Search

Hydro-pedotransfer functions (PTFs) relate easy-to-measure and readily available soil information to soil hydraulic properties (SHPs) for applications in a wide range of process-based and empirical models, thereby enabling the assessment of soil hydraulic effects on hydrological, biogeochemical, and ecological processes. At least more than 4 decades of research have been invested to derive such relationships. However, while models, methods, data storage capacity, and computational efficiency have advanced, there are fundamental concerns related to the scope and adequacy of current PTFs, particularly when applied to parameterise models used at the field scale and beyond. Most of the PTF development process has focused on refining and advancing the regression methods, while fundamental aspects have remained largely unconsidered. Most soil systems are not represented in PTFs, which have been built mostly for agricultural soils in temperate climates. Thus, existing PTFs largely ignore how parent material, vegetation, land use, and climate affect processes that shape SHPs. The PTFs used to parameterise the Richards–Richardson equation are mostly limited to predicting parameters of the van Genuchten–Mualem soil hydraulic functions, despite sufficient evidence demonstrating their shortcomings. Another fundamental issue relates to the diverging scales of derivation and application, whereby PTFs are derived based on laboratory measurements while often being applied at the field to regional scales. Scaling, modulation, and constraining strategies exist to alleviate some of these shortcomings in the mismatch between scales. These aspects are addressed here in a joint effort by the members of the International Soil Modelling Consortium (ISMC) Pedotransfer Functions Working Group with the aim of systematising PTF research and providing a roadmap guiding both PTF development and use. We close with a 10-point catalogue for funders and researchers to guide review processes and research.

Soil hydraulic properties (SHPs), particularly soil water retention capacity and hydraulic conductivity of unsaturated soils, are among the key properties that determine the hydrological functioning of terrestrial systems. Some large collections of SHPs, such as the UNSODA and HYPRES databases, have already existed for more than 2 decades. They have provided an essential basis for many studies related to the critical zone. Today, sample-based SHPs can be determined in a wider saturation range and with higher resolution by combining some recently developed laboratory methods. We provide 572 high-quality SHP data sets from undisturbed, mostly central European samples covering a wide range of soil texture, bulk density and organic carbon content. A consistent and rigorous quality filtering ensures that only trustworthy data sets are included. The data collection contains (i) SHP data, which consist of soil water retention and hydraulic conductivity data, determined by the evaporation method and supplemented by retention data obtained by the dewpoint method and saturated conductivity measurements; (ii) basic soil data, which consist of particle size distribution determined by sedimentation analysis and wet sieving, bulk density and organic carbon content; and (iii) metadata, which include the coordinates of the sampling locations. In addition, for each data set, we provide soil hydraulic parameters for the widely used van Genuchten–Mualem model and for the more advanced Peters–Durner–Iden model. The data were originally collected to develop and test SHP models and associated pedotransfer functions. However, we expect that they will be very valuable for various other purposes such as simulation studies or correlation analyses of different soil properties to study their causal relationships. The data are available at https://doi.org/10.5880/fidgeo.2023.012 (Hohenbrink et al., 2023).

The link between landscape properties and hydrological functioning is the very foundation of hydrological sciences. The fundamental perception that landscape organisation and its hydrological and biogeochemical processes co-develop is often discussed. However, different landscape characteristics and hydrological processes interact in complex ways. Hence, the causal links between both are usually not directly deducible from our observations. So far no common concepts have been established to connect observations, properties and functions at and between different scales. This special issue hosts a broad set of original studies indicating the current state and progress in our understanding of different facets of dynamic hydrological systems across various scales. It is organised as a joint special issue in HESS and ESSD, with the purpose of providing the scientific insights in combination with the underlying data sets and study design. While the individual studies contribute to distinct aspects of the link between landscape characteristics and hydrological functioning, it remained difficult to compile their specific findings to more general conclusions. In this preface, we summarise the contributions. In the search for ways to synthesise these individual studies to the overall topic of linking landscape organisation and hydrological functioning, we suggest four major points how this process could be facilitated in the future: (i) formulating clear and testable research hypotheses, (ii) establishing appropriate sampling designs to test these hypotheses, (iii) fully providing the data and code, and (iv) clarifying and communicating scales of observations and concepts as well as scale transfers.

