1. Introduction
Ocean winds are an important element of the global climate system, influencing (and being influenced by) surface fluxes of momentum, energy, and mass (e.g., Taylor 2000; Jones and Toba 2001; Donelan et al. 2002). As well, sea surface winds represent a potentially significant energy resource (e.g., Liu et al. 2008; Capps and Zender 2009). Until recently, statistical characterizations of surface winds across the global ocean were not possible on fine space and time scales. Buoy-mounted anemometers measure wind at fine temporal resolution (e.g., 10-min or hourly averages), but are virtually absent throughout most of the open ocean. In contrast, ship-based observations provide larger-scale coverage, but the transience of the observation platforms and the concentration of ship tracks along major shipping routes result in only a small number of observations in a typical finescale domain (e.g., a 1° × 1° box) within any typical month (e.g., Monahan 2006a; Risien and Chelton 2008). Furthermore, these ship-based estimates are heterogeneously distributed in space and time even within any such domain, complicating estimates of the temporal structure of surface wind variability on submonthly time scales.
With the advent of remotely sensed observations of vector winds, it has become possible to characterize global surface wind statistics on fine scales in space (1° × 1° or finer) and time (daily mean or finer). For example, global-scale 25-km resolution climatologies of surface wind stresses, along with their divergence and curl, were presented in Chelton et al. (2004) and Risien and Chelton (2008). These analyses produced a spatially high-resolution characterization of large-scale wind forcing and revealed fine details in the surface flow resulting from local-scale air–sea interactions. Sampe and Xie (2007) produced a global climatology of the frequency of high wind speeds (exceeding 20 m s−1), relating maxima in occurrence frequency to the influence of large-scale dynamics and local surface stability and orographic effects. Chavas and Emanuel (2010) used scatterometer winds to develop a climatology of tropical cyclone size. The first global-scale observationally based characterization of the probability distribution function of day-to-day fluctuations in sea surface winds (both vector and wind speed) was presented in Monahan (2006a). This analysis revealed the existence of large-scale structure in the shapes of the probability distributions of the vector winds and wind speed, which could be understood mechanistically using an idealized model of the boundary layer momentum budget (Monahan 2004, 2006a, 2007).
The acf of surface winds is physically relevant as it characterizes the time scales governing wind variability; by the Wiener–Khinchin theorem, the acf of a stationary process is the Fourier transform of its variance-normalized power spectrum (e.g., von Storch and Zwiers 1999). As the contribution of higher frequencies to the variability increases, the memory as measured by the acf decreases. Determination of these dominant time scales allows wind variability to be characterized as “fast” or “slow” relative to other components of the climate system. For example, the acf structure of surface winds enters into studies of air–sea coupling exploiting the time scale separation between fast winds and slow sea surface temperatures (e.g., Frankingoul and Hasselmann 1977; Sura and Newman 2008; Ciasto et al. 2011; Monahan and Culina 2011). Furthermore, the autocorrelation structure of surface winds is of relevance to their statistical predictability, as it provides a measure of how much information regarding the state of the winds at time t + s is carried in knowledge of the state of the winds at time t (e.g., von Storch and Zwiers 1999; Lange and Focken 2005).
In an analysis of sampling errors associated with scatterometer surface wind observations, Schlax et al. (2001) computed the acf of the zonal and meridional wind components at a number of locations in the western North Pacific Ocean. It was shown that the vector wind components in this region decorrelate with a time scale on the order of a few days, and that the acf of the meridional wind component decays much more quickly than that of the zonal wind component. Gille (2005), computing frequency spectra of remotely sensed and reanalysis vector wind stresses averaged zonally over 5° latitude bands, found that spectral slopes are relatively steep in the subtropics and high latitudes and relatively shallow in the midlatitudes. Furthermore, Gille found that the meridional wind stresses tend to have shallower slopes than the zonal wind stresses, particularly in the extratropics. Shallower spectra imply proportionally larger contributions from high-frequency variability and therefore are associated with shorter autocorrelation times. We are not aware of any global-scale characterizations of the temporal autocorrelation structure of surface winds that consider both its meridional and zonal variations, or of systematic comparisons between the autocorrelation structure of the vector wind components and wind speed.
