and TO, as calculated by Ponte and Rosen (2001), are used here for comparison with the satellite-based estimates of TO and for analyses of TO in the context of the M budget. Full details of all the quantities, including their mathematical definitions and time series plots, are given by Huang et al. (1999) and Ponte and Rosen (1999, 2001).
The spectra of Ṁ and the total torque T(=TL + TO) considered by Ponte and Rosen (2001) exhibit peaks at frequency bands centered at the annual and semiannual periods,1 along with a clear imbalance between the variance of Ṁ and T over the same bands. Our analysis focuses therefore on the annual and semiannual cycles. The amplitude and phase of the annual and semiannual harmonics of Ṁ and T shown in Fig. 1 highlight more clearly the seasonal discrepancies in the M budget. Harmonics were determined by conventional Fourier analysis. The values of T used in Fig. 1 include contributions from Tgw; given its uncertain role in the budget (Huang et al. 1999; Ponte and Rosen 2001), results without Tgw effects are also considered later in section 4. The imbalance at the annual period is large, mostly because of phase differences between Ṁ and T. For the semiannual period, amplitude and phase agreement is considerably better. From the values of TO also plotted in Fig. 1, it is clear that TO is an important component of T and that possible uncertainties in TO could play a role in the observed discrepancies between Ṁ and T.
b. Ocean torque from SSM/I winds
With the idea of enhancing the quality of wind fields provided by operational weather centers, Atlas et al. (1991) pioneered a variational approach in which SSM/I-derived surface wind estimates are merged with the gridded wind fields from the European Centre for Medium-Range Weather Forecasts (ECMWF) to produce satellite-enhanced 6-hourly surface fields on a 1° × 1° global grid. Production of such wind fields has continued (Atlas et al. 1996), and a multiyear dataset spanning the period 1987–99 is now available.
Following Ponte and Rosen (1993), we use the multiyear SSM/I-based wind dataset to calculate TO based on two different estimates of the wind stress τ. One set of τ values was provided by J. C. Jusem (2000, personal communication) and is based on a complete treatment of boundary layer processes using the model of Liu et al. (1979) and relevant input surface variables from ECMWF. This τ dataset spans only the period 1994–98 because auxiliary input fields were not available for other years. In addition, values for January 1997 are missing; we have used mean January values calculated from the available years to fill in this gap.
We calculated a second set of τ values for the entire 1987–99 period using the bulk formulation of Large and Pond (1982). In this calculation, the drag coefficient is dependent only on wind speed; dependencies on other parameters like the air–sea temperature difference and relative humidity are neglected. Time series of TO based on this simple scheme, hereafter denoted as SSMILP (for Large and Pond), will be later contrasted with the GSFC series, denoted simply as SSMI, for the overlapping period.
c. Ocean torque from scatterometer winds
Data from several scatterometer instruments flown to date [on ERS-1, ERS-2, and the NASA scatterometer (NSCAT) on ADEOS] have been processed and objectively mapped into weekly 1° × 1° surface wind fields over the global oceans (80°S–80°N) at the Centre ERS d'Archivage et de Traitement (CERSAT) in Brest, France. We have used the data distributed on CD-ROM by CERSAT (2000) to calculate TO time series based on ERS-1 and ERS-2 data. Besides wind speed values, gridded stress data based on the bulk formulation of Smith (1988) are also provided on the CD. We have used these τ values and also τ values computed by us as described in section 2b to calculate two sets of TO, denoted hereafter as SCAT and SCATLP, respectively.
3. Analysis of TO
a. How well is TO known?
For the purposes of comparing different TO products, it is desirable to use the longest period of overlap available, to obtain as stable an estimate of the annual and semiannual harmonics as possible. To this end, we compare TO time series from NCEP–NCAR, SSMILP, and SCATLP for the overlapping 8-yr period from 1992 to 1999. (The first complete year of SCATLP series is 1992, while the SSMILP series ends in 1999.) We work with SSMILP values, based on our simple stress model, because the available SSMI series is only five years long. For consistency, SCATLP is also used. Dependence of results on the stress model is discussed in section 3b.
