1. Introduction
The Southern Ocean (SO) governs the global ocean uptake of anthropogenic heat and CO2 (Gnanadesikan 1999; Swart et al. 2018; Gruber et al. 2019), and projections of future climate change depend on our of understanding SO ventilation (Sabine et al. 2004; Boé et al. 2009; Kuhlbrodt and Gregory 2012; Soloviev and Lukas 2013; Flato et al. 2013), trends in water mass transformation (Roemmich et al. 2015; Haumann et al. 2016), and mode water formation (Hanawa and Talley 2001; Naveira Garabato et al. 2009; Holte et al. 2012; Gao et al. 2018; Cerovečki et al. 2019). Changes in the SO mixed layer are largely driven by a combination of surface stresses and atmosphere–ocean heat fluxes, which together ventilate the upper ocean through stirring and mixing, with the strongest ventilation during intermittent and highly variable events.
The strong link between surface winds and ventilation of the SO mixed layer (ML) suggests that the southern annular mode (SAM), as the leading-order mode of the Southern Hemisphere atmospheric variability (Thompson and Wallace 2000), impacts long-term mixed layer changes (Meijers et al. 2019; Cerovečki et al. 2019). However, it remains unclear how large-scale month-to-month atmospheric variability drives short-term intense wind events under storms (Risien and Chelton 2008; Lin et al. 2018). This paper explores how short-term wind and stress variability relate to SAM, how they vary in time, and how well they are represented in observational products.
SO flux buoy observations suggest that only a few episodic wind extremes (>12 m s−1 or so) per year are responsible for most ventilation and deepening of the mixed layer (Schulz et al. 2012; Ogle et al. 2018; Bharti et al. 2019; Tamsitt et al. 2020), and similar intermittent effects emerge in other regions and model studies as well (Giglio et al. 2017; Whitt et al. 2019). Because the strength of mixing is also sensitive to the ocean mixed layer stratification, it remains unclear when mixed layer ventilation is more sensitive to mechanical wind forcing and when it is more sensitive to to surface heat fluxes. In both cases, strong mixing may be associated with extreme winds that are embedded in larger, more persistent wind patterns extending over hundreds of kilometers under extratropical storms. Rare high-wind (or high-stress) events under storms initiate highly nonlinear processes that transfer energy from the wind-generated waves to the upper ocean (Phillips 1985) and eventually to the large-scale flow. Extreme winds initiate a cascade of complex processes that influence mixing far beyond the location where they occur (Cavaleri et al. 2012).
Extremes in Southern Ocean surface winds are difficult to observe. The severe weather and lack of access to the region around Antarctica limit in situ observations and make remote sensing the dominant technique for recording surface winds. Satellite scatterometers observe surface capillary waves (centimeter-scale surface roughness) that are used to estimate the local 10-m surface winds (Atlas et al. 2011). However, the sparseness of in situ SO observations has impeded the calibration of remote sensing estimates for high wind speeds (Bourassa et al. 2019). In particular, a lack of observations of extreme winds under cyclones and gaps in our knowledge of air–sea coupling under severe conditions make biases potentially largest where the winds are strongest (Rascle et al. 2008; Ardhuin et al. 2010; Chawla et al. 2013). These biases might correspond to differences between assimilated atmospheric reanalysis models (Wen et al. 2019; Ramon et al. 2019; McDonald and Cairns 2020), or between estimates of heat and momentum fluxes to the ocean (Bidlot et al. 2002; Cavaleri 2009; Li et al. 2013; Bourassa et al. 2013; Yagi and Kutsuwada 2020), and they can lead to biases in ocean forcing or upper-ocean mixing (Li et al. 2016; Taboada et al. 2019). All of these processes affect the assessment of the total wind energy input to the ocean (Rascle et al. 2008; Ferrari and Wunsch 2010).
The goal of the present study is to characterize the surface wind and stress over the SO in light of the complex relations between the surface stress and wind vector. We will use the time-varying probability density functions (PDFs) of surface stress and wind to understand their relation without assuming particular PDF shapes.
Surface winds on typical atmosphere model scales [daily time scales and O(100) km length scales] are often characterized entirely by their mean and standard deviation. Hence, they are handled as Gaussian distributions defined by averaged quantities of the model output that is used to force the ocean. Wentz et al. (1984) and Wanninkhof (1992, 2014) describe the commonly used approach of using time-averaged quantities to estimate parameters of a Weibull distribution for the surface wind speed in each grid cell, which is then used to model air–sea fluxes. However, a number of studies have shown that surface stress depends on more than just the mean surface wind vector and its standard deviation (e.g., Ponte and Rosen 2004; Monahan 2006a, 2008). These studies have shown that higher-order moments of the joint surface wind PDF must be known to derive a joint PDF of surface stress. Hence, the question arises of how to account for the deviations from Gaussian distributed winds, especially over the Southern Ocean, where winds regularly violate the Gaussian assumption (Tuller and Brett 1984; Pavia and O’Brien 1986; Simmonds and Dix 1989; Wanninkhof et al. 2002).
With the need for improved seasonal and climate predictions and more available computational power, the spatial and temporal resolution of weather and climate models continues to increase (Delworth et al. 2012; Small et al. 2014; Haarsma et al. 2016; Mizuta et al. 2017). As computational capabilities improve, models explicitly resolve more nonlinear surface processes and enhance the non-Gaussianity of surface variables, such that they have begun to advance beyond the assumption of Gaussian distributed surface variables (Blein et al. 2020, and references therein). Unsurprisingly, atmosphere–ocean interaction and related model biases have been identified as some of the biggest challenges in long-range weather forecast and climate models (White et al. 2017; Huang et al. 2020; Lin et al. 2020). To better represent highly nonlinear fluxes, parameterizations of bulk air–sea fluxes need to account for the non-Gaussianity of variables at high spatial resolution (Wanninkhof 1992; Wanninkhof et al. 2002; Edson et al. 2013).
In this paper, we represent surface wind variability in terms of PDFs to understand its physical drivers on time scales longer than five days. We also use time-varying PDFs to learn about SO surface wind biases and the occurrence of extreme surface stress (>0.4 Pa). First, we derive time-varying PDFs from reanalysis and scatterometer data (section 2a) and then apply a principal component analysis (section 2d) to decompose the PDFs into their leading modes. Second, we show the close relation of the leading modes in zonal wind and stress to the SAM (section 3). Third, we represent the zonal and meridional covariability in the surface wind and stress as the superposition of a few patterns that are driven by changes in the strength or position of extratropical cyclones, their frontal structure, and the seasonal cycle (section 4). Fourth, we show how the leading modes map into the climatological wind differences (section 5) and how surface wind extremes can be understood with respect to these climatological differences (section 6). Although we acknowledge that correlation is not causation, we finish by suggesting how this empirical mode can be linked to nonlinear surface processes and therefore the dynamics that influence SO surface climate (section 7a).
