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applied over long time periods ( Rhein et al. 2013 ; Bindoff et al. 2019 ). Linear regressions are not optimal when evident nonlinearities are present in the underlying data ( Trenberth et al. 2007 ); linear trend lines can also be subject to large start- and end-point sensitivity. The IPCC-AR5 calculated the linear rate of OHC increase for 1971–2010 ( Rhein et al. 2013 ; IPCC 2019 ), but there is no physical reason to expect linear changes over this period. Rather, there is an expectation of small
applied over long time periods ( Rhein et al. 2013 ; Bindoff et al. 2019 ). Linear regressions are not optimal when evident nonlinearities are present in the underlying data ( Trenberth et al. 2007 ); linear trend lines can also be subject to large start- and end-point sensitivity. The IPCC-AR5 calculated the linear rate of OHC increase for 1971–2010 ( Rhein et al. 2013 ; IPCC 2019 ), but there is no physical reason to expect linear changes over this period. Rather, there is an expectation of small
Imbard 1996 ). These grids are always nonuniform, which complicates the definition of zonal values. To work with the data on curvilinear grids, we employ a zigzag setup that is elaborated upon in detail by Outten et al. (2018) (see their Fig. 2). In short, we work on the original multipole grid and follow the native zonal directions when performing numerical operations. 3) Statistical analysis Intending to explore the relations between different variables, we performed linear regressions on various
Imbard 1996 ). These grids are always nonuniform, which complicates the definition of zonal values. To work with the data on curvilinear grids, we employ a zigzag setup that is elaborated upon in detail by Outten et al. (2018) (see their Fig. 2). In short, we work on the original multipole grid and follow the native zonal directions when performing numerical operations. 3) Statistical analysis Intending to explore the relations between different variables, we performed linear regressions on various
relates to budget closure. We saw earlier that approximate energy and ocean mass budget closure was achieved after dedrifting for the ACCESS-CM2 model ( Figs. 1d,e ), but nonclosure of the atmospheric water budget remained ( Fig. 1f ). To extend this budget closure analysis to the entire ensemble, we regress the various (decadal mean) dedrifted time series against one another to test for corresponding variability ( Fig. 6 ). For reference, the ACCESS-CM2 linear regression coefficients were 0.99 ( Q r
relates to budget closure. We saw earlier that approximate energy and ocean mass budget closure was achieved after dedrifting for the ACCESS-CM2 model ( Figs. 1d,e ), but nonclosure of the atmospheric water budget remained ( Fig. 1f ). To extend this budget closure analysis to the entire ensemble, we regress the various (decadal mean) dedrifted time series against one another to test for corresponding variability ( Fig. 6 ). For reference, the ACCESS-CM2 linear regression coefficients were 0.99 ( Q r
atmospheric model comprising a finite-volume dynamical core with a resolution of 0.5° × 0.625° and 72 vertical levels. MERRA-2 uses a 3DVAR algorithm based upon the gridpoint statistical interpolation (GSI) analysis system with 6-hourly updates. Clouds in MERRA-2 are generated internally and their radiative properties are parameterized. The radiative transfer code is based upon Chou and Suarez (1999) for SW radiation and Chou et al. (2001) for LW radiation. Sea surface temperature (SST) and sea ice
atmospheric model comprising a finite-volume dynamical core with a resolution of 0.5° × 0.625° and 72 vertical levels. MERRA-2 uses a 3DVAR algorithm based upon the gridpoint statistical interpolation (GSI) analysis system with 6-hourly updates. Clouds in MERRA-2 are generated internally and their radiative properties are parameterized. The radiative transfer code is based upon Chou and Suarez (1999) for SW radiation and Chou et al. (2001) for LW radiation. Sea surface temperature (SST) and sea ice
reanalysis and found that the implied change from month to month was not physically possible—energy was not conserved—as it was far too large compared with the changes inferred from CERES. The CERES 12-month running mean EEI variations had a standard deviation of 0.4 W m −2 (global), but all OHC analyses had values over 3.6 W m −2 with the sole exception being ORAP5 (Ocean Re-Analysis Pilot v5) from ECMWF ( Zuo et al. 2017 ), which was 1.4 W m −2 ( Trenberth et al. 2016 ). In several products, the
reanalysis and found that the implied change from month to month was not physically possible—energy was not conserved—as it was far too large compared with the changes inferred from CERES. The CERES 12-month running mean EEI variations had a standard deviation of 0.4 W m −2 (global), but all OHC analyses had values over 3.6 W m −2 with the sole exception being ORAP5 (Ocean Re-Analysis Pilot v5) from ECMWF ( Zuo et al. 2017 ), which was 1.4 W m −2 ( Trenberth et al. 2016 ). In several products, the
temperature, are routinely observed by satellites. However, budget diagnostics additionally require exact knowledge of subsurface properties, such as sea ice thickness and vertically resolved ocean temperature. For example, SB14 made use of early-generation atmospheric reanalyses such as the 40-yr ECMWF Re-Analysis (ERA-40; Uppala et al. 2005 ), but their ocean and sea ice diagnostics had to rely on very sparse in situ data and low-resolution ocean model simulations. In recent years, dynamical
temperature, are routinely observed by satellites. However, budget diagnostics additionally require exact knowledge of subsurface properties, such as sea ice thickness and vertically resolved ocean temperature. For example, SB14 made use of early-generation atmospheric reanalyses such as the 40-yr ECMWF Re-Analysis (ERA-40; Uppala et al. 2005 ), but their ocean and sea ice diagnostics had to rely on very sparse in situ data and low-resolution ocean model simulations. In recent years, dynamical
absorption of shortwave radiation, however, have not been updated since the estimate by Peixoto et al. (1991) was made. Goody (2000) extended work by Peixoto et al. (1991) and estimated entropy produced by irreversible processes within the Earth system. Lucarini et al. (2011) used climate models and estimated entropy production by nonradiative irreversible processes. The analysis of thermodynamics of the climate system is also used to understand how general circulation changes under a warming
absorption of shortwave radiation, however, have not been updated since the estimate by Peixoto et al. (1991) was made. Goody (2000) extended work by Peixoto et al. (1991) and estimated entropy produced by irreversible processes within the Earth system. Lucarini et al. (2011) used climate models and estimated entropy production by nonradiative irreversible processes. The analysis of thermodynamics of the climate system is also used to understand how general circulation changes under a warming
Kimoto 2009 ), EN ( Ingleby and Huddleston 2007 ), PMEL ( Lyman and Johnson 2008 ), and WIL ( Willis et al. 2004 ). WIL, however, starts in 1993, as their mapping relies on regressions with sea level from satellite altimeter ( WCRP Global Sea Level Budget Group 2018 ). A summary of the six mapping methods is found in Boyer et al. (2016) . All gridded OHCA estimates ( Table 1 ) are relative to the same monthly mean baseline climatology from Alory et al. (2007) , corresponding to the “C1_H (or H
Kimoto 2009 ), EN ( Ingleby and Huddleston 2007 ), PMEL ( Lyman and Johnson 2008 ), and WIL ( Willis et al. 2004 ). WIL, however, starts in 1993, as their mapping relies on regressions with sea level from satellite altimeter ( WCRP Global Sea Level Budget Group 2018 ). A summary of the six mapping methods is found in Boyer et al. (2016) . All gridded OHCA estimates ( Table 1 ) are relative to the same monthly mean baseline climatology from Alory et al. (2007) , corresponding to the “C1_H (or H