Articles | Volume 25, issue 10
https://doi.org/10.5194/hess-25-5337-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-25-5337-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
05 Oct 2021
Research article |
| 05 Oct 2021
| 05 Oct 2021
Preferential pathways for fluid and solutes in heterogeneous groundwater systems: self-organization, entropy, work
Karlsruhe Institute of Technology (KIT), Institute of Water and River Basin Management, Karlsruhe, Germany
Ralf Loritz
Karlsruhe Institute of Technology (KIT), Institute of Water and River Basin Management, Karlsruhe, Germany
Yaniv Edery
Technion – Israel Institute
of Technology, Haifa, Israel
Brian Berkowitz
Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot, Israel
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Ashish Manoj J, Ralf Loritz, Hoshin Gupta, and Erwin Zehe
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Svenja Hoffmeister, Rafael Bohn Reckziegel, Ben du Toit, Sibylle K. Hassler, Florian Kestel, Rebekka Maier, Jonathan P. Sheppard, and Erwin Zehe
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We identified and analysed the major atmospheric components of rain-intense thunderstorms that can eventually lead to flash floods: high atmospheric moisture, sufficient latent instability, and weak thunderstorm cell motion. Between 1981 and 2020, atmospheric conditions became likelier to support strong thunderstorms. However, the occurrence of extreme rainfall events as well as their rainfall intensity remained mostly unchanged.
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Short summary
Short summary
In this study, we combine a deep-learning approach that predicts sap flow with a hydrological model to improve soil moisture and transpiration estimates at the catchment scale. Our results highlight that hybrid-model approaches, combining machine learning with physically based models, are a promising way to improve our ability to make hydrological predictions.
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Hydrol. Earth Syst. Sci., 26, 3125–3150, https://doi.org/10.5194/hess-26-3125-2022, https://doi.org/10.5194/hess-26-3125-2022, 2022
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In hydrology the formation of landform patterns is of special interest as changing forcings of the natural systems, such as climate or land use, will change these structures. In our study we developed a thermodynamic framework for surface runoff on hillslopes and highlight the differences of energy conversion patterns on two related spatial and temporal scales. The results indicate that surface runoff on hillslopes approaches a maximum power state.
Brian Berkowitz
Hydrol. Earth Syst. Sci., 26, 2161–2180, https://doi.org/10.5194/hess-26-2161-2022, https://doi.org/10.5194/hess-26-2161-2022, 2022
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Short summary
Extensive efforts have focused on quantifying conservative chemical transport in geological formations. We assert that an explicit accounting of temporal information, under uncertainty, in addition to spatial information, is fundamental to an effective modeling formulation. We further assert that efforts to apply chemical transport equations at large length scales, based on measurements and model parameter values relevant to significantly smaller length scales, are an unattainable
holy grail.
Alexander Sternagel, Ralf Loritz, Brian Berkowitz, and Erwin Zehe
Hydrol. Earth Syst. Sci., 26, 1615–1629, https://doi.org/10.5194/hess-26-1615-2022, https://doi.org/10.5194/hess-26-1615-2022, 2022
Short summary
Short summary
We present a (physically based) Lagrangian approach to simulate diffusive mixing processes on the pore scale beyond perfectly mixed conditions. Results show the feasibility of the approach for reproducing measured mixing times and concentrations of isotopes over pore sizes and that typical shapes of breakthrough curves (normally associated with non-uniform transport in heterogeneous soils) may also occur as a result of imperfect subscale mixing in a macroscopically homogeneous soil matrix.
Yaniv Edery, Martin Stolar, Giovanni Porta, and Alberto Guadagnini
Hydrol. Earth Syst. Sci., 25, 5905–5915, https://doi.org/10.5194/hess-25-5905-2021, https://doi.org/10.5194/hess-25-5905-2021, 2021
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The interplay between dissolution, precipitation and transport is widely encountered in porous media, from CO2 storage to cave formation in carbonate rocks. We show that dissolution occurs along preferential flow paths with high hydraulic conductivity, while precipitation occurs at locations close to yet separated from these flow paths, thus further funneling the flow and changing the probability density function of the transport, as measured on the altered conductivity field at various times.
