Abstract. This study explores the suitability of a single hillslope as a parsimonious representation of a catchment in a physically based model. We test this hypothesis by picturing two distinctly different catchments in perceptual models and translating these pictures into parametric setups of 2-D physically based hillslope models. The model parametrizations are based on a comprehensive field data set, expert knowledge and process-based reasoning. Evaluation against streamflow data highlights that both models predicted the annual pattern of streamflow generation as well as the hydrographs acceptably. However, a look beyond performance measures revealed deficiencies in streamflow simulations during the summer season and during individual rainfall-runoff events as well as a mismatch between observed and simulated soil water dynamics. Some of these shortcomings can be related to our perception of the systems and to the chosen hydrological model, while others point to limitations of the representative hillslope concept itself. Nevertheless, our results confirm that representative hillslope models are a suitable tool to assess the importance of different data sources as well as to challenge our perception of the dominant hydrological processes we want to represent therein. Consequently, these models are a promising step forward in the search for the optimal representation of catchments in physically based models.

Abstract. The increasing diversity and resolution of spatially distributed data on terrestrial systems greatly enhance the potential of hydrological modeling. Optimal and parsimonious use of these data sources requires, 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 mesoscale 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 (DEM); 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 (NMI) 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 emerge 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.

Abstract. We propose an alternative model concept to represent rainfall-driven soil water dynamics and especially preferential water flow and solute transport in the vadose zone. Our LAST-Model (Lagrangian Soil Water and Solute Transport) is based on a Lagrangian perspective of the movement of water particles (Zehe and Jackisch, 2016) carrying a solute mass through the subsurface which is separated into a soil matrix domain and a preferential flow domain. The preferential flow domain relies on observable field data like the average number of macropores of a given diameter, their hydraulic properties and their vertical length distribution. These data may be derived either from field observations or by inverse modelling using tracer data. Parameterization of the soil matrix domain requires soil hydraulic functions which determine the parameters of the water particle movement and particularly the distribution of flow velocities in different pore sizes. Infiltration into the matrix and the macropores depends on their respective moisture state, and subsequently macropores are gradually filled. Macropores and matrix interact through diffusive mixing of water and solutes between the two flow domains, which again depends on their water content and matric potential at the considered depths. The LAST-Model is evaluated using tracer profiles and macropore data obtained at four different study sites in the Weiherbach catchment in southern Germany and additionally compared against simulations using HYDRUS 1-D as a benchmark model. While both models show qual performance at two matrix-flow-dominated sites, simulations with LAST are in better accordance with the fingerprints of preferential flow at the two other sites compared to HYDRUS 1-D. These findings generally corroborate the feasibility of the model concept and particularly the implemented representation of macropore flow and macropore–matrix exchange. We thus conclude that the LAST-Model approach provides a useful and alternative framework for (a) simulating rainfall-driven soil water and solute dynamics and fingerprints of preferential flow as well as (b) linking model approaches and field experiments. We also suggest that the Lagrangian perspective offers promising opportunities to quantify water ages and to evaluate travel and residence times of water and solutes by a simple age tagging of particles entering and leaving the model domain.

Abstract. Interpolation of spatial data has been regarded in many different forms, varying from deterministic to stochastic, parametric to nonparametric, and purely data-driven to geostatistical methods. In this study, we propose a nonparametric interpolator, which combines information theory with probability aggregation methods in a geostatistical framework for the stochastic estimation of unsampled points. Histogram via entropy reduction (HER) predicts conditional distributions based on empirical probabilities, relaxing parameterizations and, therefore, avoiding the risk of adding information not present in data. By construction, it provides a proper framework for uncertainty estimation since it accounts for both spatial configuration and data values, while allowing one to introduce or infer properties of the field through the aggregation method. We investigate the framework using synthetically generated data sets and demonstrate its efficacy in ascertaining the underlying field with varying sample densities and data properties. HER shows a comparable performance to popular benchmark models, with the additional advantage of higher generality. The novel method brings a new perspective of spatial interpolation and uncertainty analysis to geostatistics and statistical learning, using the lens of information theory.

Abstract. 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.