An Eddy Perspective of Global Air–Sea Covariation

1.   Introduction

Oceans are a vital component of the earth’s climate system, and the air–sea interface (ASI) process is at the center of this system. The transfer of momentum, heat, and water at the ASI is responsible for ocean–atmosphere energy transmission. In general, the air–sea interaction takes place on three scales, namely, large, meso, and small scales. The large-scale air–sea interaction is mainly dominated by atmospheric processes (Zeng et al., 2009; Liang et al., 2018), whereas the mesoscale is mainly dominated by marine processes (Zeng and Wang, 2017). In this study, the characteristics of climatological variation at the ASI are analyzed from the perspective of mesoscale ocean eddies.

Compared with large-scale ocean phenomena, the study of mesoscale eddy effects on the atmosphere started relatively late, and there are few studies on the daily timescale (Frenger et al., 2013). This is mainly because the mesoscale air–sea interaction involves intricate two-way response and feedback effects between the air and sea (Xie, 2004). Therefore, data with higher spatial resolution and shorter time steps are required to determine coupling at the mesoscale. In recent decades, understanding of the mesoscale ocean–atmosphere coupling has improved considerably with increasing resolution in satellite observations (Chelton and Xie, 2010). For example, Chelton et al. (2001) used multiyear satellite observations to reveal the linear relationship between surface wind stress and sea surface temperature (SST) in the eastern tropical Pacific. High-resolution satellite data make the studies on mesoscale air–sea interaction feasible. This is also a basis for our study.

An ocean eddy is a rotating, circumfluence-closed water body. As a type of mesoscale marine phenomenon, it not only plays an important role in ocean circulation structure and marine ecology by affecting the ocean flow field and chemical transport (Yang Y. K. et al., 2019), but also leaves an imprint on meteorological parameters, such as wind, cloud, and precipitation, through the air–sea interaction. In addition, although mesoscale eddies cause weaker abnormal signals than other mesoscale marine phenomena, such as fronts (Shi et al., 2017), they are superior in quantity and spread over almost the whole global oceans, resulting in more extensive implications on the atmosphere. Many previous studies have pointed out that the atmospheric response to mesoscale eddies has regional differences (Frenger et al., 2013; Ma et al., 2015; Liu H. Y. et al., 2018, 2019; Shan and Dong, 2019). Frenger et al. (2013) investigated the effects of more than 600,000 eddies on local winds, clouds, and precipitation in the Southern Ocean. Anderson et al. (2011), Yang H. Y. et al. (2019), and Liu et al. (2020) studied the eddy–wind interaction in North Atlantic, the energy balance relationship of the air–sea interaction of mesoscale eddies in the Kuroshio Extension area, and the features of mesoscale eddy-related SST and air–sea heat flux anomalies in the South China Sea, respectively.

The marine atmospheric boundary layer is directly affected by sea-surface eddies, and its kinematic and thermodynamic structures have a rich response to the SST below. Mesoscale eddy-induced SST anomalies can exert a great impact on the wind by changing the atmospheric stability near the sea surface. Winds over the sea surface induce ocean circulation and stimulate sea-surface evaporative cooling. Water vapor released into the atmosphere is mixed throughout the marine atmospheric boundary layer and transported to the troposphere, where it forms clouds and precipitation through condensation. The consequent latent heat release is a source of energy that drives atmospheric circulation, potentially affecting global weather patterns (Chelton and Xie, 2010). Frenger et al. (2013) coupled atmospheric parameters with mesoscale eddies and concluded that the atmospheric variation pattern is consistent with the change in atmospheric boundary layer turbulence caused by eddy-induced SST anomalies. In addition, they found that cyclonic eddies usually bring about a decrease in atmospheric parameters, whereas anticyclonic eddies have the reverse effect. Later, Liu X. et al. (2018) conducted a composite analy-sis of winter and summer precipitation from different data sources with eddies. They subtracted the composite value of cold eddies from that of warm eddies, and found that the response of precipitation induced by warm eddies is stronger than that induced by cold eddies, and that the eddy effects from different data sources are similar. In this way, eddy activities can significantly affect the air–sea momentum transfer process and the behavior of the marine atmospheric boundary layer above it. Therefore, it is meaningful to study the climatological coupling effect between mesoscale eddies and ASI parameters.