Root water uptake (RWU), as an important process in the terrestrial water cycle, can help us to better understand the interactions in the soil–plant–atmosphere continuum. We conducted a field study monitoring soil moisture profiles in the rhizosphere of beech trees at two sites with different soil conditions. We present an algorithm to infer RWU from step-shaped, diurnal changes in soil moisture. While this approach is a feasible, easily implemented method for moderately moist and homogeneously textured soil conditions, limitations were identified during drier states and for more heterogeneous soil settings. A comparison with the time series of xylem sap velocity underlines that RWU and sap flow (SF) are complementary measures in the transpiration process. The high correlation between the SF time series of the two sites, but lower correlation between the RWU time series, suggests that soil characteristics affect RWU of the trees but not SF.

Soil water content and matric potential are central hydrological state variables. A large variety of automated probes and sensor systems for state monitoring exist and are frequently applied. Most applications solely rely on the calibration by the manufacturers. Until now, there has been no commonly agreed-upon calibration procedure. Moreover, several opinions about the capabilities and reliabilities of specific sensing methods or sensor systems exist and compete. A consortium of several institutions conducted a comparison study of currently available sensor systems for soil water content and matric potential under field conditions. All probes were installed at 0.2 m b.s. (metres below surface), following best-practice procedures. We present the set-up and the recorded data of 58 probes of 15 different systems measuring soil moisture and 50 further probes of 14 different systems for matric potential. We briefly discuss the limited coherence of the measurements in a cross-correlation analysis. The measuring campaign was conducted during the growing period of 2016. The monitoring data, results from pedophysical analyses of the soil and laboratory reference measurements for calibration are published in Jackisch et al. (2018, https://doi.org/10.1594/PANGAEA.892319).

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 present study confirms that a thermodynamic perspective on soil water is well suited to distinguishing the typical interplay of gravity and capillarity controls on soil water dynamics in different landscapes. To this end, we express the driving matric and gravity potentials by their energetic counterparts and characterize soil water by its free energy state. The latter is the key to defining a new system characteristic determining the possible range of energy states of soil water, reflecting the joint influences of soil physical properties and height over nearest drainage (HAND) in a stratified manner. As this characteristic defines the possible range of energy states of soil water in the root zone, it also allows an instructive comparison of top soil water dynamics observed in two distinctly different landscapes. This is because the local thermodynamic equilibrium at a given HAND and the related equilibrium storage allow a subdivision of the possible free energy states into two different regimes. Wetting of the soil in local equilibrium implies that free energy of soil water becomes positive, which in turn implies that the soil is in a state of storage excess, while further drying of the soil leads to a negative free energy and a state of storage deficit. We show that during 1 hydrological year the energy states of soil water visit distinctly different parts of their respective energy state spaces. The two study areas compared here exhibit furthermore a threshold-like relation between the observed free energy of soil water in the riparian zone and observed streamflow, while the tipping points coincide with the local equilibrium state of zero free energy. We found that the emergence of a potential energy excess/storage excess in the riparian zone coincides with the onset of storage-controlled direct streamflow generation. While such threshold behaviour is not unusual, it is remarkable that the tipping point is consistent with the underlying theoretical basis.

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.

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

The phrase form and function was established in architecture and biology and refers to the idea that form and functionality are closely correlated, influence each other, and co-evolve. We suggest transferring this idea to hydrological systems to separate and analyze their two main characteristics: their form, which is equivalent to the spatial structure and static properties, and their function, equivalent to internal responses and hydrological behavior. While this approach is not particularly new to hydrological field research, we want to employ this concept to explicitly pursue the question of what information is most advantageous to understand a hydrological system. We applied this concept to subsurface flow within a hillslope, with a methodological focus on function: we conducted observations during a natural storm event and followed this with a hillslope-scale irrigation experiment. The results are used to infer hydrological processes of the monitored system. Based on these findings, the explanatory power and conclusiveness of the data are discussed. The measurements included basic hydrological monitoring methods, like piezometers, soil moisture, and discharge measurements. These were accompanied by isotope sampling and a novel application of 2-D time-lapse GPR (ground-penetrating radar). The main finding regarding the processes in the hillslope was that preferential flow paths were established quickly, despite unsaturated conditions. These flow paths also caused a detectable signal in the catchment response following a natural rainfall event, showing that these processes are relevant also at the catchment scale. Thus, we conclude that response observations (dynamics and patterns, i.e., indicators of function) were well suited to describing processes at the observational scale. Especially the use of 2-D time-lapse GPR measurements, providing detailed subsurface response patterns, as well as the combination of stream-centered and hillslope-centered approaches, allowed us to link processes and put them in a larger context. Transfer to other scales beyond observational scale and generalizations, however, rely on the knowledge of structures (form) and remain speculative. The complementary approach with a methodological focus on form (i.e., structure exploration) is presented and discussed in the companion paper by Jackisch et al.(2017).

