1. Introduction
The Southern Hemisphere (SH) surface westerly wind stress is a major forcing for driving the Antarctic Circumpolar Current (ACC) and upwelling of deep waters in the Southern Ocean (SO). The SH westerly wind stress has strengthened significantly over the last few decades and is projected to continue to do so in the future, which may have important implications for the global climate system via modulating the rate at which the SO uptakes heat and carbon (e.g., Thompson and Solomon 2002; Le Quéré et al. 2007; Marshall and Speer 2012; Wang et al. 2015, 2017). The strength of the SO wind stress is found to be closely related to the phase of the southern annular mode (SAM), the dominant mode of atmospheric variability in the SH, with wind stress being stronger (and also poleward shifted) during the positive phase of the SAM (e.g., Marshall 2003; Swart and Fyfe 2012). However, the SAM index is often defined based on the monthly, seasonal-, or annual-mean zonal sea level pressure difference between 40° and 65°S (Gong and Wang 1999), and as such is a measure of the monthly-, seasonal-, or annual-mean strength of the westerly winds, rather than westerly wind stress. This could be problematic, since it is well known that the surface wind stress depends nonlinearly on surface wind velocity (e.g., Large et al. 1994; Zhai et al. 2012).
Because of the aforementioned nonlinear dependence of wind stress on surface wind, high-frequency wind fluctuations contribute to wind stress variability at both high and low frequencies (Zhai et al. 2012; Zhai 2013). For example, including wind fluctuations with time scales less than 1 month in the wind stress calculation significantly enhances the strength of the time-mean and seasonal-mean wind stress, particularly at mid- and high latitudes. In turn, this increases wind power input to the ocean general circulation by over 70% (Zhai et al. 2012; Wu et al. 2016). Therefore, studies on the changes of SO wind stress and their impact on the ocean need to take into account changes of not only the low-frequency (e.g., interannual) variability of the westerly jet, but also wind fluctuations at much shorter time scales (e.g., days).
The strong positive trend of SO wind stress seen in observations, as well as atmospheric reanalysis products, has spurred a great deal of interest in how the SO responds to changes of surface wind stress forcing (e.g., Hallberg and Gnanadesikan 2001, 2006; Meredith and Hogg 2006; Böning et al. 2008; Farneti et al. 2010; Dufour et al. 2012; Munday et al. 2013; Bishop et al. 2016). This includes a number of steady-state sensitivity modeling studies where the mean SO wind stress is strengthened and/or shifted (e.g., Downes et al. 2011; Zhai and Munday 2014; Spence et al. 2014; Munday and Zhai 2015; Bishop et al. 2016; Hogg et al. 2017), as well as some observational and modeling studies of the transient response of the ACC and SO eddy field to changes of the SAM (e.g., Meredith and Hogg 2006; Screen et al. 2009; O’Kane et al. 2013; Langlais et al. 2015). Two dynamical phenomena—eddy saturation (Straub 1993) and eddy compensation (Viebahn and Eden 2010), which refer to the loss and reduced sensitivity of ACC transport and SO meridional overturning circulation to wind stress changes, respectively—emerge from model studies with resolved or permitted, rather than parameterized, mesoscale ocean eddies.1 Model investigations into the eddy saturation and eddy compensation phenomena typically involve directly varying the magnitude of the mean wind stress in the SO. The underlying assumption of this approach is that the stress varies due to changes of the mean wind.2 In reality, however, some of the observed and predicted wind stress changes may be brought about by changes in the variability of the atmospheric wind, owing to the nonlinear nature of the stress law (Zhai 2013).
An exception to this common practice of directly varying the mean wind stress is a recent study by Munday and Zhai (2017), who investigated the impact of wind fluctuations on the sensitivity of SO stratification and circulation to wind stress changes. In their study, changes of the mean wind stress felt by the ocean were made through alteration of the wind variability, as opposed to the mean wind. Stronger wind variability is found to enhance near-surface energy dissipation and increase near-surface viscous and diffusive mixing (see also Jouanno et al. 2016; Sinha and Abernathey 2016). The increased vertical mixing deepens the surface mixed layer and results in a much greater sensitivity (more than doubled) of the SO meridional overturning circulation to the increased wind stress, when compared to equivalent experiments forced by changing the mean wind. This result has important implications for understanding the SO response to past and future wind stress changes, should changes in wind stress be brought about not only by changes of the mean wind, but also by changes of wind variability. However, to our knowledge, there have been few studies (Zhai et al. 2012; Zhai 2013; Franzke et al. 2015) so far assessing the role of wind fluctuations in determining the mean, variability, and trend of the observed wind stress in the SO. A number of studies exist on the changes of the SH storm track and cyclone activities (Simmonds and Keay 2000; Yin 2005; Grieger et al. 2014; Wang et al. 2016; Chang 2017). However, the link between changes in these synoptic atmospheric systems and changes in SO wind stress has not yet been made.
