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Surface runoff over time shapes the morphology of the landscape. The resulting forms and patterns have been shown to follow distinct rules, which hold throughout almost all terrestrial catchments. Given the complexity and variety of the earth’s runoff processes, those findings have inspired researchers for over a century, and they resulted in many principles and sometimes proclaimed laws to explain the physics that govern the evolution of landforms and river networks. Most of those point to the 1st and 2nd law of thermodynamics, which describe conservation and dissipation of free energy through fluxes depleting their driving gradients. Here we start with both laws but expand the related principles to explain the coevolution of surface runoff and hillslope morphology by using measurable hydraulic and hydrological variables. We argue that a release of the frequent assumption of steady states is key, as the maximum work that surface runoff can perform on the sediments relates not only to the surface structure but also to “refueling” of the system with potential energy by rainfall events. To account for both factors, we introduce the concept of relative dissipation, relating frictional energy dissipation to the energy influx, which essentially characterises energy efficiency of the hillslope when treated as an open, dissipative power engine. Generally, we find that such a hillslope engine is energetically rather inefficient, although the well-known Carnot limit does not apply here, as surface runoff is not driven by temperature differences. Given the transient and intermittent behaviour of rainfall runoff, we explore the transient free energy balance with respect to energy efficiency, comparing typical hillslope forms that represent a sequence of morphological stages and dominant erosion processes. In a first part, we simulate three rainfall-runoff scenarios by numerically solving the shallow water equations and we analyse those in terms of relative dissipation. The results suggest that older hillslope forms, where advective soil wash erosion dominates, are less efficient than younger forms which relate to diffusive erosion regimes. In the second part of this study, we use the concept of relative dissipation to analyse two observed rainfall runoff extremes in the small rural Weiherbach catchment. Both flood events are extreme, with estimated return periods of 10000 years and produced considerable erosion. Using a previously calibrated, distributed physics-based model, we analyse the free energy balance of surface runoff simulated for the 169 model hillslopes and determine the work that was performed on the eroded sediments. This reveals, that relative dissipation is largest on hillslope forms which relate to diffusive soil creep erosion, and lowest for hillslope profiles relating to advective soil wash erosion. We also find that power in surface runoff and power in the complementary infiltration flux are during both events almost identical. Moreover, there is a clear hierarchy of work, which surface runoff expended on the sediments and relative dissipation between characteristic hillslope clusters. For hillslope forms that are more energy efficient in producing surface-runoff, on average a larger share of the free energy of surface runoff performs work on the sediments (detachment and transport) and vice versa. We thus conclude that the energy efficiency of overland flow during events does indeed constrain erosional work and the degree of freedom for morphological changes. We conjecture that hillslope forms and overland dynamics coevolve, triggered by an overshoot in power during intermittent rainfall runoff events, towards a decreasing energy efficiency in overland flow. This implies a faster depletion of energy gradients during events, and a stepwise downregulation of the available power to trigger further morphological development.

We present a robust approach for quantitative precipitation estimation (QPE) for water resources management in mountainous catchments, where rainfall sums and variability are correlated with orographic elevation, but density of rain gauges does not allow for advanced geostatistical interpolation of rainfall fields. Key of the method is modelling rainfall at unobserved locations by their elevation-dependent expected daily mean, and a daily fluctuation which is determined by spatial interpolation of the residuals of neighbouring rain gauges, scaled according to the elevation difference. The scaling factor is defined as the ratio of covariance and variance, in analogy to the “beta” used in economics. The approach is parameterized and illustrated for the Chirilu catchments (Chillón, Rímac, Lurín) in the Andes near Lima, Peru. The results are compared to conventional IDW (inverse-distance weighting) interpolation and a merged national rainfall product. The method results in QPE that are better matching with observed discharges. The combination of inverse-distance weighting with β-scaling thus provides a robust and flexible means to estimate rainfall input to mesoscale mountainous catchments.

The virtual research environment V-FOR-WaTer provides functionalities to store and access hydrological and other environmental data from various sources and disciplines. We propose a framework to run containerized tools within the V-FOR-WaTer toolbox, that is intended to solve the problem of combining software or scripts developed in different programming languages.The framework is used to manage Docker containers, which can contain software like tools for data analysis or environmental modeling. Alongside the well-known advantages of containerization, such as development speed and efficiency, isolation from the local system, dependency management and portability, the usage of containers also ensures a high degree of reproducibility.Given a scientific context, containers are especially useful to combine scripts in different languages following different development paradigms. To do so, we developed a framework-agnostic container specification which standardizes inputs and outputs from and to containers to ease the development of new tools. As of now we also provide templates for tools developed in Python, R, Octave and NodeJS.We present an exemplary workflow for the CATFLOW hydrological model. Data from the V-FOR-WaTer environment is loaded using a Python tool and preprocessed with an existing R tool. After running the FORTRAN model, existing tools in Python, R and MATLAB are used for analysis and presentation of results. When executing the workflow, the user does not need to be familiar with the different programming languages of individual tools, since the containerized tools are self-contained by definition.

The amount of digitally available environmental data and methods to process these data is continuously increasing. With the DFG project ISABEL, we build on the existing virtual research environment V-FOR-WaTer to support making this data abundance available in an easy-to-use web portal, foster data publications, and facilitate data analyses. Environmental scientists get access to data from different sources, e.g. state offices or university projects, and can share their own data and tools through the portal. Already integrated tools help to easily pre-process and scale the data and make them available in a consistent format. V-FOR-WaTer already contains many of the necessary functionalities to provide and display data from various sources and disciplines. The detailed metadata scheme is adapted to water and terrestrial environmental data. Present datasets in the web portal originate from university projects and state offices. A connection of V-FOR-WaTer to the GFZ Data Services, an established repository for geoscientific data, will ease publication of data from the portal and in turn provides access to datasets stored in this repository. Key to being compatible with GFZ Data Services and other systems is the compliance of the metadata scheme with international standards (INSPIRE, ISO19115). The web portal is designed to facilitate typical workflows in environmental sciences. Map operations and filter options ensure easy selection of the data, while the workspace area provides tools for data pre-processing, scaling, and common hydrological applications. The toolbox also contains more specific tools, e.g. for geostatistics and for evapotranspiration. It is easily extendable and will ultimately include user-developed tools, reflecting the current research topics and methodologies in the hydrology community. Tools are accessed through Web Processing Services (WPS) and can be joined, saved and shared as workflows, enabling complex analyses and ensuring reproducibility of the results.