The basic eddy shape has not been absolutely determined owing to its diversity and complexity (Chen et al., 2019). Xing and Yang (2021) obtained diverse eddy shapes (Fig. 1) by detecting eddies in the South China Sea in three different ways. Traditionally, standard circles have been used to fit the eddy shape, such as in Henrick et al. (1979), Small et al. (2008), and Amores et al. (2017). However, owing to the influence of other eddies and ocean currents, eddy shapes differ from a standard circle on the horizontal scale. Later, Brown et al. (1983), Hooker and Olson (1984), Park and Cornillon (2002), Park et al. (2006), Fernandes (2009), and Early et al. (2011) used elliptical shapes to fit the Gulf Stream rings and the idea of elliptical eddy fitting was proposed. They manually fitted the digital outer boundary of the SST of the Gulf Stream rings with ellipses obtained by the least-squares method [such as Fig. 1 in Park and Cornillon (2002), Figs. 2, 3 in Park et al. (2006), and Fig. 7 in Early et al. (2011)], the shape deviation of which is minimal, at least for the conditions considered. Recently, using satellite altimeter data, Chen et al. (2019) found that the relative error of elliptical eddy fitting is smaller than that of circles, and obtained an optimal analytic ellipse and its probability distribution for all possible orientations. Their study also found that the elliptical shape is maintained during the whole lifetime of long-lived eddies. Hence, this ellipse, which has a semimajor axis of a = 87.0 km and a semiminor axis of b = 54.0 km (Chen et al., 2019), is used in this study to fit eddies for the eddy egg direction normalization.

This study aims to explore the climatological composite average distribution of ASI parameters on the eddy space scale and on the diurnal timescale from the perspective of global mesoscale ocean eddies using four normalization methods. The regulating effects of eddies on these parameters are also investigated in terms of climate, which can help us to better explain the physical mechanisms involved and is of great significance to the exploration of global climate change. In terms of timescale, the multiyear composite averaging of the parameters at the ASI over an eddy can separate the climatic effects from the weather changes. Spatially, as eddies are widely distributed in the global ocean, unlike previous regional studies with specific conditions for the selection of mesoscale eddies, we conduct a global study to obtain the global universal characteristics. Of course, the trade-off is a lack of recognition of regional characteristics and zonal mechanisms. In addition, although the effects of mesoscale eddies on the atmosphere in different regions may vary in intensity, the eddy explained variations (EVs) summarize the contribution of global eddies to these natural variations.

The rest of this paper is organized as follows. Section 2 introduces the data sources as well as the data processing and analysis methods. Section 3 describes the ASI responses to mesoscale eddies with a comparison of four normalization methods and quantitative results of variations in ASI parameters caused by eddies. Section 4 discusses the innovation of the study and some relevant physical mechanisms for the results in Section 3. Section 5 provides the conclusions from this study.

2.   Data and methods

2.1   Data

The analysis is based on satellite observation data: we analyzed sea level anomaly (SLA) from Aviso; wind speed and wind direction from Windsat (microwave radiometer); sea surface 2-m air temperature (Temp2m) and evaporation from the Objectively Analyzed Air–Sea Fluxes (OAFlux) dataset (from Woods Hole Oceanographic Institution); SST, water vapor, cloud liquid water, and rain rate from the Tropical Rainfall Measuring Mission Microwave Imager (TRMM/TMI); and the u and v components (eastward and northward sea water velocity) and the flow direction from the GOFS 3.0 analysis dataset at https://www.hycom.org/dataserver/gofs-3pt0/analysis. Both Windsat (Wentz et al., 2013) and TRMM/TMI data are available from Remote Sensing Systems sponsored by NASA at www.remss.com.

The data are not time-filtered, which keeps the temporal resolution on a daily scale. On this basis, generalized results for daily eddies can be obtained. The spatial resolution is 1/4° × 1/4°, except for the sea surface 2-m air temperature (1° × 1°), evaporation rate (1° × 1°), and the flow direction (1/12° × 1/12°).

With respect to eddy data, Tian et al. (2020) improved the eddy identification algorithm by Liu et al. (2016) to recognize eddies from SLA data. The detailed algorithm is provided in the Appendix. Using this eddy identification and tracking algorithm, Tian et al. (2020) compiled an eddy dataset for the global ocean, detailed at http://coadc.ouc.edu.cn/tfl/. This dataset has a spatial resolution of 1/4° × 1/4°, diurnal temporal resolution, and a time span from January 1993 to September 2016. In the following analysis, the eddy boundaries are fitted as circles or ellipses in the eddy coordinate system on the basis of the maximum geostrophic velocity.