2. Methods
a. Time-varying PDFs of Southern Ocean wind and stress from ERA5
The 10-m surface winds (u10 and υ10) and surface stresses (τx and τy) from the ERA5 reanalysis (European Centre for Medium-Range Weather Forecasts fifth-generation reanalysis for the global climate and weather; Hersbach et al. 2018a, 2020) between 55° and 63°S (the latitude limits of Drake Passage) are used to derive statistically robust, empirical time-evolving PDFs in the Southern Hemisphere (SH) between 1979 and 2017. The latitude limits are chosen such that the wind patterns and fronts over the ocean are solely driven by extratropical storms, rather than by flow around topography or subtropical dynamics (Figs. 1a,b). This region also coincides with the areas of most intense and most frequent extratropical storms over the SO (Turner et al. 1996; Hoskins and Hodges 2005; Lim and Simmonds 2007). The same analysis for a broader latitude range leads to similar results, albeit with increased noise levels (appendix A; Gille 2005).
(a) Surface wind stress magnitude over the Southern Ocean on 19 Jul 2000. Data from the Drake Passage range are in red shading. (b) Zonal surface winds u10 for the same date as in (a).
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
Note that these surface winds differ from zonal-mean zonal winds or even meandering jets (Fig. 1), also indicated by the fact that the surface eddy kinetic energy exceeds the mean surface kinetic energy by about a factor of 2 (Lin et al. 2018, 2020). However, the midlatitude zonal-mean jet and surface wind variability are still related, as detailed in section 7a.
Without any prior averaging, the hourly and 0.25° data are divided into 5-day chunks starting on 1 January each year. (Leap years have a 6-day chunk at the end of February for computational convenience.) Five-day chunks are selected in order to capture the characteristic time scale of baroclinic wave activity (Blackmon 1976; Wallace et al. 1988; Randel and Held 1991). The 5.4 × 106 data points in each block (1440 longitudes × 31 latitudes × 120 h) are used to derive joint histograms of winds and stresses in the zonal and meridional directions for every 5-day period between 1979 and 2017 (see the example PDFs in Fig. 2). Histograms of only the zonal or meridional components are derived from the joint histograms by summing in the respective orthogonal direction. All histograms are then represented as probability density functions D(u, t) or D(τ, t) by dividing by the bin width and the total number of data points used in the respective 5-day mean.
(a) Zonal wind PDFs for the 1-h time step shown in Fig. 1b (dashed black line), 5-day periods including this time step (thick black line, white shading), and the climatology (thin black line with filled gray area). The background coloring corresponds to the color scale in Fig. 1b. (b) As in (a), but for the meridional wind component. (c) The corresponding joint wind PDFs for a 5-day time step and the climatological joint distribution in black contours in 4 × 10−4 intervals. The black dash-dotted lines indicate the climatological distribution medians.
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
Figure 3 shows the resulting time-varying PDFs for 5-day increments of zonal wind and stress. For the SO, zonal wind PDFs have a nonzero mean, with a long tail on the negative side of the PDF that can be diagnosed from negative skewness (Fig. 3a). This suggests low-frequency covariability between the distribution’s mean and skewness (Monahan 2004). These changes in the 5-day zonal wind PDFs are echoed by similar variability patterns in the zonal stress PDFs (Fig. 3b). Increases in the mean zonal wind are associated with extreme zonal stresses (exceeding the 90th percentile ≈ 0.4 Pa; Fig. 3b, green dashed line), and weak zonal winds coincide with exceptionally weak zonal stress (episodes in September and December in Fig. 3). This covarying behavior of mean and skewness distinguishes the derived PDFs from a Gaussian PDF, a feature that will be further analyzed in sections 3 and 4.
(a) One year of time-varying zonal wind PDFs. Each pixel indicates the probability of wind occurring in a 0.5 m s−1 wind interval within 5 days. The black dashed lines indicate the PDF mean, and the green dashed lines are the 0.1 and 0.9 quantiles of the climatological distribution. The blue lines in the subpanel show the higher moments of the PDF: variance (m2 s−2), skewness (unitless), and excess kurtosis (unitless). The variance is rescaled by a factor of 0.02. (b) As in (a), but for zonal stress. In this case the variance (Pa2) is rescaled by 10−5.
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
Note that this analysis requires data on short time intervals. ERA5 is one of a few datasets that provides hourly data over the reanalysis period with improved wind statistics compared to ERA-Interim (especially over the SO and along the Antarctic coast; Belmonte Rivas and Stoffelen 2019; Tetzner et al. 2019). Datasets that only provide coarser temporal resolution may miss the dynamics seen in Fig. 3 and likely prohibit possible interpretations of the results.
b. Time-varying PDFs from CCMPv2 and scatterometer winds
We also derive surface wind PDFs using three additional Southern Ocean surface wind products. The CCMPv2 (Cross-Calibrated Multi-Platform version 2.0) winds provide 6-hourly fields on a 0.25° grid. The CCMPv2 dataset is derived from ERA-Interim winds blended with all available wind observations to produce a gridded product: observational gaps between scatterometer swaths are filled with winds from ERA-Interim (Wentz et al. 2015). For this study, data points between these swaths are ignored, and CCMPv2 data are used only if they are informed by one or more observation.
In addition to the blended winds, we also analyze two Level 3 (L3) wind products that are based on the Advanced Scatterometer (ASCAT) aboard the European Meteorological Operational Satellites MetOp-A, MetOp-B, and MetOp-C. Remote Sensing Systems (RSS) provides ASCAT winds on a 0.25° grid for ascending and descending swaths. We treat these as quasi-twice-daily observations (Ricciardulli and Wentz 2016). Similarly, Global Ocean L3 MetOp-A winds from CMEMS (Copernicus Marine Environment Monitoring Service) are also provided twice daily at 0.25° grid spacing [based on the Royal Netherlands Meteorological Institute (KNMI); Driesenaar et al. 2019]. Time-evolving PDFs for 5-day bins are derived for the three scatterometer wind products in the same way as for ERA5. CCMPv2, RSS ASCAT, and MetOp-A ASCAT each provide 4%–13% as many data points as provided by ERA5, with large seasonal variability due to sea ice cover. (Satellite products have a spatial coverage 50%–85% per 5-day period compared to ERA5; see Fig. B1 in appendix B) Here, RSS ASCAT and MetOp-A ASCAT includes data points under rain. Since rain biases are mainly limited to low winds, the results are not expected to be sensitive to them (Driesenaar et al. 2019).
