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We present a method to simulate fluid flow with reactive solute transport in structured, partially saturated soils using a Lagrangian perspective. In this context, we extend the scope of the Lagrangian Soil Water and Solute Transport Model (LAST) (Sternagel et al., 2019) by implementing vertically variable, non-linear sorption and first-order degradation processes during transport of reactive substances through a partially saturated soil matrix and macropores. For sorption, we develop an explicit mass transfer approach based on Freundlich isotherms because the common method of using a retardation factor is not applicable in the particle-based approach of LAST. The reactive transport method is tested against data of plot- and field-scale irrigation experiments with the herbicides isoproturon and flufenacet at different flow conditions over various periods. Simulations with HYDRUS 1-D serve as an additional benchmark. At the plot scale, both models show equal performance at a matrix-flow-dominated site, but LAST better matches indicators of preferential flow at a macropore-flow-dominated site. Furthermore, LAST successfully simulates the effects of adsorption and degradation on the breakthrough behaviour of flufenacet with preferential leaching and remobilization. The results demonstrate the feasibility of the method to simulate reactive solute transport in a Lagrangian framework and highlight the advantage of the particle-based approach and the structural macropore domain to simulate solute transport as well as to cope with preferential bypassing of topsoil and subsequent re-infiltration into the subsoil matrix.

Soil moisture at the headwater scale exhibits a huge spatial variability and single or even distributed TDR measurements yield non-representative data (Zehe et al., 2010, p. 874 l. 11–14). This suggests that even a huge amount of observation points would not be able to capture soil moisture variability. Here we ask whether spatial variability is the dead-end to spatially distributed point sampling – or whether point networks yield representative data on dynamic changes nevertheless? We present a measure to capture the spatial dissimilarity, or dispersion, and its change over time. Statistical dispersion among observation points is related to their distance to describe spatial patterns. We analyzed the temporal evolution and emergence of these patterns and use Mean shift clustering algorithm to identify and analyze clusters. We found that soil moisture observations from the Colpach catchment in Luxembourg to cluster in two fundamentally different states. On the one hand, we found rainfall-driven data clusters, usually characterized by strong relationships between dispersion and distance. Their spatial extent roughly matches the hillslope scale. On the other hand, we found clusters covering the vegetation period. In drying and then dry soil conditions there is no particular spatial dependence in soil moisture patterns, but the values are highly similar beyond hillslope scale. By combining uncertainty propagation with information theory, we were able to calculate the information content of spatial similarity with respect to measurement uncertainty (when are patterns different outside of uncertainty margins?). We were able to prove that the spatial information contained in soil moisture observations is highly redundant and can be compressed to only a fragment of the original data volume without significant information loss. Our most interesting finding is that even a few soil moisture time series bear a considerable amount of information about dynamic changes of soil moisture. We argue that distributed soil moisture sampling reflects an organized catchment state, where soil moisture variability is not random. Thus, only a small amount of observation points is necessary to capture soil moisture dynamics.

© Author(s) 2018. Editors of several journals in the field of hydrology met during the General Assembly of the European Geosciences Union (EGU) in Vienna in April 2017. This event was a follow-up of similar meetings held in 2013 and 2015. These meetings enable the group of editors to review the current status of the journals and the publication process, and to share thoughts on future strategies. Journals were represented at the 2017 meeting by their editors, as shown in the list of authors. The main points on invigorating hydrological research through journal publications are communicated in this joint editorial published in the above journals. ispartof: HYDROLOGY AND EARTH SYSTEM SCIENCES vol:22 issue:11 pages:5735-5739 status: published

