scholarly journals Transient Climate Response in a Two-Layer Energy-Balance Model. Part I: Analytical Solution and Parameter Calibration Using CMIP5 AOGCM Experiments

2013 ◽  
Vol 26 (6) ◽  
pp. 1841-1857 ◽  
Author(s):  
O. Geoffroy ◽  
D. Saint-Martin ◽  
D. J. L. Olivié ◽  
A. Voldoire ◽  
G. Bellon ◽  
...  
Keyword(s):  
Thermal Properties ◽  
Energy Balance ◽  
Analytical Solution ◽  
Deep Ocean ◽  
Energy Balance Model ◽  
Balance Model ◽  
Model Parameters ◽  
Climate Change Scenarios ◽  
Ocean Heat Uptake ◽  
Transient Climate Response

Abstract This is the first part of a series of two articles analyzing the global thermal properties of atmosphere–ocean coupled general circulation models (AOGCMs) within the framework of a two-layer energy-balance model (EBM). In this part, the general analytical solution of the system is given and two idealized climate change scenarios, one with a step forcing and one with a linear forcing, are discussed. These solutions give a didactic description of the contributions from the equilibrium response and of the fast and slow transient responses during a climate transition. Based on these analytical solutions, a simple and physically based procedure to calibrate the two-layer model parameters using an AOGCM step-forcing experiment is introduced. Using this procedure, the global thermal properties of 16 AOGCMs participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5) are determined. It is shown that, for a given AOGCM, the EBM tuned with only the abrupt 4×CO2 experiment is able to reproduce with a very good accuracy the temperature evolution in both a step-forcing and a linear-forcing experiment. The role of the upper-ocean and deep-ocean heat uptakes in the fast and slow responses is also discussed. One of the main weaknesses of the simple EBM discussed in this part is its ability to represent the evolution of the top-of-the-atmosphere radiative imbalance in the transient regime. This issue is addressed in Part II by taking into account the efficacy factor of deep-ocean heat uptake.

scholarly journals Transient Climate Response in a Two-Layer Energy-Balance Model. Part II: Representation of the Efficacy of Deep-Ocean Heat Uptake and Validation for CMIP5 AOGCMs

2013 ◽  
Vol 26 (6) ◽  
pp. 1859-1876 ◽  
Author(s):  
O. Geoffroy ◽  
D. Saint-Martin ◽  
G. Bellon ◽  
A. Voldoire ◽  
D. J. L. Olivié ◽  
...  
Keyword(s):  
Thermal Properties ◽  
Energy Balance ◽  
Surface Temperature ◽  
General Circulation ◽  
Deep Ocean ◽  
Energy Balance Model ◽  
Balance Model ◽  
Ocean Heat Uptake ◽  
Transient Climate Response ◽  
Heat Uptake

Abstract In this second part of a series of two articles analyzing the global thermal properties of atmosphere–ocean coupled general circulation models (AOGCMs) within the framework of a two-layer energy-balance model (EBM), the role of the efficacy of deep-ocean heat uptake is investigated. Taking into account such an efficacy factor is shown to amount to representing the effect of deep-ocean heat uptake on the local strength of the radiative feedback in the transient regime. It involves an additional term in the formulation of the radiative imbalance at the top of the atmosphere (TOA), which explains the nonlinearity between radiative imbalance and the mean surface temperature observed in some AOGCMs. An analytical solution of this system is given and this simple linear EBM is calibrated for the set of 16 AOGCMs of phase 5 of the Coupled Model Intercomparison Project (CMIP5) studied in Part I. It is shown that both the net radiative fluxes at TOA and the global surface temperature transient response are well represented by the simple EBM over the available period of simulations. Differences between this two-layer EBM and the previous version without an efficacy factor are analyzed and relationships between parameters are discussed. The simple model calibration applied to AOGCMs constitutes a new method for estimating their respective equilibrium climate sensitivity and adjusted radiative forcing amplitude from short-term step-forcing simulations and more generally a method to compute their global thermal properties.

scholarly journals Development of a Mass and Energy Balance Model and Its Application for HBI Charged EAFs

Metals ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 311
Author(s):  
Niloofar Arzpeyma ◽  
Rutger Gyllenram ◽  
Pär G. Jönsson
Keyword(s):  
Energy Balance ◽  
Slag Composition ◽  
Electricity Consumption ◽  
Electric Arc ◽  
Energy Balance Model ◽  
Balance Model ◽  
Model Parameters ◽  
Metal Oxidation ◽  
Arc Furnaces ◽  
Hot Briquetted Iron

