Articles | Volume 24, issue 9
https://doi.org/10.5194/hess-24-4523-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-24-4523-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics
Stephanie Thiesen
CORRESPONDING AUTHOR
Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany
Diego M. Vieira
Department for Microsystems Engineering, University of Freiburg,
Freiburg, Germany
Bernstein Center Freiburg, University of Freiburg, Freiburg, Germany
Mirko Mälicke
Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany
Ralf Loritz
Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany
J. Florian Wellmann
Computational Geosciences and Reservoir Engineering, RWTH Aachen
University, Aachen, Germany
Uwe Ehret
Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany
Related authors
Stephanie Thiesen, Paul Darscheid, and Uwe Ehret
Hydrol. Earth Syst. Sci., 23, 1015–1034, https://doi.org/10.5194/hess-23-1015-2019, https://doi.org/10.5194/hess-23-1015-2019, 2019
Short summary
Short summary
We present a data-driven approach created to explore the full information of data sets, avoiding parametric assumptions. The evaluations are based on Information Theory concepts, introducing an objective measure of information and uncertainty. The approach was applied to automatically identify rainfall-runoff events in discharge time series, however it is generic enough to be adapted to other practical applications.
Denise Degen, Moritz Ziegler, Oliver Heidbach, Andreas Henk, Karsten Reiter, and Florian Wellmann
EGUsphere, https://doi.org/10.5194/egusphere-2024-2932, https://doi.org/10.5194/egusphere-2024-2932, 2024
Short summary
Short summary
Obtaining reliable estimates of the subsurface state distributions is essential to determine the location of e.g. potential nuclear waste disposal sites. However, providing these is challenging since it requires solving the problem numerous times yielding high computational cost. To overcome this, we use a physics-based machine learning method to construct surrogate models. We demonstrate how it produces physics-preserving predictions, which differentiates it from purely data-driven approaches.
Andrea L. Campoverde, Uwe Ehret, Patrick Ludwig, and Joaquim G. Pinto
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-134, https://doi.org/10.5194/gmd-2024-134, 2024
Preprint under review for GMD
Short summary
Short summary
We looked at how well the model WRF-Hydro performed during the 2018 drought event in the River Rhine basin, even though it is typically used for floods. We used the meteorological ERA5 reanalysis dataset to simulate River Rhine’s streamflow and adjusted the model using parameters and actual discharge measurements. We focused on Lake Constance, a key part of the basin, but found issues with the model’s lake outflow simulation. By removing the lake module, we obtained more accurate results.
Eduardo Acuna Espinoza, Ralf Loritz, Frederik Kratzert, Daniel Klotz, Martin Gauch, Manuel Álvarez Chaves, Nicole Bäuerle, and Uwe Ehret
EGUsphere, https://doi.org/10.5194/egusphere-2024-2147, https://doi.org/10.5194/egusphere-2024-2147, 2024
Short summary
Short summary
Data-driven techniques have shown the potential to outperform process-based models in rainfall-runoff simulations. Hybrid models, combining both approaches, aim to enhance accuracy and maintain interpretability. Expanding the set of test cases to evaluate hybrid models under different conditions we test their generalization capabilities for extreme hydrological events.
Ralf Loritz, Alexander Dolich, Eduardo Acuña Espinoza, Pia Ebeling, Björn Guse, Jonas Götte, Sibylle K. Hassler, Corina Hauffe, Ingo Heidbüchel, Jens Kiesel, Mirko Mälicke, Hannes Müller-Thomy, Michael Stölzle, and Larisa Tarasova
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-318, https://doi.org/10.5194/essd-2024-318, 2024
Revised manuscript accepted for ESSD
Short summary
Short summary
The CAMELS-DE dataset features data from 1555 streamflow gauges across Germany, with records spanning from 1951 to 2020. This comprehensive dataset, which includes time series of up to 70 years (median 46 years), enables advanced research on water flow and environmental trends, and supports the development of hydrological models.
Sarah Quỳnh Giang Ho and Uwe Ehret
EGUsphere, https://doi.org/10.5194/egusphere-2024-2167, https://doi.org/10.5194/egusphere-2024-2167, 2024
Short summary
Short summary
In this paper, we use models to demonstrate that even small flood reservoirs – which capture water to avoid floods downstream – can be repurposed to release water in drier conditions without affecting their ability to protect against floods. By capturing water and releasing once water levels are low, we show that reservoirs can greatly increase water available in drought. Having more water coming in, however, is not necessarily better for drought protection.