The relatively small number of studies of the temporal autocorrelation structure of winds contrasts strongly with the considerable amount of effort that has been directed toward characterizing and understanding the spatial autocorrelation structure of winds in terms of the spatial power spectrum. Particularly since the work of Nastrom and Gage (1985), a number of theoretical and observational studies have considered the spatial power spectrum of free-tropospheric winds; this analysis has recently been extended to surface winds by Xu et al. (2011). Although wavenumber and frequency spectra are simply related for flow that is statistically stationary in time and spatially homogeneous, no such simple connection exists for large-scale surface winds because the vector wind statistics are spatially inhomogeneous.
The goals of the present study are to characterize the lag acfs of sea surface vector wind components and wind speed on global scales, to investigate the relationships between these, and to develop idealized models of these relationships. This analysis makes use of wind data from both the SeaWinds scatterometer and from reanalysis products. Scatterometer winds are obtained from remotely sensed observations of surface wind stress, translated to 10-m winds assuming neutral stratification; the reanalysis winds are obtained by assimilating observations into a numerical forecast model. While the scatterometer data have the benefit of being closer to direct observations of surface winds than wind data from reanalysis products, reanalyses allow consideration of winds over longer time periods and at levels above 10 m. In fact, we will demonstrate that for the statistical quantities being considered in this study, the scatterometer and reanalysis datasets are similar in their essential features (as has been found to be the case for the wind moments; e.g., Monahan 2006b).
Autocorrelation maps at lags of 1, 2, and 3 days for zonal wind, meridional wind, and wind speed computed from the SeaWinds data (and assuming temporally stationary statistics) are displayed in Fig. 1. These maps are not substantially different if the acf is computed separately in different seasons. Inspection of these maps reveals three particularly noteworthy features. First, there is considerable spatial variability in how rapidly the acfs decay: in general, autocorrelation values decrease faster in the midlatitudes than in the tropics and subtropics. Second, values of the wind speed autocorrelations are generally smaller than the larger of the zonal wind or meridional wind autocorrelation values. Third, the vector wind acf is strongly anisotropic in the extratropics: in general, fluctuations in the meridional wind component have shorter memory than those in the zonal wind component. This last fact demonstrates that the vector wind acf anisotropy noted in the North Pacific by Schlax et al. (2001) is present across much of the ocean. As well, this result is consistent with the relatively shallow midlatitude meridional wind stress spectral slopes found by Gille (2005).
Lag autocorrelation fields of (left) surface zonal wind, (middle) meridional wind, and (right) wind speed for lags of 1, 2, and 3 days. These fields were computed from SeaWinds data.
Citation: Journal of Climate 25, 19; 10.1175/JCLI-D-11-00698.1
The data used in this study are discussed in detail in section 2. Section 3 presents a detailed discussion of the vector wind acf anisotropy and its physical origin. The relationship between the autocorrelation structure of wind speed and those of the vector wind components are discussed in the context of an idealized Gaussian model of vector wind fluctuations in section 4. A discussion and conclusions follow in section 5.
2. Data and notation
The primary surface wind dataset considered in this study consists of level 3.0 gridded SeaWinds scatterometer equivalent neutral 10-m zonal and meridional winds between 60°S and 60°N from the National Aeronautics and Space Administration Quick Scatterometer (QuikSCAT) satellite (Perry 2001), available twice daily at a resolution of 0.25° × 0.25° from 19 July 1999 to 23 November 2009. These data are available for download from the NASA Jet Propulsion Laboratory (JPL) Distributed Active Archive Center (http://podaac-www.jpl.nasa.gov/dataset/QSCAT_LEVEL_3). Those data points flagged as having been possibly corrupted by rain were excluded from the analysis. No further processing (e.g., seasonal stratification or time averaging) of the dataset was carried out.