In this study, we use reanalysis data products to investigate the contributions of wind fluctuations on different time scales (6 h–2 days, 2–8 days, and 8 days–1 yr) to the mean, variability, and trend of SO wind stress for the first time. The paper is organized as follows. We begin in section 2 by describing the reanalysis products and analysis methods used in this study. In section 3, we first examine the effect of wind fluctuations on the time-mean and seasonal-mean wind stresses in the SO, and this is followed by an investigation of the contribution of wind fluctuations to wind stress differences between positive and negative SAM years, as well as their contribution to the observed strengthening trend of SO wind stress. Finally, section 4 provides a summary and some concluding remarks.
2. Data and methods
a. Reanalysis data
Six-hourly, 10-m wind fields from two widely used atmospheric reanalysis products are analyzed in this study: National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) reanalysis (NCEP-1; Kalnay et al. 1996) and the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim; Dee et al. 2011). The NCEP-1 and ERA-Interim 10-m winds are provided on spectral T62 (~210 km) and T255 (~80 km) grids, respectively. Prior to 1979, the strength of the SH westerly jet in the NCEP-1 reanalysis product shows large spurious trends when compared to that derived from station data, owing to the gradual reduction of errors in the NCEP-simulated sea level pressure field at high southern latitudes (Hines et al. 2000; Marshall 2003). The situation is much improved with the introduction of the Television Infrared Observation Satellite (TIROS) Operational Vertical Sounder data into the reanalysis assimilation scheme after 1979. Because of this, we choose the analysis period in this study to be from January 1979 to December 2016. Previous studies find that although ERA-Interim is somewhat better in representing the characteristics of extratropical cyclones than NCEP-1 due to its higher spatial resolution (e.g., Jung et al. 2006; Tilinina et al. 2013), both reanalysis products tend to underestimate the dynamical intensity (e.g., maximum wind speed) of mesoscale atmospheric features, such as mesocyclones and polar lows (Zappa et al. 2014; Verezemskaya et al. 2017). Figure 1 shows the comparison between the reanalysis winds and observed winds at four automatic weather stations from the Scientific Committee on Antarctic Research (SCAR) Reference Antarctic Data for Environmental Research (READER) project (Turner et al. 2004). The two reanalysis products reproduce reasonably well the salient features of wind variability at the four locations, but they both underestimate the amplitude of wind variability, most notably at high frequencies (e.g., 6 h–2 days). Therefore, results from our study should be considered as a lower bound of the contribution of wind fluctuations to the SO wind stress, particularly at high frequencies.
Comparison of the time series and power spectra of 10-m wind speeds from NCEP-1 and ERA-Interim with automatic weather station data at four locations in 1989 (with the annual mean removed). The wind speeds are observed at 10, 10, 6, and 11 m at O’Higgins, Great Wall, Orcadas, and Faraday, respectively.
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
The NCEP–DOE reanalysis product (NCEP-2; Kanamitsu et al. 2002), an improved version of NCEP-1,3 and the Japanese 55-year Reanalysis product (JRA-55; Kobayashi et al. 2015) provided on the spectral T319 (~63 km) grid are also analyzed in this study. Since the results from NCEP-2 and JRA-55 are very similar to those from NCEP-1 and ERA-Interim, except for the trend, we only include results from NCEP-2 and JRA-55 when comparing trends of SO wind stress among different reanalysis products.