Eduardo Acuña Espinoza, Ralf Loritz, Manuel Álvarez Chaves, Nicole Bäuerle, and Uwe Ehret
Hydrol. Earth Syst. Sci., 28, 2705–2719, https://doi.org/10.5194/hess-28-2705-2024, https://doi.org/10.5194/hess-28-2705-2024, 2024
Short summary
Short summary
Hydrological hybrid models promise to merge the performance of deep learning methods with the interpretability of process-based models. One hybrid approach is the dynamic parameterization of conceptual models using long short-term memory (LSTM) networks. We explored this method to evaluate the effect of the flexibility given by LSTMs on the process-based part.
Denise Degen, Daniel Caviedes Voullième, Susanne Buiter, Harrie-Jan Hendricks Franssen, Harry Vereecken, Ana González-Nicolás, and Florian Wellmann
Geosci. Model Dev., 16, 7375–7409, https://doi.org/10.5194/gmd-16-7375-2023, https://doi.org/10.5194/gmd-16-7375-2023, 2023
Short summary
Short summary
In geosciences, we often use simulations based on physical laws. These simulations can be computationally expensive, which is a problem if simulations must be performed many times (e.g., to add error bounds). We show how a novel machine learning method helps to reduce simulation time. In comparison to other approaches, which typically only look at the output of a simulation, the method considers physical laws in the simulation itself. The method provides reliable results faster than standard.
Michael Hillier, Florian Wellmann, Eric A. de Kemp, Boyan Brodaric, Ernst Schetselaar, and Karine Bédard
Geosci. Model Dev., 16, 6987–7012, https://doi.org/10.5194/gmd-16-6987-2023, https://doi.org/10.5194/gmd-16-6987-2023, 2023
Short summary
Short summary
Neural networks can be used effectively to model three-dimensional geological structures from point data, sampling geological interfaces, units, and structural orientations. Existing neural network approaches for this type of modelling are advanced by the efficient incorporation of unconformities, new knowledge inputs, and improved data fitting techniques. These advances permit the modelling of more complex geology in diverse geological settings, different-sized areas, and various data regimes.
Uwe Ehret and Pankaj Dey
Hydrol. Earth Syst. Sci., 27, 2591–2605, https://doi.org/10.5194/hess-27-2591-2023, https://doi.org/10.5194/hess-27-2591-2023, 2023
Short summary
Short summary
We propose the
c-u-curvemethod to characterize dynamical (time-variable) systems of all kinds.
Uis for uncertainty and expresses how well a system can be predicted in a given period of time.
Cis for complexity and expresses how predictability differs between different periods, i.e. how well predictability itself can be predicted. The method helps to better classify and compare dynamical systems across a wide range of disciplines, thus facilitating scientific collaboration.
Mohammad Moulaeifard, Simon Bernard, and Florian Wellmann
Geosci. Model Dev., 16, 3565–3579, https://doi.org/10.5194/gmd-16-3565-2023, https://doi.org/10.5194/gmd-16-3565-2023, 2023
Short summary
Short summary
In this work, we propose a flexible framework to generate and interact with geological models using explicit surface representations. The essence of the work lies in the determination of the flexible control mesh, topologically similar to the main geological structure, watertight and controllable with few control points, to manage the geological structures. We exploited the subdivision surface method in our work, which is commonly used in the animation and gaming industry.
Patrick Ludwig, Florian Ehmele, Mário J. Franca, Susanna Mohr, Alberto Caldas-Alvarez, James E. Daniell, Uwe Ehret, Hendrik Feldmann, Marie Hundhausen, Peter Knippertz, Katharina Küpfer, Michael Kunz, Bernhard Mühr, Joaquim G. Pinto, Julian Quinting, Andreas M. Schäfer, Frank Seidel, and Christina Wisotzky
Nat. Hazards Earth Syst. Sci., 23, 1287–1311, https://doi.org/10.5194/nhess-23-1287-2023, https://doi.org/10.5194/nhess-23-1287-2023, 2023
Short summary
Short summary
Heavy precipitation in July 2021 led to widespread floods in western Germany and neighboring countries. The event was among the five heaviest precipitation events of the past 70 years in Germany, and the river discharges exceeded by far the statistical 100-year return values. Simulations of the event under future climate conditions revealed a strong and non-linear effect on flood peaks: for +2 K global warming, an 18 % increase in rainfall led to a 39 % increase of the flood peak in the Ahr river.