2.2   Data processing

A 3 × 3 linear spatial sliding filter is applied to all grid data to remove the obvious noise. In the normalizations, linear interpolation is used to fill in the grid where there is no data after normalization. All the ASI anomalies in Section 3 are obtained by subtracting the outliers of parameters in a grid on a certain day over an eddy from the climatological mean of ASI parameters in this grid, and then averaging multiple eddies over many years.

2.3   Direction normalization methods

2.3.1   Wind direction normalization

Both wind speed and direction respond to mesoscale SST anomalies, especially those caused by eddies. As different wind directions are regulated by different dynamics in this study, SST anomalies and other air–sea parameters above ocean eddies are studied with the impact factor of wind direction removed, which means that the wind direction over each eddy is rotated to the same direction. The wind direction has undergone vector synthesis based on the grid resolution (0.25°), and is called the resultant wind direction. After synthesis, there is a resultant wind direction above each eddy position every day. This direction and the corresponding ASI anomalies over the eddy are rotated to due east.

2.3.2   Flow direction normalization

Here, the flow direction refers to the direction of ocean currents in the background field of ocean eddies. Nof (1985) reported that the Gulf Stream rings are a fixed ellipsoidal shape due to shearing, and their orientation depends on the environmental flow. Furthermore, Wang et al. (2020) illustrated that the Kuroshio intrusion influences the velocity vector of mesoscale eddies. Therefore, this study aligns the flow directions and eddy egg directions (Section 2.3.3), and then determines the distribution of the overlying ASI anomalies after normalization in these directions. To separate the motion orientation of the eddy itself from the background currents, the flow directions are normalized by rotating them uniformly to due east (same as the wind direction normalization), and the corresponding parameters that we analyze are rotated at the same angle.

2.3.3   Eddy egg direction normalization

All the tracked eddies are fitted into elliptical shapes. The least-squares method is used to determine the best-fit ellipse for each eddy according to the effective boundary of the eddy. Then, the eddy oval shapes are averaged to a standard mathematical ellipse with a semimajor axis of a = 97.0 km and a semiminor axis of b = 54.0 km (Chen et al., 2019). The azimuth of the major axis of the ellipse is defined as the eddy egg direction. Finally, the different eddy egg directions and the relevant ASI anomalies are aligned to due east. Owing to the non-central symmetry of the fitting ellipse, this study can better superpose the eddies and the parameters above them. Compared with previous studies on eddy coupling (e.g., Liu H. Y. et al., 2018; Greaser et al., 2020), different directions and better shape fitting of eddies are considered.

2.4   Composite analysis method

To explore the potential influencing mechanisms of mesoscale eddies on the ASI parameters, mean composites of the spatial pattern of ASI anomalies over all identified eddies are calculated. First, we center these anomalies relative to the eddy cores. Second, the anomalies are scaled and interpolated to be displayed within twice the eddy radius (2R, where R is the eddy radius) on a uniform grid of the same pixel numbers depending on the eddy sizes. In other words, an eddy coordinate system is established to display the normalized distribution of the ASI parameter anomalies inside 2R. Then, the normalized distributions of each parameter are directly averaged by superposition, or composited after alignment of wind directions, flow directions, and eddy egg directions around the eddy core. All the composite analyses are performed for anticyclonic eddies (AEs) and cyclonic eddies (CEs).

2.5   Explained variation (EV) calculation

EV refers to the percentage of the eddy-related anomalies of the ASI parameters in the total natural anomalies:

where ${V}_{{\rm{e}}}$ is the EV, ${\sigma}_{{\rm{e}}}^{2}$ is the variance of the eddy-related anomalies, and ${\sigma}_{n}^{2}$ is the variance of the total natu-ral anomalies. EV is calculated in grid units. The eddy-related anomaly represents the difference between the eddy effect region [a circle within 2R of the eddy core, namely ${X}_{2R}$ in Eq. (2)] and the background [a ring between 2R and 3R (Frenger et al., 2013)] mean [i.e., ${\overline X }_{2R\_3R}$ in Eq. (2)]. Each grid within 2R (1/5R in the corresponding eddy coordinate system) has an eddy-related anomaly. Therefore,

where n is the total number of eddies. At the same time,

where n is also the total quantity of eddies, ${X}_{{\rm{day}}}$ is the ASI value in a grid on a given day over an eddy within 2R, and $\overline X$ is the climatological mean value of each grid in a normalized eddy 2R. The EV owing to AEs and CEs for all the ASI parameters is calculated separately and the unrotated normalizations are processed.