c. Effective degrees of freedom
The data from ERA5 and scatterometer products are spatially and temporally correlated, such that their effective degrees of freedom (DOF) are much less than the number of data points used to establish each 5-day distribution. This effect is illustrated in Fig. 2, where we compare ERA5 PDFs derived from a single time step (1 h, dashed black lines), five days (solid black lines), and the climatology (gray shading). We see that the 5-day PDFs are smooth compared to the 1-day PDFs. The effective DOF is calculated by estimating the spatial and temporal decorrelation scales in ERA5 (appendix B). The effective DOF for the zonal wind u10 is 175 and for the meridional wind υ10 1070. The e-folding scales are 2.4 days and 1100 km in the zonal and 40 km in the meridional direction for u10, and 1.4 days and 130 km in the zonal and 40 km in the meridional direction for υ10 (Fig. B1). These characteristic scales suggest that we can assume each 5-day PDF to be a robust estimate, which implies that differences between successive PDFs are due to changes in physical drivers, rather than uncertainties in the estimate of the PDF. The 5-day joint PDFs have more noise than their meridional or zonal projections because the same number of effective DOF as in the one-dimensional PDFs is now spread over the squared number of spatial data points (Fig. 2c).
d. Principal component analysis of time-varying PDFs
To derive the covariances between the time-varying PDFs, the PDFs of zonal wind
We have decomposed both the one-dimensional PDFs in the zonal and meridional directions, and the joint PDFs. The following analysis primarily focuses on the leading modes in the zonal direction as well as the leading modes from the joint PDFs, because the other decompositions mainly express the same variability (Fig. 4). The cross-correlation between PCs of all decompositions as well as estimates of the nonlinear dependence of the PCs can be found in the online supplemental material.
Squared correlations (explained variances) between leading PCs and the southern annular mode (SAM). Modes in the green boxes are used in sections 3 and 4, namely the first PCs of the
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
The first three EOFs of the zonal and meridional wind PDFs are very similar for all four wind products (Fig. 5; higher modes are in the supplemental material), and each EOF explains a similar fraction of the total variance in the respective data products. The fraction of variance explained exceeds a null-hypothesis threshold defined by decomposing Gaussian noise, implying that the EOF has more structure than we would expect to see if the signal were simply Gaussian white noise (Figs. 5g,h; Preisendorfer N test, Preisendorfer and Mobley 1988; von Storch and Zwiers 1999, ch. 13).
First three leading EOFs of (a),(c),(e) zonal and (b),(d),(f) meridional wind for ERA5 (black), CCMPv2 (blue), RSS ASCAT (orange), and MetOp-A ASCAT (green) with their fraction of explained variance in the title. Explained variance for the first 10 modes in log-scale for the (g) zonal wind and (h) meridional wind PDFs. Gray shading indicates the fraction of variance explained by a decomposition of Gaussian noise (Preisendorfer N test).
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
The first two EOFs of
Note that relative to ERA5, the spatial coverage and amount of data vary between the scatterometer wind products from a minimum of 30% for MetOp-A ASCAT in austral winter to about 85% in austral summer in CCMPv2, and the effective DOF of the scatterometer wind PDFs is substantially less than for ERA5 (appendix B). Despite the varying effective DOF, the decomposition of all scatterometer wind PDFs appears to be robust, even for the joint PDFs that have a weaker signal-to-noise ratio (Fig. 2c and section 2a). Hence, the analysis in sections 3 and 4 focuses on ERA5 because it provides a complete dataset of surface wind and stress PDFs with the highest signal-to-noise ratio. Equivalent results can also be derived from the scatterometer data, although the climatologies of the scatterometer PDFs differ relative to ERA5, as outlined in section 5.
3. Zonal wind and stress covariability and its relation to SAM
In this section we show that the leading modes of the surface stress PDFs, and therefore the ocean’s forcing, are tightly linked to the leading modes in the zonal wind PDFs. For both wind and surface stress, the first two modes explain 90% of the variance, while the PCs of the first and second modes of wind and stress are nearly identical.
Figures 6a and 6b compare the first three EOFs of the zonal wind and zonal stress PDFs from ERA5 with their climatology. The first zonal wind PDF EOF (
Leading EOFs for (a) zonal wind and (b) stress. The climatology is indicated in black, the median with dashed gray lines, and the 0.9 quantiles (12 m s−1 and 0.4 Pa) as green dashed lines. The EOFs’ explained variances are indicated in the legend. (c) PCs of the first mode of zonal wind (
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
The second EOFs of the zonal wind and stress PDFs are both roughly symmetric around their median (Figs. 6a and 6b, dotted gray lines), indicating fluctuations in wind or stress that might be captured by their variance. This mode shows that increases in the likelihood of winds being concentrated near the PDF’s center are accompanied by a roughly symmetric reduction in the likelihood of winds occurring in the tails of the PDF, and vice versa. The PCs of the second EOFs are also well correlated between the wind and wind stress PDFs (correlation coefficient r = 0.92; Fig. 6d) but only explain about 18% of the overall variance in probability density. The PCs of the third EOFs explain even less variance in probability density (<5%) and are close to the noise level (section 2d).
Figures 6c and 6d show the PCs of the leading two EOFs in the zonal wind and zonal stress PDF for 15 years. The similarity between the wind and stress PDF PCs suggests that the zonal stress PDF variability can be mostly explained by the zonal wind PDF. The first two PCs of
(a) Power spectra of
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
The first PCs of the wind and stress PDF exhibit strong year-to-year variability. This variability is coherent with the SAM with zero phase lag on all scales between a month and four years except on the seasonal and semiseasonal cycle (Figs. 7b and 7c; the correlation coefficient of
The second PCs of
Note that, by construction, the EOFs of the PDFs are uncorrelated but not independent. Even though the leading EOFs are an orthogonal, linear independent basis, they can still covary in a more complex fashion. Indeed, the scatter of the first and second zonal wind PDF PCs indicate that very strong, or very weak events of PC1 are more likely during a negative PC2; that is, extreme zonal stresses are more frequent during short events in austral winter (March–October) and less frequent in austral summer (December and January; see the supplemental material). This shows that the derived basis set is neither completely independent nor necessarily unique, and that there are some richer dynamics on the seasonal scale that are not explored at this point (Fig. 7a). Nevertheless, we show in the following sections 5 and 6 that even the linear, empirical decomposition used here is useful for simplifying and elucidating the leading-order dynamics.
