Processes Contributing to Bering Sea Temperature Variability in the Late Twentieth and Early Twenty-First Century

a. Ocean warming and marine heatwaves in the Bering Sea

While this analysis is relevant to the full spectrum of ocean temperature anomalies, recent interest has focused on marine heatwaves (MHWs), discrete periods of anomalously high sea surface temperature (SST) (Hobday et al. 2016). MHWs have increased globally in frequency, intensity, and extent in recent decades (Scannell et al. 2016), a trend that is likely to accelerate with continued global warming (Frölicher et al. 2018). The North Pacific has not been immune to the increasing trend in MHWs, with exceptional events occurring in 2014/15 (Bond et al. 2015; Di Lorenzo and Mantua 2016) and again in 2019 (Amaya et al. 2020). MHWs have also increased in frequency and longevity in the Bering Sea since 2010 (Carvalho et al. 2021), and their timing aligns with the multiyear warm/cold periods that have come to describe the climate of the Bering Sea (Overland et al. 2012; Danielson et al. 2020). It is relevant to note that the choice of baseline period affects the depiction of MHWs and their projected trends: the use of a fixed baseline period can lead to a “saturation” of MHW events (Oliver et al. 2021) because of underlying global warming trends and the choice of a static threshold for defining an MHW. Regardless of how MHWs are defined and identified, the Bering Sea is warming at both the surface and subsurface (Fig. 1).

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(a) Observed trend (per 44 years) in annual mean SST (°C) from the ERA5 reanalysis for the period 1979–2022 and (b) observed trend (per 26 years) in ECCO annual mean MLT (°C), 1992–2017. The Bering Sea study region of interest in this analysis is outlined in black. These trends were computed from linear regression coefficients of annual mean temperature multiplied by the record length of 43 years for the SST trend and the record length of 26 years for the MLT trend.

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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The increase in MHWs is occurring in tandem with ocean warming trends in large swaths of the global oceans (Johnson and Lyman 2020). Global mean SST has increased due to anthropogenic warming and is projected to continue increasing (Pachauri et al. 2014). In the Bering Sea, a long-term surface warming trend has been observed in the contemporaneous data record (Steele et al. 2008; Danielson et al. 2020), with a likely long-term warming trend at depth that is obscured by decadal-scale variability and uncertainties due to data scarcity (Danielson et al. 2020). These ocean warming trends are clear in Fig. 1, with some of the strongest warming occurring in the Bering Sea. Studies project that the high-latitude Northern Hemisphere will experience the greatest absolute increase in SST, relative to other oceans, in both near-term and future long-term emission scenarios (Ruela et al. 2020). Arctic warming since the mid-twentieth century is occurring 2 or more times faster than other parts of the globe (Tokinaga et al. 2017), with surface ocean temperatures projected to increase 2–3 times faster than the global average by the end of the century (Hassol and Corell 2004; Davy and Outten 2020).

Although the incidence of MHWs is increasing globally and in the North Pacific, there are key features of the Bering Sea that suggest that MHWs occurring there may be mechanistically different from other regions, such as the Gulf of Alaska to the south. The Bering Sea is unique as a semi-enclosed marginal sea with minimal exchanges with the Arctic and North Pacific Oceans (Stabeno et al. 1999). It is a region of seasonal extremes, including winter sea ice (Stabeno and Schumacher 1998), intense insolation fluctuations (Stabeno et al. 1999), and freshwater fluxes (Danielson et al. 2010). Because of these unique features, we do not necessarily expect MHWs and ocean warming in the Bering Sea to share the same characteristics as elsewhere.

While this work does not specifically address sea ice variability, the processes contributing to ocean surface temperature variability in the Bering Sea are relevant to explaining at least some of the observed sea ice variability. In contrast to much of the Arctic, sea ice extent in the Bering Sea did not display a significant negative trend over the period 1979–2010 (Parkinson and Cavalieri 2008; Cavalieri and Parkinson 2012); however, an increase in the variability of both interannual sea ice extent (Danielson et al. 2011) and of the timing of sea ice advance (Stabeno et al. 2007) has been observed since the end of the twentieth century and into the twenty-first century. Concurrent with the recent increase in sea ice variability, historic anomalies in sea ice extent and concentration have been observed over the last decade. Sea ice in the Bering Sea reached its lowest recorded wintertime maximum extent on record during the Northern Hemisphere winter of 2017/18 (Stabeno and Bell 2019), driven by anomalously elevated ocean temperatures, higher than normal surface air temperatures, and pronounced anomalies in wind speed and direction (Stabeno and Bell 2019; Basyuk and Zuenko 2020). Future projections suggest a decrease in maximal sea ice extent and increase in the length of the ice-free season by midcentury (Wang et al. 2018) and continuing through the end of the century (Wang et al. 2020).

b. Bering Sea heat content

Air–sea heat fluxes have been shown to be the dominant driver of upper ocean heat content variability over the shallow Bering Sea shelf (Reed 1978; Reed and Stabeno 2002; Danielson et al. 2010) and in the deep basin (Wirts and Johnson 2005). Strong solar insolation generates shallow mixed layer depths (MLDs) during the summer, while increased evaporative heat loss due to winter storms drives wintertime deepening of the mixed layer (Coachman 1986; Luchin et al. 1999; Wirts and Johnson 2005). Heat content changes in the shallow shelf not described by the air–sea heat fluxes have been hypothesized to be the result of oceanic heat advection and diffusion, which were estimated to contribute between 4% (Reed and Stabeno 2002) and 10% (Danielson et al. 2010) to ocean heat content variability. In the deep basin, the changes not captured by the air–sea heat fluxes have been hypothesized to be the result of ocean circulation anomalies transporting anomalously warm water (Wirts and Johnson 2005).