We also consider winds at 10 m and on a number of pressure levels from the 40-yr European Centre for Medium-Range Weather Forecasting (ECMWF) Reanalysis (ERA-40) (available online at http://data-portal.ecmwf.int/data/d/era40_daily/). Relative to the SeaWinds data, the reanalysis winds are of long duration and high temporal resolution (45 years at 6-hourly resolution from 1957 to 2002). The spatial resolution of the ERA-40 winds is relatively coarse (2.5° × 2.5°). As with the SeaWinds data, no further processing of these data was carried out.
Throughout this study, u and υ will denote generic orthogonal horizontal vector wind components. The precise alignment of these components will be arbitrary, unless specifically noted. Zonal and meridional wind components will be denoted by U and V, respectively. The wind speed will be denoted by
3. Anisotropy in vector wind autocorrelation structure
Polar plots (black curves) of the 1-day lag correlation c1(θ) [Eq. (3)] of sea surface vector wind projections around the compass, computed from the SeaWinds data at three representative locations. The inner and outer gray circles represent correlation values of 0.5 and 1.0 in the two left-hand plots and 0.25 and 0.5 in the right-hand plot.
Citation: Journal of Climate 25, 19; 10.1175/JCLI-D-11-00698.1
A map of R1 over the global ocean for the SeaWinds data is presented in Fig. 3. The vector wind acf anisotropy is weakest in the subtropics and the high latitudes where the value of R1 is generally close to one. Elsewhere R1 is considerably less than one, particularly in the Atlantic–Indian Ocean sectors of the Southern Ocean across the equatorial Pacific and Atlantic Oceans and over the subpolar North Atlantic and Pacific Oceans. The lowest values of R1, found in the Southern Ocean, are below 0.2. The orientation of the maximum 1-day vector wind lag autocorrelation, θmax, is primarily zonal in the midlatitude open ocean (Fig. 4). Throughout the tropics and high latitudes, and near coastlines, θmax takes a strong meridional orientation at many locations.
Global distribution of the 1-day vector wind lag autocorrelation anisotropy from SeaWinds data, as measured by the ratio R1 of the smallest to the largest correlation value [Eq. (4)]. The white circles indicate the positions of the polar plots of c1(θ) illustrated in Fig. 2 and the acf illustrated in Fig. 11.
Citation: Journal of Climate 25, 19; 10.1175/JCLI-D-11-00698.1
Orientation of the direction of maximum 1-day vector wind lag autocorrelation, computed from SeaWinds data. The vectors show the unit vectors emax = (cosθmax, sinθmax), with magnitudes scaled by the degree of the autocorrelation anisotropy
Citation: Journal of Climate 25, 19; 10.1175/JCLI-D-11-00698.1
This acf anisotropy is characteristic not just of surface winds, but extends to winds throughout the troposphere. Maps of R1 from 1000 to 200 hPa computed from the ERA-40 reanalysis winds (Fig. 5) demonstrate that, in general throughout the midlatitudes, the acf anisotropy is strongest near the surface and decreases gradually with increasing altitude. In contrast, the acf anisotropy in the tropics is strongest between 850 and 700 hPa and is negligible above the midtroposphere. The R1 field computed from the ERA-40 1000-hPa winds compares favorably with that computed from the SeaWinds observations in terms of both spatial distribution and magnitude, as does the R1 field computed from the ERA-40 10-m winds (not shown). This lag autocorrelation anisotropy is not an artifact of either dataset.
One-day lag vector wind anisotropy factor R1 [Eq. (4)] at different pressure levels, as estimated from the ERA-40 reanalysis winds.
