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Wenhui Cui and Ting Fong May Chui

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

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Ziwei Xu, Yanfei Ma, Shaomin Liu, Wenjiao Shi, and Jiemin Wang

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

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Gregory R. Foltz, Claudia Schmid, and Rick Lumpkin

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

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Ryan M. Holmes, Jan D. Zika, and Matthew H. England

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

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Tristan S. L’Ecuyer, H. K. Beaudoing, M. Rodell, W. Olson, B. Lin, S. Kato, C. A. Clayson, E. Wood, J. Sheffield, R. Adler, G. Huffman, M. Bosilovich, G. Gu, F. Robertson, P. R. Houser, D. Chambers, J. S. Famiglietti, E. Fetzer, W. T. Liu, X. Gao, C. A. Schlosser, E. Clark, D. P. Lettenmaier, and K. Hilburn

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

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Oleg A. Saenko, Jonathan M. Gregory, Stephen M. Griffies, Matthew P. Couldrey, and Fabio Boeira Dias

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

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Quran Wu, Xuebin Zhang, John A. Church, and Jianyu Hu

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

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Damien Irving, Will Hobbs, John Church, and Jan Zika

fluxes into the atmosphere and ocean. For instance, changes in meridional transports of ocean heat and freshwater can be inferred from cumulative surface heat and freshwater fluxes (e.g., Levang and Schmitt 2015 ; Nummelin et al. 2017 ; Irving et al. 2019 ) and changes in ocean salinity can be used to infer global water cycle changes ( Skliris et al. 2016 ), but only if there is approximate closure of the relevant global budgets. If model leakage causes a substantial mismatch between changes in

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Carol Anne Clayson and Alec S. Bogdanoff

climatological energy and water budgets. Several researchers have estimated the change in fluxes due to the use of a diurnally varying SST, typically for very short time periods and limited areas. Schiller and Godfrey (2005) used a coupled one-dimensional ocean–atmosphere model at a mooring in the tropical Pacific Ocean during one week in November 1992, and found an average increase in fluxes of 10 W m −2 . A profiler deployed in the Gulf of California for a total of 976 profiles showed net heat flux

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B. I. Moat, B. Sinha, S. A. Josey, J. Robson, P. Ortega, F. Sévellec, N. P. Holliday, G. D. McCarthy, A. L. New, and J. J.-M. Hirschi

spatially variable maximum mixed layer depth (MLD) to differentiate the near-surface layer in contact with the atmosphere from the rest of the ocean. Unlike Buckley et al. (2014) they used observationally based gridded OHC products and surface fluxes from atmospheric reanalyses with a Kalman filter–based method to obtain an estimated heat budget with error bounds for both the mixed layer and the rest of the ocean, evaluating ocean heat transport convergence as a residual. Their results indicated that

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