Previous studies broadly emphasized the importance of air–sea heat exchange in Bering Sea climate variability and change, with the general consensus that air–sea heat fluxes drive the majority of observed upper ocean temperature variability. However, the computation of closed budgets was hindered by a lack of available measurements. The roles of vertical and horizontal advection and turbulent diffusion were typically estimated, with differing conclusions regarding their relative importance in driving ocean temperature variability (Reed and Stabeno 2002; Danielson et al. 2010). Therefore, questions remain regarding the processes responsible for setting the ocean mixed layer temperature structure of the Bering Sea. In addition to a lack of understanding regarding the role of ocean dynamical processes in MLT variability, the recent (2014–18) increase in both incoming and outgoing air–sea heat fluxes (Danielson et al. 2020) is suggestive of the need to evaluate recent Bering Sea ocean temperature structure in the context of a closed heat budget. To analyze these gaps in understanding, we compute a closed mixed layer heat budget for the Bering Sea using the ECCO Ocean State and Sea Ice Estimate, over the ECCO record length spanning the 26-yr period 1992–2017. Our analysis expands on earlier assessments by diagnosing the spatially and temporally varying roles of surface forcing, and horizontal and vertical advection and diffusion in driving MLT tendency variability. We analyzed long-term variability in Bering Sea MLT tendency and quantified the role of the atmosphere and ocean dynamics in driving this variability. To our knowledge, our work provides the first assessment of the Bering Sea heat budget using ECCO and is the first long-term closed heat budget for the region.

a. ECCO ocean state estimate

We used the NASA/JPL ECCO Version 4 release 4 (V4r4) Ocean State and Sea Ice Estimate (ECCO Consortium et al. 2017a, 2021) to compute a closed mixed layer heat budget for the Bering Sea. Its temporal coverage is commensurate with the satellite altimetry data record beginning with TOPEX-Poseidon in 1992 and currently extends through 2017 (ECCO Consortium et al. 2021). The ECCO ocean state estimate is based on a free-running MITgcm simulation and its adjoint, where the adjoint has been iteratively implemented (Wang et al. 2020) to minimize differences between the model and a host of satellite and in situ ocean surface and subsurface observations. Use of this adjoint method allows synthesis of observations, while satisfying physical and dynamical conservation laws, and thus, the state estimate conserves heat, salt, volume, and momentum. The state estimate accounts for all heat and buoyancy sources (Forget et al. 2015), and it can be used in a quantitative assessment of closed budgets (Piecuch 2017).

The current version of ECCO (V4) improves on previous versions through its incorporation of newly available observations, increased coverage of the Arctic, improved model algorithms, and increased temporal coverage (ECCO Consortium et al. 2021). ECCO V4r4 is provided on the so-called “lat-lon cap” (LLC90) nonuniform horizontal grid, corresponding to horizontal grid sizes of nominally 110 km near the equator, decreasing with latitude to approximately 60 km in the Bering Sea (Forget et al. 2015). There are 50 vertical levels, with a grid thickness of 10 m near the ocean surface and increasing nonlinearly with depth below 50 m.

At high latitudes, sea ice plays a key role in the climate, but its hemispheric variability and trends and its interactions with the global climate system are not well resolved in many GCMs (Losch et al. 2010). By incorporating ocean and sea ice data to constrain a numerical, coupled system model, MITgcm computes dynamically consistent ocean and sea ice state estimates with closed budgets (Losch et al. 2010). Brine rejection that occurs due to the formation of sea ice is accounted for in ECCO by distributing the resultant surface salts in the vertical down to their neutral buoyancy depth (Nguyen et al. 2009; Forget et al. 2015) without any explicit flux of heat. The density anomaly which results from brine rejection is thus entirely salinity driven. The corresponding impact of brine rejection on the MLD in ECCO is not clear but is likely a small effect that is localized to regions and times of active sea ice formation. MITgcm parameterizes sea ice using a zero-layer thermodynamic model, in which the sea ice has zero heat capacity and simply melts or freezes as it conducts heat between the ocean and the atmosphere, and a viscous-plastic rheology dynamical model (Losch et al. 2010). The sea ice adjoint method that is incorporated into the MITgcm forward model is disabled over sea ice in the ECCO adjoint, as significant model instability is introduced due to highly nonlinear sea ice equations (Forget et al. 2015; Nguyen et al. 2021). Rather, a pseudoadjoint method that accounts for the shielding of the ocean surface from the atmosphere by sea ice is used in ECCO V4r4, which tapers the air–sea heat fluxes according to the fractional area coverage of the surface grid cell by sea ice (Forget et al. 2015). The effect of excluding the full sea ice adjoint model in ECCO over the Bering Sea has not been assessed in detail; however, Lyu et al. (2021) found that, in the Arctic, it resulted in an incomplete representation of sea ice area and concentration, overestimating winter sea ice extent and underestimating summer sea ice extent in comparison to observations. Despite uncertainties in the representation of sea ice properties, the ECCO ocean state estimate generally captures the temperature and salinity structure of the Arctic Ocean (Lyu et al. 2021). The ECCO state estimate is the best available product for computing a closed heat budget that can be used to diagnose ocean temperature anomalies and their drivers.

