1. Introduction
A prominent band of convergence overlies the Gulf Stream in the time-mean surface winds, which is hereafter referred to as the Gulf Stream convergence zone (GSCZ). The current perception is that the GSCZ perseveres in the time-mean surface winds as a result of a local atmospheric response to persistent Gulf Stream SST fronts (e.g., Minobe et al. 2008). It has been hypothesized that SST-induced surface convergence within the GSCZ drives a deep atmospheric response while enhancing rainfall, suggesting a pathway for the local influence of mesoscale SST fronts in shaping the climate in the Atlantic (Minobe et al. 2008; Joyce et al. 2009; Minobe et al. 2010; Brachet et al. 2012; Takatama et al. 2012; Lambaerts et al. 2013). This analysis proposes an alternative explanation for the existence of the GSCZ in the time-mean wind and pressure fields.
This work is motivated by a map of the time-mean surface wind divergence field in the northwest Atlantic (Fig. 1a). This map was constructed from 10 years of QuikSCAT wind observations spanning the time period November 1999–October 2009, as described in section 2a. Since both raining and rain-free conditions are included in this mean, it is referred to as the all-weather (AW) mean. The band of time-mean convergence—the GSCZ—overlies the approximate position of the Gulf Stream, from the Charleston Bump off the coast of South Carolina, separating from the shelf near Cape Hatteras, extending to the northeast south of Nova Scotia, where the Gulf Stream transitions into the North Atlantic Current, and finally terminating near 47°W. Its cross-frontal width is between roughly 300 km in the southwest to about 600 km east of 65°W, and its along-frontal length is about 2500 km.
Maps of the QuikSCAT 10-m divergence averaged (colors) over the 10-yr period November 1999–October 2009 in (a) all-weather, (b) rain-free, and (d) rain-only conditions, divided by 2.5 to fit within the color scale. (c) The difference between the all-weather and rain-free time-mean divergence, multiplied by 2 to fit within the color scale. The contours are of the 10-yr-mean Reynolds SST with a contour interval of 2°C.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
Unexpectedly, the GSCZ nearly vanishes when only rain-free conditions are considered in the time mean, as shown by a map of the rain-free conditional-mean divergence (Fig. 1b). The rain-free mean divergence shows widespread positive divergence nearly everywhere. The difference between the all-weather and rain-free time-mean divergence fields (Fig. 1c) shows that exclusion of raining conditions does not uniformly shift the mean divergence to positive values. Rather, the differences are largest along a 200–600-km-wide band centered roughly along the Gulf Stream. Rain occurs less than 20% of the time in this region, as shown by satellite-derived rain frequency estimates (Fig. 2a; these rain estimates are described in section 2c), suggesting that the location of the storm track plays a role in the existence of the GSCZ in the time-mean wind fields. This differs from the current hypothesis that a local marine atmospheric boundary layer (MABL) response to SST fronts generates this band of low-level convergence associated with the GSCZ (e.g., Minobe et al. 2008; Joyce et al. 2009; Minobe et al. 2010; Brachet et al. 2012; Takatama et al. 2012).
(a) Rain frequency and (b) time-mean rain-rate estimates from the TMPA merged satellite analysis for the 10-yr period November 1999–October 2009. Black contours are of the Reynolds SST with a contour interval of 2°C during the same 10-yr period. The thick gray contour is the isoline of the time-mean AW QuikSCAT divergence shown in Fig. 1a of −0.25 × 10−5 s−1 and indicates the extent of the GSCZ in the time-mean surface winds.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
Differences in the rain-free and all-weather time-mean divergence and wind stress curl are not a regional effect but include most of midlatitude storm tracks throughout the World Ocean (Milliff et al. 2004; Kilpatrick and Xie 2016). The differences are particularly acute over the Gulf Stream, where the GSCZ apparently exists only when winds in raining conditions are included in the time mean (O’Neill et al. 2015).
The conditional averages shown in Figs. 1b and 1c suggest that extratropical cyclones complicate isolation of the atmospheric response to the Gulf Stream SST distribution. They also suggest that storms play a significant role in the appearance of the GSCZ in the time-mean surface wind fields. Time averaging is often thought to mitigate the effects of synoptic weather variability, but these maps suggest otherwise. Despite this apparently strong influence from storms, a relatively robust local atmospheric response to SST is expected in the time-mean winds since the Gulf Stream SST signature is both persistent and spatially confined regardless of the exact response mechanism. Indeed, a strong response of the MABL winds and surface fluxes to the Gulf Stream SST frontal zone is well established from previous observational and modeling studies (e.g., Weissman et al. 1980; Sweet et al. 1981; Wai and Stage 1989; Bane and Osgood 1989; Singh Khalsa and Greenhut 1989; Warner et al. 1990; Friehe et al. 1991; Kudryavtsev et al. 1996; Alexander and Scott 1997; Smahrt et al. 2004; Song et al. 2006; O’Neill et al. 2010a; Shaman et al. 2010; Bryan et al. 2010; Kelly et al. 2010; O’Neill 2012; Plagge et al. 2016). Add to these complications that the Gulf Stream SST influences the atmosphere in other ways besides a local MABL response. The Gulf Stream actively generates and intensifies synoptic and mesoscale disturbances in the atmosphere (e.g., Miller 1946; Lau 1988; Hoskins and Valdes 1990; Doyle and Warner 1993; Giordani and Caniaux 2001; Hoskins and Hodges 2002; Chang et al. 2002; Businger et al. 2005; Brayshaw et al. 2009; Booth et al. 2010; Czaja and Blunt 2011; Booth et al. 2012). Additionally, the impact of SST distribution on the storm track is not entirely a local effect. Gulf Stream SST gradients contribute to a baroclinically unstable environment and enhanced low-level moisture and heat fluxes, but do not necessarily lead to a direct correlation between local SST and dynamic variables, just a preferred region of storm development and propagation.
This preferred region of storm growth and propagation is referred to as the storm track, and the storm track has been observed to coincide closely with the Gulf Stream in the northwest Atlantic. In a review of storm-track literature, Chang et al. (2002) offered a definition of the storm track as the “synoptic classification of such preferred regions of storm (cyclone) activity” (p. 2163). Its usage encompasses a broad category of atmospheric variability, including the “geographical organization of these transients, whether in terms of their preferred paths of travel, relative frequency of occurrence, or the average magnitude of variability” (p. 2163). Previous work has indicated that storm tracks occur preferentially along SST frontal zones associated with western boundary currents (e.g., Hoskins and Valdes 1990; Nakamura et al. 2008; Brayshaw et al. 2009; Kuwano-Yoshida et al. 2010; Small et al. 2014), due at least in part to enhanced baroclinicity and land–sea temperature contrast. In the northwest Atlantic, Blender et al. (1997) showed that storms tend to cluster along two main paths: one approximately along the mean path of the Gulf Stream and the GSCZ with a diffuse downstream trajectory north of the British Isles, and one over land across Canada with a downstream trajectory along roughly 50°N (see their Fig. 7).
SST is just one of several factors contributing to the development of storms and the preferred position of the storm track in the northwest Atlantic (e.g., Chang et al. 2002; Brayshaw et al. 2009). For instance, the temperature contrast between the North American continent and the Atlantic Ocean enhances development of storms via baroclinic instability.
Current hypotheses about the local relation between SST and divergence assume that time averaging of wind and pressure fields removes the influence of storms. Conventional wisdom is that the existence of the GSCZ is instead attributable primarily to a surface hydrostatic pressure response to SST, driven by SST-induced MABL temperature variations (e.g., Feliks et al. 2004, 2007; Minobe et al. 2008; Joyce et al. 2009; Minobe et al. 2010; Brachet et al. 2012; Takatama et al. 2012; Lambaerts et al. 2013). These studies concluded that spatially varying SST generates small but dynamically important sea level pressure (SLP) gradients as the MABL adjusts its temperature. This SST-induced pressure adjustment was concluded to drive near-surface convergence through a MABL wind adjustment governed by steady Ekman-layer dynamics. The fundamental role of the turbulent stress divergence is hypothesized to be a passive drag responding to the SST-induced pressure-driven accelerations. Consequently, surface convergence was hypothesized to be proportional to the spatial Laplacian of SLP, consistent with the proportionality of convergence and geostrophic vorticity in an Ekman layer (e.g., section 5 in Holton 1992; Feliks et al. 2004). Mass and SST-induced thermodynamic adjustments are coupled through a direct proportionality between the SLP and SST Laplacians, which assumes that the boundary layer quickly adjusts its vertically averaged temperature to the local SST. Thus, a simple relationship exists between surface divergence and the SLP and SST Laplacians. Hereafter, the MABL adjustment to the SST Laplacian is referred to as an Ekman-balanced mass adjustment (EBMA) mechanism. This mechanism describes an SST-induced mass (pressure) adjustment driving a steady Ekman-balanced adjustment of the near-surface winds.
