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A New Robust Frontal Disturbance Index of the Oyashio Extension Sea Surface

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Temperature Front.

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Richard J Hall1, Arnaud Czaja1, Gokhan Danabasoglu2, Clara Deser2,

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Claude Frankignoul3,4, Young-Oh Kwon3

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Department of Physics, Imperial College, London

National Center for Atmospheric Research, Boulder Colorado

Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
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LOCEAN, Sorbonne Université/IRD/CNRS/MNHN, Paris, France

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Corresponding author

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Richard J. Hall

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Department of Physics

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Imperial College

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London SW7 2BW

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rjhall@imperial.ac.uk
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Abstract

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The Oyashio Extension (OE) frontal zone in the Northwest Pacific Ocean is associated with37

strong gradients of sea-surface temperature (SST) and salinity. Like other frontal zones, the38

OE front enhances baroclinicity and anchors the storm tracks; thus, changes in its position

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and strength may impact atmospheric variability. North-south shifts in the OE front are often

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defined using the leading principal component for the latitude of the absolute maximum SST

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gradient in the Northwest Pacific (145-170°E)-the so-called Oyashio Extension Index (OEI).

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We show that the OEI is sensitive to the choice of SST dataset used in its construction, and43

that regressions of atmospheric fields onto the OEI also depend on the choice of SST

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datasets, leading to non-robust results. This sensitivity primarily stems from the fact that the45

longitudinal domain used to define the OEI includes a region with parallel or indistinct

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frontal zones in its central section (155-164°E), leading to divergent results across datasets.

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In particular, we advise against the use of ERA5 SST data for such analyses, as it is a clear

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outlier. To circumvent the robustness issue, we introduce a new index that considers the49

degree of continuity of the SST front across this central section - the Frontal Disturbance50

Index (FDI). We show that the FDI produces more robust results on the influence of the OE

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front on air-sea interactions and associated high-frequency storm-track metrics than the52

conventional OEI. There are significant asymmetric associations between the FDI and storm-

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track metrics dependent on the sign of the FDI.

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Significance Statement56

In this study we aim to understand how the choice of dataset may influence the interpretation57

of interactions between the ocean and the overlying atmosphere near sea-surface temperature

58(SST) fronts. We find that using different SST datasets affects the results, due to slight59

differences in the representation of the location of the maximum SST gradient. As a response60

to this we develop a new index which relates to the degree of disturbance of the SST front.

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This produces results that are more consistent across the different datasets. We also identify

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Some possible links between the frontal disturbance and the presence of ocean eddies. We

63advise that the sensitivity to dataset choice is given due consideration in regions near SST

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fronts.

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1.Introduction

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Oceanic western boundary currents (WBCs) transport significant quantities of heat eastwards

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and polewards in both the North Atlantic and Pacific Oceans. In the Atlantic the WBC is the69

Gulf Stream, while in the Pacific the configuration is different: to the south is the Kuroshio

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current, while to the north and forming part of the subpolar gyre, is the Oyashio current (Qiu,

712019). Both currents turn eastwards away from the coast of Japan and into the Pacific basin

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where they are known as the Kuroshio Extension (KE) and Oyashio Extension (OE; also

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sometimes referred to as the subarctic current or front), located at around 35°N and 41°N

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respectively (Kwon et al., 2010). The OE is associated with strong gradients of sea-surface

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temperature (SST) and salinity, whereas the KE is more clearly defined by a gradient in sea-

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surface height (SSH) (Qiu et al., 2017). These features are shown schematically in Figure 1.

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The region is very complex, with a number of diverging and converging currents between the78

two extensions (Kida et al., 2015; Yasuda, 2003)

SAC

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Mean OE

OY

J2

J1

KENB/KBF
KE

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Figure 1. Schematic of the location of fronts referred to in the text. KE: Kuroshio Extension;
KENB/KBF: Kuroshio Extension Northern Branch/Kuroshio Bifurcation Front; OY: Oyashio
Current; SAC: Subarctic Current; OE: Oyashio Extension (143-173°E, shown in white); J1, J2:
Isoguchi jets. Background field is the mean December-March (DJFM) SST gradient from the
Reynold optimally interpolated (OI) SST dataset. (SST is not detrended). Meridional lines (1and 2) mark the longitudinal segment within the OE used to calculate the Frontal DisturbanceIndex (FDI: 155-164°E). Data are not detrended.

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The strong meridional gradients of SST in the OE region may act to enhance baroclinicity and89

anchor the storm track in the overlying atmosphere (Hoskins and Valdes, 1990; Nakamura et90

al., 2008) and have been the focus of numerous observational and modelling studies concerning91

air-sea interactions (Kwon et al., 2010; Frankignoul et al., 2011; Taguchi et al., 2012; Smirnov

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et al., 2015; Révelard et al., 2016; 2018). Air-sea heat fluxes associated with mesoscale air-sea

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interaction are robust in the vicinity of WBCs (Seo et al., 2023). The SST signal from94

mesoscale processes such as eddies and SST fronts modify the surface turbulent heat and95

momentum fluxes and cause local responses in the marine atmospheric boundary layer (Small96

et al., 2008). This in turn drives a non-local response in the storm-track (e.g. Czaja et al., 2019;97

Seo et al., 2023). A poleward decrease in sensible heat flux across the frontal zone sustains

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the strong near-surface baroclinicity against the relaxing effect of strong poleward eddy heat99

transport (Sampe et al., 2010).

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It is important to better understand the nature of SST variability and associated air-sea

102interactions along oceanic frontal zones, to improve the process level understanding of ocean-103

to-atmosphere feedbacks as well as the performance of model simulations. Crucial questions

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are the extent to which air-sea interactions over the OE region influence the wider atmospheric105

circulation, and how this depends on the sharpness of the SST gradient, location of the gradient106

and magnitude of the associated SST anomalies more generally (Small et al., 2019). Many

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modelling studies (e.g. Smirnov et al., 2015; Ma et al., 2017; Kuwano-Yoshida and Minobe,108

2017; Yook et al., 2022) impose observed SST anomalies in the Kuroshio-Oyashio Extensions

109(KOE) region in an atmospheric model to investigate causal linkages. The atmospheric110

response may depend not only on the spatial resolution of the model, but also on that of the111

imposed SST anomalies. Only when the model has sufficient horizontal resolution can the full112

impact of mesoscale forcing by SST fronts on the storm track be correctly simulated (e.g.

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Smirnov et al., 2015; Ma et al., 2017).