b. Bering Sea mixed layer heat budget

c. Climatologies and anomalies

d. Defining the H angle as an indicator of the dominant driver of MLT tendency anomalies

To isolate the relative contributions of surface forcing and ocean dynamics in driving mixed layer temperature tendency anomalies (MLTa), we developed a simple metric inspired by earlier metrics for vertical density gradients and horizontal frontal processes (e.g., Turner 1979; Rudnick and Ferrari 1999; Yeager and Large 2007). Our version is called the H angle and is defined as

$H={\text{tan}}^{-1}\left(\frac{{\widehat{G}}_{\text{SF}}^{{\theta }^{\prime }}}{{\widehat{G}}_{\text{OD}}^{{\theta }^{\prime }}}\right).$(7)

The angle H is summarized schematically in Fig. 2, with the surface forcing contribution to MLTa placed on the vertical axis and the ocean dynamics contribution placed on the horizontal axis. The value of H in each grid cell and at each time indicates the relative importance of each term in driving MLTa.

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Schematic illustration of the H angle in the polar plane, with the vertical y axis defined as the surface forcing contribution (${\widehat{G}}_{\text{SF}}^{{\theta }^{\prime }}$) to MLTa (${\widehat{G}}_T^{{\theta }^{\prime }}$) and the horizontal x axis as the ocean dynamics contribution (${\widehat{G}}_{\text{OD}}^{{\theta }^{\prime }}$). The dashed line that stretches from −45° to +135° defines angles for which MLTa is positive (to the upper right of the line) and angles for which MLTa is negative (to the lower left of the line). The gray regions depict the angles for which ${\widehat{G}}_{\text{SF}}^{{\theta }^{\prime }}$ is the dominant forcing term, with H = ±90°, defining values where surface forcing accounts for all of MLTa. The white regions are the angles for which ${\widehat{G}}_{\text{OD}}^{{\theta }^{\prime }}$ drives MLTa, with H = 0° and ±180° describing the values where ocean dynamics account for all of the MLTa.

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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e. Balance metric M_B

In this work, we use M_B to assess the spatial and temporal variability of the processes that drive MLTa in the ECCO heat budget. Because the heat budget is balanced (T_t = P₁ + P₂, where T_t represents MLT tendency, P₁ represents surface forcing, and P₂ represents the oceanic contribution), P₁ and P₂ are defined such that they fully describe the MLTa tendency, and the value of M_B is therefore diagnostic of the percent variability each process is responsible for.

f. Dominance analysis

To account for coupled interactions between the four terms in the net surface heat flux [Eq. (1)] in a concise and statistically sound manner, we present a third analysis technique called dominance analysis (DA). DA was developed initially for use in the field of psychology as a method to evaluate the relative importance of predictors in multiple linear regression and classification models (Budescu 1993) and is based on the familiar concept of quantifying the variance explained using linear regression modeling techniques. It builds on these concepts by considering a hierarchy of models that attributes variance to different combinations of processes. The multiple linear regression model of a dependent variable Y for N predictors that DA is based on is defined as

$Y={\displaystyle \sum _{i=1}^N{\beta }_i}{X}_i+ϵ,$(9)

where the dependent variable Y is modeled as a linear regression against the predictors X_i and their associated regression coefficients β_i. The term ϵ is a random variable giving the departure of Y from the linear regression model. DA examines the proportion of variance in Y that is explained by X_i, denoted as R², for all possible combinations of predictors. By comparing R² for all subset models, DA determines which predictor variable contributes the most to the variance of Y after accounting for the effects of all other predictors and their possible cross covariances. Azen and Budescu (2003) refined the DA methods described by Budescu (1993), by assessing conditional and general dominance of predictors in a multiple linear regression model. It is conventional to present the DA in terms of a table of cross correlations of all possible submodels, as shown for a hypothetical case of three predictors in Table 1, which we describe below.

Table 1.

Hypothetical dominance analysis for the case of a multiple linear regression model with three predictor variables (Azen and Budescu 2003), such as the case we will examine specifically with the ECCO net air–sea heat flux analysis in the next section. Each column headed by X_i lists the fractional contribution to the variance of Y from predictor X_i when it is added to the subset regression model defined in column $R_{Y\cdot \mathbf{X}}^2$. The rows k = 1 average and k = 2 average describe conditional dominance of the predictor variables relative to one another and are computed by taking the mean of the rows directly above that are models of size k. The bottom row describes the general dominance of the predictor variables X_i of that column and is computed by taking the mean of each k average. Cells with dashes indicate that a statistic for a submodel with this combination of variables is not possible.

