@article{BloschlZehe2005,
  author    = {Bloschl, G{\"u}nter and Zehe, Erwin},
  title     = {Invited commentary : on hydrological predictability},
  year      = {2005},
  language  = {en}
}
@article{ZeheBloeschl2004,
  author    = {Zehe, Erwin and Bl{\"o}schl, G{\"u}nter},
  title     = {Predictability of hydrologic response at the plot and catchment scales : the role of initial conditions},
  year      = {2004},
  abstract  = {[1] This paper examines the effect of uncertain initial soil moisture on hydrologic response at the plot scale (1 m(2)) and the catchment scale (3.6 km(2)) in the presence of threshold transitions between matrix and preferential flow. We adopt the concepts of microstates and macrostates from statistical mechanics. The microstates are the detailed patterns of initial soil moisture that are inherently unknown, while the macrostates are specified by the statistical distributions of initial soil moisture that can be derived from the measurements typically available in field experiments. We use a physically based model and ensure that it closely represents the processes in the Weiherbach catchment, Germany. We then use the model to generate hydrologic response to hypothetical irrigation events and rainfall events for multiple realizations of initial soil moisture microstates that are all consistent with the same macrostate. As the measures of uncertainty at the plot scale we use the coefficient of variation and the scaled range of simulated vertical bromide transport distances between realizations. At the catchment scale we use similar statistics derived from simulated flood peak discharges. The simulations indicate that at both scales the predictability depends on the average initial soil moisture state and is at a minimum around the soil moisture value where the transition from matrix to macropore flow occurs. The predictability increases with rainfall intensity. The predictability increases with scale with maximum absolute errors of 90 and 32\% at the plot scale and the catchment scale, respectively. It is argued that even if we assume perfect knowledge on the processes, the level of detail with which one can measure the initial conditions along with the nonlinearity of the system will set limits to the repeatability of experiments and limits to the predictability of models at the plot and catchment scales},
  language  = {en}
}
@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}
}
@misc{ZeheBloeschl2004,
  author    = {Zehe, Erwin and Bl{\"o}schl, G{\"u}nter},
  title     = {Predictability of hydrologic response at the plot and catchment scales: Role of initial conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60119},
  year      = {2004},
  abstract  = {This paper examines the effect of uncertain initial soil moisture on hydrologic response at the plot scale (1 m2) and the catchment scale (3.6 km2) in the presence of threshold transitions between matrix and preferential flow. We adopt the concepts of microstates and macrostates from statistical mechanics. The microstates are the detailed patterns of initial soil moisture that are inherently unknown, while the macrostates are specified by the statistical distributions of initial soil moisture that can be derived from the measurements typically available in field experiments. We use a physically based model and ensure that it closely represents the processes in the Weiherbach catchment, Germany. We then use the model to generate hydrologic response to hypothetical irrigation events and rainfall events for multiple realizations of initial soil moisture microstates that are all consistent with the same macrostate. As the measures of uncertainty at the plot scale we use the coefficient of variation and the scaled range of simulated vertical bromide transport distances between realizations. At the catchment scale we use similar statistics derived from simulated flood peak discharges. The simulations indicate that at both scales the predictability depends on the average initial soil moisture state and is at a minimum around the soil moisture value where the transition from matrix to macropore flow occurs. The predictability increases with rainfall intensity. The predictability increases with scale with maximum absolute errors of 90 and 32\% at the plot scale and the catchment scale, respectively. It is argued that even if we assume perfect knowledge on the processes, the level of detail with which one can measure the initial conditions along with the nonlinearity of the system will set limits to the repeatability of experiments and limits to the predictability of models at the plot and catchment scales.},
  language  = {de}
}