The study deals with the identification and characterization of rapid subsurface flow structures through pedo- and geo-physical measurements and irrigation experiments at the point, plot and hillslope scale. Our investigation of flow-relevant structures and hydrological responses refers to the general interplay of form and function, respectively. To obtain a holistic picture of the subsurface, a large set of different laboratory, exploratory and experimental methods was used at the different scales. For exploration these methods included drilled soil core profiles, in situ measurements of infiltration capacity and saturated hydraulic conductivity, and laboratory analyses of soil water retention and saturated hydraulic conductivity. The irrigation experiments at the plot scale were monitored through a combination of dye tracer, salt tracer, soil moisture dynamics, and 3-D time-lapse ground penetrating radar (GPR) methods. At the hillslope scale the subsurface was explored by a 3-D GPR survey. A natural storm event and an irrigation experiment were monitored by a dense network of soil moisture observations and a cascade of 2-D time-lapse GPR trenches. We show that the shift between activated and non-activated state of the flow paths is needed to distinguish structures from overall heterogeneity. Pedo-physical analyses of point-scale samples are the basis for sub-scale structure inference. At the plot and hillslope scale 3-D and 2-D time-lapse GPR applications are successfully employed as non-invasive means to image subsurface response patterns and to identify flow-relevant paths. Tracer recovery and soil water responses from irrigation experiments deliver a consistent estimate of response velocities. The combined observation of form and function under active conditions provides the means to localize and characterize the structures (this study) and the hydrological processes (companion study Angermann et al., 2017, this issue).

The baffling diversity of runoff generation processes, alongside our sketchy understanding of how physiographic characteristics control fundamental hydrological functions of water collection, storage, and release, continue to pose major research challenges in catchment hydrology. Here, we propose innovative data-driven diagnostic signatures for overcoming the prevailing status quo in catchment inter-comparison. More specifically, we present dimensionless double mass curves (dDMC) which allow inference of information on runoff generation and the water balance at the seasonal and annual timescales. By separating the vegetation and winter periods, dDMC furthermore provide information on the role of biotic and abiotic controls in seasonal runoff formation. A key aspect we address in this paper is the derivation of dimensionless expressions of fluxes which ensure the comparability of the signatures in space and time. We achieve this by using the limiting factors of a hydrological process as a scaling reference. We show that different references result in different diagnostics. As such we define two kinds of dDMC which allow us to derive seasonal runoff coefficients and to characterize dimensionless streamflow release as a function of the potential renewal rate of the soil storage. We expect these signatures for storage controlled seasonal runoff formation to remain invariant, as long as the ratios of release over supply and supply over storage capacity develop similarly in different catchments. We test the proposed methods by applying them to an operational data set comprising 22 catchments (12–166 km2) from different environments in southern Germany and hydrometeorological data from 4 hydrological years. The diagnostics are used to compare the sites and to reveal the dominant controls on runoff formation. The key findings are that dDMC are meaningful signatures for catchment runoff formation at the seasonal to annual scale and that the type of scaling strongly influences the diagnostic potential of the dDMC. Adding discrimination between growing season and winter period was of fundamental importance and easy to implement by means of a temperature-index model. More specifically, temperature aggregates explain over 70 % of the variability of the seasonal summer runoff coefficients. The results also show that the soil topographic index, i.e. the product of topographic gradient and saturated hydraulic conductivity, is significantly correlated with winter runoff coefficients, whereas the topographic gradient and the hydraulic conductivity alone are not. We conclude that proxies for gradients and resistances should be interpreted as a pair. Lastly, the dDMC concept reveals memory effects between summer and winter runoff regimes that are not relevant in spring between the transition from winter to summer.

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.