3.   Results and analysis

3.1   Impact of mesoscale eddies on the atmosphere

The influence of mesoscale eddies on the atmosphere is determined by the normalization and composite analysis of the anomalies at the ASI over global ocean eddies. Note that our results are all in the eddy coordinate system, and all parameters are normalized by using four methods: non-rotated normalization and normalizations based on wind direction, flow direction, and eddy egg direction, which correspond to all panels (a, e), (b, f), (c, g), and (d, h) in Figs. 1–7 in this section. In addition, before the composite analysis, seasonal and regional samplings are conducted for all the global eddies to test the significance of the mean distribution of the global eddies (see Appendix for details). The significance test indicates that there is no significant difference between the ASI distribution over the seasonally or regionally sampled eddies and the overall eddies in this study; therefore, it makes sense to use the population mean to represent the composite in different seasons and different regions. Moreover, it should be noted that the climatological data here are the average of all years that are available for each parameter (1997–2014 for SST, water vapor, rain rate, and cloud liquid water; 2010–2016 for surface wind speed; and 1985–2019 for Temp2m and evaporation rate). In addition, the outliers are calculated by subtracting the current value from the average of the climatological data. However, the time range of the data used in the composite average is selected as the overlapping years of the following three datasets: all the parameters above, the eddy data (1993–2018), and the wind direction data (2010–2016). In this case, there may be all positive composite anomalies over an eddy, which does not affect the numerical value distribution but embodies the global warming effect in a way.

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Fig  1.  The coupling of SST anomalies from the TRMM/TMI (2010–2014) and the eddy datasets. The four columns from left to right are non-rotated normalization, and normalization based on the alignment of wind direction, flow rotation, and eddy egg rotation.

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Fig  2.  As in Fig. 1, but for coupling of wind speed anomalies of the Windsat radiometer (2010–2016) and the eddy datasets.

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Fig  3.  As in Fig. 1, but for coupling of Temp2m anomalies of the OAFlux (2010–2016) and the eddy datasets.

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Fig  4.  As in Fig. 1, but for coupling of water vapor anomalies of the TRMM/TMI (2010–2014) and the eddy datasets.

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Fig  5.  As in Fig. 1, but for coupling of evaporation rate anomalies of the OAFlux (2010–2016) and the eddy datasets.

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Fig  6.  As in Fig. 1, but for coupling of cloud liquid water anomalies of the TRMM/TMI (2010–2014) and the eddy datasets.

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Fig  7.  As in Fig. 1, but for coupling of rain rate anomalies of the TRMM/TMI (2010–2014) and the eddy datasets.

3.1.1   Eddies and SST

SST is one of the most crucial factors connecting the ocean and the atmosphere. The reaction of the atmosphere to SST anomalies may lead to the modification of air–sea exchanges. As can be clearly seen in Figs. 1a, e, there is a high (low)-value center of SST anomalies over the west side of the warm (cold) eddy center within R, whereas there is a low (high)-value center on the east side over the annular region between R and 2R. Figures 1b, 1f, 1c, and 1g show similar dipole structures, indicating that the SST anomaly over an eddy has an almost symmetrical distribution both upwind and downwind, as well as upstream and downstream of the current. This proves that the wind and flow have a similar effect on SSTs over eddies in terms of climate. For Figs. 1d, h, a high (low)-value center exists within R over the anticyclonic (cyclonic) eddy. Meanwhile, in the area between R and 2R, there is a low (high)-value center over both the north and south sides, which is called a “north–south symmetric north–south–middle tripole (NSNT)” structure here (the center and the north and south poles are in inverse phase). Surprisingly, it is found that this structure has similar pattern to Figs. 12b, d, f of Chen et al. (2019), which shows normalized composite distributions of drifter-derived eddy velocity. In contrast, the north–south low (high)-value region in Figs. 1d, h is more toward the north and south poles. It is preliminarily conjectured that this is an outward shift of the upper SST anomalies relative to the eddy core due to the centrifugal force induced by the eddy fluid rotating. At the same time, the patterns in Figs. 1a, e resemble the South China Sea SST anomalies (Liu H. Y. et al., 2018), as well as the global SST anomalies (Liu X. et al., 2018). Owing to Ekman pumping, the upwelling (downwelling) flow caused by sea surface divergence (convergence) accompanied by a CE (AE) incurs a cold (warm) SST anomaly. Thus, the pattern in Fig. 1 is formed. Among the four normalization methods, the one based on eddy egg directions (Figs. 1d, h) clearly better shows the high (low) outliers on the north and south sides of the CE (AE) within the range between R and 2R.