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The concept of “relative importance” (Budescu 1993; Azen and Budescu 2003) is a key consideration for our choice of using DA for quantitatively evaluating the predominant forcing terms in the net air–sea heat flux anomaly. The values in the k = 1 and k = 2 rows of Table 1 describe conditional dominance for the three predictors X_i and are calculated by taking the mean of the R² values for that subset of models. It is a “weaker” level of dominance that describes how the addition of the predictor within that column contributes to all subset models described by the rows above them. The strongest dominance type and the one we emphasize here is general dominance, described by the bottom row of the table, which we call the generalized dominance metric hereafter. It is computed by taking the average of the conditional dominance values, k = 1 and k = 2 rows, for that predictor. The predictor with the highest average value is defined as the generally dominant term.

One of the primary strengths of using DA to assess the importance of predictors in a regression model is its ability to partition the variance observed in the dependent variable of the regression model among the predictor variables. The sum of the average contribution of each predictor variable to describing the variance of the model (bottom row of Table 1) is equal to the total variance of the full model $R_{Y\cdot \mathbf{X}}^2$. In the case considered here of the net air–sea heat flux anomaly, the sum of the fractional variance of Y described by each predictor will be equal to 1, as the model fully describes $Q_{\text{net}}^{\prime }$ (note that in empirical regression models, this is not necessarily the case). In addition, DA provides increased insight relative to regression coefficients and their confidence intervals, as it accounts for correlations and interactions between predictor variables.

a. Mixed layer depth variability

The Bering Sea is a region with unique oceanographic properties, with a density-compensated vertical structure within the mixed layer, where the relative roles of temperature and salinity in setting the structure vary in both space and time (Ladd and Stabeno 2012; Johnson and Stabeno 2017). Surface forcing plays a key role in the seasonal variability of temperature and salinity, with insolation driving summertime warming and mixed layer shoaling, and the turbulent heat fluxes cooling and deepening the mixed layer in the wintertime (Coachman 1986; Luchin et al. 1999; Wirts and Johnson 2005). Air–sea heat fluxes are the dominant control on seasonal MLD variability, but sea ice variability can result in relatively small and short-lived alterations to the temperature and salinity structure of the Bering Sea shelf. Sea ice can alter MLD variability by reducing wind mixing and therefore decreasing the energy transfer from the atmosphere to the ocean (Sullivan et al. 2014). It can also contribute to stratification of the water column as it advances southward in the winter and then melts and retreats northward in the spring (Ladd and Stabeno 2012; Sullivan et al. 2014). Because the MLD modulates the response of the mixed layer to a given surface forcing, and because it is determined by seasonally varying processes, we investigate ECCO MLD variability and how it is affected by temperature and salinity structure in the Bering Sea. We additionally evaluate the relationship between SST and MLT in the Bering Sea to determine if SST is an appropriate proxy for MLT in our mixed layer heat budget.

In the off-shelf region of the Bering Sea (water column depth > 125 m in Fig. 3), the MLD typically reaches its maximum in March and shoals from April through July/August. The shallow summertime mixed layer is a result of intense insolation thermally stratifying the upper water column that is reinforced by a lack of wind-driven vertical mixing (Wirts and Johnson 2005). During the summer, there is a sharp seasonal thermocline directly below the mixed layer, and heat is diffused downward. The MLD begins to deepen in September and continues to deepen through the winter. Beginning in November, the MLD reaches the sea floor in the shallowest part of the shelf (water column depth < 125 m), and by December, the mixed layer extends to the sea floor in the midshelf. Strong winter storms cool the ocean surface, and the intense cold winds associated with the storms drive evaporation at the surface that cools the ocean (Wirts and Johnson 2005). Because of the cooling of the ocean surface by the turbulent heat fluxes and intense vertical mixing, the mixed layer is cold, high in salinity, and reaches its maximum depth in the winter (Wirts and Johnson 2005). Beginning in January and continuing through April, the deepening mixed layer encroaches upon the warm inversion layer, warming the mixed layer through upward diffusion. The MLD remains near the seafloor until shoaling begins in February and March due to increasing solar insolation. The MLD is similar over the shallow shelf ($\text{depth}\lesssim 125\hspace{0.17em}\mathrm{m}$) and off-shelf region from June to September but diverges during the fall through spring. The mixed layer is shallow and highly stratified in July–August when insolation is greatest over the shallow shelf (Reed 2003). The MLD increases in September and October in response to decreasing net shortwave radiation, increased evaporative cooling of the ocean surface, and increased wind mixing (Reed 2003).

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Monthly climatological distance–depth cross sections of the region of strong MLT gradient, along the points shown in the inset map at the upper-right. ECCO monthly mean potential temperature (shading; °C) and salinity (black contours; psu) from the surface to depth, 1992–2017, over this transect are shown in the remaining panels. The left-hand side of each panel denotes the farthest southwest point of the transect, and the right-hand side denotes the farthest northeast point of the transect. The white contours depict the monthly mean MLD. The y axis is depth (m).

