scholarly journals Maximum entropy production: can it be used to constrain conceptual hydrological models?

2013 ◽  
Vol 17 (8) ◽  
pp. 3141-3157 ◽  
Author(s):  
M. C. Westhoff ◽  
E. Zehe
Keyword(s):  
Boundary Conditions ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Maximum Power ◽  
Hydrological Models ◽  
Maximum Entropy Production ◽  
Physically Based ◽  
Maximum Power Principle ◽  
Optimality Principles ◽  
Principle Of Maximum

Abstract. In recent years, optimality principles have been proposed to constrain hydrological models. The principle of maximum entropy production (MEP) is one of the proposed principles and is subject of this study. It states that a steady state system is organized in such a way that entropy production is maximized. Although successful applications have been reported in literature, generally little guidance has been given on how to apply the principle. The aim of this paper is to use the maximum power principle – which is closely related to MEP – to constrain parameters of a simple conceptual (bucket) model. Although, we had to conclude that conceptual bucket models could not be constrained with respect to maximum power, this study sheds more light on how to use and how not to use the principle. Several of these issues have been correctly applied in other studies, but have not been explained or discussed as such. While other studies were based on resistance formulations, where the quantity to be optimized is a linear function of the resistance to be identified, our study shows that the approach also works for formulations that are only linear in the log-transformed space. Moreover, we showed that parameters describing process thresholds or influencing boundary conditions cannot be constrained. We furthermore conclude that, in order to apply the principle correctly, the model should be (1) physically based; i.e. fluxes should be defined as a gradient divided by a resistance, (2) the optimized flux should have a feedback on the gradient; i.e. the influence of boundary conditions on gradients should be minimal, (3) the temporal scale of the model should be chosen in such a way that the parameter that is optimized is constant over the modelling period, (4) only when the correct feedbacks are implemented the fluxes can be correctly optimized and (5) there should be a trade-off between two or more fluxes. Although our application of the maximum power principle did not work, and although the principle is a hypothesis that should still be thoroughly tested, we believe that the principle still has potential in advancing hydrological science.

scholarly journals Maximum entropy production: can it be used to constrain conceptual hydrological models?

2012 ◽  
Vol 9 (10) ◽  
pp. 11551-11581
Author(s):  
M. C. Westhoff ◽  
E. Zehe
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Degrees Of Freedom ◽  
Hydrological Models ◽  
Model Concept ◽  
Maximum Entropy Production ◽  
Principle Of Maximum Entropy ◽  
Optimality Principles ◽  
The Right ◽  
Principle Of Maximum

Abstract. In recent years, optimality principles have been proposed to constrain hydrological models. The principle of Maximum Entropy Production (MEP) is one of the proposed principles and is subject of this study. It states that a steady state system is organized in such a way that entropy production is maximized. However, within hydrology, tests against observations are still missing. The aim of this paper is to test the MEP principle to reduce equifinality of a simple conceptual (bucket) model. We used the principle of maximizing power, which is equivalent to MEP when a constant temperature is assumed. Power is determined by multiplying a flux with its gradient. We thus defined for each flux in the model a gradient and checked if parameter sets that maximize power also reproduce the observed water balance. Subsequently we concluded that with the used model concept, this does not work. It would be easy to reject the MEP hypothesis to explain our findings, but we believe that our test is incomplete. By referring to the flaws in our own model concept, we believe that many issues can be learned about how to use MEP to constrain hydrological models. Among others, the most important are: (1) fluxes should be defined as a gradient divided by a resistance, where the flux feeds back on the gradient; (2) there should be a trade-off between two or more different fluxes, where, in principle, only one resistance can be optimized and (3) each process should have the right degrees of freedom: what are the feedbacks on this flux and what limits the flux?

scholarly journals ESD Reviews: Thermodynamic optimality in Earth sciences. The missing constraints in modeling Earth system dynamics?

2019 ◽  
Author(s):  
Martijn Westhoff ◽  
Axel Kleidon ◽  
Stan Schymanski ◽  
Benjamin Dewals ◽  
Femke Nijsse ◽  
...  
Keyword(s):  
Earth Sciences ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Maximum Power ◽  
Model Parameters ◽  
Earth System ◽  
Maximum Entropy Production ◽  
Flux Gradient ◽  
Conversion Rates ◽  
Maximum Power Principle