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To address these questions concerning air-sea interactions, there must be high confidence in

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determining the location and shifts in these SST frontal zones, and the nature of the associated117

SST anomalies. Frankignoul et al. (2011) developed an OE Index (OEI) based on the location

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of the maximum SST gradient in the OE region (145-170°E), which has been used in a number

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of subsequent studies (e.g. Kwon and Joyce, 2013; Smirnov et al., 2015; Qiu et al., 2017, Wu

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et al., 2018; Yao et al., 2018a,b). Frankignoul et al. (2011) identified that north-south shifts in121

the SST front were associated with large-scale atmospheric responses up to three months later.

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Subsequent work (Qiu et al., 2017) concluded that the western (145-153°E) and eastern (153-123

173°E) sections of the OEI were in fact uncorrelated on a synchronous basis over a range of

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different timescales, although lagged relationships did occur. The different sections of the front

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were driven by different physical mechanisms (Wu et al., 2018), and were associated with126

different SST anomaly patterns. It therefore makes sense to treat the variability of the two4

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sections of the front separately. Other studies identify SST frontal indices based on simple

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regional anomalies, although these are often applied to the general KOE region (e.g. 36-42°N,

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140-171°E) and may provide different information about air-sea interactions that are not130necessarily connected to shifts in SST fronts (e.g. Taguchi et al., 2012; Wills and Thompson,

1312018).

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The reliability of analyses of SST-front-driven air-sea interactions depends on the ability of134

SST datasets to accurately represent the SST front. New high-resolution gridded SST datasets

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are available, with horizontal resolutions commonly of 0.25° in latitude and longitude or136

higher. The credibility of these SST products depends upon the availability of observations and137

the gridding procedure used (Huang et al., 2021). Gridded SST datasets capture well large-

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scale modes of variability such as El-Nino-Southern Oscillation (ENSO) with high correlations

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between time series derived from different datasets (Yang et al., 2021). However, for assessing

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air-sea interactions over the WBCs and associated SST fronts, there is considerable variation

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between datasets and the sharpness of a front in the dataset is not necessarily proportional to142

the grid resolution used (Martin et al., 2012; Fiedler et al., 2019). These differences are related

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to distinctive retrieval and interpolation methods and interpolation grid-size, and bias-

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correction of input data (Yang et al., 2021).

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We are therefore motivated to calculate the OEI for a range of SST datasets to determine first,

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their level of agreement and second, to identify whether the differences impact significantly on

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the interpretation of air-sea interactions. We also investigate whether any discrepancies in the149

OEI have any physical basis, and the significance of this for future studies. We find that the150

OEI interaction with atmospheric variables is dataset dependent. This leads us to develop a151

new index, the Frontal Disturbance Index (FDI), which, we think, is more robust to variations

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between datasets. The data used in the study are described in section 2, and methods are

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explained in section 3. Section 4 presents our results, and section 5 is a discussion and summary154

of our findings.

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2.Data157

In assessing air-sea interactions associated with SST fronts, reliable high-resolution SST

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datasets, which resolve mesoscale processes are required. One option is to obtain these from159

the newest generation of gridded observational datasets, with increased temporal and spatial

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resolution. The National Oceanic and Atmospheric Administration (NOAA) optimum5

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interpolated (OI) SST version 2.1 dataset (Reynold et al., 2007; Banzon et al., 2016; Huang et162al., 2020) is available at daily resolution on a 0.25° grid from 1981 to the present for the163

AVHRR-only product. The Operational Sea Surface Temperature and Sea Ice Analysis

164(OSTIA) dataset (Donlon et al., 2012; Good et al., 2020) is available from October 1981

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onwards at a daily resolution on a 0.05° grid. In addition, we use the Group for High-Resolution

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SST Multi-Product Ensemble (GMPE, Martin et al., 2012; Fiedler et al., 2019) analysis for167

1981 to 2016 at daily resolution on a 0.25° grid. The GMPE uses an ensemble of six high-168

resolution products (including OSTIA and OI; Fiedler et al., 2019) and takes the ensemble

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median value for each grid box, having regridded the data to a common grid. Details of the170

method are described by Martin et al. (2012). We also compare these products to the SSTs in171

the ERA5 reanalysis (Hersbach et al., 2020), available on a 0.25° grid with an hourly timestep

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from 1940 onwards. ERA5 uses Hadley Centre Ice and Sea Surface Temperature version 2.1.0

173(HadISST2.1.0) for the period to 2007 (at 5-day and 1° resolutions; J.J. Kennedy, pers.comm),

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and OSTIA thereafter. It should be stressed that none of these datasets is independent, as they175

use many of the same satellite, and in-situ data sources; however they are selected as being176

representative of typical datasets that may be used in the analysis of air-sea interactions. We

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calculate monthly means of daily data for the common period January 1982 to December 2016,178

regridding to a common 0.25° grid. The OEI and FDI are calculated separately for each SST

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dataset (see section 3).

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Atmospheric and surface flux variables (sea-level pressure (SLP), meridional wind, total

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precipitation, latent and sensible heat fluxes, vertical velocity (omega)) are obtained from the183

ERA5 reanalysis, to assess the impact of different OEI and FDI indices on storm-track

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variability. Sea-surface height (SSH) data are obtained by using the sea-level anomaly dataset

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from the Copernicus Marine Environment Monitoring Service (CMEMS). This is an altimeter

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satellite product available as gridded data at 0.25° and daily resolution, from 1993 (doi:187

10.48670/moi-00148). For SSH we use the period 1993-2016, to ensure a common period with188

other datasets.

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3. Methods

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3.1 Definition of the Oyashio Extension Index (OEI)

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Following Frankignoul et al. (2011), we calculate the OEI as the monthly standardised

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principal component (PC) monthly timeseries for the first empirical orthogonal function (EOF)

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of the latitude of the absolute maximum meridional SST gradient for the September-to-April

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period, based on the monthly SST data. This period is chosen to avoid the summer season,

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because the summer SST gradient has different characteristics. We identify the latitude of the197

maximum SST gradient at each longitude over the OEI region at each timestep, but restrict the198

EOF calculation domain to the eastern part of the region (35-47°N, 153-173°E) following Qiu

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et al. (2017). We detrend the latitude of maximum SST gradients using a third order polynomial

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fit for the 1982-2016 period, and the mean seasonal cycle is removed by subtracting the201

climatological monthly means prior to the calculation of the EOF.

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Based on the monthly OEIs calculated from each dataset following the above procedure, three204

versions of the OEI are calculated for the December-March seasonal window: 1) monthly; 2)205

seasonal mean; and 3) monthly intra-seasonal (anomalies from the seasonal mean for each

206year). These indices allow us to compare how similar the indices are at different temporal

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resolutions. We also calculate an extended monthly series from September to April. The OEIs

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from different datasets for each of these versions are compared by computing pair-wise209

correlation coefficients and a time series of average pair-wise differences (the “Difference210

index”) is calculated for the September-April monthly timeseries.