Using simple Fourier analysis, we calculate amplitudes and phases of the annual and semiannual cycles for the three time series of TO (Fig. 2). The 4 times daily TO values from NCEP–NCAR and SSMILP series are weekly averaged to be consistent with SCATLP series before performing the harmonic analysis. Phases of the various TO estimates in Fig. 2 are all similar but vary over a range of ∼5°–30° (annual maxima from late January to early February; semiannual maxima around mid-to late May and six months later). Differences in amplitude are noticeable (∼1 or 2 hadleys, where 1 hadley ≡ 1018 kg m2 s−2), with SCATLP having the smallest values. Uncertainties in the semiannual cycle seem to be bigger than for the annual cycle, relative to their amplitudes. Similar conclusions can be drawn from the 3-month-average values of TO shown in Fig. 3. The strong annual cycle for SSMILP comes from larger torques during the northern winter and summer seasons. SCATLP values are generally the smallest. The estimated range of seasonal variability in Figs. 2 and 3 is not inconsistent with the spread of values that can be inferred from previous calculations of TO based on observations (Ponte and Rosen 1993, 1994; Bryan 1997) and models (Boer 1990).
b. Sources of uncertainty in TO
One of the uncertain aspects in the calculation of TO relates to the many different formulations of the boundary layer model that can be used to convert wind speed to stress τ. Sensitivity to the stress model can be examined by comparing values of TO based on the same winds but different schemes to estimate τ. Comparisons of SCAT and SCATLP, based on the same scatterometer winds (1992–99), and SSMI and SSMILP, based on the same SSM/I winds (1994–98), can serve this purpose. Annual and semiannual harmonics calculated for these two pairs of TO time series are shown in Fig. 4.
Although the series in Fig. 4 are calculated using different bulk and boundary layer stress models (see section 2), their amplitudes and phases are very similar for SCAT and SSMI pairs. The largest difference is ∼1 hadley for the annual cycle calculated with the scatterometer data. Differences between SSMI and SSMILP values are much smaller. In fact, the differences among TO values in Fig. 2 are generally larger than the differences between SSMI and SSMILP or between SCAT and SCATLP in Fig. 4. Sensitivity of TO to the stress model is thus small.
The TO is likely more sensitive to other factors, such as the temporal resolution of the wind fields. The SCATLP series is based on weekly wind fields, in contrast with the 6-hourly winds used for NCEP–NCAR and SSMILP series. Because of the nonlinear relation between wind speed and τ, the seasonal cycle in τ can depend on wind variability at periods other than annual and semiannual. Wind variability even at subweekly timescales could be relevant. To assess the effects of temporal resolution of the wind fields on TO, we calculate another TO time series (denoted
Differences between SSMILP and NCEP–NCAR values in Figs. 2 and 3 are not affected by time resolution issues and give a good idea of the sensitivity of TO to different wind fields, assuming that differences introduced by the stress models are relatively modest (Fig. 4). The quality of the wind fields may be regionally dependent, and regional comparisons of τ fields can indicate where uncertainties in wind and τ fields might be large. Such an analysis is illustrated in Fig. 6 by showing gridded, 3-month-averaged τ fields used to calculate the SSMILP and NCEP–NCAR series of TO and the respective difference for June–August, which is the season of the largest discrepancy between SSMILP and NCEP–NCAR torques (Fig. 3). General τ patterns are similar in the two cases, but there are significant differences in amplitude, typically ∼0.01–0.02 N m−2, which are not small compared with τ values. Strong disagreements can be seen in the Tropics (e.g., eastern Pacific, Atlantic, and Indian Oceans) and some extratropical southern latitudes. The SSMILP minus the NCEP–NCAR difference field shows large-scale patterns similar to the original fields, indicative of generally larger amplitudes in the SSMILP data. In particular, negative values are seen over most of the northern tropics and southern extratropics, where systematically larger negative τ values for SSMILP are observed. These two latitudinal bands contribute the most to the larger negative SSMILP values in Fig. 3.