The EBMA mechanism shares its essential dynamics and thermodynamics with the Lindzen and Nigam (1987) model. This model was developed to explain modification of the trade winds by the Pacific equatorial cold tongue but has often been used to describe mesoscale surface wind–SST interactions in midlatitudes (e.g., Chen et al. 2003; Small et al. 2008; Tokinaga et al. 2009; Tanimoto et al. 2011). This basic model has endured despite numerous studies since then showing other neglected processes to be important. Nonetheless, recent work suggests that the EBMA mechanism may be appropriate for the limiting case of very weak background surface winds (Lambaerts et al. 2013; Schneider and Qiu 2015). Whether this condition is satisfied in the northwest Atlantic remains an open question.
An appealing feature of the EBMA mechanism is that it proposed a dynamical explanation of the correlation between the time-mean surface divergence and the SST Laplacian noted from satellite and model fields as, for instance, in Fig. 1 of Minobe et al. (2008). The GSCZ in the time-mean winds approximately overlies minima in the SST Laplacian field, which itself is strongest where the SST fronts are strongest. Further work has shown complementary collocations of the time-mean boundary layer height, MABL vertically averaged temperature, and 850-hPa vorticity within the GSCZ (e.g., Brachet et al. 2012; Small et al. 2014).
Given this correlation, a link was proposed between this local MABL response to the SST Laplacian and the climate of the northwestern Atlantic basin (Minobe et al. 2008). A deep tropospheric response to the Gulf Stream SST front was hypothesized to be confined not just to the MABL but extending vertically into the free troposphere. In this theory, spatial SST variability drives surface wind convergence (i.e., the GSCZ), which is speculated to force upward motion directly through mass conservation or possibly indirectly by triggering deep convection. Earlier analytical work suggested that mass conservation coupled with the pressure response to SST drives Ekman pumping at the top of the Ekman layer (Feliks et al. 2004, 2007). This hypothesis suggested a mechanism where upward motion is “anchored” to the north wall of the Gulf Stream. It was further hypothesized that the GSCZ fuels a maximum in rainfall along the Gulf Stream (e.g., Minobe et al. 2008, 2010; Kuwano-Yoshida et al. 2010; Brachet et al. 2012). Both the rain frequency and the 10-yr-mean rain rate indeed have maxima collocated with the GSCZ, as shown from the satellite rain-rate estimates in Figs. 2a and 2b, respectively. In this figure, the isoline of the time-mean QuikSCAT convergence of −0.25 × 10−5 s−1 shows the approximate location of the GSCZ. It was never reconciled how this hypothesized mechanism of ocean–atmosphere coupling interacted with the location of the storm track. This analysis aims to shed some insight into this question.
In this study, we analyze satellite data and simulations from an atmospheric model to investigate how synoptic weather variability affects the time-mean divergence and surface pressure fields in the northwest Atlantic associated with the GSCZ. Since the free-tropospheric response is hypothesized to be driven by the EBMA mechanism, we also analyze the vertical velocity throughout the troposphere and the surface pressure from high-resolution atmospheric simulations to determine how intermittent storm variability affects them. In section 3, satellite observations of surface winds, SST, and rain rate are used to identify how intermittent storm systems affect the time-mean divergence over the Gulf Stream. In light of this effect, the dynamical connections between the time-mean surface convergence and the SLP and sea surface temperature (SST) Laplacians predicted by the EBMA mechanism are revisited in section 4 from a 1-yr high-resolution atmospheric model simulation. We also show from this simulation that the time-mean vertical velocity throughout the depth of the troposphere is likewise affected strongly by storms. Finally, in section 6, we show briefly from satellite wind and SST observations that SST does appear to systematically influence the surface divergence in a way that is more consistent with earlier empirical studies and the Schneider and Qiu (2015) analytical model for moderate background surface winds and earlier empirical studies (e.g., Chelton et al. 2004; O'Neill et al. 2010a).
2. Observational data
a. Satellite ocean vector winds
Vector winds over most of the ice-free global oceans were measured by the SeaWinds scatterometer on board the QuikSCAT satellite (herein referred to simply as QuikSCAT). We use the recently updated version 3 of the QuikSCAT geophysical data record produced by the Jet Propulsion Laboratory (JPL) over the 10-yr period November 1999–October 2009 (SeaPAC 2013; Fore et al. 2014). As detailed in Fore et al. (2014), among the improvements over previous data versions include increased wind accuracy in raining conditions, reduced cross-track wind biases, and enhanced ambiguity selection and removal. These wind retrievals are based on the updated Ku-2011 geophysical model function (GMF) (Ricciardulli and Wentz 2015), with enhanced postprocessing of retrieved winds.
The QuikSCAT winds were obtained in level 2B format, which provides retrieved wind vectors within an 1800-km-wide measurement swath at a nominal spacing of 12.5 km, although the spatial scale of the individual measurement footprints is roughly 25 km. These winds were then gridded onto a uniform ¼° spatial grid using a two-dimensional locally weighted scatterplot smoother (LOESS) (Schlax et al. 2001) with a half-power filter cutoff wavelength of 40 km. The QuikSCAT divergence was computed from the gridded AW zonal and meridional wind components using standard centered finite differences. The QuikSCAT time-mean divergence fields were computed using the spatial derivatives first, time averaging second (DFAS; O’Neill et al. 2015) method, whereby the requisite spatial derivatives were computed first from the instantaneous gridded vector wind components in swath and then the divergence was time averaged.
Rain in QuikSCAT grid cells was detected using two methods—one using a scatterometer-only rain flag and the second using collocated rain-rate estimates from passive microwave radiometers on other satellite platforms, which are provided by the remote sensing systems (RSS) (Ricciardulli et al. 2013). Fields of rain-free (RF) divergence were determined by simply flagging and removing the AW divergence fields at the times and grid cells where rain was indicated by the RSS rain flag. Similarly, fields of rain-only (RO) divergence were determined by keeping the divergences at grid cells where rain was indicated and removing all others.
Since Ku-band scatterometers such as QuikSCAT are affected by rain, it is fair to question how robust the divergence estimates are in raining conditions. This question is addressed briefly here through comparison with independent AW divergence estimates from the Advanced Scatterometer on MetOp-A (ASCAT-A) (KNMI 2010), which operates in C band and is less affected by rain. We do not use ASCAT-A for the bulk of the analysis because of its shorter data record and because it only measures roughly half the surface area per day as QuikSCAT. The comparison is done for the 2-yr period August 2007–July 2009, which was near the start of the ASCAT-A mission. Since QuikSCAT and ASCAT-A do not measure winds very closely in time, direct comparison of collocated divergence estimates is not possible. The next best thing is to test the hypothesis that both instruments have distributions that are statistically indistinguishable, thus providing some measure of assurance that rain is not significantly affecting our results based on the QuikSCAT observations. Figure 3a shows histograms of instantaneous AW divergence estimates centered on a region over the Gulf Stream for QuikSCAT (black) and ASCAT-A (green). The histograms are qualitatively very similar, with very similar means, medians, and skewness (as listed in the panel). Comparison of the far tails of the distribution are also favorable, as seen more clearly when the histograms shown in Fig. 3a are plotted with a logarithmic y axis, as shown in Fig. 3b. A more robust quantitative evaluation is performed using the two-sample Kolmogorov–Smirnov hypothesis test (Kolmogorov 1933; Smirnov 1948; Press et al. 1992) at each spatial grid point, which tests whether the hypothesis that the QuikSCAT and ASCAT-A divergence distributions are equal can be rejected at some significance level, chosen here to be 95%. This test quantitatively compares both the relative shapes and locations of the distributions and can be applied broadly to most classes of distributions. Figure 3c shows a map with grid points where the hypothesis is rejected in red, indicating regions where the QuikSCAT and ASCAT-A divergence distributions have a statistically significant difference. The differences between the two distributions are statistically insignificant at 91.5% of the grid points, with no clear systematic geographical pattern in the few grid points which do not pass the test at this level. This indicates that the two instruments yield divergence distribution estimates that are statistically indistinguishable for most of this region.
