scholarly journals Morphological controls on Hortonian surface runoff: An interpretation of steady-state energy patterns, maximum power states and dissipation regimes within a thermodynamic framework

2021 ◽  
Author(s):  
Samuel Schroers ◽  
Olivier Eiff ◽  
Axel Kleidon ◽  
Ulrike Scherer ◽  
Jan Wienhöfer ◽  
...  
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Surface Runoff ◽  
Overland Flow ◽  
Dynamic Equilibrium ◽  
Flow Path ◽  
Maximum Power ◽  
Rainfall Simulation ◽  
Sheet Flow ◽  
Thermodynamic Framework

Abstract. Recent developments in hydrology have led to a new perspective on runoff processes, extending beyond the classical mass dynamics of water in a catchment. For instance, stream flow has been analysed in a thermodynamic framework, which allows the incorporation of two additional physical laws and enhances our understanding of catchments as open environmental systems. Related investigations suggested that energetic extremal principles might constrain hydrological processes, because the latter are associated with conversions and dissipation of free energy. Here we expand this thermodynamic perspective by exploring how hillslope structures at the macro- and microscale control the free energy balance of Hortonian overland flow. We put special emphasis on the transitions of surface runoff processes at the hillslope scale, as hillslopes energetically behave distinctly different in comparison to fluvial systems. To this end, we develop a general theory of surface runoff and of the related conversion of geopotential energy gradients into other forms of energy, particularly kinetic energy as the driver of erosion and sediment transport. We then use this framework at a macroscopic scale to analyse how combinations of typical hillslopes profiles and width distributions control the spatial patterns of steady-state stream power and energy dissipation along the flow path. At the microscale, we analyse flow concentration in rills and its influence on the distribution of energy and dissipation in space. Therefore, we develop a new numerical method for the Catflow model, which allows a dynamical separation of Hortonian surface runoff between a rill- and a sheet flow domain. We calibrated the new Catflow-Rill model to rainfall simulation experiments and observed overland flow in the Weiherbach catchment and found evidence that flow accumulation in rills serves as a means to redistribute energy gradients in space, therefore minimizing energy expenditure along the flow path, while also maximizing overall power of the system. Our results indicate that laminar sheet flow and turbulent rill flow on hillslopes develop to a dynamic equilibrium that corresponds to a maximum power state, and that the transition of flow from one domain into the other is marked by an energy maximum in space.

scholarly journals Hortonian Overland Flow, Hillslope Morphology and Stream Power I: Spatial Energy Distributions and Steady-state Power Maxima

2021 ◽  
Author(s):  
Samuel Schroers ◽  
Olivier Eiff ◽  
Axel Kleidon ◽  
Jan Wienhöfer ◽  
Erwin Zehe
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Energy Dissipation ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Overland Flow ◽  
Slope Angle ◽  
Order Estimate ◽  
Energy Fluxes ◽  
Stream Power

Abstract. Recent developments in hydrology have led to a new perspective on runoff processes, extending beyond the classical mass dynamics of water in a catchment. For instance, stream flow has been analyzed in a thermodynamic framework, which allows the incorporation of two additional physical laws and enhances our understanding of catchments as open environmental systems. Related investigations suggested that energetic extremal principles might constrain hydrological processes, because the latter are associated with conversions and dissipation of free energy. Here we expand this thermodynamic perspective by exploring how macro and micro hillslope structures control the free energy balance of Hortonian overland flow. This may ultimately help understanding why these structures have evolved to their present shape. To this end, we develop a general theory of surface runoff and of the related conversion of geopotential energy gradients into other forms of energy, particularly kinetic energy as driver of erosion and sediment transport. We then use this framework to analyze how combinations of typical hillslopes profiles and width distributions control the spatial patterns of steady state stream power and energy dissipation along the flow path. Additionally, we provide a first order estimate whether and when rills reduce the overall energy dissipation compared to sheet flow. Finally, we relate accumulated stream power of linear hillslopes to slope angles, closing the loop to Horton's original formulation of erosion force. The analytical analysis of stream power reveals that the common formulation, a function of the depth-discharge product is a reduced version of the more general equations if we neglect changes in velocity and discharge in space. The full equations of stream power result in maximum energy fluxes in space for sinusoidal and exponential hillslope profiles, while linear and negative exponential forms unlimitedly increase these fluxes in the downstream direction. Depending on geometry, rill flow increases or decreases kinetic energy fluxes downslope, effectively counteracting or increasing the dissipation of potential energy. For accumulated power in space for steady state runoff, we find that on linear hillslopes a slope angle of 45° maximizes the conversion of potential energy into dissipation and an angle of 35° maximizes the conversion of potential energy into kinetic energy.