Predictions of catchment hydrology have been performed generally using either physically based, distributed models or conceptual lumped or semi-distributed models. In recognition of the disadvantages of using either of these modeling approaches, namely, detailed data requirements in the case of distributed modeling, and lack of physical basis of conceptual/lumped model parameters, Reggiani et al. (1998, 1999) derived, from first principles and in a general manner, the balance equations for mass, momentum and energy at what they called the Representative Elementary Watershed (or REW) scale. However, the mass balance equations of the REW approach include mass exchange flux terms which must be defined externally before their application to real catchments. Developing physically reasonable "closure relations'' for these mass exchange flux terms is a crucial pre-requisite for the success of the REW approach. As a guidance to the development of closure relations expressing mass exchange fluxes as functions of relevant state variables in a physically reasonable way, and in the process effectively parameterizing the effects of sub-grid or sub-REW heterogeneity of catchment physiographic properties on these mass exchange fluxes, this paper considers four different approaches, namely the field experimental approach, a theoretical/analytical approach, a numerical approach, and a hybrid approach combining one or more of the above. Based on the concept of the scaleway (Vogel and Roth, 2003) and the disaggregation-aggregation approach (Viney and Sivapalan, 2004), and using the data set from Weiherbach catchment in Germany, closure relations for infiltration, exfiltration and groundwater recharge were derived analytically, or on theoretical grounds, while numerical experiments with a detailed fine-scale, distributed model, CATFLOW, were used to obtain the closure relationship for seepage outflow. The detailed model, CATFLOW, was also used to derive REW scale pressure-saturation (i.e., water retention curve) and hydraulic conductivity-saturation relationships for the unsaturated zone. Closure relations for concentrated overland flow and saturated overland flow were derived using both theoretical arguments and simpler process models. In addition to these, to complete the specification of the REW scale balance equations, a relationship for the saturated area fraction as a function of saturated zone depth was derived for an assumed topography on the basis of TOPMODEL assumptions. These relationships were used to complete the specification of all of the REW-scale governing equations (mass and momentum balance equations, closure and geometric relations) for the Weiherbach catchment, which are then employed for constructing a numerical watershed model, named the Cooperative Community Catchment model based on the Representative Elementary Watershed approach (CREW). CREW is then used to carry out sensitivity analyses with respect to various combinations of climate, soil, vegetation and topographies, in order to test the reasonableness of the derived closure relations in the context of the complete catchment response, including interacting processes. These sensitivity analyses demonstrated that the adopted closure relations do indeed produce mostly reasonable results, and can therefore be a good basis for more careful and rigorous search for appropriate closure relations in the future. Three tests are designed to assess CREW as a large scale model for Weiherbach catchment. The first test compares CREW with distributed model CATFLOW by looking at predicted soil moisture dynamics for artificially designed initial and boundary conditions. The second test is designed to see the applicabilities of the parameter values extracted from the upscaling procedures in terms of their ability to reproduce observed hydrographs within the CREW modeling framework. The final test compares simulated soil moisture time series predicted by CREW with observed ones as a way of validating the predictions of CREW. The results of these three tests, together, demonstrate that CREW could indeed be an alternative modelling framework, producing results that are consistent with those of the distributed model CATFLOW, and capable of ultimately representing processes actually occurring at the larger scale in a physically sound manner.

Within this study we present a robust method for generating precipitation time series for the Anas catchment in North Western India. The method employs a multivariate stochastic simulation model that is driven by a time series of objectively classified circulation patterns (CPs). In a companion study (Zehe et al., 2006) it was already shown that CPs classified from the 500 or 700 Hpa levels are suitable to explain space-time variability of precipitation in that area. The model is calibrated using observed rainfall time series for the period 1985–1992 for two different CP time series, one from the 500 Hpa level and the over from the 700 Hpa level, and 200 realizations of daily rainfall are simulated for the period 85–94. Simulations using the CPs from the 500 Hpa level as input yield a good match of the observed averages and standard deviations of daily rainfall. They show furthermore good performance at the monthly scale. When used with the 700 Hpa level CPs as inputs the model clearly underestimates the standard deviation and performs much worse at the monthly scale, especially in the validation period 93–94. The presented results give evidence that CPs from the 500 Hpa, level in combination with a multivariate stochastic model, make up a suitable tool for reducing the sparsity of precipitation data in developing regions with sparse hydro-meteorological data sets.

