Observed Relative Contributions of Anomalous Heat Fluxes and Effective Heat Capacity to Sea Surface Temperature Variability

Sea surface temperatures (SSTs) vary not only due to heat exchange across the air‐sea interface but also due to changes in effective heat capacity as primarily determined by mixed layer depth (MLD). Here, we investigate seasonal and regional characteristics of the contribution of MLD anomalies to the month‐to‐month variability of SST using observational datasets. First, we propose a metric called Flux Divergence Angle, which can quantify the relative contributions of surface heat fluxes and MLD anomalies to SST variability. Using this metric, we find that MLD anomalies tend to amplify SST anomalies in the extra‐tropics, especially in the eastern ocean basins, during spring and summer. In contrast, MLD anomalies tend to suppress SST anomalies in the eastern tropical Pacific during December‐January‐February. This paper provides the first global picture of the observed importance of MLD anomalies to the local SST variability.

• Relative contributions of mixed layer depth (MLD) and surface heat flux anomalies to sea surface temperature (SST) variability are investigated using the Flux Divergence Angle metric • MLD anomalies tend to amplify SST anomalies in the extra-tropics, especially in eastern part of ocean basin, during the spring and summer • MLD anomalies tend to suppress SST anomalies in the eastern tropical Pacific during December-January-February

Supporting Information:
Supporting Information may be found in the online version of this article.
float data, finding that seasonal variations of the horizontal gradient of MLD strongly contribute to the strength of the SST front. In the present study, we revisit the relative importance of surface heat flux and MLD anomalies to SST variability and explore their seasonal and regional characteristics over the global oceans.
The key scientific questions are "How large is the contribution of MLD anomalie to SST variability compared to the contribution of surface heat flux anomalies?" and "When/Where are they most important?." To answer these questions, we (a) propose a metric for quantifying the relative contributions of surface heat flux and MLD anomalies to the month-to-month variations of local SST anomalies and (b) reveal their seasonal (e.g., summer vs. winter) and regional characteristics (e.g., tropics vs. extra-tropics).
The remainder of the paper is organized as follows. In Section 2, we describe the datasets used in this study, and propose a metric to quantify the relative contributions of surface heat flux and MLD anomalies to local SST variability. In Section 3, we present the results on seasonality and regionality of the contribution of MLD anomaly.
In Section 4, we summarize our results and discuss the possible role of MLD anomalies in major climate modes.

Data Sets
In this study, we utilize three variables; SST, surface heat fluxes, and MLD. Each variable is obtained from observational data sources; CERES-EBAF (Loeb et al., 2018) for radiative fluxes, OAFlux (Yu et al., 2008) for turbulent heat fluxes, OISST (Reynolds et al., 2002) for SST, and IPRC-Argo products (http://apdrc.soest.hawaii. edu/projects/argo/) for MLD. MLD is defined as the depth at which density increases by around 0.05 kg/m 3 from 10-m. The density increase is equivalent to a temperature decrease of 0.2˚C. All variables are monthly-averaged, for 15 years from January 2005 to December 2019. The horizontal resolution of all variables is 1° in both zonal and meridional directions. Note that our results remain robust when using a shorter data period (e.g., January 2010 to December 2019) that excludes the sparsely distributed Argo profiles in the 2000s. The results are also not overly sensitive to the choice of data set used or the definition of MLD using a smaller density changes, for example, MILA-GPV product (Hosoda et al., 2010).