Jan Bondy, Jan Wienhöfer, Laurent Pfister, and Erwin Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2021-174, https://doi.org/10.5194/hess-2021-174, 2021
Manuscript not accepted for further review
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The Budyko curve is a widely-used and simple framework to predict the mean water balance of river catchments. While many catchments are in close accordance with the Budyko curve, others show more or less significant deviations. Our study aims at better understanding the role of soil storage characteristics in the mean water balance and offsets from the Budyko curve. Soil storage proved to be a very sensitive property and potentially explains significant deviations from the curve.
Alexander Sternagel, Ralf Loritz, Julian Klaus, Brian Berkowitz, and Erwin Zehe
Hydrol. Earth Syst. Sci., 25, 1483–1508, https://doi.org/10.5194/hess-25-1483-2021, https://doi.org/10.5194/hess-25-1483-2021, 2021
Short summary
Short summary
The key innovation of the study is a method to simulate reactive solute transport in the vadose zone within a Lagrangian framework. We extend the LAST-Model with a method to account for non-linear sorption and first-order degradation processes during unsaturated transport of reactive substances in the matrix and macropores. Model evaluations using bromide and pesticide data from irrigation experiments under different flow conditions on various timescales show the feasibility of the method.
Samuel Schroers, Olivier Eiff, Axel Kleidon, Jan Wienhöfer, and Erwin Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2021-79, https://doi.org/10.5194/hess-2021-79, 2021
Manuscript not accepted for further review
Short summary
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In this study we ask the basic question why surface runoff forms drainage networks and confluences at all and how structural macro form and micro topography is a result of thermodynamic laws. We find that on a macro level hillslopes should tend from negative exponential towards exponential forms and that on a micro level the formation of rills goes hand in hand with drainage network formation of river basins. We hypothesize that we can learn more about erosion processes if we extend this theory.
Nicolas Björn Rodriguez, Laurent Pfister, Erwin Zehe, and Julian Klaus
Hydrol. Earth Syst. Sci., 25, 401–428, https://doi.org/10.5194/hess-25-401-2021, https://doi.org/10.5194/hess-25-401-2021, 2021
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Different parts of water have often been used as tracers to determine the age of water in streams. The stable tracers, such as deuterium, are thought to be unable to reveal old water compared to the radioactive tracer called tritium. We used both tracers, measured in precipitation and in a stream in Luxembourg, to show that this is not necessarily true. It is, in fact, advantageous to use the two tracers together, and we recommend systematically using tritium in future studies.
Ralf Loritz, Markus Hrachowitz, Malte Neuper, and Erwin Zehe
Hydrol. Earth Syst. Sci., 25, 147–167, https://doi.org/10.5194/hess-25-147-2021, https://doi.org/10.5194/hess-25-147-2021, 2021
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This study investigates the role and value of distributed rainfall in the runoff generation of a mesoscale catchment. We compare the performance of different hydrological models at different periods and show that a distributed model driven by distributed rainfall yields improved performances only during certain periods. We then step beyond this finding and develop a spatially adaptive model that is capable of dynamically adjusting its spatial model structure in time.
Conrad Jackisch, Samuel Knoblauch, Theresa Blume, Erwin Zehe, and Sibylle K. Hassler
Biogeosciences, 17, 5787–5808, https://doi.org/10.5194/bg-17-5787-2020, https://doi.org/10.5194/bg-17-5787-2020, 2020
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We developed software to calculate the root water uptake (RWU) of beech tree roots from soil moisture dynamics. We present our approach and compare RWU to measured sap flow in the tree stem. The study relates to two sites that are similar in topography and weather but with contrasting soils. While sap flow is very similar between the two sites, the RWU is different. This suggests that soil characteristics have substantial influence. Our easy-to-implement RWU estimate may help further studies.