Susanna Mohr, Uwe Ehret, Michael Kunz, Patrick Ludwig, Alberto Caldas-Alvarez, James E. Daniell, Florian Ehmele, Hendrik Feldmann, Mário J. Franca, Christian Gattke, Marie Hundhausen, Peter Knippertz, Katharina Küpfer, Bernhard Mühr, Joaquim G. Pinto, Julian Quinting, Andreas M. Schäfer, Marc Scheibel, Frank Seidel, and Christina Wisotzky
Nat. Hazards Earth Syst. Sci., 23, 525–551, https://doi.org/10.5194/nhess-23-525-2023, https://doi.org/10.5194/nhess-23-525-2023, 2023
Short summary
Short summary
The flood event in July 2021 was one of the most severe disasters in Europe in the last half century. The objective of this two-part study is a multi-disciplinary assessment that examines the complex process interactions in different compartments, from meteorology to hydrological conditions to hydro-morphological processes to impacts on assets and environment. In addition, we address the question of what measures are possible to generate added value to early response management.
Michał P. Michalak, Lesław Teper, Florian Wellmann, Jerzy Żaba, Krzysztof Gaidzik, Marcin Kostur, Yuriy P. Maystrenko, and Paulina Leonowicz
Solid Earth, 13, 1697–1720, https://doi.org/10.5194/se-13-1697-2022, https://doi.org/10.5194/se-13-1697-2022, 2022
Short summary
Short summary
When characterizing geological/geophysical surfaces, various geometric attributes are calculated, such as dip angle (1D) or dip direction (2D). However, the boundaries between specific values may be subjective and without optimization significance, resulting from using default color palletes. This study proposes minimizing cosine distance among within-cluster observations to detect 3D anomalies. Our results suggest that the method holds promise for identification of megacylinders or megacones.
Ralf Loritz, Maoya Bassiouni, Anke Hildebrandt, Sibylle K. Hassler, and Erwin Zehe
Hydrol. Earth Syst. Sci., 26, 4757–4771, https://doi.org/10.5194/hess-26-4757-2022, https://doi.org/10.5194/hess-26-4757-2022, 2022
Short summary
Short summary
In this study, we combine a deep-learning approach that predicts sap flow with a hydrological model to improve soil moisture and transpiration estimates at the catchment scale. Our results highlight that hybrid-model approaches, combining machine learning with physically based models, are a promising way to improve our ability to make hydrological predictions.
Mirko Mälicke
Geosci. Model Dev., 15, 2505–2532, https://doi.org/10.5194/gmd-15-2505-2022, https://doi.org/10.5194/gmd-15-2505-2022, 2022
Short summary
Short summary
I preset SciKit-GStat, a well-documented and tested Python package for variogram estimation. The variogram is the core means of geostatistics, which almost all other methods rely on. Geostatistical interpolation and field generation are widely spread in geoscience, i.e., for data assimilation or modeling.
While SciKit-GStat focuses on effective and intuitive variogram estimation, it can interface with other prominent packages and make its variograms available for a multitude of methods.
Alexander Sternagel, Ralf Loritz, Brian Berkowitz, and Erwin Zehe
Hydrol. Earth Syst. Sci., 26, 1615–1629, https://doi.org/10.5194/hess-26-1615-2022, https://doi.org/10.5194/hess-26-1615-2022, 2022
Short summary
Short summary
We present a (physically based) Lagrangian approach to simulate diffusive mixing processes on the pore scale beyond perfectly mixed conditions. Results show the feasibility of the approach for reproducing measured mixing times and concentrations of isotopes over pore sizes and that typical shapes of breakthrough curves (normally associated with non-uniform transport in heterogeneous soils) may also occur as a result of imperfect subscale mixing in a macroscopically homogeneous soil matrix.
Erwin Zehe, Ralf Loritz, Yaniv Edery, and Brian Berkowitz
Hydrol. Earth Syst. Sci., 25, 5337–5353, https://doi.org/10.5194/hess-25-5337-2021, https://doi.org/10.5194/hess-25-5337-2021, 2021
Short summary
Short summary
This study uses the concepts of entropy and work to quantify and explain the emergence of preferential flow and transport in heterogeneous saturated porous media. We found that the downstream concentration of solutes in preferential pathways implies a downstream declining entropy in the transverse distribution of solute transport pathways. Preferential flow patterns with lower entropies emerged within media of higher heterogeneity – a stronger self-organization despite a higher randomness.
Alexander Schaaf, Miguel de la Varga, Florian Wellmann, and Clare E. Bond
Geosci. Model Dev., 14, 3899–3913, https://doi.org/10.5194/gmd-14-3899-2021, https://doi.org/10.5194/gmd-14-3899-2021, 2021
Short summary
Short summary
Uncertainty is an inherent property of any model of the subsurface. We show how geological topology information – how different regions of rocks in the subsurface are connected – can be used to train uncertain geological models to reduce uncertainty. More widely, the method demonstrates the use of probabilistic machine learning (Bayesian inference) to train structural geological models on auxiliary geological knowledge that can be encoded in graph structures.