Metric to Determine the Relative Contributions of the Surface Heat Flux and MLD Anomalies to Local SST Variability
Here, we propose a metric to quantify the relative contributions of the surface heat flux and MLD anomalies to local SST variability. We start to develop the metric from the simplified mixed layer temperature budget equation (Moisan & Niiler, 1998) considering only surface forcing: where is the density of sea water, is the specific heat capacity at constant pressure, is MLD, and is the sum of contributions from all other oceanic processes not explicitly written in the equation (e.g., three-dimensional advection, entrainment, and diffusion) and observational error. is vertical mean temperature within the mixed layer. In this study, we assume that is equivalent to SST. is the surface heat flux into the mixed layer and calculated as the difference between net surface heat flux ( 0 ) and penetrative shortwave radiation at the bottom of mixed layer ( pen ): = 0 − pen . The pen is calculated following Paulson and Simpson (1977). Hereafter, we focus on month-to-month SST variations and define anomalies of all variables as the deviations from the monthly climatology at each grid point. Considering the heat budget equation for T anomalies, we can decompose the anomalies of the first term on the right-hand-side (rhs) of Equation 1 into contributions from the surface heat flux and MLD anomalies (Alexander & Penland, 1996;Morioka et al., 2010;Yokoi et al., 2012). We rewrite the heat budget equation for the anomaly field: where overbars ( ) and primes ( ′ ) denote the monthly climatology and anomalies, respectively. The first term on the rhs represents the contribution of the surface heat flux anomalies ( ′ ) acting on a climatological MLD ( ) and the second term represents the contribution of the MLD anomalies ( ′ ) under climatological heating/ cooling ( ). We ignore second and higher order terms of the Taylor Expansion in Equation 2 (e.g., the non-linear contribution of both anomalies) because they are typically much smaller than the sum of the first two terms (∼1/10), except in the Antarctic Circumpolar Current region and the Labrador Sea where the subduction zone of the Atlantic Meridional Overturning Circulation is located. The first two terms can explain more than 90% of the total variances of the surface forcing term in most of the region ( Figure S1 in Supporting Information S1).
Next, we formulate a temperature variance budget equation (Boucharel et al., 2015;Guan et al., 2019;Santoso et al., 2010) by multiplying the SST anomaly ( ′ ) on both sides of Equation 2: 1 2 The left-hand-side of the equations are equivalent to half of the time tendency of T′ squared, hence we can diagnose the dominant processes that result in an increase or decrease of the T′ squared. The reason why we employ the variance budget equation (Equation 4) instead of the heat budget equation (Equation 2) is that the role of surface forcing processes in the SST evolution can be captured by the variance budget equation.
As noted in Section 1, Tozuka et al. (2018) proposed a metric for quantifying the relative contribution of horizontal gradients of the surface heat flux and MLD to the seasonal variation of frontogenesis. A similar metric was also applied to the sea surface salinity front (Ohishi et al., 2019). The method is analogous to the Turner angle (Ruddick, 1983;You, 2002) which can be used to diagnose relative contributions of vertical gradients of temperature and salinity to double-diffusive convection. Here, following the basic concepts of these studies, we define a new metric called the Flux Divergence Angle (FDA; Θ ), which quantifies the relative contributions of surface heat flux and MLD anomalies to local SST variability, in terms of the four-quadrant arctangent function, namely: (Note, tan −1 ( ) = tan −1 ( ∕ ) with the angle dependent on the sign of both and .) The two indices of Q Q and Q H are a part of the Equation 4, have the same unit of ˚C*W/m 2 , and represent the product of anomalies of SST and surface heat flux (or the product of anomalies of SST and equivalent heat flux anomalies due to the MLD anomaly with climatological heating/cooling). Positive and negative values of these indices represent that the heat flux anomalies amplify and dampen the local SST anomalies, respectively. Note that the term of "FDA" was selected to describe the role of the MLD and surface heat flux in modulating the divergence of the heat flux within the mixed layer. Figures 1a-1c are snapshots of SST, surface heat flux, and MLD anomalies on June 2015. In addition, a snapshot of FDA on June 2015 is shown in Figure 1d, calculated via Equation 5 at each grid point. Figure 1f shows a two-dimensional histogram of all pairs of Q Q and Q H , showing that there is no apparent linear relationship between them (e.g., correlation coefficient of all pairs of Q Q and Q H : r = −0.11).
Next, we illustrate the physical meaning of the FDA using a schematic in Figure 1e. When the FDA has a positive value (i.e., when the sum of Q Q and Q H is positive), the product of total surface forcing and SST anomaly is positive, so that the surface forcing term in Equation 4 acts to amplify the local SST anomalies. This is referred to as "Growth" stage of the SST evolution by surface forcing. Analogous, when the FDA has a negative value (i.e., when the sum of Q Q and Q H is negative), the product of total surface forcing and SST anomaly is negative, so that the surface forcing term in Equation 4 acts to dampen the local SST anomalies ("Decay" stage). Additionally, when the contribution of the surface heat flux is larger than that of MLD, FDA has a specific value range of 0 • < Θ < 90 • for the "Growth" stage and −180 • < Θ < −90 • for the "Decay" stage. In contrast, when the contribution of MLD is larger than that of the surface heat flux, FDA has the range of 90 • < Θ < 180 • for the "Growth" and −90 • < Θ < 0 • for the "Decay" stage. Depending on the relative importance, we add the header of "Q Q " or "Q H " before the name of "Growth" or "Decay" stage (e.g., "Q Q Growth" when 0 • < Θ < 90 • ). Note that a term of "dominant" in the following text indicates their relative importance of the surface heat flux and MLD terms but not necessarily their absolute importance relative to other terms in the full variance heat budget. For example, oceanic processes associated with upwelling and lateral advection have large impacts on SST variability in the eastern tropical Pacific and in western boundary current regions, respectively ( Figure S2 in Supporting Information S1). Also, the oceanic processes tend to be the primary driver of local SST variability in the winter hemisphere ( Figure S3 in Supporting Information S1). In such cases, surface forcing processes are less important than oceanic processes. Hence, the term "dominant" used in this manuscript refers to only the relative importance of the surface heat flux anomaly or MLD anomaly among the surface forcing processes.
To further investigate the regional characteristics of the FDA histogram (Figure 1g), we calculate the occurrence frequencies of the four sectors ( ) at each grid point during specific seasons as below, where is the count number of events with a specific value range of FDA. N ALL is the total count number at one grid point, which is 45 for each season (i.e., each 3-month seasonal average during 15 years). Horizontal maps of tell us the regionality of the dominant processes for the local SST evolution at each grid point.