This study presents an application of an innovative sampling strategy to assess soil moisture dynamics in a headwater of the Weißeritz in the German eastern Ore Mountains. A grassland site and a forested site were instrumented with two Spatial TDR clusters (STDR) that consist of 39 and 32 coated TDR probes of 60 cm length. Distributed time series of vertically averaged soil moisture data from both sites/ensembles were analyzed by statistical and geostatistical methods. Spatial variability and the spatial mean at the forested site were larger than at the grassland site. Furthermore, clustering of TDR probes in combination with long-term monitoring allowed identification of average spatial covariance structures at the small field scale for different wetness states. The correlation length of soil water content as well as the sill to nugget ratio at the grassland site increased with increasing average wetness and but, in contrast, were constant at the forested site. As soil properties at both the forested and grassland sites are extremely variable, this suggests that the correlation structure at the forested site is dominated by the pattern of throughfall and interception. We also found a very strong correlation between antecedent soil moisture at the forested site and runoff coefficients of rainfall-runoff events observed at gauge Rehefeld. Antecedent soil moisture at the forest site explains 92% of the variability in the runoff coefficients. By combining these results with a recession analysis we derived a first conceptual model of the dominant runoff mechanisms operating in this catchment. Finally, we employed a physically based hydrological model to shed light on the controls of soil- and plant morphological parameters on soil average soil moisture at the forested site and the grassland site, respectively. A homogeneous soil setup allowed, after fine tuning of plant morphological parameters, most of the time unbiased predictions of the observed average soil conditions observed at both field sites. We conclude that the proposed sampling strategy of clustering TDR probes is suitable to assess unbiased average soil moisture dynamics in critical functional units, in this case the forested site, which is a much better predictor for event scale runoff formation than pre-event discharge. Long term monitoring of such critical landscape elements could maybe yield valuable information for flood warning in headwaters. We thus think that STDR provides a good intersect of the advantages of permanent sampling and spatially highly resolved soil moisture sampling using mobile rods.

Rainfall-runoff response in temperate humid headwater catchments is mainly controlled by hydrological processes at the hillslope scale. Applied tracer experiments with fluorescent dye and salt tracers are well known tools in groundwater studies at the large scale and vadose zone studies at the plot scale, where they provide a means to characterise subsurface flow. We extend this approach to the hillslope scale to investigate saturated and unsaturated flow paths concertedly at a forested hillslope in the Austrian Alps. Dye staining experiments at the plot scale revealed that cracks and soil pipes function as preferential flow paths in the fine-textured soils of the study area, and these preferential flow structures were active in fast subsurface transport of tracers at the hillslope scale. Breakthrough curves obtained under steady flow conditions could be fitted well to a one-dimensional convection-dispersion model. Under natural rainfall a positive correlation of tracer concentrations to the transient flows was observed. The results of this study demonstrate qualitative and quantitative effects of preferential flow features on subsurface stormflow in a temperate humid headwater catchment. It turns out that, at the hillslope scale, the interactions of structures and processes are intrinsically complex, which implies that attempts to model such a hillslope satisfactorily require detailed investigations of effective structures and parameters at the scale of interest.

The present study tests whether an explicit treatment of worm burrows and tile drains as connected structures is feasible for simulating water flow, bromide and pesticide transport in structured heterogeneous soils at hillslope scale. The essence is to represent worm burrows as morphologically connected paths of low flow resistance in a hillslope model. A recent Monte Carlo study (Klaus and Zehe, 2010, Hydrological Processes, 24, p. 1595–1609) revealed that this approach allowed successful reproduction of tile drain event discharge recorded during an irrigation experiment at a tile drained field site. However, several "hillslope architectures" that were all consistent with the available extensive data base allowed a good reproduction of tile drain flow response. Our second objective was thus to find out whether this "equifinality" in spatial model setups may be reduced when including bromide tracer data in the model falsification process. We thus simulated transport of bromide for the 13 spatial model setups that performed best with respect to reproduce tile drain event discharge, without any further calibration. All model setups allowed a very good prediction of the temporal dynamics of cumulated bromide leaching into the tile drain, while only four of them matched the accumulated water balance and accumulated bromide loss into the tile drain. The number of behavioural model architectures could thus be reduced to four. One of those setups was used for simulating transport of Isoproturon, using different parameter combinations to characterise adsorption according to the Footprint data base. Simulations could, however, only reproduce the observed leaching behaviour, when we allowed for retardation coefficients that were very close to one.

