@article{ZeheElsenbeerLindenmaieretal.2007,
  author    = {Zehe, Erwin and Elsenbeer, Helmut and Lindenmaier, Falk and Schulz, K. and Bl{\"o}schl, G{\"u}nter},
  title     = {Patterns of predictability in hydrological threshold systems},
  issn      = {0043-1397},
  doi       = {10.1029/2006wr005589},
  year      = {2007},
  abstract  = {[1] Observations of hydrological response often exhibit considerable scatter that is difficult to interpret. In this paper, we examine runoff production of 53 sprinkling experiments on the water-repellent soils in the southern Alps of Switzerland; simulated plot scale tracer transport in the macroporous soils at the Weiherbach site, Germany; and runoff generation data from the 2.3-km(2) Tannhausen catchment, Germany, that has cracking soils. The response at the three sites is highly dependent on the initial soil moisture state as a result of the threshold dynamics of the systems. A simple statistical model of threshold behavior is proposed to help interpret the scatter in the observations. Specifically, the model portrays how the inherent macrostate uncertainty of initial soil moisture translates into the scatter of the observed system response. The statistical model is then used to explore the asymptotic pattern of predictability when increasing the number of observations, which is normally not possible in a field study. Although the physical and chemical mechanisms of the processes at the three sites are different, the predictability patterns are remarkably similar. Predictability is smallest when the system state is close to the threshold and increases as the system state moves away from it. There is inherent uncertainty in the response data that is not measurement error but is related to the observability of the initial conditions.},
  language  = {en}
}
@article{SchulzSeppeltZeheetal.2006,
  author    = {Schulz, K. and Seppelt, Ralf and Zehe, Erwin and Vogel, Hans-J{\"o}rg and Attinger, Sabine},
  title     = {Importance of spatial structures in advancing hydrological sciences},
  doi       = {10.1029/2005wr004301},
  year      = {2006},
  abstract  = {[1] Spatial patterns of land surface and subsurface characteristics often exert significant control over hydrological processes at many scales. Recognition of the dominant controls at the watershed scale, which is a prerequisite to successful prediction of system responses, will require significant progress in many different research areas. The development and improvement of techniques for mapping structures and spatiotemporal patterns using geophysical and remote sensing techniques would greatly benefit watershed science but still requires a significant synthesis effort. Effective descriptions of hydrological systems will also significantly benefit from new scaling and averaging techniques, from new mathematical description for spatial pattern/structures and their dynamics, and also from an understanding and quantification of structure and pattern-building processes in different compartments ( soils, rocks, and land surface) and at different scales. The advances that are needed to tackle these complex challenges could be greatly facilitated through the development of an interdisciplinary research framework that explores instrumentation, theory, and simulation components and that is implemented in a coordinated manner},
  language  = {en}
}
@article{ZeheEhretPfisteretal.2014,
  author    = {Zehe, E. and Ehret, U. and Pfister, L. and Blume, Theresa and Schroeder, Boris and Westhoff, M. and Jackisch, C. and Schymanski, Stanislauv J. and Weiler, M. and Schulz, K. and Allroggen, Niklas and Tronicke, Jens and van Schaik, Loes and Dietrich, Peter and Scherer, U. and Eccard, Jana and Wulfmeyer, Volker and Kleidon, Axel},
  title     = {HESS Opinions: From response units to functional units: a thermodynamic reinterpretation of the HRU concept to link spatial organization and functioning of intermediate scale catchments},
  series = {Hydrology and earth system sciences : HESS},
  volume    = {18},
  journal   = {Hydrology and earth system sciences : HESS},
  number    = {11},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {1027-5606},
  doi       = {10.5194/hess-18-4635-2014},
  pages     = {4635 -- 4655},
  year      = {2014},
  abstract  = {According to Dooge (1986) intermediate-scale catchments are systems of organized complexity, being too organized and yet too small to be characterized on a statistical/conceptual basis, but too large and too heterogeneous to be characterized in a deterministic manner. A key requirement for building structurally adequate models precisely for this intermediate scale is a better understanding of how different forms of spatial organization affect storage and release of water and energy. Here, we propose that a combination of the concept of hydrological response units (HRUs) and thermodynamics offers several helpful and partly novel perspectives for gaining this improved understanding. Our key idea is to define functional similarity based on similarity of the terrestrial controls of gradients and resistance terms controlling the land surface energy balance, rainfall runoff transformation, and groundwater storage and release. This might imply that functional similarity with respect to these specific forms of water release emerges at different scales, namely the small field scale, the hillslope, and the catchment scale. We thus propose three different types of "functional units" - specialized HRUs, so to speak - which behave similarly with respect to one specific form of water release and with a characteristic extent equal to one of those three scale levels. We furthermore discuss an experimental strategy based on exemplary learning and replicate experiments to identify and delineate these functional units, and as a promising strategy for characterizing the interplay and organization of water and energy fluxes across scales. We believe the thermodynamic perspective to be well suited to unmask equifinality as inherent in the equations governing water, momentum, and energy fluxes: this is because several combinations of gradients and resistance terms yield the same mass or energy flux and the terrestrial controls of gradients and resistance terms are largely independent. We propose that structurally adequate models at this scale should consequently disentangle driving gradients and resistance terms, because this optionally allow sequifinality to be partly reduced by including available observations, e. g., on driving gradients. Most importantly, the thermodynamic perspective yields an energy-centered perspective on rainfall-runoff transformation and evapotranspiration, including fundamental limits for energy fluxes associated with these processes. This might additionally reduce equifinality and opens up opportunities for testing thermodynamic optimality principles within independent predictions of rainfall-runoff or land surface energy exchange. This is pivotal to finding out whether or not spatial organization in catchments is in accordance with a fundamental organizing principle.},
  language  = {en}
}