Soil moisture measurements are very popular. Yet they provide a very incomplete picture about the state of the partially saturated zone and the capillary binding of soil water. Here we propose that the free energy of the soil water stock offers a superior perspective on storage dynamics, as it combines soil water content, gravity potential and matric potential data. Based on this new state variable, we show that the partially saturated zone is characterized by a system-specific balance of storage and release corresponding to local state of minimum free energy. The latter depends on the soil water retention curve and topography/depth to groundwater. In the absence of an external rainfall or radiative forcing, the system will thus naturally relax back to and persist in this equilibrium. Hydrological systems are however not isolated, they are frequently forced out of their equilibrium either by rainfall or by radiation driven evaporation. Here we show that the corresponding storage dynamics manifests as deviations of the free energy from and relaxations back the local equilibrium and that the latter separates two different regimes, which are either associated with a storage excess and overshoot of potential energy or a storage deficit and overshoot of capillary binding energy. We demonstrate that these pseudo oscillations are distinctly different in different hydrological landscapes. As the free energy state of the soil water stock, the storage equilibrium and the ranges of both storage regimes depend jointly on depth to groundwater and the soil water retention curve, we combine both controls into a hydrological system characteristics we call the ‘energy state function’ of the soil. We show that the latter allows an insightful inter-comparison of storage dynamics with in different hydrological landscapes, and a priory estimate of depth to groundwater, based on available soil moisture and matric potential data. Finally, we demonstrate a threshold-like relation between the free energy of soil water in the riparian zone and streamflow generation, where the tipping points coincides with the transition from a storage deficit to a storage excess.

We develop an integrated model framework for the simulation of a multitude of soil hydrological processes, such as (reactive) solute transport together with (preferential) water flow and diffusive mixing on the pore scale. This framework is called the Lagrangian Soil Water and Solute Transport (LAST) Model. It bases on a new theoretical concept and should serve as alternative to the common theories of the Darcy-Richards equation and the advection-dispersion-equation (ADE), which have limitations under more natural conditions.In the LAST-Model framework, soil water is represented by discrete water particles of constant mass. The model applies a Lagrangian perspective on the trajectories of particles through a partially saturated soil domain. Particle displacements along the trajectories are calculated by a non-linear, space domain random walk that combines physics and stochastic. We gradually extend the scope of the LAST-Model framework by additional routines.We implement routines for solute transport and preferential flow. Water particles are assigned by a solute mass and in this way, solutes are distributed together with the displacement of water particles. For preferential flow, a structural macropore domain is implemented as a second flow domain. Particles can infiltrate and travel purely by gravity in the macropore domain, independent from capillary-flow conditions in the soil matrix. As a result, they can bypass the bulk water fractions in the soil matrix before re-infiltrating the matrix and accumulating in greater depths.We modify the solute transport routine to allow for the simulation of the transport of reactive substances. Specific routines for sorption and degradation processes are implemented. Sorption is represented by an explicit solute mass transfer between water particles and the solid phase by means of non-linear Freundlich isotherms, and driven by a concentration gradient. Adsorbed solutes are then assumed to be microbially degraded following first-order decay kinetics.We introduce the diffusive pore mixing (DIPMI) approach as additional routine for the simulation of pore-size-dependent diffusive mixing of water and solutes over the pore space. This approach should produce more reliable descriptions of frequently observed (imperfect) mixing behaviours, in contrast to the common assumption of averaging concentrations over all pore sizes in a single time step.Each model extension is tested by simulations of field and laboratory experiments as well as sensitivity analyses. Simulation results are compared against observed data and results of a benchmark model that uses the Darcy-Richards theory and the ADE. The most important findings of the studies can be summarized as:The structural macropore domain is key for a successful representation of preferential water flow and (reactive) solute transport. In heterogeneous soils, LAST simulations match better the observed redistribution and depth-accumulation of solutes compared to simulations with the Darcy-Richards + ADE model. Imperfect, diffusive mixing on the pore scale has a significant influence on macroscopic leaching behaviours and chemical/isotopic compositions of soil water fractions. The particle-based approach of the LAST-Model framework is a promising tool for further soil- and ecohydrological application fields.

The understanding of soil hydrological processes in agroforestry systems has increased in recent years. However, key aspects determining the successful functionality of agroecosystems (e.g. plant-water availability, nutrient supply) are influenced by many factors and are therefore challenging to generalize. Such information is critical for management and planning strategies. If dominant processes such as evapotranspiration and the related controls on the soil water stock can be represented adequately in hydrological models at the plot scale, they can provide useful insights for practitioners.Here, we tested whether the physically-based CATFLOW model is capable of reproducing soil moisture dynamics in a South African agroforestry system consisting of windbreaks and irrigated blackberry plants. We initialised the model with matric potential measurements and calibrated it to soil moisture dynamics at two locations with differing vegetation within the test site. After successful calibration, several numerical experiments were performed to shed light on the presence and absence of windbreaks and of different irrigation strategies on the seasonal dynamics of plant available soil water at the test site. The model and observations were also compared in the frequency domain by using empirical mode decomposition as an additional model verification.The measured soil moisture time series are dominated by a gradual drying of the soil throughout the summer, which is less pronounced in the deeper soil ranges, while several rain events interrupted this general pattern. The model captured the drying as well as the amplitudes of the rain peaks well. However, there was an offset between measured and modelled absolute values due to the initiation based on matric potential. The simulated water balance revealed distinct differences between the windbreak and berry rows due to differences in rain interception, and evapotranspiration or irrigation patterns. Similarities in the frequency spectrum of observed and modelled values were apparent. On the other hand, the modelled time series showed more distinct spectra and less noise. Currently, more detailed analyses are being carried out to extract information from the frequency spectra.

Convective rainfall extremes usually trigger due to their highly localised and intense input of mass and momentum ‘hot moments’ in water and matter cycling. Terrestrial systems then respond with strong Hortonian overland flow and erosion up to the formation of flash floods. While heavy precipitation events are characterised by multi-decadal variability, it is noteworthy that the largest observed floods in many rivers of Europe have occurred in the last three decades. Similarly, flash floods have also intensified. The recent clustering of extremes likely reflects the ongoing acceleration of the hydrological cycle, with expected increasing frequencies of intense convective rainstorms and related flash flood and erosion events due to Clausius-Clapeyron scaling. This urgently calls for an improved understanding and models that allow the design of strategies to mitigate onsite and catchment-wide offsite damages of flash floods and erosion events.Hortonian overland flow occurs when precipitation intensity exceeds the soil’s infiltration capacity. The latter depends on the soil water content, soil hydraulic properties and the density and connectivity of vertical preferential flow paths and are often biologically mediated, as in the case of worm borrow and root channels. Whether locally generated surface runoff reaches the stream depends on the generated spatial connectivity of overland flow paths to the river network.Here we propose that land use management and soil surface preparation bear the key to reducing the formation of Hortonian overland flow and the connectivity of its flow path, e.g., through a locally elevated infiltration capacity and roughness, thereby reducing the overland flow velocity and favouring its re-infiltration. Moreover, we demonstrate that physically based hydrological models are key to quantifying how changes in landuse and surface preparation techniques (including buffer areas, vegetation barriers, and fascines) in combination with local flood defense reservoirs reduce the formation of flood runoff during convective extremes. Specifically, we use the model CATFLOW and the representative hillslope approach to investigate flash floods observed in four ungauged headwaters catchments in the Kraichgau, Baden-Württemberg (Germany) in 2016. While each catchment drains into a regulated flood defense reservoir, we inverted the flood hydrograph/ inflow into the flood reservoirs using water level measurements and reservoir geometry equations. LULC maps are derived from LANDSAT images using spectral profiles obtained from field surveys over the region. Since flash floods are often associated with localised short-duration, high-intensity rainfall of convective origin, the model is forced using commercial radar-based precipitation products. The CATFLOW model was set up separately for the four headwaters by transferring a completed hillslope setup (soil catena, soil hydraulic properties, plant roughness parameters) from a gauged Weiherbach experimental catchment in the same landscape while deriving the representative hillslope profiles from the digital elevation data. Our results indicate that physically based models perform well in capturing the dynamics of the reconstructed hydrographs, which speaks a) for the transferability of physically based model structures within the same hydrological landscape and b) the feasibility of representative hillslope approach and c) the usefulness of the radar product.

