A Monthly Index for the Large-Scale Sea Surface Temperature Gradient Across the Separated Gulf Stream

The strong sea-surface temperature (SST) gradient associated with the Gulf Stream (GS) is widely acknowledged to play an important role in shaping mid-latitude weather and climate. Despite this, an index for the GS SST gradient has not yet been standardized in the literature. This paper introduces a monthly index for the large-scale SST gradient across the separated GS based on the time-varying

Furthermore, distinct air-sea interaction mechanisms have been linked to a broad range of spatiotemporal scales in SST gradients.For example, the "oceanic baroclinic adjustment" (Hotta & Nakamura, 2011;Taguchi et al., 2009), hypothesized to be a crucial component in maintaining baroclinicity in the mid-latitude storm track, is primarily associated with a large-scale SST gradient (like that spanning most of the separated GS ∼51°-75°W).
Local and fine-scale SST gradients in the GS region have been shown to significantly influence diabatic frontogenesis in the lower atmosphere (Parfitt et al., 2016;Reeder et al., 2021).
Despite the importance of the SST gradient, most published indices focus on variability of GS position rather than the SST difference across the GS (Chi et al., 2021;Joyce et al., 2000;Peña-Molino & Joyce, 2008;Pérez-Hernández & Joyce, 2014;Taylor, 1996).To the authors' knowledge, an index tracking the observed (and moving) GS SST gradient has not been published.The purpose of this letter is to develop and introduce such an index for wider community use, and to use the index to examine drivers of the GS SST gradient and its role in North Atlantic air-sea interaction.To demonstrate the methodology and assess the usefulness of an observational index, the GS SST index initially developed here captures the large-scale SST gradient across the entire separated (rather than topographically bound) GS from the separation point near Cape Hatteras to ∼51°W, on a monthly timescale.As such, analysis focuses on month-to-month variability associated with the separated GS SST gradient.
The methods used to calculate the index are provided in Section 2. Drivers of the SST gradient index, as well as potential atmospheric impacts on a monthly timescale and the basic properties of the index time series, are investigated in Section 3. A discussion is provided in Section 4.

Data and Methods
The SST used in this study is from a high-resolution satellite-derived data set, the 0.25° National Oceanic and Atmospheric Administration Optimum Interpolation SST (NOAA OISST v2), primarily based on the Advanced Very High Resolution Radiometer measurement, which is available since September 1981 (Reynolds et al., 2007).The surface heat fluxes and sea level pressure (SLP) are taken from the European Centre for Medium-Range Weather Forecasts reanalysis 5 (ERA5, Hersbach et al., 2020), provided on a 0.25° longitude-latitude grid (native horizontal resolution ∼0.28°), since 1979.The time-varying monthly mean GS path is defined using the 25 cm isoline (e.g., Andres, 2016;Lillibridge & Mariano, 2013;Rossby et al., 2014) of the sea-surface height (SSH) from Copernicus Marine Service, provided at 1/4° resolution, from 1993 to 2019.The black line in Figure 1a illustrates this monthly mean GS path for December 1998 (along with the December 1998 average SST plotted in color).GS rings are excluded from the definition through identification of the longest contiguous isoline.Note that we use the GS path in each month of each year, rather than the climatological monthly mean paths.From each monthly mean GS path, a 'northern' region is defined from 0.5° to 3° latitude to the north for each longitude in the longitudinal range 51°-75°W (blue boundary).Similarly, a "southern" region is defined to the south (red boundary).In the event there is more than one latitude occupied by the GS path at a particular longitude (as at 65°W in Figure 1a), the northernmost (or southernmost) path latitude is used for the northern (southern) region definition.In the case that 3° latitude north of the GS at any given longitude is over land, the coastline is used as the border at that longitude.It is emphasized that the northern and southern regions are not fixed here due to the large monthly variability in GS path (Andres, 2016), although fixed regions may be sufficient for other current systems (e.g., Ohishi et al., 2016Ohishi et al., , 2017)).Within each of these time-varying areas, the spatially averaged SST is calculated and the respective climatological monthly means for 1993-2019 are removed from each to obtain a northern and a southern SST anomaly.Subsequently, the large-scale separated GS SST gradient index value for any particular month in 1993-2019 is defined as the northern SST anomaly minus the southern SST anomaly.Negative (positive) values imply a stronger (weaker) GS SST gradient than usual for that particular month.Figures 1c and 1d show the time-series of the separated GS SST gradient index (color bars) with the time-series for the monthly SST anomalies averaged across the northern and southern regions respectively.The SST anomalies averaged across the northern and southern regions exhibit similar trends of 0.031 °Cyr −1 and 0.039 °Cyr −1 respectively, which nearly cancel such that the GS SST gradient index trend is only −0.008 °Cyr −1 .Seasonality of the GS SST index shows anomalies in the large-scale GS SST gradient from the long-term monthly means that are smaller in summer and fall than in winter and spring (Figure S1 in Supporting Information S1) Figure 1b illustrates the autocorrelation function of the GS SST gradient index time-series (Figures 1c and 1d), and is the subject of further discussion in Section 3.2.