Summary of the comparison between the AW divergence estimates from QuikSCAT and ASCAT-A over the 2-yr period August 2007–July 2009: (a) histograms of instantaneous divergence for QuikSCAT (black) and ASCAT-A (green), with the means, medians, and skewnesses listed; (b) as in (a), but with a log scale on the y axis to emphasize the negative skewnesses of the distributions; (c) map showing the grid points (red) where the instantaneous QuikSCAT and ASCAT-A divergence distributions are statistically different at the 95% confidence level according to the two-sample Kolmogorov–Smirnov test; (d) map showing the grid points where the time-mean AW QuikSCAT and ASCAT-A divergence fields are statistically different at the 95% significance level according to the unpaired two-sample t test with unequal variances; (e) time-mean QuikSCAT AW divergence; and (f) time-mean ASCAT-A AW divergence. Contours in (c)–(f) are of the 2-yr-mean Reynolds SST with an interval of 2°C.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
While this tests the instantaneous AW divergence fields, the significance of differences in the time-mean divergence fields between QuikSCAT and ASCAT-A are also evaluated. Maps of each are shown in Figs. 3e and 3f, respectively. Overall, the two fields agree very well, although the ASCAT-A mean shows slightly stronger GSCZ. The differences in these time means are statistically insignificant at the 95% confidence level at most grid points according to a standard unpaired two-sample t test with unequal variances; exceptions are those grid points shown in red in the map in Fig. 3d; overall, 94.1% of grid points in these maps show statistically insignificant differences in the time-mean divergence.
These evaluations give us confidence that rain or other systematic measurement or sampling errors are not adversely impacting the statistics of the instantaneous AW QuikSCAT divergence distributions or the resulting time-mean fields.
b. Reynolds SST analysis
In this analysis, we used the NOAA optimum interpolation (OI) SST fields (National Climatic Data Center 2007; Reynolds et al. 2007), commonly known as the Reynolds daily OI SST analysis. This dataset combines SST observations from a variety of AVHRR infrared satellite and in situ SST observations and is available at daily intervals globally over ice-free areas on the same ¼° spatial grid and 10-yr time span of the QuikSCAT geophysical data record.
c. Rain-rate estimates
Besides the QuikSCAT rain flag, quantitative rain-rate estimates are utilized from the TRMM Multisatellite Precipitation Analysis (TMPA) dataset (version 7; Tropical Rainfall Measurement Mission Project 2011; Huffman et al. 2007, 2010). The so-called research-grade TMPA, sometimes referred to simply as the TRMM 3B42 merged rain-rate analysis, includes rain-rate estimates from infrared sensors calibrated to, and merged with, those from a series of passive microwave instruments. The TMPA analysis is constructed at 3-h intervals and on a ¼° spatial grid between 50°N and 50°S latitudes. Maps of the rain frequency and the time-mean rain rate over the 10-yr period November 1999–October 2009 are shown in Figs. 2a and 2b, respectively, and are discussed throughout this analysis. The rain frequency determined from the QuikSCAT rain flag matches that shown in Fig. 2a quite closely (not shown).
d. Satellite observations of an example extratropical cyclone
Figure 4a shows an example of the QuikSCAT all-weather wind measurements for 1 January 2009, which captures a fairly strong extratropical cyclone, with its clearly defined cold front. Days earlier, it produced exceptionally strong winds throughout the northeastern United States. These measurements show strong surface wind speeds in significant portions of the frontal and postfrontal regions. The parent surface low is visible just southeast of Nova Scotia. The surface divergence field estimated from the QuikSCAT vector winds in Fig. 4a is shown in Fig. 4b. The surface cold front, bent back occlusion, and postfrontal cold sector are all evident as areas of strong surface convergence. Note that the absolute magnitude of the convergence features associated with the frontal regions are O(10−4) s−1, which is at least 10–20 times larger than both the climatological-mean divergence shown in Fig. 1a and the divergence perturbations forced by mesoscale SST features. The rain flag used in QuikSCAT is shown in Fig. 4c by regions of red shading. This shows that rain is occurring over most of the regions of extremely strong convergence.
Satellite observations of an extratropical cyclone at approximately 1000 UTC 1 Jan 2009 over the northwest Atlantic: (a) QuikSCAT gridded 10-m wind vector observations, with every third wind vector plotted; (b) QuikSCAT 10-m divergence; (c) QuikSCAT rain flag, where red indicates raining grid cells; and (d) GridSat-B1 merged 11-μm infrared brightness temperature. The contours in (a) are of the 3-day-averaged AMSR-E SST with a contour interval of 2°C, with thicker contours labeled. The thick black contour in (c) and (d) is the isoline of the QuikSCAT divergence with a value of −10−4 s−1. The QuikSCAT divergence has been spatially smoothed using a two-dimensional LOESS filter with a half-power radius of 80 km.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
Rain and strong convergence collocate fairly well with localized minima of infrared brightness temperature (Fig. 4d) as obtained from the merged geostationary infrared temperature at 11 μm from the GridSat-B1 dataset valid at 0900 UTC. Along the cold front, the strong convergence is clearly associated with clouds and rain. This example storm system is shown here to motivate one of the main conclusions of this analysis, namely, that intermittent but intense extratropical cyclones have a large effect on the time-mean surface divergence field in this region.
3. Sensitivity of the appearance of the GSCZ to storms
a. Sensitivity of time-mean divergence to extreme weather events
Figure 1 suggests that raining storms strongly affect the interpretation of the time-mean divergence field in the northwest Atlantic. Given potential uncertainties associated with the determination of rain from satellites, we show a second independent analysis that demonstrates the sensitivity of the time-mean divergence to episodic convergences and divergences in the far tails of the divergence distribution. Extreme events are defined here by application of an extreme value filter to the time series of the AW divergence at each grid point, which removes (or filters) extreme values of convergence and positive divergence with absolute values greater than two standard deviations σ from the time mean at each grid point.
Figure 5b shows a map of the time-mean AW divergence after application of this 2σ extreme-value filter, which is compared side by side with the unfiltered time-mean AW divergence in Fig. 5a. Even though fewer than 4% of the data points are removed by the extreme-value filter (Fig. 5d), it removes most traces of the GSCZ, consistent with the conditional average of the RF divergence shown in Fig. 1b. Besides elimination of the GSCZ, regions of positive time-mean divergence north of the Gulf Stream become stronger in magnitude after application of the filter. This result indicates that the extreme-value filter preferentially removes extreme convergences compared to extreme positive divergences, leaving a time-mean divergence shifted toward stronger positive values nearly everywhere in this region. Discrete, instantaneous events thus leave prominent residuals in the time-mean fields. This analysis also corroborates the interpretation of the rain-free time-mean divergence shown in Fig. 1b, although the extreme-value filter indicates that the GSCZ can be accounted for by a very small number of storm events.
Maps of the 10-yr-mean QuikSCAT AW divergence (a) consisting of all points; (b) after application of the 2σ temporal extreme-value filter at each grid point; (c) difference between (a) and (b)—that is, the unfiltered minus filtered divergence, multiplied by 2 to fit within the color scale; and (d) the percentage of divergence points removed by the 2σ extreme-value filter at each grid point. The contours in each panel are of the 10-yr-mean Reynolds SST with a contour interval of 2°C.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
The shift toward positive time-mean divergence in the filtered fields is not spatially uniform, however, as shown by the map of the difference between the filtered and unfiltered AW divergence in Fig. 5c. The differences are largest over the Gulf Stream and decrease sharply away from it, consistent with the difference between the AW and RF time-mean divergence in Fig. 1c. Thus, episodes of extreme convergences associated with storms do not simply “bias” the time-mean all-weather divergence fields uniformly over the entire region.