Stephanie Thiesen, Diego M. Vieira, Mirko Mälicke, Ralf Loritz, J. Florian Wellmann, and Uwe Ehret
Hydrol. Earth Syst. Sci., 24, 4523–4540, https://doi.org/10.5194/hess-24-4523-2020, https://doi.org/10.5194/hess-24-4523-2020, 2020
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A spatial interpolator has been proposed for exploring the information content of the data in the light of geostatistics and information theory. It showed comparable results to traditional interpolators, with the advantage of presenting generalization properties. We discussed three different ways of combining distributions and their implications for the probabilistic results. By its construction, the method provides a suitable and flexible framework for uncertainty analysis and decision-making.
Cited articles
Ababou, R., McLaughlin, D., Gelhar, L. W., and Tompson, A. F. B.: Numerical
simulation of three-dimensional saturated flow in randomly heterogeneous
porous media, Transport Porous Med., 4, 549–565, 1989.
Applebaum, D.: Probability and Information, 1st edn., Cambridge University Press, Cambridge, 1996.
Becker, M. W. and Shapiro, A. M.: Tracer transport in fractured crystalline
rock: Evidence of nondiffusive breakthrough tailing, Water Resour.
Res., 36, 1677–1686, 2000.
Ben-Naim, A.: A Farewell to Entropy, World Scientific, chap. 1,
https://doi.org/10.1142/6469, 2008.
Berkowitz, B.: Characterizing flow and transport in fractured geological
media: A review, Adv. Water Resour., 25, 861–884, 2002.
Berkowitz, B. and Scher, H.: Anomalous transport in correlated velocity
fields, Phys. Rev. E., 81, 11128, https://doi.org/10.1103/PhysRevE.81.011128, 2010.
Berkowitz, B. and Zehe, E.: Surface water and groundwater: unifying conceptualization and quantification of the two “water worlds”, Hydrol. Earth Syst. Sci., 24, 1831–1858, https://doi.org/10.5194/hess-24-1831-2020, 2020.
Berkowitz, B., Cortis, A., Dentz, M., and Scher, H.: Modeling non-Fickian transport in geological formations as a continuous time random walk, Rev. Geophys., 44, RG2003, https://doi.org/10.1029/2005RG000178, 2006.
Beven, K. and Germann, P.: Water-Flow In Soil Macropores .2. A Combined
Flow Model, J. Soil Sci., 32, 15–29, 1981.
Beven, K. and Germann, P.: Macropores And Water-Flow In Soils, Water
Resour. Res., 18, 1311–1325, 1982.
Bianchi, M. and Pedretti, D.: Geological entropy and solute transport in
heterogeneous porous media, Water Resour. Res., 53, 4691–4708,
https://doi.org/10.1002/2016wr020195, 2017.
Bianchi, M. and Pedretti, D.: An entrogram-based approach to describe
spatial heterogeneity with applications to solute transport in porous media,
Water Resour. Res., 54, 4432–4448, https://doi.org/10.1029/2018wr022827, 2018.
Bianchi, M., Zheng, C., Wilson, C., Tick, G. R., Liu, G., and Gorelick, S. M.:
Spatial connectivity in a highly heterogeneous aquifer: From cores to
preferential flow paths, Water Resour. Res., 47, W05524,
https://doi.org/10.1029/2009WR008966, 2011.
Bolt, G. H. and Frissel, M. J.: Thermodynamics of soil moisture, Neth.
J. Agr. Sci., 8, 57–78, 1960.
Chiogna, G. and Rolle, M.: Entropy-based critical reaction time for
mixing-controlled reactive transport, Water Resour. Res., 53,
7488–7498, https://doi.org/10.1002/2017WR020522, 2017.
Cirpka, O. A. and Kitanidis, P. K.: Characterization of mixing and dilution in
heterogeneous aquifers by means of local temporal moments, Water Resour.
Res., 36, 1221–1236, 2000.
Clausius, R.: Über die Art der Bewegung, welche wir Wärme nennen,
Annalen der Physik und Chemie, 79, 353–380, 1857.
de Dreuzy, J.-R., Carrera, J., Dentz, M., and Le Borgne, T.: Time evolution of
mixing in heterogeneous porous media, Water Resour. Res., 48, W06511,
https://doi.org/10.1029/2011WR011360, 2012.
