Annual Cycle in Upper-Ocean Heat Content and the Global Energy Budget

Yuying Pan aInternational Center for Climate and Environment Sciences, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
bCenter for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China
cUniversity of Chinese Academy of Sciences, Beijing, China

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Lijing Cheng aInternational Center for Climate and Environment Sciences, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
bCenter for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China
cUniversity of Chinese Academy of Sciences, Beijing, China

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https://orcid.org/0000-0002-9854-0392
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Karina von Schuckmann dMercator Ocean International, Toulouse, France

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Kevin E. Trenberth eNational Center for Atmospheric Research, Boulder, Colorado
fUniversity of Auckland, Auckland, New Zealand

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Guancheng Li gEco-Environmental Monitoring and Research Center, Administration of Ecology and Environment of the Pearl River Basin and South China Sea, Ministry of Ecology and Environment, Guangzhou, China

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John Abraham hSchool of Engineering, University of St. Thomas, St. Paul, Minnesota

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Yuanxin Liu aInternational Center for Climate and Environment Sciences, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
bCenter for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China
iCollege of Meteorology and Oceanography, College of Computer Science and Technology, National University of Defense Technology, Changsha, China

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Viktor Gouretski aInternational Center for Climate and Environment Sciences, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
bCenter for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China

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Yongqiang Yu jState Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
bCenter for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China
cUniversity of Chinese Academy of Sciences, Beijing, China

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Hailong Liu jState Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
bCenter for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China
cUniversity of Chinese Academy of Sciences, Beijing, China

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Chunlei Liu kSouth China Sea Institute of Marine Meteorology, Guangdong Ocean University, Zhanjiang, China

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Abstract

As a major component of Earth’s energy budget, ocean heat content (OHC) plays a vital role in buffering climate change. The annual cycle is the most prominent change in OHC but has always been removed to study variations and changes in Earth’s energy budget. Here, we investigate the annual cycle of the upper-2000-m OHC at regional to global scales and assess the robustness of the signals using the spread of multiple observational products. The potential drivers are also investigated by comparing the annual OHC signal with the corresponding change in top-of-atmosphere radiation, surface heat flux, ocean heat divergence, and meridional heat transport. Results show that the robust signal of annual OHC change is significant down to a 1000-m depth globally and can reach down to 1500 m in some areas such as the tropical ocean. The global OHC (0–1500 m) changes from positive anomalies within September–February to negative anomalies within March–August, mainly because of the larger ocean area in the Southern Hemisphere and the seasonal migration of solar irradiance. Owing to the huge ocean heat capacity, the annual cycle of OHC dominates that of the global energy budget. The difference among the OHC annual cycles in the three major ocean basins is mainly attributed to ocean heat transport, especially in the tropics. In the upper 1500 m at mid- and high latitudes and in the upper 50 m of the tropics, the net sea surface heat flux dominates the OHC annual cycle, while in the tropics below 50 m, wind-driven Ekman heat transport associated with the geostrophic flow is the main driver.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Lijing Cheng, chenglij@mail.iap.ac.cn

Abstract

As a major component of Earth’s energy budget, ocean heat content (OHC) plays a vital role in buffering climate change. The annual cycle is the most prominent change in OHC but has always been removed to study variations and changes in Earth’s energy budget. Here, we investigate the annual cycle of the upper-2000-m OHC at regional to global scales and assess the robustness of the signals using the spread of multiple observational products. The potential drivers are also investigated by comparing the annual OHC signal with the corresponding change in top-of-atmosphere radiation, surface heat flux, ocean heat divergence, and meridional heat transport. Results show that the robust signal of annual OHC change is significant down to a 1000-m depth globally and can reach down to 1500 m in some areas such as the tropical ocean. The global OHC (0–1500 m) changes from positive anomalies within September–February to negative anomalies within March–August, mainly because of the larger ocean area in the Southern Hemisphere and the seasonal migration of solar irradiance. Owing to the huge ocean heat capacity, the annual cycle of OHC dominates that of the global energy budget. The difference among the OHC annual cycles in the three major ocean basins is mainly attributed to ocean heat transport, especially in the tropics. In the upper 1500 m at mid- and high latitudes and in the upper 50 m of the tropics, the net sea surface heat flux dominates the OHC annual cycle, while in the tropics below 50 m, wind-driven Ekman heat transport associated with the geostrophic flow is the main driver.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Lijing Cheng, chenglij@mail.iap.ac.cn

1. Introduction

The ocean has a large heat capacity and plays a central role in the climate system (Cheng et al. 2022a,b). Ocean heat content (OHC) and its variations are vital for understanding climate change and its variability, especially in terms of Earth’s energy flow and budget (Trenberth et al. 2016; von Schuckmann et al. 2016; Cheng et al. 2017; Abram et al. 2022; Johnson et al. 2021). The ocean is the dominant thermal reservoir with respect to the human-caused Earth energy imbalance (Fox-Kemper et al. 2021; von Schuckmann et al. 2020). Qualitatively, this has been known for a long time and is manifested in the distinguishing of “maritime” from “continental” climates. Consequently, knowledge of the temporal variations in OHC sets the stage for a variety of climatic phenomena, such as the climatic responses to greenhouse gases (e.g., Barnett et al. 2001, 2005; Pierce et al. 2006) and the prediction of climatic modes (Palmer et al. 2011) and climate extremes such as hurricane intensity (Shay and Brewster 2010; Trenberth et al. 2018).

An early estimate of the annual cycle in OHC, documented by Ellis et al. (1978), showed that the world’s ocean stores and releases heat in phase with the annual variation in the accumulated radiation balance relative to mean, thereby revealing the dominant role the ocean plays in Earth’s climate response. Levitus (1984) investigated the annual changes in temperature and heat storage for the global ocean and individual ocean basins using ocean observations before 1980 with limited coverage. With newly available data, Antonov et al. (2004) extended the Levitus (1984) analysis and further disclosed the annual cycle of zonally integrated OHC (0–250 m) in global and three major basins. Trenberth and Fasullo (2008) and Fasullo and Trenberth (2008a,b) used the Levitus data and top-of-the-atmosphere (TOA) radiation to provide an estimate of seasonal changes in OHC and the annual cycle in ocean meridional heat transports. von Schuckmann et al. (2009) studied the vertical structure of ocean temperature annual cycle in the upper 400 m based on Argo data. The depths that previous studies focused on were chosen mainly according to data availability, for example, upper 250 m in Antonov et al. (2004), upper 275 m in Trenberth and Fasullo (2008), and 1500 m in Wang et al. (2018).

The sparseness of ocean observations has been a major constraint on the understanding of the annual cycle, with respect to not only OHC, but also the energy budget. Before Argo implementation in 1999, the historical datasets relied on shipboard and moored instrument types, and subsurface temperature sampling was limited globally (e.g., Abraham et al. 2013). The Argo profiling float network achieved its implementation goal of 3000 floats circa 2006 (Roemmich et al. 2019) and enabled improved estimates of historical changes in OHC (i.e., the pre-Argo era) (e.g., Balmaseda et al. 2013a; Abraham et al. 2013; Cheng and Zhu 2014a,b; Cheng et al. 2017, 2022a). The availability of multiple gridded products from different research groups (e.g., von Schuckmann et al. 2020; Gulev et al. 2021; Cheng et al. 2022a) enables intercomparisons to test the robustness of findings.

There is still a lack of a quantitative and comprehensive description of the OHC annual cycle at global to regional scales and their drivers. Here, we address questions such as the following: At which depth can the annual cycle of ocean temperature be robustly detected? What are the (potential) drivers of OHC annual cycle in the subsurface of the global ocean and in individual ocean basins? What is the role of ocean mixed layer, as ocean mixed layer is critical for air–sea interactions and heat exchanges between the surface layer and the deep ocean (Kara et al. 2003; Buongiorno Nardelli et al. 2017; Chen et al. 1994)?