To put the number of data points removed by the 2σ extreme-value filter into perspective, note that there are roughly 7000 data points at each 0.25° grid point over the 10-yr QuikSCAT data record. The 2σ filter therefore removed about 350 data points. If half of these points removed by the filter are from extreme convergences (an underestimate, but suitable for our purposes here), then fewer than 175 extreme convergences need to be removed to effectively eliminate the GSCZ from the time mean. Spread out over the 10-yr QuikSCAT data record, this averages to fewer than ~17 data points per year, which equates to about one to two strong convergence events per month passing through each grid point. This result is reasonable given the relative frequency of storms in this region. Some of the extreme divergences and convergences removed by this filter may also be attributable to measurement errors in the QuikSCAT winds. Random errors in wind components, however, do not favor either positive or negative divergence, so they are not expected to impact the filtered mean divergence significantly.
b. Properties of the divergences’ statistical distribution
The preferential removal of extreme convergence events by the 2σ extreme-value filter is a consequence of a highly asymmetric all-weather divergence distribution in the northwest Atlantic, as shown by the divergence histogram in Fig. 6a (black curve). Note the logarithmic scale of the y axis. This histogram, as well as the others in the figure that are discussed shortly, were computed for all grid points between 35° and 44°N and 70° and 50°W. This region was chosen since it is large enough to contain a significant portion of the GSCZ, yet small enough so that these histograms are representative of the distributions at all inclusive grid points. The AW histogram shown in black is the exact sum of the rain-free and rain-only histograms shown by the red and blue curves, respectively. No time averaging or spatial smoothing was applied to the data points prior to computing the histograms.
Histograms of the instantaneous QuikSCAT divergence in a variety of conditions over the northwest Atlantic for the 10-yr period November 1999–October 2009: (a) AW (black), RF (red), and RO (blue) conditions; (b) for AW conditions and all months [solid; a repeat of the black curve in (a)], and AW DJF (thick blue), AW JJA (thick orange), AW MAM (thin green), and AW SON (thin brown); and (c) the ratio of the number of divergence points within each bin in RO and RF conditions (for all months). These histograms were computed for all grid points between 35° and 44°N and between 70° and 50°W. The bin width is 0.1 × 10−5 s−1.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
While the mean of the AW divergence distribution is negative (−0.2 × 10−5 s−1), its median and mode are both positive, as shown in Table 1 (0.3 × 10−5 and 0.6 × 10−5 s−1, respectively). These differences between the mean, median, and mode are consistent with a highly asymmetric distribution that has more extreme convergences than extreme divergences. Indeed, in this region, extreme convergences less than −10 × 10−5 s−1 occur 3 times more often than extreme positive divergences greater than 10 × 10−5 s−1. Note that the asymmetry in the divergence distribution is clearer in Fig. 3b because of the log scale on the y axis.
Statistics of the QuikSCAT divergence distributions. All statistics are in units of 10−5 s−1, except the skewness coefficient, which is unitless. These statistics were computed for the same data used in the histograms in Fig. 6—that is, for the area bounded by 35°–45°N, 50°–70°W, and the 10-yr period November 1999–October 2009.
Asymmetry in a distribution is quantified by its skewness. The value of the AW divergence skewness is −1.8, indicating a highly negatively skewed distribution. This all-weather divergence skewness is greater in magnitude than either the rain-free or rain-only skewness (which are both −1.1) because the rain-only divergence distribution is shifted to the left toward stronger convergence relative to the rain-free divergence distribution (blue and red curves in Fig. 6a, respectively). The shift of the rain-only distribution relative to the rain-free distribution is consistent with the association between convergence, rain, and storms noted previously. Storms enhance the left tail (convergence) of the AW divergence distribution relative to its right tail (positive divergence).
A peculiar association between extreme positive divergences and rain is also apparent in the rain-only divergence histogram (blue curve in Fig. 6a), which belies this simple association between rain and surface convergence. This is seen more clearly from the ratio of the number of rain-only to rain-free observations within each divergence bin (Fig. 6c; it is simply the ratio of the blue and red curves in Fig. 6a). This ratio exceeds one for extreme positive divergences greater than about 10 × 10−5 s−1; for divergence values greater than this, rain is more likely than otherwise. An association between strong positive divergence and rain is inconsistent with the common conception that surface convergence causes rain. We believe that this is a consequence of the circulation within storm systems, such as conveyor belt-type circulations. While storms predominantly contain strong surface convergence, smaller areas of extreme positive divergences are often embedded within them that are insufficient to end rain. Thus, it seems plausible that there is either some relatively local mass compensation between upward and downward motion within the storm that manifests itself in the surface divergence field. A second related possibility is that gravity waves cause alternating bands of positive and negative divergence within storm systems. In any event, this discrepant observation is subject to ongoing investigation, as it appears to have important consequences for our understanding of the association between surface convergence and rain. Nevertheless, rain is much more likely in extreme convergences than extreme positive divergences. Thus, the association between rain and convergence holds, despite the discrepancies that evidently occur.
A straightforward consequence of the negatively skewed divergence distribution is that the surface area covered by positive divergence exceeds that covered by convergence by a margin of 57.8% to 42.2%, respectively, obtained from the instantaneous divergence fields. Despite the overall negative time-mean divergence for the whole region, 15.6% more area experiences positive divergence rather than convergence.
Skewed distributions have been noted explicitly in other variables impacted by storm variability (e.g., Nakamura and Wallace 1991; Garfinkel and Harnik 2017). Despite the knowledge of asymmetric and highly skewed distributions in certain regions, its relevance to both the surface divergence field in general, and the time-mean divergence in particular, has not been realized previously, and is one of the main results of this paper.
Is this negative skewness representative of all geographic regions in the northwest Atlantic? Figure 7a shows a map of the skewness coefficient for the QuikSCAT AW divergence computed for each 1/4° grid point for the 10-yr QuikSCAT data record. The divergence skewnesses are less than −1 for 80.4% of the grid points, so negative skewness characterizes the divergence distribution over the entire northwest Atlantic; this indicates highly negatively skewed (or, equivalently, left skewed) distributions over most of the region. The statistical significance of the skewness at each grid point can be estimated by whether the skewness magnitude is significantly greater than the quantity 
(a) Map of moment coefficient of skewness of the QuikSCAT AW divergence distribution at each 1/4° grid point for the 10-yr period November 1999–October 2009. (b) Time series of QuikSCAT divergence skewness in the northwest Atlantic, computed at 30-day intervals over the region shown in (a).
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
Time series of the divergence skewness shown in Fig. 7b is consistent with our hypothesized influence of storms in generating asymmetry in the divergence distribution. This skewness time series was computed at 30-day intervals for the entire region shown in Fig. 7a. The AW divergence skewness is roughly a factor of 2 greater in magnitude during November–March compared with the other months, consistent with increased storm frequency and intensity during wintertime.
c. Temporal median and mode of all-weather divergence
Other measures of the central tendency of the AW divergence distribution, including its median and mode, show significant differences from its mean value. This provides a third independent assessment of the sensitivity of the AW divergence distribution to synoptic weather events. For instance, the 10-yr-median AW divergence field (Fig. 8b) is much more divergent than the time-mean AW divergence (Fig. 8a) and closely matches the time-mean rain-free divergence (Fig. 1b). Note in particular that little trace of the GSCZ exists in the median divergence field. Additionally, the AW median field is virtually indistinguishable from either the time-mean RF divergence field (Fig. 1b) or the 2σ-filtered time mean (Fig. 5b).
Three measures of the central tendency of the QuikSCAT AW divergence at each grid point over the 10-yr period November 1999–October 2009: (a) mean, (b) median, and (c) mode. The contours in each panel are of the 10-yr-mean Reynolds SST with a contour interval of 2°C.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
The temporal mode of the AW divergence (Fig. 8c) was computed as the maximum of the AW divergence probability density function at each grid point estimated using the nonparametric kernel density estimation method (Rosenblatt 1956; Parzen 1962). This method provided a more robust estimate of the mode than the more common histogram method. Overall, the AW divergence mode shows widespread divergence, similar to the median, although somewhat stronger in magnitude. Note that there is also little trace of either the GSCZ or a divergence minimum over the Gulf Stream in the mode divergence field, in contrast to the mean and median fields. This discrepancy between these three measures of the AW divergence distributions’ central tendency (i.e., the mean, median, and mode) is consistent with the distributions shown in Fig. 6a and the statistics summarized in Table 1.