Abstract. Thermodynamic optimality principles have been often used in Earth sciences to estimate model parameters or fluxes. Applications range from optimizing atmospheric meridional heat fluxes to sediment transport and from optimizing spatial flow patterns to dispersion coefficients for fresh and salt water mixing. However, it is not always clear what has to be optimized and how. In this paper we aimed to clarify terminology used in the literature and to infer how these principles have been used and when they give proper predictions of observed fluxes and states. We distinguish roughly four classes of applications: predictions using a flux-gradient feedback, predictions using a constant thermodynamic potential boundary conditions, predictions based on information theoretical approaches and comparative studies quantifying entropy production rates from observations at different sites. Here we mainly focus on the flux-gradient feedback, since it results in clear physical limits of energy conversion rates occurring in the Earth system and its subsystems. We show that within the flux-gradient feedback application, maximum entropy production is in many cases equivalent to maximum power and maximum energy dissipation. We advocate the maximum power principle above the more widely used maximum entropy production principle because entropy can be produced by all kinds of fluxes, but only optimized fluxes performing work coincided with observations. Furthermore, the maximum power principle links to the maximum amount of free energy that can be converted into another form of energy. This clearly separates the well defined physical conversion limit from the hypothesis that a system evolves to that limit of maximum power. Although attempts have been made to fundamentally explain why a system would evolve to such a maximum in power, there is still no consensus. Nevertheless, we think that when the maximum power approach is correctly and consistently used, the positive (or negative) results will speak for themselves. We end this review with some open research questions that may guide further research in this area.

A blueprint for thermodynamically consistent box models and a test bed for thermodynamic optimality principles

2020 ◽  
Author(s):  
Stan Schymanski ◽  
Martijn Westhoff
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Maximum Power ◽  
Great Promise ◽  
Mathematical Framework ◽  
System Boundaries ◽  
Maximum Entropy Production ◽  
Power Extraction ◽  
Box Models ◽  
Optimality Principles

<p>Thermodynamic optimality principles, such as maximum entropy production or maximum power extraction, hold a great promise to help explain self-organisation of various compartments of planet Earth, including the climate system, catchments and ecosystems. There is a growing number of examples for more or less successful use of these principles in earth system science, but a common systematic approach to the formulation of the relevant system boundaries, state variables and exchange fluxes has not yet emerged. Here we present a blueprint for the thermodynamically consistent formulation of box models and rigorous testing of optimality principles, in particular the maximum entropy production (MEP) and the maximum power (MP) principle. We investigate under what conditions these principles can be used to predict energy transfer coefficients across internal system boundaries and demonstrate that, contrary to common perception, these principles do not lead to similar predictions if energy and entropy balances are explicitly considered for the whole system and the defined sub-systems. We further highlight various pitfalls that may result in thermodynamically inconsistent models and potentially wrong conclusions about the implications of thermodynamic optimality principles. <br>The analysis is performed in an open source mathematical framework, using the notebook interface Jupyter, the programming language Python, Sympy and a newly developed package for Python, "Environmental Science using Symbolic Math" (ESSM, https://github.com/environmentalscience/essm). This ensures easy verifiability of the results and enables users to re-use and modify variable definitions, equations and mathematical solutions to suit their own thermodynamic problems. </p>

scholarly journals A Statistical Inference of the Principle of Maximum Entropy Production

2021 ◽  
Author(s):  
Martijn Veening
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Statistical Inference ◽  
Explanatory Power ◽  
Second Law Of Thermodynamics ◽  
General Validity ◽  
Maximum Entropy Production ◽  
Principle Of Maximum Entropy ◽  
Theoretical Paper ◽  
Principle Of Maximum

The maximization of entropy S within a closed system is accepted as an inevitability (as the second law of thermodynamics) by statistical inference alone. The Maximum Entropy Production Principle (MEPP) states that not only S maximizes, but $\dot{S}$ as well: a system will dissipate as fast as possible. There is still no consensus on the general validity of this MEPP, even though it shows remarkable explanatory power (both qualitatively and quantitatively), and has been empirically demonstrated for many domains. In this theoretical paper I provide a generalization of entropy gradients, to show that the MEPP actually follows from the same statistical inference, as that of the 2nd law of thermodynamics. For this generalization I only use the concepts of super-statespaces and microstate-density. These concepts also allow for the abstraction of 'Self Organizing Criticality' to a bifurcating local difference in this density, and allow for a generalization of the fundamentally unresolved concepts of 'chaos' and 'order'.

scholarly journals Using the Maximum Entropy Production approach to integrate energy budget modeling in a hydrological model

2019 ◽  
Author(s):  
Audrey Maheu ◽  
Islem Hajji ◽  
François Anctil ◽  
Daniel F. Nadeau ◽  
René Therrien
Keyword(s):  
Climate Change ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Energy Budget ◽  
Hydrological Model ◽  
Soil Column ◽  
Hydrologic Model ◽  
Hydrological Models ◽  
Potential Evaporation ◽  
Maximum Entropy Production

