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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. [ABSTRACT FROM AUTHOR]

The Budyko curve is a widely used framework for predicting the steady-state water balance --solely based on the hydro-climatic setting of river basins. While this framework has been tested and verified across a wide range of climates and settings around the globe, numerous catchments have been reported to considerably deviate from the predicted behavior. Here, we hypothesize that storage capacity and field capacity of the root zone are important controls of the water limitation of evapotranspiration and thus deviations of the mean annual water balance from the Budyko curve. For testing our hypothesis, we selected 16 catchments of different climatic settings and varied the corresponding parameters of a simple water balance model that was previously calibrated against long-term data and investigated the corresponding variations of the simulated water balance in the Budyko space. We found that total soil storage capacity --by controlling water availability and limitation of evapotranspiration-- explains deviations of the evaporation ratio (EVR) from the Budyko curve. Similarly, however to a lesser extent, the evaporation ratio showed sensitivity to alterations of the field capacity. In most cases, the parameter variations generated evaporation ratios enveloping the Budyko curve. The distinct soil storage volumes that matched the Budyko curve clustered at a normalized storage capacity equivalent to 5-15 % of mean annual precipitation. The second, capillarity-related soil parameter clustered at around 0.6-0.8, which is in line with its hydropedological interpretation. A simultaneous variation of both parameters provided additional insights into the interrelation of both parameters and their joint control on offsets from the Budyko curve. Here we found three different sensitivity patterns and we conclude the study with a reflection relating these offsets to the concept of catchment coevolution. The results of this study could also be useful to facilitate evaluation of the water balance in data-scarce regions, as they help constrain parameterizations for hydrological models a priori using the Budyko curve as a predictor. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Diagnostics of hydrological models is pivotal for a better understanding of catchment functioning. The analysis of dominating parameters for the simulation of streamflow plays a key role for region specific model diagnostics, model calibration or parameter transfer. A major challenge in this analysis of parameter sensitivity is the assessment of both temporal and spatial differences of parameter influences on simulated streamflow response. A methodical approach is presented, wherein a two-tiered global sensitivity analysis on a spatially distributed hydrological model is applied to 14 mesoscale headwater catchments of the river Ruhr in western Germany. The analysis of parameter sensitivity is geared towards two complementary forms of streamflow response targets. The analysis of the temporal dynamics of parameter sensitivity (TEDPAS) is contrasted with sensitivity analysis directed to hydrological fingerprints, i.e. temporally independent and temporally aggregated characteristics of streamflow (INDPAS). The two-tiered approach allows to discern a clarified sensitivity pattern pinpointed to diverse response characteristics, to detect regional differences and to reveal the regional relevance of the response target. Small local differences in the hydroclimatic and topographic setting of the headwaters lead to slight differences in the hydrological functioning, which was revealed by gradual differences in TEDPAS and INDPAS. [ABSTRACT FROM AUTHOR]

Despite the numerous hydrological models existing in hydrology we are limited to a few forms of conceptualization when abstracting hydrological systems into different model frameworks. Speaking in black and white terms, in most cases hydrological systems are either represented spatially lumped with conceptual models or spatially explicit with physically-based models. Physically-based models are often parameter-rich, making the parametrization challenging, while conceptual models are parsimonious, with only a few parameters needing to be identified. But this simplistic mathematical expression is often also their drawback since their model states and parameters are difficult to translate to the physical properties of a catchment. It is interesting to note that both hydrological modeling approaches often start with the drawing of a perceptual model. This follows the hydrologist's philosophy to separate dominant patterns and processes from idiosyncratic system details. Due to the importance of hillslopes as key landscape elements perceptual models are often displayed as 2D cross-sections. In this study we examine whether we can step beyond the qualitative character of perceptual models by using them as blueprint for setting up representative hillslope models. Thereby we test the hypothesis if a single hillslope can represent the functioning of an entire lower mesoscale catchment in a spatially aggregated way. We do this by setting up and testing two hillslope models in catchments located in two different geological settings, Schist and Marl, using a two-dimensional physically-based model. Both models are parametrized based on intensive field data and literature values without automatic calibration. Remarkably we are able to not only match the water balance of both catchments but further have some success in simulating runoff generation as well as soil moisture and sap flow dynamics. Particularly, our findings demonstrate that both models performed well during the winter season and clearly worse during the summer period. Virtual experiments revealed that this was most likely either due to a poor representation of the onset of vegetation in the Schist catchment or due to emergence of soil cracks in the Marl area. Both findings underpin that a static parameterization of hydrological models might be problematical in case of emergent behavior. Additional virtual experiments indicate that the storage of water in the bedrock and not so much the topographic gradient is a first order control on the hydrological functioning of the Schist catchment. We conclude that the representative hillslope concept is a feasible approach in data rich regions and that this form of abstraction provides an added value to the established conceptualization frameworks in hydrology. [ABSTRACT FROM AUTHOR]