Citation: Journal of Climate 25, 19; 10.1175/JCLI-D-11-00698.1
The extratropical vector wind lag acf anisotropy is most pronounced in the storm tracks where variability is strongly influenced by the propagation of coherent synoptic-scale eddies (e.g., Jones and Simmonds 1993; Hoskins and Hodges 2002, 2005; Lim and Simmonds 2007; Dos Santos Mesquita et al. 2008). As a storm passes a particular location, the character of wind anomalies is different in the along- and across-track directions. For a cyclonic eddy in the Northern Hemisphere, assuming circular symmetry for simplicity, the temporal profile of anomalous along-track winds will be monopolar: always westerly if the storm passes to the north of the given point and always easterly if it passes to the south. In contrast, the anomalous across-track winds will be a dipole in time: first southerly, then switching to northerly as the center of the storm passes. It follows that the winds in the across-track direction display more rapid changes than do those in the along-track direction. In the presence of a population of such eddies with a preferred direction of motion, such as is characteristic of storms in the storm track, this asymmetry will imprint itself on a corresponding anisotropy in the vector wind lag acf structure.
Lag autocorrelation functions of the along- and across-track vector wind components (u and υ) from the idealized model of propagating eddies in a storm track, neglecting other contributions to wind variability [i.e.,
Citation: Journal of Climate 25, 19; 10.1175/JCLI-D-11-00698.1
The idealized kinematic eddy model predicts that the vector wind lag acf anisotropy should be concentrated where the wind variance is dominated by propagating storms, that it should be oriented along the preferred direction of storm propagation, and that its magnitude should depend on the propagation speeds of storms relative to their sizes. In broad terms, these predictions are consistent with the observed midlatitude lag acf anisotropy. In the Northern Hemisphere extratropics, the surface anisotropy is strongest in the Pacific and Atlantic storm tracks where storm track density and intensity are the greatest (e.g., Hoskins and Hodges 2002, Fig. 5); the orientation, ranging from westward to northwestward, is consistent with the typical lower-tropospheric trajectories of synoptic-scale eddies (e.g., Hoskins and Hodges 2002, Fig. 14). The anisotropy in the Southern Hemisphere extratropics is similarly concentrated in the storm track and is most pronounced over the Atlantic and Indian Ocean sector of the Southern Ocean where eddy speeds are largest (e.g., Lim and Simmonds 2007, Fig. 4). The orientation of the maximum lag autocorrelation varies from westward to southwestward, again consistent with the preferred tracks of storms (e.g., Jones and Simmonds 1993, Fig. 8). The decrease in the magnitude of the anisotropy with altitude (Fig. 5) over the Southern Ocean is consistent with the observation that lower-troposopheric eddies are smaller and faster than those in the midtroposphere (Lim and Simmonds 2007, Table 1).



4. Wind speed autocorrelation function
As noted in section 1, a feature evident from inspection of the maps in Fig. 1 is that that the wind speed acf corr(wt, wt+s) drops off faster than the acf of at least one of the vector wind components. In fact, corr(wt, wt+1) is found to be bounded above everywhere by c1(θmax) in SeaWinds data (Fig. 7): across the entire ocean, the wind speed acf decreases faster than the acf of the vector wind component with the longest memory. We will investigate the relationship between the acf structures of the vector wind components and the wind speed by considering an idealized model in which the vector winds are assumed to be bivariate Gaussian. While the vector winds are known to display markedly non-Gaussian structure (particularly in the tropics and the Southern Ocean; Monahan 2004, 2006a, 2007), approximating the vector wind fluctuations as Gaussian greatly simplifies the following calculations.
Kernel density estimate of the spatial scatter of the wind speed 1-day lag autocorrelation corr(wt, wt+1) and the maximum 1-day lag vector wind autocorrelation, c1(θmax) = corr[ut(θmax), ut+1(θmax)], estimated from the SeaWinds data.