Abstract. Total terrestrial evaporation is a key process to understand the hydrological impacts of climate change given that warmer surface temperatures translate into an increase in the atmospheric evaporative demand. To simulate this flux, many hydrological models rely on the concept of potential evaporation (PET) although large differences have been observed in the response of PET models to climate change. The Maximum Entropy Production (MEP) model of land surface fluxes offers an alternative approach to simulate terrestrial evaporation in a simple and parsimonious way while fulfilling the physical constraint of energy budget closure and providing a distinct estimation of evaporation and transpiration. The objective of this work is to use the MEP model to integrate energy budget modeling within a hydrological model. We coupled the MEP model with HydroGeoSphere, an integrated surface and subsurface hydrologic model. As a proof-of-concept, we performed one-dimensional soil column simulations at three sites of the AmeriFlux network. The coupled HGS-MEP model produced realistic simulations of soil water content (RMSE between 0.03 and 0.05 m3 m−3, NSE between 0.30 and 0.92) and terrestrial evaporation (RMSE between 0.31 and 0.71 mm day−1, NSE between 0.65 and 0.88) under semiarid, Mediterranean and temperate climates. HGS-MEP outperformed the standalone HGS model where total terrestrial evaporation is derived from potential evaporation which we computed using the Penman-Monteith equation. This research demonstrated the potential of the MEP model to improve the simulation of total terrestrial evaporation in hydrological models, including for hydrological projections under climate change.

scholarly journals Statistical optimization for passive scalar transport: maximum entropy production versus maximum Kolmogorov–Sinai entropy

2015 ◽  
Vol 22 (2) ◽  
pp. 187-196 ◽  
Author(s):  
M. Mihelich ◽  
D. Faranda ◽  
B. Dubrulle ◽  
D. Paillard
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Passive Scalar ◽  
Scalar Transport ◽  
Zero Range Process ◽  
Maximum Entropy Production ◽  
Passive Scalar Transport ◽  
Optimal Resolution ◽  
Principle Of Maximum ◽  
Non Equilibrium

Abstract. We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov–Sinai entropy for a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov–Sinai entropy, seen as functions of a parameter f connected to the jump probability, admit a unique maximum denoted fmaxEP and fmaxKS. The behaviour of these two maxima is explored as a function of the system disequilibrium and the system resolution N. The main result of this paper is that fmaxEP and fmaxKS have the same Taylor expansion at first order in the deviation from equilibrium. We find that fmaxEP hardly depends on N whereas fmaxKS depends strongly on N. In particular, for a fixed difference of potential between the reservoirs, fmaxEP(N) tends towards a non-zero value, while fmaxKS(N) tends to 0 when N goes to infinity. For values of N typical of those adopted by Paltridge and climatologists working on maximum entropy production (N ≈ 10–100), we show that fmaxEP and fmaxKS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N* such that fmaxEP and fmaxKS coincide, at least up to a second-order parameter proportional to the non-equilibrium fluxes imposed to the boundaries. We find that the optimal resolution N* depends on the non-equilibrium fluxes, so that deeper convection should be represented on finer grids. This result points to the inadequacy of using a single grid for representing convection in climate and weather models. Moreover, the application of this principle to passive scalar transport parametrization is therefore expected to provide both the value of the optimal flux, and of the optimal number of degrees of freedom (resolution) to describe the system.

scholarly journals Maximum entropy production in environmental and ecological systems

2010 ◽  
Vol 365 (1545) ◽  
pp. 1297-1302 ◽  
Author(s):  
Axel Kleidon ◽  
Yadvinder Malhi ◽  
Peter M. Cox
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Atmospheric Composition ◽  
Maximum Entropy Production ◽  
Gaia Hypothesis ◽  
Atmosphere System ◽  
Global Biogeochemical Cycles ◽  
Principle Of Maximum ◽  
Thermodynamic Processes

The coupled biosphere–atmosphere system entails a vast range of processes at different scales, from ecosystem exchange fluxes of energy, water and carbon to the processes that drive global biogeochemical cycles, atmospheric composition and, ultimately, the planetary energy balance. These processes are generally complex with numerous interactions and feedbacks, and they are irreversible in their nature, thereby producing entropy. The proposed principle of maximum entropy production (MEP), based on statistical mechanics and information theory, states that thermodynamic processes far from thermodynamic equilibrium will adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate. This issue focuses on the latest development of applications of MEP to the biosphere–atmosphere system including aspects of the atmospheric circulation, the role of clouds, hydrology, vegetation effects, ecosystem exchange of energy and mass, biogeochemical interactions and the Gaia hypothesis. The examples shown in this special issue demonstrate the potential of MEP to contribute to improved understanding and modelling of the biosphere and the wider Earth system, and also explore limitations and constraints to the application of the MEP principle.

scholarly journals The two-box model of climate: limitations and applications to planetary habitability and maximum entropy production studies

2010 ◽  
Vol 365 (1545) ◽  
pp. 1349-1354 ◽  
Author(s):  
Ralph D. Lorenz
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Box Model ◽  
Maximum Entropy Production ◽  
First Order ◽  
Production Studies ◽  
Principle Of Maximum Entropy ◽  
Temperature Contrast ◽  
Planetary Habitability ◽  
Principle Of Maximum

The ‘two-box model’ of planetary climate is discussed. This model has been used to demonstrate consistency of the equator–pole temperature gradient on Earth, Mars and Titan with what would be predicted from a principle of maximum entropy production (MEP). While useful for exposition and for generating first-order estimates of planetary heat transports, it has too low a resolution to investigate climate systems with strong feedbacks. A two-box MEP model agrees well with the observed day : night temperature contrast observed on the extrasolar planet HD 189733b.

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