A remarkably consistent picture thus emerges that strong convergence associated with synoptic storms significantly influences the AW time-mean divergence over the northwest Atlantic. Evidence in support of this conclusion came from the time-mean RF divergence, the time-mean 2σ extreme-value-filtered AW divergence, and the AW divergence median and mode; these appear to be better estimates of the central tendency of the AW divergence distribution than its time mean.
d. Meridional wind variance
A more direct link between storm variability and the GSCZ can be established by the geographical distribution of the surface meridional wind variance. The meridional wind variance approximates the northward flux of meridional momentum by transient atmospheric eddies and can thus serve as an Eulerian-type indication of storm-track position in midlatitudes (e.g., Blackmon et al. 1977; Hoskins and Hodges 2002; Chang 2009; Booth et al. 2010; Wettstein and Wallace 2010; Small et al. 2014). Figure 9a shows a map of the QuikSCAT 10-yr-mean AW divergence in colors with contours of the meridional wind variance overlaid. A band of maximum meridional wind variance coincides almost exactly with the GSCZ. This association between time-mean convergence and the meridional wind variance maximum has not been noted previously. A variance maximum is likewise clear in the meridional winds filtered in time to retain variability with periods less than 6 days (Fig. 9b), although there is approximately a factor of 2 difference in the magnitude of the variance maxima between the filtered and unfiltered meridional wind. Insofar as the meridional wind variance is a measure of the storm-track location, the collocation between the GSCZ and the meridional wind variance maxima is consistent with our view that synoptic storms strongly influence the time-mean surface winds near the Gulf Stream.
The 10-yr-mean QuikSCAT AW divergence (colors) as shown in Fig. 1a with overlaid contours of the temporal variance of the (a) unfiltered QuikSCAT AW meridional wind component and (b) temporally high-pass- filtered QuikSCAT AW meridional wind component. The temporal filter attenuates variability with periods longer than 6 days. The contour interval in both panels is 2 m2 s−2.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
e. Seasonal divergence and GSCZ variability
Do the results based on the long-term time-mean divergence shown thus far apply on seasonal time scales as well? To shed light on this question, we compare seasonal-average maps of the time-mean QuikSCAT divergence for DJF and JJA 1999–2009 (Figs. 10a and 10b, respectively) with each other and with the long-term mean already shown in Fig. 1a. The GSCZ west of 70°W does not change significantly between seasons. East of 70°W, however, there are two noteworthy seasonal differences. First, the GSCZ is more widespread in DJF. A way to quantify this is to compute the surface area enclosed within time-mean divergences less than −0.25 × 10−5 s−1. During DJF, the area is 1.15 × 106 km2, while during JJA, the area is 0.64 × 106 km2, a reduction of 44% in areal coverage. Second, the magnitude of time-mean convergence is stronger east of 70°W during DJF compared to JJA, presumably because storms with strong convergences are more frequent during winter compared to summer.
Maps of the seasonal-mean QuikSCAT divergence averaged for (a) DJF and (b) JJA during the 10-yr period November 1999–October 2009. (c),(d) The DJF and JJA means for the 2σ extreme-value-filtered divergence, respectively.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
This latter point is further supported by histograms of the instantaneous QuikSCAT divergence segregated by season (DJF and JJA) in Fig. 6b. The MAM and SON distributions are also shown for reference. Note that the MAM distribution is quite similar to DJF and the SON distribution is similar to the JJA. Extreme convergences occur about twice as often in DJF compared to JJA. This leads to a larger AW divergence skewness magnitude in DJF compared with JJA (Table 1).
These seasonal divergence histograms also reveal that, while extremes of either sign are more common during DJF, the mode of the divergence distribution is significantly more positive during DJF compared to JJA (which are, respectively, 0.8 × 10−5 and 0.5 × 10−5 s−1). The seasonal shift of the mode offsets the more frequent occurrence of extreme convergences during DJF associated with storms, leading to only a modest seasonal change in the mean of the divergence distribution: −0.3 × 10−5 s−1 in DJF and −0.2 × 10−5 s−1 in JJA. The time-mean AW divergence is thus a woefully incomplete characterization of the seasonal variability of the AW divergence over the northwest Atlantic.
Why are positive divergences more frequent during DJF compared to JJA, even though extreme convergences are more frequent during DJF? In short, we believe it is a manifestation of the aforementioned increase in rain frequency for extreme positive divergences shown in Fig. 6c. Storms are more frequent during DJF compared to JJA, so it seems plausible that extreme positive divergences, embedded within storm systems, are also more frequent during DJF.
f. Time-mean spatially high-pass-filtered divergence
Even though the GSCZ evidently owes its existence to storms rather than local air–sea interaction as suggested previously, a divergence minimum exists in the time-mean 2σ-filtered divergence field shown in Fig. 5b. This leaves open the possibility that the SST signature of the Gulf Stream contributes to the time-mean divergence field, but in a way that affects mainly smaller scales while the aggregate effect of storms occurs over comparatively larger spatial scales. The divergence minimum can be seen more clearly by applying a spatial high-pass filter to the AW QuikSCAT temporally unfiltered and 2σ-filtered fields, where the high-pass filter attenuates variability on spatial scales less than 1000 km. Maps of the resultant 10-yr-mean spatially high-pass-filtered fields are shown in Figs. 11a and 11b; the complementary spatially low-pass-filtered fields are shown in Figs. 11c and 11d. Perhaps the most significant result here is that the spatially high-pass-filtered fields are nearly identical for the temporally unfiltered and 2σ-filtered fields. The corresponding spatially low-pass-filtered fields, however, are much different, as evident from comparing the panels in Figs. 11c and 11d. This indicates that the synoptic weather variability discarded in the 2σ-filtered fields essentially leaves a large-scale residual convergence pattern in the time-mean divergence fields.
Maps of the 10-yr time-mean QuikSCAT divergence (colors) and Reynolds SST Laplacian (contours). Each map differs in the spatial and temporal filtering applied to the divergence and SST Laplacian as follows: (a) temporally unfiltered and spatially high-pass filtered, (b) temporally 2σ extreme-value filtered and spatially high-pass filtered, (c) temporally unfiltered and spatially low-pass filtered, and (d) temporally 2σ extreme-value filtered and spatially low-pass filtered. The spatial high (low)-pass filter attenuates spatial variability with wavelengths longer (shorter) than 1000 km. For the SST Laplacian contours, the contour interval is 1 × 10−10 °C m−2, positive contours are solid and negative dashed, and the zero contour has been omitted for clarity.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
While a minimum of time-mean AW divergence over the Gulf Stream may be evidence of an atmospheric response to SST, it does not imply that SST forces a deep atmospheric response according to the EBMA mechanism. A minimum of surface divergence does not by itself provide the necessary forcing to achieve a deep atmospheric response. In this case, if the large-scale fields are interpreted as evidence of forcing by storms and small-scale SST, then storms are still necessary to explain the “anchoring” of convergence and upward motion over the Gulf Stream.
Finally, it is noted that none of these techniques perfectly remove all traces of storms from the instantaneous divergence, so the divergence minima along the Gulf Stream in the filtered mean fields is not a clear indication of local air–sea interaction but could very well be storm related. Nonetheless, our conclusion is that the existence of the GSCZ in the time-mean winds owes its existence to extreme storm convergences, since removing a relatively small number of data points associated with storms removes the time-mean convergence. We argue in section 5 that SST does have a systematic influence on the surface divergence, but that it nonetheless cannot account for the GSCZ.
4. Effects of synoptic weather variability on time-mean winds and surface pressure
Thus far, we have shown that the GSCZ is sensitive to a relatively small number of extreme weather events. This is difficult to reconcile with the hypothesized EBMA mechanism, since the Gulf Stream SST fronts do not vary much on synoptic time scales. Because the GSCZ virtually vanishes when storms are excluded from the data, the natural question arises about how storms affect the time-mean pressure and vertical velocity fields and how they appear to correlate with the time-mean convergence band. To shed insight into this question, we investigate whether SLP and vertical velocity are likewise affected by synoptic weather variability and how this relates to the underlying SST distribution. Model simulations using the U.S. Navy’s Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS)1 are used to analyze variables involved in the hypothesized atmospheric response to SST that cannot be observed directly—specifically, the SLP and the vertical velocity.
a. Description of COAMPS simulations
High-resolution atmosphere simulations using COAMPS (Hodur 1997) were performed in an uncoupled configuration for the calendar year 2009 in the northwest Atlantic. This simulation included a nested grid, with the innermost nest having a 9-km horizontal grid spacing and 50 vertical levels, with 15 levels residing within the lowest 1000 m. A map of the boundary of the inner nest is shown in Fig. 12. We considered only grid points from the inner nest and over the ocean for the analysis presented here. Instantaneous prognostic variables were output at hourly intervals to capture the rapid temporal evolution and propagation of synoptic weather disturbances. Outer boundary conditions were supplied every 6 h by the U.S. Navy’s Operational Global Atmospheric Prediction System (NOGAPS; Hogan and Rosmond 1991). The SST surface boundary condition was provided by the high-resolution U.S. Navy 3DVAR Navy Coupled Ocean Data Assimilation (NCODA) SST analysis (Cummings 2005), which was updated every 12 h using ship, buoy, and satellite SST observations and analyzed onto the model’s 9-km grid using the two-dimensional optimum interpolation analysis procedure described by Cummings (2005).