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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In the Bering Sea basin, salinity dominates the climatological vertical density gradient (Johnson and Stabeno 2017), with temperature playing a secondary role, except in the seasonal thermocline (Johnson and Stabeno 2017). This is evident in Fig. 3, with the year-round presence of a vertical salinity gradient at depths > 125 m. Temperature inversions > 1°C are common at these depths in all months of the year (Ohno et al. 2009), for example, in February between ∼100- and ∼175-m water column depth (Fig. 3). Over the shelf (Fig. 3), there is little stratification in the winter and early spring (January–April), with stratification beginning to increase in May due to the combined effects of freshwater input from ice melt and surface warming due to increasing air–sea heat fluxes into the ocean (Ladd and Stabeno 2012). Stratification over the shelf continues to increase through the summer (June–August), with very warm temperature near the surface. Stratification rapidly declines in September and October (Fig. 3), driven by surface cooling and wind mixing (Ladd and Stabeno 2012) due to the onset of fall storms.

Past research has concluded that the seasonal ocean temperature variability is driven by both surface air–sea heat fluxes and heat redistribution below the surface by horizontal and vertical motion (Luchin et al. 1999). Salinity variability on seasonal time scales is driven by the formation of sea ice, river outflow, and the balance between precipitation and evaporation (Luchin et al. 1999). It is sometimes assumed that SST is a reasonable proxy for MLT when considering the physical processes controlling upper ocean temperatures. However, a practical implication of the temporal and spatial variability of the temperature and salinity distributions and their varying roles in the Bering Sea density structure is the possibility of a disparity between SST and MLT. To determine the validity of assuming SST as an appropriate proxy for MLT, we assessed the root-mean-square (RMS) difference between ECCO SST and MLT on both annual (Fig. 4) and monthly (Fig. 5) time scales. On annual time scales, the area-mean RMS difference between SST and MLT is ∼0.13°C, with the largest difference over the deep, southwest basin of the Bering Sea and the smallest over the northeast shelf and through the Bering Strait. The difference between SST and MLT is more pronounced on monthly time scales, with a clear seasonality in the magnitude of the difference. The basin-scale RMS difference increases through the year, beginning with an area-mean value of ∼0.08°C in January, reaching its maximum area-mean value in June (∼0.15°C), and remaining high from July (∼0.15°C) through September (∼0.11°C). The area-mean RMS difference reaches a minimum in November and December (∼0.05°–0.16°C).

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RMS difference between monthly averaged ECCO SST and MLT, over the record length, 1992–2017. The area-mean RMS difference between SST and MLT for all grid points in the domain over the full record length is approximately 0.13°C.

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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RMS difference between monthly ECCO SST and MLT (°C), over the record length, 1992–2017.

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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Because of the spatial and seasonal variability in the drivers of stratification in the Bering Sea, and the seasonally varying RMS difference between SST and MLT, they are not linearly coupled in this region and SST is not an appropriate proxy for MLT for our analysis. Therefore, we computed our balanced mixed layer heat budget using MLT as defined by ECCO. Because surface forcing is a key driver of seasonal MLD variability, we next assess the seasonal cycle of the net air–sea heat flux and its component terms, before evaluating MLT tendency seasonal variability.

b. Surface air–sea heat flux variability

The area-mean seasonal value of the ECCO net air–sea heat flux and each component term [Eq. (1)] is shown in Fig. 6 and Table 2. In this and succeeding sections, we define winter as January–March (JFM), spring as April–June (AMJ), summer as July–September (JAS), and fall as October–December (OND). In the winter, the Bering Sea acts as a net heat source to the atmosphere, and this ocean cooling flux is dominated by the sensible and latent heat flux anomalies. In the spring, the Bering Sea transitions to an atmospheric heat sink, with a net ocean warming heat flux that is dominated by the radiative flux term. Net shortwave radiation is the dominant term during the spring, as solar insolation rapidly increases in advance of the summer solstice. There is some rectification of the radiative warming by the upward turbulent heat flux, but its effect is relatively small. The summer surface heat flux magnitude and spatial pattern are similar to those of spring, with ocean warming dominated by solar insolation and a slight rectification of this warming by the turbulent flux components. In the fall, the Bering Sea transitions back to an atmospheric heat source, with the latent heat flux driving most of the cooling, with smaller contributions from the sensible and radiative terms. There is latitudinal variation in the magnitude of the dominant term driving the net heat flux that is most apparent in the fall and winter. In the winter, the sensible heat flux drives an amplified cooling in the northern Bering Sea, and in the fall, it drives a similar northerly amplified cooling with an overall magnitude that is decreased relative to the winter.

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Area-mean seasonal value of the ECCO (first row) net air–sea heat flux (Q_net), (second row) sensible (Q_SH) and (third row) latent (Q_LH) components, and (fourth row) radiative component (Q_RAD). The seasonal means (W m⁻²) are computed over the record length, 1992–2017. Positive values (warm colors) indicate an ocean warming flux, and negative values (cool colors) indicate an ocean cooling flux.

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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Table 2.

Area mean of the ECCO seasonal net air–sea heat flux and each component term (W m⁻²). Negative flux values indicate heat loss to the atmosphere and vice versa.