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3.2. Definition of the Frontal Disturbance Index (FDI)213

The OE SST front is relatively weak and diffuse in the central portion of the domain (Fig. 1).

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To assess the extent to which the location of OE front departs from the climatology across this215

section, we compute a “Frontal Disturbance Index” (FDI) as follows. First, we calculate the216

detrended (third-order polynomial fit) standardised anomaly of the latitude of the SST front F

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as the latitude of the maximum SST gradient (f) as a function of longitude (l) and time218

(t=1…N) within 155-164°E:

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𝐹!,# =

𝜙!,# − 𝜙&#$' 1 ∑%+𝜙!,# − 𝜙&# ,
!&'
𝑁−1

(1)

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where the overbar denotes time mean. Then, we find the root mean square deviation of these222

standardised anomalies with respect to longitude (l=1…M):
(

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1
𝐹𝐷𝐼! = 1 3 𝐹!,# $
𝑀
#&'

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(2)

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Higher FDI values indicate a higher overall departure from the climatological time-mean. As

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constructed, the FDI captures both absolute departures from the time mean latitude, and also

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the extent to which the maximum SST gradient makes large latitudinal jumps between adjacent228

longitudes.

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A schematic diagram of the FDI calculated for synthetic data is shown in Figure 2. For this231

example, the climatology has an FDI value of zero, the minimum possible. SST gradient232

locations are chosen to show that the FDI value is proportional to the absolute magnitude of233

the mean displacement from climatology, not the sign (red and blue lines have equal FDI values

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even though they are on opposite sides of the climatology). As distance from climatology

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increases, so does the FDI (gray line). While the green line is purely zonal in orientation, it has

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an FDI of 4.5 as it intersects climatology at an angle, with increasing differences further from237

the intersection. The two stepped lines are the reverse of each other. However, their FDIs are

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different, as with the orange line the step down is broadly aligned with climatology whereas in239

the purple line, as climatological values decrease eastwards, the step broadly increases in240

latitude. In the SST datasets analysed here, the range of FDI values is from around 0.3 to 1.9.

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We also calculate a mean FDI, which is the ensemble mean of the FDIs calculated for different

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datasets at a given monthly timestep. For use in asymmetric regression, we remove the243

climatological monthly mean FDI from the timeseries, thus the large negative FDI values

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indicate the frontal positions close to climatology.

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Figure 2. Diagram of synthetic data simulating different locations of maximum SST gradients,
over the longitude and latitude range of the central section of the OE (155-164°E). The
synthetic climatological maximum SST gradient is shown by the bold black line, and fivedifferent synthetic gradient locations are shown, together with the FDI value for each.

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To assess any physical mechanisms that might be linked to the FDI, we isolate oceanic254

mesoscale features (including coherent eddies) in the region 150-170°E, 30-50°N. We use a255

two-dimensional fast Fourier transform (FFT) spatial filter to isolate high and low

256wavenumbers in the SST data. We filter daily data, using a filter length-scale of 420km as a257

cutoff, (wave number equal to 0.0024 km-1) to separate eddy length-scales from larger scales

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and then calculate the monthly standard deviation of the resulting data. The highpass filter

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isolates the mesoscale eddies, but produces a field with a lot of noise. To identify any large-

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scale patterns in the mesoscale eddies, we additionally apply a FFT lowpass spatial filter with261

the same cutoff as the highpass filter to the monthly standard deviation fields of the highpass262

data. For full details of the method used, see Sroka et al. (2022). For comparison we also263

calculate daily surface Eddy Kinetic Energy from the SSH data according to:

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1
1
𝑔 𝜕ℎ*
𝑔 𝜕ℎ*
𝐸𝐾𝐸 = +𝑢)*$ + 𝑣)*$ , = :;−A + ;A C, (3)
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2
𝑓 𝜕𝑦
ℎ 𝜕𝑥

3.3. Other Calculations

$

$

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where u’g and v’g are the zonal and meridional components of the geostrophic current anomaly267

respectively, f is the Coriolis parameter, g is the gravitational acceleration, h’ are the SSH

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anomalies and y and x are distances along the latitudinal and longitudinal directions

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respectively.

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We calculate the monthly standard deviation of 8-day highpass-filtered daily data of surface

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turbulent heat flux (THF, the sum of sensible and latent heat fluxes) and 500hPa vertical273

velocity (omega) by applying a 4-point highpass Butterworth filter to the daily data, to isolate

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variability at the synoptic timescale. These fields can give an indication of storm-track activity,

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increased variance being associated with passage of low-pressure systems, where both276

enhanced positive and negative heat fluxes and vertical velocity can occur in different locations

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within the same system, associated with warm and cold sectors and fronts. We also calculate278

indicators of surface storm-tracks, using an alternative highpass filtering approach involving

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daily differencing (Wallace, 1998). We apply this to 850hPa meridional wind and total

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precipitation. In addition, the Eady Growth Rate (EGR) at 800hPa is calculated according to:
𝐸𝐺𝑅 = −0.31

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𝑔 𝜕𝜃
(4)
𝑁𝜃+ 𝜕𝑦282

where N is buoyancy frequency, 𝜃 is potential temperature and 𝜃+ is the climatological monthly

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mean temperature (e.g., Small et al. 2014). The EGR is an important measure for identifying

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baroclinic eddy development (e.g. Hoskins and Valdes, 1990).

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We identify large-scale air sea interactions associated with the OEI and FDI by regressing the287

different atmospheric variables including storm-track metrics from ERA5 (section 2) on the288monthly timeseries. We use both conventional symmetric linear regression and asymmetric289

regression to accommodate potential non-linear associations with respect to the sign of the290

index (e.g. Révelard et al., 2016). The asymmetric regression method is described in detail in

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Frankignoul and Kwon (2022). Negative and positive values of the index (recall the FDI is292

adjusted by removal of the climatological mean, creating positive and negative values) are

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regressed separately against the relevant time steps of the cubic-detrended anomaly field,

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having first removed the time mean for negative and positive index values, separately, from295

each set of data to provide an unbiased estimate. Statistical significance for regressions is296

determined using the Wald test (similar to the Student’s t-test; Wald, 1943) and we present

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results for two levels of significance (p<0.1, p<0.2). We apply the False Discovery Rate (FDR;

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Benjamini and Hochberg, 1996; Wilks, 2015) to compensate for spatial autocorrelation and299

multiple testing.

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4.Results.

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4.1 The Sensitivity of the OEI to Choice of Dataset.