4. Balance between Ṁ and T revisited
Given the uncertainties suggested by the analysis in section 3, it is useful to assess the extent to which errors in TO are responsible for seasonal imbalances between Ṁ and T. We would also like to assess whether any of the TO time series considered are clearly superior in this regard. Based on (1), our approach is to compare the various TO estimates to the residual R = Ṁ − TL calculated from the NCEP–NCAR reanalysis. Uncertainties in R can also be large, mostly because of issues regarding the calculation of TL and in particular Tgw (Ponte and Rosen 2001). To provide a measure of possible uncertainties in R, Fig. 7 shows the annual and semiannual phasors for residuals calculated with Tgw included (denoted by R̃) and without Tgw (denoted by
The impact of Tgw on R is indeed very large, particularly for the annual cycle. The annual amplitude is much larger when Tgw is included, and a change in phase also yields substantial differences in the semiannual residuals. Differences resulting from the extreme cases of including Tgw versus omitting it altogether are taken here as upper bounds on the uncertainties in R, given that other components of TL are likely to be better determined. Comparing then the uncertainties in R with the spread of TO estimates in Fig. 7, one concludes that errors in TO can contribute substantially to the imbalances between Ṁ and T at the seasonal timescale. Differences in TO phasors have amplitudes on the order of 1 or 2 hadleys and are ∼25% and 100% of the maximum uncertainties in R at annual and semiannual periods, respectively.
The match between
5. Summary and discussion
Our analysis of multiyear TO time series based on SSM/I and scatterometer wind data quantifies the expected uncertainties in the available estimates of TO and highlights the role of TO in M budget imbalances at the seasonal timescale. Errors in TO are directly related to those in the τ fields. The limiting factor in improving the latter seems to be the quality of the input surface winds, rather than the boundary layer models used to infer τ from the winds. Good knowledge of wind variability is needed from seasonal to subweekly timescales. Surface winds over the Tropics and extratropical southern latitudes seem to be currently most uncertain. Examination of the balance between Ṁ and T suggests that TO estimates involving satellite winds are generally superior in quality to those based on the NCEP–NCAR reanalysis. A more definite conclusion is hampered, however, by the presence of other large uncertainties in T stemming in part from poor knowledge of Tgw.
Ultimately more data will be needed to narrow the uncertainties in the estimates of TO. We have treated the effects of direct wind field estimates, but other data and methodologies can be used. Such efforts may involve, for example, ocean data assimilation systems that use altimeter (sea level) and other types of data to infer corrections to the surface oceanic forcing fields (including Ï„) consistent with an improved estimate of the ocean state (Stammer et al. 2002). Preliminary attempts at calculating corrections to TO in such a way are discussed by Ponte et al. (2001, 2002). More conventionally, the use of satellite surface winds in atmospheric data assimilation systems may also provide for very efficient ways of extracting all the useful information contained in the wind data (e.g., Atlas et al. 2001) and for more accurate determination of TO.
The importance of subweekly wind variability for seasonal TO signals raises a set of broader issues. Our finding is a clear example of nonlinearities playing a role in climate variability; that is, synoptic winds can affect the amplitude and phase of seasonal or longer period signals in the oceanic forcing fields and ultimately in the ocean's response. As such, one may need to have very good temporal resolution of variables like near-surface winds for ocean modeling purposes. How fine that resolution may have to be (e.g., is 6-hourly data sufficient for our TO problem?) is still an unanswered question. In this light, effects of high-frequency noise also become important and will have to be dealt with in tandem.
Finally, we return to the difficulties in finding a good seasonal Ṁ and T balance and the controversial role of Tgw. Results in Fig. 7 indicate that agreement between Ṁ and T at annual and semiannual periods tends to be better when Tgw effects are included. These findings do not contradict those of Huang et al. (1999), who question the quality of Tgw values based on the large bias they introduce in the balance between Ṁ and T in all seasons. Such biases are related to the total value of Tgw and thus strongly affected by the large annual mean of Tgw. We, in turn, have focused on the torque variability about the annual mean. While questions about the quality of the mean values of Tgw remain, our analysis indicates that the variability in Tgw is usefully incorporated in seasonal M budgets. In this context, continuing research on the nature of Tgw and on improving its parameterization in atmospheric models and analyses is very relevant. Improved estimates of TO would also help check the quality of future estimates of Tgw.
