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Surface topography is an important source of information about the functioning and form of a hydrological landscape. Because of its key role in explaining hydrological processes and structures, and also because of its wide availability at good resolution in the form of digital elevation models (DEMs), it is frequently used to inform hydrological analyses. Not surprisingly, several hydrological indices and models have been proposed for linking geomorphic properties of a landscape with its hydrological functioning; a widely used example is the “height above the nearest drainage” (HAND) index. From an energy-centered perspective HAND reflects the gravitational potential energy of a given unit mass of water located on a hillslope, with the reference level set to the elevation of the nearest corresponding river. Given that potential energy differences are the main drivers for runoff generation, HAND distributions provide important proxies to explain runoff generation in catchments. However, as expressed by the second law of thermodynamics, the driver of a flux explains only one aspect of the runoff generation mechanism, with the driving potential of every flux being depleted via entropy production and dissipative energy loss. In fact, such losses dominate when rainfall becomes runoff, and only a tiny portion of the driving potential energy is actually transformed into the kinetic energy of streamflow. In recognition of this, we derive a topographic index called reduced dissipation per unit length index (rDUNE) by reinterpreting and enhancing HAND following a straightforward thermodynamic argumentation. We compare rDUNE with HAND, and with the frequently used topographic wetness index (TWI), and show that rDUNE provides stronger discrimination of catchments into groups that are similar with respect to their dominant runoff processes. Our analysis indicates that accounting for both the driver and resistance aspects of flux generation provides a promising approach for linking the architecture of a system with its functioning and is hence an appropriate basis for developing similarity indices in hydrology.

Rapid flow processes in connected preferential flow paths are widely accepted to play a key role in the rainfall–runoff response at the hillslope scale, but a quantitative description of these processes is still a major challenge in hydrological research. This paper investigates the approach of incorporating preferential flow paths explicitly in a process-based model for modelling water flow and solute transport at a steep forested hillslope. We conceptualise preferential flow paths as spatially explicit structures with high conductivity and low retention capacity, and evaluate simulations with different combinations of vertical and lateral flow paths in conjunction with variable or constant soil depths against measured discharge and tracer breakthrough. Out of 122 tested realisations, six set-ups fulfilled our selection criteria for the water flow simulation. These set-ups successfully simulated infiltration, vertical and lateral subsurface flow in structures, and allowed predicting the magnitude, dynamics and water balance of the hydrological response of the hillslope during successive periods of steady-state sprinkling on selected plots and intermittent rainfall on the entire hillslope area. The number of equifinal model set-ups was further reduced by the results of solute transport simulations. Two of the six acceptable model set-ups matched the shape of the observed breakthrough curve well, indicating that macrodispersion induced by preferential flow was captured well by the topology of the preferential flow network. The configurations of successful model set-ups suggest that preferential flow related to connected vertical and lateral flow paths is a first-order control on the hydrology of the study hillslope, whereas spatial variability of soil depth is secondary especially when lateral flow paths are present. Virtual experiments for investigating hillslope controls on subsurface processes should thus consider the effect of distinctive flow paths within the soil mantle. The explicit representation of flow paths in a hydrological process model was found to be a suitable approach for this purpose.