Citation: Journal of Climate 25, 19; 10.1175/JCLI-D-11-00698.1



Kernel density estimate of the joint distribution (in space) of the 1-day lag autocorrelation of wind speed, corr(wt, wt+1), and squared wind speed,
Citation: Journal of Climate 25, 19; 10.1175/JCLI-D-11-00698.1
Kernel density estimate of the spatial probability density function of the ratio of the standard deviation to the mean of wind speed, from SeaWinds observations between 60°S and 60°N.
Citation: Journal of Climate 25, 19; 10.1175/JCLI-D-11-00698.1


Kernel density estimates of spatial scatter of observed and modeled wind speed lag correlations (left) 1 day, (middle) 2 day, and (right) 3 day. Black contours correspond to predictions using the full model in Eq. (26), while red contours correspond to predictions made using the simplified model in Eq. (28). The observed and predicted values were determined using the SeaWinds data.
Citation: Journal of Climate 25, 19; 10.1175/JCLI-D-11-00698.1
It is evident from Eq. (26) for the squared wind speed autocorrelation structure that the sizes of the terms involving the vector wind lag autocorrelations ρuu, ρυυ relative to those involving the lag cross-correlations ρuυ, and ρυu depend on the asymmetry of the vector wind fluctuations through the factor σu/συ. As this factor becomes much greater than one, the lag autocorrelations ρuu become increasingly important. Similarly, as this factor becomes much less than one, the influence of ρυυ on corr(w1, w2) increases. When the fluctuations are approximately isotropic [as is observed over most of the World Ocean, Monahan (2007)], all of the vector wind lag auto- and cross-correlations contribute to the wind speed autocorrelations on equal footings.
Furthermore, we see that the contributions of the vector wind lag auto- and cross-correlations relative to their squares depends on the magnitudes of the mean vector winds relative to the vector wind fluctuations:

These different wind speed autocorrelation regimes are illustrated by the lag acfs of vector wind components and wind speed displayed in Fig. 11, computed from 10-m ERA-40 reanalysis winds rather than SeaWinds observations because of the relatively high temporal resolution and duration of the reanalysis product. At all three locations, the observed wind speed autocorrelation function is predicted well by Eq. (28). The left panel of Fig. 11 corresponds to a high-σ location for which corr(w1, w2) is well approximated by Eq. (33). In this case, the wind speed correlation decays faster than either of the vector wind components for the first two days and is always much smaller than the larger of the vector wind autocorrelations. In contrast, the middle panel of Fig. 11 corresponds to a low-σ regime for which corr(w1, w2) is given by Eq. (31). Over the first four days, the wind speed lag autocorrelation function is bracketed above and below by the larger and smaller vector wind autocorrelation functions, respectively. The same is true of the rightmost panel of Fig. 11, which also corresponds to a low-σ regime. The middle and right panels of this figure differ in the degree of anisotropy in the vector wind 1-day lag, which is greater at the location corresponding to the right panel (recall Fig. 2). Note that this third location is located in the Southern Hemisphere storm track, and the zonal and meridional lag acfs resemble the along- and across-track vector wind acfs predicted by the idealized kinematic eddy model (Fig. 6).
Observed lag autocorrelation functions of 10-m zonal wind (dashed line), meridional wind (dot–dashed line), and wind speed (solid black line) at three different locations over the ocean (Fig. 3), as calculated from ERA-40 data. The gray solid line is the lag autocorrelation function predicted by Eq. (28). The first location (32.5°S, 197.5°E) is characterized by relatively strong vector wind fluctuations (
Citation: Journal of Climate 25, 19; 10.1175/JCLI-D-11-00698.1
5. Discussion and conclusions
This study has reached the following conclusions:
The lag autocorrelation functions of the surface vector wind components and wind speeds decrease at substantially different rates at different locations over the ocean. In particular, the autocorrelation functions tend to drop off more slowly in the tropics than in the midlatitudes.
Over much of the ocean, and particularly in the extratropics, the autocorrelation function of the meridional wind decreases much more rapidly than that of the zonal wind. The wind speed autocorrelation also tends to decrease faster than that of the zonal wind. No general relationship is apparent between the decay rates of the meridional wind and the wind speed.