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We now assess the seasonal variability of the mixed layer heat budget, in relationship to the seasonal cycle of the net air–sea heat flux, and its role in altering mixed layer temperature.

c. Seasonal variability in the drivers of MLT tendency

Seasonal variability in the Bering Sea mixed layer heat budget [Eq. (4)] is described by Fig. 7 and Table 3. In the winter, the mixed layer is cooling (−0.43°C month⁻¹), and surface forcing (${\widehat{G}}_{\text{SF}}^{\theta }$) is the dominant term (−0.83°C month⁻¹). The turbulent components of the net heat flux dominate the surface forcing (Table 2). Ocean dynamics (${\widehat{G}}_{\text{OD}}^{\theta }$) contribute to mixed layer warming (0.40°C month⁻¹) at approximately half the strength of the surface forcing contribution, with the majority of the signal driven by vertical diffusion (0.25°C month⁻¹). Surface forcing drives mixed layer cooling throughout the Bering Sea, with the strongest signal in the northern shelf region, and vertical diffusion (not explicitly shown) “redistributes” this cooling vertically. Vertical and horizontal advection (0.07° and 0.08°C month⁻¹, respectively) account for the remaining ocean-driven warming.

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Mean seasonal value of each term (°C month⁻¹) in the mixed layer ECCO heat budget [Eq. (5)]. Values are computed over the record length, 1992–2017. (top) The seasonal evolution of the total temperature tendency (${\widehat{G}}_T^{\theta }$), (middle) the surface forcing contribution (${\widehat{G}}_{\text{SF}}^{\theta }$), and (bottom) the ocean contribution (diffusion plus advection; ${\widehat{G}}_{\text{OD}}^{\theta }$). Positive values (warm colors) indicate warming, and negative values (cool colors) indicate cooling.

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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Table 3.

Area-mean seasonal values of ECCO mixed layer heat budget terms (°C month⁻¹).

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In the spring, the mixed layer is warming (1.70°C month⁻¹), and surface forcing continues to dominate (1.76°C month⁻¹) the MLT tendency, with the radiative component of the air–sea heat flux dominating the signal (Table 2). There is a rapid increase in solar insolation during the spring, with daylight hours reaching a maximum in June. Ocean dynamics weakly oppose the warming, but their cooling contribution (−0.06°C month⁻¹) is a fraction of the size of the surface forcing signal.

Mixed layer warming continues through the summer (0.85°C month⁻¹), with surface forcing continuing to be the dominant term (1.96°C month⁻¹), a result of the summertime maxima of solar radiation (Table 2). Ocean dynamics contribute strongly to MLT tendency variability in the summer (−1.11°C month⁻¹), dampening the impact of surface forcing in warming the mixed layer. Vertical diffusion (−1.06°C month⁻¹) is the dominant ocean dynamics term in the summertime, redistributing the heat that is fluxed into the ocean surface downward through the base of the mixed layer. The increasing role of ocean dynamics in affecting MLT tendency may be related to intensifying stratification in the summer (Fig. 3).

In the fall, the mixed layer cools rapidly (−1.76°C month⁻¹) with surface forcing driving the majority of the mixed layer variability (−1.72°C month⁻¹), while ocean dynamics contribute much less to the cooling (−0.04°C month⁻¹) relative to the surface forcing. Furthermore, during this period, daily solar radiation rapidly decreases and winter storms are increasing in frequency and intensity, cooling the ocean through the latent and sensible heat fluxes (Table 2).

Our main results indicate that surface forcing dominates the MLT tendency in all seasons. Seasonality of the individual terms in the surface forcing is key: the radiative flux dominates the net surface flux during the spring and summer, while the latent and sensible heat fluxes dominate during the fall and winter. In the following section, we assess anomalies in the mixed layer heat budget and the processes that drive them.

a. Subseasonal-to-seasonal variability in MLT anomalies

We now assess the drivers of monthly mixed layer temperature tendency anomalies (MLTa), computed relative to a 1992–2017 monthly climatology, and assess the role of the atmosphere in forcing ocean temperature anomalies. We computed the H angle comparing surface forcing anomalies (${\widehat{G}}_{\text{SF}}^{{\theta }^{\prime }}$) to ocean dynamic anomalies (${\widehat{G}}_{OD}^{{\theta }^{\prime }}$), to assess their relative importance in driving MLTa. Over the record length (1992–2017) (Fig. 8, black solid line), surface forcing anomalies dominate MLTa, contributing to anomalous mixed layer warming ∼34% of the total time (Fig. 8, red shaded area) and cooling ∼32% of the total time (Fig. 8, blue shaded area). The H angle for the recent decade (2010–17) (Fig. 8, red solid line) shows both a slight increase in mixed layer warming driven by surface forcing anomalies (∼36%) and a slight decrease in ocean cooling driven by surface forcing anomalies (∼30%). We note that the record length of ECCO precludes drawing definitive conclusions about how trends in surface forcing are contributing to trends in surface warming.

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Probability distribution function of the H angle comparing Bering Sea ECCO mixed layer heat budget surface forcing anomalies (${\widehat{G}}_{\text{SF}}^{\theta }$) to ocean dynamic anomalies (${\widehat{G}}_{\text{OD}}^{\theta }$). Values for the full record length (1992–2017) are shown in black, and recent (2010–17) values are shown in red. The red shaded region depicts the H angles for which surface forcing anomalies are dominant and result positive in MLTa. The blue shaded region defines the H angles where surface forcing anomalies are dominant, but MLTa tendency is negative.