Topography exerts influence on the spatial precipitation distribution over different scales, known typically at the large scale as the orographic effect, and at the small scale as the wind-drift rainfall (WDR) effect. At the intermediate scale (1~10 km), which is characterized by secondary mountain valleys, topography also demonstrates some effect on the precipitation pattern. This paper investigates such intermediate-scale topographic effects on precipitation patterns, focusing on narrow-steep valleys in the complex terrain of southern Germany, based on the daily observations over a 48 yr period (1960~2007) from a high-density rain-gauge network covering two sub-areas, Baden-Wuerttemberg (BW) and Bavaria (BY). Precipitation data at the valley and non-valley stations are compared under consideration of the daily general circulation patterns (CPs) classified by a fuzzy rule-based algorithm. Scatter plots of precipitation against elevation demonstrate a different behavior of valley stations comparing to non-valley stations. A detailed study of the precipitation time series for selected station triplets, each consisting of a valley station, a mountain station and an open station have been investigated by statistical analysis with the Kolmogorov–Smirnov (KS) test supplemented by the One-way analysis of variance (One-way ANOVA) and a graphical comparison of the mean precipitation amounts. The results show an interaction of valley orientation and the direction of the CPs at the intermediate scale, i.e. when the valley is shielded from the CP which carries the precipitation, the precipitation amount within the valley is comparable to that on the mountain crest, and both larger than the precipitation at the open station. When the valley is open to the CP, the precipitation within the valley is similar to the open station but much less than that on the mountain. Such phenomenon where the precipitation is "blind" to the valleys at the intermediate scale conditioned on CPs is defined as the "narrow-valley effect" in this work. Such an effect cannot be captured by the widely used elevation–precipitation relationship, which implies that the traditional geostatistical interpolation schemes, e.g. ordinary kriging (OK) or external drift kriging (EDK) applying digital elevation model (DEM) as external information, are not sufficient. An interpolation experiment applying EDK with orographic surrogate elevation defined in this paper as auxiliary information to account for the valley effects shows improvement for the cross-validation.

The increasing diversity and resolution of spatially distributed data on terrestrial systems greatly enhances the potential of hydrological modeling. Optimal and parsimonious use of these data sources implies, however, that we better understand (a) which system characteristics exert primary controls on hydrological dynamics and (b) to what level of detail do those characteristics need to be represented in a model. In this study we develop and test an approach to explore these questions that draws upon information theoretic and thermodynamic reasoning, using spatially distributed topographic information as a straightforward example. Specifically, we subdivide a meso-scale catchment into 105 hillslopes and represent each by a two dimensional numerical hillslope model. These hillslope models differ exclusively with respect to topography related parameters derived from a digital elevation model; the remaining setup and meteorological forcing for each are identical. We analyze the degree of similarity of simulated discharge and storage among the hillslopes as a function of time by examining the Shannon information entropy. We furthermore derive a compressed catchment model by clustering the hillslope models into functional groups of similar runoff generation using normalized mutual information as a distance measure. Our results reveal that, within our given model environment, only a portion of the entire amount of topographic information stored within a digital elevation model is relevant for the simulation of distributed runoff and storage dynamics. This manifests through a possible compression of the model ensemble from the entire set of 105 hillslopes to only 6 hillslopes, each representing a different functional group, which leads to no substantial loss in model performance. Importantly, we find that the concept of hydrological similarity is not necessarily time-invariant. On the contrary, the Shannon entropy as measure for diversity in the simulation ensemble shows a distinct annual pattern, with periods of highly redundant simulations, reflecting coherent and organized dynamics, and periods where hillslopes operate in distinctly different ways. We conclude that the proposed approach provides a powerful framework for understanding and diagnosing how and when process organization and functional similarity of hydrological systems emerges in time. Our approach is neither restricted to the model, nor to model targets or the data source we selected in this study. Overall, we propose that the concepts of hydrological systems acting similarly (and thus giving rise to redundancy) or displaying unique functionality (and thus being irreplaceable) are not mutually exclusive. They are in fact of complementary nature, and systems operate by gradually changing to different levels of organization in time.