Modelling of Solute Transfer to Surface Runoff

1992 ◽  
Vol 26 (7-8) ◽  
pp. 1851-1856 ◽  
Author(s):  
J. L. Lai ◽  
K. S. L. Lo
Keyword(s):  
Potassium Chloride ◽  
Surface Runoff ◽  
Laboratory Experiments ◽  
Overland Flow ◽  
Chloride Concentration ◽  
Runoff Water ◽  
Mixing Depth ◽  
Change Rate ◽  
Solute Transfer ◽  
The Media

A mixing-based model for describing solute transfer to overland flow was developed. This model included a time-dependent mixing depth of the top layer and a complete-mixed surface runoff zone. In a series of laboratory experiments, runoff was passed at various velocities and depths over a medium bed. The media were saturated with uniform concentration of potassium chloride solution. Runoff water was sampled at the beginning and end of the flume and the potassium chloride concentration analyzed. Using this model, dimensionless ultimate mixing depth and dimensionless change rate of mixing depth from experimental data were investigated and implemented. The results showed that the Reynolds number and relative roughness are two important factors.

Transport of herbicides and nutrients in surface runoff from corn cropland in southern Ontario

1994 ◽  
Vol 74 (1) ◽  
pp. 59-66 ◽  
Author(s):  
B. T. Bowman ◽  
G. J. Wall ◽  
D. J. King
Keyword(s):  
Water Quality ◽  
Surface Runoff ◽  
Soil Nutrient ◽  
Rainfall Simulation ◽  
Simulated Rainfall ◽  
Runoff Water ◽  
Surface Transport ◽  
Nitrate N ◽  
Runoff Losses ◽  
Water Quality Objectives

The risk of surface-water contamination by herbicides is greatest following application to cropland when the active ingredients are at the maximum concentration and the soil is the most vulnerable to erosion following cultivation. This study determined the magnitude of surface runoff losses of herbicide and nutrients at, and subsequent to, application. The first of three weekly 10-min, 2.6-cm rainfalls were simulated on triplicated 1-m plots (a set) on which corn had been planted and the herbicide (metolachlor/atrazine, 1.5:1.0) and fertilizer (28% N at 123 kg ha−1) had just been applied. Identical simulations were applied to two other adjacent plot sets (protected from rainfall) 1 and 2 wk following herbicide application. Runoff (natural, simulated) was monitored for soil, nutrient and herbicide losses. Concentrations of total phosphorus in surface runoff water and nitrate N in field-filtered samples were not significantly influenced by the time of the rainfall simulation but exceeded provincial water-quality objectives. Atrazine and metolachlor runoff losses were greatest from simulated rainfall (about 5% loss) immediately following application. Subsequent simulated rainfall usually resulted in < 1% herbicide runoff losses. Herbicide concentrations in all plot runoff samples exceeded provincial drinking-water quality objectives. Since herbicide surface transport is primarily in the solution phase (not via association with soil particles), water-management conservation technologies are the key to retaining these chemicals on cropland. Key words: Herbicide, runoff, rainfall simulation, partitioning, water quality

scholarly journals Verification of Equation for Evaluating Dislocation Density during Steady-state Creep of Metals

2017 ◽  
Vol 6 (2) ◽  
pp. 20 ◽  
Author(s):  
Manabu Tamura
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Dislocation Density ◽  
Shear Modulus ◽  
Strain Rate ◽  
Gibbs Free Energy ◽  
Steady State Creep ◽  
Austenitic Steels ◽  
Exponential Factor ◽  
Delta G