A static mass and energy balance model combined with a MgO saturation slag model is developed for electric arc furnaces. The model parameters including distribution ratios and dust factors are calibrated for a specific furnace using experimental data. Afterward, the model is applied to study the effect of charging different amounts of hot briquetted iron (HBI) on energy consumption, charged slag former amount, and slag composition. The following results were obtained per each 1% increase of HBI additions: (i) a 0.16 Nm3/t decrease in the amount of injected oxygen for metal oxidation, (ii) a 1.29 kWh/t increase in the electricity consumption, and (iii) a 34 kg increase in the amount of the slag.

scholarly journals On the Meaning of Feedback Parameter, Transient Climate Response, and the Greenhouse Effect: Basic Considerations and the Discussion of Uncertainties

2010 ◽  
Vol 4 (1) ◽  
pp. 137-159 ◽  
Author(s):  
Gerhard Kramm ◽  
Ralph Dlugi
Keyword(s):  
Energy Balance ◽  
Greenhouse Effect ◽  
Equilibrium Temperature ◽  
Energy Balance Model ◽  
Balance Model ◽  
Radiation Balance ◽  
Climate Response ◽  
Transient Climate Response ◽  
Feedback Parameter ◽  
The Earth

In this paper we discuss the meaning of feedback parameter, greenhouse effect and transient climate response usually related to the globally averaged energy balance model of Schneider and Mass. After scrutinizing this model and the corresponding planetary radiation balance we state that (a) this globally averaged energy balance model is flawed by unsuitable physical considerations, (b) the planetary radiation balance for the Earth in the absence of an atmosphere is fraught by the inappropriate assumption of a uniform surface temperature, the so-called radiative equilibrium temperature of about 255 K, and (c) the effect of the radiative anthropogenic forcing, considered as a perturbation to the natural system, is much smaller than the uncertainty involved in the solution of the model of Schneider and Mass. This uncertainty is mainly related to the empirical constants suggested by various authors and used for predicting the emission of infrared radiation by the Earth's skin. Furthermore, after inserting the absorption of solar radiation by atmospheric constituents and the exchange of sensible and latent heat between the Earth and the atmosphere into the model of Schneider and Mass the surface temperatures become appreciably lesser than the radiative equilibrium temperature. Moreover, both the model of Schneider and Mass and the Dines-type two-layer energy balance model for the Earthatmosphere system, containing the planetary radiation balance for the Earth in the absence of an atmosphere as an asymptotic solution, do not provide evidence for the existence of the so-called atmospheric greenhouse effect if realistic empirical data are used.

Insights into the Zonal-Mean Response of the Hydrologic Cycle to Global Warming from a Diffusive Energy Balance Model

2018 ◽  
Vol 31 (18) ◽  
pp. 7481-7493 ◽  
Author(s):  
Nicholas Siler ◽  
Gerard H. Roe ◽  
Kyle C. Armour
Keyword(s):  
Global Warming ◽  
Energy Balance ◽  
Spatial Pattern ◽  
Radiative Forcing ◽  
Energy Transport ◽  
Hydrologic Cycle ◽  
Energy Balance Model ◽  
Balance Model ◽  
Ocean Heat Uptake ◽  
Heat Uptake

Recent studies have shown that the change in poleward energy transport under global warming is well approximated by downgradient transport of near-surface moist static energy (MSE) modulated by the spatial pattern of radiative forcing, feedbacks, and ocean heat uptake. Here we explore the implications of downgradient MSE transport for changes in the vertically integrated moisture flux and thus the zonal-mean pattern of evaporation minus precipitation ( E − P). Using a conventional energy balance model that we have modified to represent the Hadley cell, we find that downgradient MSE transport implies changes in E − P that mirror those simulated by comprehensive global climate models (GCMs), including a poleward expansion of the subtropical belt where E > P, and a poleward shift in the extratropical minimum of E − P associated with the storm tracks. The surface energy budget imposes further constraints on E and P independently: E increases almost everywhere, with relatively little spatial variability, while P must increase in the deep tropics, decrease in the subtropics, and increase in middle and high latitudes. Variations in the spatial pattern of radiative forcing, feedbacks, and ocean heat uptake across GCMs modulate these basic features, accounting for much of the model spread in the zonal-mean response of E and P to climate change. Thus, the principle of downgradient energy transport appears to provide a simple explanation for the basic structure of hydrologic cycle changes in GCM simulations of global warming.