Global Characteristics of FDA
First, we provide an overview of the general characteristics of the FDA over the global ocean and in all seasons. Figure 1g shows a histogram of FDAs normalized by total count numbers. The number below each label indicates the occurrence frequency of each sector. The histogram has two sharp peaks at around 45° and −135°. The occurrence frequency of "Q Q Growth" is 32.19% and that of "Q Q Decay" is 37.99%. These results demonstrate that surface heat flux anomalies are the main factor determining anomalies of the total surface forcing term. This is consistent with previous results on the relationship between the surface heat flux and SST, that is, SST anomalies can be caused by wind or radiative forcing and can be dampened by heat release from the sea surface (Hasselmann, 1976). Although the surface heat flux anomalies are the main driver of the SST anomalies in most of the cases investigated here, in some cases MLD anomalies contribute more to the SST anomalies than the surface heat flux anomalies. For example, FDA around Hawaii on June 2015 (Figure 1d) had positive values greater than 90° (i.e., orange color shading), suggesting that the SST anomalies were primarily determined by the "Q H Growth" process rather than "Q Q Growth" and "Q Q Decay." In the next subsection, we further explore the regional and seasonal characteristics of the "Q H Growth" and "Q H Decay" processes.  (Figures 3a, 3c, 3e, 3g, 3i, 3k, 3m, and 3o). Hereafter, we will describe the details of the contributions of MLD anomalies (i.e., "Q H Growth" and "Q H Decay") compared to the contribution of surface heat flux anomalies (i.e., "Q Q Growth" and "Q Q Decay").

Q H Growth Process: Contribution of MLD Anomalies to the Growth of SST Anomalies
In the extra-tropics (Figures 2a and 2b), the histograms show a clear seasonal difference between summer and winter. In the winter hemisphere (i.e., DJF in the Northern Hemisphere and JJA in the Southern Hemisphere), occurrence frequencies of "Q Q Growth" and "Q Q Decay" are larger than those of "Q H Growth" and "Q H Decay." In the summer hemisphere (i.e., JJA in the Northern Hemisphere and DJF in the Southern Hemisphere), the surface forcing term is the primary driver of extra-tropical SST variability ( Figure S3 in Supporting Information S1). Occurrence frequencies of "Q Q Growth" and "Q Q Decay" are also large in spring and summer, however, the occurrence frequency of "Q H Growth" is clearly larger than that in winter. This suggests that the contribution of MLD anomalies is more pronounced in the spring and summer seasons than in the winter season, which is consistent with previous research (Alexander & Penland, 1996;Alexander et al., 2000;Cronin et al., 2013;Elsberry & Garwood, 1978;Lanzante & Harnack, 1983). The "Q H Growth" sector reflects the negative product of anomalies of SST and MLD under climatological heating. In this situation, SST easily increases under a shallow MLD anomaly and climatological surface heating in the summer hemisphere.
As noted in the previous paragraph, the "Q H Growth" sector is dominant in the summer hemisphere, particularly in the eastern part of the ocean basins (Figures 3d, 3h, 3l, and 3p). The region with a large contribution of MLD anomalies exhibits a horseshoe-like pattern, especially in the North Pacific (Figures 3h and 3l). One reason for the large contribution of MLD anomalies is large variability of MLD anomalies in subtropical regions ( Figure  S4a in Supporting Information S1), particularly due to strong surface friction velocity in the subtropical Pacific (Zhu & Zhang, 2018). Another reason is a large value of the ratio of the mean surface heat flux to mean MLD in the North Pacific and Atlantic (>50˚N in Figure S4b in Supporting Information S1), which is mainly due to the shallow climatological mean MLD under the strong climatological heating at the sea surface during the summer ( Figures S4c and S4d in Supporting Information S1). From left to right, the "Q Q Decay," "Q H Decay," "Q Q Growth," and "Q H Growth" sectors are displayed, respectively. Each row shows the results in DJF (1st row), MAM (2nd row), JJA (3rd row), and SON (4th row). Light gray hatches indicate the grid where relative contribution of surface forcing term is not the primary driver of T variability (i.e., linear regression coefficient of surface forcing term onto the total tendency term during each season [ Figures S3a, S3c, S3e, and S3g in Supporting Information S1] is less than 0.5).