4. Synoptic variability in the joint wind and stress PDF decompositions
In this section, we extend the analysis of the zonal wind and stress PDF covariability to include the meridional component. This allows us to represent a significant fraction of variance with a small number of functions, which also reveals the synoptic-scale drivers of the variance. Figure 8 shows the first two EOFs of the joint surface wind (uPDF EOF1 and uPDF EOF2 in Figs 8c,d) and the joint surface stress (τPDF EOF1 and τPDF EOF2 in Figs 8f,g), as well as the projected means in the meridional and zonal directions (Figs 8a,b,e,h,i,j). The first two modes of the joint surface wind PDF show the same patterns as the one-dimensional decomposition, but they explain less variance (together 58% of the total variance). A smaller fraction of explained variance is not surprising since the joint decompositions have to represent the variance for the square of the number of grid points compared to the one-dimensional decomposition.
(a),(b) Meridional mean of the first (blue) and second (blue dashed) joint wind EOFs. Also shown are the first two EOFs of the joint PDFs of (c),(d) wind and (f),(g) stress and their projections, as well as (e) the zonal mean of the first and second joint wind EOFs, (h) the zonal mean of the first (red) and second (red dashed) joint stress EOFs, and (i),(j) the meridional mean of the first and second joint stress EOFs, respectively. The orange and green dots in (c) and (f) indicate the maximum and minimum of the respective EOF. The shading for stress modes is adjusted following a (·)1/4 scale.
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
The first joint wind mode (uPDF EOF1; 41% variance explained) includes the variability of the
In addition to enhancing eastward zonal winds, this SAM mode of the joint PDF EOF corresponds to a poleward shift of the PDF’s maximum (similar to
The cyclones’ imprint on the surface wind PDFs is characterized by intensified winds in the cyclones’ cold sectors that shift the PDF maximum toward more frequent strong westerlies (Fig. 9a, horizontal red arrows). The stronger westerlies are accompanied by intense, but narrow southward flow ahead of the cold front (low-level jet; Fig. 9a, curved red arrow). These cold-front winds add the southward inclination of the dipole pattern of the joint PDF (Fig. 8c, green dot). The surface winds on both sides of the cold front imprint on the first EOFs for both wind and stress PDFs. While the joint wind PDF’s maximum shifts along a diagonal through the PDF’s median (Fig. 8c black dot), the joint wind stress PDF weakens at the peak and is enhanced mainly in the southeastward direction (Figs. 8f and 8g, orange and green dots, note the nonlinear color scale). At times when the first PC is positive, the EOFs indicate less equatorward flow and less weak zonal wind regimes, as they typically appear in the wake of an eastward propagating storm (gray arrows in Fig. 9a correspond to orange dot in Fig. 8c).
Schematic of surface winds in the moving frame of an extratropical cyclone in the SH for (a) positive and (b) negative SAM inferred from Shapiro and Keyser (1990), Neiman and Shapiro (1993), Bengtsson et al. (2009), Catto (2018), and Sinclair et al. (2020). In (a) strong westerly winds behind the cold front and alongfront winds ahead of the cold front (in red) are enhanced during positive SAM phase. In (b) southeasterly winds not associated with the cold front (in blue) are enhanced during negative SAM. Light gray lines show idealized sea level pressure lines, and the orange arrow indicates the average travel direction of the cyclone.
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
The leading mode of the joint PDF can be understood as a measure of the cyclone activity in the latitude limits of Drake Passage. The cyclone activity is highly coherent with SAM (Fig. 7b blue line; power spectra of uPDF PC1 and
The second joint wind mode has a more circular structure and captures changes in the width of the joint PDF (Fig. 8, explained variance 16%). The projections of the uPDF EOF2 on the zonal and meridional axes are similar to the
The second mode of the joint wind PDF also leads to a dipole in the joint stress PDF [r(τPDF PC2, uPDF PC2) = 0.84]. The dipole structure arises because the second joint wind EOF is not precisely symmetric. Nevertheless, the second joint stress mode is mostly confined around the origin (within ±0.2 Pa), which illustrates again how changes similar to the wind’s variance are not solely responsible for extreme surface stresses. Higher-order modes are not judged to be statistically different from what we would expect to find by computing EOFs of Gaussian noise and are not explored here (Fig. 10; Monahan and Fyfe 2006).
Explained variances for the joint wind PDF (in blue) and the joint stress PDF (in red) on a log scale. The orange and light blue lines show the 95% levels for the joint stress and wind estimated from the Preisendorfer and Mobley (1988) N test after 1000 repetitions.
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
5. Differences in reanalysis and scatterometer products
The leading-order modes of the surface wind PDFs provide a framework for interpreting differences between surface wind products. Figure 11 shows climatologies of meridional and zonal wind PDFs derived from ERA5 (1979–2017), CCMPv2 (1978–2017), RSS ASCAT (2007–16), and MetOp-A ASCAT (2007–16). The log-scaling exposes velocity differences of up to 30% at a given probability density level (for
PDFs of (a) zonal and (b) meridional wind between 55° and 63°S derived from ERA5 reanalysis (black), observationally constrained CCMPv2 winds (blue line and shading), MetOp-A ASCAT (green), and RSS ASCAT scatterometer winds (orange) with log scaling. The scaling on the right ordinate is the area equivalent for a given probability density in 103 km2. (c),(d) As in (a) and (b), but shown as ratios compared to the ERA5 PDF. (e),(f) As in (a) and (b), but shown as differences from the ERA5 PDF for zonal and meridional wind, respectively.
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
Differences near the PDF centers fall into two simple patterns that approximately match the leading EOFs for the
(a) Zonal wind and (b) meridional wind statistics in the Drake Passage limits as box-and-whisker plots for ERA5 (gray), CCMPv2 (blue), MetOp-A ASCAT (orange), and RSS ASCAT (green). The boxes indicate the limits of the first and third quartiles surrounding the medians (horizontal black lines), and the whiskers indicate the 1% and 99% quantiles. The colored dots are the mean centered between the range of ±1 standard deviation (dashed lines between triangles).
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
A different behavior appears in the meridional direction (Figs. 11b,d,f). The scatterometer PDFs show a symmetric difference relative to ERA5 and CCMPv2, with fewer winds around zero and more winds at about ±10 m s−1. This widening of the PDF implies a difference in variance (section 3). However, these differences are not well captured by the variance metric because differences in the center may be partly compensated by differences in the tails such that changes in variances are rather small (Fig. 12b dashed lines). As an alternative to the metrics provided by mean and variance, the climatological bias pattern in Fig. 11f is better understood as resembling the
This analysis shows that differences between scatterometer-based products and model-based winds (ERA5) are systematic, and resemble the signatures of SAM-related wind variability (sections 3 and 4). Moreover, these results imply that estimates of SO winds can be improved by combining observed winds with constraints from larger-scale dynamics.
6. Leading modes of the most extreme winds
Informed by the differences between PDFs for different wind products, we can now investigate the leading modes for the most extreme values in the
First EOFs of the (a) zonal and (b) meridional wind added to their climatology and shown on a log scale. Data between ±21 m s−1 are masked out to emphasize the variability in the tails.