Map showing the geographical boundary of the inner nest of the COAMPS simulation analyzed here (red box). Shading shows relative topography or bathymetry.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
b. Covariability of time-mean divergence and the SLP and SST Laplacians
1) All-weather means
Maps depicting the time-mean COAMPS divergence and the SLP and SST Laplacians in all-weather conditions are qualitatively similar, as shown in the left column of Fig. 13. Hereafter, any reference to a time-mean variable from the COAMPS simulation refers to a 1-yr mean for 2009. Although the COAMPS AW divergence is only a 1-yr mean (Fig. 13a), it agrees well in terms of spatial structure and amplitude with the 10-yr-mean QuikSCAT AW divergence shown in Fig. 1a. Particularly relevant features of interest for this study that COAMPS appears to simulate well include the GSCZ, the region of positive divergence north of the Gulf Stream, and the strong divergence near the Grand Banks (42°N, 50°W).
Maps of surface fields from the 1-yr COAMPS simulation for 2009: (a)–(c) 10-m AW divergence, (d)–(f) AW 
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
The SLP Laplacian is mapped as its negative (i.e., as 
The degree of covariability between the time-mean divergence, 
Cross-correlation coefficients between the time-mean AW variables that were computed from the 1-yr COAMPS simulation. The 10-m surface wind divergence is denoted as 
2) Conditional means in rain-free and rain-only conditions
When the fields of the surface divergence and the SLP Laplacian are averaged conditionally into rain-free and rain-only components, a much different picture emerges compared to the all-weather time means, as shown in the middle and right columns of Fig. 13, respectively. The presence of rain was determined from nonzero values of the COAMPS 1-h accumulated rain amount. The COAMPS rain frequency for 2009 matches the 10-yr-mean satellite-based estimate shown in Fig. 2a to within about ±3%.
The time-mean AW divergence and the SLP and SST Laplacians agree fairly well with each other, consistent with the aforementioned previous studies supporting the EBMA mechanism. The rain-free 
One subregion where there is qualitative agreement between the time-mean RF divergence and SLP Laplacian is along the northern edge of the Gulf Stream frontal zone northeast of Cape Cod, where there is strong positive divergence in the time mean. Even in this subregion, however, the time-mean SST Laplacian (Fig. 13h) is not well correlated with the time-mean RF SLP Laplacian (Fig. 13e), and it is thus likely that other processes discussed in more detail below are affecting the divergence and SLP that are unaccounted for in the hypothesized EBMA mechanism. Most importantly, the time-mean RF divergence bears no resemblance to the SST Laplacian, as seen from comparison of Figs. 13b and 13h. A clear SST influence on the surface divergence consistent with the EBMA mechanism thus does not exist in rain-free conditions, on average, which occur in this region more than 80% of the time.
A clear SST influence on the time-mean divergence is likewise not apparent in the rain-only time means, as shown in the rightmost column of maps in Fig. 13. Note that the RO time-mean divergence and SLP Laplacian fields have been divided by 3 to fit the same color scale as the AW and RF time means, which underscores the much stronger dynamics involved in raining weather systems compared to the relative quiescence of rain-free conditions. While the RO divergence is strongly negative everywhere, the RO SLP Laplacian changes sign from north to south near 30°N latitude. Indeed, the large difference between the RF and RO SLP Laplacian fields indicates that storm systems strongly influence the SLP Laplacian. Not surprisingly, however, the SST Laplacian forcing is virtually the same regardless of whether it is raining or not.
The additional information provided by the COAMPS simulation indicates that the surface pressure forcing is strongly affected by raining synoptic weather disturbances, consistent with the conditionally averaged satellite divergence shown in the previous section.
3) Extreme weather effects on the time-mean AW divergence and SLP Laplacian
The time-mean COAMPS divergence and SLP Laplacian both exhibit similar sensitivities to removal of extreme events as was shown in section 3 for the QuikSCAT AW divergence. This is evident from comparing the time-mean divergence computed before and after application of the same 2σ extreme-value filter used in section 3a in Figs. 14a,b; the likewise filtered 
Maps of the time-mean surface fields from the 1-yr COAMPS simulation: (a) AW divergence, (b) AW divergence after application of 2σ extreme-value temporal filter, (c) percentage of AW divergence points removed by the filter, (d) AW 
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
Focusing momentarily on the time-mean 
c. Covariability of the instantaneous AW divergence and the SLP and SST Laplacians
Quite surprisingly, the significant correlations between the SST Laplacian and either the divergence or the SLP Laplacian are not preserved when considering instantaneous fields rather than the time means. As listed in Table 2, the cross-correlation coefficient between the AW divergence and 
One intriguing result from the COAMPS simulation is the almost identical cross correlation between the divergence and SLP Laplacian in both the instantaneous and the time-mean fields. Some insight into why this is the case can be seen by considering Fig. 15, which shows a snapshot of the COAMPS surface divergence (colors) and SLP Laplacian (contours) at approximately the same time as the satellite observations shown in Fig. 4 of a typical extratropical cyclone traversing this region. Solid and dashed contours correspond to positive and negative values of the SLP Laplacian, respectively. The anticorrelation is very strong in this snapshot (ρ = −0.75), which we found is typical for variability in extratropical cyclones. Along the main cold and warm frontal boundaries, very strong convergence is accompanied by strong positive perturbations in the SLP Laplacian. The amplitude of the positive SLP Laplacian along the frontal zone is between 20 and 60 × 10−9 Pa m−2, which is one to two orders of magnitude larger than typical values of the time-mean SLP Laplacian shown in Fig. 13d. Smaller amplitude collocated perturbations of positive divergence and negative SLP Laplacian are also evident in the cold-air pool behind the front and in the prefrontal region to the northeast of the disturbance. Animations of the model hourly divergence and SLP Laplacian fields also indicate that this example is indicative of typical conditions and is not an isolated event (not shown), which can also be inferred from the cross correlations presented here. It is thus apparent that a strong correlation exists between divergence and SLP Laplacian that is independent of local SST forcing on instantaneous time scales. At least some of the spatial correlation between the time-mean divergence and time-mean SLP Laplacian can thus be attributable to synoptic-scale processes along the storm track.
Snapshot of COAMPS 10-m divergence (colors) and SLP Laplacian (contours) for 0700 UTC 1 Jan 2009. Solid and dashed contours correspond to positive and negative SLP Laplacians, respectively, while the zero contour has been omitted for clarity; the contour interval of the SLP Laplacian is 4 × 10−9 Pa m−2. The maximum SLP Laplacian value associated with this storm is about 60 × 10−9 Pa m−2 at 35°N, 60°W, whose magnitude is more than 20 times greater than the magnitude of the largest time-mean value shown in Fig. 13.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
Ekman theory predicts that the surface convergence is forced directly by the geostrophic vorticity, which is just the SLP Laplacian scaled by the Coriolis parameter. The COAMPS fields shown in Fig. 15 are consistent with this frictional Ekman convergence, although surface convergence may also be influenced by other distinct processes operating in synchrony. For instance, on synoptic time scales, deep moist convection can force upward vertical motion and hence, via mass conservation, near-surface convergence (e.g., Skyllingstad and Edson 2009; Parfitt and Czaja 2016), differential temperature advection, and vorticity advection (the last two being the components of the quasigeostrophic omega equation). This process differs from traditional interpretations often used for longer time scales that surface convergence forces upward motion. A strong anticorrelation between convergence and the SLP Laplacian in this scenario, such as occurs in extratropical cyclones, for example, would thus not give definitive insight into cause and effect between the two. Regardless, these results indicate that a strong anticorrelation between surface divergence and the SLP Laplacian does exist in both the time mean and instantaneous fields that is independent of local SST effects. A strong negative correlation between the surface divergence and SLP Laplacian is therefore not an indication that the EBMA mechanism explains the existence of the GSCZ.