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Correlations between the OEIs show considerable variation between dataset pairs and depend

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on the temporal window and resolution used (Table 1).
correlation

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SONDJFMA DJFM
DJFM
DJFM
separate
separate
Seasonal
subseasonalmonthsmonthsmeananomalies
ERA5 vs. OI
0.72
0.62
0.69
0.49
ERA5 vs. GMPE
0.71
0.61
0.71
0.46
ERA5 vs. OSTIA
0.71
0.57
0.75
0.24
OI vs. GMPE
0.81
0.78
0.88
0.58
OI vs. OSTIA
0.80
0.72
0.77
0.53
GMPE vs.OSTIA
0.78
0.72
0.86
0.41
Table 1. Pearson correlations between the PC-based OEI timeseries for different SST datasets,
and for different temporal resolutions. All correlations are calculated for 1982-2016. All
correlations are significant (p<0.05).

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The correlations are higher for the September-April monthly resolution timeseries than for the310

extended winter (DJFM) monthly series, indicating weaker correlations in the winter months.

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Correlations for DJFM seasonal means are quite high (0.69-0.88), while those for subseasonal

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anomalies are much lower (0.24-0.58). The correlations for time series of separate DJFM

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months lie somewhere in between. Correlations with ERA5 and other datasets are generally

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lower than those between other dataset pairs.

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The September-April (SONDJFMA) OEI with monthly resolution shows good agreement317

across datasets at multiannual timescales (Figure 3a), while the Difference Index shows that318

there can be considerable disagreements on monthly timescales (Figure 3b). Over the319

September to April window, a seasonal cycle in correlations between ERA5 and the other320

datasets is evident (Figure 3c) with lower correlations in the winter months (generally February

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and March). The lower ERA5 correlations in February and March are also present in the322

subseasonal anomalies, although here the correlations are even lower, with increased noise in323

the datasets at subseasonal timescales (Figure 3d). These correlation statistics suggest that the324

OEI may be most suitable for use with seasonal means for calculating interannual variability.

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Figure 3 (a). The OEIs (eastern section, 153-173°E) for September to April with monthly
resolution based on the 4 different SST datasets, and (b) the mean absolute difference between
the indices, calculated between all indices (4-dataset difference) and without ERA5 (3-dataset
difference). (c) Interannual correlations between OEIs for each month in the window
September - April based on different pairs of SST datasets. (d) As in (c) but for the subseasonal
anomalies in DJFM. In c) and d) correlations between ERA5 and other datasets are shown asdashed lines and the horizontal dashed lines denote the significance threshold for p<0.1.

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When atmospheric and SST fields are regressed on these different OEIs, the results are336

inconsistent across the datasets, leading to concerns regarding interpretation when a single

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dataset is used (Figure S1). When OEI timeseries and SST datasets are swapped, so that for

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example the OI SST is regressed on the ERA5 OEI, the same spatial patterns of regression339

coefficients are obtained as that when regressing the ERA5 SST on the ERA5 OEI. This340

suggests that inconsistencies arise from the OEIs.

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From the results shown in Figure 3, ERA5 seems to be an outlier in that it disagrees with other343

SST datasets considered. Thus, we do not consider this SST product further in the subsequent344

analysis.

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4.2 Reasons for OEI Discrepancies

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Here we investigate the differences in the OEI across datasets to identify their origin. Our focus

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is on the spatial structure of SST gradients within the OE region.

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The SST gradient pattern in the OE region is complex. As an example, the February-mean SST

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gradient pattern for the OSTIA dataset is shown in Figure 4a. The region does not contain a352

single continuous front: there are parallel fronts, single well-defined fronts and regions where353

the front is poorly defined. Other datasets have very similar patterns (Figure S2) and those for354

other months are qualitatively similar (not shown).

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Figure 4. (a) Spatial pattern of the February mean SST gradient from OSTIA for 1982-2016.
White line shows the February climatological absolute maximum SST gradient. (b) Box andwhisker plots showing the February latitudinal distribution of the maximum poleward absolute
SST gradient at each longitude, for each dataset for 1982-2016 (OSTIA in blue, OI in gray and
GMPE in orange). The central box at each longitude shows the interquartile range (IQR), thehorizontal black line indicates the median. The whiskers extend from each box by 1.5 times
the IQR and dots indicate values that occur outside these ranges.

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The latitudinal occurrences of absolute maximum poleward SST gradients shown for February

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in Figure 4b illustrate these distinct regions. Within 150-155°E and 165-170°E there are strong,366

well-defined SST gradients. These clearly defined SST fronts to the west and east correspond367

to the locations of the Isoguchi jets (Isoguchi et al., 2006; Kida et al., 2015; J1 and J2 in Figure3681). These quasi-stationary geostrophic jets transport warm water polewards. This explains their369

consistent representation amongst the datasets and the relatively narrow interquartile ranges

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(IQR) in Figure 4b. However, within 155-165°E, the pattern of SST gradients is more complex.

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Two parallel SST gradient fronts are evident from 155-160°E (one near 40°N, and the other372

near 43°N (Figures 4a and S2). The broad IQRs on the boxplots here indicate sampling of the373

maximum SST gradient from both regions of strong SST gradients (figure 4b), with datasets

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showing different preferred latitudes at different longitudes and times. While OSTIA and

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GMPE show a skewed distribution with more frequent sampling of the northern front, the376

median value for OI is located further south, particularly between 156-157°E, indicating that377

the maximum SST gradient occurs more frequently along the more southern SST gradient378

region in OI. At around 159°E, OSTIA has a much wider IQR than either OI or GMPE.

379

Between 160-164°E there is a more diffuse front, with fragmented sections of stronger and380

weaker gradients. In February this zone of weak overall gradients is broadest latitudinally and381

may contribute to the low correlations in OEI timeseries in February (Figure 3c,d). Some of382

the differences between the OEIs arise from the central section: either slight differences in the383

representations of the relative strengths of the parallel fronts in its western half means that384

different latitudes are selected by the datasets, or over the diffuse, shallow front in the eastern

385

half, small differences in gradient strength could result in large latitudinal discrepancies

386

between datasets. Other months are qualitatively similar and display the same regions of387

discrepancies (not shown).

388
389

4.3 OE Variability and Frontal disturbance for 155-164°E

390

We now examine the central section of the OE SST front, using the FDI calculated over 155-391

164°E. This longitude range comprises just under half the length of the OE used to calculate392

the Eastern OEI (153-173°E). Recall that a high FDI indicates the OE front has a large393

departure from climatology, whereas the smaller the value, the closer the front is to394

climatology. The correlations between the GMPE and other FDI timeseries from different

395

datasets, at different temporal resolutions, are not as strong as those obtained from the OEI,

396

except for the DJFM subseasonal anomalies which are of similar magnitude. (Table 2,397

compared with Table 1). This may be a consequence of the methodology used in constructing

398

the GMPE: selection of the median value from an ensemble at each grid point may not reflect399

the actual disturbance of the front. Correlations between the OI and OSTIA FDI are of similar

400

magnitude to those of the OEI (greater in the case of subseasonal anomalies) and the401correlations for individual months are the lowest in December-April (Figure S3).