This study provides a comprehensive description of the annual variation in OHC from the surface to a 2000-m depth. Multiple vertical intervals are analyzed: 0–300, 300–700, 700–1500, and 0–1500 m, from 0 to the mixed layer, and from the mixed layer to 1500 m, based on observations, and we examine the factors driving them at a global scale. To this end, the uncertainty in the annual cycle of OHC must be rigorously quantified to assess the reliability. The data and methods are introduced in section 2. The results in section 3 show the annual mean and annual variation of OHC and the OHC variations for a latitude–longitude plane and zonal–depth sections, and all are compared with surface fluxes. The derived ocean heat divergence or transport is also analyzed. A summary and further discussion is given in section 4.

2. Data and methods

a. Ocean temperature and salinity products

The primary product of observed ocean observational temperature from the Institute of Atmospheric Physics (IAP; Cheng and Zhu 2016; Cheng et al. 2017) is an ocean objective analysis monthly dataset (Table 1). It has advantages in both its instrumental error reduction and its gap-filling method. The IAP mapping technique used spatial covariance from model simulations to help provide spatial interpolation. This product merges all the available in situ ocean temperature observations from a variety of instruments held in the World Ocean Database (Boyer et al. 2018). However, large spatial gaps exist prior to 1958 (the International Geophysical Year). Six other ocean temperature and salinity products are also used, mainly for verification, intercomparison, and uncertainty evaluation (Table 1). Four of these products—IAP, the EN4 ocean objective analysis product from the Met Office Hadley Centre (Good et al. 2013); the Ishii product (termed ISHII2017; Ishii et al. 2017) from the Japanese Meteorological Agency; and WOCE/Argo Global Hydrographic Climatology (WAGHC) from the University of Hamburg; Gouretski 2018)—comprise a combination of Argo data with all other available instruments mentioned above (Table 1). The main differences among them are the mapping method, which defines how to fill the data gaps and smooth the fields, and data processing (including quality control, bias correction, etc.). Besides, each product has adopted a few regional observations; for example, ISHII2017 has added some Japanese data that are not present in other datasets, and WAGHC climatology used Canadian data and data from the Alfred Wegener Institute, which also were not available for other products.

Table 1.

List of seven datasets interpolated to 1° × 1° mesh grid before analysis.

Table 1.

Two Argo-only gridded products—one from the Scripps Institution of Oceanography (SCRIPPS) (Roemmich and Gilson 2009) and another from the Barnes objective analysis (BOA) Argo product (Li et al. 2017)—are also employed, as well as an ocean reanalysis from ECMWF’s Ocean Reanalysis System 4 (ORAS4), which uses a methodology that assimilates all delayed-mode ocean in situ observations, altimeter data, and surface flux data (Balmaseda et al. 2013b) (ORAS5 is similar to ORAS4). All data were interpolated into the 41 levels used by the IAP and a horizontal resolution of 1°. The data from 2001 to 2016 are averaged together to construct a monthly climatology which is used to analyze the annual cycle; the period is chosen to be consistent with the availability of surface flux data. In addition, to test the impact of interannual variability and trend in OHC on the climatology calculation, we analyzed several different time periods (1960–2017, 1960–2000, and 2000–17) and did not find a significant difference (see Fig. S1 in the online supplemental material).

b. TOA and surface flux data

Sea surface flux and TOA net energy flux are also quantified in this study. Based on improved observations of net energy budget observations at the TOA (Loeb et al. 2021) and atmospheric reanalysis of ERA-Interim (Dee et al. 2011), a high-quality measure for net sea surface heat flux can be obtained as a residual, which provides a new opportunity to investigate the air–sea heat flux (Trenberth et al. 2001; Trenberth and Fasullo 2008; Trenberth et al. 2019; Trenberth and Zhang 2019). Two products are used: Trenberth and Fasullo (2018, hereafter TF2018) and the reconstructed product DEEP-C, version 5.0, from Reading University (Liu et al. 2020; Liu and Allan 2022). It has been shown that surface heat flux derived from the residual method is superior to that based on reanalysis and objective analysis (Liu et al. 2017; Trenberth et al. 2019).

In addition, we use two net radiation flux datasets at the TOA—one from Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) observations since March 2000 (Loeb et al. 2018), and the other from DEEP-C version 5.0. Based on surface and TOA net flux, the atmospheric energy content (AHC) can also be derived.

For both OHC and flux data, a three-month running temporal smoother (1–2–1) is applied to reduce the month-to-month data noise, and a five-point spatial smoother is used to better depict the large-scale patterns.

c. Wind stress curl and Ekman heat transports

As a source of vorticity, the curl of the wind stress acting on the sea surface is a fundamental forcing agent for dynamic ocean processes (Trenberth et al. 1990; Bakun and Nelson 1991) and is important dynamically to the seasonal variation of sea temperature as well as ocean heat (Trenberth et al. 1990; Murphree et al. 2003; Zhou et al. 2019). Therefore, the curl of the wind stress, curlz(τ), and Ekman pumping, which is implied by wind stress curl, are investigated.

The wind stress field data used are from the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2) monthly data, which are produced by the NASA Global Modeling and Assimilation Office with 0.5° × 0.625° spatial resolution (GMAO 2015). The Ekman pumping velocity is calculated as follows:
WE=1fρ×τ+1f2ρβτx,
where the Coriolis parameter f = 2Ω sinφ, Ω is the angular velocity of Earth’s rotation, and φ is the latitude (Hobbs and Willis 2012). The term β is the variation of f against latitude, ρ is the seawater density, τ is the wind stress vector, and τx is the wind stress component in the zonal direction.
Ekman currents are forced by winds at the surface and develop due to the drag at the wind–water interface. They are deflected to the right (Northern Hemisphere) and left (Southern Hemisphere) due to the Coriolis effect (Price et al. 1987; Talley et al. 2011). The heat transports occur with the flow of ocean currents. The meridional Ekman heat transport is calculated using the MERRA-2 monthly averaged wind stress data as
QE(t)=xExCpEτxfθdx,
where f is the Coriolis parameter. Since the Coriolis parameter f goes to zero at the equator, where Ekman balance of forces is no longer valid (Levitus 1987; Ferrari and Wunsch 2009), the calculation of Ekman heat transport and Ekman pumping velocity between 3.5°S and 3.5°N is not performed in our study, similar to other studies, e.g., Levitus (1987) for 4.5°S/N and Yang et al. (2015) for 4°S/N. The terms CpE and θ are the averaged specific heat capacity and potential temperature of the Ekman layer (here, 0–50-m averages are used), respectively; xE is the eastern boundary; x is the grid point west of xE; and τx is the zonal wind stress, which is typically obtained from bulk parameterizations that estimate turbulent fluxes using standard meteorological data (Fairall et al. 2003). The resultant wind stress data were interpolated onto a horizontal resolution of 1°.

d. OHC and mixed layer calculation

OHC contained in a certain depth layer is calculated by integrating the temperature within a certain layer (from z1 to z2) as follows:
OHC=z1z2ρCpTdz,
where ρ, Cp, and T are the potential density of seawater, the thermal capacity, and the conservative temperature, respectively. The values of ρ are calculated from the monthly temperature and salinity fields produced by the International Thermodynamic Equation Of Seawater–2010 (TEOS-10; IOC et al. 2010). Parameters z1 and z2 define the lower and upper limits of the layer depth.

We define the mixed layer depth (MLD) as the depth at which the difference in potential density exceeds a threshold of 0.03 kg m−3 from the potential density at a 10-m depth (de Boyer Montégut et al. 2004). This definition has been shown to accurately detect the mixed layer depth in different ocean basins. We have tested the sensitivity to the definition of the mixed layer, and the results are not sensitive to the definition, although the magnitudes of the annual cycle are slightly different (not shown). The ensemble average of mixed layer calculated by seven products is used.

e. Heat budget analysis

Ocean heat content is affected by various processes, such as air–sea heat exchange (Tamsitt et al. 2016; Cronin et al. 2019) and the melting and formation of ice (Timmermans et al. 2018; Haumann et al. 2020), as well as by ocean dynamic processes, including Ekman and geostrophic heat transport and the horizontal and vertical eddy advection of heat (Armour et al. 2016; Tamsitt et al. 2016). To estimate the effects of the freezing and melting of sea ice, we assume a latent heat of fusion of 3.34 × 105 J kg−1 and an ice density of 900 kg m−3 to derive the heat change related to the melt and formation of sea ice. For the Arctic, we use Pan-Arctic Ice Ocean Modeling and Assimilation System (PIOMAS) estimates of volume changes (Schweiger et al. 2011). The magnitude of annual cycle heat related to Arctic sea ice is about 5.2% of the global OHC annual variation of the upper 1500 m (see Fig. S2). The Antarctic sea ice also shows a notable annual cycle (Handcock and Raphael 2020), but there is no directly available ice volume data for the Antarctic. Based on a reanalysis data of Global Ice-Ocean Modeling and Assimilation System (GIOMAS), the amplitude of the annual cycle of heat related to Antarctic sea ice is about 4.9% of the global OHC annual variation of the upper 1500 m (Fig. S1). Arctic and Antarctic sea ice annual variations are out of phase (anticorrelated) and largely cancel out globally. Based on GIOMASS data (Zhang and Rothrock 2003), the sum of the heat related to the sea ice of the Arctic and Antarctic is equal to ∼3.7% of the global OHC annual cycle. Therefore, the impact of sea ice on changes in global OHC can be ignored in this study. At regional scales, however, heat exchanges between ocean and ice might be very important and nonnegligible. Trenberth et al. (2019) and Mayer et al. (2019) indicated that the Arctic sea ice change becomes nonnegligible in the North Atlantic.