b. SAM index
c. Wind stress
To quantify the effect of wind fluctuations on different time scales on the SO wind stress, we apply 2-day running mean, 8-day running mean, and annual-mean averaging to the original 6-hourly reanalysis wind field to filter out wind fluctuations that last less than 2 days, less than 8 days, and less than 1 year, respectively. Threshold time scales of 2 and 8 days are chosen here because atmospheric variability (e.g., wind and air temperature) on time scales of 2–8 days is generally thought to be associated with synoptic weather systems and baroclinic storm activities (e.g., Trenberth 1991; Inatsu and Hoskins 2004; Yin 2005). Figure 2 shows the magnitude of peak zonal-mean zonal wind stress in the SO as a function of the running mean time scale. The magnitude of peak zonal-mean zonal wind stresses in both NCEP-1 and ERA-Interim decreases rapidly with increasing running mean time scale up to synoptic time scales (~8 days) and then decreases much more gently afterward. For example, increasing the running mean time scale to 10 or 15 days leads to only a 3% or 8% decrease in the calculated wind stresses, compared to those calculated from the 8-day running mean winds. Wind fluctuations on time scales of 2–8 days are calculated by taking the difference between the 2-day running mean and 8-day running mean wind fields. The 2–8-day filtered winds are then obtained by removing wind fluctuations on 2–8 days from the original 6-hourly wind field (Table 1). We recalculate the zonal wind stresses using these filtered winds (
The magnitude of peak zonal-mean zonal wind stress in the SO (35°–65°S) averaged over 1979–2016 as a function of the running mean time scale from NCEP-1 (black line) and ERA-Interim (blue line). Red and green crosses (asterisks) mark peak zonal-mean zonal wind stresses calculated from NCEP-1 (ERA-Interim) 2- and 8-day running mean winds, respectively.
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
List of variables and the formulas used to calculate them. Overbars 
In addition to surface wind stress calculations, we also quantify kinetic energy of the wind field to help interpret some of the results shown in section 3. Mean kinetic energy in each year (MKEyr) is calculated from the annual-mean wind field, and eddy kinetic energy is calculated from wind fluctuations on time scales of 6 h–2 days (EKE2d), 2–8 days (EKE2–8d), 6 h–8 days (EKE8d), and 6 h–1 yr (
3. Results
a. Mean
We first assess the effect of including wind fluctuations on different time scales on the mean wind stress in the SO. Figure 3 shows the 1979–2016 time-mean zonal wind stress calculated from the NCEP-1 (Figs. 3a–f) and ERA-Interim (Figs. 3g–l) reanalysis winds. Wind fluctuations are found to strengthen the mean wind stress almost everywhere in both reanalysis products, with the difference between multiyear mean 
The 1979–2016 time-mean wind stress (N m−2) in the SO from (a)–(f) NCEP-1 and (g)–(l) ERA-Interim. Mean 
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
The 1979–2016 zonal-mean and time-mean zonal wind velocity (dashed; m s−1), zonal wind stresses (solid; N m−2), and MKE and EKE (m2 s−2) from (a),(b) NCEP-1 and (c),(d) ERA-Interim. 
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
To understand the effect of including wind fluctuations on different time scales on the mean wind stress, it is instructive to examine the magnitude and spatial structure of the MKE and EKE. Figure 5 shows the time-mean zonal wind velocity, MKE, and EKE calculated from wind fluctuations on different time scales from NCEP-1 (Figs. 5a–f) and ERA-Interim (Figs. 5g–l). The spatial patterns of the mean winds (Figs. 5a,g) are very similar to those of the mean wind stresses (Figs. 3a,g), with large values located in the south Indian Ocean sector. This similarity is also found in the zonal-mean patterns of the mean wind and mean stress (solid red and dashed blue lines in Figs. 4a,c), with the peak values of both quantities found at 52°–53°S. Another striking feature in Fig. 5 is the much broader and more uniform meridional (and zonal) distribution of the EKE, compared to the MKE (Figs. 5b,c,h,i). The zonal-mean EKE increases gradually southward in the latitude band of 40°–60°S and experiences somewhat sharper drops only north of ~40°S and south of ~60°S (Figs. 4b,d). This more-or-less uniform distribution of the EKE explains why the mean wind and mean stress peak at the same latitude: the strengthening of the mean stress owing to wind variability is largest where the mean wind is strongest.
The 1979–2016 time-mean zonal wind velocity (m s−1), MKE (m2 s−2), and EKE (m2 s−2) in the SO from (a)–(f) NCEP-1 and (g)–(l) ERA-Interim.
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
EKE calculated from wind fluctuations on time scales of 6 h–2 days, 2–8 days, and 6 h–8 days is found to account for about 32%, 28%, and 71%, respectively, of the total EKE for both NCEP-1 (Fig. 4b) and ERA-Interim (Fig. 4d). These EKE percentages are broadly comparable to the percentage increases of the mean stress after including wind fluctuations on different time scales, demonstrating that the effect of wind variability on the strength of the mean stress via the nonlinear stress law depends on the magnitude of the wind variability. Stronger wind variability in ERA-Interim also contributes to the larger mean stress in ERA-Interim than NCEP-1 (red lines in Figs. 4a,c), although the mean winds in the two reanalysis products are comparable in strength (dashed blue).