Ninety-two sets of observed dislocation densities for crept specimens of 21 types of ferritic/martensitic and austenitic steels, Al, W, Mo, and Mg alloys, Cu, and Ti including germanium single crystals were collected to verify an equation for evaluating the dislocation density during steady-state creep proposed by Tamura and Abe (2015). The activation energy, Qex, activation volume, Vex, and Larson–Miller constant, Cex, were calculated from the creep data. Using these parameter constants, the strain rate, and the temperature dependence of the shear modulus, a correction term, Gamma, was back-calculated from the observed dislocation density for each material. Gamma is defined in the present paper as a function of the temperature dependences of both the shear modulus and pre-exponential factor of the strain rate. The values of Gamma range from −394 to 233  and average 2.1 KJmol-1, which is a value considerably lower than the average value of Qex (410.4 KJmol-1), and values of Gamma are mainly within the range from 0 to 50 KJmol-1. The change in Gibbs free energy, Delta G, for creep deformation is obtained using the calculated value of , and the empirical relation Delta G~Delta GD is found, where Delta GD is the change in Gibbs free energy for self-diffusion of the main componential element of each material. Experimental data confirm the validity of the evaluation equation for the dislocation density.

Experimental evidence for the need of thermodynamic considerations in modelling of anaerobic environmental bioprocesses

1997 ◽  
Vol 36 (10) ◽  
pp. 109-115 ◽  
Author(s):  
Choon-Yee Hoh ◽  
Ralf Cord-Ruwisch
Keyword(s):  
Free Energy ◽  
Experimental Evidence ◽  
Positive Reaction ◽  
Rate Equation ◽  
Dynamic Equilibrium ◽  
Reaction Rates ◽  
Product Inhibition ◽  
Experimental Results ◽  
Biological Processes ◽  
Laws Of Thermodynamics

For modeling of biological processes that operate close to the dynamic equilibrium (eg. anaerobic processes), it is critical to prevent the prediction of positive reaction rates when the reaction has already reached dynamic equilibrium. Traditional Michaelis-Menten based models were found to violate the laws of thermodynamics as they predicted positive reaction rates for reactions that were endergonic due to high endproduct concentrations. The inclusion of empirical “product inhibition factors” as suggested by previous work could not prevent this problem. This paper compares the predictions of the Michaelis-Menten Model (with and without product inhibition factors) and the Equilibrium Based Model (which has a thermodynamic term introduced into its rate equation) with experimental results of reactions in anaerobic bacterial environments. In contrast to the Michaelis-Menten based models that used traditional inhibition factors, the Equilibrium Based Model correctly predicted the nature and the degree of inhibition due to endproduct accumulation. Moreover, this model also correctly predicted when reaction rates must be zero due to the free energy change of the conversion reaction being zero. With these added advantages, the Equilibrium Based Model thus seemed to provide a scientifically correct and more realistic basis for a variety of models that describe anaerobic biosystems.

scholarly journals Enhanced DEM-based flow path delineation methods for urban flood modelling

2012 ◽  
Vol 15 (2) ◽  
pp. 568-579
Author(s):  
J. P. Leitão ◽  
D. Prodanović ◽  
S. Boonya-aroonnet ◽  
Č. Maksimović
Keyword(s):  
Urban Areas ◽  
Overland Flow ◽  
Flow Path ◽  
Flow Paths ◽  
Urban Flood ◽  
Bouncing Ball ◽  
Digital Elevation ◽  
Synthetic Test ◽  
Water Accumulation ◽  
Flooding Events

In order to simulate surface runoff and flooding, one-dimensional (1D) overland flow networks can be automatically delineated using digital elevation models (DEM). The resulting network comprises flow paths and terrain depressions/ponds and is essential to reliably model pluvial (surface) flooding events in urban areas by so-called 1D/1D models. Conventional automatic DEM-based flow path delineation methods have problems in producing realistic overland flow paths when detailed high-resolution DEMs of urban areas are used. The aim of this paper is to present the results of research and development of three enhanced DEM-based overland flow path delineation methods; these methods are triggered when the conventional flow path delineation process stops due to a flow obstacle. Two of the methods, the ‘bouncing ball and buildings’ and ‘bouncing ball and A*’ methods, are based on the conventional ‘bouncing ball’ concept; the third proposed method, the ‘sliding ball’ method, is based on the physical water accumulation concept. These enhanced methods were tested and their results were compared with results obtained using two conventional flow path delineation methods using a semi-synthetic test DEM. The results showed significant improvements in terms of the reliability of the delineated overland flow paths when using these enhanced methods.