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
The first
The first
We note that here the SVD decomposes the covariances of very different scales and must be treated with caution. The SVD is an axis rotation along the most common mode of variability in the covariance matrix and these axes (EOFs) are mainly defined by fluctuations in the PDF centers [O(10−2)], while small fluctuations in the tails [O(10−6)] only marginally contribute to the modes of the covariance matrix.
To test the robustness of the modal decomposition, we rederive the SVD for the log-PDFs log[D(u, t)]. Use of the log enhances the variability of the tail compared to fluctuations in the center. The overall shape of the leading-order modes remains robust under a log-weighting for all wind products but with less explained variance for the first modes (supplemental material). The enhancement of the most extreme winds in the u10 PDF EOF1, as observed in Fig. 13, also remains robust, while changes in the υ10 PDF EOF1 are not.
7. Discussion
a. Large-scale circulation establishes surface winds and stress PDFs
As we showed in section 3, the time evolution of the first two modes of both the one-dimensional and joint surface wind PDFs resembles that of the leading modes in surface stress PDF (Figs. 4 and 6). These two modes trace changes in the conversion of excess atmospheric angular momentum to surface momentum fluxes, without explicitly resolving the cascade of processes involved in converting atmospheric momentum to stress.
The first mode is mainly a positional shift of the zonal wind PDF maximum that leads to more frequent extreme zonal stresses (>0.4 Pa; Figs. 6a,b) accompanied by changes in the PDF’s shape. Southern Ocean zonal surface winds are negatively skewed and limited in their extremes (>12 m s−1) due to their nonlinear relation with surface drag [Eq. (1)]; we showed that a shift in the PDF maximum does not imply a proportional increase in the PDF’s extreme quantile (Figs. 3 and 6a). Instead, the higher-order dependence of surface stress on wind leads to changes in the mean, skewness, and kurtosis; this is captured in the first EOF (PC1
Explained variances between PCs from the SVDs of directional wind and stress and first four moments of the PDF. Explained variances are shown for measures of zonal surface wind (u10), meridional surface wind (υ10), east–west stresses (ewss), and north–south stresses (nsss).
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
The EOF decomposition of the time-varying joint PDFs adds a meridional component to predominantly zonal wind and stress variability. As the zonal wind PDF maximum increases in the leading-order mode, the meridional component shifts southward (Figs. 8c,e). This joint mode is highly coherent with SAM as a measure of the zonal-mean zonal wind in the free troposphere (Thompson and Woodworth 2013; Thompson and Barnes 2014).
Our analysis indicates some relation between the dynamics that establish SAM and perturbations of the (mainly zonal) wind statistics. We hypothesize that the changes in the shapes of the PDFs are the reason why the first mode EOFs can be related to dynamical drivers, as we outline below. This is potentially one of the few examples where EOF decompositions of the variance align well with a dynamical interpretation (section 3).
Dynamical links are not required to create patterns like the uPDFor τPDF EOF1s, but in this case the patterns result from links across several dynamical scales. One could design a two-dimensional shape function that accounts for deviations of a joint wind PDF from a two-dimensional Gaussian as it changes its mean zonal wind (Thompson et al. 1983; Monahan and Fyfe 2006, 2009). By requiring that the mean meridional winds as well as the zonal skewness and kurtosis correlate with the mean zonal wind (section 2d; Fig. 14), one would obtain a modeled PDF with a shape that changes systematically with perturbations of the mean zonal wind. A decomposition of a perturbation ensemble of this modeled joint PDF (section 2a) would then return a dipole patterns that could look like Figs. 8c and 8d. This statistical exercise would mimic some of the physical constraints that stem from the nonlinearities in the atmospheric boundary layer (ABL). While the statistics of synoptic-scale eddies (i.e., storms) alter the mean wind components, asymmetric PDF shapes result from the perturbations of the ABL by the mean and the synoptic scale (Monahan 2006a). Hence, SAM can be interpreted as an integrator of synoptic-scale ABL perturbations that results in characteristic wind and stress distribution changes in the tails of the distribution.
In our analysis we find the PDF’s covariability with SAM to be intrinsic for the empirically derived modes. This is interesting, because SAM is a proxy for the eddy-momentum flux convergence in midlatitudes (Karoly 1990; Feldstein and Lee 1998; Hartmann and Lo 1998; Limpasuvan and Hartmann 2000; Lorenz and Hartmann 2001) and hypothesized to be altered with climate change [as summarized in Screen et al. (2018)]. This would suggest that the interaction between eddy activity and the surface establishes the leading mode of the joint stress PDF (section 4). In this context we suggest that SAM is better viewed as a tracer for intensity of fronts and/or latitudinal shifts in the storm activity, rather than changes in the zonal mean surface winds (Lorenz and Hartmann 2001; Fig. 8) because this storm activity dominates the surface wind distribution over the SO (Fig. 9; Lin et al. 2018). Hence, we think we can go beyond a statistical interpretation of the empirical modes. Based on our observations, we outline in the following paragraphs how the observed leading joint PDF EOFs are consistent with dynamics that are linked to the transformed Eulerian mean (TEM) circulation (Andrews and McIntyre 1976, 1978; Edmon et al. 1980), part of which are captured by SAM (section 3, section 4, and Fig. 7).
The approximate short-term zonal-mean balance [Eq. (4)] also suggests a hypothesis for the origin of the observed dipole structure in uPDFand τPDFEOF1. While the off-zero center of the joint distribution (Figs. 8c,f, black dot and Fig. 2c, black contours) again represents the climatological balance of surface drag against upper-level eddy momentum flux convergence, the dipole in the EOF1 patterns is a signature of variability that one would expect from synoptic adjustment processes of the TEM circulation. By sampling in 5-day increments, we have sufficient temporal resolution to distinguish adjustments that seem to perturb the meridional overturning circulation, including its Eulerian part, the “Ferrell cell” (Vallis 2006, ch. 11.7). The wind and stress EOFs vary in response to perturbations of the eddy momentum flux convergence aloft that are partly balanced by meridional flow near the surface (“downward control”; Haynes et al. 1991). It means that anomalously strong momentum flux convergence (i.e., positive SAM) is partly balanced by equatorward flow, which in turn leads to poleward (southward) flow near the surface to conserve mass. This anomalous poleward Coriolis acceleration in the boundary layer leads to anomalous zonal surface winds and stresses (Figs. 8c,f, green dots; Peixoto and Oort 1992, ch. 11; Limpasuvan and Hartmann 2000). Hence, it is plausible that the observed dipole structures of the leading joint PDF modes are created by the superposition of the vertically integrated balance suggested in Eq. (4) and dynamic adjustments that are needed to maintain this balance. While the processes described here are still at the hypothesis stage, we suggest that idealized model studies should be able to elucidate the role of large-scale adjustment processes on surface stress statistics.