For both reanalysis products, the zonal-mean wind peaks in austral spring and autumn (dashed green and blues lines in Figs. 6a,c), while it shifts equatorward in austral summer (dashed red) and becomes weaker but broader in austral winter (dashed black). Interestingly, the zonal-mean wind stress in austral winter (solid black) is greater than that in austral summer (solid red), even in the latitude band of 44°–56°S, where the mean wind is noticeably weaker in austral winter than in austral summer (dashed black vs dashed red). This paradox is explained by the pronounced seasonal cycle of the EKE in the SO (Figs. 6b,d), characterized by EKE being the largest in austral winter (dashed black) and smallest in austral summer (dashed red). Stronger wind variability in austral winter increases the magnitude of the mean stress much more significantly than that in austral summer, resulting in the larger mean stress seen in austral winter. It is worth pointing out that EKE is greater than MKE in the SO in all four seasons for both reanalysis products (Figs. 6b,d).
The 1979–2016 zonal-mean and seasonal-mean zonal wind velocity (dashed; m s−1), zonal wind stress (solid; N m−2), MKE (solid; m2 s−2), and EKE (dashed; m2 s−2) from (a),(b) NCEP-1 and (c),(d) ERA-Interim.
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
b. Variability
In this section, we investigate the role of wind fluctuations in determining wind stress differences between positive and negative SAM years. Here, a year with SAM > 0.5 is defined as a positive SAM year, and a year with SAM < −0.5 is a negative SAM year (Fig. 7).
The 1979–2016 station-based SAM index from Marshall (2003; updated online). Years with SAM > 0.5 are defined here as positive SAM years, and those with SAM < −0.5 are negative SAM years.
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
Figure 8 shows the mean stress, 
The mean 
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
(a),(d) Zonal-mean 
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
To further assess the role of wind fluctuations in determining the wind stress differences seen between positive and negative SAM years, we recalculate the mean stress using a combination of the mean wind averaged over all the positive SAM years and wind fluctuations from each negative SAM year (Figs. 8b,j), and also using a combination of the mean wind averaged over all the negative SAM years and wind fluctuations from each positive SAM year (Figs. 8f,n). Remarkably, there is virtually no difference between the mean stress in positive SAM years and the mean stress calculated using a combination of the mean wind from positive SAM years and wind fluctuations from negative SAM years (Fig. 8a vs Fig. 8b; Fig. 8i vs Fig. 8j). The same is true for the mean stress in negative SAM years and the mean stress calculated using a combination of the mean wind from negative SAM years and wind fluctuations from positive SAM years (Figs. 8e,f,m,n). This result suggests that as far as the nonlinear stress law is concerned, it is the magnitude of wind fluctuations that matters for determining the magnitude of the mean stress, not whether wind fluctuations and the mean wind are dynamically linked. The result also shows that differences in the mean wind are the key cause for the differences in the mean stress found between positive and negative SAM years, although the presence of wind fluctuations significantly amplifies these mean stress differences; in the absence of wind fluctuations, the mean stress difference between positive and negative SAM years is much smaller (not shown). The situation in the SO appears to be in contrast to that at midlatitude North Atlantic, where stronger westerly wind stress during years of positive North Atlantic Oscillation is found to be mostly a result of enhanced synoptic wind variability, rather than a stronger background mean wind (Zhai and Wunsch 2013).
c. Trend
We now assess the contribution of wind fluctuations to the strengthening trend of SO wind stress over the last four decades. Results from NCEP-2 and JRA-55 are also included here since they are significantly different from NCEP-1 and ERA-Interim.