Dell'Oca, A., Guadagnini, A., and Riva, M.: Interpretation of multi-scale permeability data through an information theory perspective, Hydrol. Earth Syst. Sci., 24, 3097–3109, https://doi.org/10.5194/hess-24-3097-2020, 2020.
Domenico, P. A. and Schwartz, F. W.: Physical and Chemical Hydrogeology,
John Wiley, New York, 1990.
Edery, Y., Guadagnini, A., Scher, H., and Berkowitz, B.: Origins of
anomalous transport in disordered media: Structural and dynamic controls,
Water Resour. Res., 50, 1490–1505, https://doi.org/10.1002/2013WR015111, 2014.
Edery, Y., Stolar, M., Porta, G., and Guadagnini, A.: Feedback mechanisms between precipitation and dissolution reactions across randomly heterogeneous conductivity fields, Hydrol. Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/hess-2021-238, in review, 2021.
Fiori, A. and Jankovic, I.: On Preferential Flow, Channeling and
Connectivity in Heterogeneous Porous Formations, Math. Geosci., 44, 133–145,
https://doi.org/10.1007/s11004-011-9365-2, 2012.
Fahle, M., Hohenbrink, T. L., Dietrich, O., and Lischeid, G.: Temporal
variability of the optimal monitoring setup assessed using information
theory, Water Resour. Res., 51, 7723–7743, https://doi.org/10.1002/2015WR017137, 2015.
Flury, M., Flühler, H., Leuenberger, J., and Jury, W. A.: Susceptibility
of soils to preferential flow of water: a field study, Water Resour.
Res., 30, 1945–1954, 1994.
Groves, C. G. and Howard, A. D.: Early development of karst systems: 1.
Preferential flow path enlargement under laminar flow, Water Resour.
Res., 30, 2837–2846,
https://doi.org/10.1029/94WR01303, 1994.
Gómez-Hernánez, J. J., Sahuquillo, A., and Capilla, J.: Stochastic
simulation of transmissivity fields conditional to both transmissivity and
piezometric data – I. Theory, J. Hydrol., 203, 162–174,
https://doi.org/10.1016/S0022-1694(97)00098-X, 1997.
Haken, H.: Synergetics: An Introduction; Nonequilibrium Phase Transitions and Self-organization in Physics, Chemistry and Biology, 355 pp., Springer, Berlin, 1983.
Jackisch, C., Angermann, L., Allroggen, N., Sprenger, M., Blume, T., Tronicke, J., and Zehe, E.: Form and function in hillslope hydrology: in situ imaging and characterization of flow-relevant structures, Hydrol. Earth Syst. Sci., 21, 3749–3775, https://doi.org/10.5194/hess-21-3749-2017, 2017.
Jaynes, E. T.: Information theory and statistical mechanics, Phys. Rev. Lett., 106, 620–630, 1957.
Guadagnini, A. and Neuman, S. P.: Nonlocal and localized analyses of
conditional mean steady state flow in bounded, randomly nonuniform domains,
1, theory and computational approach, Water Resour. Res., 35, 2999–3018,
1999.
Hergarten, S., Winkler, G., and Birk, S.: Transferring the concept of minimum energy dissipation from river networks to subsurface flow patterns, Hydrol. Earth Syst. Sci., 18, 4277–4288, https://doi.org/10.5194/hess-18-4277-2014, 2014.
Howard, A. D.: Optimal angles of stream junctions: geometric stability to capture and minimum power criteria, Water Resour. Res., 7, 863–873, 1971.
Howard, A. D.: Theoretical model of optimal drainage networks, Water Resour.
Res., 26, 2107–2117, 1990.
Klaus, J. and Zehe, E.: A novel explicit approach to model bromide and pesticide transport in connected soil structures, Hydrol. Earth Syst. Sci., 15, 2127–2144, https://doi.org/10.5194/hess-15-2127-2011, 2011.
Kleidon, A.: Thermodynamic foundations of the Earth system, Cambridge University Press, New York
NY, 2016.
Kleidon, A., Zehe, E., Ehret, U., and Scherer, U.: Thermodynamics, maximum power, and the dynamics of preferential river flow structures at the continental scale, Hydrol. Earth Syst. Sci., 17, 225–251, https://doi.org/10.5194/hess-17-225-2013, 2013.