3.1.2   Eddies and sea surface wind

In the atmosphere, the troposphere is affected by vertical motion caused by convergence and divergence of surface winds. In the ocean, the upwelling and downwelling related to wind stress curl change the ocean circulation, and thus have a feedback role on the SST (Chelton and Xie, 2010).

Figure 2 shows the anomalous wind speed normalized distributions over an AE (CE) for multiyear data (2010–2016). Figures 2a, 2b, 2e, and 2f show dipole patterns that are asymmetrical relative to the center, while Figs. 2c, 2d, 2g, and 2h show axisymmetric dipole patterns. Figures 2c and 2g are almost east–west symmetric, whereas Figs. 2d and 2h are nearly north–south symmetric and possess NSNT structures. In general, from the global eddy perspective, the distribution patterns of the normalized climatological wind speed anomalies strongly resemble that of the SST anomalies in Section 3.1.1, except for a slight angular deviation in Figs. 2b, f. This is consistent with the positive correlation between wind speed and SST on the mesoscale in previous studies (Skyllingstad et al., 2007; O’Neill et al., 2010a; Frenger et al., 2013; Ma et al., 2015). This positive correlation indicates that an AE (CE) increases (decreases) the turbulent exchange between it and the overlying atmosphere through warm (cold) SST anomalies, which then enhances (weakens) the sea surface wind speed. This confirms a vertical mixing mechanism to some extent (Putrasahan et al., 2013). Meanwhile, in contrast to Fig. 1, Figs. 2b, f show a degree of pattern rotation whereas Figs. 2c, g do not, indicating that the influence of flow direction and other factors on the sea surface wind speed are greater than that of the wind direction.

3.1.3   Eddies and Temp2m, water vapor, and evaporation rate

There are some peculiarities in Figs. 3, 4 compared with the above parameter couplings with eddies. For instance, Figs. 3b, f; 4b, f show that for both the composite AE and CE, the upwind direction of the eddy has a low Temp2m anomaly and water vapor anomaly area, whereas a high-value area exists in the downwind direction. This structure confirms that the wind over an eddy induces changes in Temp2m and water vapor, that is, the augmented anomalies. In addition, as for Figs. 3b, f; 4b, f, both parameters indicate an AE (CE) protruding from the high (low)-value center to the eddy center, but the bulge of Temp2m is more evident than that of water vapor.

Moreover, unlike the eddy egg normalized distribution pattern of the previous parameters, Figs. 3d, h possess evident east–west dipole structures, which can be viewed as a weakening mode of the NSNT structure. Further understanding is that Temp2m is slightly less but still significantly affected by eddies than other parameters. The Temp2m anomalies in all subgraphs of Fig. 3 are all positive values, related to global warming, but their patterns are still similar to that of the SST anomalies in Fig. 1. Compared with Figs. 1c, g, Figs. 3c, g show that the wind direction has a greater influence on Temp2m above a CE than above an AE, and the effect of wind direction is greater than the flow direction, which is related to the changes in the heat flux resulting from eddies.

The water vapor content in the atmosphere is of great importance to climate. The oceans provide 86% of the water vapor in the atmosphere, especially at low latitudes, which are the primary source of atmospheric moisture. As eddies are widely distributed in the ocean, they also have an impact on water vapor. In particular, the high/low outlier centers in Figs. 4b, f roughly concentrate at the edge of R and further outside, which demonstrates that the wind direction normalization makes the abnormal water vapor values deviate from their original distribution pattern and also greatly changes the values. Therefore, this normalization method is not as ideal as other normalization methods.

In general, the ocean loses approximately 126 cm of seawater through evaporation each year. This evaporation transports the remaining heat (about 90%) of the radiation process into the atmosphere. The latent heat of evaporation remains when water vapor condenses, which becomes a vital heat source to the atmosphere. As expected, Figs. 5a–c, e–g are in keeping with the patterns of the corresponding subgraphs in Figs. 1, 2. Figures 5d and 5h present a similar attenuated mode of the NSNT structure to Figs. 3d, h, with the abnormal minimum (maximum) value of evaporation rate over an AE (CE) situated in the left half ring between R and 2R, enclosing the closed core of the maximum (minimum) value within R. We also calculated the Pearson correlation coefficient between the global air–sea temperature difference (i.e., SST minus Temp2m) and the evaporation rate over eddies. The correlation coefficient can reach 0.5028 without any quality control, with a moderate correlation, which is consistent with the relationship among the distribution patterns in Figs. 1, 3, 5.