Globally, the atmospheric energy budgets are closed by the net upward turbulent fluxes of latent and sensible heat, penetrating shortwave and outgoing longwave radiation at the surface, and the TOA radiative fluxes, which consist principally of shortwave and longwave radiation (Trenberth and Fasullo 2008). Regional changes in OHC are mainly dominated by the net heat surface flux and divergence of vertically integrated ocean heat transport:
dOHC/dt=Fs+FO+Re,
where dOHC/dt is the OHC tendency, calculated by taking centered differences in monthly OHC; FS is the ocean net surface heat flux; ∇ ⋅ FO is the divergence of the transport of thermal energy, including horizontal/vertical transport by advection and diffusive fluxes; and Re denotes some neglected terms including kinetic energy of ocean currents, exchanges with sea ice and coastal influences, and the geothermal heat flux, which are small (Munk and Wunsch 1998; Ferrari and Wunsch 2009). Re also includes seasonal variation of OHC below 1500 m and the vertical heat transport at the 1500-m interface, which is assumed to be negligible, as the magnitude of the 1500–2000-m OHC annual cycle is only 0.69 ZJ, implying a small contribution of deep ocean changes. Ignoring the Re term and integrating Eq. (4), an expression for regional OHC is obtained:
OHC=t0t1FSdt+t0t1FOdt,
where t0 is the start time of the analysis (January 2001) and t1 is December 2016. When estimating the annual cycle of the integrated quantity, the impact of an integration constant should be properly dealt with. Here, we calculate the monthly climatology from the integrated time series and then remove the annual mean.
For the global ocean, as the divergence term is zero, the equation becomes
dOHC/dt=FS.
Integrating Eq. (6) gives
OHCglobal(t)=t0t1FSdt,
where t is month of the year (from January to December). In this study, we assume that the signature of seasonal OHC change below 1500 m and the vertical heat transport at the 1500-m interface is negligible (see Fig. S3), and so we apply Eqs. (6) and (7) to the upper 1500 m of oceans.

f. Robustness of the OHC annual variation

We use a signal-to-noise ratio method (Liu et al. 2021). The difference between the maximum (Smax) and minimum (Smin) sea temperatures within 12 months from January to December (i.e., the range) is calculated as SVm = SmaxSmin, representing the magnitude of the annual variation (SVm). To date, there has been no quantification of the uncertainty in the annual variations in temperature in currently available products, nor a test of robustness, and the sources of annual cycle errors are unclear and could arise from data sampling and mapping, etc. (Lyman and Johnson 2014). This study uses the spread of the annual variation in temperature among products as an approximation for data uncertainty, which leads to an overestimation of the actual uncertainty because some datasets contain substantial errors.

The uncertainty range is quantified by twice the standard deviation (SD) (±2 SD error range) of the temperature variation among seven products (SDm = 4·SD, i.e., 4 times the standard deviation), assuming that the seven products could sample a Gaussian error distribution, corresponding to a confidence level of ∼95%. Here, the standard deviation is calculated by
SD=i=17(xix¯)2/7,
where xi is the OHC for each dataset and x¯ is the average of seven datasets. Better quantification of uncertainty requires understanding and modeling of the error sources, which are not yet available (von Schuckmann et al. 2020; Wunsch 2020). Adopting a straightforward method with a “data democracy” (each individual dataset has been treated equally and averaged together with the same weight) strategy has been chosen as a starting point (e.g., von Schuckmann et al. 2020). A careful evaluation of the annual cycle products will be performed in a separate analysis.

Through quantification of the magnitude of the temperature range (SVm) and the uncertainty level (SDm), we define a signal-to-noise ratio (SNR) to quantify how robust the signal is: SNR = SVm/SDm. If SNR > 1, the annual variation is larger than the noise level from the ensemble approach and can be robustly detected. As presented in the appendix, most of the global ocean surface shows larger seasonal change than the data error (SNR > 1), with a few exceptions in some parts of the polar regions. The area with SNR > 1 decreases at depth. Below 300 m, the areas with SNR > 1 are mostly located in the tropical regions within 30°S–30°N and in the North Atlantic Ocean owing to the large signal (SVm; Fig. A1) and small data uncertainty (SDm, Fig. A2). The global-mean SNR is reduced from 8 to 10 in the upper 30 m to ∼0.9 below 1800 m (Fig. A4a), and the global-mean SNR drops to <1 at 1000–1500 m, above which depth the robust annual variations can be detected. Therefore, in this paper, we focus on the annual changes from the surface down to 1500 m.

3. Results

a. Climatological OHC

Because OHC is a quantity defining thermal energy change, only its anomalies are physically meaningful. The annual-mean state of OHC in depth ranges of 0–1500 m (Fig. 1a) shows the spatial differences of OHC relative to its global mean. The OHC 0–1500-m pattern reveals the vertical structure of the zonal-mean subsurface temperature field (Fig. 1b). The temperature here is the in situ temperature. The maximum value of OHC 0–1500 m appears at 20°–40° of the ocean. Although there is greater solar radiative heating in low compared with higher latitudes, the higher OHC within 20°–40°N is associated with the heat convergence driven by subtropical gyres (an anticyclonic circulation) including the strong western boundary currents which effectively transport heat from the tropics to the midlatitudes (e.g., Kuroshio, Gulf Stream, East Australia Current). This convergence/transport results in a deeper mixed layer and thermocline and larger amounts of warm water storage (Fig. 1b, Atkinson 2010; Hu et al. 2015). Evaporative cooling is strong at mid- and high latitudes, especially where dry air is advected over the ocean from continents, and these areas are characterized by strong ocean heat release to the atmosphere (Trenberth and Stepaniak 2004). This is especially true in the western boundary currents and the northern North Atlantic Ocean (Trenberth 2022). The polar regions are characterized by lower temperatures and thus lower OHC anomalies (Fig. 1).

Fig. 1.
Fig. 1.

(a) Spatial patterns of climatological-mean OHC above 1500-m depth. As OHC anomalies relative to a global mean are shown, there are some regions with negative OHC. (b) Zonal-mean climatological sea temperature (color; °C) and MLD (magenta line; m), averaged over the period 2001–16. The minimum temperature is about −1.8°C (the freezing point).

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

b. Annual variation in zonal-mean structure of subsurface temperature

This section compares the zonally averaged ocean temperature anomalies (relative to the annual mean) in the upper-1500-m depth range with the accumulated ocean surface fluxes Fs [Fs, Eq. (5)] (Figs. 2a–f). In the upper mixed layer (∼60 m for global mean), the annual variations in temperature are consistent with the annual variations in Fs (Fig. 2). The largest temperature anomalies (>4°C or <−4°C) occur at the midlatitudes and in the upper 200 m, together with strong annual variations in Fs (up to 3.2 or −3 ZJ) in March and September. The temperature shifts from positive to negative phase in December in the Northern Hemisphere (NH), and then to positive phase in June, as does the Fs.

Fig. 2.
Fig. 2.