SST Structures Associated With the GS SST Gradient Index
With a monthly SST gradient index for the separated GS defined, that index is used to explore drivers of the monthly large-scale SST gradient, as well as the temporal behavior of the SST gradient itself.A natural first question relates to the SST structures that contribute to variability in the large-scale separated GS SST gradient.To address this, Figure 2a plots the simultaneous correlation between the SST gradient index and the monthly de-seasoned SST anomalies at each grid-point, with all variables detrended and de-seasoned prior to correlation analyses.Interestingly, a tri-pole pattern emerges across much of the North Atlantic, with positive correlations to the north of the GS, negative correlations further to the south ∼30°N, and positive correlations in the eastern subtropical North Atlantic (although the positive correlations associated with this southern pole are barely statistically significant at 90%).The spatial extent of this correlation pattern suggests that variability in the SST gradient index is linked to large-scale forcing.Indeed, the leading empirical orthogonal function of North Atlantic SST, which is also a well-known SST tri-pole pattern, is associated with the North Atlantic Oscillation.The details of the tri-pole spatial structures, however, are not the same (Marshall et al., 2001), particularly in the GS region.
Notably, the region of significant negative correlation in Figure 2a occurs far south (∼10°) of the time average separated GS position, and south of the GS meander envelope.The lack of correlation in the region directly south of the GS suggests that the primary SST signal driving the large-scale SST gradient is in fact associated with the region to the north of the GS.Correlations (after detrending and de-seasoning) between the monthly SST gradient index and the time-series of the monthly SST averaged over the northern and southern regions (e.g., Figure 1a) indeed confirm this-for the northern region it is 0.75, whereas for the southern region it is −0.17.In other words, a strengthening of the SST gradient results primarily from colder SST to the north of the GS.It is also noted that this strong co-variability between the SST gradient and the SST averaged across the northern region is strong on an annual time-scale as well-recalculating the correlation on yearly means still results in a correlation of 0.67.The SST anomalies averaged over the northern and southern regions are modestly correlated (r = 0.44).
For reference, Figure 2b illustrates the correlation between the monthly SST at each grid-point and the monthly SST averaged over the northern region.The signal is of single sign and primarily localized to the north of the GS, although a weaker signal of the same sign occurs to the south of the GS.Interestingly, the correlation vanishes along the narrow GS path, which suggests that the broad warm anomalies surrounding the GS may be forced by the atmosphere, while the SST along the GS itself may be driven by a separate oceanic process, such as the heat transport by the GS.Examination of the correlation between the monthly SST at each grid-point and the monthly SST averaged over the southern region (Figure 2c) demonstrates a basin-wide relationship, with the spatial structure highly reminiscent of that induced by fluctuations in the North Atlantic Oscillation (NAO; Cayan, 1992;Deser et al., 2010).It is noted that the correlation patterns in the southern regions in Figures 2a and 2c are not similar (whereas in the northern regions in Figures 2a and 2b, they are highly similar).

Persistence of the GS SST Gradient Index
Next, we briefly examine whether the GS SST gradient index exhibits any temporal persistence.Accordingly, Figure 1b illustrates the autocorrelation of the GS SST gradient index.The autocorrelation exhibits a characteristic timescale of ∼5 months, consistent with typical SST persistence timescales in the mid-latitudes (Buckley et al., 2019;Bulgin et al., 2020).A statistically significant autocorrelation is also found at a lag of ∼2 years, indicating that processes driving the large-scale separated GS SST gradient may exhibit some degree of periodicity.One possibility could be a remote influence on the GS SST gradient of El Ninõ-Southern Oscillation (ENSO), which is known to impact North Atlantic SSTs directly to the north of the GS (Kwon et al., 2010;Rodríguez-Fonseca et al., 2016).However, while the autocorrelation of the time series associated with the northern region SSTs exhibits a similar peak at a lag of ∼2 years, it is not significant at 90% (Figure S2 in Supporting Information S1).