The AE-induced (CE-induced) abnormally warm (cold) SST enhances (weakens) the air–sea temperature difference, which accelerates (restrains) the sensible heat exchange. At the same time, the AE (CE) corresponds to the increasing (decreasing) air–sea surface humidity difference, consequently increasing (decreasing) the evaporation rate, which promotes (inhibits) the latent heat transport. In other words, eddy-induced heat flux anomalies give rise to the changes in Temp2m, water vapor, and evaporation rate above eddies.

3.1.4   Eddies and cloud liquid water, rain rate

Mesoscale eddies modify clouds and precipitation through the anomalous secondary circulation that they create (Chen et al., 2017). Intensified (subdued) condensation of moisture above AEs (CEs) will enhance (reduce) these two physical processes.

Cloud liquid water is a crucial component of the atmospheric water balance. It has a great impact on the radiation and energy budget of earth. In addition, owing to the strong interaction between liquid water and radiation in cloud, its feedback effect can have a far-reaching influence on global climate change. Figures 6a and 6e are in accordance with the above parameters, but it can be seen that each color edge is relatively less smooth, indicating that the spatial distributions of cloud liquid water anomalies above eddies oscillate slightly more under the condition of no directional rotation. Intuitively, the distribution characteristics in Figs. 6b, f and 3b, f resemble each other, which illustrates that the climatic effects of eddies on Temp2m and cloud liquid water are similar. Figures 6c, 6d, 6g, and 6h show a similar pattern to the above ASI parameters.

Owing to the uncertainty associated with precipitation observations, rainfall is the most difficult parameter to quantify among the various atmospheric responses to oceanic mesoscale eddies, and is subject to considerable uncertainty (Liu X. et al., 2018). Overall, although the signals of the unrotated and oval-based rotation categories (Figs. 7a, d, e, h) are slightly weaker than the other parameters for the coupling of rain rate anomalies and eddies, there are still evident similarities under our algorithm. Moreover, it is found that the distribution shown in Fig. 7 is surprisingly similar to Fig. 4, apart from its uneven edge (this unevenness is related to the precipitation variability and the observation uncertainty). It is speculated that there is a positive correlation mechanism between precipitation and water vapor, which is in agreement with the physical process of water vapor condensation promoting precipitation. Sufficient water vapor contributes to the formation of low clouds, most of which are likely to produce precipitation.

3.2   Eddy EV

The eddy EV of each ASI parameter is determined and the normalized spatial distribution without rotation is shown in Fig. 8. It should be noted that the low abnormal values at the edges of all maps are all caused by automatic interpolation and do not have any statistical significance.

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Fig  8.  Normalized distribution diagrams of eddy EVs of (a, b) SST, (c, d) wind speed, (e, f) Temp2m, (g, h) vapor, (i, j) evaporation rate, (k, l) cloud liquid water, and (m, n) rain rate (unrotated).

In Fig. 8, apart from the weak signals of Fig. 8m, n, which may be due to observations, all the subgraphs show a pattern of a large outer EV and small inner EV. Figures 8a, 8c–h, and 8j–l show approximately east–west elliptical monopole structures. As can be seen, the elliptical eccentricities of Temp2m (Figs. 8e, f) and water vapor (Figs. 8e, f) are larger. This shows the effect of the elliptical eddy structure on the corresponding ASI parameters. To some extent, this confirms the credibility of the elliptical eddy structure used in this study and verifies the feasibility of using an elliptical shape to fit eddies. Both Figs. 8b and 8i have a minimum value in the east–west direction at the edge R, which may be connected to temperature advection over an eddy.

The normalized EVs of AEs and CEs for each ASI parameter are shown in Table 1. For AEs and CEs, although their normalized EVs show a discrepancy in spatial distribution, the ranges of EV are similar in value, and the eddy EV of SST is the largest. As a result, the eddy effect on SST can be viewed as the source of eddy-induced changes at the ASI here, consistent with the current general understanding (e.g., Chen et al., 2017).