We present a robust approach for quantitative precipitation estimation (QPE) for water resources management in mountainous catchments, where rainfall sums and variability are correlated with orographic elevation, but density of rain gauges does not allow for advanced geostatistical interpolation of rainfall fields. Key of the method is modelling rainfall at unobserved locations by their elevation-dependent expected daily mean, and a daily fluctuation which is determined by spatial interpolation of the residuals of neighbouring rain gauges, which are scaled according to the elevation difference. The scaling factor is defined as the ratio of covariance and variance, in analogy to the "beta" used in economics.The approach is illustrated for the Chirilu catchments (Chillón, Rímac, Lurín) in the Andes near Lima, Peru. The results are compared to conventional IDW interpolation and a merged national rainfall product. The method results in QPE that are better matching with observed discharges. The β-IDW approach thus provides a robust and flexible means to estimate rainfall input to mesoscale mountainous catchments.

We provide an extension of a well established geostatistical software to allow for effective and interactive assessment of environmental scenarios in a geostatistical context. The extension comprises a pre-built interface and a freely accessible demo application.The heat of the approach relies on replacing a sample variogram with its uncertainty bound. Doing so enables one to fully and consistently embed various sources of uncertainties stemming from available datasets and methodological approaches employed for their interpretation. Methodological approaches included in the software include capabilities leading to: i) a statistical estimation of uncertainty bounds from residual point-pair distributions; ii) a statistical robustness test for uncertainty bounds; and iii) a Monte Carlo simulation tool to propagate a variety of aleatory uncertainties. We illustrate the capabilities of our approach and software through the analysis of two different datasets. We focus on manual variogram estimation to comprehensively illustrate how insights on uncertainty can be used to reject candidate variogram models or model parameter sets.

In recent years, major floods triggered by convective events during the summer months repeatedly occurred in central western Europe, where flood regimes had previously been characterised by slowly developing inundations in winter. This imposes a great challenge on conceptual hydrological models, as other runoff mechanisms seem to dominate during convective storms than the storage-driven runoff production, which dominates flood formation in the wet season. Hence, most hydrological models that are used for operational flood forecasting struggle when applied to convective events and show deficiencies in capturing peak flows and timing flood volumes. It is thereby unclear to which extent the uncertainty in precipitation input and discharge observations, the influence of the catchment state, the model structure itself, or a combination of several or all of these factors, compromise successful predictions. To shed light on this question, we will compare how different model structures perform during high flows across a range of catchment physiographic settings. We will analyse the performance of a conceptual hydrological water balance model and identify its deficiencies by comparing it to a data driven model. This comparison will reveal whether uncertainties in the input and output data or model structural deficiencies are the major source of error. This will allow us to identify systematic errors, compare them and improve the model structure.

The amount and diversity of digitally available environmental data is continuously increasing. However, they are often hardly accessible or scientifically usable. The virtual research environment V-FOR-WaTer aims at simplifying data access for environmental sciences, fostering data publications and facilitating data analyses.V-FOR-WaTer already contains many of the necessary functionalities to provide and display data from various sources and disciplines. The detailed metadata scheme is adapted to water and terrestrial environmental data. Present datasets in the web portal originate from university projects and state offices. We are also finalising the connection of V-FOR-WaTer to GFZ Data Services, an established repository for geoscientific data. This will ease publication of data from the portal and in turn give access to datasets stored in this repository. Key to being compatible with GFZ Data Services and other systems is the compliance of the metadata scheme with international standards (INSPIRE, ISO19115).The web portal is designed to facilitate typical workflows in environmental sciences. Map operations and filter options ensure easy selection of the data, while the workspace area provides tools for data pre-processing, scaling, and common hydrological applications. The toolbox also contains more specific tools, e.g. for geostatistics and for evapotranspiration. It is easily extendable and will ultimately include user-developed tools, reflecting the current research topics and methodologies in the hydrology community. Tools are accessed through Web Processing Services (WPS) and can be joined, saved and shared as workflows, enabling complex analyses and ensuring reproducibility of the results. To build workflows we include an easy-to-use drag and drop user interface.

Estimates of evapotranspiration (ET) which can be derived from in-situ measurements are often difficult to compare because they originate from different research disciplines, were collected at different scales using a range of methods, and they entail method-specific uncertainties.The BRIDGET toolbox – developed within the Digital Earth project – aims to support the harmonisation and scaling of diverse in-situ ET measurements by providing tools for storage, merging and visualisation of multi-scale and multi-sensor ET data. This requires an appropriate metadata description for the various measurements as well as an assessment of method-specific uncertainties.BRIDGET is implemented both as a standalone Python package and as part of the existing virtual research environment V-FOR-WaTer. It is organised as a toolbox consisting of several sub-sections which deal with the different in-situ measurement methods, their typical scaling approaches and most relevant analysis functions. A corresponding uncertainty framework is developed separately as a Python package and as a tool in V-FOR-WaTer. Our first focus for BRIDGET is upscaling tree-level sap flow measurements and comparing them to respective transpiration estimates from eddy covariance and lysimeters.