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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To evaluate the spatially and seasonally varying roles of the mixed layer heat budget forcing terms in driving MLTa, we used the balance metric (M_B) developed by Halkides et al. (2015) (Fig. 9). Anomalies in MLT tendency are largely driven by surface forcing anomalies, which on average drive ∼72% of monthly MLTa for all months. Of the two months in which ${\widehat{G}}_{\text{SF}}^{{\theta }^{\prime }}$ is not the dominant forcing term, in August, surface forcing and ocean dynamics contribute approximately equally to MLTa, while in September, ocean dynamics are slightly more dominant than surface forcing (∼60% vs ∼40%). Ocean dynamic anomalies are driven primarily by vertical diffusion anomalies in August (account for ∼76% of ${\widehat{G}}_{OD}^{{\theta }^{\prime }}$) and September (account for ∼68% of ${\widehat{G}}_{OD}^{{\theta }^{\prime }}$) (not shown). There is typically a transition from a shallow, stratified mixed layer to a deeper mixed layer in August and September (Fig. 3), which is reflected in the increasing role of ocean dynamics in driving MLTa during these months through the vertical turbulent diffusion and, to a lesser extent, the horizontal diffusion and advection terms.

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The ECCO balance metric M_B comparing the role of monthly mean surface forcing anomalies (${\widehat{G}}_{\text{SF}}^{\theta }$) to ocean dynamic anomalies (${\widehat{G}}_{\text{OD}}^{\theta }$) in driving MLTa, over the record length, 1992–2017. When M_B is equal to 1, surface forcing anomalies drive the variability in the MLTa. When M_B is equal to −1, ocean dynamic anomalies drive the variability in the MLTa. When M_B is equal to 0, the surface forcing and ocean dynamics contribute equally. The monthly area-mean percent of the variance in MLTa explained by the surface forcing anomalies is noted in the upper left of each map.

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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b. Anticorrelation between vertical and horizontal advection

The importance of vertical advection in altering Bering Sea heat content has been suggested by previous work, but a lack of data has generally precluded an analysis of the magnitude of its role. Our closed heat budget allows us to evaluate its role in the context of monthly MLTa. A comparison of the area average vertical, horizontal, and net advection anomalies in the mixed layer is shown in Fig. 10. We show only 2010–17 in the time series in Fig. 10a in order to show the relationship between variables in detail, but the relationship holds over the full ECCO data record. Horizontal (solid gray) and vertical (dashed gray) advection anomalies are anticorrelated (ρ² = −0.98), such that the net advection anomalies (solid black) are small compared to the total tendency anomalies (solid red). Although each advection term is of a similar magnitude as the total MLTa, the net advection term is quite small and does not contribute significantly to ${\widehat{G}}_{OD}^{{\theta }^{\prime }}$ or MLTa on the time and space scales considered here. The anticorrelation indicates that heat anomalies transported vertically into the mixed layer are spread horizontally and contribute little to local mixed layer warming or cooling. Considering only horizontal or vertical heat advection thus gives an incomplete depiction of the role of ocean circulation anomalies in forcing MLT anomalies. We note that this result may be scale dependent such that fully resolving oceanic mesoscale or submesoscale variability may lead to a different relationship between horizontal and vertical heat transport processes. Nonetheless, this result indicates that mixed layer horizontal and vertical heat advection compensate each other on the O(60–100) km spatial scales resolved by the ECCO state estimate.

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(a) Area mean of ECCO mixed layer horizontal advection anomalies (${\widehat{G}}_{\text{AH}}^{{\theta }^{\prime }}$; solid gray); vertical advection anomalies (${\widehat{G}}_{\text{AV}}^{{\theta }^{\prime }}$; dashed gray); net advection anomalies (${\widehat{G}}_A^{{\theta }^{\prime }}$; solid black); and total tendency anomalies (${\widehat{G}}_T^{{\theta }^{\prime }}$, solid red), 2010–17. (b) Scatterplot of mixed layer horizontal advection anomalies (x axis) and vertical advection anomalies (y axis), and their squared correlation coefficient ρ² = −0.98.

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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c. Seasonal variability of air–sea heat fluxes that drive surface forcing anomalies

To determine the seasonal variability of the contribution of the component terms of the net air–sea heat flux anomaly to surface forcing anomalies, we used the multiple linear regression model of Eq. (10) and computed the generally dominant term at each grid cell in each month using DA methods (Table 4). This table was computed as the mean of all grid points in the analysis domain and gives a broad summary of the dominance of each component of the net surface heat flux anomaly. From January to April, anomalies in the turbulent heat flux, $Q_{\text{SH}}^{\prime }$ and $Q_{\text{LH}}^{\prime }$, dominate the net heat flux anomaly and account for a similar fraction of the total $Q_{\text{net}}^{\prime }$ variance during these months. Anomalies in the radiative heat flux, $Q_{\text{RAD}}^{\prime }$, dominate the net heat flux anomaly from May to August. From September to December, anomalies in the turbulent heat flux again dominate the net heat flux anomaly.

Table 4.