This study investigates whether a thermodynamically optimal hillslope structure can, if existent, serve as a first guess for uncalibrated predictions of rainfall–runoff. To this end we propose a thermodynamic framework to link rainfall–runoff processes and dynamics of potential energy, kinetic energy and capillary binding energy in catchments and hillslopes. The starting point is that hydraulic equilibrium in soil corresponds to local thermodynamic equilibrium (LTE), characterized by a local maximum entropy/minimum of free energy of soil water. Deviations from LTE occur either due to evaporative losses, which increase absolute values of negative capillary binding energy of soil water and reduce its potential energy, or due to infiltration of rainfall, which increases potential energy of soil water and reduces the strength of capillary binding energy. The amplitude and relaxation time of these deviations depend on climate, vegetation, soil hydraulic functions, topography and density of macropores. Based on this framework we analysed the free energy balance of hillslopes within numerical experiments that perturbed model structures with respect to the surface density of macropores. These model structures have been previously shown to allow successful long-term simulations of the water balances of the Weiherbach and the Malalcahuello catchments, which are located in distinctly different pedological and climatic settings. Our findings offer a new perspective on different functions of preferential flow paths depending on the pedological setting. Free energy dynamics of soil water in the cohesive soils of the Weiherbach is dominated by dynamics of capillary binding energy. Macropores act as dissipative wetting structures by enlarging water flows against steep gradients in soil water potential after long dry spells. This implies accelerated depletion of these gradients and faster relaxation back towards LTE. We found two local optima in macropore density that maximize reduction rates of free energy of soil water during rainfall-driven conditions. These two optima exist because reduction rates of free energy are, in this case, a second-order polynomial of the wetting rate, which implicitly depends on macroporosity. An uncalibrated long-term simulation of the water balance of the Weiherbach catchment based on the first optimum macroporosity performed almost as well as the best fit when macroporosity was calibrated to match rainfall–runoff. In the Malalcahuello catchment we did not find an apparent optimum density of macropores, because free energy dynamics of soil water during rainfall-driven conditions is dominated by increases of potential energy. Macropores act as dissipative drainage structures by enhancing export of potential energy. No optimum macropore density exists in this case because potential energy change rates scale linearly with the wetting rate. We found, however, a distinguished macroporosity that assures steady-state conditions of the potential energy balance of the soil, in the sense that average storage of potential energy is compensated by average potential energy export. This distinguished macroporosity was close to the value that yielded the best fit of rainfall–runoff behaviour during a calibration exercise and allowed a robust estimate of the annual runoff coefficient. Our findings are promising for predictions in ungauged catchments (PUB) as the optimal/distinguished model structures can serve as a first guess for uncalibrated predictions of rainfall–runoff. They also offer an alternative for classifying catchments according to their similarity of the free energy balance components.

Despite considerable progress in recent years, output of both global and regional circulation models is still afflicted with biases to a degree that precludes its direct use, especially in climate change impact studies. This is well known, and to overcome this problem, bias correction (BC; i.e. the correction of model output towards observations in a post-processing step) has now become a standard procedure in climate change impact studies. In this paper we argue that BC is currently often used in an invalid way: it is added to the GCM/RCM model chain without sufficient proof that the consistency of the latter (i.e. the agreement between model dynamics/model output and our judgement) as well as the generality of its applicability increases. BC methods often impair the advantages of circulation models by altering spatiotemporal field consistency, relations among variables and by violating conservation principles. Currently used BC methods largely neglect feedback mechanisms, and it is unclear whether they are time-invariant under climate change conditions. Applying BC increases agreement of climate model output with observations in hindcasts and hence narrows the uncertainty range of simulations and predictions without, however, providing a satisfactory physical justification. This is in most cases not transparent to the end user. We argue that this hides rather than reduces uncertainty, which may lead to avoidable forejudging of end users and decision makers. We present here a brief overview of state-of-the-art bias correction methods, discuss the related assumptions and implications, draw conclusions on the validity of bias correction and propose ways to cope with biased output of circulation models in the short term and how to reduce the bias in the long term. The most promising strategy for improved future global and regional circulation model simulations is the increase in model resolution to the convection-permitting scale in combination with ensemble predictions based on sophisticated approaches for ensemble perturbation. With this article, we advocate communicating the entire uncertainty range associated with climate change predictions openly and hope to stimulate a lively discussion on bias correction among the atmospheric and hydrological community and end users of climate change impact studies.

This paper proposes a method for rainfall-runoff model calibration and performance analysis in the wavelet-domain by fitting the estimated wavelet-power spectrum (a representation of the time-varying frequency content of a time series) of a simulated discharge series to the one of the corresponding observed time series. As discussed in this paper, calibrating hydrological models so as to reproduce the time-varying frequency content of the observed signal can lead to different results than parameter estimation in the time-domain. Therefore, wavelet-domain parameter estimation has the potential to give new insights into model performance and to reveal model structural deficiencies. We apply the proposed method to synthetic case studies and a real-world discharge modeling case study and discuss how model diagnosis can benefit from an analysis in the wavelet-domain. The results show that for the real-world case study of precipitation – runoff modeling for a high alpine catchment, the calibrated discharge simulation captures the dynamics of the observed time series better than the results obtained through calibration in the time-domain. In addition, the wavelet-domain performance assessment of this case study highlights which frequencies are not well reproduced by the model, which gives specific indications about how to improve the model structure.