The concept of canopy-scale resistances was developed to investigate and evaluate the transfer of momentum, heat and mass from the leaf surface to the canopy air space and to the atmosphere. Therefore, reliable estimates of resistances are of fundamental importance for studying the ecosystem scale fluxes and land-atmosphere interaction. The canopy-scale resistance has two components: the leaf boundary layer resistance and canopy-air-to-atmosphere resistance. In big-leaf conceptualizations, canopy-scale resistances are represented in a single term called aerodynamic resistance, which refers to the resistance between an idealized ‘big-leaf’ and the atmosphere for the transfer of momentum, heat and mass. A decent amount of literature exists on the estimation of aerodynamic resistances for various ecosystems based on the roughness length parametrizations and atmospheric stability correction. Most of these parametrizations do not include the leaf boundary layer explicitly and therefore rely on a conceptual 'aerodynamic temperature' at some distance above the leaf surface. This gap hampers reliable modelling of canopy gas exchange (transpiration and CO2 assimilation) as these processes happen directly at the leaf surface and strongly rely on accurately capturing the leaf surface temperature. To bridge this gap, an additional resistance based on a ‘kB-1' parametrization is commonly added to the classical aerodynamic resistance. The objective of the present study is to estimate the total resistance to heat transfer from the heat exchanging surfaces to the measurement height and to find the most appropriate mathematical formulation for this resistance. We used radiometric and eddy covariance (EC) measurements from a wide range of land cover types and estimated the total resistance to heat transport using measured fluxes and radiometric surface temperatures by inverting the flux-profile equation. We also performed a comprehensive comparison of total resistance estimates with commonly used stability and roughness-based resistance formulations, including ‘KB-1' parametrizations and the momentum flux resistance inverted from EC measurements. We found that total resistances were consistently greater than the roughness length-based resistance parametrizations at most of the study sites. We further found that the difference between the total and aerodynamic resistance can be largely explained by dominant leaf sizes at the individual sites. Based on these results, we propose a consistent canopy resistance formulation by explicitly considering leaf sizes and leaf boundary layer resistances in combination with an adequate representation of aerodynamic canopy-atmosphere resistance. This approach will enable a consistent coupling of the aerodynamic process with physiological leaf-scale processes such as photosynthesis and stomatal control, which depend on and interact with leaf temperature, and aerodynamic stability.

Agroforestry systems (AFSs) are associated with many benefits such as augmented soil fertility or enhanced biodiversity. However, in water-limited areas the competition over water resources between trees and crops can reduce the productivity of the crop component. We want to share some of our results gained from in-depth analyses of time series (October 2019 to March 2020) and campaign (September 2019) data of soil moisture and matric potential in a South African AFS.Soil water content was measured in a soil profile at two locations within an AFS plot: alongside a windbreak consisting of Italian Alders (Alnus cordata) and amongst the crop i.e. within blackberry rows. Matric potential time series are only available at the windbreak soil profile. Surficial soil samples taken along transects perpendicular to the windbreak were analysed for physical properties (e.g. texture, water retention curve).Based on extracted water retention curves and matric potential time series, we found no evidence for plant water limitation during the measurement period (summer months) within the field site. Estimated root water uptake indicated that the trees take water from a greater range of depths, including deeper layers, than the blackberry plants. We observed divergent hydrological behaviour of the soil at the two locations during precipitation events, potentially resulting from dissimilar storage capacities and runoff formation potentials. Furthermore, the matric potential revealed hydrological information on plant water usage that was not as obvious from the soil moisture data.

Sap flow encodes information about how plants regulate opening and closing of stomata in response to varying soil water supply and atmospheric water demand. This study leverages this valuable information with data-model integration and deep learning to estimate canopy conductance in a hybrid catchment-scale model for more accurate hydrological simulations. Using data from three consecutive growing seasons, we first highlight that integrating canopy conductance inferred from sap flow data in a hydrological model leads to more realistic soil moisture estimates than using the conventional Jarvis-Stewart equation, particularly during drought conditions. The applicability of this first approach is, however, limited to the period where sap flow data are available. To overcome this limitation, we subsequently train a deep learning network to predict catchment-averaged sap velocities based on standard hourly meteorological data. These simulated velocities are then used to estimate canopy conductance, allowing simulations for periods without sap flow data. We show that the hybrid model, which uses the canopy conductance from the machine learning approach, matches soil moisture and transpiration equally well as model runs using observed sap flow data and has good potential for extrapolation beyond the study site. We conclude that such hybrid approaches open promising perspectives for more parsimonious process parametrizations by improving our ability to incorporate novel or untypical data sets into hydrological models.

Vegetation exhibits critical feedback with runoff generation. Trees show distinct water uptake patterns relying on soil water from different depths and groundwater with a mixture of water sources that is commonly very different from runoff in terms of age distribution and isotopic composition. Here we present a multi-method and multi-model approach to study the spatio-temporal patterns of sap flow and age distribution of tree water uptake and streamflow in a headwater catchment (mixed forest, 43 ha). For this, we monitored sap flow spatially distributed at >30 trees over two years, sampled 2H and 18O bi-weekly and spatially distributed in xylem for two years and in streamflow sub-daily for four years. This was supplemented by tritium sampling in streamflow over two years for different flow stages. We used statistical modeling to determine spatio-temporal patterns of transpiration and isotopic composition of xylem water and their drivers. We used a multi-model approach to derive catchment travel times through (i) composite Storage Selection (SAS) functions, (ii) conceptual hydrological modeling, and (iii) coupled land surface-subsurface modeling (ParflowCLM) combined with particle tracking. Statistical data analysis revealed that tree species, tree diameter, and topographic wetness index at the tree location were the main driver of spatial variability of sap flow, while soil water was the main source of xylem water with little groundwater influence. The travel time modeling showed a strong seasonal and event-based variability of travel times and allowed to include information on vegetation behavior with different complexity. Last, our detailed sampling of vegetation offers a blueprint for a sampling strategy of isotopes in xylem water for travel time studies. Our data revealed that approximately 20 sampled trees are sufficient to capture the mean isotopic value of xylem water of a species at our study site, while we needed around 100 samples to detect landscape influence on the xylem isotopes needed for considering spatial patterns in the travel time analysis. Our results underline the feedbacks between vegetation and runoff generation and show their relevance for better simulating catchment travel times.

A recent experiment of Bowers et al. (2020) revealed that diffusive mixing of water isotopes (δ2H and δ18O) over a fully saturated soil sample of a few centimetres in length required several days to equilibrate completely. In this study, we present an approach to simulate such time-delayed diffusive mixing processes, on the pore scale, beyond instantaneously and perfectly mixed conditions. The diffusive pore mixing (DIPMI) approach is based on a Lagrangian perspective on water particles moving by diffusion over the pore space of a soil volume and carrying concentrations of solutes or isotopes. The idea of DIPMI is to account for the self-diffusion of water particles across a characteristic length scale of the pore space using pore-size-dependent diffusion coefficients. The model parameters can be derived from the soil-specific water retention curve, and no further calibration is needed. We test our DIPMI approach by simulating diffusive mixing of water isotopes over the pore space of a saturated soil volume using the experimental data of Bowers et al. (2020). Simulation results show the feasibility of the DIPMI approach for reproducing the measured mixing times and concentrations of isotopes at different tensions over the pore space. This result corroborates the finding that diffusive mixing in soils depends on the pore size distribution and the specific soil water retention properties. Additionally, we perform a virtual experiment with the DIPMI approach by simulating mixing and leaching processes of a solute in a vertical, saturated soil column and compare the results against simulations with the common perfect mixing assumption. The results of this virtual experiment reveal that the frequently observed steep rise and long tailing of breakthrough curves, which are typically associated with non-uniform transport in heterogeneous soils, may also occur in homogeneous media as a result of imperfect subscale mixing in a macroscopically homogeneous soil matrix.