Acknowledgments
We are grateful to R. Atlas, J. C. Jusem, and J. Ardizzone for the SSM/I wind and stress data and to K. Weickmann and H.-P. Huang for the NCEP–NCAR reanalysis torque data. P. Nelson helped with calculations and figures. This research is based upon work supported by the NASA Solid Earth and Natural Hazards Program and the EOS Project through Grant NAG5-9989, and 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 , 201–208.
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 , 869–882.
Atlas, R., and Coauthors. 2001: The effects of marine winds from scatterometer data on weather analysis and forecasting. Bull. Amer. Meteor. Soc., 82 , 1965–1990.
Boer, G. J., 1990: The earth–atmosphere exchange of angular momentum simulated in a model and implications for the length of day. J. Geophys. Res., 95 , 5511–5531.
Bryan, F. O., 1997: The axial angular momentum balance of a global ocean general circulation model. Dyn. Atmos.–Oceans, 25 , 191–216.
CERSAT, 2000: Mean surface wind fields from the ERS-AM1 and ADEOS-NSCAT microwave scatterometers, August 1991 to May 2000. WOCE Global Data, Version 2.0, CD-ROM.
Huang, H-P., and P. D. Sardeshmukh, 2000: Another look at the annual and semiannual cycles of atmospheric angular momentum. J. Climate, 13 , 3221–3238.
Huang, H-P., P. D. Sardeshmukh, and K. M. Weickmann, 1999: The balance of global angular momentum in a long-term atmospheric data set. J. Geophys. Res., 104 , 2031–2040.
Large, W. G., and S. Pond, 1982: Sensible and latent heat flux measurements over the oceans. J. Phys. Oceanogr., 12 , 464–482.
Lejenäs, H., R. A. Madden, and J. J. Hack, 1997: Global atmospheric angular momentum and earth–atmosphere exchange of angular momentum simulated in a general circulation model. J. Geophys. Res., 102 , 1931–1941.
Liu, W. T., K. B. Katsaros, and J. A. Businger, 1979: Bulk parameterization of air–sea exchanges of heat and water vapor including molecular constraints at the interface. J. Atmos. Sci., 36 , 1722–1735.
Ponte, R. M., and R. D. Rosen, 1993: Determining torques over the ocean and their role in the planetary momentum budget. J. Geophys. Res., 98 , 7317–7325.
Ponte, R. M., and R. D. Rosen, 1994: Oceanic angular momentum and torques in a general circulation model. J. Phys. Oceanogr., 24 , 1966–1977.
Ponte, R. M., and R. D. Rosen, 1999: Torques responsible for evolution of atmospheric angular momentum during the 1982–83 El Niño. J. Atmos. Sci., 56 , 3457–3462.
Ponte, R. M., and R. D. Rosen, 2001: Atmospheric torques on land and ocean and implications for Earth's angular momentum budget. J. Geophys. Res., 106 , 11793–11799.
Ponte, R. M., D. Stammer, and C. Wunsch, 2001: Improving ocean angular momentum estimates using a model constrained by data. Geophys. Res. Lett., 28 , 1775–1778.
Ponte, R. M., A. Mahadevan, J. Rajamony, and R. D. Rosen, 2002: Effects of SSM/I winds on stress torques over the ocean and the atmospheric angular momentum balance. Proc. WCRP/SCOR Workshop on Intercomparison and Validation of Ocean–Atmosphere Flux Fields, WCRP-115, WMO/TD-1083, Potomac, MD, WCRP, 99–102.
Rosen, R. D., 1993: The axial momentum balance of Earth and its fluid envelope. Surv. Geophys., 14 , 1–29.
Rosen, R. D., D. A. Salstein, and T. M. Wood, 1991: Zonal contributions to global momentum variations on intraseasonal through interannual timescales. J. Geophys. Res., 96 , 5145–5151.
