Maximum Entropy Production as a Constraint in Climate Models

Abstract. The representation of atmospheric convection induced by radiative forcing is a longstanding question mainly because turbulence plays a key role in the transport of energy as sensible heat, geopotential and latent heat. Recent works have tried to use Maximum Entropy Production as a closure hypothesis in Simple Climate Models in order to compute implicitly temperatures and vertical energy flux. However, these models failed to compute realistic profiles. To solve this problem, we prescribe a simplified 1D mass scheme transport which ensures energy fluxes. The later appears as a mechanical constraint which imposes the direction and/or limits the amplitudes of energy fluxes. This leads to a different MEP steady state which depends on the considered energy transfers in the model. Results using such model are improved with respect to another model, not including such effect: temperature and energy flux are closer to the observations and we naturally reproduce stratification when we consider geopotential. Variations of the atmospheric composition, such as doubling of the carbon dioxide concentration, is also investigated.

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A radiative-convective model based on constrained maximum entropy production

Earth System Dynamics ◽

10.5194/esd-10-365-2019 ◽

2019 ◽

Vol 10 (3) ◽

pp. 365-378 ◽

Cited By ~ 1

Author(s):

Vincent Labarre ◽

Didier Paillard ◽

Bérengère Dubrulle

Keyword(s):

Entropy Production ◽

Maximum Entropy ◽

Energy Flux ◽

Radiative Forcing ◽

Climate Models ◽

Carbon Dioxide Concentration ◽

Atmospheric Composition ◽

Energy Fluxes ◽

Maximum Entropy Production ◽

Energy Gradient

Abstract. The representation of atmospheric convection induced by radiative forcing is a long-standing question mainly because turbulence plays a key role in the transport of energy as sensible heat, geopotential, and latent heat. Recent works have tried using the maximum entropy production (MEP) conjecture as a closure hypothesis in 1-D simple climate models to compute implicitly temperatures and the vertical energy flux. However, these models fail to reproduce realistic profiles. To solve the problem, we describe the energy fluxes as a product of a positive mass mixing coefficient with the corresponding energy gradient. This appears as a constraint which imposes the direction and/or limits the amplitude of the energy fluxes. It leads to a different MEP steady state which naturally depends on the considered energy terms in the model. Accounting for this additional constraint improves the results. Temperature and energy flux are closer to observations, and we reproduce stratification when we consider the geopotential. Variations in the atmospheric composition, such as a doubling of the carbon dioxide concentration, are also investigated.

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The mechanics of granitoid systems and maximum entropy production rates

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2009.0202 ◽

2010 ◽

Vol 368 (1910) ◽

pp. 53-93 ◽

Cited By ~ 15

Author(s):

Bruce E. Hobbs ◽

Alison Ord

Keyword(s):

Entropy Production ◽

Maximum Entropy ◽

Melt Inclusions ◽

Selection Process ◽

Finite Thickness ◽

Control Valve ◽

Entropy Production Rate ◽

Constitutive Behaviour ◽

Maximum Entropy Production ◽

Physical Height

A model for the formation of granitoid systems is developed involving melt production spatially below a rising isotherm that defines melt initiation. Production of the melt volumes necessary to form granitoid complexes within 10 4 –10 7 years demands control of the isotherm velocity by melt advection. This velocity is one control on the melt flux generated spatially just above the melt isotherm, which is the control valve for the behaviour of the complete granitoid system. Melt transport occurs in conduits initiated as sheets or tubes comprising melt inclusions arising from Gurson–Tvergaard constitutive behaviour. Such conduits appear as leucosomes parallel to lineations and foliations, and ductile and brittle dykes. The melt flux generated at the melt isotherm controls the position of the melt solidus isotherm and hence the physical height of the Transport/Emplacement Zone. A conduit width-selection process, driven by changes in melt viscosity and constitutive behaviour, operates within the Transport Zone to progressively increase the width of apertures upwards. Melt can also be driven horizontally by gradients in topography; these horizontal fluxes can be similar in magnitude to vertical fluxes. Fluxes induced by deformation can compete with both buoyancy and topographic-driven flow over all length scales and results locally in transient ‘ponds’ of melt. Pluton emplacement is controlled by the transition in constitutive behaviour of the melt/magma from elastic–viscous at high temperatures to elastic–plastic–viscous approaching the melt solidus enabling finite thickness plutons to develop. The system involves coupled feedback processes that grow at the expense of heat supplied to the system and compete with melt advection. The result is that limits are placed on the size and time scale of the system. Optimal characteristics of the system coincide with a state of maximum entropy production rate.

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