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.

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.

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.

In recent years, flash floods occurred repeatedly in temperate regions of central Western Europe (e.g., Orlacher Bach (GER), Hupselsebeek (NL), White Ernz (LUX)). This type of extreme flood events is unusual for these regions, as opposed to Mediterranean catchments that are more prone to flash floods. In the second half of the 20th century, and more specifically in the 1990’s, westerly atmospheric fluxes were the dominating triggering factor of large scale (winter) floods in central Western Europe.With a view to gain a better understanding of the mechanisms controlling the recent flash flood events at higher latitudes, we explore various avenues related to the non-stationarity of environmental systems. We hypothesize that an increase in the occurrence of flash flood prone atmospheric conditions has recently led to higher precipitation totals and a subsequent increase in flash flood events in central Western Europe.Therefore, we first analysed relevant atmospheric parameters from the ERA 5 reanalysis dataset. Second, we linked the atmospheric parameters to the concept of general circulation patterns as per Hess and Brezowsky (1977). Third, we analysed precipitation data from a set of stations located in the Moselle river basin (35.000 km2). These three pillars build the base for identifying flash flood prone atmospheric conditions over space and time that are then compared to actual occurrences of extreme discharge events in streams within the Moselle river basin.To validate our hypothesis, spatial and temporal patterns in the occurrence of extreme precipitation and discharge events need to match atmospheric patterns. Preliminary results suggest that daily precipitation data and meridional circulation patterns do not show a clear trend towards an increased occurrence of precipitation events or higher precipitation amounts. Due to the limitations inherent to the available long-term dataset of daily data, the hypothesis can only be partly evaluated, and more detailed analyses are added. For that reason, discharge data with a 15-minute resolution, along with precipitation radar data of 5-minute time steps will be employed at a limited spatial extent in future analyses. In case of rejection of our working hypothesis this may pinpoint to other flash flood triggering mechanisms, such as changes in land use, soil moisture conditions or cultivation methods.

Since Horton’s famous reinterpretation of Playfair’s law hydrologists have marvelled over the organization of drainage networks in catchments and on hillslopes. We start at the cross junction of hillslope hydraulics and geomorphology, trying to interpret the formation of hydraulic networks and erosion alike and wondering why movement of fluid creates structure at all.In its most basic form structure and form has been explained as the result of optimization, either of certain types of energy such as free energy or its thermodynamic counterpart entropy. Research has shown that river networks and river junctions tend to minimize dissipation of kinetic energy and it has been suggested that simultaneously other forms of free energy, such as sediment transport tend to increase along the flow path. Studies have focused on hydraulic networks on the hillslope scale as well as on the catchment scale. Surprisingly little attention has been given to the question why these networks exists in the first place and why discharge confluences towards the catchment outlet.In the first part of our study we put Hortonian surface runoff into a thermodynamic framework and derive the energy balance for steady state runoff. We derive the equations on the hillslope scale, where we observe the transition from evenly distributed potential energy (the rainfall) to spatially organized discharge in micro rills to larger rills and gullies. In hydraulic terms we distinguish between sheet- and rill flow. We then apply Manning-Strickler’s equation to estimate the distribution of hydraulic variables and compare energy conversion rates on typical 1D hillslope profiles for sheet- and rill flow. Interestingly, we find that only certain hillslope forms lead to spatial maxima of stream power.In the second part of the study we extend the energy balance to transient flow and analyse power maxima during typical rainfall-runoff events. Finally, we relate our findings to observable, measurable hydraulic structures such as rill systems and estimate past work on sediments. We believe that current energy dynamics of surface runoff reflects past optimization and therefore holds potential for the understanding of landscape evolution and surface runoff contributions alike.

Comparing estimates of evapotranspiration (ET) from different in-situ measurements – or between in-situ measurements and remote sensing products or modelling outputs – always entails the challenge of different scales and method-specific uncertainties. Especially when the estimates originate in different research disciplines, addressing and quantifying the various sources of uncertainty of the scaled ET values becomes a difficult task for individual researchers who are not familiar with all the methodological details.The BRIDGET toolbox – developed within the Digital Earth project – wants to support the integration and scaling of diverse in-situ ET measurements by providing tools for storage, merging and visualisation of multi-scale and multi-sensor ET data. This requires an appropriate metadata description for the various measurements as well as an assessment of method-specific uncertainties which need to be supported by domain experts. We combine these tools in a standalone python package and also implement them in an existing virtual research environment (V-FOR-WaTer).Our first use case defines and quantifies the various sources of uncertainty when scaling sap flow values from individual sensor measurements in a tree up to the transpiration estimate of a stand. Comparison estimates come from eddy covariance measurements, lysimeters and remote sensing products.

The virtual research environment V-FOR-WaTer aims at simplifying data access for environmental sciences, fostering data publications and facilitating data analyses. By giving scientists from universities, research facilities and state offices easy access to data, appropriate pre-processing and analysis tools and workflows, we want to accelerate scientific work and facilitate the reproducibility of analyses.The prototype of the virtual research environment consists of a database with a detailed metadata scheme that is adapted to water and terrestrial environmental data. Present datasets in the web portal originate from university projects and state offices. We are also finalising the connection of V-FOR-WaTer to GFZ Data Services, an established repository for geoscientific data. This will ease publication of data from the portal and in turn give access to datasets stored in this repository. Key to being compatible with GFZ Data Services and other systems is the compliance of the metadata scheme with international standards (INSPIRE, ISO19115).The web portal is designed to facilitate typical workflows in environmental sciences. Map operations and filter options ensure easy selection of the data, while the workspace area provides tools for data pre-processing, scaling, and common hydrological applications. The toolbox also contains more specific tools, e.g. for geostatistics and soon for evapotranspiration. It is easily extendable and will ultimately also include user-developed tools, reflecting the current research topics and methodologies in the hydrology community. Tools are accessed through Web Processing Services (WPS) and can be joined, saved and shared as workflows, enabling more complex analyses and ensuring reproducibility of the results.