The trends of the strength of SO wind stress during 1979–2016 are 0.000 38 N m−2 yr−1 in NCEP-1 (Fig. 10a), 0.000 67 N m−2 yr−1 in NCEP-2 (Fig. 10b), and 0.000 23 N m−2 yr−1 in ERA-Interim (Fig. 10c), all significant at <1% level by t test, while no significant trend (<5%) is detected in JRA-55. This is consistent with the results in Thomas et al. (2015), who also found the largest trend of SO wind stress in NCEP-2 but no significant trend in JRA-55 for the period of 1980–2004. To separate out contributions from the mean wind and wind fluctuations to the wind stress trends found in the reanalysis products, we randomly reshuffle the annual-mean wind and wind fluctuations in each year over the whole 38-yr period. First, the annual-mean wind fields are randomly reshuffled for 38 times. Each time, a new time series of wind stress is calculated using a combination of the reshuffled annual-mean wind and unshuffled wind fluctuations. We then average the 38 time series of wind stress and find the trend of the averaged stress (black lines in Fig. 10). This new trend obtained by randomizing the annual-mean winds excludes the effect of changes of the annual-mean wind and thus enables us to see how the increased intensity of wind fluctuations with time contributes to the strengthening trend of the wind stress. Similarly, we randomly reshuffle wind fluctuations of each year 38 times, calculate 38 time series of wind stress using a combination of the reshuffled wind fluctuations and unshuffled annual-mean winds, and find the trend of the time series of the averaged stress (blue lines in Fig. 10). The new trend obtained by randomizing wind fluctuations excludes the effect of changing intensity of wind fluctuations, enabling us to see how the strengthening of the annual-mean wind contributes to the strengthening trend of the wind stress.
Time series (red solid) and trend (red dashed) of SO wind stress averaged between 35° and 65°S during 1979–2016 from (a) NCEP-1, (b) NCEP-2, and (c) ERA-Interim. Black lines are for wind stress obtained by randomizing the annual-mean winds, and blue lines are for that obtained by randomizing wind fluctuations. Percentages in brackets show statistical significance of the trends. Note that although the overall wind stress trends are positive when averaged between 35° and 65°S, there are regions of negative trends, particularly between 35° and 45°S (not shown).
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
After randomizing the annual-mean winds over the last four decades, the trends of the strength of SO wind stress are 0.000 14 N m−2 yr−1 for NCEP-1, 0.000 34 N m−2 yr−1 for NCEP-2, and 0.000 03 N m−2 yr−1 for ERA-Interim (black lines in Fig. 10). Importantly, the trends for both NCEP reanalysis products are significant at <5% level, whereas the trend for ERA-Interim is not statistically significant. Therefore, changes of wind fluctuations explain about one-third and one-half of the strengthening trend of Southern Ocean wind stress in NCEP-1 and NCEP-2, respectively, but make no significant contribution in ERA-Interim. The positive wind stress trend in ERA-Interim is due entirely to the increase in the strength of the annual-mean wind. These conclusions are supported by the calculations based on the randomization of wind fluctuations (see blue lines in Fig. 10 for the trends, as well as their statistical significance). Our study, therefore, highlights the large discrepancies among the widely used reanalysis products regarding the relative contributions of the annual-mean wind and wind fluctuations to the observed changes of SO wind stress. These discrepancies may have contributed to the diverging responses of the SO simulated by ocean models forced with different reanalysis products (Gent 2016; Munday and Zhai 2017).
Figure 11 compares the trends of 
Time series (solid) and trends (dashed) of 
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
The trends of the seasonal-mean SO wind stress are significant at <5% level in all four seasons in NCEP-1, with larger trends in austral summer and autumn (Fig. 12a). In comparison, the trends of the seasonal-mean wind stress in ERA-Interim (Fig. 12c) are much smaller and only significant in austral summer and autumn. The trends of the seasonal-mean EKE in NCEP-1 (Fig. 12b) are again found to be significant in all seasons, with larger values in austral summer and autumn, while no significant trend is found in ERA-Interim in any season (Fig. 12d). These results show that wind fluctuations in NCEP-1 contribute to the strengthening of not only the annual-mean wind stress, but also the seasonal-mean wind stress in the SO. The greater contribution to the annual-mean trend by trends in austral summer and autumn is consistent with results from previous Antarctic radiosonde data and model studies, which showed that the trend of the SH circumpolar westerly is stronger during austral summer and autumn (Thompson and Solomon 2002; Fogt et al. 2009; Jones et al. 2016), as a result of the development of the Antarctic ozone depletion during the austral summer season (Gillett and Thompson 2003; Thompson et al. 2011).