Role of the Atmosphere in the GS SST Gradient Index
The spatial structures of SSTs associated with the large-scale separated GS SST gradient, as well as those associated with the SSTs in the northern and southern regions were explored in Section 3.1.Lastly, we examine here how these SST structures are related to atmospheric variability.Figures 3a-3c illustrate correlations between the GS SST gradient index and anomalies (i.e., detrended and annual cycle removed) in both the SLP (contour) and net surface heat flux (positive downward, shading) at lags = −1, 0, +1 month (positive lag when the GS SST gradient index leads).Comparison of Figures 3a and 3b with Figure 2a indicates spatial coherence between heat flux anomalies and SST anomalies associated with variability in the GS SST gradient index.For positive values

10.1029/2022GL100914
6 of 9 of the GS SST gradient index, regions of increased heat flux into the ocean (i.e., positive anomalies) correspond with warmer SST and vice versa, indicating that the heat flux is driving the SST anomalies.The corresponding SLP anomalies exhibit high pressure anomalies over the subpolar gyre (Figure S3 in Supporting Information S1 shows a regression analysis of SLP with the GS SST gradient index)-the accompanying easterly anomalies between 40 and 50°N will act to reduce the strength of the overall westerlies, and thus the turbulent heat flux out of the ocean.These correlation patterns for the heat flux and SLP anomalies are strongest when the fields precede the GS SST index by 1 month (Figure 3a), and disappear when the GS SST index leads by 1 month (Figure 3c), which suggests forcing from atmospheric circulation variability on the GS SST index.This is consistent with the idea that an increase in low-pressure systems and associated atmospheric cold fronts will more frequently bring cold dry air over the GS region, resulting in increased heat loss from the upper ocean (Shaman et al., 2010).The lack of signal when the GS SST index leads by 1 month (Figure 3c) suggests no persistent ocean-atmosphere feedback via the large-scale separated GS SST gradient throughout the year, at least on a monthly timescale.
For completeness,Figures 3d-3f and 3g-3i illustrate analogous lead-lag composites, but for the SSTs averaged over the northern and southern regions, respectively.Similar patterns of heat flux and SLP variability are found in the relationship with the northern SSTs (Figures 3d-3f) as for the SST gradient index itself (Figures 3a-3c), though Figure 3d exhibits anomaly patterns shifted to the south.As such, the positive heat flux anomalies straddling the GS (Figure 3d) are consistent with broad warm SST anomalies to both the north and south of GS (Figure 2b).In addition, the lack of correlation with the heat flux in the narrow strip along the GS path (Figure 3d) is consistent with the lack of correlation with SST along the GS path (Figure 2b).This is also consistent with the results in Section 3.1, providing further evidence that the GS SST gradient index is primarily driven by SSTs in the northern region, which themselves are influenced by atmospheric forcing.For the SSTs in the southern region, Figure 3g again suggests that the SST variability is impacted by strong atmospheric forcing, which exhibits a north-south dipole similar to the NAO.Interestingly however, the absence of statistically significant correlations between heat flux anomalies and southern region SST anomalies at zero lag (Figure 3h) suggests the associated large-scale atmospheric forcing via air-sea heat exchange may not continue to persist once SST anomalies in the southern region have formed.This short duration during which heat fluxes determine southern region SSTs may be another potential factor in the primary importance of the northern SSTs for the GS SST gradient index.As for the GS SST gradient index, no evidence is found for a persistent ocean-to-atmosphere feedback via SSTs to the north or south of the GS throughout the year on a monthly timescale.