Table  1.  Normalized EV ranges of AEs and CEs for each ASI parameter over 2R

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ASI parameter	AE (%)	CE (%)
SST	28−70	24−78
Sea surface wind	12−20	12−21
Temp2m	3−35	4−33
Water vapor	8−22	8−22
Evaporation rate	9−15	9−18
Cloud liquid water	0−51	0−53
Rain rate	0−58	0−58

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4.   Discussion

4.1   Coupling of ASI anomalies and mesoscale eddies in eddy coordinate system

Four normalization methods are utilized to determine the composite average distribution of abnormal ASI parameters above an eddy under the conditions of no rotation and identical wind directions, flow directions, and eddy egg directions. This demonstration is done in an eddy coordinate system. The unrotated normalization is a simple space–time match between ASI anomalies and eddies. As for the other three normalizations, the resultant background wind directions, resultant background flow directions, and eddy egg directions, respectively, become the new x axis after normalized rotation, and then the background ASI anomalies above eddies are rotated accordingly. The wind direction normalization here is similar to that in Park et al. (2006) and Gaube et al. (2013), whereas the flow and eddy egg direction normalizations have not been used in previous studies.

The coupling shown in this study uses the eddy coordinate system instead of the earth coordinate system. That is, the coordinate system takes the eddy core as the center (the origin of coordinate) and moves with the motion of the eddies, which is equivalent to conducting a “close-up” of the ASI over each eddy. Some of the coupling features may not be so noticeable in the earth coordinate system, but are obvious in the eddy coordinate system; therefore, the latter can be used to better determine the coupling rules.

In terms of eddy shape fitting, each fitting method has its limitations. In this study, a circle and an ellipse are used to approximate the eddy shape, and errors are unavoidable. However, the elliptical fitting method is considered to be the optimal method under maximum fitting. In the normalization process, the eddy egg direction normalization is more sensitive to eddy shapes, so the ellipse is used. The other three normalizations are less affected, hence the traditional circle is still used to represent the eddy. The eddy core is the center of the circle or ellipse.

4.2   Explained variation

In this study, the normalized space distribution of eddy EV for each parameter is presented. Although previous studies have calculated the EV, they were all numerical descriptions (Frenger et al., 2013; Byrne et al., 2015; Liu H. Y. et al., 2018) and lack their spatial distribution from the perspective of eddies. Figure 8 provides a visual representation of the normalized EVs and a distribution of the direct response of the atmosphere to mesoscale eddies. The elliptical structure in Fig. 8 may be due to the internal rotation of the eddy, that is, the rotation of the internal flow field. Therefore, it is important to not only study the air–sea interaction from the perspective of global eddies but also verify the elliptical eddy hypothesis used in this paper.

4.3   Physical mechanism

Two mechanisms (vertical mixing and pressure adjustment) are generally used to explain the response of the atmosphere to oceanic mesoscale features (e.g., Putrasahan et al., 2013; Chen et al., 2017), but the contributions of both mechanisms still remain controversial. According to Chen et al. (2017), the vertical mixing mechanism is usually more suitable for SST anomalies with relatively small spatial scales, so it is more distinct for mesoscale eddies. Here, we focus on the vertical mixing mechanism to explain the atmospheric signatures of mesoscale eddies, as shown in Fig. 9.

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Fig  9.  Schematic of the interaction between parameters at the interface of eddies and the atmosphere (only one pair of warm and cold eddies are shown as examples here).

It is well known that the key to the impact of mesoscale eddies on the atmosphere lies in the SST anomalies caused by them (Gaube et al., 2015). Owing to Ekman pumping, a CE (AE) is usually accompanied by divergence (convergence) of the ocean surface, and the subsequent upwelling (downwelling) gives rise to cold (warm) SST anomalies. When the mesoscale eddies are located in an area with a large SST gradient, the temperature advections arising from their rotation will bring about the SST cold (warm) tongue on both sides of the eddy or between two eddies (Gaube et al., 2015). Mesoscale eddies change the state of the upper atmosphere by changing the turbulent heat flux on the sea surface. The warm SST anomaly created by an AE increases the temperature difference between the air and the sea, which increases the sensible heat flux from the ocean to the atmosphere. Meanwhile, it also increases the saturation ratio of humidity, amplifies the difference in air–sea surface humidity, and enhances the evaporation of the ocean surface (in line with Fig. 5), thereby enhancing the latent heat flux. As a consequence, an AE triggers an upward turbulent heat flux anomaly and the ocean heats the atmosphere. A CE, on the other hand, triggers a downward turbulent heat flux anomaly and the ocean gets heat from the atmosphere.