14

correlation

OI-GMPE
OI-OSTIA
GMPE-OSTIASONDJFMA
separatemonths
0.61
0.76
0.64

DJFM
separatemonths
0.55
0.69
0.62

DJFM
Seasonal
mean
0.56
0.67
0.77

DJFM
subseasonal
anomalies
0.55
0.55
0.40

402
403
404
405
406

Table 2. Pearson correlations between the FDI timeseries for 155-164°E for different datasetsand timesteps. All correlations are over the 1982-2016 period and all correlations are
significant (p<0.05).

407

During September-April at monthly resolution, the FDI shows no significant (p<0.1)408

correlations with the OEI in any of the datasets. However, if the OEI and FDI are partitioned

409

based on the negative and positive OEI phases a different picture emerges. The positive phases

410of the OEI are positively correlated (OI: 0.54; GMPE: 0.59; OSTIA: 0.52) with the FDI,

411

whereas for the negative phases of the OEI, they are negatively correlated (OI: -0.47; GMPE:

412-0.54; OSTIA: -0.50) with the FDI. These results explain why the correlations are negligible

413

when the full timeseries are considered, but also identify a moderate association between

414

poleward shifts (OEI) and increased frontal disturbance (FDI) in the positive phase. When the415

OEI is negative, a southward shift is also associated with a more disturbed front (a more416

positive FDI). The FDI increases as the OE front moves away from the climatological location

417

in either direction. The relationship between the OEI and FDI is summarised in Figure 5.

418
419
420
421

Figure 5. Scatterplots of the monthly OEI against monthly FDI for September-April, for (a)OI) (b) GMPE and (c) OSTIA datasets, 1982-2016.

422

In February, of the 12 years with the lowest OEI Difference Index, six have a low FDI, and423

one has a high FDI. Conversely, when the OEI Difference Index in February is high, three of424

the 12 years have a low FDI and seven have a high FDI. This makes sense as a broken, less
15

425

well-defined front may well be detected more ambiguously in different datasets. Additional

426

contributions to the Difference Index come from the more well-defined regions of the front,

427

where differences still occur for each timestep.

428
429

Using the OI SST dataset and considering the SST gradients in February as an example, the430

FDI is high in the year 1991 (1.25) and low in 1995 (0.42) (Figure 6). In Figure 6a, the431

climatological mean for the locations of the maximum SST gradients (black curve) does not432

coincide with the climatological February-mean for the SST gradient field (shading). In the433west it lies between the two regions of strong poleward SST gradients, a consequence of the

434

average location reflecting fluctuations in the relative strength of the northern and southern

435

SST fronts. In 1991, large sections of the maximum SST gradient are located well to the north436

and south of the climatology (Figure 6b), with the maximum around 35°N likely associated437

with the KE. Such a large overall disturbance results in a high FDI in 1991. In contrast, in 1995,438

the maximum SST gradients are close to but either side of the climatological values, with an

439

overall more zonal location and a low FDI.

440
441

A summary of the latitudinal distributions (density) of the absolute maximum SST gradients442

for all Februarys (Figure 6d-f) shows that when the FDI is high (red), the distribution has a443

greater spread, with higher and lower latitude values in the tails; whereas for low FDI years

444(blue), the distribution has increased frequency around 40°N. High FDI months sample the445

maximum SST gradients from higher or lower latitudes more frequently, with fewer

446

occurrences at around 40°N.

16

447
448
449
450
451
452
453
454
455
456

Figure 6. February-mean poleward SST gradient (color shading, °C per 100km) for (a)February climatology 1982-2016, (b) February 1991 (a high FDI case) and (c) February 1995
(a low FDI case) from the OI SST dataset. In (a), the locations of the maximum absolute SST
gradients are shown with a black solid line which is drawn as black dashed lines in (b) and (c).
Data are not detrended in (a–c). (d-f) Kernel density estimates of the distribution for latitudesof the February maximum absolute SST gradients, at each longitude and for each February in
1982-2016 for (d), OI, (e) GMPE and (f) OSTIA. Blue (red) curves show the third of months
with the lowest (highest) FDI, and black curve is for all the February months.

457

4.4 Physical Factors Associated with the FDI.

458

The FDI is moderately associated with the magnitude of the poleward SST gradient averaged459

over 39-41°N, 155-164°E. Specifically, correlations between the FDI and SST gradient are

460

0.43(OI), 0.30 (GMPE) and 0.38 (OSTIA), based on monthly data during 1982-2016). All these461

values are highly significant (p < 0.01) and indicate that a stronger (more negative) poleward462

temperature gradient at 40°N is associated with a lower FDI, closer to climatology. This implies463

a stronger SST gradient at this latitude is more likely to be selected as part of the OE front

464

defined along the maximum absolute SST gradient. Figure 6 provides an example of this: in465

the high FDI case (Figure 6b), there are regions of stronger (than climatology) positive466

poleward SST gradients to the north and south of 40°N, whereas in the low FDI case (Figure

4676c) the gradients along 40°N are the strongest in the domain. The probability density functions

468

in Figure 6d,e,f reinforce this. There is a clear increase in occurrences of maximum SST

469

gradients at around 40°N for low FDI months (blue lines), while for high FDI years, this470

frequency decreases, with increased frequency particularly at lower latitude (35-37°N, red
17

471

lines, in the KE region). There is a secondary frequency peak at around 43°N, where changes

472

in frequency are dependent on dataset. The magnitude of the SST gradient at around 40°N

473

explains only a part of the FDI, as it is likely to be a result of interactions between a range of

474

variables related to local SST, SST gradients and SSH gradients, some of which may be non-475

linear.

476
477

We now consider whether mesoscale oceanic eddy activity has any influence on the FDI. The

478

amplitude of mesoscale eddy activity is calculated from the monthly standard deviation of daily

479

OI SST data that have been highpass-filtered by application of a spatial FFT filter (Section 3.3;

480

Figure 7). There is high mesoscale eddy activity in the region between the KE and OE (Figure4817a) (~35-41°N). In addition, there is increased eddy activity along the two quasi-stationary

482

regions of strong SST gradient associated with the OE Front (150-160°E, 40-44°N, and 165-483

170°E, 40-43°N).