Kleidon, A., Renner, M., and Porada, P.: Estimates of the climatological land surface energy and water balance derived from maximum convective power, Hydrol. Earth Syst. Sci., 18, 2201–2218, https://doi.org/10.5194/hess-18-2201-2014, 2014.
Kitanidis, P. K.: The concept of the Dilution Index, Water Resour.
Res., 30, 2011–2026, https://doi.org/10.1029/94WR00762,
1994.
Kondepudi, D. and Prigogine, I.: Modern Thermodynamics: From Heat Engines
to Dissipative Structures, John Wiley Chichester, UK, 1998.
LaBolle, E. M. and Fogg, G. E.: Role of molecular diffusion in contaminant
migration and recovery in an alluvial aquifer system, Transport Porous
Med., 42, 155–179, 2001.
Levy, M. and Berkowitz, B.: Measurement and analysis of non-Fickian
dispersion in heterogeneous porous media, J. Contam. Hydrol., 64, 203–226,
2003.
Loritz, R., Gupta, H., Jackisch, C., Westhoff, M., Kleidon, A., Ehret, U., and Zehe, E.: On the dynamic nature of hydrological similarity, Hydrol. Earth Syst. Sci., 22, 3663–3684, https://doi.org/10.5194/hess-22-3663-2018, 2018.
Loritz, R., Kleidon, A., Jackisch, C., Westhoff, M., Ehret, U., Gupta, H., and Zehe, E.: A topographic index explaining hydrological similarity by accounting for the joint controls of runoff formation, Hydrol. Earth Syst. Sci., 23, 3807–3821, https://doi.org/10.5194/hess-23-3807-2019, 2019.
Loritz, R., Hrachowitz, M., Neuper, M., and Zehe, E.: The role and value of distributed precipitation data in hydrological models, Hydrol. Earth Syst. Sci., 25, 147–167, https://doi.org/10.5194/hess-25-147-2021, 2021.
Lotka, A. J.: Contribution to the energetics of evolution, P. Natl. Acad.
Sci. USA, 8, 147–151, 1922a.
Lotka, A. J.: Natural selection as a physical principle, P. Natl. Acad. Sci.
USA, 8, 151–154, 1922b.
Mälicke, M., Hassler, S. K., Blume, T., Weiler, M., and Zehe, E.: Soil moisture: variable in space but redundant in time, Hydrol. Earth Syst. Sci., 24, 2633–2653, https://doi.org/10.5194/hess-24-2633-2020, 2020.
Morvillo, M., Bonazzi, A., and Rizzo, C. B.: Improving the computational
efficiency of first arrival time uncertainty estimation using a
connectivity-based ranking Monte Carlo method, Stoch. Environ. Res. Risk
A., 35, 1039–1049, https://doi.org/10.1007/s00477-020-01943-5, 2021.
Nowak, W., Rubin, Y., and de Barros, F. P. J.: A hypothesis-driven approach to optimize field campaigns, Water Resour. Res., 48, https://doi.org/10.1029/2011WR011016, 2012.
Paltridge, G. W.: Climate and thermodynamic systems of maximum dissipation, Nature, 279, 630–631, https://doi.org/10.1038/279630a0, 1979.
Rinaldo, A., Maritan, A., Colaiori, F., Flammini, A., and Rigon, R.:
Thermodynamics of fractal networks, Phys. Rev. Lett., 76, 3364–3367,
1996.
Riva, M., Guadagnini, A., and Sanchez-Vila, X.: Effect of sorption
heterogeneity on moments of solute residence time in convergent flows, Math.
Geosci., 41, 835–853, https://doi.org/10.1007/s11004-009-9240-6, 2009.
Shannon, C. E.: A Mathematical Theory Of Communication, Bell Syst. Tech. J., 27, 623–656,
1948.
Sternagel, A., Loritz, R., Wilcke, W., and Zehe, E.: Simulating preferential soil water flow and tracer transport using the Lagrangian Soil Water and Solute Transport Model, Hydrol. Earth Syst. Sci., 23, 4249–4267, https://doi.org/10.5194/hess-23-4249-2019, 2019.