Global annual variations in zonal-mean ocean temperature changes (°C) from 1 to 1500 m compared with the Fs (positive value means downward net heat flux) in (top) January, March, and May and (bottom) July, September, and November. The color figures are the zonal temperature anomalies at depths of 0–500 and 500–1500 m. The magenta lines represent the mixed layer depth. Note that the vertical scales are not linear. The means of seven datasets are shown.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

The upper-ocean temperature annual cycle is linked to mixed layer changes, especially in the extratropics (20°–60°; Figs. 2 and 3). Note that in the ocean, winter surface cooling creates convection and readily mixes cold dense values to deeper layers, while summer heating increases stratification and warm waters tend to remain near the surface. In the NH, relative to the annual mean, the summer mixed layer is shallower by ∼40 m and deeper in winter by ∼140 m. Changes in the Southern Hemisphere (SH) are of opposite sign.

Fig. 3.
Fig. 3.

Seasonal-mean Hovmöller diagram of zonal-mean anomalies of the MLD with respect to its annual mean (m). The means of seven datasets are shown.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

In the subsurface (below the mixed layer), there are two distinct annual variations of ocean temperature: one is approximately in the upper 300 m at mid- and high latitudes in both hemispheres, and the other is approximately in the upper 200 m in the tropical oceans (Fig. 2). These two variations are not in phase. Within 5°S–20°N, the largest range of the annual variation occurs below the depth of ∼50 m, where the changes in ocean temperature and Fs are inconsistent, or even opposite. For example, the Fs value is positive in the NH in September, but the maximum negative temperature anomalies appear near 150 m in the subsurface layer. This indicates that the subsurface ocean dynamical processes play a more important role, as explored later.

The results (Figs. 2 and 9) also show that the magnitude of the temperature annual variation decreases with increasing depth. The SNR analysis (appendix) suggests a robust annual variation for the upper 1000–1500 m globally. Here, 1000–1500 m is conservative and warrants an update after a thorough analysis of datasets and observation techniques.

c. Spatial pattern of annual variations in OHC

The spatial patterns of bimonthly OHC 0–1500 m and Fs (Fig. 4) indicate the widespread annual variation over most global areas (appendix). The strongest OHC (0–1500 m) anomalies (bigger than 1.5 × 109 J m−2) occur in the tropical regions 5°S–20°N and in the northwest Pacific and northwest Atlantic near 40°N. The northern tropics (∼10°N at the location of the intertropical convergence zone) have the strongest annual fluctuation for zonal average OHC, magnitude ±0.9 × 109 J m−2. The maximum values in the tropics and at midlatitudes emerge at different times of the year.

Fig. 4.
Fig. 4.

Seasonal distribution of OHC seasonal anomalies in the upper 1500 m in (left) January, May, and September and (right) March, July, and November, compared with the Fs (contours) relative to the annual mean. Every second month is shown because the data have a 3-month running average. Blue contours indicate negative anomalies, while red contours show positive anomalies of Fs. The stippled areas indicate OHC anomalies not statistically significant at the 90% confidence level for seven observation products. The right panels show the zonal-mean OHC and Fs.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

The annual variation of OHC in the upper ocean is broadly consistent with the Fs for 20°–60°N. In the NH, the Fs (negative) indicates heat released into the atmosphere by the ocean, with negative OHC anomalies in January–May. Positive values of Fs indicate energy entering the ocean from the atmosphere, corresponding to positive OHC anomalies from July to November. As Fs corresponds to dOHC/dt, OHC corresponds to the Fs [Eqs. (4)(7)]. It is dominated by solar radiation and reaches a maximum around September (autumnal equinox) in the NH when Fs changes sign and Fs peaks (see next sections for more details). However, in the tropics, the changes in OHC and Fs are not in phase. For example, there is a strong negative OHC anomaly (around −1.7 × 109 J m−2) in the eastern equatorial Pacific from 180° to 30°W in November, but the corresponding Fs anomaly is positive (up to 0.3 × 109 J m−2). The inconsistency indicates the key role of ocean dynamics associated with thermocline changes, discussed later.

d. Annual variations in different vertical layers

To depict the zonal structure of OHC at different depths, we divide the upper 1500 m of the ocean into three layers: 0–300 m (Fig. 5d), 300–700 m (Fig. 5e), and 700–1500 m (Fig. 5f). For OHC 0–1500 m, the largest annual variation occurs for midlatitudes in both hemispheres (located at 20°–60°N and 20°–60°S), with a distinct maximum and minimum near 40° latitude. Peak values occur around September–October and March–April, coinciding roughly with the equinoxes. Near the equator, from approximately 5° to 20°N, another maximum occurs during May, exceeding 2 ZJ, and with a minimum (<−2 ZJ) in November.

Fig. 5.
Fig. 5.

Zonally integrated anomalies of OHC at (a) 0–1500, (d) 0–300, (e) 300–700, and (f) 700–1500 m, along with the (b) Fs and (c) FO for the global ocean except for the polar regions. Red areas signify ocean heat gain, and blue areas signify ocean heat loss. Regions not statistically significant at the 90% confidence level are stippled.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

The pattern of OHC at 0–300 m (Fig. 5d) is very similar to that at 0–1500 m (Fig. 5a), with a smaller magnitude of change in the north tropics. That is associated with the similar annual variation of OHC 300–700 and OHC 700–1500 m compared with OHC 0–300 m at 0°–20°N. This suggests that deep ocean changes cannot be neglected, as below 300 m, OHC change accounts for about 30% of the magnitude of the annual changes in OHC 0–1500 m at 0°–20°N. Indeed, the pattern of OHC at 700–1500 m (Fig. 5f) is generally the same as that at 300–700 m (Fig. 5e), albeit with a smaller magnitude of change, confirming the existence of a deep ocean annual cycle below 700 m, consistent with our SNR analysis in section 3b. In the midlatitudes, the magnitude of OHC 300–700, OHC 700–1500-m variation is roughly 1 order smaller than OHC 0–300; thus, OHC 0–300 m dominates the upper-1500-m changes (Figs. 5a,d vs Figs. 5e,f). But there is a phase difference compared with OHC 300–700, OHC 700–1500 m, with OHC 0–300 m at 30°–65°N and 65°–30°S. The monthly evolution of the vertical structure of midlatitude changes will be explored later (section 3f).

To explicitly discuss the relative importance of air–sea heat flux and ocean processes in determining the zonal OHC annual cycle, the difference between OHC and Fs—accumulated ocean heat divergence (AOHD)—is shown (Fig. 5c). AOHD is positive from February to July and negative from August to January within 10°–20°N, which is nearly opposite as compared to the evolution of Fs (Fig. 5b vs Fig. 5c). Along the equator, AOHD alters to positive sign during January–June, and becomes negative from July to December, largely compensating Fs. The result confirms that AOHD plays a more crucial role in the OHC (0–300 and 0–1500 m) annual cycle in the tropics (5°S–20°N). Outside of the tropics (20°–60°N and 20°–60°S), patterns of OHC (0–300 and 0–1500 m) are generally consistent with those of Fs (Fig. 5b).

e. Annual variation of temperature in the tropics

Figure 6 shows the temperature anomalies at different layers in the tropics (20°S–20°N) where the MLD and thermocline are superimposed, and pertain mainly to the Pacific and Atlantic (see section 3g). It is apparent that there are two mechanisms: one manifested in the upper ∼80 m, the temperature annual cycle is consistent with Fs and the major signals of anomalies are within the ML; the other is manifested below ∼80 m, the annual cycle of temperature change is distinct from the upper layer, and the peak anomalies occur along the thermocline (defined as 20°C isotherm) and have a 2–4-month phase lag compared to the upper-80-m change, indicating that thermocline dynamics play a central role. The thermocline depth is shallower in September–January in the north tropics (Fig. 6a).

Fig. 6.
Fig. 6.