scholarly journals Multiple solutions and numerical analysis to the dynamic and stationary models coupling a delayed energy balance model involving latent heat and discontinuous albedo with a deep ocean

2014 ◽  
Vol 470 (2170) ◽  
pp. 20140376 ◽  
Author(s):  
J. I. Díaz ◽  
A. Hidalgo ◽  
L. Tello
Keyword(s):  
Energy Balance ◽  
Latent Heat ◽  
Deep Ocean ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Ocean Model ◽  
Energy Balance Model ◽  
Balance Model ◽  
Finite Volume Scheme ◽  
Two Phase

We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge–Kutta total variation diminishing for time integration.

scholarly journals A preliminary assessment of glacier melt-model parameter sensitivity and transferability in a dry subarctic environment

2011 ◽  
Vol 5 (4) ◽  
pp. 1011-1028 ◽  
Author(s):  
A. H. MacDougall ◽  
B. A. Wheler ◽  
G. E. Flowers
Keyword(s):  
Energy Balance ◽  
Parameter Sensitivity ◽  
Energy Balance Model ◽  
Balance Model ◽  
Model Parameters ◽  
Temperature Index ◽  
Model Parameter ◽  
Index Model ◽  
Degree Day ◽  
Model Tuning

Abstract. Efforts to project the long-term melt of mountain glaciers and ice-caps require that melt models developed and calibrated for well studied locations be transferable over large regions. Here we assess the sensitivity and transferability of parameters within several commonly used melt models for two proximal sites in a dry subarctic environment of northwestern Canada. The models range in complexity from a classical degree-day model to a simplified energy-balance model. Parameter sensitivity is first evaluated by tuning the melt models to the output of an energy balance model forced with idealized inputs. This exercise allows us to explore parameter sensitivity both to glacier geometric attributes and surface characteristics, as well as to meteorological conditions. We then investigate the effect of model tuning with different statistics, including a weighted coefficient of determination (wR2), the Nash-Sutcliffe efficiency criterion (E), mean absolute error (MAE) and root mean squared error (RMSE). Finally we examine model parameter transferability between two neighbouring glaciers over two melt seasons using mass balance data collected in the St. Elias Mountains of the southwest Yukon. The temperature-index model parameters appear generally sensitive to glacier aspect, mean surface elevation, albedo, wind speed, mean annual temperature and temperature lapse rate. The simplified energy balance model parameters are sensitive primarily to snow albedo. Model tuning with E, MAE and RMSE produces similar, or in some cases identical, parameter values. In twelve tests of spatial and/or temporal parameter transferability, the results with the lowest RMSE values with respect to ablation stake measurements were achieved twice with a classical temperature-index (degree-day) model, three times with a temperature-index model in which the melt parameter is a function of potential radiation, and seven times with a simplified energy-balance model. A full energy-balance model produced better results than the other models in nine of twelve cases, though the tuning of this model differs from that of the others.

scholarly journals The Sensitivity of the Rate of Transient Climate Change to Ocean Physics Perturbations

2007 ◽  
Vol 20 (10) ◽  
pp. 2315-2320 ◽  
Author(s):  
M. Collins ◽  
C. M. Brierley ◽  
M. MacVean ◽  
B. B. B. Booth ◽  
G. R. Harris
Keyword(s):  
Climate Change ◽  
Climate Models ◽  
Climate Model ◽  
Deep Ocean ◽  
Time Dependent ◽  
Model Parameters ◽  
Climate Feedbacks ◽  
Ocean Heat Uptake ◽  
Transient Climate Response ◽  
Surface Climate

Abstract “Perturbed physics” ensembles of Hadley Centre climate models have recently been used to quantify uncertainties in atmospheric and surface climate feedbacks under enhanced levels of CO2, and to produce probabilistic estimates of the magnitude of equilibrium climate change. The rate of time-dependent climate change is determined both by the strength of atmosphere–surface climate feedbacks and by the strength of processes that remove heat from the surface to the deep ocean. Here a first small ensemble of coupled atmosphere–ocean climate model experiments in which the parameters that control three key ocean physical processes are perturbed is described. It is found that the perturbations have little impact on the rate of ocean heat uptake, and thus have little impact on the time-dependent rate of global warming. Under the idealized scenario of 1% yr−1 compounded CO2 increase, the spread in the transient climate response is of the order of a few tenths of a degree, in contrast to the spread of order of 1° caused by perturbing atmospheric model parameters.

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