At the surface, this strong coherence between SAM and the leading modes also reveals how SAM relates to extreme winds within synoptic-scale systems (Claud et al. 2009; Booth et al. 2010). A positive SAM increases the probability of wind patterns that are associated with fronts under storms (Fig. 9a, red arrows; Rudeva and Simmonds 2015). Extreme zonal winds and stresses behind the cold front and stronger southward stress ahead of the cold front lead to the southeastward shift of the maximum in uPDF EOF1 and τPDF EOF1 (Figs. 6a,b and 8c,f). In turn, a negative SAM is associated with fewer extreme westerly winds (or even no predominant westerly winds) and instead enhanced equatorward winds and stresses from the southwest. This SAM mode can be attributed either to shifts of the cyclone centers (storm tracks) into or out of Drake Passage latitudes (Lorenz and Hartmann 2001) or to changes in their intensity (Shaw et al. 2016, 2018). Either mechanism alters the wind and stress PDFs, with an EOF pattern that also extends to the tails of the PDF (section 6; Sampe and Xie 2007; Lin et al. 2018).
The second mode of variability is by construction linearly independent of the first mode, but there are higher-order dependencies (see the supplemental material). The second mode describes symmetric contraction and widening of the PDF that can be captured by a change of the variance, with small changes in the mean (Figs. 5b, 6, and 14). This mode explains about 18% of the zonal and 53% of the meridional wind variability, mainly due to changes on annual and semiannual time scales (Figs. 7a and 14). It is symmetric and concentrated around the PDF’s center with little or no influence on extreme winds and only mild impact on extreme stresses (Figs. 8d,g).
b. Implications for the SO eddy activity
We have shown that SAM variability and trends represent more complex changes of the atmospheric forcing than just changes in the mean winds and stresses. This provides a new perspective on the observed increase of eddy activity in the SO that is accompanied by only weak changes in the SO zonal transport (“eddy saturation”; e.g., Hallberg and Gnanadesikan 2006; Meredith and Hogg 2006; Böning et al. 2008). While changes in the mean zonal wind stress (i.e., a trend in SAM) may change the larger-scale SO baroclinicity and subsequent mesoscale eddy activity (Thompson and Solomon 2002; Meredith et al. 2012), sections 3 and 6 show that trends in SAM also have a significant impact on extreme stress statistics. Extreme localized wind stress under storms (sections 4 and 7c) can imply stronger wind stress curls leading to localized strengthened Ekman pumping (e.g., O’Neill et al. 2003, 2005; Schneider 2020), which then interact with the mesoscale eddy field. In addition, extreme winds under storms also enhance near-inertial oscillations in the upper ocean (Pollard 1980; Thomson and Huggett 1981; Gill 1984; D’Asaro et al. 1995) and can possibly provide energy for the mesoscale eddy field (Xie and Vanneste 2015; Asselin and Young 2020). Hence, we speculate that a positive SAM trend could increase upper-ocean mesoscale activity by increasing wind extremes, in addition to increasing the mean wind speed and subsequent balances of the larger-scale baroclinicity.
c. Interpreting the leading-order mode as a dominant mode of SO atmosphere–ocean interaction
The empirical decomposition of surface wind and stress into two leading modes leads us to ask which mode is responsible for strong air–sea fluxes of energy, momentum, freshwater, and gas associated with SO mixed layer ventilation events (Schulz et al. 2012; Ogle et al. 2018; Tamsitt et al. 2020) and marine cold-air outbreaks (Bracegirdle and Kolstad 2010; Papritz et al. 2015; Fletcher et al. 2016). While SO mixed layer ventilation is observed to be driven by extreme turbulent heat fluxes that often coincide with equatorward winds advecting cold air from the south (Ogawa and Spengler 2019; Bharti et al. 2019; Tamsitt et al. 2020; Song 2020; Song et al. 2020), the same process, described as a marine cold-air outbreak, leads to atmospheric boundary layer deepening (Grossman and Betts 1990; Brümmer 1996; Renfrew and Moore 1999) and affects the synoptic-scale circulation (Papritz and Pfahl 2016). The other possibility of anomalous mixed layer deepening due to purely mechanical forcing from strong zonal winds is unlikely because turbulent kinetic energy fluxes alone are less effective at mixing a stratified boundary layer (Alford 2020). In addition, zonal winds are also likely less effective in maintaining the surface temperature gradients needed for large buoyancy fluxes (Ogle et al. 2018; Tamsitt et al. 2020).
Equatorward winds occur during a negative SAM mode (Figs. 8c,e and 5d) and also during a negative second mode (∝ increasing variance; Figs. 8d,e and 5b), while both modes show some higher-order dependence (supplemental material). Both modes, or their superposition, could capture events that create strong air–sea fluxes associated with mixed layer ventilation and marine cold-air outbreaks. While this second mode has a dominant seasonal cycle, as observed in the mixed layer ventilation (dashed orange-red line in Fig. 7; Tamsitt et al. 2020), SAM explains 67% of the wind variance (Fig. 4) and 33% of the stress variance (not shown).
We suggest that SO mixed layer ventilation is a result of the superposition of SAM and oceanographic preconditions such that enhanced equatorward winds during negative SAM are likely to be conducive to increased turbulent heat fluxes by winter cold air advection (section 4; Fig. 9b). This mechanism is plausible even when taking into account observed long-term trends of SO ventilation and heat content (Gille 2008; Sallée et al. 2010), SAM-like variations in SO mixed layer depths (Cerovečki et al. 2019; Meijers et al. 2019), and the long-term trend to a more positive SAM with more westerly wind extremes in the Drake Passage latitudes (Thompson et al. 2000; Thompson and Solomon 2002; Lin et al. 2018). Because mixed layer ventilation relies on additional limiting factors like seasonal changes in the meridional surface temperature gradient, local insolation, and mixed layer stratification, it is likely that the northward advection of cold polar air during negative SAM modes is more effective in winter when thermodynamic preconditioning favors mixed layer ventilation. This is in agreement with observed mixed layer ventilation and marine cold-air outbreak events that occur preferentially in austral winter (Papritz et al. 2015; Fletcher et al. 2016; Tamsitt et al. 2020): even if SAM exhibits weak seasonality (Fig. 7a) and a small, long-term trend to more positive values, its negative phase is likely the important contributor to trends in highly nonlinear atmosphere–ocean interactions. We hypothesize that exceptionally strong westerly winds (positive SAM) are not enough to drive deep mixed layer ventilation, because they are not the only factor in determining ocean ventilation and they are also not observed as the dominant mechanism perturbing the atmospheric boundary layer.