Annual cycle of vertical section of ocean temperature for (a)–(c) 5°–20°N, (d)–(f) 20°–5°S, and (g)–(i) 5°S–5°N and time series at 1, 20, 30, 50, 70, 100, and 140 m in (a), (e), and (h) and at 140, 160, 200, 250, 300, 800, and 1000 m in (c), (f), and (i). In the left panels, the magenta lines represent the mixed layer depth, and black lines represent the thermocline depth (defined as 20°C isotherm). In the right panels, the colored solid lines represent the temperature at different depths, and black dashed lines represent Fs. The means of the seven temperature datasets and two surface heat flux datasets are shown.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

The adjustment of the annual thermocline is influenced by both local responses to wind forcing (Liu et al. 2001; Schott and McCreary 2001) via Ekman pumping (Kessler 1990; Wang et al. 2000) and by the propagation of Rossby and Kelvin waves, which are generated by remote wind forcing (Meyers 1979a,b; Kessler 1990; Kessler and McCreary 1993; Hui et al. 2020). For example, in the northern tropics, westerly winds intensify from about April (Fig. 7a), while northward meridional heat transport (MHT) decreases (Fig. 7b), and anticyclonic wind stress curl gradually moves further north (Fig. 7c) following the intertropical convergence zone (ITCZ). In late boreal summer (e.g., September), the southeast trades become strongest, and an intensified positive wind stress curl is now located north of 10°N, that is, when the ITCZ is located at its northernmost position. The reduced northward Ekman MHT, together with enhanced Ekman upwelling, leads to an OHC decrease in the 0°–20°N latitude band during this period (Figs. 5a and 7a). During boreal autumn, the positive wind stress curl gradually moves south over time (Fig. 7c). During December to January, the ITCZ in tropical Pacific and Atlantic oceans shifts toward the equator, while the South Pacific convergence zone (SPCZ) and South Atlantic convergence zone (SACZ) intensify. This in turn leads to enhanced Ekman pumping at about 0°–10°N and 10°–30°S due to positive wind stress curl anomalies, which contribute to OHC decrease at corresponding latitudes (Fig. 5a). However, seasonal wind curl change and concurrent OHC change are not in phase, which is associated with westward-propagating Rossby waves as discussed in Hui et al. 2020 (their Fig. 9). Global-mean tropical seasonal change is dominated by processes in the Pacific and Atlantic basins, and Indian Ocean seasonal variations are strongly linked to the Asian monsoon (e.g., Saha 1970; Ummenhofer et al. 2021; see section 3g).

Fig. 7.
Fig. 7.

(a) Zonally averaged anomalies of zonal wind stress (N m−2). Red colors denote the enhanced westerly wind. (b) Zonally averaged anomalies of Ekman MHT (PW). Red colors denote the enhanced northward heat transport. (c) Zonally averaged anomalies of the wind stress curl (N m−3). Red denotes cyclonic curls, and blue denotes anticyclonic curls in the NH. (d) Zonally averaged anomalies of Ekman pumping velocity (m s−1). Red denotes enhanced Ekman upwelling. The results are all calculated from MERRA-2 wind stress monthly data.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

f. Annual variation of temperatures in the mid- and high latitudes

Outside of the tropics, the upper-layer changes extend into the subsurface, and show a more depth-coherent feature of the annual cycle (Fig. 2). There is a slow penetration of heat from the near-surface to subsurface layers, and the changes in temperature at 500 m lag SST by almost 6–7 months (Figs. 8e,f). For example, the transition from negative to positive phase at the sea surface occurs from May to June, but the transition at 500 m occurs from December to January in the NH. This lag of ocean temperature changes with increasing depth indicates the important roles of diabatic heating and mixing downward from the sea surface, associated with seasonal change of mixed layer depth in the mid- and high latitudes, which is ∼210 m deeper than the annual mean in winter and ∼60 m shallower in summer for 40°–65°N of the NH (the annual-mean mixed layer is ∼70 m) (Fig. 3). The time lag of 6–7 months may likely be related to the baroclinic adjustment of the ocean through Rossby waves (i.e., Wang et al. 2000).

Fig. 8.
Fig. 8.

Annual variation of vertical section of ocean temperature (a) for the global ocean, (b) in the SH, (c) in the NH, and for (d) 20°S–20°N, (e) 60°–20°S, and (f) 20°–60°N. The magenta lines represent the mixed layer depth. The means of the seven datasets are shown.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

The phase shift of the global ocean temperature seasonal variation is synchronized with that of the SH (also with that of 60°–20°S, Figs. 8a,b,e) (von Schuckmann et al. 2009), because the amplitude of the annual cycle of temperature anomalies in the SH is larger than that in the NH (Fig. 8b vs Fig. 8c; Fig. 8e vs Fig. 8f), due to the larger ocean area in the SH. There are seemingly upward propagating signals in the tropics in Fig. 8d, which is not explained in this study and deserves further analysis.

g. Annual variation of OHC in major ocean basins

The zonal OHC annual cycle for the Pacific (Figs. 9a–c), Atlantic (Figs. 9d–f), and Indian (Figs. 9g–i) Oceans reveals that the Pacific and Atlantic Oceans have similar annual cycles, with a larger magnitude of OHC annual variation in the NH than in the SH as linked to land distribution asymmetry (Figs. 9a–c vs Figs. 9d–f). Maximum annual variations (1.5–2 ZJ within 10°–15°N) in the tropical Pacific are considerably higher than midlatitudes (maximum of 0.5–0.8 ZJ within 30°–40°N). In the tropical Atlantic, the maximum OHC annual cycle (0.2 ZJ) is smaller than at midlatitudes (maximum of 0.6 ZJ at ∼40°N). This notable difference between the two basins is mainly associated with AOHD, which is stronger in the tropical Pacific Ocean (1.5–2 ZJ) than in the Atlantic Ocean (0.6–0.8 ZJ) (Fig. 9c vs Fig. 9f).

Fig. 9.
Fig. 9.

(a),(d),(g) Zonally integrated anomalies of OHC at 0–1500 m, (b),(e),(h) time-integrated Fs, and (c),(f),(i) time-integrated ∇ ⋅ FO for (top) the Pacific Ocean, (middle) the Atlantic Ocean, and (bottom) the Indian Ocean. Stippling represents areas that are not statistically significant at the 90% confidence level estimated based on seven observation products. The red areas signify ocean heat gain, and the blue areas signify ocean heat loss. The means of the seven temperature datasets and two surface heat flux datasets are shown.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

The equatorial and north Indian Ocean (5°S–25°N) shows quite a different OHC annual cycle compared to the other two basins, with positive (negative) OHC from February to July (August–January) (Fig. 9g vs Figs. 9a,d) at maximum values of ∼0.2 ZJ, i.e., 2–3 times smaller than the maximum in the Pacific and Atlantic basins. This highlights the importance of monsoon and associated wind changes in setting the energy budget of the tropical Indian Ocean. The equatorial and North Indian OHC are mainly driven by AOHD (Figs. 9h,i), while the surface flux in the North Indian is the opposite of the OHC change in the other two basins. In the north Indian Ocean, northeasterly winds prevail during DJF and drive a counterclockwise upper-ocean circulation, corresponding to the positive wind stress curl as well. The positive wind stress curl anomalies induce shoaling of tropical thermocline, allowing cold subsurface water to be upwelled, which finally reduces the OHC (Fig. 9g). The reverse applies during the Asian monsoon in JJA. In the south Indian Ocean (60° ∼ 20°S), the phase and magnitude of the Indian OHC annual variation are similar to those in the Atlantic and Pacific Oceans, despite the much smaller volume. Both surface fluxes and ocean transports in the south Indian Ocean are stronger than in the South Atlantic and South Pacific Oceans and indicate a key role in the global energy budget annually.

h. Annual variation in the global energy budget

The atmosphere, land, cryosphere, and ocean are four major heat reservoirs of the climate system, and the ocean stores the vast majority of Earth’s energy imbalance (EEI) (∼90%) on multidecadal time scales (Trenberth et al. 2016). On a seasonal scale, the contribution of ocean heat content change to the global energy budget is less clear.

Figure 10 shows a robust annual cycle of TOA net downward radiation (RT, black line), with an annual cycle standard deviation of ∼8.2 PW owing mostly to the perihelion (closest point of Earth to the Sun) in early January. The global RT decreases more quickly (from February to June) as compared to its seasonal increase (from June to February). Its maximum amounts to 3.7 PW in February and decreases to a minimum of −4.5 PW in June, mainly representing the seasonal changes of solar radiation and cloud (Trenberth and Fasullo 2008).

Fig. 10.
Fig. 10.