scholarly journals Scaling of Power Output in Fast Muscle Fibres of the Atlantic Cod During Cyclical Contractions

1992 ◽  
Vol 170 (1) ◽  
pp. 143-154 ◽  
Author(s):  
M. ELIZABETH ANDERSON ◽  
IAN A. JOHNSTON
Keyword(s):  
Steady State ◽  
Power Output ◽  
Standard Length ◽  
Atlantic Cod ◽  
Maximum Power ◽  
Fast Muscle ◽  
Muscle Fibres ◽  
Cycle Frequency ◽  
Maximum Power Output ◽  
Length Changes

Fast muscle fibres were isolated from abdominal myotomes of Atlantic cod (Gadus morhua L.) ranging in size from 10 to 63 cm standard length (Ls). Muscle fibres were subjected to sinusoidal length changes about their resting length (Lf) and stimulated at a selected phase of the strain cycle. The work performed in each oscillatory cycle was calculated from plots of force against muscle length, the area of the resulting loop being net work. Strain and the number and timing of stimuli were adjusted to maximise positive work per cycle over a range of cycle frequencies at 8°C. Force, and hence power output, declined with increasing cycles of oscillation until reaching a steady state around the ninth cycle. The strain required for maximum power output (Wmax) was ±7-11% of Lf in fish shorter than 18 cm standard length, but decreased to ±5 % of Lf in larger fish. The cycle frequency required for Wmax also declined with increasing fish length, scaling to Ls−0.51 under steady-state conditions (cycles 9–12). At the optimum cycle frequency and strain the maximum contraction velocity scaled to Ls−0.79. The maximum stress (Pmax) produced within a cycle was highest in the second cycle, ranging from 51.3 kPa in 10 cm fish to 81.8 kPa in 60 cm fish (Pmax=28.2Ls0.25). Under steady-state conditions the maximum power output per kilogram wet muscle mass was found to range from 27.5 W in a 10 cm Ls cod to 16.4 W in a 60 cm Ls cod, scaling with Ls−0.29 and body mass (Mb)−0.10 Note: To whom reprint requests should be sent

scholarly journals The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet

2011 ◽  
Vol 5 (3) ◽  
pp. 727-740 ◽  
Author(s):  
M. A. Martin ◽  
R. Winkelmann ◽  
M. Haseloff ◽  
T. Albrecht ◽  
E. Bueler ◽  
...  
Keyword(s):  
Steady State ◽  
Dynamic Equilibrium ◽  
Ice Sheet ◽  
Surface Velocity ◽  
Surface Mass ◽  
Ross Ice Shelf ◽  
Bed Topography ◽  
Melt Distribution ◽  
Spreading Rates ◽  
Equilibrium Simulation

Abstract. We present a dynamic equilibrium simulation of the ice sheet-shelf system on Antarctica with the Potsdam Parallel Ice Sheet Model (PISM-PIK). The simulation is initialized with present-day conditions for bed topography and ice thickness and then run to steady state with constant present-day surface mass balance. Surface temperature and sub-shelf basal melt distribution are parameterized. Grounding lines and calving fronts are free to evolve, and their modeled equilibrium state is compared to observational data. A physically-motivated calving law based on horizontal spreading rates allows for realistic calving fronts for various types of shelves. Steady-state dynamics including surface velocity and ice flux are analyzed for whole Antarctica and the Ronne-Filchner and Ross ice shelf areas in particular. The results show that the different flow regimes in sheet and shelves, and the transition zone between them, are captured reasonably well, supporting the approach of superposition of SIA and SSA for the representation of fast motion of grounded ice. This approach also leads to a natural emergence of sliding-dominated flow in stream-like features in this new 3-D marine ice sheet model.

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