The vector wind acf anisotropy is not aligned precisely along zonal and meridional coordinate axes. While in the midlatitude open oceans, the alignment of the axis of longest memory is approximately zonal, in many locations throughout the tropics and higher latitudes the alignment has a strong meridional component. Furthermore, the anisotropy in vector wind decorrelation time scales is a feature not only of the surface winds but extends into the free troposphere. In the midlatitude storm tracks in particular, this anisotropy is evident throughout the troposphere.
The vector wind acf anisotropy in the midlatitude storm tracks can be understood in terms of the differences in the character of the along- and across-track wind anomalies in a moving synoptic-scale eddy. For the along-track component, the temporal structure of the vector wind anomaly is monopolar; in the cross-track direction, it is dipolar. An idealized kinematic model of propagating eddies predicts that the orientation of the lag acf anisotropy will be determined by the direction of eddy propagation, while its magnitude will be determined by the time it takes a single eddy to pass any particular location. The predictions of this model are broadly consistent with observed features of eddy activity in the storm tracks.
In the tropics, the vector wind acf anisotropy can be understood in terms of the superposition of variability from equatorial waves and convection. The former is large-scale and anisotropic, while the latter is small-scale and isotropic. Because the meridional winds in equatorial Kelvin waves are much smaller than the zonal winds (exactly zero for linear waves around a state of rest), the small-scale convection contributes relatively more variance to the meridional wind fluctuations than to the zonal wind fluctuations. It follows that fluctuations of the meridional wind should decorrelate faster than those of the zonal wind.
With the assumption that the vector surface winds are bivariate Gaussian with specified autocorrelation structure, an explicit expression for the autocorrelation structure of wind speed is obtained. This result is an approximation making use of the fact that the lag autocorrelation structures of the wind speed and the wind speed squared are quantitatively very similar, and the latter is easier to work with mathematically. We find that the wind speed lag autocorrelation is bounded above by the larger of the two vector wind component autocorrelations. Furthermore, the model predicts that, when the vector wind fluctuations are relatively large compared to the mean vector wind, the wind speed autocorrelation should scale as the square of the vector wind autocorrelation. In contrast, when the vector wind fluctuations are relatively weak, the autocorrelation should simply scale with the vector component fluctuations (bounded above by the larger, and below by the smaller). These results are consistent with the observed autocorrelation structure of wind speeds.
We have shown that the temporal autocorrelation structure of observed sea surface winds contains a rich structure that, to a first approximation, can be understood in terms of idealized kinematic and probabilistic models. These models are highly simplified and will be quantitatively incorrect in many particulars. Baroclinic eddies in the storm tracks are not circularly symmetric; if they were, there would be no eddy momentum transport. Neither do these eddies propagate rectilinearly at constant speed, with constant depth and extent. Furthermore, observed equatorial waves are not independent of convective activity; rather, these waves are convectively coupled (e.g., Kiladis et al. 2009). Finally, surface vector winds are both non-Gaussian (e.g., Monahan 2004, 2006a) and nonstationary, with statistics that display both diurnal and annual modulations (e.g., Dai and Deser 1999; Monahan 2006b). Nevertheless, the approximate models considered in this study provide a useful—if idealized—framework for understanding the temporal structure of fluctuations in the vector winds and wind speed.
Acknowledgments
The author gratefully acknowledges helpful comments on the manuscript from John Fyfe, John Scinocca, Paul Kushner, Chris Garrett, Aaron Culver, Peter Bartello, and Tim Rees. The manuscript was also greatly improved through comments by two anonymous reviewers. This research was supported by the Natural Sciences and Engineering Research Council of Canada.
APPENDIX A
Idealized Kinematic Eddy Model




APPENDIX B
Calculation of corr(w, w2)

APPENDIX C
Squared Wind Speed Autocorrelation Function








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