Global annual variation in TOA net flux (black), ocean net surface flux (red), land net surface flux (green), ocean content heat trend (blue), and atmospheric heat content trend (magenta) during the period 2001–16. The error range (shading around the lines) is ±1.64σ.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

The annual changes in OHC tendencies (blue line) are generally consistent with RT, indicating that the annual variation in the global energy storage is dominated by the ocean. In May–July, both RT and OHC tendency (OHCT) reach a minimum, but the minimum OHCT is ∼2.4 PW smaller than that of the former; and they both peak in December–February, with the maximum value of OHCT being ∼0.8 PW larger than RT. The amplitude of OHCT annual cycle is ∼1.4 times the TOA amplitude.

Globally, the difference between the RT and OHCT arises primarily from contributions from the atmospheric energy content trends (AHCT; magenta line) and the land surface flux (green line). The global AHCT is out of phase with the OHCT (and the net TOA flux) as a result of the global land–sea distribution. The maximum and minimum AHCT occur during June and December, respectively. Second, the annual variation of the land surface flux is opposite to that of OHCT because of the different land–sea distribution in the two hemispheres. Comparing the land surface flux with OHCT (or the sea surface flux), the amplitude of the annual variation in OHCT is nearly 3 times that of the land surface heat flux, especially due to the high heat capacity of the ocean. For comparison, the amplitude of land and atmosphere heat annual change is ∼0.5 and ∼0.3 times the TOA amplitude, respectively. Note that the annual changes in OHCT (blue line) and ocean net surface heat flux Fs (red line) are consistent globally within the margin of error [consistent with Eq. (6)], which indicates our results are robust. The annual cycle standard deviation is 4.2 PW for OHCT and 4.5 PW for FS. As shown in Fig. 10, FS falls into the 90% confidence interval of the OHCT estimate, and the difference between the two variables is not significant. The slight difference between OHCT and FS comes from data uncertainties and missing terms (Re) in Eq. (4).

We also analyze the global and hemispheric OHC on the seasonal scale (Fig. 11). For comparison with OHC, Fs and TOA radiation are integrated across time and surface area of the oceans. For the global OHC, a positive (negative) peak occurs around March (September) at the end of the southern summer.

Fig. 11.
Fig. 11.

Annual variation in OHC, time-integrated TOA net flux over the ocean, and oceanic time-integrated Fs for (a) the global ocean, (b) oceans in the SH, and (c) oceans in the NH, in which shading represents the error (±1.64σ) of the seven datasets.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

The two hemispheres show opposite annual variation in OHC, which is associated with the annual change of solar radiation and different distribution of land and sea (Figs. 11b,c). The annual cycle standard deviation is 40 and 28 ZJ for OHC in the SH and NH, respectively. OHC in the SH peaks in March at 65.6 ZJ, while in the NH it peaks in September at only 37.4 ZJ. Uncertainty in the annual cycle of OHC, estimated by one standard deviation (1σ) of seven datasets, exceeds 2 ZJ in the SH and NH during much of the year and exceeds 3.5 ZJ in the global ocean throughout the year. Because there is a larger ocean area in the SH than in the NH, the SH has a larger magnitude of variation in OHC. Consequently, global-mean annual variations in OHC, time-integrated Fs, and time-integrated TOA net flux over the ocean are consistent with those in the SH. This emphasizes the importance of the ocean to the global energy budget.

Putting this together, Figs. 12a–c (for dOHC/dt, FS, and derived ∇ ⋅ FO) support the view that it is the sea surface heat flux (maximum of ∼0.4 PW) that drives the changes in OHC of the midlatitude ocean, while it is the wind-driven heat transport that drives the changes in OHC of the tropical oceans (maximum of ∼0.4 PW). Note, the equatorial Atlantic Ocean and equatorial Pacific are directly affected by the trade winds associated with the ITCZ, SPCZ, and SACZ, while the equatorial western Pacific and Indian Oceans are regions that are directly affected by the monsoon and the trade winds. Both wind systems have prominent annual variations. The amplitude of change in OHCT is slightly larger than that of FS in the extratropics of both hemispheres (maximum of ∼0.1 PW), suggesting that the ocean heat transport also plays a secondary but nonnegligible role. The calculated April–September and October–March means of MHT based on the approach in Trenberth et al. (2016) suggest a substantial annual variation of MHT (Fig. 12d). Within April–September, the heat in the ocean is transported from north to south with a maximum of 6.2 PW at ∼8°N, and from October to March, the direction of ocean heat transport is opposite (with a maximum of −5 PW at ∼8°S) since solar radiation gradients are the driving force for heat transport in both atmosphere and ocean. This suggests ocean transports heat from the summer hemisphere to the winter hemisphere. The peaks of seasonal-mean MHT occur between tropical 20°S and 20°N, which is consistent with Fig. 12c. As the annual-mean maximum MHT is 1.5–2 PW, our result indicates a substantial annual modulation of the MHT. Breakdown of the major basins suggests that the Pacific Ocean dominates the global annual cycle, similar to the findings in Trenberth and Zhang (2019). However, the net MHT is not zero at the south end of the ocean (∼78°S, <0.5 PW), indicating a nonclosure of the ocean energy budget. This error should be addressed in a careful analysis (as it was in Trenberth et al. 2019 and Trenberth and Zhang 2019).

Fig. 12.
Fig. 12.

Zonally integrated anomalies of (a) OHCT at 0–1500 m, (b) Fs, and (c) ∇ ⋅ FO for the global ocean except for the polar regions. Regions not statistically significant at the 90% confidence level are stippled. Red areas signify ocean heat gain, and blue areas signify ocean heat loss. (d) The meridional heat transports for annual mean, for summer and winter of global ocean (solid lines), Indo-Pacific (dotted lines), and Arctic–Atlantic Ocean (star lines) calculated following the method provided in Trenberth and Zhang (2019). The error bars are ±1.64σ (90% confidence level) calculated by a combination of the two surface flux products and five OHC products (Argo-only data are not used), which serves as a conservative estimate.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

4. Discussion

a. OHC annual cycle compared with previous studies

Various previous studies examined the annual change in global OHC in the context of Earth’s energy flow (Jayne and Marotzke 2001; Trenberth and Caron 2001; Fasullo and Trenberth 2008a,b; Trenberth and Fasullo 2008). However, early studies were severely limited by the data available. Using new ocean datasets, this study provides a more accurate and holistic view of OHC annual cycle, although several results in previous studies (Fasullo and Trenberth 2008a,b; Trenberth and Fasullo 2008) provided quite good estimates.

Compared with previous results (i.e., Fig. 4 in Levitus 1984), the vertical structures of the temperature annual cycle are generally consistent. A significant difference is that the anomalies (contour lines in Fig. 2) are less patchy and more reliable. This is because the improved gap-filling technique uses more physical covariance estimates, e.g., the spatial variability should be highly anisotropic (section 2; Cheng et al. 2017). Antonov et al. (2004) mainly focused on upper 250 m where earlier XBT and mechanical bathythermograph (MBT) data, which suffered from systematic biases, were mainly distributed (Cheng et al. 2016). Even in the simulations, only the upper-250-m OHC was explored by Gleckler et al. (2006), for the objective of the comparison with the World Ocean Atlas (WOA04) observation-based estimates. Thus, the updated estimates in this study provide a more complete and accurate view. The vertical structure of the temperature annual cycle in this study is generally consistent with von Schuckmann et al. (2009) with Argo data within the period 2003–08, although for a different period, indicating the interannual variations do not significantly impact the investigation of seasonal OHC.

The annual cycle of zonal OHC 0–1500 m (Fig. 5a) is also consistent with the results obtained by Trenberth and Fasullo (2008, hereafter TF08) for full-depth OHC using an ocean reanalysis product, but some regional differences exist, especially in the SH and high-latitude regions, likely revealing the improvement of data coverage in recent years. Our new estimate of OHC 0–300 m (Fig. 5d) is again similar to that of Antonov et al. (2004), but the semiannual variation of upper OHC at the equator is more apparent in our analysis, and is also well represented in altimeter records and regional in situ observations (Qu et al. 2008).The improved data result in a slightly smaller magnitude of global OHC annual variation in this study (Fig. 10) than in Trenberth and Fasullo (2008).