Q H Decay Process: Contribution of MLD Anomalies to the Decay of SST Anomalies
Tropical SST variability is primarily driven by the oceanic term rather than the surface forcing term (Figures S2 and S3 in Supporting Information S1). However, the thermal damping process described as the surface forcing term play a crucial role in the decaying phase of El Niño-Southern Oscillation (e.g., Boucharel et al., 2015;Guan et al., 2019;Timmerman et al., 2018). Histogram of FDA in the tropics (Figure 2c) shows that the contribution of surface heat flux anomalies is basically dominant. In addition, occurrence frequency of "Q H Decay" is slightly larger in SON and DJF than in other seasons. Horizontal maps of the "Q H Decay" occurrence frequency (Figures 3b,3f,3j,and 3n) show that this process is dominant in the eastern tropical Pacific during DJF. The "Q H Decay" sector reflects the positive product of anomalies of SST and MLD under climatological heating. It is consistent with the regionality of positive covariance between anomalies of SST and MLD in the oceanic upwelling zone (Carton et al., 2008;Cronin & Kessler, 2002;Huang et al., 2012;Wang & McPhaden, 2000), resulting in negative anomalies of equivalent heat flux with deeper MLD under climatological heating in the tropics that act to dampen positive SST anomalies. Although there are various important processes that modulate the MLD anomaly in the tropics, such as wind stirring, surface buoyancy forcing derived from fresh water flux, and lateral advection (e.g., Pookkandy et al., 2016), we will not further discuss the formation mechanism of the MLD anomaly.

Summary and Discussion
To reveal the seasonal and regional characteristics of the role of MLD anomalies in modulating SST variability, we propose a metric called FDA that quantifies the relative contributions of surface heat flux and MLD anomalies to the month-to-month variations of SST anomalies. The FDA is defined in terms of the four-quadrant arctangent function and based on a metric proposed by Tozuka et al. (2018). Using the FDA, we investigate the seasonal and regional characteristics of their relative contributions. The contribution of MLD anomalies has two distinct features. First, MLD anomalies amplify local SST anomalies particularly in the extra-tropics during spring and summer, relative to the contribution of surface heat flux anomalies. Second, MLD anomalies suppress local SST anomalies particularly in the eastern part of the tropical Pacific during DJF. This paper provides the first global picture of the relative importance of surface heat flux and MLD anomalies to the local SST variability based on observational datasets.
Our results show that the spatial pattern with pronounced contributions of MLD anomalies in the North Pacific during spring and summer is horseshoe-like ( Figure 3). This implies that MLD anomalies might play a critical role in modulating the climate variability in the North Pacific. Recent papers pointed out the importance of MLD anomalies in modulating major modes of climate variability such as the Pacific Decadal Oscillation (Dawe & Thompson, 2007), Atlantic Meridional Mode (Kataoka et al., 2019), and the Atlantic Multidecadal Oscillation (Yamamoto et al., 2020). Kataoka et al. (2019) also revealed that variations in MLD have the potential to more than double the wind-evaporation-SST feedback rate. Thus, the role of MLD anomalies in climate variability should be paid more attention to and its further investigation is needed.
Although our results demonstrate the observed contribution of MLD anomalies to the local SST variability, it is widely recognized that large uncertainties associated with summertime MLD exist in ocean and coupled general circulation models (Ezer, 2000;Huang et al., 2014). The presence of MLD biases in climate models is a potential source of SST biases (Zhu et al., 2020). Thus, improved understanding of the different formation mechanisms of MLD anomalies is required, especially for physical processes associated with the MLD variability driven by wind stirring, surface buoyancy forcing derived from fresh water flux, and lateral advection (Lee et al., 2015;Pookkandy et al., 2016;Ushijima & Yoshikawa, 2019;Yoshikawa, 2015). Furthermore, quantifying the feedback process between SST and MLD via aforementioned physical processes would be valuable. Finally, we highlight that our simple metric based on only three variables is a useful diagnostic when considering the representation of the upper ocean in climate models.

Data Availability Statement
Most of the datasets used in this study can be downloaded from Asia-Pacific Data Research Center; http://apdrc. soest.hawaii.edu/data/data.php, which is a part of the International Pacific Research Center at the University of Hawaiʻi at Mānoa, funded in part by the National Oceanic and Atmospheric Administration (NOAA). Original data sources are listed below; OISSTv2 is from https://www.ncei.noaa.gov/products/optimum-interpolation-sst. CERES data were obtained from the NASA Langley Research Center CERES ordering tool at https://asdc.larc. nasa.gov/project/CERES/CERES_EBAF_Edition4.1. The global ocean heat flux and evaporation data provided by the Woods Hole Oceanographic Institution OAFlux project (https://oaflux.whoi.edu/data-access/) were funded by the NOAA Climate Observations and Monitoring (COM) program.