Non-uniform infiltration and subsurface flow in structured soils is observed in most natural settings. It arises from imperfect lateral mixing of fast advective flow in structures and diffusive flow in the soil matrix and remains one of the most challenging topics with respect to match observation and modelling of water and solutes at the plot scale. This study extends the fundamental introduction of a space domain random walk of water particles as an alternative approach to the Richards equation for diffusive flow (Zehe and Jackisch, 2016) to a stochastic–physical model framework simulating soil water flow in a representative, structured soil domain. The central objective of the proposed model is the simulation of non-uniform flow fingerprints in different ecohydrological settings and antecedent states by making maximum use of field observables for parameterisation. Avoiding non-observable parameters for macropore–matrix exchange, an energy-balance approach to govern film flow in representative flow paths is employed. We present the echoRD model (ecohydrological particle model based on representative domains) and a series of application test cases. The model proves to be a powerful alternative to existing dual-domain models, driven by experimental data and with self-controlled, dynamic macropore–matrix exchange from the topologically semi-explicitly defined structures.

Diagnostics of hydrological models are pivotal for a better understanding of catchment functioning, and the analysis of dominating model parameters plays a key role for region-specific calibration or parameter transfer. A major challenge in the analysis of parameter sensitivity is the assessment of both temporal and spatial differences of parameter influences on simulated streamflow response. We present a methodological approach for global sensitivity analysis of hydrological models. The multilevel approach is geared towards complementary forms of streamflow response targets, and combines sensitivity analysis directed to hydrological fingerprints, i.e. temporally independent and temporally aggregated characteristics of streamflow (INDPAS), with the conventional analysis of the temporal dynamics of parameter sensitivity (TEDPAS). The approach was tested in 14 mesoscale headwater catchments of the Ruhr River in western Germany using simulations with the spatially distributed hydrological model mHM. The multilevel analysis with diverse response characteristics allowed us to pinpoint parameter sensitivity patterns much more clearly as compared to using TEDPAS alone. It was not only possible to identify two dominating parameters, for soil moisture dynamics and evapotranspiration, but we could also disentangle the role of these and other parameters with reference to different streamflow characteristics. The combination of TEDPAS and INDPAS further allowed us to detect regional differences in parameter sensitivity and in simulated hydrological functioning, despite the rather small differences in the hydroclimatic and topographic setting of the Ruhr headwaters.

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.

This article introduces an improvement in the Series Distance (SD) approach for improved discrimination and visualisation of timing and magnitude uncertainties in streamflow simulations. SD emulates visual hydrograph comparison by distinguishing periods of low-flow and periods of rise and recession in hydrological events. Within these periods, it determines the distance of two hydrographs not between points of equal time, but between points that are hydrologically similar. The improvement comprises an automated procedure to emulate visual "coarse-graining", i.e. the determination of an optimal level of generalization when comparing two hydrographs, a scaled error model which is better applicable across large discharge ranges than its non-scaled counterpart, and "error dressing", a concept to construct uncertainty ranges around deterministic simulations or forecasts. Error dressing includes an approach to sample empirical error distributions by increasing variance contribution, which can be extended from standard 1-dimensional distributions to the 2-dimensional distributions of combined time and magnitude errors provided by SD. In a case study we apply both the SD concept and a benchmark model (BM) based on standard magnitude errors to a six-year time series of observations and simulations from a small alpine catchment. Time-magnitude error characteristics for low-flow, rising and falling limbs of events were substantially different. Their separate treatment within SD therefore preserves useful information which can be used for differentiated model diagnostics, and which is not contained in standard criteria like the Nash-Sutcliffe-Efficiency. Construction of uncertainty ranges based on the magnitude of errors of the BM approach and the combined time- and magnitude errors of the SD approach revealed that the BM derived ranges were visually more narrow and statistically superior to the SD ranges. This suggests that the combined use of time- and magnitude errors to construct uncertainty envelopes implies a trade-off between the added value of explicitly considering timing errors and the associated, inevitable time-spreading effect which "inflates" the related uncertainty ranges. Which effect dominates depends on the characteristics of timing errors in the hydrographs at hand. Our findings corroborate that Series Distance is an elaborated concept for the comparison of simulated and observed stream flow time series which can be used for detailed hydrological analysis, model diagnostics and to inform about uncertainties related to hydrological predictions.