Ecohydrological systems are a result of long-term co-evolution of soils, biota and atmospheric conditions, and often respond to perturbations in non-intuitive ways. Their short-term responses can be explained and sometimes predicted if we understand the underlying dynamic processes and if we can observe the initial state precisely enough. However, how do they co-evolve in the long-term after a change in the boundary conditions? In 1922, Alfred Lotka hypothesised that the natural selection governing the evolution of biota and composition of ecosystems may be obeying some thermodynamic principles related to maximising energy flow through these systems. Similar thoughts have been formulated for various components of the Earth system and individual processes, such as heat transport in the atmosphere and oceans, erosion and sediment transport in river systems and estuaries, the formation of vegetation patterns, and many others. Different thermodynamic optimality principles have been applied to predict or explain a given system property or behaviour, of which the maximum entropy production and the maximum power principles are most widespread. However, the different studies did not use a common systematic approach for the formulation of the relevant system boundaries, state variables and exchange fluxes, resulting in considerable ambiguity about the application of thermodynamic optimality principles in the scientific community. Such a systematic framework has been developed recently and can be tested online at:https://renkulab.io/projects/stanislaus.schymanski/thermodynamic_optimality_blueprintIn the present study, we illustrate how such a common framework can be used to classify and compare different applications of thermodynamic optimality principles in the literature, and discuss the insights gained and key criteria for a more rigorous testing of such principles.

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.

This study proposes an alternative framework to quantify and explain the enigmatic emergence of preferential flow and transport in heterogeneous saturated porous media, using concepts from thermodynamics and information theory. We examined simulations of two-dimensional fluid flow and solute transport based on the methods of Edery et al. (2014) at total head differences of 100 and 10 characterized the discrete probability distribution of solute particles to cross a distinct transversal position in a plane normal to the direction of the mean flow by means of the Shannon entropy. In general, we found a declining entropy with increasing downstream transport distance, reflecting a growing downstream self-organization due to the increasing concentration of particles in preferential flow paths. Strikingly, preferential flow patterns with lower entropies emerged when analyzing simulations in media with larger variances in hydraulic conductivity, and this enhanced self-organization appeared even stronger for simulations at lower head differences. This implies that macro-states of higher order are established, despite the higher randomness of ln(K) for a range of Peclet numbers representing strong and intermediate importance of advective transport. The key to explain this almost paradoxical behavior is the finding that power in the vertical flow components grows with the variance of the hydraulic conductivity field. Due to this larger energy input, the vertical/transversal flow component may perform more work to increase the order in the flow path distribution, through steepening transversal concentration gradients as reflected in lower entropies. The emergence of spatially organized preferential transport and the related decline in flow path entropy essentially requires that the entropy is exported from the system. Consistently, we found that a declining entropy in lateral distribution of flow paths goes along with a rising entropy in the associated breakthrough curve. This space-time asymmetry in entropy implies that perfect organization and certainty about both flow paths and travel times can never simultaneously occur. This required consummation of entropy and thus violation of the second law of thermodynamics. We thus propose that the combined use of free energy and entropy holds the key to characterize, quantify and predict the self-organized emergence of preferential flow phenomena and to explain the underlying cause of their emergence.References:Edery, Y., Guadagnini, A., Scher, H., and Berkowitz, B.: Origins of anomalous transport in disordered media: Structural and dynamic controls, Water Resour. Res., 50, 1490-1505, doi:10.1002/2013WR015111, 2014.

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.

This study investigates the role and value of distributed rainfall for the runoff generation of a mesoscale catchment (20 km2). We compare the performance of three hydrological models at different periods and show that a distributed model driven by distributed rainfall yields only to improved performances during certain periods. These periods are dominated by convective storms that are typically characterized by higher spatial and temporal variabilities compared to stratiform precipitation events that dominate the rainfall generation in winter. Motivated by these findings we develop a spatially adaptive model that is capable to dynamically adjust its spatial structure during runtime to represent the varying importance of distributed rainfall within a hydrological model without losing predictive performance compared to a spatially distributed model. Our results highlight that adaptive modeling might be a promising way to better understand the varying relevance of distributed rainfall in hydrological models as well as reiterate that it might be one way to reduce computational times. They furthermore show that hydrological similarity concerning the runoff generation does not necessarily mean similarity for other dynamic variables such as the distribution of soil moisture.

Soil moisture plays an important role for the understanding of hydrological processes due to its influence on water and energy fluxes between the soil surface and the atmosphere. Knowledge of soil water dynamics is especially critical in water-scarce areas. In agroforestry systems, for instance, excessive competition for water between the trees and crops might outweigh the benefits of the system, thus preventing a successful implementation.Several techniques exist for measuring soil moisture and commercial devices vary widely in cost, reliability and efficiency. An alternative approach could be to estimate soil moisture dynamics from soil thermal dependencies. Similar approaches are already being used in remote sensing, as soil moisture influences the soil thermal properties and thus the surface energy balance and soil heat transfer. However, few studies have tested the feasibility of estimating in-situ soil moisture dynamics from soil temperature dynamics within a soil profile. Temperature sensors are cheaper, smaller and technically robust and could thus provide an interesting alternative to available commercial soil moisture sensors.In this study, we quantify the effect of soil moisture on phase shift and amplitude attenuation of soil temperature to estimate soil moisture content. We investigate these relationships from two different angles. Firstly, we use virtual measurements in coupled model simulations of soil water and soil heat dynamics to infer the general feasibility and precision of the method in an idealized error-free world. A sensitivity analysis can give insights on how the parametrization of the thermal diffusivity affects the precision and feasibility. Secondly, we compare findings from these simulations to results from analyzing time series of both soil moisture and soil temperature measured in an agroforestry field site in South Africa. A tentative analysis of these time series reveals that the amplitude attenuation and phase shift in the daily temperature signal is clearly sensitivity to changes in soil moisture. Finally, we aim to setup a coupled model for the study site based on the available soil hydraulic and textural data and compare simulated with observed phase shifts and attenuations at different depths.

Catchment travel time distributions (TTDs) are an integrative measure of time-varying flow paths and hydrological processes, commonly derived from tracer data (e.g. 2-H, 3-H). Recently, it has been argued that the use of stable isotopes of O and H compared to tritium neglects the long tails of TTDs and thus truncates our vision on streamflow age. However, the reasons for the truncation of the TTD remain obscured by methodological and data limitations, including different mathematical models and sampling strategies. In this study, we apply composite SAS functions to a forested headwater catchment in Luxembourg, where the complexity of streamflow generation leads to flow paths with highly different TTDs. We calibrate the model with high-frequency (sub-daily) deuterium measurements, as well as nearly 30 tritium stream samples collected over a two-year period. We simulated TTDs based on each tracer individually and jointly. We found that, when using the two tracers in a coherent methodological framework, both tracers result in similar TTD and storage for the studied catchment. We found small differences in the TTDs that might be explained by calculation uncertainties, as well as by the limited sampling frequency for tritium. Using both stable and radioactive isotopes of H as tracers reduced uncertainties in the water age and storage calculations. While tritium and stable isotopes delivered redundant information about younger water, the use of both tracers leveraged the more specific information content of tritium on longer ages in the system. The two tracers had overall different information contents. We found that 30 tritium samples contained more bits of information than approximately 1000 deuterium samples, underlying the importance of complementing stable isotopes studies with tritium data.