Even though we do not explicitly analyze atmosphere–ocean heat fluxes in this study, the oceanic and atmospheric processes outlined above suggest that equatorward winds are important for the evolution of both boundary layers and for the exchange of heat and CO2. As suggested above, upper tropospheric wave breaking controls the statistics of equatorward surface winds, but it can only control the statistics of intensified atmosphere–ocean fluxes if the ocean stratification is responsive to the atmospheric forcing.
d. Dynamic drivers of climatological differences
The leading modes of zonal and meridional winds resemble the climatological differences between ERA5, CCMPv2, RSS ASCAT, and MetOp-A ASCAT (section 5). These differences also extend to the PDFs’ most extreme values (Fig. 11; Gille 2005). The probability of velocities larger than ±20 m s−1 is about 100 times higher for CCMPv2 and RSS ASCAT than for ERA5 and MetOp-A ASCAT.
These climatological differences also appear in the most extreme values of the leading EOFs (section 6). We found more extreme wind events during positive SAM in RSS ASCAT products than in ERA5 or MetOp-A ASCAT products. However, SVD results from the PDF tails must be treated with caution because a distribution’s tail is the least certain portion of a PDF given the rarity of these most extreme events, and the covariance is largely determined by the PDF’s center (section 6 and appendix B).
These results agree with central-moment-based validations of reanalysis surface winds (Monahan 2006a) in which ERA5 winds show systematic differences compared to ASCAT and wave-buoy observations (Belmonte Rivas and Stoffelen 2019; Yagi and Kutsuwada 2020). Additionally, the analysis in section 5 hints at reasons why reanalysis surface winds differ (Taboada et al. 2019; Wen et al. 2019; McDonald and Cairns 2020): since differences in surface wind PDFs resemble the leading mode of atmospheric angular-momentum flux convergence (section 7a), they might arise, whether from reanalyses or scatterometers, from errors in the parameterization of boundary layer turbulence or wind retrieval algorithms, errors in representing mesoscale processes associated with cold fronts (Blein et al. 2020), or large-scale biases in the reanalysis momentum budget (Pithan et al. 2016).
The high correlation of the large-scale flow and interproduct surface wind differences can potentially improve surface wind products and subsequently surface wave models (Durrant et al. 2014; Wentz et al. 2015; Ribal and Young 2020; Trindade et al. 2020; Allen et al. 2020). Spectral wave models rely on accurate surface winds and are particularly sensitive to surface wind extremes (Cavaleri 1994; Cardone et al. 1996; Ponce and Ocampo-Torres 1998; Feng et al. 2006; Durrant et al. 2013; Stopa and Cheung 2014; Janssen and Bidlot 2018; Osinski and Radtke 2020). Due to the differences described above and deficits in the momentum balance of atmospheric general circulation models (Pithan et al. 2016), wave hindcast models are commonly tuned to wave buoy observations by adjusting high surface wind speeds. This practice cannot be applied in “free-running” surface wave models as part of coupled climate models (Li et al. 2016; Bourassa et al. 2019) because biases in the model mean state of other model components hinder direct validation with in situ observations. At the same time, including surface wave models in a coupled model framework might improve estimates of Cd, which plays a critical role in shaping the surface stress PDF (section 7a; Edson et al. 2013) as well as the large-scale atmospheric flow (Mbengue and Woollings 2019).
8. Conclusions
Southern Ocean surface winds play an important role in ventilating the upper ocean, mainly through short, extreme events of atmosphere–ocean interaction. This study has investigated a statistical representation of surface wind and stress PDFs that connects large-scale modes of atmospheric variability with short-term processes at the atmosphere–ocean interface.
We have derived leading modes of variability of PDFs of surface winds and stresses between 55° and 63°S using four wind products (ERA5, CCMPv2, RSS ASCAT, MetOp-A ASCAT). After calculating time-varying PDFs from all available data points in longitude and latitude in 5-day chunks, we use an SVD of the zonal, meridional, or joint PDF. The first two modes of the zonal or meridional wind together explain 90%–92% of the total variance, while the first three modes of the joint wind SVD explain about 65% of the total variance. These decompositions are robust between the wind products, despite differences in their degrees of freedom (section 2d and appendix B).
The first two PCs of the surface stress PDFs explain an equivalent or greater fraction of variance than the first two PCs of the wind PDFs (Figs. 6 and 10), and the temporal variability of the leading wind stress modes (PC1 and PC2) is nearly identical (section 3). This surprising covariability occurs despite the different noise levels in their SVDs (Fig. 6), and may appear because the joint stress PDFs are functionally related to the joint surface wind PDFs [Eq. (1); Monahan 2008].
We would like to put the result in the broader context of atmosphere–ocean coupling:
PDFs, used in place of mean quantities, are a cornerstone of stochastic climate modeling (Hasselmann 1976). Here we have expanded on this idea, but, instead of creating PDFs for large ensembles (Kay et al. 2015; Maher et al. 2019; Deser et al. 2020; Reimann and von Storch 2020), we have assumed that the governing processes are ergodic in the latitudes of Drake Passage and over short time periods. This has allowed us to derive a time-evolving PDF from a single realization of the winds (here ERA5 reanalysis or direct scatterometer winds). The leading-order variability of the wind PDFs can then be analyzed using an SVD and compared to other models or wind-products. We choose a standard SVD in order to reduce the complexity of the PDF variability to a set of linearly independent lower-dimensional EOFs, although other forms of modal decomposition might be similarly illuminating. One might imagine that analyses that do not constrain orthogonality (rotated EOFs) or incorporate oscillatory behavior (like POPs) would be better for identifying dynamical drivers of the PDF. However, we have shown that even the leading modes of standard EOFs of surface wind and stress PDFs can be related to the leading-order terms of the zonal momentum balance modes [Eq. (4)]. EOFs are an efficient way of capturing larger-scale modes of atmospheric variability (SAM) in surface fields.
We suggest that the leading modes of decomposed PDFs are dynamically linked to larger-scale drivers. We point out that these links are imperfect because EOF analysis can in general not reconstruct isolated degrees of freedom of a system (Monahan and Fyfe 2006). EOFs of any kind always decompose the variability to a linear basis set that cannot align with the dynamic drivers of a nonlinear system as in this analysis (Figs. S4a,b in the online supplemental material). In addition, the time-varying PDFs themselves are already a reduced representation of the variability, while their decompositions are generic and can be approximated by derivatives of their shape. Given these simplifications, it is interesting that the dynamics that close the zonal momentum balance can apparently be explained by the leading PDF modes (section 7a).