Almost all catchments plot within a small envelope around the Budyko curve. This apparent behaviour suggests that organizing principles may play a role in the evolution of catchments. In this paper we applied the thermodynamic principle of maximum power as the organizing principle. In a top-down approach we derived mathematical formulations of the relation between relative wetness and gradients driving run-off and evaporation for a simple one-box model. We did this in an inverse manner such that, when the conductances are optimized with the maximum-power principle, the steady-state behaviour of the model leads exactly to a point on the asymptotes of the Budyko curve. Subsequently, we added dynamics in forcing and actual evaporation, causing the Budyko curve to deviate from the asymptotes. Despite the simplicity of the model, catchment observations compare reasonably well with the Budyko curves subject to observed dynamics in rainfall and actual evaporation. Thus by constraining the model that has been optimized with the maximum-power principle with the asymptotes of the Budyko curve, we were able to derive more realistic values of the aridity and evaporation index without any parameter calibration. Future work should focus on better representing the boundary conditions of real catchments and eventually adding more complexity to the model.

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.

Throughout its historical development, hydrology as an earth science, but especially as a problem-centred engineering discipline has largely relied (quite successfully) on the assumption of stationarity. This includes assuming time invariance of boundary conditions such as climate, system configurations such as land use, topography and morphology, and dynamics such as flow regimes and flood recurrence at different spatio-temporal aggregation scales. The justification for this assumption was often that when compared with the temporal, spatial, or topical extent of the questions posed to hydrology, such conditions could indeed be considered stationary, and therefore the neglect of certain long-term non-stationarities or feedback effects (even if they were known) would not introduce a large error., Hydrology and Earth System Sciences, 18 (2), ISSN:1027-5606, ISSN:1607-7938

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 allows equifinality 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., Hydrology and Earth System Sciences, 18 (11), ISSN:1027-5606, ISSN:1607-7938

The mechanisms allowing the rapid release of stored water to streams are poorly understood. Here we use a tile-drained field site to combine macroporous soils at the hillslope scale with the advantage of at least partly controlled lower boundary conditions. We performed a series of three irrigation experiments combining hydrometric measurements with stable isotope and bromide tracers to better understand macropore–matrix interactions and stored water release processes at the hillslope scale. Stable isotope concentrations were monitored in the irrigation water, the tile-drain discharge and the soil water before and after the experiment. Bromide was measured every 5–15 min in the tile-drain hydrograph. Different initial conditions for each experiment were used to examine how these influenced flow and transport. Different amounts of irrigation water were necessary to increase tile-drain discharge above the baseflow level. Hydrograph separation based on bromide data revealed that irrigation water contributions to peak tile-drain discharge were on the order of 20%. Oxygen-18 and deuterium data were consistent with the bromide data and showed that pre-event soil water contributed significantly to the tile-drain event flow. However, the isotopic composition of soil water converged towards the isotopic composition of irrigation water through the course of the experiment. Mixing calculations revealed that by the end of the irrigation experiments 20% of the soil water in the entire profile was irrigation water. The isotopic data showed that the pre-event water in the tile drain was mobilized in 20–40 cm soil depth where the macropore–matrix interaction leads to an initiation of macropore flow after a moisture threshold is exceeded.

Research on regionalisation in hydrology has been constantly advancing due to the need for prediction of streamflow in ungauged catchments. There are two types of studies that use regionalisation techniques for ungauged catchments. One type estimates parameters of streamflow statistics, flood quantiles in most cases. The other type estimates parameters of a rainfall-runoff model for simulating continuous streamflow or estimates continuous streamflow without using a model. Almost all methods applied to the latter can be applied to the former. This paper reviews all methods that are applied to continuous streamflow estimation for ungauged catchments. We divide them into two general categories: (1) distance-based and (2) regression-based. Methods that fall within each category are reviewed first and followed with a discussion on merits or problems associated with these various methods.

