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hypothesized that neglecting lateral heat fluxes in the subsurface could contribute to the energy imbalance over the heterogeneous surface and that the level of energy balance closure could be improved if the lateral heat fluxes were considered. 2. Method Field measurements were performed using an eddy covariance system and an array of temperature and water-level sensors. The eddy covariance system was used to obtain the energy budget of a vegetated area, and the sensors were used to capture the
hypothesized that neglecting lateral heat fluxes in the subsurface could contribute to the energy imbalance over the heterogeneous surface and that the level of energy balance closure could be improved if the lateral heat fluxes were considered. 2. Method Field measurements were performed using an eddy covariance system and an array of temperature and water-level sensors. The eddy covariance system was used to obtain the energy budget of a vegetated area, and the sensors were used to capture the
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
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
included an intensive flux observation matrix in an oasis–desert area. An average EBR of 0.92 was obtained using the entire 30-min dataset from 22 EC sets. This provided an overall impression of EBR in the oasis–desert area of western China, which has been the subject of intensive study. Generally, soil heat storage must be considered, and the heat storage terms (canopy and photosynthesis storage) in the energy budget improved the total closure of the maize surface by approximately 6%, demonstrating
included an intensive flux observation matrix in an oasis–desert area. An average EBR of 0.92 was obtained using the entire 30-min dataset from 22 EC sets. This provided an overall impression of EBR in the oasis–desert area of western China, which has been the subject of intensive study. Generally, soil heat storage must be considered, and the heat storage terms (canopy and photosynthesis storage) in the energy budget improved the total closure of the maize surface by approximately 6%, demonstrating
cycle for most parameters. 3. Methodology To determine the processes responsible for the seasonal cycle of SST in the NETA, we analyze the heat budget in the surface mixed layer: This formulation follows Kraus and Turner (1967) and Moisan and Niiler (1998) . Changes in heat storage (left-hand term) are expressed in terms of horizontal heat advection (first term on the right), the net surface heat flux adjusted for the amount of SWR that penetrates the base of the mixed layer (second term on the
cycle for most parameters. 3. Methodology To determine the processes responsible for the seasonal cycle of SST in the NETA, we analyze the heat budget in the surface mixed layer: This formulation follows Kraus and Turner (1967) and Moisan and Niiler (1998) . Changes in heat storage (left-hand term) are expressed in terms of horizontal heat advection (first term on the right), the net surface heat flux adjusted for the amount of SWR that penetrates the base of the mixed layer (second term on the
for energy inputs and outputs at the infinitesimal interface between atmosphere and land and it is assumed that the energy budget must balance; that is, the SEB equation is a balance equation. Thus, the classical formulation of the SEB equation is (4) H S + H L + G = R net , where G is the soil heat flux, R net is the net radiation defined as the balance between downwelling and upwelling SW and LW radiation: (5) R net = SW down − SW up + LW down − LW up . Note that unlike the momentum
for energy inputs and outputs at the infinitesimal interface between atmosphere and land and it is assumed that the energy budget must balance; that is, the SEB equation is a balance equation. Thus, the classical formulation of the SEB equation is (4) H S + H L + G = R net , where G is the soil heat flux, R net is the net radiation defined as the balance between downwelling and upwelling SW and LW radiation: (5) R net = SW down − SW up + LW down − LW up . Note that unlike the momentum
does not appear in the internal heat content budget considered by Holmes et al. (2019) , which instead depends directly on the surface heat flux and diffusive fluxes of heat across isotherms. This is an advantage as G is a differentiated quantity that can be more difficult to robustly estimate from model simulations. Acknowledgments We thank S. Griffies and S. Groeskamp for useful comments. This project was supported by the Earth Science and Climate Change Hub of the Australian Government
does not appear in the internal heat content budget considered by Holmes et al. (2019) , which instead depends directly on the surface heat flux and diffusive fluxes of heat across isotherms. This is an advantage as G is a differentiated quantity that can be more difficult to robustly estimate from model simulations. Acknowledgments We thank S. Griffies and S. Groeskamp for useful comments. This project was supported by the Earth Science and Climate Change Hub of the Australian Government
both the atmospheric and surface energy budgets when independent estimates of the component fluxes are combined because choices concerning the manner by which balance is achieved have resulted in substantial differences in downwelling longwave and shortwave radiation (DLR and DSR, respectively) and turbulent heat fluxes. Thus, while these reconstructions utilize high-quality inputs and make reasonable arguments for adjusting component fluxes based on either assessments against in situ datasets or
both the atmospheric and surface energy budgets when independent estimates of the component fluxes are combined because choices concerning the manner by which balance is achieved have resulted in substantial differences in downwelling longwave and shortwave radiation (DLR and DSR, respectively) and turbulent heat fluxes. Thus, while these reconstructions utilize high-quality inputs and make reasonable arguments for adjusting component fluxes based on either assessments against in situ datasets or
mixing, while in the diathermal framework the role of temperature advection in the heat budget is not considered ( Walin 1982 ; Holmes et al. 2019 ). For our purposes of separating the role of ocean physics and dynamics at different scales, the applied projection of the Eulerian heat budget onto the position of potential density surfaces is as follows. Consider the whole ocean domain, so that Eq. (5) takes the form (9) All scales = Large + Meso + Small + Flux δ ( z − η ) , where we assume
mixing, while in the diathermal framework the role of temperature advection in the heat budget is not considered ( Walin 1982 ; Holmes et al. 2019 ). For our purposes of separating the role of ocean physics and dynamics at different scales, the applied projection of the Eulerian heat budget onto the position of potential density surfaces is as follows. Consider the whole ocean domain, so that Eq. (5) takes the form (9) All scales = Large + Meso + Small + Flux δ ( z − η ) , where we assume
( Boyer et al. 2018 ), we investigate the spatial and temporal distribution of the OHC change over the past 70 years and quantify the warming trend in the GOM. We further discuss the heat budget closure in the GOM using the net surface heat flux from multiple heat flux products and the estimated Loop Current net advective heat flux. 2. Data and methods a. Data The warming trend in the GOM is quantified using running pentadal (5-yr) objectively analyzed gridded temperature anomaly fields. The
( Boyer et al. 2018 ), we investigate the spatial and temporal distribution of the OHC change over the past 70 years and quantify the warming trend in the GOM. We further discuss the heat budget closure in the GOM using the net surface heat flux from multiple heat flux products and the estimated Loop Current net advective heat flux. 2. Data and methods a. Data The warming trend in the GOM is quantified using running pentadal (5-yr) objectively analyzed gridded temperature anomaly fields. The
is the nabla operator at constant . The terms and are temperature tendencies due to surface forcing and diffusive processes, respectively. The heat budget analysis is formulated by volume integrating Eq. (1) and applying Gauss’s theorem, where is the specific heat capacity, is the density of seawater, is the three-dimensional velocity vector ( ), is the diffusive heat flux vector (standard outputs of ECCOv4), is the SHF vector, and is the inward unit vector normal to the
is the nabla operator at constant . The terms and are temperature tendencies due to surface forcing and diffusive processes, respectively. The heat budget analysis is formulated by volume integrating Eq. (1) and applying Gauss’s theorem, where is the specific heat capacity, is the density of seawater, is the three-dimensional velocity vector ( ), is the diffusive heat flux vector (standard outputs of ECCOv4), is the SHF vector, and is the inward unit vector normal to the