Discussion
A methodology for calculating the large-scale SST gradient of the separated GS on a monthly timescale has been developed.When all months of the year are considered, the large-scale SST gradient primarily results from SST variability to the north of the GS.These SSTs appear to be forced by atmospheric anomalies via changes in air-sea heat exchange.Analysis of the year 2019 (figures not shown) indicates this mechanism plays a role in setting the exceptionally strong large-scale GS SST gradient observed in that year, when the index exceeds −2°C (Figures 1c  and 1d).Both SST and heat flux variability in the region north of the GS can also be influenced by warm core rings shed from the GS (e.g., Gangopadhyay et al., 2020;Silver et al., 2021).However, initial analysis suggests that no simple relationship exists between the number of warm core rings formed in a given month and the monthly SST anomalies averaged over the northern region nor between the number of rings and the SST gradient index (not shown).This lack of relationship underscores the importance of atmospheric forcing for monthly heat flux gradient changes associated with the large-scale separated GS SST gradient.In contrast, the SST along the GS itself appears to be driven by a distinct oceanic process (e.g., heat transport by the GS).This is consistent with recent studies highlighting that mesoscale SSTs and air-sea heat fluxes along the western boundary currents are generally ocean driven on monthly timescales (Bishop et al., 2017;Small et al., 2019).Furthermore, the GS SST gradient index appears to exhibit a statistically significant autocorrelation at ∼2 years.This might represent forcing from the Pacific through the impact of ENSO on SSTs to the north of the GS.Such a relationship could in theory provide statistical information regarding the likelihood of a strong large-scale separated GS SST gradient impacting the atmosphere years into the future.
Despite the recent literature documenting the importance of the large-scale separated GS SST gradient for weather and climate, no evidence is found here of a persistent impact on the atmosphere throughout the year.This is not necessarily surprising, as the large-scale separated GS SST gradient is significantly stronger in winter than it is throughout the rest of the year (Figure S1 in Supporting Information S1).Furthermore, in wintertime, atmospheric cold fronts are significantly more frequent and bring much colder and dryer air, leading to far greater air-sea heat exchanges in the GS region, both on average and in individual events.The average net turbulent heat flux in summertime is less than half it is in winter (Yu & Weller, 2007).Indeed, recalculation of Figure 3, but restricting correlations to just the December-February season illustrates much stronger correlations than when calculated for all the months (Figure 4).Furthermore, Figure 4c reveals statistically significant heat flux and SLP anomalies when the GS SST gradient index leads the atmosphere by 1 month.This suggests evidence of ocean-atmosphere feedback in wintertime that does not exist at other times of the year, that may contribute to increased persistence of monthly atmospheric SLP anomalies.Such a relationship has previously been observed by Ciasto and Thompson (2004) and Wills et al. (2016) using an index based on SST anomalies averaged over the GS region.
Several other avenues of research are natural extensions to this initial study of the large-scale SST gradient across the separated GS.It would be useful to perform a similar investigation into the SST gradient associated with the topographically bound GS to the south of the GS separation point near Cape Hatteras, as well as with the Mid-Atlantic Bight shelfbreak front to the north.This would aid in comparing the relative importance of surface temperature gradients at the land-sea boundary versus that across the separated GS front.Additionally, application of the method to the Kuroshio Extension would allow comparisons between the Pacific and Atlantic, although difficulties may arise from the complicated oceanic structure (e.g., Kida et al., 2016).It would also be interesting to explore the relationship between the GS SST gradient index and the latitudinal and path length variability of the GS, although preliminary analysis suggests no obvious co-variability on a monthly timescale (not shown).Application of an analogous methodology for daily timescales is also warranted, given that several studies have noted the importance of the GS SST gradient on daily timescales or shorter (Parfitt & Seo, 2018;Reeder et al., 2021).In relation to this last point, it may also be prudent to investigate whether the SST itself can be used to define such a GS SST gradient metric, which would provide the benefit of a longer record (1982-present for SST vs. 1993-present for SSH) and also all analysis would be limited to one data product.Indeed, atmospheric variability has been shown to vary significantly between data products because of differing SSTs (Masunaga et al., 2015(Masunaga et al., , 2018;;Parfitt et al., 2017).Lastly, the large-scale separated GS SST gradient index presented here captures only some of the fine-scale SST gradient variability along the GS (Figure S4 in Supporting Information S1), since the relatively broad regions used to define the index likely dampen much of the mesoscale SST variability.The development of indices to represent the local SST gradients across the GS region is critical, as many studies have indicated the significance of fine-scale turbulent heat flux gradients (e.g., Gentemann et al., 2020), that are present with sharp local SST gradients, for the development of atmospheric fronts and the associated circulation and precipitation (Jacobs et al., 2008;Parfitt et al., 2017).These avenues of research are currently underway.

Figure 1 .
Figure 1.(a) The definitions of the regions for calculating the Gulf Stream (GS) sea-surface temperature (SST) gradient index, as defined for December 1998, with monthly average SST shown in color.The black line represents the monthly mean GS path based on the 25 cm isoline, the blue and red boundaries denote the northern and southern regions, respectively.(b) Autocorrelation function of the GS SST gradient index time series in (c-d).The light blue curves indicate statistical significance at 90%.(c) GS SST gradient index (color bars).Also shown in blue is the SST anomaly averaged over the northern region of the GS path.(d) As in (c), but with the SST anomaly averaged over the southern region shown in red.Note the time series for the southern region is multiplied by −1 to be consistent with the definition of the GS SST gradient index, and that the time series shown in (c-d) include their respective long-term linear trends.

Figure 2 .
Figure 2. Correlation between monthly de-seasoned sea-surface temperature (SST) anomalies at each grid-point and (a) the Gulf Stream SST gradient index, (b) the SST averaged over the northern region, and (c) the SST averaged over the southern region.Black contours indicate statistical significance at 90%.All variables are detrended prior to calculating correlations.

Figure 3 .
Figure 3. Correlation for the anomalies in the net surface heat flux (positive downward, color shading) and sea level pressure (SLP) (contours) against (a-c) the Gulf Stream sea-surface temperature (SST) gradient index (d-f) the SST anomalies averaged over the northern region, and (g-i) the SST anomalies averaged over the southern region.All variables are detrended prior to calculating correlations.The first row (a, d, g) is when the heat flux and SLP lead by 1 month.The second row (b, e, h) are simultaneous.The third row (c, f, i) is when the heat flux and SLP lag by 1 month.Thick black contours indicate statistical significance at 90% for heat flux correlations.The SLP correlations are statistically significant at 90% for correlations of 0.2 or higher.The thin red, blue and black contours indicate positive, negative, and zero correlations for SLP, with 0.1 interval.