Mesoscale eddies affect wind speed through changes in the turbulent heat flux induced by the eddies (O’Neill et al., 2010b). An AE (CE) increases (decreases) the turbulent heat flux, which increases (decreases) the atmospheric boundary layer, with weakening (enhancement) of the atmospheric boundary layer stability, impacting the vertical momentum transport (Businger and Shaw, 1984). This process eventually manifests as an intensified (reduced) wind speed in the warm-core (cold-core) eddy, and wind divergence (convergence) upwind and convergence (divergence) downwind over eddies. Furthermore, heat flux variations will also induce changes in the air temperature (corresponding to Temp2m above) and humidity (corresponding to water vapor above), which will affect the sea surface pressure. The additional pressure gradient forces arising therefrom will also alter wind speed.

Eddy-related variations in atmospheric stability and anomalous vertical secondary circulation (Chen et al., 2017) will subsequently modify the local cloud content (corresponding to cloud liquid water above) and precipitation (corresponding to rain rate above). There are two pathways through which eddies affect the cloud content and rain rate: dynamic and thermal. The dynamic path is due to vertical motion, whereas the thermal path arises from modification in the form of heat and water vapor transport.

5.   Conclusions

Marine mesoscale processes, especially marine eddies, are a key element of large-scale ocean circulation with substantial implications for climate and marine biogeochemistry (Byrne et al., 2016). All the composite ASI parameters exhibit different distributions under the four different normalization methods. The relationship among these distributions and a series of physical changes caused by eddies can be explained by a vertical mixing mechanism (see Section 4.3).

This study innovatively proposes normalizations based on flow direction and eddy egg direction, which have not been used in previous studies. In effect, the composite analysis results (Figs. 1–7) indicate that these two normalization methods are visibly better than the wind direction and non-rotated methods. However, whether the wind-direction-based normalization or non-rotated normalization works best depends on the specific ASI parameters. For SST, sea surface wind, Temp2m, water vapor, evaporation, cloud liquid water content, and precipitation, an AE usually gives rise to obvious positive anomalies of these parameters, whereas CE causes some negative anomalies. At the same time, the maximum fluctuation value is generally located within R of the eddy.

In this study, the normalized composite spatial distribution of several ASI parameters over eddies is shown in the eddy coordinate system and the variation ratio of these parameters induced by eddies is quantitatively calculated. The eddy EV of each air–sea parameter is 24%–78%, 12%–21%, 3%–35%, 8%–22%, 9%–18%, 0–53%, and 0–58%, respectively. In particular, the eddy EV of SST can reach more than 24%, which confirms that mesoscale eddies play a crucial role in the regulation of ocean climate and even global climate.

As stated above, the oceanic eddies provide mesoscale conduits for the transfer of energy between the ocean and atmosphere. This research is meaningful for the investigation of climatological thermodynamic and kinetic effects between the ocean and the overlaying atmosphere. Certainly, the variation of the eddy-induced ASI parameters can also have a feedback effect of restraining or promoting marine eddies (e.g., Xie, 2004; Xu et al., 2016; Yang H. Y. et al., 2019). Moreover, many mesoscale marine phenomena, such as tropical instability waves, can exert an influence on large-scale air–sea coupling processes such as El Niño–Southern Oscillation (ENSO) through eddy heat transport (Hashizume et al., 2001), which shows that mesoscale air–sea interactions may also have unknown impacts on the large scale. These may be explored in future studies.

Acknowledgments. The authors gratefully acknowledge that Windsat data are produced by Remote Sensing Systems and sponsored by the NASA Earth Science Measures Discover Project and the NASA Earth Science Physical Oceanography Program. RSS Windsat data are available at www.remss.com.

Appendix

A1.   Eddy identification principle

(1) Conducting spatial high-pass filtering on global SLA data; (2) dividing the global SLA field into blocks; (3) searching possible AE (CE) cores as seed points by identifying local (3 × 3 neighborhood) maximum (minimum) values of SLA, and screen seed points with vortex properties to determine the identified eddy cores; (4) SLA contours being spaced at 0.25 cm apart, and eddy boundaries corresponding to the maximum average geostrophic velocity regions within the closed SLA contours; and (5) seamless combination of all blocks.

A2.   Significance test

The significance test in this paper uses the following formula:

where μ₀ is overall average for each of the normalization in the grid, $\overline x$ is the mean value of each normalized sampling grid, S is the standard deviation of each normalized sampling grid, and n is the sum of samples, which means the number of eddies extracted.