V-FOR-WaTer, as a virtual research environment, wants to simplify data access for environmental sciences, foster data publications and facilitate preparation of data and their analyses with a comprehensive toolbox. A large number of datasets, covering a wide range of spatial and temporal resolution, is still hardly accessible for others than the original data collector. Frequently these datasets are stored on local storage devices. By giving scientists from universities and state offices open access to data, appropriate pre-processing and analysis tools and workflows, we accelerate scientific work and facilitate the reproducibility of analyses.The prototype of the virtual research environment was developed during the last three years. Today it consists of a database with a detailed metadata scheme that is adapted to water and terrestrial environmental data and compliant with international standards (INSPIRE, ISO19115). Data in the web portal originate from university projects and state offices. The connection of V-FOR-WaTer to established repositories, like the GFZ Data Services, is work in progress. This will simplify both, the process of accessing publicly available datasets and publishing the portal users’ data, which is increasingly demanded by journals and funding organisations.The appearance of the web portal is designed to reproduce typical workflows in environmental sciences. A filter menu, based on the metadata, and a graphical selection on the map gives access to the data. A workspace area provides tools for data pre-processing, scaling, common hydrological applications and more specific tools, e.g. geostatistics. The toolbox is easily extendable due to the modular design of the system and will ultimately also include user-developed tools. The selection of the tools is based on current research topics and methodologies in the hydrology community. They are implemented as Web Processing Services (WPS); hence, the tool executions can be joined with one another and saved as workflows, enabling more complex analyses and reproducibility of the research.

Recently, we proposed 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 is based on a Lagrangian perspective on the movement of water particles (Zehe and Jackisch, 2016) carrying solute masses through the subsurface which is separated into a soil matrix domain and a preferential flow domain (Sternagel et al., 2019). 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 either be derived 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 pores 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 was evaluated using tracer profiles and macropore data obtained at four different study sites in the Weiherbach catchment in south Germany and additionally compared against simulations using HYDRUS 1-D as benchmark model. The results generally corroborated the feasibility of the model concept and particularly the implemented representation of macropore flow and macropore-matrix exchange. We thus concluded that the LAST-Model approach provides a useful and alternative framework for simulating rainfall-driven soil water and solute dynamics and fingerprints of preferential flow.This study presents an extension of the model allowing for the simulation of reactive solute transport. Transformation kinetics are considered by transferring mass from the parent to the child components in each water particle according to the corresponding reaction rates, which is limited by the compound solubility. A retardation coefficient is not helpful in the particle-based framework, as the solute mass is carried by the water particles and travels thus by default at the same velocity. Ad- and desorption are explicit represented through transfer of dissolved mass from the water particles at a given depth to surrounding adsorption sites of the soil solid phase and vice versa. This may either operate under rate-limited or non-limited conditions. Adsorbed solute masses will be considered to be degraded following first-order reaction kinetics. The retardation process delays the solute displacement and enables a suitable time scale for the degradation process, which must be smaller than the time scale for the re-mobilization of the solutes. The proposed extension will be benchmarked against observations of pesticide transport in soil profiles and at tile-drained field sites. Zehe, E., Jackisch, C.: A Lagrangian model for soil water dynamics during rainfall-driven conditions, Hydrol. Earth Syst. Sci., 20, 3511–3526, https://doi.org/10.5194/hess-20-3511-2016, 2016. Sternagel, A., Loritz, R., Wilcke, W., and Zehe, E.: Simulating preferential soil water flow and tracer transport using the Lagrangian Soil Water and Solute Transport Model, Hydrol. Earth Syst. Sci., 23, 4249–4267, https://doi.org/10.5194/hess-23-4249-2019, 2019.

How important is information about distributed precipitation when we do rainfall-runoff modeling on the catchments scale?The latter is surely one of the more frequently asked research questions in hydrological modeling. Most studies tackling the issue seem thereby to agree that distributed precipitation becomes more important if the ratio of catchment size against storm size decreases or if the spatial gradients of the rainfall field increase. Furthermore, is it often highlighted that catchments are surprisingly effective in smoothing out the spatial variability of the meteorological forcing, at least, if the focus is simulation integral fluxes and average states.However, despite these agreements there is no straightforward guidance in the hydrological literature when these thresholds have been reached and when the spatial distribution of the precipitation starts dominating. This is because the answer to the above drawn question depends on the spatial variability of system characteristics, on the system state variables as well as on the strength of the rainfall forcing and its space-time variability. As all three controls vary greatly in space and time it is challenging to identify generally valid rules when information about the distribution of rainfall becomes important for predictive modelling.The present study aims to overcome this limitation by developing a model framework to identify periods where the spatial gradients in rainfall intensity are larger than the ability of the landscape to internally dissipate those. This newly developed spatially adaptive modeling approach, uses the spatial information content of the precipitation to control the spatial distribution of our model. The main underlying idea of this approach is to use distributed models only when they are actually needed resulting in 1) a drastic decrease in computational times as well as 2) in a more appropriate representation of a hydrological system. Our results highlight that only during a few periods throughout a hydrological year do distributed precipitation data actually matter. However, they also show that these periods are often highly relevant with respect to certain extremes and that the successful simulation of these extremes require distributed information about the forcing and state of a given system.

Predictions in ungauged basins still present one of the major challenges in hydrology. In many cases, the absence of a stream gauge also implies a low density of the meteorological monitoring network in these catchments and surroundings as well as little available data on water management infrastructure and agricultural consumptions. This combination creates a circle of uncertainties and thus individual influences of relevant water balance components are difficult to disentangle and quantify. The original Budyko curve presents a very general model that yields, to first order, an estimate of the steady-state water balance of a catchment at the climatological scale, assuming its landscape and functioning has evolved naturally and free of anthropogenic interferences. Even at smaller time scales, the Budyko relationship allows approximating the water partitioning in the catchment, and thus helps correct erroneous assumptions[JW1] or missing information about for instance unknown human-induced alterations. On the other hand, an increasing variety of global remote-sensing data products is becoming available providing spatial estimates of land surface properties such as for instance vegetation indexes or soil moisture. Even if the predictive power of such products in terms of absolute values remains questionable, it is possible to derive coarse spatial patterns or temporal dynamics to narrow down zones and orders of magnitude of interferences with the natural hydrological cycle such as reservoirs or irrigated lands. This study combines these two general approaches in order to improve hydrological modelling and system understanding of the semi-arid Lurín catchment in the Western Andes of Peru.