The derived ∇ ⋅ FO (Fig. 12c) is broadly consistent with TF08 in the NH. However, there are major differences within 78°–30°S, where the new estimate indicates negative anomalies from November to February and positive anomalies from March to October, which indicates the opposite annual cycle of the two hemispheres directly influenced by the seasonal migration of solar irradiance. Observations show that the robust signal of annual OHC change is significant down to a 1000-m depth globally and can reach down to about a 1500-m depth in some areas such as the tropical ocean. The global OHC (0–1500 m) changes from positive anomalies within September–February to negative anomalies within March–August mainly because of the larger ocean area in the Southern Hemisphere and the seasonal migration of solar irradiance.

b. Drivers contributing to the OHC annual cycle

In the upper 1500 m at mid- and high latitudes and in the upper 50 m of the tropical ocean, the net sea surface heat flux dominates the OHC annual cycle. In the tropical ocean (20°S–20°N) below 50 m, we show that wind-driven Ekman heat transport, Ekman pumping, and Rossby wave dynamics are likely the main drivers (Kessler 1990; Kessler and McCreary 1993; Yu and McPhaden 1999; Hui et al. 2020). Similar results have been obtained by Jayne and Marotzke (2001), who reviewed the dynamics of ocean heat transport (OHT) mainly using ocean model data, while also emphasizing the role of winds for triggering the OHT annual cycle in the tropics. Trenberth (2022) further attributes seasonal variation in ocean temperatures in the upper 150 m between 5°S and 20°N to substantial changes in ocean currents, which occur much more rapidly in low compared with high latitudes owing to the smaller Coriolis parameter and how the ocean adjusts to perturbations. Intraseasonal variability has been, for example, observed in the tropical ocean current system, such as northward in the Mindanao Undercurrent, the southward Luzon Undercurrent (Chen et al. 2013; Hu et al. 2013), the North Equatorial Current, and the North Equatorial Undercurrent (Zhang et al. 2017), or in the equatorial band (e.g., von Schuckmann et al. 2008).

Outside of the tropics, the surface heat flux plays a more important role than ocean heat transport. Considering the longer time scale of diabatic heating below the mixed layer, the ocean dynamics could still be important in the subsurface. Jayne and Marotzke (2001) argue for weaker heat transport variability associated with the depth-independent gyre and depth-dependent circulations as compared to Ekman variability. However, eddy-driven advection of heat appears to be important in some regions (Sallée et al. 2008 and Tamsitt et al. 2016), for example, in the Antarctic Circumpolar Current (ACC) and western boundary current regions characterized by high eddy kinetic energy, such as the Kuroshio Extension (Vivier et al. 2010; Yang et al. 2021a,b). Besides, baroclinic adjustment of the ocean through Rossby waves also plays a role and determines the time lag of the subsurface changes relative to the upper ocean (Wang et al. 2000).

The OHC in the mixed layer is critical for vertical heat exchanges. For example, mode water is formed when winter cooling leads to convection and the formation of a deep mixed layer (McCartney 1977). The mode water then enters the deeper ocean by advection and diffusion, where it contributes to the ventilation of the thermocline. Here, we briefly investigate the OHC change above and below the mixed layer (Fig. 13). At NH midlatitudes, the OHC 0–MLD anomalies are positive in winter/spring (from November to March). While this seems unintuitive, as solar heating is weaker in NH winter/spring, it is associated with a deeper mixed layer (Fig. 3) because OHC is not only a function of temperature but also ocean volume. The volume change is also critical to heat through the heat capacity and thermal inertia of the ocean. The result suggests a larger amount of heat available in NH winter/spring, which keeps the atmosphere warmer than without an ocean. OHC MLD-1500 m shows an opposite annual cycle compared with OHC0-MLD in the midlatitudes (Fig. 13 vs Fig. 5) but is consistent with OHC 0–1500 m (Fig. 13 vs Fig. 5).

Fig. 13.
Fig. 13.

Zonally integrated anomalies of OHC (a) above the MLD, (b) below the MLD down to 1500-m depth. Red areas signify ocean heat gain, and blue areas signify ocean heat loss.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

The consistency between OHC 0–1500 m, Fs, and OHC MLD–1500 m indicates seasonal anomalies of heat driven by surface heat fluxes can cross the base of the mixed layer and penetrate deeper layers. The opposite OHC changes for 0–MLD and MLD–1500 m largely cancel during the full volume integration, and the OHC 0–1500 m shows different changes from both 0–MLD and MLD–1500 m OHC (for both phase and magnitude). The SH shows similar but opposite changes. In the tropics, both OHC 0–MLD and OHC MLD–1500 m show little similarity with OHC 0–1500 m (Fig. 13 vs Fig. 5), suggesting that mixed layer dynamics are not the sole controlling factor. Our results indicate that the thermocline variation is the main driver in the tropics.

5. Concluding remarks

This study provides a holistic description of the annual variations in OHC from global to regional scales. We found that there are robust annual variations in ocean temperature from the surface down to 1500 m in many regions of the global ocean. The better datasets have improved the quantification of the vertical structures in the seasonal cycle of OHC. The ocean dominates the changes in global energy on the seasonal scale owing to its collectively huge heat capacity. The annual variation in OHC in the SH has a larger amplitude than that in the NH, because there is a larger ocean area in the SH. The changes in global OHC are ultimately consistent with the changes in OHC of the SH. Different regional changes and their drivers are summarized below.

Our results show that surface heat fluxes dominate the OHC change outside of the tropics, while in the tropics, surface winds and ocean thermocline dynamics, which is controlled by both the Ekman pumping and equatorial wave propagation, play a more important role. In the tropics, there is an opposite phase change in temperature 0–80 m compared with 80–1500 m. While the change in the upper 80 m is mainly driven by surface heat flux related to solar heating, below ∼80 m, the temperature changes are not in phase because of Ekman heat transport and thermocline dynamics. The annual variation and movement of the zonal trade-wind stress leads to changes in Ekman MHT, which dominates the total MHT within 20°S–20°N. The annual changes in MHT and thermocline directly dominate the annual changes in OHC in the tropics.

At midlatitudes, there is a seasonal variation of OHC from the near surface to ∼1500 m. The sea–air heat flux mainly drives the changes in temperature at the sea surface, and then the near-surface anomalies are gradually transferred downward to the deeper waters. Below the mixed layer, the time scales of diabatic heating are ≫1 year. Hence, diabatic heating plays a smaller role and instead, the heat transport processes, including currents, Rossby wave adjustment, and eddies, become important.

Our observational representation of OHC and surface flux changes can be further used for model discrimination and assessment. Gleckler et al. (2006) remarked that “An important hindrance in this area has been the availability of observational data.” Therefore, with better observational datasets available nowadays, a quantitative evaluation of OHC annual cycle for state-of-the-art climate models is a research priority.

When explaining regional OHC annual changes, several regions have been poorly represented, including the ice-covered regions. For example, Fig. 4 shows the existence of a polar OHC annual cycle. The contribution of the latent heat of the Arctic and Antarctic sea ice changes to the regional and global energy budget should be included in future to gain a more complete view of Earth’s energy budget. The key difficulty is the lack of volume observations for Antarctic sea ice. Refining these key uncertainties will contribute to a more complete understanding of Earth’s energy flows.

Another follow-up question to be addressed is why the annual cycle can be found in the layers deeper than >1000 m. We speculate that different mechanisms are responsible for these variations. For example, Huang et al. (2018) and Chen et al. (2020) found that equatorial Kelvin waves, forced by zonal wind variations in the western half of the basin, transfer energy downward and eastward, reflecting into Rossby waves at the eastern boundary. These reflected Rossby waves also transfer energy downward and westward, contributing to the deep ocean changes. Ishizaki et al. (2014) and Brandt and Eden (2005) observed the deep-reaching equatorial Rossby waves in the tropical Pacific Ocean and tropical Atlantic Ocean, respectively. A thorough analyses of deep penetration of OHC annual cycle over the global scale is planned.

While this study mainly explores the annual changes in OHC, there is also the semiannual cycle, which plays a role in the annual changes of OHC in the tropics in all three major ocean basins (Antonov et al. 2004; Qu et al. 2008). Here, we simply calculated the monthly averages, and hence, the semiannual cycles were included. They are obvious only in a relatively small area of global ocean (Qu et al. 2008).

