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).