484
485
486
487
488
489
490
491
492
493
494

Figure 7. (a) OI SST monthly standard deviation of spatially high-pass filtered daily data
averaged over DJFM, 1982-2016. Black contours show the DJFM mean SST. (b) Monthly
standard deviation of daily spatially highpass filtered SST, with additional lowpass filter
applied to the monthly standard deviations prior to regression, regressed against the OI FDI(for positive FDI months only). (c) monthly mean Eddy Kinetic Energy standardised anomalies
regressed against the average FDI (positive regression only). Stippling indicates significanceat p<0.1 (fine black) and p<0.2 (coarse gray) after the application of the False Discovery Rate.
The monthly SST data are detrended prior to regression. The DJFM mean location of the OE
is shown in white in (a) and magenta in (b) and (c).

495

The FFT-filtered OI SST fields regressed onto the FDI for December-March results in496

significant increased mesoscale eddy energy in positive regression (Figure 7b) to the north of497

the climatological SST. The additional lowpass filtering cleans up the very noisy highpass-498

filtered fields. A similar pattern is observed using OSTIA data, although the field is noisier and499

results are not significant (not shown). However, if the regressions are repeated for December-

500

January or January-February, significance is found using both OI and OSTIA (not shown; note
18

501

that we do not use GMPE for these results as the median method of calculation used for creating

502

GMPE may potentially have a smoothing effect on mesoscale features). A high FDI indicative503

of a more disturbed maximum SST gradient, is associated with increased eddy activity to the504north. To confirm the association between mesoscale eddy activity to the north of the Oyashio

505

SST front and the FDI, we regress the eddy kinetic energy (EKE) monthly-mean standardised506

anomalies against the average FDI (Figure 7c). In agreement with the results derived from507

spatial highpass-filtered SST, the EKE from SSH indicates increased eddy activity to the north508

of the SST front for a positive FDI. If the monthly standard deviation of standardised EKE

509

anomalies is regressed against the average FDI, a similar pattern emerges (not shown)510

suggesting a shift in both the mean and spread of EKE with an increased FDI.

511
512

There is evidence of significant oceanic mesoscale eddy activity leading the FDI by one month513(not shown), further suggesting the mesoscale eddy activity is influencing the FDI. While the514

FDI shows an association with SST mesoscale eddy activity, there is no significant association

515

with local unfiltered SST variability (not shown).

516
517

4.5 Impacts of Changes in Frontal Continuity

518

We now address whether the variability of the FDI is manifested in atmospheric fields over a

519

North Pacific domain defined by the region between 130-240°E and 30-65°N by regressing the520

various storm-track metrics (highpass-filtered turbulent heat flux (THF) and 500hPa omega;521

daily-differenced 850hPa meridional wind and total precipitation and 800hPa EGR) and SLP

522against the FDI. We compare the results with analogous regressions based on the more familiar

523

OEI. We primarily examine significant regressions at one-month lag between the respective524

FDI and OEI in January and February (JF) and the February and March (FM) atmospheric

525

fields, at monthly resolution. This time lag is chosen to capture the influence of the changes in526

frontal disturbance or OE shift on the atmosphere, avoiding atmospheric influences on the527

ocean which dominate at zero lag. Significant changes can also be observed at longer lags (not528

shown); however we do not aim to be exhaustive here, focussing instead on the novel result529

that the frontal disturbance of the central section of the OE is associated with significant

530

changes in atmospheric variables at one-month lag. We focus on a small number of metrics

531

below for clarity, and also average the indices across the different datasets, to reduce noise.

532
533

Symmetric and asymmetric regression results are summarised in Table 3, with statistical534

significance at p<0.1 and p<0.2 indicated by dark and light blue shading, respectively. Recall
19

535

that for these regressions we remove the climatological mean FDI to create positive and536

negative values. It is notable that for the FDI, there are no significant negative results for the537

individual datasets, (i.e. when the fronts are closer to their climatological mean position).

538

Similarly for the OEI, significances for positive regressions, when the front shifts to the north,539

are much more frequent than for negative regressions. In addition, for the FDI, significance is540

found for positive regressions of SST mesoscale eddy activity (Figure 7) and the storm-track541

metrics (Figure 9; Table 3) against the FDI, suggesting a possible causal link between SST

542

mesoscale eddies and storm-track metrics a month later.

543
(a)
FDI
dataset
JF
OI
GMPE
OSTIA
MEAN
Agreementscore

THF SD
highpass

February-March atmospheric field
500hPa850hPaTotal
800hPaomega SDv windPrecip.
Eadyhighpass
differences
differences
Growth
SD
SD
Rate

SLP

+

-

s

+

-

s

+

-

s

+

-

s

+

-

s

+

-

s

0

0

3

4

0

0

5

0

0

3

0

0

4

0

0

4

0

3

544
(b)
OEI
dataset
JF
OI
GMPE
OSTIA
MEAN
Agreement
score
545
546
547
548
549
550
551
552
553
554
555

February-March atmospheric field
THF SD
highpass

500hPaomega SD
highpass

850hPav winddifferences
SD

Total
Precip.
differences
SD

800hPaEady
Growth
Rate

SLP

+

-

s

+

-

s

+

-

s

+

-

s

+

-

s

+

-

s

0

0

0

2

0

0

2

0

0

4

0

0

0

0

0

5

0

0

Table 3 Table showing where significant regression coefficients occur in regression maps of(a) the JF FDI and (b) the JF OEI, for indices derived from each dataset against atmosphericand storm-track variables. +, - and s denote positive, negative and symmetric regression cases
respectively. Light blue indicates that the regression map shows regions of significance at
p<0.2, and dark blue indicates that there is significance at p<0.1, after application of the False
Discovery Rate. SD = monthly standard deviation of daily highpass-filtered or dailydifferenced data.
The FDI shows closer agreement than the OEI for the significant regressions of storm-track
fields against different dataset indices. For example, all three datasets show significant positive

20

556

regressions of the meridional wind differences against the FDI. However, for the OEI there is557

less agreement between the different dataset indices. A simple agreement score is employed to558

quantify this. If two of the three dataset indices (the mean indices are not included) agree in559

showing regions of significance, points are awarded, two for p<0.1, one for p<0.2. Based on

560

the agreement score, there is a moderate to high level of agreement between the FDI regressions

561

for the different dataset indices in positive regressions which suggests that these features are

562

robust. For the OEI, there are fewer instances of agreement in significance, and much of the563

agreement is at a lower significance threshold. When considering SLP, indicative of impacts564

on large-scale atmospheric variability, both the OEI and FDI show good agreement between

565

the different datasets for the positive phase regression, while disagreeing on the negative and566

symmetric regressions.