Salstein, D. A., K. Cady-Pereira, C-K. Shum, and J. Xu, 1996: ERS-1 scatterometer observations of ocean surface winds as applied to the study of the Earth's momentum balance. Preprints, Eighth Conf. on Satellite Meteorology and Oceanography, Atlanta, GA, Amer. Meteor. Soc., 439–442.
Smith, S. D., 1988: Coefficients for sea surface wind stress, heat flux, and wind profiles as a function of wind speed and temperature. J. Geophys. Res., 93 , 15467–15472.
Stammer, D., and Coauthors. 2002: Global ocean circulation during 1992–1997, estimated from ocean observations and a general circulation model. J. Geophys. Res., 107 . (C9), 3118, doi:10.1029/2001JC000888.
Wahr, J. M., and A. H. Oort, 1984: Friction- and mountain-torque estimates from global atmospheric data. J. Atmos. Sci., 41 , 190–204.
White, R. M., 1949: The role of the mountains in the angular momentum balance of the atmosphere. J. Meteor., 6 , 353–355.
Widger, W. K., 1949: A study of the flow of angular momentum in the atmosphere. J. Meteor., 6 , 291–299.
Xu, J., 1997: Application of satellite scatterometer to the study of Earth angular momentum balance. Ph.D. dissertation, University of Texas at Austin, 181 pp.
Annual and semiannual amplitude and phase of Ṁ, T, and TO, based on NCEP–NCAR reanalysis data for 1968–98, plotted in a phasor diagram, where amplitude and phase are represented by the length and direction of a vector, respectively. Amplitudes are given in units of hadleys (1 hadley = 1018 kg m2 s−2). Phase is plotted increasing counterclockwise, with 90° given by a phasor pointing straight upward. A phase of 0° corresponds to an annual maximum on 1 Jan or semiannual maxima on 1 Jan and ∼6 months later.
Citation: Journal of Climate 16, 4; 10.1175/1520-0442(2003)016<0715:UISWTO>2.0.CO;2
As in Fig. 1 but for TO phasors derived from NCEP–NCAR, SSMILP, and SCATLP series based on the period 1992–99
Citation: Journal of Climate 16, 4; 10.1175/1520-0442(2003)016<0715:UISWTO>2.0.CO;2
Seasonal averages of NCEP–NCAR, SSMILP, and SCATLP estimates of TO for the period 1992–99. The x-axis labels denote the three months of each season [e.g., Dec–Jan–Feb (DJF)]. Annual means have been removed
Citation: Journal of Climate 16, 4; 10.1175/1520-0442(2003)016<0715:UISWTO>2.0.CO;2
As in Fig. 1 but for TO phasors derived from SSMI and SSMILP series for the period 1994–98, and SCAT and SCATLP series for the period 1992–99, illustrating the effect of different stress models on TO
Citation: Journal of Climate 16, 4; 10.1175/1520-0442(2003)016<0715:UISWTO>2.0.CO;2
As in Fig. 1 but for SSMILP and
Citation: Journal of Climate 16, 4; 10.1175/1520-0442(2003)016<0715:UISWTO>2.0.CO;2
Estimates of zonal wind stress τ on the atmosphere for JJA season during 1992–99 for SSMILP, NCEP–NCAR, and their difference (SSMILP minus NCEP–NCAR). Annual means have been removed. Contour interval is 0.02 N m−2. Light shading denotes negative values
Citation: Journal of Climate 16, 4; 10.1175/1520-0442(2003)016<0715:UISWTO>2.0.CO;2
Comparison of the estimates of TO with the residual R = Ṁ − TL, calculated for the period 1992–99. Phasor with Tgw included is denoted by R̃; phasor without Tgw is denoted by
Citation: Journal of Climate 16, 4; 10.1175/1520-0442(2003)016<0715:UISWTO>2.0.CO;2
Unlike M, most of the variance in Ṁ is at subseasonal periods (cf. Table 1 in Ponte and Rosen 1993; Fig. 1 in Huang et al. 1999). Thus, although the Ṁ spectrum shows peaks at the annual and semiannual bands, the seasonal signal is small compared to the total variance in Ṁ. This makes analysis of the seasonal torque balance difficult.