Furthermore, on a global scale, there is still substantial spread of the OHC annual cycle across different datasets (Fig. 14). The standard deviation of the magnitude of OHC annual variation across different products is ∼7 ZJ, indicating a substantial uncertainty in the OHC annual cycle whose magnitude is ∼59 ZJ. The standard deviation of the SH OHC magnitude is ∼7.5 ZJ, while the spread in the NH is larger ∼7.1 ZJ. The cancellation between the annual cycles in the two hemispheres highlights the NH differences, which may relate to the Arctic, in part. The Argo products and WAGHC cover 65°S–65°N, while IAP/EN4/Ishii/ORAS4 covers the global ocean but their land–ocean masks are slightly different. The differences among the seven datasets come from different mapping strategies (e.g., first guess and covariance), data quality control, horizontal/vertical interpolation methods, instrumental errors, choices of data (Argo only or all instruments), and even model error (from ORAS4). Thus, although instrumental errors might be underestimated, inclusion of the other factors means that it is likely that our approach overestimates the true uncertainty. Identifying the sources of uncertainty in representing OHC annual cycle will also be a research priority.

Fig. 14.
Fig. 14.

Annual cycle of OHC of the upper 1500 m (a) for the global ocean, (b) in the NH, and (c) in the SH. Seven different datasets are presented.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

Finally, another caveat is the substantial biases in the currently available wind datasets, caused by the physical assumptions, limitations, assimilation of observations, and model errors (Gelaro et al. 2017; Carvalho 2019). Biases in the value and the direction of wind lead to biases in the calculation of wind stress, Ekman pumping, and Ekman MHT.

Acknowledgments.

This study was supported by the National Natural Science Foundation of China (Grants 42122046, 42076202, 42075036), the Youth Promotion Association of the Chinese Academy of Sciences (2020077), and the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB42040402). NCAR is sponsored by the National Science Foundation.

Data availability statement.

All data used in this study are publicly available. The sea temperature and salinity data were accessed from the following freely available sources: the IAP products from http://www.ocean.iap.ac.cn/; ECMWF’s ORAS4 data from https://www.cen.uni-hamburg.de/en/icdc/data/ocean/easy-init-ocean/ecmwf-ocean-reanalysis-system-4-oras4.html; ISHII2017 data from https://climate.mri-jma.go.jp/pub/ocean/ts/v7.2/; EN4 data from https://www.metoffice.gov.uk/hadobs/en4/index.html; WAGHC at https://www.cen.uni-hamburg.de/icdc/data/ocean/waghc.html#zitat; SCRIPPS data at http://sio-argo.ucsd.edu/RG_Climatology.html; BOA data at http://www.argo.ucsd.edu/Gridded_fields.html; DEEP-C data at https://doi.org/10.17864/1947.000347; CERES data from https://ceres-tool.larc.nasa.gov/ord-tool/jsp/EBAFTOA41Selection.jsp; PIOMAS ice volume data at http://psc.apl.uw.edu/research/projects/arctic-sea-ice-volumeanomaly/; and the surface wind stress data from MERRA-2 at https://doi.org/10.5067/0JRLVL8YV2Y4.

APPENDIX

Empirical Quantification of the Vertical Extension of Annual Variation in OHC

Although we explore the annual changes in OHC down to 2000 m in this paper, the annual variation gets smaller with depth (Fig. 2). The temperature anomalies below 350 m are generally less than ±0.2°C, while the SST anomalies can exceed 3°C. Here, we compare the magnitude (range) of the annual variation (SVm) at each depth with the spread among multiple observational products (SDm) (see section 2f for their definitions).

The magnitude of the annual variation in ocean temperature (SVm, Fig. A1) at 1, 100, 300, 700, 1000, and 1500 m is much smaller than annual changes in SST (>10°C; here, 10°C denotes the 95th percentile of the regional SVm) in the areas beyond the equator (10°–50°S and 10°–60°N) (Fig. A1a). The amplitudes of the annual variation in temperature in the tropical and high latitudes are less than 3°C. As the depth increases, the influence of solar radiation weakens, while ocean dynamics (mixing, convection, advection, etc.) effects increase. The pattern of SVm at 100 m is slightly different to that of SST, owing to the large variation in the amplitude of temperature (over 6°C) in the equatorial eastern Pacific, western boundary current, North Atlantic, and Antarctic Circumpolar Currents (Fig. A1b). The subsurface patterns of SVm are very different from that of SST—for example, areas with higher magnitudes of change in temperature at 300 m (>0.9°C) are within 30°S–30°N in the Indian, Pacific, and Atlantic Oceans, and within 45°–65°N in the North Atlantic (Fig. A1c). Also, there is consistency in the patterns of SVm below 300 m (Figs. A1c–f). Even at 1500 m, there are some regions with annual variations in temperature of >1°C near the equator (Fig. A1f).

Fig. A1.
Fig. A1.

Magnitude (defined as the difference between the maximum and minimum of the temperature annual variation) of the annual variation (SVm) in temperature at (a) 1, (b) 100, (c) 300, (d) 700, (e) 1000, and (f) 1500 m. The maximum SVm is 25.52, 9.63, 2.47, 10.99, 24.57, and 3.59 at 1, 100, 300, 700, 1000, and 1500 m, respectively.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

The SDm reveals a consistency in the annual variations among the data products (Fig. A2). Generally, areas with large data uncertainty occur in regions with large annual variation (Fig. A2 vs Fig. A1)—for example, at mid- to high latitudes and in the coastal regions for SST, and in the Southern Ocean and North Atlantic Ocean for temperature at 1000 and at 1800 m. The temperature in the Southern Ocean has larger uncertainty because of both larger variations and fewer data than elsewhere.

Fig. A2.
Fig. A2.

Magnitude of the observational uncertainty (SDm) at (a) 1, (b) 100, (c) 300, (d) 700, (e) 1000, and (f) 1500 m.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

For the SNR (Fig. A3), most of the global ocean surface shows larger seasonal change in temperature than data error (SNR > 1), with the exception of the Arctic. The area with SNR > 1 decreases with depth. Below a depth of 300 m, the areas with SNR > 1 are mostly located within 30°S–30°N and in the subpolar Atlantic Ocean (45°–65°N), due to the large signal (SVm; Fig. A1) but small data uncertainty (SDm; Fig. A2).

Fig. A3.
Fig. A3.

SNR of the annual variation in temperature at (a) 1, (b) 100, (c) 300 m (d) 700, (e) 1000, and (f) 1500 m. The contours denote the regions with SNR = 1, and hatching denotes areas with SNR < 1.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

In global average terms, the magnitude of the annual variation in ocean temperature (SVm) decreases with depth from ∼4°C at the surface to ∼0.1°C at 2000 m (Fig. A4; IAP data). The differences among datasets also get smaller with depth, from ∼0.135° to 0.023°C below 1800 m. The global-mean SNR is reduced from 8–10 in the upper 30 m to ∼1 below 1800 m (Fig. A4a). A critical point is 1300–1500 m, where the global-mean SNR of most of the data we used becomes <1. Notably, the ISHII2017 data show larger signals at 850–1800 m (SVm) than the other six data products, so this dataset results in a larger SNR (within 1.0–1.8 below 850 m). As the sources of in situ observations are virtually the same for ISHII2017, WAGHC, ORAS4, and IAP or EN4, the difference might come from the different gap-filling methods employed (Boyer et al. 2016; Cheng et al. 2017; Ishii et al. 2017; Meyssignac et al. 2019; Gouretski 2018). The other six products show an SNR < 1 at 1000–1800 m.

Fig. A4.
Fig. A4.

The global-mean (a) SNR and (b) SDm represented by different datasets, and (c) the SVm.

Citation: Journal of Climate 36, 15; 10.1175/JCLI-D-22-0776.1

According to this analysis, although the SNR of each dataset is close to 1 below a depth of 800 m, Figs. A1 and A3 indicate that below 300 m the area of SNR > 1 only occurs in the tropics and North Atlantic, and there are robust annual variations from the surface down to 1500 m (Figs. A1, A3, and A4).

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