2 First Institute of Oceanography, Ministry of Natural Resources, Qingdao 266061, China;
3 Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266237, China;
4 Key Laboratory of Marine Sciences and Numerical Modeling, Ministry of Natural Resources, Qingdao 266061, China
The ocean plays a considerable Part Ⅰn the global energy budget because it is the primary heat reservoir for climate change (global warming), as it stores more than 90% of the excess heat (Palmer and McNeall, 2014; Von Schuckmann et al., 2016). The variations of ocean heat content (OHC) are essential elements of the global and regional climate variability (Jin, 1997; Meehl et al., 2011; Roberts et al., 2015) and the transient response to climate change (Kuhlbrodt and Gregory, 2012; Geoffroy et al., 2013). The OHC variation has become an important indicator of climate change and its variability (Abraham et al., 2013).
Changes in the OHC also represents the global energy imbalance caused by anthropogenic climate change, and thus projections of future changes in this quantity need to be as accurate as possible for the projection of future global temperature changes and sea level rises. However, numerical models, including ocean general circulation models, coupled climate models, and earth system models, have deficiencies in simulating the OHC (Gregory et al., 2004; Achutarao et al., 2007). Previous studies have suggested that including volcanic forcing (Church et al., 2005; Gleckler et al., 2006) and other variable climate forcings can improve the simulation of the climate models (Delworth et al., 2005). Numerous studies have shown an increase in the global OHC over the past few decades (Abraham et al., 2013).
Involving the important physical processes of the real ocean is a part of the unremitting development of numerical models. The more attention of including the oceanic surface waves in the climate system has recently received (Huang et al., 2012, 2014; Qiao et al., 2013; Fan and Griffies, 2014). Recent research found that wave-induced mixing can change the OHC in both ocean models (Stoney et al., 2018) and climate coupled models (Chen et al., 2018). Nevertheless, the vertical mixing does not create, but redistributes, heat.
In the present study, we focus on understanding the mechanisms underlying the changes in OHC in the upper ocean caused by surface wave-induced vertical mixing (which we henceforth refer to simply as Bv, for convenience). Domingues et al. (2008) compared the linear trend in ocean heat content in the upper 700 m and 300 m, and found that 91% of it stored in the upper 300 m. Adopting the same definition as used in previous studies (Domingues et al., 2008; Balmaseda et al., 2013; Williams et al., 2015), we consider 0–300 m as the object of study in this research. Using two identical numerical experiments, one with and one without Bv, we reveal how incorporating the effects of Bv improves the simulation of the OHC in the global upper ocean. The paper is organized as follows. The numerical models and data are described in Section 2. The results are presented in Sections 3, and the main conclusions are summarized in Section 4.2 MODEL, DATA AND METHOD 2.1 The setup of numerical experiments
The FIO-ESM (First Institute of Oceanography Earth System Model), developed by Qiao et al. (2013), was used to carry out the numerical experiments in this paper. FIO-ESM comprises coupled physical climate and carbon cycle models. The details of the FIO-ESM can be found in Qiao et al. (2013).
Two experiments, one with Bv and the other without, were performed to identify the contribution of Bv to the heat content in the global upper ocean. FIO-ESM was used for the two numerical experiments. Bv is expressed analytically as:
where α is a constant set to 1 following Qiao et al. (2013),
The experiment incorporating Bv adopts the numerical experiment design and forcing data recommended by the CMIP5 (Coupled Model Intercomparison Project Phase 5). A historical run was conducted for the 1850–2005 period to match the run period of the physical climate model. The other run was identical, except for Bv being not included. We chose the 20-year averaged model results (1986– 2005) for the comparison of OHC simulations with Bv, and without Bv.2.2 Observation data
The EN4 (Good et al., 2013) 1985–2006 objective analysis temperature data set was used to evaluate the upper ocean thermal content. In addition, we compared this climatological data with the World Ocean Atlas (2009) data (Locarnini et al., 2010); the results of the two data sets were almost the same.2.3 Method
We calculated the upper OHC, integrated between the surface and the depth of 300 m, using:
where T is the potential temperature, x is the zonal dimension, y is the meridional dimension, z is height, t is time, and cp and ρ0 are the heat capacity and density of sea water, respectively. In spherical coordinates:
where R is the radius of the Earth, ϕ is latitude, and θ is longitude. The OHC can be intuitively characterized as the average temperature.
The geographical distribution of OHC can be characterized by the vertically-integrated temperature (VIT, units: m℃). We calculated VIT using: No.2 CHEN et al.: Surface wave contribution to ocean heat content 309
where T a is the climatological monthly average temperature for the period 1986–2005.3 RESULT 3.1 Effects of Bv on the simulation of OHC
Here we investigated the OHC using the average temperature in the 0–300 m layer. Figure 1 shows the climatological monthly average temperature of the upper ocean over the simulation period (1986–2005). The mean of the EN4 data set was 12.90℃ and the mean of the case without Bv was 12.70℃. The mean temperature rose to 12.76℃ when Bv was included. The global average temperature of the upper ocean increased by almost 0.06℃ when incorporating Bv, and was closer to the observational data. Thus, the simulation bias (0.2) was improved by 30% (to 0.14) when Bv was included.
