Thermodynamics, maximum power, and the dynamics of preferential river flow structures at the continental scale

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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 logtransformed 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.

Section: Discussionmentioning

confidence: 99%

Section: Model Set-upmentioning

confidence: 99%

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

Westhoff

Zehe

2013

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“…This limit results fundamentally from the laws of thermodynamics, as shown in the brief derivation in the Appendix A1, and surface exchange fluxes 525 are subjected to this limit. This limit relates very closely to a range of previous applications of thermodynamic limits to similar systems, e.g., to turbulent phenomena (Ozawa et al, 2001), planetary heat transport (Lorenz et al, 2001), to the atmospheric circulation (Kleidon et al, 2003(Kleidon et al, , 2006, and 530 to hydrology (Kleidon and Schymanski, 2008;Zehe et al, 2010;Kleidon et al, 2013;Zehe et al, 2013). While the existence of this thermodynamic limit should hence not be a concern, the question is rather whether land surface fluxes indeed operate at this limit, and whether the assumption of 535 the steady state is justified.…”

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confidence: 99%

Estimates of the climatological land surface energy and water balance derived from maximum convective power

Kleidon

Renner

Porada

2014

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Abstract. The land surface energy and water balances are tightly coupled by the partitioning of absorbed solar radiation into terrestrial radiation and the turbulent fluxes of sensible and latent heat, as well as the partitioning of precipitation into evaporation and runoff. Evaporation forms the critical link between these two balances. Its rate is strongly affected by turbulent exchange as it provides the means to efficiently exchange moisture between the heated, moist surface and the cooled, dry atmosphere. Here, we use the constraint that this mass exchange operates at the thermodynamic limit of maximum power to derive analytical expressions for the partitioning of the surface energy and water balances on land. We use satellite-derived forcing of absorbed solar radiation, surface temperature and precipitation to derive simple spatial estimates for the annual mean fluxes of sensible and latent heat and evaluate these estimates with the ERA-Interim reanalysis data set and observations of the discharge of large river basins. Given the extremely simple approach, we find that our estimates explain the climatic mean variations in net radiation, evaporation, and river discharge reasonably well. We conclude that our analytical, minimum approach provides adequate first order estimates of the surface energy and water balance on land and that the thermodynamic limit of maximum power provides a useful closure assumption to constrain the energy partitioning at the land surface.

“…In the PUB research program, data acquisition techniques (Hilgersom and Luxemburg, 2012), experimental studies (McMillan et al, 2012;Ali et al, 2012), advanced models and strategies (Harman, 2008), and new hydrological theories (Kleidon et al, 2013) have been developed to improve hydrological prediction results for ungauged zones.…”

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confidence: 99%

Stream flow simulation and verification in ungauged zones by coupling hydrological and hydrodynamic models: a case study of the Poyang Lake ungauged zone

Zhang

Chen

et al. 2017

Abstract. To solve the problem of estimating and verifying stream flow without direct observation data, we estimated stream flow in ungauged zones by coupling a hydrological model with a hydrodynamic model, using the Poyang Lake basin as a test case. To simulate the stream flow of the ungauged zone, we built a soil and water assessment tool (SWAT) model for the entire catchment area covering the upstream gauged area and ungauged zone, and then calibrated the SWAT model using the data in the gauged area. To verify the results, we built two hydrodynamic scenarios (the original and adjusted scenarios) for Poyang Lake using the Delft3D model. In the original scenario, the upstream boundary condition is the observed stream flow from the upstream gauged area, while, in the adjusted scenario, it is the sum of the observed stream flow from the gauged area and the simulated stream flow from the ungauged zone. The experimental results showed that there is a stronger correlation and lower bias (R 2 = 0.81, PBIAS = 10.00 %) between the observed and simulated stream flow in the adjusted scenario compared to that (R 2 = 0.77, PBIAS = 20.10 %) in the original scenario, suggesting the simulated stream flow of the ungauged zone is reasonable. Using this method, we estimated the stream flow of the Poyang Lake ungauged zone as 16.4 ± 6.2 billion m 3 a −1 , representing ∼ 11.24 % of the annual total water yield of the entire watershed. Of the annual water yield, 70 % (11.48 billion m 3 a −1 ) is concentrated in the wet season, while 30 % (4.92 billion m 3 a −1 ) comes from the dry season. The ungauged stream flow significantly improves the water balance with the closing error decreased by 13.48 billion m 3 a −1 (10.10 % of the total annual water resource) from 30.20 ± 9.1 billion m 3 a −1 (20.10 % of the total annual water resource) to 16.72 ± 8.53 billion m 3 a −1 (10.00 % of the total annual water resource). The method can be extended to other lake, river, or ocean basins where observation data is unavailable.