In this paper we review threshold behaviour in environmental systems, which are often associated with the onset of floods, contamination and erosion events, and other degenerative processes. Key objectives of this review are to a) suggest indicators for detecting threshold behavior, b) discuss their implications for predictability, c) distinguish different forms of threshold behavior and their underlying controls, and d) hypothesise on possible reasons for why threshold behaviour might occur. Threshold behaviour involves a fast qualitative change of either a single process or the response of a system. For elementary phenomena this switch occurs when boundary conditions (e.g., energy inputs) or system states as expressed by dimensionless quantities (e.g. the Reynolds number) exceed threshold values. Mixing, water movement or depletion of thermodynamic gradients becomes much more efficient as a result. Intermittency is a very good indicator for detecting event scale threshold behavior in hydrological systems. Predictability of intermittent processes/system responses is inherently low for combinations of systems states and/or boundary conditions that push the system close to a threshold. Post hoc identification of "cause-effect relations" to explain when the system became critical is inherently difficult because of our limited ability to perform observations under controlled identical experimental conditions. In this review, we distinguish three forms of threshold behavior. The first one is threshold behavior at the process level that is controlled by the interplay of local soil characteristics and states, vegetation and the rainfall forcing. Overland flow formation, particle detachment and preferential flow are examples of this. The second form of threshold behaviour is the response of systems of intermediate complexity – e.g., catchment runoff response and sediment yield – governed by the redistribution of water and sediments in space and time. These are controlled by the topological architecture of the catchments that interacts with system states and the boundary conditions. Crossing the response thresholds means to establish connectedness of surface or subsurface flow paths to the catchment outlet. Subsurface stormflow in humid areas, overland flow and erosion in semi-arid and arid areas are examples, and explain that crossing local process thresholds is necessary but not sufficient to trigger a system response threshold. The third form of threshold behaviour involves changes in the "architecture" of human geo-ecosystems, which experience various disturbances. As a result substantial change in hydrological functioning of a system is induced, when the disturbances exceed the resilience of the geo-ecosystem. We present examples from savannah ecosystems, humid agricultural systems, mining activities affecting rainfall runoff in forested areas, badlands formation in Spain, and the restoration of the Upper Rhine river basin as examples of this phenomenon. This functional threshold behaviour is most difficult to predict, since it requires extrapolations far away from our usual experience and the accounting of bidirectional feedbacks. However, it does not require the development of more complicated model, but on the contrary, only models with the right level of simplification, which we illustrate with an instructive example. Following Prigogine, who studied structure formation in open thermodynamic systems, we hypothesise that topological structures which control response thresholds in the landscape might be seen as dissipative structures, and the onset of threshold processes/response as a switch to more efficient ways of depleting strong gradients that develop in the case of extreme boundary conditions.

Spatial patterns as well as temporal dynamics of soil moisture have a major influence on runoff generation. The investigation of these dynamics and patterns can thus yield valuable information on hydrological processes, especially in data scarce or previously ungauged catchments. The combination of spatially scarce but temporally high resolution soil moisture profiles with episodic and thus temporally scarce moisture profiles at additional locations provides information on spatial as well as temporal patterns of soil moisture at the hillslope transect scale. This approach is better suited to difficult terrain (dense forest, steep slopes) than geophysical techniques and at the same time less cost-intensive than a high resolution grid of continuously measuring sensors. Rainfall simulation experiments with dye tracers while continuously monitoring soil moisture response allows for visualization of flow processes in the unsaturated zone at these locations. Data was analyzed at different spacio-temporal scales using various graphical methods, such as space-time colour maps (for the event and plot scale) and binary indicator maps (for the long-term and hillslope scale). Annual dynamics of soil moisture and decimeter-scale variability were also investigated. The proposed approach proved to be successful in the investigation of flow processes in the unsaturated zone and showed the importance of preferential flow in the Malalcahuello Catchment, a data-scarce catchment in the Andes of Southern Chile. Fast response times of stream flow indicate that preferential flow observed at the plot scale might also be of importance at the hillslope or catchment scale. Flow patterns were highly variable in space but persistent in time. The most likely explanation for preferential flow in this catchment is a combination of hydrophobicity, small scale heterogeneity in rainfall due to redistribution in the canopy and strong gradients in unsaturated conductivities leading to self-reinforcing flow paths.