567
568

Next we present the results from the OEI regressions using the mean OEI averaged over three569

datasets (Figure 8). All significant regressions occur for the positive regression case, when the570

OE is shifted northwards. A significant (p<0.1) low sea-level pressure (SLP) monopole is571

centred over the Aleutian Islands (dashed magenta contours in Figure 8), and significant

572

regression coefficients for the storm-track metrics occur consistently on the southern flank of573

the low-pressure anomalies: a northward shift of the OE is associated one month later with574

increases in the standard deviation of meridional wind and total precipitation daily differences,575

and an increase in 800hPa EGR, mainly between 180-140°W (Figure 8d). This indicates an576

eastward extension of storm-track activity downstream of the OE, with the OE leading by one

577

month. The daily-differenced parameters are associated with the transit of low-pressure578

systems along the storm-track. The increased variability reflects the increased passage of fronts579

or stronger storms, which are accompanied by changes in wind direction; and the warm and580

cold sectors, where rainfall and meridional winds are more vigorous and also more changeable.

581

Significant increases in omega at 500hPa are located on the northern flank of the climatological582

storm-track (figure 8a). Descending cold air (positive omega) is associated with the cold sector

583

behind the cold front, and ascending warm air (negative omega) is linked to the warm front

584

ahead of the warm sector, which will combine to increase variability of omega when storm-

585

track activity increases.

21

586
587
588
589
590
591
592
593
594
595
596
597

Figure 8. Asymmetric (positive) regression on the dataset averaged OEI, 153-173°E for JF,
for various FM atmospheric fields related to storm tracks. Maps are only shown where there
are significant regression coefficients (p<0.2), after the FDR is applied. Shading shows
significance at p<0.2 (coarse gray) or p<0.1(fine black). The contours of the SLP regression
coefficients are shown in magenta, dotted for negative values and the zero contour is omitted(contour interval 1hPa). The solid black line shows the mean position of the OE front. Green
contours show the climatological mean values of the respective atmospheric field. Contour
intervals: 0.1 Pa s-1 (highpass-filtered omega SD); 2ms-1 (v wind differences); 5mm (total
precipitation differences); 0.25 day-1 (EGR); 50W m-2 (highpass-filtered turbulent heat fluxes).

598

such that as the OEI becomes more positive, the heat flux variability increases just downstream599

of the OE region (180-160°W,40°N) and to the south of the OE front (Figure 8e). The heat flux

600

variability reflects the passage of the warm and cold sectors of a low-pressure system over the601

ocean; fluxes are upwards (positive) in the cold sector and downwards (negative) in the warm

602

sector. Increased variability reflects an increased frequency of large positive and negative

There is a positive association of the highpass-filtered THF with the OEI in positive regression,

22

603

values, which indicates increased storm-track activity as the OEI becomes more positive and604

the front shifts northwards.

605
606

The regressions using the FDI show similar asymmetry to those based on the OEI. Meridional

607

wind shows a higher level of significance, and significance is more widespread for EGR

608(Figure 9b, Table 3). Significance for omega at 500hPa are shifted southwards relative to those609

for the OEI (Figure 9a). An increase in SST front disturbance from climatology is associated610with a low-pressure monopole a month later, with increased storm-track activity to the south

611

of the monopole.

612
613
614
615
616
617

Figure 9. As for Figure 8, except for regression on the average FDI, 155-164°E for positive
regressions. SLP contours are 4hPa. Note the colorbar scales are different from those in Figure
8.

6183a) are regressed onto the mean FDI, but not for any of the individual datasets. These are not

619

shown in Figure 9, but are located upstream over the Sea of Okhotsk. There is also higher

Significant negative regressions are found when precipitation differences and omega (Table

23

620

agreement in the THF regression field between datasets for the FDI compared with OEI (Table6213) although this is not reflected in the mean index.

622
623

A notable aspect of these results is that the spatial patterns of significant regression coefficients624

for the OEI and FDI in positive regression are very similar (Figures 8a-d and Figure 9), as

625

discussed in section 4.3. Specifically, the positive phases of the FDI and OEI are significantly

626

positively correlated (r=0.52-0.59), which suggests that the atmospheric response to each time627

series in this phase would show similarities. Both indices project onto a pressure monopole

628

near the Aleutians (thin magenta lines show SLP in Figures 8 and 9). For the OEI, this indicates629

a deepening of the climatological low pressure centered over the Aleutians, enhancing the630

storm-track activity to the south. For the FDI, the monopole is shifted about 10° further south,

631

representing a southward displacement of the climatological low pressure. However,632

significant storm-track metric responses are at very similar locations, on the southern flank of633

this monopole. This indicates a strengthening and eastward extension of the climatological634

storm-track steered by the enhanced poleward low-pressure region, as seen by comparing with635

the location of the climatological values of the metrics (green contours). However, the636

associated SST front changes associated with the very similar atmospheric responses are

637

different: for the OEI, it is a northward (southward) shift that increases (decreases) storm track638

activity when the OE is in the positive phase (recall that the mean is subtracted in asymmetric639

regressions). For the FDI, it is increased (decreased) disturbance from the mean, when the FDI

640

is already in the positive (increased displacement) phase, that is associated with the increased

641(decreased) storm track variability. As seen in section 4.4, the FDI is an indicator of ocean642

mesoscale eddy variability, so an increase in mesoscale eddy activity polewards of 40°N in the643

central OE region is associated with increased storm-track activity.

644
645

To summarise the regression patterns for the FDI, in positive regressions (when the central OE

646

has an SST front displaced from the mean), changes in frontal disturbance have a significant

647

association with atmospheric variability (Table 3, Figure 9), indicating a downstream extension

648

or contraction of the storm-track as the positive FDI decreases or increases.

649
650

5. Discussion and Summary651

We have shown that the OEI and subsequent regressions with atmospheric fields are dataset

652

dependent. Dataset selection is therefore an important aspect of a study’s design and we would

653

recommend considering more than one dataset, along with using different metrics for

24

654

quantifying the SST fronts, to identify the robust features of air-sea interactions. SSTs used in

655

ERA5 in particular appear to be an outlier, showing weaker correlations with indices from656

other datasets, and markedly different responses in regression maps. On average, ERA5

657

underestimates the SST variability in the KE region compared with an ensemble median of658

SST datasets (Yang et al., 2021). These WBC regions have higher mesoscale eddy activity,659

and it is possible that the SSTs used in ERA5 underestimate the SST fluctuations in this region

660(Sroka et al., 2022). Calculating the amplitude of the SST mesoscale eddy activity for ERA5,661

as for Figure 7a, confirms this (not shown).