Time series (solid) and trends (dashed) of the (a),(c) seasonal-mean 
Citation: Journal of Climate 31, 9; 10.1175/JCLI-D-17-0481.1
4. Summary and conclusions
The Southern Ocean plays a key role in regulating the global climate via its residual meridional overturning circulation and the Antarctic Circumpolar Current. It is therefore an important task to understand how the SO responds to the observed and predicted strengthening of the westerly wind stress. Recently, Munday and Zhai (2017) showed that the sensitivity of SO stratification and circulation to wind stress changes depends strongly on whether these changes in wind stress are brought about by changes of the mean wind or wind fluctuations. However, it is yet unknown whether wind fluctuations have played a role in shaping the observed wind stress changes in the SO. In this study, we have analyzed two widely used atmospheric reanalysis products to assess the contribution of wind fluctuations to the mean, variability, and trend of SO wind stress over the last four decades. Our main findings are as follows:
Wind fluctuations, particularly those associated with weather systems and baroclinic storms, significantly enhance the strength of the mean wind stress in the SO. The magnitude of peak zonal-mean wind stresses is found to be doubled when wind fluctuations are included in the stress calculation. Over 70% of this doubling effect is owing to fluctuations that last less than 8 days, that is, associated primarily with weather systems/baroclinic storms.
The SAM index is a good indicator for the mean westerly wind and wind stress, but it is not as good a measure for wind fluctuations. Both the mean wind and mean wind stress are considerably stronger and also shifted poleward (by a few degrees) during positive SAM years. In comparison, no significant differences in wind fluctuations are found between positive and negative SAM years. Therefore, stronger wind stresses during positive SAM years are due mainly to the stronger background mean winds, not enhanced wind variability, although the presence of wind fluctuations significantly amplifies wind stress differences between positive and negative SAM years.
Large discrepancies are found among the reanalysis products analyzed in this study regarding the contribution of wind fluctuations to the strengthening trend of SO wind stress. The intensities of wind fluctuations in NCEP-1 and NCEP-2 have increased significantly over the last four decades and are found to contribute to about one-third and one-half of the increase in the strength of SO wind stress, respectively. In contrast, the intensity of wind fluctuations only experiences a very modest increase in ERA-Interim, and as such, the wind stress trend in ERA-Interim is explained almost entirely by the strengthening of the mean westerly wind. Furthermore, the majority (over 80%) of the increase in wind fluctuations in NCEP-1 and NCEP-2 is found to be associated with weather systems and baroclinic storms. No significant trend is detected in JRA-55.
The intensity of wind fluctuations exhibits a pronounced seasonal cycle, being highest in austral winter and lowest in austral summer. As a result, the peak zonal-mean wind stress is greater in austral winter than in austral summer, despite the mean westerly wind being stronger in austral summer than austral winter. Furthermore, trends in austral summer and autumn are found to contribute most to the annual trend in the SO.
Results from this study highlight the important contributions of wind fluctuations, especially those associated with weather systems and baroclinic storms, to the mean, variability, and trend of SO wind stress. Both NCEP reanalysis and ERA-Interim products show that the SO has become stormier over the last four decades, although the increase in atmospheric storminess is very modest in ERA-Interim. The large discrepancies found among reanalysis products regarding the contributions of wind fluctuations to the strengthening trend of SO wind stress are worrying, since not only the magnitude of the increased wind stress, but also how this increase comes about matters for the SO response to changes in wind stress forcing (Munday and Zhai 2017). The discrepancies among reanalysis products also highlight the need to have sustained observations with better coverage in the SO in order to better understand the atmospheric forcing and its changes in a region that is vital for the global climate system.
Acknowledgments
This study is supported by the National Key R&D Program of China (2016YFA0601804). XL is supported by a scholarship from the Chinese Scholarship Council and by the National Natural Science Foundation of China (41406214). XZ acknowledges additional support from the School of Environmental Sciences, University of East Anglia. ZW is supported by the Fundamental Research Funds for the Central Universities (2017B04814 and 2017B20714). DRM is supported by the Natural Environment Research Council (ORCHESTRA; Grant NE/N018095/1). We wish to thank Clothilde Langlais and two anonymous reviewers for their constructive comments that led to an improved manuscript.
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Non-eddy-resolving ocean models with a variable eddy parameterization coefficient are found to be capable of achieving partial eddy compensation (e.g., Farneti et al. 2010; Gent 2016).
If the increase in the magnitude of the mean wind stress is a result of increased wind variability, there should be a concurrent increase in wind stress variability, but this is absent in sensitivity model experiments where the strength of the mean stress is directly varied (e.g., doubled). High-frequency wind stress fluctuations are known to be important in setting the surface mixed layer depth (e.g., Zhou et al. 2018).
The improvements include an updated model with better physical parameterizations and fixing known data assimilation errors in NCEP-1.