Cross-compartment fluxes of mass and energy play a key role in the functioning of the earth system. Yet their understanding is largely hampered by the fact that related observations occur on multiple scales, involve multiple sensors, and data are collected across different research disciplines. Evapotranspiration (ET) is one of these fluxes and of key importance in the Earth’s water and energy cycle, and comparisons and scaling of in-situ ET measurements face the same challenges.BRIDGET aims to provide tools that will allow storage, merging and visualisation of multi-scale and multi-sensor ET data and ultimately facilitate their scientific analysis. Approaches to estimate ET are manifold with respect to the underlying observations, scales, footprints and associated uncertainties, and measurements are gathered within various research disciplines. For this toolbox we therefore need to incorporate the appropriate metadata catalogue that describes the data comprehensively across disciplines. Special emphasis is placed on providing uncertainty estimates for the data, particularly when scaling functions are applied. Finally, we develop tools for visualisation including the different support of the measurements and (geo-)statistical analysis of the various ET data.The BRIDGET toolbox is envisioned as a standalone python package but will also be implemented in an already existing virtual research environment (V-FOR-WaTer), facilitating the merging of different ET estimates across sensors and scales.

The structural properties of hydrological systems such as topography, soils or land use often show a considerable degree of spatial variability, and so do the drivers of systems dynamics, such as rainfall. Detailed statements about system states and responses therefore generally require spatially distributed and temporally highly resolved hydrological models. This comes at the price of substantial computational costs. However, even if hydrological sub systems potentially behave very differently, in practice we often find groups of these sub systems that behave similarly, but the number, size and characteristics of these groups varies in time. If we have knowledge of such clustered behavior of sub systems while running a model, we can increase computational efficiency by computing in full detail only a few representatives within each cluster, and assign results to the remaining cluster members. Thus, we avoid costly redundant computations. Unlike other methods designed to dynamically remove computational redundancies, such as adaptive gridding, dynamical clustering does not require spatial proximity of the model elements.In our contribution, we present and discuss at the example of a distributed, conceptual hydrological model of the Attert basin in Luxembourg, i) a dimensionless approach to express dynamical similarity, ii) the temporal evolution of dynamical similarity in a 5-year period, iii) an approach to dynamically cluster and re-cluster model elements during run time based on an analysis of clustering stability, and iv) the effect of dynamical clustering with respect to computational gains and the associated losses of simulation quality.For the Attert model, we found that there indeed exists high redundancy among model elements, that the degree of redundancy varies with time, and that the spatial patterns of similarity are mainly controlled by geology and precipitation. Compared to a standard, full-resolution model run used as a virtual reality ‘truth’, computation time could be reduced to one fourth, when modelling quality, expressed as Nash-Sutcliffe efficiency of discharge, was allowed decreasing from 1 to 0.84. Re-clustering occurred at irregular intervals mainly associated with the onset of precipitation, but on average the patterns of similarity were quite stable, such that during the entire six-year simulation period, only 165 re-clusterings were carried out, i.e. on average once every eleven days.

A common issue with large scale erosion modelling is that local processes are often unaccounted for, either because they haven’t been included in the model conceptually, or because they are undetected yet. On the other hand, significant deviations from such a general soil erosion model to the measurements can reveal those local processes. We compared the average yearly sediment amounts of a network of turbidity measurement stations in the catchment of the alpine River Inn to the results of the large scale erosion model RUSLE2015 (Panagos et. al.) for long term yearly erosion amounts and found a significant underestimation of sediment loads in three sub catchments. An important source of sediments in alpine rivers comes from glaciers, which explains the high loads in one of the stations, but two of the three high sediment load sub catchments are too low to have substantial valley glaciers. But another potential source of glacial sediment exists in the form of permafrost soils and in this case a specific permafrost form: rock glaciers. Rock glaciers in particular have been spotted in those two high sediment load catchments, but since they are hard to detect from remote sensing due to the surface being covered with rocks, the existence or the exact spatial extent is often unknown. But with rising temperatures in the Alps, the areas in which permafrost rock glaciers can exist decreases every year and the depth of the seasonal melting layer increases.We propose the hypothesis that the high sediment loads in those sub catchments are caused by increasingly deeper melting of permafrost rock glaciers. This process releases fine materials which have been trapped frozen since the glacial period and are now being eroded and transported to the alpine streams. To get an estimation of potential erodible material from rock glacier melting in the respective sub catchments, we developed a model to simulate the heat diffusion from the air into the frozen ground, while accommodating for the change in specific thermal capacity. The model (developed in Python) takes air temperature time series data as input and can be configured for varying ground stratification setups with different thermal diffusivity values depending on the ground properties.From the simulated melting depth of an average square meter of rock glacier we extrapolate the mass of melted material to the potential permafrost erosion material available in the River Inn sub catchments. We show that this source of sediments can be significant and needs to be factored in should an erosion model be used to calculate sediment input into the rivers. But, with the estimation of sediment load from permafrost origins narrowed down, improving a large-scale erosion model like the RUSLE2015 for this alpine mountain region by accounting for local processes like this one is possible.

In the second half of the 20th century, hydrological regimes in central Western Europe were largely characterised by large-scale winter floods. This type of event was predominantly triggered by westerly atmospheric fluxes, bringing moist and mild air masses from the Atlantic Ocean to the European continent. Since the late 1990’s, major flooding events seem to have shifted in time and magnitude. Flash flood events, while being a well-known phenomenon in Mediterranean catchments, are increasingly also reported at higher latitudes. Unlike the large-scale winter flood events, flash floods are of very narrow spatial extension and triggered by rather short, but highly intense rainfall events.Here, we focus on the specific case of rivers in Luxembourg that have experienced several flash flood events in recent years, while only small to moderate winter flood events have been reported since the late 1990’s. National hydro-meteorological monitoring and flood forecasting systems have been designed for large-scale floods and are not suited for simulating local flash flood events. Therefore, there is a need to increase our understanding of the hydro-meteorological processes underlying flash flood occurrences in our area of interest.While increasing air temperature is known to allow a higher air moisture content that can lead to more intense rainfall events and possible flooding, we moreover hypothesize that the recent increase in flash flood occurrences in Luxembourg is reinforced by a change in atmospheric circulation patterns. To test this hypothesis, we analyse the prevailing atmospheric patterns on rainy days during summer and winter months over the period 1954 - 2019, with a particular focus on rainfall events that lead to moderate and extreme floods. In a next step, we intend to extend our findings for Luxembourg in a larger European context. This analysis should allow to better assess the current situation of hydrological extreme events in central Western Europe in order to take precaution measures and prepare for a diversifying hazard.