Applying metrics to quantify the similarity or dissimilarity of hydrographs is a central task in hydrological modelling, used both in model calibration and the evaluation of simulations or forecasts. Motivated by the shortcomings of standard objective metrics such as the Root Mean Square Error (RMSE) or the Mean Absolute Peak Time Error (MAPTE) and the advantages of visual inspection as a powerful tool for simultaneous, case-specific and multi-criteria (yet subjective) evaluation, we propose a new objective metric termed Series Distance, which is in close accordance with visual evaluation. The Series Distance quantifies the similarity of two hydrographs neither in a time-aggregated nor in a point-by-point manner, but on the scale of hydrological events. It consists of three parts, namely a Threat Score which evaluates overall agreement of event occurrence, and the overall distance of matching observed and simulated events with respect to amplitude and timing. The novelty of the latter two is the way in which matching point pairs on the observed and simulated hydrographs are identified: not by equality in time (as is the case with the RMSE), but by the same relative position in matching segments (rise or recession) of the event, indicating the same underlying hydrological process. Thus, amplitude and timing errors are calculated simultaneously but separately, from point pairs that also match visually, considering complete events rather than only individual points (as is the case with MAPTE). Relative weights can freely be assigned to each component of the Series Distance, which allows (subjective) customization of the metric to various fields of application, but in a traceable way. Each of the three components of the Series Distance can be used in an aggregated or non-aggregated way, which makes the Series Distance a suitable tool for differentiated, process-based model diagnostics. After discussing the applicability of established time series metrics for hydrographs, we present the Series Distance theory, discuss its properties and compare it to those of standard metrics used in Hydrology, both at the example of simple, artificial hydrographs and an ensemble of realistic forecasts. The results suggest that the Series Distance quantifies the degree of similarity of two hydrographs in a way comparable to visual inspection, but in an objective, reproducible way.

Investigation of transient soil moisture profiles yields valuable information of near- surface processes. A recently developed reconstruction algorithm based on the telegraph equation allows the inverse estimation of soil moisture profiles along coated, three rod TDR probes. Laboratory experiments were carried out to prove the results of the inversion and to understand the influence of probe rod deformation and solid objects close to the probe in heterogonous media. Differences in rod geometry can lead to serious misinterpretations in the soil moisture profile but have small influence on the average soil moisture along the probe. Solids in the integration volume have almost no effect on average soil moisture but result in locally slightly decreased moisture values. Inverted profiles obtained in a loamy soil with a clay content of about 16% were in good agreement with independent measurements.

The temporal dynamics of hydrological model performance gives insights into errors that cannot be obtained from global performance measures assigning a single number to the fit of a simulated time series to an observed reference series. These errors can include errors in data, model parameters, or model structure. Dealing with a set of performance measures evaluated at a high temporal resolution implies analyzing and interpreting a high dimensional data set. This paper presents a method for such a hydrological model performance assessment with a high temporal resolution and illustrates its application for two very different rainfall-runoff modeling case studies. The first is the Wilde Weisseritz case study, a headwater catchment in the eastern Ore Mountains, simulated with the conceptual model WaSiM-ETH. The second is the Malalcahuello case study, a headwater catchment in the Chilean Andes, simulated with the physics-based model Catflow. The proposed time-resolved performance assessment starts with the computation of a large set of classically used performance measures for a moving window. The key of the developed approach is a data-reduction method based on self-organizing maps (SOMs) and cluster analysis to classify the high-dimensional performance matrix. Synthetic peak errors are used to interpret the resulting error classes. The final outcome of the proposed method is a time series of the occurrence of dominant error types. For the two case studies analyzed here, 6 such error types have been identified. They show clear temporal patterns which can lead to the identification of model structural errors.