Monthly generalized dominance metric of each ECCO net air–sea heat flux predictor variable $Q_{\text{SH}}^{\prime }$, $Q_{\text{LH}}^{\prime }$, and $Q_{\text{RAD}}^{\prime }$ computed as the mean of each variable’s conditional dominance as obtained from the last row of the dominance table (Table 1). Values express the fraction of the variance of the full model ($Q_{\text{net}}^{\prime }$) that is accounted for by the addition of each predictor term to the full model. Bold values indicate that the predictor is assessed as dominant over all other predictors for that month. When two terms are bold, they account for a similar fraction of the variance of the full model.

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A more detailed assessment of the dominance of the heat flux components is achieved by presenting maps of the generalized dominance metric over the analysis region and for each month (Fig. 11), where the shading corresponds to the dominant flux component. Sensible heat flux anomalies are slightly greater in magnitude and dominate over a larger region of the Bering Sea in winter, with latent heat flux anomalies dominant near the Aleutian Islands during the same time period. In April, the latent heat flux anomalies account for slightly more of the net air–sea heat flux variance, and their spatial dominance continues to be over the southern Bering Sea. In May–August, anomalies in the net radiative flux are the primary driver of net heat flux anomalies over the vast majority of the Bering Sea, accounting for the largest fraction of the net air–sea flux variance in June and July. In September, there is a shift to the latent heat flux anomalies generally dominating over the majority of the Bering Sea, accounting for more than half of the normalized net air–sea flux variance. Latent heat flux anomalies continue to be generally dominant in October, with sensible heat flux anomalies increasing in dominance in the northern Bering Sea. By November, sensible heat flux anomalies dominate the northern Bering Sea, and latent heat flux anomalies dominate in the south, with a similar fraction of the variance accounted for by each term. December displays patterns similar to those in November, with each turbulent flux anomaly term accounting for a similar amount of the net variance. A key result derived from Fig. 11 is that during months that are not dominated by the radiative flux component, the sensible heat flux tends to dominate in the northern part of the domain and along the eastern continental shelf, and the latent heat flux tends to dominate in the southern part of the domain. This result indicates that the Bering Sea is a transition region between the relative dominance of evaporative heat gain/loss to the south in the North Pacific subpolar gyre and sensible heat gain/loss to the north in the Arctic Ocean.

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Generally dominant term in the monthly ECCO net air–sea heat flux anomaly multiple linear regression model described in Eq. (10). The shading corresponds to the term with the largest generalized dominance metric. Dark green indicates the dominance of radiative flux anomalies ($Q_{\text{rad}}^{\prime }$) in driving the net heat flux anomaly ($Q_{\text{net}}^{\prime }$); medium green describes the dominance of latent heat flux anomalies ($Q_{\text{LH}}^{\prime }$); and light green denotes the dominance of sensible heat flux anomalies ($Q_{\text{SH}}^{\prime }$). The generalized dominance metric, from which the seasonally dominant terms were determined, was computed using monthly averaged fields, with anomalies computed relative to the monthly climatology for 1992–2017.

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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d. Atmospheric processes and their role in ocean temperature anomalies

To understand the role of surface atmospheric processes in MLTa, we now compare the variability of the dominant monthly mean net heat flux anomaly terms to that of the monthly mean drivers of MLTa. In November through April, surface forcing anomalies drive, on average, 78% of MLTa (Fig. 9), with sensible and latent heat flux anomalies dominant over the vast majority of the Bering Sea (Fig. 11) and accounting for ≥80% of the net heat flux anomaly (Table 4). There is a distinct shift to the radiative flux anomalies generally dominating the net air–sea heat flux anomaly in May–July (Fig. 11), with surface forcing anomalies responsible for an average of 78% of the MLTa over the same period. Radiative heat flux anomalies continue to generally dominate the surface forcing anomaly term in August. August and September are transition months, with a shift from surface forcing anomalies dominating MLTa to ocean dynamics (Fig. 9). August and September also mark a shift in the relative dominance of the radiative and turbulent heat fluxes; beginning in September, turbulent heat flux anomalies dominate the net surface forcing (Fig. 11 and Table 4).

e. Spatially varying trends in MLD

Because of the dominant role of surface forcing anomalies in driving MLTa, and because surface forcing plays a role in the seasonal variability of the MLD, we evaluated trends in the ECCO MLD. Over the ECCO data record length (1992–2017), MLD in the southwestern Bering Sea basin shoaled by ∼0.5 m yr⁻¹ while there was a slight deepening of <0.2 m yr⁻¹ off of Cape Navarin and a deepening of ∼0.5 m yr⁻¹ off of the southwestern Siberian coast (Fig. 12a). Over the shelf, there was little change in the MLD on an annual scale. There is a similar spatial pattern in MLD trends on monthly time scales (Fig. 12b), with shoaling maximized in April, reaching a value > 1.5 m yr⁻¹ in the deep basin.

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(a) ECCO MLD trend (m yr⁻¹) over full record, 1992–2017. Regions where the change in MLD is not statistically different than zero at a 95% confidence level are noted by black x marks. The trend was computed from daily MLD data, using a univariate linear regression model, and the effective sample size N^* was computed using the long-lag artificial skill method described by Chelton (1983). (b) Time series of the monthly maximum MLD trend (m yr⁻¹) over full record, 1992–2017.

Citation: Journal of Climate 37, 1; 10.1175/JCLI-D-23-0331.1

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