Although not explicit in previous work developing the EBMA mechanism, it appears that the assumed equivalence between the SLP and SST Laplacians implies the surface pressure adjustment to SST to be nearly instantaneous, or at least fairly rapid compared to the vertical and horizontal advective time scales. As shown above, however, the cross correlations between the SST Laplacian and the SLP Laplacian are insignificant when considering instantaneous time scales, and we could find no systematic interdependence between them over the Gulf Stream. At least part of the correlation between the SLP and SST Laplacians in their time means is thus due to the position of the storm track over the Gulf Stream, which focuses extremely large positive SLP Laplacian anomalies over the SST frontal zone that coincidentally contains nonzero SST Laplacian values. Our contention is not that the SLP does not respond to SST through MABL modification but rather that a definitive causal link between the divergence and the SST and SLP Laplacians consistent with the EBMA mechanism cannot be established simply through spatial cross correlations of their time means. It also does not imply that the SLP is not responding to SST in a dynamically meaningful way. For instance, recent work by Plagge et al. (2016) has identified a significant SLP response to the Gulf Stream frontal zone using high-precision barometric observations on a moored buoy at the edge of the Gulf Stream. They also inferred spatial shifts in the pressure response consistent with previous modeling studies and from work in the tropics (e.g., Wai and Stage 1989; Warner et al. 1990; Tomas et al. 1999; Cronin et al. 2003; Small et al. 2005; Song et al. 2006; Small et al. 2008; O’Neill et al. 2010b; Kilpatrick et al. 2014). It may be that the details of this spatial shift render the assumption of a pointwise equivalence between the SLP and SST Laplacians too simplistic. In any event, the location of the storm track right over the Gulf Stream confounds statistical identification of any SST-induced response consistent with the EBMA mechanism.
d. Time-mean vertical velocity w
The major thrust for examining the GSCZ from time-mean surface winds was predicated on the hypothesis that SST-induced convergence fuels upward motion, which in turn anchors rainfall to its observed position in the northwest Atlantic (Minobe et al. 2008). In this scenario, near-surface convergence serves as an intermediary process linking SST to the upper troposphere. We now test whether the differences in conditional averages shown in the surface divergence demonstrated thus far in this paper also extend to the COAMPS vertical velocity.
First we show a latitude–height section of the vertical velocity across the GSCZ along a similar track shown in Minobe et al. (2008) and Brachet et al. (2012) (Fig. 16a). This figure shows the 1-yr-mean COAMPS w averaged over the range of longitudes indicated by the red box in the map. The gray lines indicate the position of the 12° and 22°C time-mean SST isotherms, which give an indication of the latitudinal position of the main SST frontal region associated with the north wall of the Gulf Stream. The contours in this figure show the time-mean horizontal divergence, with horizontal convergence indicated by dashed contours and positive divergence by solid contours. Upward vertical motion and boundary layer convergence dominate the all-weather time mean over the Gulf Stream near the core of the GSCZ at 39°N. The time-mean w achieves a maximum velocity of ~8 mm s−1 at about 8-km height, while maximum time-mean vertical velocities in the coarser-resolution ECMWF fields shown in Minobe et al. (2008) were 4–5 km above the surface. The latitude of the maximum upward motion is within the mean SST frontal zone. The RF and RO conditional averages are shown in Figs. 16b and 16c, respectively. These show a clear difference in sign with each other. More specifically, widespread weak subsidence and low-level divergence are apparent in the RF means, while widespread vigorous ascent and low-level convergence occur, on average, in the RO means. Additionally, the mean RO ascent is about 6 times larger in magnitude than the RF subsidence. So while rain is relatively infrequent, the extremely strong ascent within storm systems dominates the time-mean vertical velocity. This result is consistent with that expected based on the surface divergence fields shown thus far in this analysis and that the sign of the time-mean w is influenced by infrequent storm events.
Latitude–height section of the 1-yr-mean COAMPS vertical velocity w (colors) and horizontal divergence (contours; positive divergence contours are solid and dashed contours are convergence, both with an interval of 0.2 × 10−5 s−1). This cross section represents a longitudinal mean over the range of longitudes indicated by the red box within the inset map; the contours in this map represent the time-mean COAMPS SST with a contour interval of 2°C. The time means are for (a) all-weather, (b) rain-free, and (c) rain-only conditions. Here w is defined as positive for upward motion and vice versa. The magnitude of the vertical velocity for the rain-only conditional average has been scaled by a factor of 6 to fit within the color scale of the other two panels. The gray bars represent the latitudes of the 12° and 22°C mean SST isotherms as indicated and roughly indicate the mean position of the north wall of the Gulf Stream.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
Further evaluation of the COAMPS vertical velocity over the northwest Atlantic domain is shown in the maps in Fig. 17 near the model levels of 200 (top row), 1500 (middle row), and 5000 m (bottom row). The three columns correspond to the time-mean vertical velocity w averaged for AW, RF, and RO conditions. There is a band of upward vertical velocity in the AW time mean collocated with the GSCZ at all three levels. Within the GSCZ, the time-mean w increases from roughly ~2 cm s−1 at 200 m to ~8 cm s−1 at 5000 m. Conversely, there is mostly weak downward motion in the time mean throughout the surrounding areas which were marked by weak surface divergence in Fig. 13a. The mean RF w (Figs. 17b,e,h) does not exhibit any clear response near the Gulf Stream SST front, other than subsidence evident on the north side of the Gulf Stream in the lowest 200 m, which is consistent with low-level surface divergence. The mean RO vertical velocity (Figs. 17c,f,i) is strongly upward everywhere and its magnitude is more than 5 times greater than the RF mean w. There is no clear collocation of upward vertical velocity and the Gulf Stream SST front in the RF or RO means.
Maps of the time-mean COAMPS vertical velocity w at heights of (a)–(c) 200, (d)–(f) 1500, and (g)–(i) 5000 m for the 2009 simulation. The time means are for (left) all-weather, (center) rain-free, and (right) rain-only conditions. Note the difference in the dynamic range of the color scale for each height.
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
From these results, we conclude that the band of time-mean upward vertical motion is a residual associated mainly with the passage of extratropical cyclones, analogous to our earlier conclusions concerning the existence of the GSCZ in the time-mean surface winds. Upward vertical motion is thus not a persistent feature anchored to the Gulf Stream. Parfitt and Czaja (2016) recently found that the time-mean atmospheric vertical motion field was strongly influenced by synoptic weather disturbances over the Gulf Stream using ERA-Interim data, consistent with the results of this analysis. Brachet et al. (2012) found that the time-mean vertical velocity in the troposphere was influenced by the Gulf Stream SST gradient. However, their findings were based on long term time means, and they did not separate SST effects on the storm-track variability from the storm-free atmospheric response to SST. We also note that the vertical velocity fields are strongly skewed (e.g., Pendergrass and Gerber 2016), even more so than the surface divergence reported here. While not shown here, this asymmetry in the distribution of the vertical velocity field also influences the sign of the time-mean w in much the same way as asymmetry in the divergence distribution influences the time-mean surface divergence.
5. Evidence for SST influence on surface divergence and rainfall
The insignificant correlations between the divergence and SST Laplacian shown in the preceding sections of this analysis may leave the impression that SST does not influence the surface divergence in any meaningful way through a local MABL response. Our results show that the existence of the GSCZ in the time-mean wind field is due mainly to storms and the position of the storm track near the Gulf Stream. While a detailed observational analysis of the SST influence on surface divergence is outside the scope of this paper, we do make the point that SST does have a demonstrated influence on the time-mean divergence in the northwest Atlantic, even if it does not lead directly to a persistent GSCZ. A simple way to show this influence is by presenting the 10-yr-mean QuikSCAT divergence conditionally averaged based on the sign of the downwind SST gradient, computed from the QuikSCAT wind vectors and the Reynolds SST. Figures 18a and 18b show maps of these conditional means for negative and positive downwind SST gradient conditions, respectively. Based on the hypothesis that the wind speed is stronger over the warmer side of an SST front compared to the cold side, the divergence is expected to be positive when winds blow from cold to warm SSTs (i.e., positive downwind SST gradient), and convergence is expected in the converse case, when winds blow from warm to cold SSTs (i.e., negative downwind SST gradient). Indeed, when the downwind SST gradient is positive, there is very strong positive divergence near the Gulf Stream (Fig. 18b). Strong convergence appears, on average, when the downwind SST gradient is negative (Fig. 18a). There is thus compelling evidence that the Gulf Stream SST front affects the time-mean divergence in the MABL in addition to the aforementioned effects of synoptic weather variability.