In this study we propose an uspcaling approach for the assessment of (a) sub-catchment/REW scale state variables, and (b) of catchment/REW scale soil hydraulic functions which embed/reflect the effects of critical subscale soil heterogeneities in the unsaturated zone on parameterizations of water flow at the next higher scale. The test area for this investigation is the well observed and studied Weiherbach catchment, which is located in a Loess area in south-west Germany. The approach adopted is to use the spatially averaged outputs and internal state variables generated by a highly detailed physically based numerical model that represents the dominant heterogeneities which are typical for this Loess area, and which has been previously shown to closely portray the dynamics of various state variables and fluxes within the study catchment. For these reasons, this detailed numerical model is deemed to be landscape and process compatible. By running this landscape and process compatible model with boundary and initial conditions observed in the Weiherbach catchment, and different assumed structures for soil heterogeneities, we generated time series of catchment-scale average soil saturations in the unsaturated zone by averaging the corresponding distributed model outputs. Due to the differences in assumed spatial patterns of soil heterogeneities and of macropores, the resulting different model structures yield clearly different time series of catchment scale average soil saturation values. The time series of catchment-scale average soil saturation values generated in this way from the landscape and process compatible model structure are, therefore, deemed as best estimates of the actual time series of average catchment scale soil saturation within the study catchment since the model embeds the fingerprints of typical patterns of soils and macropores and is shown to be physically consistent with a distributed set of soil moisture and discharge observations inside the catchment. Finally, we also derive hillslope scale soil hydraulic functions from simulated hillslope scale drainage experiments for the different assumed hillslope model structures. Different patterns of soil and macroporosity within the hillslope yield clearly different hillslope scale soil hydraulic functions, and these differences are consistent with the REV soil pore spectra of the soils. Assuming simple parametric functions for the soil water retention curve and the hydraulic conductivity curve we then obtain different parameters characterizing these soil hydraulic functions for the different assumed model structures. The different parameters obtained for these different model structures thus embed within them fingerprints of the assumed subscale soil patterns and structures on water flow in the unsaturated zone at the next higher scale, in the sense of Vogel and Roth (2003). The ultimate motivation for this analysis is that the so derived, hillslope or sub-catchment scale soil hydraulic functions will become intrinsic components of physically based numerical models, which use subcatchments as building blocks. Lee et al. (2006; this issue) have utilized hillslope scale soil hydraulic functions, derived similarly with the use of the same landscape and process compatible model, for the parameterisation of the CREW model, which is a numerical implementation of the REW approach (Reggiani et al., 1998, 1999), and showed that these lead to successful implementation of the model in the Weiherbach catchment. Their findings show clearly that the presented upscaling approach does indeed yield useful constitutive relations and target state variables for development and validation of meso-scale hydrological models based on the REW approach, embedding within them the fingerprints of the dominant within-catchment heterogeneities on simulated subsurface flow dynamics at the REW-scale.

Within the present study we shed light on the question whether objective circulation patterns (CP) classified from either the 500 HPa or the 700 HPa level may serve as predictors to explain the spatio-temporal variability of monsoon rainfall in the Anas catchment in North West India. To this end we employ a fuzzy ruled based classification approach in combination with a novel objective function as originally proposed by (Stehlik and BᲤossy, 2002). After the optimisation we compare the obtained circulation classification schemes for the two pressure levels with respect to their conditional rainfall probabilities and amounts. The classification scheme for the 500 HPa level turns out to be much more suitable to separate dry from wet meteorological conditions during the monsoon season. As is shown during a bootstrap test, the CP conditional rainfall probabilities for the wet and the dry CPs for both pressure levels are highly significant at levels ranging from 95 to 99%. Furthermore, the monthly CP frequencies of the wettest CPs show a significant positive correlation with the variation of the total number of rainy days at the monthly scale. Consistently, the monthly frequencies of the dry CPs exhibit a negative correlation with the number of rainy days at the monthly scale. The present results give clear evidence that the circulation patterns from the 500 HPa level are suitable predictors for explaining spatio- temporal Monsoon variability. A companion paper shows that the CP time series obtained within this study are suitable input into a stochastical rainfall model.