Figure 2 shows the VIT in the upper ocean (0– 300 m), and illustrates the geographical distribution of the OHC. The simulation bias compared to the EN4 data is highly variable in space. Although it appears that, overall, there is a negative bias for the case without Bv (Fig. 2b) and the case with Bv (Fig. 2c). However, there are slight positive biases in regions along the coast of North America in the Pacific Ocean, the northern Indian Ocean, and in some places in the Southern Ocean. Figure 2d shows the difference in VIT for the cases with and without Bv. The VIT significantly increased because of the inclusion of Bv in most areas, but not in the tropical western Pacific Ocean. However, in the equatorial Indian Ocean and the western Pacific Ocean, the reduced VIT increased model errors.
Figure 3 shows the result of the zonally-averaged vertically-integrated temperature. From the figure, we can see that the simulated OHC without BV is less than that in EN4. Because Bv typically increases the local OHC by changing the vertical mixing and stratification, improvements in the simulation tend to occur in those regions that have pre-existing negative biases. The latitude band between 13°S to 12°N is an exception to this rule. However, the reduced OHC in the latitude band between 7°N and 12°N seems to reduce the model errors of the case without Bv.3.2 Mechanism by which Bv affects OHC simulation
As is generally known, vertical mixing cannot generate heat but redistributes it vertically. In the coupled climate model, the air-sea heat flux acts as part of the source of heat. We investigated the zonallyaveraged net surface heat flux during the simulation period (Fig. 4). We found that the zonally-averaged net surface heat flux was very close for the two cases. The model is equilibrated, and the mean value of the difference of the annual mean net surface heat flux is almost zero (0.02 W/m2). Therefore, it is reasonable that the values of the zonally-averaged net surface heat flux for the two cases are close. However, in terms of heat content, the difference should be reflected in the net surface heat flux. Therefore, we consider that the change should be reflected in the initial period when Bv is included.
The numerical experiment design and forcing data recommended by the CMIP5 were adopted in the experiment that includes Bv. A historical run for the period 1850–2005 was conducted to match the period of the climate model. The other run was identical, except that Bv was closed. A control run for the preindustrial period (before 1850 AD) integrates the coupled physical climate model for 1200 years with the constant forcing fields of greenhouse gases, aerosol, and solar irradiance from 1850. Model year 701 was chosen as the initial state for the historical integration of 1850–2005 (Qiao et al., 2013). We chose the first 200 years of the control run, when Bv is first included.
Figure 5 shows the time evolution of the difference in the global average net surface heat flux between the cases with and without Bv in the first 200 years. We found that the global average net surface heat flux increased when Bv was included in the first 150 years. For the following 50 years, the difference in net surface heat flux fluctuates around zero.
In coupled climate models, the surface heat flux has a negative feedback with the sea surface temperature (SST). Figure 6 shows the global annual mean SST over 0–200 years. We found that, when Bv was included, the SST was higher than when Bv was closed in the first 150 years, especially in the 50–150- year period. This occurs because the increased mixing can transport more heat from the surface to the subsurface, thereby cooling the SST. The lower SST leads to an increased surface heat flux into the ocean, and the increased vertical mixing can transport the heat effectively, and warm the upper ocean. If the surface heat flux increases continuously, then the OHC will increase linearly. This is not reasonable. The climate model is a coupled system, and after a 150-year adjustment, it adjusts to an equilibrium state. The SST reaches a dynamic equilibrium state, with small fluctuations around an average value of 17.73℃, which is close to the observed value of 17.88℃ in 1850 obtained from the Hadley Centre Sea Ice and Sea Surface Temperature dataset (HadISST) (Rayner et al., 2006).
The increase in the surface heat flux induced increases in the upper ocean temperature as shown in Fig. 7. The accumulated net heat flux heats the upper 300 m of ocean by 0.05–0.06℃; this accords with the results shown in Fig. 1.4 SUMMARY AND CONCLUSION
In this study, we evaluated the contribution of Bv to the heat content in the global upper ocean. The mean temperature of the upper ocean was improved from 12.7℃ to 12.76℃, and was closer to the EN4 observational results (12.9℃). By including Bv in the model, the difference in the upper ocean temperature was reduced from 0.2℃ to 0.14℃. Thus, the inclusion of Bv reduced the difference for about 30%.
We analyzed the net surface heat flux for the simulation cases that included and without Bv during the experiment period, and the difference in the results is quite small. The increase in OHC by inclusion of Bv, however, was not caused by changing the surface heat flux during the experiment period. We found that the surface heat flux was higher for the first 150 years after Bv was initially included in the climate model. The surface heat flux and SST then reached a dynamic equilibrium state. We integrated the increase of the surface heat flux induced by the change of the upper ocean temperature. We found that the increase in the upper ocean temperature was 0.05–0.06℃, which is consistent with the increase from 1986–2005. Thus, the increase in the temperature in the system is the legacy of temperature increases in the first 150 years when Bv was initially included in the climate model.
We observed that the simulation of OHC was worse in the tropical regions (13°S–10°N) when Bv was included. In addition, the simulation of OHC when Bv was included was lower than that when Bv was closed. This may be because other physical processes dominate in the simulation of the tropical OHC in some regions. Because of the importance of OHC, further investigations are required to study the reasons for this discrepancy.5 DATA AVAILABILITY STATEMENT
Data supporting this article are available by any users from http://data.fio.org.cn/qiaofl/CSY-JGR-2018.
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