For understanding water and solute transport processes, knowledge about the respective hydraulic properties is necessary. Commonly, hydraulic parameters are estimated via pedo-transfer functions using soil texture data to avoid cost-intensive measurements of hydraulic parameters in the laboratory. Therefore, current soil texture information is only available at a coarse spatial resolution of 250 to 1000 m. Here, a method is presented to derive high-resolution (15 m) spatial topsoil texture patterns for the meso-scale Attert catchment (Luxembourg, 288 km2) from 28 images of ASTER (advanced spaceborne thermal emission and reflection radiometer) thermal remote sensing. A principle component analysis of the images reveals the most dominant thermal patterns (principle components, PCs) that are related to 212 fractional soil texture samples. Within a multiple linear regression framework, distributed soil texture information is estimated and related uncertainties are assessed. An overall root mean squared error (RMSE) of 12.7 percentage points (pp) lies well within and even below the range of recent studies on soil texture estimation, while requiring sparser sample setups and a less diverse set of basic spatial input. This approach will improve the generation of spatially distributed topsoil maps, particularly for hydrologic modeling purposes, and will expand the usage of thermal remote sensing products.

Within this study we propose a stochastic approach to simulate soil water dynamics in the unsaturated zone by using a non-linear, space domain random walk of water particles. Soil water is represented by particles of constant mass, which travel according to the Itô form of the Fokker–Planck equation. The model concept builds on established soil physics by estimating the drift velocity and the diffusion term based on the soil water characteristics. A naive random walk, which assumes all water particles to move at the same drift velocity and diffusivity, overestimated depletion of soil moisture gradients compared to a Richards solver. This is because soil water and hence the corresponding water particles in smaller pore size fractions are, due to the non-linear decrease in soil hydraulic conductivity with decreasing soil moisture, much less mobile. After accounting for this subscale variability in particle mobility, the particle model and a Richards solver performed highly similarly during simulated wetting and drying circles in three distinctly different soils. Both models were in very good accordance during rainfall-driven conditions, regardless of the intensity and type of the rainfall forcing and the shape of the initial state. Within subsequent drying cycles the particle model was typically slightly slower in depleting soil moisture gradients than the Richards model. Within a real-world benchmark, the particle model and the Richards solver showed the same deficiencies in matching observed reactions of topsoil moisture to a natural rainfall event. The particle model performance, however, clearly improved after a straightforward implementation of rapid non-equilibrium infiltration, which treats event water as different types of particles, which travel initially in the largest pore fraction at maximum velocity and experience a slow diffusive mixing with the pre-event water particles. The proposed Lagrangian approach is hence a promising, easy-to-implement alternative to the Richards equation for simulating rainfall-driven soil moisture dynamics, which offers straightforward opportunities to account for preferential, non-equilibrium flow.

According to Dooge (1986) intermediate-scale catchments are systems of organized complexity, being too organized and yet too small to be characterized on a statistical/conceptual basis, but too large and too heterogeneous to be characterized in a deterministic manner. A key requirement for building structurally adequate models precisely for this intermediate scale is a better understanding of how different forms of spatial organization affect storage and release of water and energy. Here, we propose that a combination of the concept of hydrological response units (HRUs) and thermodynamics offers several helpful and partly novel perspectives for gaining this improved understanding. Our key idea is to define functional similarity based on similarity of the terrestrial controls of gradients and resistance terms controlling the land surface energy balance, rainfall runoff transformation, and groundwater storage and release. This might imply that functional similarity with respect to these specific forms of water release emerges at different scales, namely the small field scale, the hillslope, and the catchment scale. We thus propose three different types of "functional units" – specialized HRUs, so to speak – which behave similarly with respect to one specific form of water release and with a characteristic extent equal to one of those three scale levels. We furthermore discuss an experimental strategy based on exemplary learning and replicate experiments to identify and delineate these functional units, and as a promising strategy for characterizing the interplay and organization of water and energy fluxes across scales. We believe the thermodynamic perspective to be well suited to unmask equifinality as inherent in the equations governing water, momentum, and energy fluxes: this is because several combinations of gradients and resistance terms yield the same mass or energy flux and the terrestrial controls of gradients and resistance terms are largely independent. We propose that structurally adequate models at this scale should consequently disentangle driving gradients and resistance terms, because this optionally allows equifinality to be partly reduced by including available observations, e.g., on driving gradients. Most importantly, the thermodynamic perspective yields an energy-centered perspective on rainfall-runoff transformation and evapotranspiration, including fundamental limits for energy fluxes associated with these processes. This might additionally reduce equifinality and opens up opportunities for testing thermodynamic optimality principles within independent predictions of rainfall-runoff or land surface energy exchange. This is pivotal to finding out whether or not spatial organization in catchments is in accordance with a fundamental organizing principle.