We showed that only using the first two moments as a basis for air–sea flux estimates is insufficient [also shown by Monahan (2008)]. This assumption is usually made when wind speed is modeled as a Weibull distribution, which can be estimated from independent Gaussian distributions in u and υ, with a nonzero mean wind (Hennessey 1977; Justus et al. 1978; Monahan 2007). Deviations from the Weibull distribution can be captured by higher-order moments (Monahan 2006b), but their relations require many degrees of freedom to be well constrained. The SVD of time-varying PDFs used here needs fewer degrees of freedom per time interval to constrain the PDF tails (Fig. 13 and section 2c), and the superposition of a few modes explains most of the time variation of the PDF.
SVDs of surface wind PDFs connect scales of upper-level Rossby wave breaking [SAM, O(106) m] with surface winds on the O(104) m scales resolved by scatterometer retrievals. This means that scatterometer observations over the SO can be directly related to the large-scale flow of the atmospheric interior [similar to the two-layer model shown in George et al. (2019)]. In addition to validating cyclone intensities in general circulation models and reanalyses, scatterometer winds provide an independent constraint on the atmospheric angular momentum balance on short time scales.
SVDs of the surface stress PDFs often show a higher signal-to-noise ratio (S/N) than surface winds because they have a steeper decay in the eigenvalues (e.g., Fig. 10). Given that the leading modes of wind and stress capture the same underlying process, the S/N in the commonly analyzed surface winds is likely weaker than in surface stress because of their square relationship [Eq. (1)]. Since scatterometers observe surface capillary waves, which are more closely related to surface stress than to surface winds, we would expect that capillary wave roughness has an even higher S/N than found in this analysis. The initial S/N from capillary wave roughness is reduced when converting to 10-m winds, and only partly recovered again when 10-m winds are converted to stress, due to assumptions about the lower 10 m of the atmosphere, surface waves, and temporal or spatial averaging.
We demonstrated that retaining the full PDFs of variables, rather than reducing them to the moments of the PDF, can be a useful tool to understand the physical processes likely to govern wind variability. This approach is especially relevant when observing variables near the surface because they are often the result of nonlinear processes that create non-Gaussian distributions. Any kind of spatial or temporal averaging will tend to change fluctuations in the PDF tails. Depending on the averaging scale, the resulting PDFs can be more Gaussian-like, or even more skewed (Proistosescu et al. 2016; Monahan 2018). Even the hourly, 0.25° wind and stress data used here are an approximation to the PDF that would arise from instantaneous point observations. The time and spatial scales that would be required for a sufficient PDF are related to the scales at which momentum is transferred to the ocean. This scale is described by the adjustment time scale of the equilibrium range of the surface wave spectrum (Phillips 1985).
Acknowledgments
MCH and STG were supported by the NASA Ocean Vector Winds Science Team (NASA award 80NSSC19K0059). BDC and STG also received support from the NASA Surface Water and Ocean Topography Science Team (NASA awards NNX16AH67G and 80NSSC20K1136). This study forms a portion of the Ph.D. dissertation of MCH. We thank Adam Monahan and two anonymous reviewers for their thoughtful reviews that have helped to improve this study.
Data availability statement
Data were generated using Copernicus Climate Change Service Information (Hersbach et al. 2018a,b). This study has been conducted using E.U. Copernicus Marine Service Information (accessed 2019). CCMP version-2.0 vector wind analyses are produced by Remote Sensing Systems. Data are available at www.remss.com. C-2015 ASCAT data are produced by Remote Sensing Systems and sponsored by the NASA Ocean Vector Winds Science Team. Data are available at www.remss.com.
APPENDIX A
Analysis of the Larger SO
To test the robustness of the Drake Passage PDFs, the joint PDFs of surface wind and stress are rederived for 25°–65°S to cover the larger SO. Figure A1 compares the EOFs derived for the latitudes of Drake Passage (55°–63°S; black) with EOFs from the SO (red). The figure also shows the EOF decomposition for CCMPv2 winds for the larger SO latitude range.
Leading three EOFs of zonal surface (a)–(c) wind and (e)–(g) stress derived from data in the latitude range of Drake Passage (55°S and 63°S) using ERA5 (black) and for the SO (25°S and 65°S, red for ERA5 and blue for CCMPv2). (d),(h) Explained variances for surface wind and stress with the significance levels derived as in Fig. 5.
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
The first PCs for the larger SO 5-day records explain less variance than do PCs for the Drake Passage latitude band, but the leading-order EOFs have the same shapes in both cases (Fig. A1). A higher noise level and hence less explained variance leads to weaker EOF amplitudes that are less well separated (Fig. A1d). The PCs of the leading modes derived for the SO correlate well with the PCs of the leading modes derived for Drake Passage when the SVDs are performed in one direction only (Fig. A2). The joint PDFs correlate less well, due to the different noise levels and more subtropical wind regimes and/or coastal winds in the large SO case. The larger SO includes additional processes that result in more Gaussian-like primary modes (Fig. A2, right panels).
Correlation of the three leading modes of the zonal
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
APPENDIX B
Effective Sample Size
Autocorrelations and time scales for zonal (red dash-dotted) and meridional wind (light blue) in the (a) zonal and (b) meridional direction, as well as (c) time. (d) Effective degrees of freedom (DOF) and coverage for ERA5 (black), CCMPv2 (blue), ASCAT (red), and MetOp-A ASCAT (orange).
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
The number of data points differs between the products because the spatial coverage and time steps differ. To calculate Neff for CCMPv2, RSS ASCAT, and MetOp-A ASCAT, we adjust N and ρtime(k). The autocorrelation ρtime is adjusted by a factor of 1/6 for the 6-hourly CCMPv2 data and by a factor of 1/12 for the twice-daily RSS ASCAT and MetOp-A ASCAT data. Figure B1d shows the effective DOF for
APPENDIX C
Southern Annular Mode
The southern annular mode (SAM) is derived from hourly zonal-mean ERA5 zonal wind data that are averaged to 5-day means (Hersbach et al. 2018b). We closely follow Thompson and Woodworth (2013) by first deriving the seasonal anomalies for each 5-day period between 1000 and 50 hPa from 1979 to 2017 at each grid point. The seasonal anomalies are weighted by the square root of the cosine of latitude and by mass, while the latter is estimated from the pressure levels prior to performing the SVD (Thompson and Wallace 2000). Figure C1 shows the results of the SVD of the zonally averaged zonal wind. The leading-order mode of this decomposition is defined as the southern annular mode in this study. SAM derived from geopotential heights rather from zonal winds leads to a nearly identical mode of of variability, and for this study we chose to use zonal wind because of its direct relation to the zonal momentum equation.
Southern annular mode decomposition. (a) First EOF of the zonal mean zonal wind between 20°S and 90°S in the troposphere. (b) Example of the corresponding first PC. (c) Explained variance for each mode.
Citation: Journal of Climate 34, 13; 10.1175/JCLI-D-20-0629.1
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