Maps of the conditionally averaged QuikSCAT all-weather divergence for the 10-yr period November 1999–October 2009 based on the following conditions: (a) negative downwind SST gradient 
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
Maps of the TPMA rain frequency and rain-rate estimates based on the sign of the downwind SST gradient for the 10-yr period November 1999–October 2009: (a),(b) negative downwind SST gradient 
Citation: Journal of the Atmospheric Sciences 74, 7; 10.1175/JAS-D-16-0213.1
Contrast this result with a similar calculation, but based on the sign of the SST Laplacian computed from the Reynolds SST fields, as shown in Figs. 18c and 18d. The time-mean divergence shows virtually no dependence on the sign of the SST Laplacian and is further evidence that the SST Laplacian forcing is not a significant factor in determining the time-mean divergence in the northwest Atlantic.
We defer exploration of this relationship between divergence and downwind SST gradient to a further study since it is outside the scope of our present analysis. Suffice it to say, however, that there is clear evidence that SST plays a significant role in modification of the surface winds, and in particular, the surface divergence. It is possible that conditions exist in which the SST Laplacian modulates near-surface convergence consistent with the EBMA mechanism. One such condition can be inferred from the analytical model of Schneider and Qiu (2015) (N. Schneider 2015, personal communication). In the scaling argument for vertical velocity w, two limiting regimes exist that depend on the strength of the imposed background wind speed, ultimately suggesting different functional forms of the mesoscale SST forcing of the MABL. In strong winds, the vertical momentum mixing dominates, which yields a divergence dependence on the downwind SST gradient as suggested previously. In weak winds, the pressure forcing dominates, which implies scaling of divergence with the SST Laplacian consistent with the EBMA mechanism. The idealized simulations of Lambaerts et al. (2013) explored the case of weak background surface winds (more precisely, a constant boundary layer vertical shear with no wind at z = 0) and indeed found a MABL response to SST more consistent with the EBMA mechanism than with the downwind SST gradient, which appears consistent with the Schneider and Qiu (2015) scaling analysis. The downwind SST gradient forcing suggests that the wind direction relative to SST fronts and the magnitude of the SST gradient are dynamically relevant, while the SST Laplacian forcing suggests that only curvature in the SST field is dynamically significant and that the magnitude of the SST gradient and the large-scale wind direction relative to the front are dynamically insignificant. An empirical relationship between the surface divergence and the downwind SST gradient has been noted previously from satellite observations (e.g., Xie et al. 1998; Chelton et al. 2001, 2004, 2007; Haack et al. 2008; O’Neill et al. 2010a). The basis of this relationship stemmed from the well observed increase in surface wind speed as winds blow from cold to warm SSTs and vice versa and showed the importance of the large-scale wind direction relative to SST fronts in determining the sign of the wind divergence (O’Neill et al. 2010a). The Schneider and Qiu (2015) analytical model provides a path forward, supported dynamically, for understanding the possible conditions where each functional form (either the SST Laplacian or the downwind SST gradient) contributes to the frontal air–sea interaction.
We conclude this section by noting a significant association of the rain frequency and rain rate with the downwind SST gradient. Figure 19 shows the mean TMPA rain rate and rain frequency contingent upon the sign of the downwind SST gradient. For negative downwind SST gradients (i.e., most often associated with southerly flow from warm to cool SSTs), rain is more frequent (Fig. 19a) and the mean rain rate is higher (Fig. 19b) compared with positive downwind SST gradients (Figs. 19d and 19e, respectively). Additionally, the band of maximum rain frequency and rain rate is shifted a few hundred kilometers south over the core of the Gulf Stream for positive downwind SST gradients compared with negative downwind SST gradients. The band of maximum rain in positive downwind SST gradient conditions appears to coincide with the shift in the divergence minimum shown in Fig. 18b. This occurs despite the fact that positive downwind SST gradients occur more frequently over the Gulf Stream, as shown by comparing Figs. 19c and 19f.
These conditional averages of the rain rate and rain frequency are consistent with the idea that SST and wind direction influence the surface divergence and convergence, which manifest themselves in the modulation of rainfall. However, it is unclear whether this is the only mechanism at work here. For instance, rain is also known to be more frequent and intense in the warm sector of extratropical cyclones, which is characterized by strong and moist southerly flow. It is likely that both storms and the MABL response to SST are at work here; however, at present, it is difficult to separate these processes.
6. Conclusions
Our analysis explored the processes leading to a prominent band of convergence in the time-mean winds which overlies the Gulf Stream, which we have named the Gulf Stream convergence zone (GSCZ). A current leading suggests that the GSCZ results from a local boundary layer response to the Gulf Stream SST Laplacian. Our results, however, show that strong convergences associated with storms explains the existence of the GSCZ in the time-mean surface winds.
Strong extratropical cyclones have surface convergence signatures one to two orders of magnitude greater than the climatological mean. This generates a highly asymmetric divergence distribution skewed toward convergence. This skewness is sufficient to change the sign of the time mean and the interpretation of the SST influence on divergence. Removing fewer than 4% of the strongest divergence events, or removing fewer than 20% of values in raining conditions, effectively eliminates the GSCZ from the time-mean surface winds. A practical consequence of the asymmetry of the surface divergence distribution is that the effects of storms on the winds cannot be reduced to a negligible level through time averaging, as is commonly assumed.
In addition to the effect of storms on convergence, vertical velocity throughout the troposphere is likewise affected. Previous work has suggested that the Gulf Stream SST anchors upward motion and rainfall, with near-surface convergence associated with the GSCZ acting as an intermediary process coupling the ocean with the free troposphere. Model simulations in this analysis, however, showed that the coincidence of upward vertical velocity throughout the troposphere with the Gulf Stream is due to strong upward motion within extratropical cyclones rather than as a local atmospheric boundary layer response to SST. These findings are difficult to reconcile with the hypothesis that the Gulf Stream SST front anchors convergence, upward motion, and precipitation through the mechanism involving atmospheric boundary layer adjustment driven by the SST Laplacian. Indeed, the significant correlations between the time-mean divergence and the time-mean SLP and SST Laplacians reported previously are not preserved when considering instantaneous fields that resolve individual storm events.
SST does appear to contribute to variability in the time-mean divergence field, but its influence depends on the wind direction relative to the SST front as encapsulated by the downwind SST gradient. This relationship between divergence and the downwind SST gradient has previously been documented in many regions of the World Ocean and is observable in instantaneous data, while the relationship between divergence and the SST Laplacian is not. Further study is needed to understand whether conditions exist for the Ekman-balanced mass adjustment (EBMA) mechanism to operate. A likely possibility is that the EBMA mechanism may be most apparent in weak surface wind speeds (Lambaerts et al. 2013; Schneider and Qiu 2015)—much weaker than commonly observed in this region.
Our conclusion is not that SST does not influence the GSCZ. Quite the contrary, the Gulf Stream SST gradients are one ingredient influencing the position of the storm track in the northwest Atlantic. Thus, our contention is that the GSCZ is linked to SST, but through its effect on the storm-track location and storm intensity rather than just as a local boundary layer response. Both mechanisms strongly influence the time-mean winds in this region, as demonstrated here and elsewhere. Further research is needed to determine how the local boundary layer response to SST interacts with the storm track.
We close by noting that the effects of the midlatitude storm tracks on the time-mean surface divergence are not unique to the northwest Atlantic. From a preliminary analysis of global satellite observations, we have found that the time-mean wind fields over most areas of the midlatitudes are affected significantly by the intense convergence and cyclonic vorticity associated with intermittent but strong storm systems. The consequences of this result for understanding large-scale ocean and atmospheric circulation and coupled ocean–atmosphere interactions are not yet clear, although this study provides an unambiguous example where the time-mean wind and pressure fields gave a very misleading impression of the processes involved in ocean–atmosphere coupling.
Acknowledgments
This paper was funded under NASA Grants NNX11AF31G, NNX14AM66G, and NNX14AM72G, and Jet Propulsion Laboratory Subcontract 1540785. We thank the numerous contributions of Justin Small and one anonymous reviewer, which significantly improved the manuscript. We also thank Thomas Kilpatrick, Ralph Milliff, Niklas Schneider, and Doug Vandemark for their many helpful technical discussions involved in this work.
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