Sternagel, A., Loritz, R., Klaus, J., Berkowitz, B., and Zehe, E.: Simulation of reactive solute transport in the critical zone: a Lagrangian model for transient flow and preferential transport, Hydrol. Earth Syst. Sci., 25, 1483–1508, https://doi.org/10.5194/hess-25-1483-2021, 2021.
Schroers, S., Eiff, O., Kleidon, A., Wienhöfer, J., and Zehe, E.: Hortonian Overland Flow, Hillslope Morphology and Stream Power I: Spatial Energy Distributions and Steady-state Power Maxima, Hydrol. Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/hess-2021-79, 2021.
Šimůnek, J., Jarvis, N. J., van Genuchten, M. T., and
Gärdenäs, A.: Review and Comparison of models for describing
non-equilibrium and preferential flow and transport in the vadose zone,
J. Hydrol., 272, 14–35, 2003.
Tietjen, B., Zehe, E., and Jeltsch, F.: Simulating plant water availability in
dry lands under climate change: A generic model of two soil layers, Water
Resour. Res., 45, W01418,
https://doi.org/10.1029/2007WR006589, 2009.
van Schaik, L., Palm, J., Klaus, J., Zehe, E., and Schroeder, B.: Linking
spatial earthworm distribution to macropore numbers and hydrological
effectiveness, Ecohydrology, 7, 401–408, 2014.
Wienhöfer, J., Germer, K., Lindenmaier, F., Färber, A., and Zehe, E.: Applied tracers for the observation of subsurface stormflow at the hillslope scale, Hydrol. Earth Syst. Sci., 13, 1145–1161, https://doi.org/10.5194/hess-13-1145-2009, 2009.
Wienhöfer, J. and Zehe, E.: Predicting subsurface stormflow response of a forested hillslope – the role of connected flow paths, Hydrol. Earth Syst. Sci., 18, 121–138, https://doi.org/10.5194/hess-18-121-2014, 2014.
Willmann, M., Carrera, J., and Sánchez-Vila, X.: Transport upscaling in
heterogeneous aquifers: What physical parameters control memory functions?,
Water Resour. Res., 44, W12437, https://doi.org/10.1029/2007WR006531, 2008.
Woodbury, A. D. and Ulrych, T. J.: Minimum relative entropy: Forward
probabilistic modeling, Water Resour. Res., 29, 2847–2860,
https://doi.org/10.1029/93WR00923, 1993.
Zehe, E. and Flühler, H.: Preferential transport of isoproturon at a plot
scale and a field scale tile-drained site, J. Hydrol., 247,
100–115, 2001.
Zehe, E., Blume, T., and Bloschl, G.: The principle of `maximum energy dissipation': A novel thermodynamic perspective on rapid water flow in connected soil structures, Philos. T. Roy. Soc. B, 365, 1377–1386, https://doi.org/10.1098/rstb.2009.0308, 2010.
Zehe, E., Ehret, U., Blume, T., Kleidon, A., Scherer, U., and Westhoff, M.: A thermodynamic approach to link self-organization, preferential flow and rainfall–runoff behaviour, Hydrol. Earth Syst. Sci., 17, 4297–4322, https://doi.org/10.5194/hess-17-4297-2013, 2013.
Zehe, E., Loritz, R., Jackisch, C., Westhoff, M., Kleidon, A., Blume, T., Hassler, S. K., and Savenije, H. H.: Energy states of soil water – a thermodynamic perspective on soil water dynamics and storage-controlled streamflow generation in different landscapes, Hydrol. Earth Syst. Sci., 23, 971–987, https://doi.org/10.5194/hess-23-971-2019, 2019.
Short summary
This study uses the concepts of entropy and work to quantify and explain the emergence of preferential flow and transport in heterogeneous saturated porous media. We found that the downstream concentration of solutes in preferential pathways implies a downstream declining entropy in the transverse distribution of solute transport pathways. Preferential flow patterns with lower entropies emerged within media of higher heterogeneity – a stronger self-organization despite a higher randomness.
This study uses the concepts of entropy and work to quantify and explain the emergence of...