662
663

We have found that the storm-track related air-sea interactions associated with the OE have a664

significant asymmetric component. The fact that the positive regression phase for OEI and FDI

665

show very similar regression patterns (even closer than some OEI regression patterns from666

different datasets) is noteworthy, and the timeseries show moderate positive correlations in the667

positive phase. Both the northward shift of the OE in its positive phase, and the increasing shift

668

away from climatology for the FDI, are associated with increased downstream storm-track669

activity and a monopole of low pressure near the Aleutian Islands. Another striking feature of670

the FDI is that although correlations between the indices of the different datasets are no better

671

than those of the OEI, there is much more agreement between the regressions of the FDI from672

different datasets.

673
674

The FDI is a novel index designed to quantify the disruption of the maximum SST gradient in675

the central section of the OE. Increased mesoscale eddy activity in the SST field to the north676

acts against the mean poleward SST gradient and the local SST gradient maximum at around677

40°N, resulting in a disrupted maximum SST gradient and an increased FDI. The increased

678

mesoscale eddy activity and increased FDI are associated with increased storm-track activity.

679

This is consistent with previous model results (Ma et al., 2017; Jia et al., 2020) where680

atmospheric baroclinic growth is modified via the presence of oceanic eddies. This results in

681

increased moisture content in the marine atmospheric boundary layer, and enhanced

682

cyclogenesis via moist baroclinic instability. The origins of this eddy activity have not been

683

determined, and will be left for future research, however there may be links with KE variability

684

and the strength of the Isoguchi jets (Isoguchi et al., 2006; Seo et al., 2014; Sugimoto and685

Hanawa, 2011; Sugimoto 2014).

686

25

687

The northward shift of the OE is easier to understand in the context of storm-tracks being

688

anchored on the northern flanks of SST fronts; high baroclinicity is maintained by the contrast689

in heat supply across the SST front (e.g. Nakamura et al., 2008), so that shifts in the SST fronts

690

will have an impact on the storm track. Considering the central section of the OE, the691

displacement of the SST front from climatology as measured by the FDI, has an impact on the692storm-track.

693
694

The association of the FDI with mesoscale eddy variability is interesting but cannot be easily

695

explained within the scope of this paper. Eddies can erode the SST front through increased696

surface heat loss (e.g. Nonaka et al., 2009). However, recent studies indicate that eddies may

697

also act to maintain SST fronts, through vertical heat transport replenishing the heat lost from698

the surface (Jing et al., 2021). Tang et al. (2022) report that most eddies weaken the SST

699

gradient within the eddies, but induce the redistribution of the SST front in the surrounding

700

ocean, which varies according to whether eddies are cyclonic or anticyclonic.

701
702

The OEI appears to perform poorly as a measure of high-frequency (i.e., storm-track related)703

air-sea interaction based on using a one-month lag between the OEI and the subsequent storm-704

track variable and when considering consistency between datasets. Previous research has

705

identified more significant air-sea-interactions than found here due to different research foci.

706

For example, Frankignoul et al. (2011) examine the OEI in the context of large-scale

707

atmospheric variability. Indeed, their results are consistent with those presented here as they708

find little significance at one month lag but stronger signals at lags of two to five months. In

709

addition, our focus is winter, whereas Frankignoul et al. (20110 find a strong response based710

on all months as well as with an August-October index and November-January atmospheric

711

fields. The growth in high-frequency weather systems as indicated by the storm-track response712

may subsequently lead to changes in diabatic heating and momentum and heat fluxes by these713

high-frequency systems, with subsequent changes in the jetstream. However, in the present

714

study we do not consider the FDI impacts at different lag times which may reveal such

715

responses. Neither do we compare early and late winter differences, or differences at other716

times in the year. Investigating the physical mechanisms which link fluctuations in the positive717

FDI to changes in the storm track is also left for future research. Here we simply present the718

FDI as a complementary approach to identifying high-frequency air-sea interactions, which at719

short timescales with a lag of around one month, produces more consistent air-sea interaction

720

results when using different datasets to derive the index than does the OEI.
26

721
722

The key findings of the study are summarised below.

723

1. The OEIs obtained from different datasets show considerable variation. Correlations are

724

stronger on seasonal or bimonthly timescale, but weak on a subseasonal scale. We do not725

recommend using indices such as the OEI for identifying subseasonal variability in air-726

sea interactions, due to the large discrepancies between datasets at this temporal scale.

727

Identifying a single best dataset to use for defining the OEI is not clearly achievable.

728

However we advise against the use of ERA5 SST data, as it is a clear outlier.

729

2. These differences arise from slight differences in the representation of SST gradients in730

the considered datasets, particularly in the more complex central regions where there are731

parallel fronts or fronts are weak.

732

3. When used to diagnose air-seas interactions, the OEIs from different SST products can

733

produce different spatial patterns, which may have significant impacts on feature734

identification and explanations.

735

4. We develop a new index, the FDI, to quantify the complex central region of the OE, and736

the extent to which the SST gradient deviates from climatology. This new index is

737

associated with the strength of the SST gradient at 40°N. This gradient is in turn affected738

by fluctuations in ocean mesoscale eddy activity to the north and south.

739

5. The FDI has an asymmetric association with air-sea interactions. When the average

740

deviation from climatology is high, a further increase in disturbance is associated with an

741

eastward extension of the storm track. These responses are linked to ocean mesoscale

742

eddy activity in the region.

743

6. Similarly, the response of storm-track metrics to the north-south shifts of the OE front is744

asymmetric. It is the positive regression phase that is significant (when the OE front is745

shifted to the north).

746

7. The FDI produces a more robust air-sea interaction signal with storm-track metrics than747

the OEI, for the one-month time lag considered here, as there is more agreement between

748

the regressions based on indices calculated from the different SST datasets and the749

significance of the regressions is often at a higher threshold. The agreement in the FDI

750

regression results across datasets is notable as the correlations between the FDI from751

different datasets are actually similar to (or in the case of GMPE, lower than) the

752

correlations between the different OEIs, yet more consistent regression results are

753

obtained.

27

754

8. An important feature of the OEI and FDI regressions is that the positive regression phase755

produces very similar spatial regression patterns. This reflects the fact that when the FDI

756

and OEI are partitioned by OEI phase, positive correlations are found in the positive757

phase.

758
759

Acknowledgements. The authors acknowledge support from the NSFGEO-NERC project760‘Large-scale atmospheric circulation response to Oyashio Extension frontal variability’, award

761

AGS-2040073. The National Center for Atmospheric Research (NCAR) is a major facility762

sponsored by the US National Science Foundation (NSF) under Cooperative Agreement763

No. 1852977.

764
765

Data availability statement. All data used in this study are available online.

766
767

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