Alexander Sternagel, Ralf Loritz, Julian Klaus, Brian Berkowitz, and Erwin Zehe
Hydrol. Earth Syst. Sci., 25, 1483–1508, https://doi.org/10.5194/hess-25-1483-2021, https://doi.org/10.5194/hess-25-1483-2021, 2021
Short summary
Short summary
The key innovation of the study is a method to simulate reactive solute transport in the vadose zone within a Lagrangian framework. We extend the LAST-Model with a method to account for non-linear sorption and first-order degradation processes during unsaturated transport of reactive substances in the matrix and macropores. Model evaluations using bromide and pesticide data from irrigation experiments under different flow conditions on various timescales show the feasibility of the method.
Elnaz Azmi, Uwe Ehret, Steven V. Weijs, Benjamin L. Ruddell, and Rui A. P. Perdigão
Hydrol. Earth Syst. Sci., 25, 1103–1115, https://doi.org/10.5194/hess-25-1103-2021, https://doi.org/10.5194/hess-25-1103-2021, 2021
Short summary
Short summary
Computer models should be as simple as possible but not simpler. Simplicity refers to the length of the model and the effort it takes the model to generate its output. Here we present a practical technique for measuring the latter by the number of memory visits during model execution by
Strace, a troubleshooting and monitoring program. The advantage of this approach is that it can be applied to any computer-based model, which facilitates model intercomparison.
Ralf Loritz, Markus Hrachowitz, Malte Neuper, and Erwin Zehe
Hydrol. Earth Syst. Sci., 25, 147–167, https://doi.org/10.5194/hess-25-147-2021, https://doi.org/10.5194/hess-25-147-2021, 2021
Short summary
Short summary
This study investigates the role and value of distributed rainfall in the runoff generation of a mesoscale catchment. We compare the performance of different hydrological models at different periods and show that a distributed model driven by distributed rainfall yields improved performances only during certain periods. We then step beyond this finding and develop a spatially adaptive model that is capable of dynamically adjusting its spatial model structure in time.
Uwe Ehret, Rik van Pruijssen, Marina Bortoli, Ralf Loritz, Elnaz Azmi, and Erwin Zehe
Hydrol. Earth Syst. Sci., 24, 4389–4411, https://doi.org/10.5194/hess-24-4389-2020, https://doi.org/10.5194/hess-24-4389-2020, 2020
Short summary
Short summary
In this paper we propose adaptive clustering as a new method for reducing the computational efforts of distributed modelling. It consists of identifying similar-acting model elements during the runtime, clustering them, running the model for just a few representatives per cluster, and mapping their results to the remaining model elements in the cluster. With the example of a hydrological model, we show that this saves considerable computation time, while largely maintaining the output quality.
Mirko Mälicke, Sibylle K. Hassler, Theresa Blume, Markus Weiler, and Erwin Zehe
Hydrol. Earth Syst. Sci., 24, 2633–2653, https://doi.org/10.5194/hess-24-2633-2020, https://doi.org/10.5194/hess-24-2633-2020, 2020
Short summary
Short summary
We could show that distributed soil moisture time series bear a considerable amount of information about dynamic changes in soil moisture. We developed a new method to describe spatial patterns and analyze their persistency. By combining uncertainty propagation with information theory, we were able to calculate the information content of spatial similarity with respect to measurement uncertainty. This does help to understand when and why the soil is drying in an organized manner.
Fabian Antonio Stamm, Miguel de la Varga, and Florian Wellmann
Solid Earth, 10, 2015–2043, https://doi.org/10.5194/se-10-2015-2019, https://doi.org/10.5194/se-10-2015-2019, 2019
Alexander Sternagel, Ralf Loritz, Wolfgang Wilcke, and Erwin Zehe
Hydrol. Earth Syst. Sci., 23, 4249–4267, https://doi.org/10.5194/hess-23-4249-2019, https://doi.org/10.5194/hess-23-4249-2019, 2019
Short summary
Short summary
We present our hydrological LAST-Model to simulate preferential soil water flow and tracer transport in macroporous soils. It relies on a Lagrangian perspective of the movement of discrete water particles carrying tracer masses through the subsoil and is hence an alternative approach to common models. Sensitivity analyses reveal the physical validity of the model concept and evaluation tests show that LAST can depict well observed tracer mass profiles with fingerprints of preferential flow.
Axel Kleidon, Erwin Zehe, and Ralf Loritz
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2019-52, https://doi.org/10.5194/esd-2019-52, 2019
Manuscript not accepted for further review
Short summary
Short summary
Many fluxes in Earth systems are not homogeneously distributed across space, but occur highly concentrated in structures, such as turbulent eddies, river networks, vascular networks of plants, or human-made infrastructures. Yet, the highly-organized nature of these fluxes is typically only described at a rudimentary level, if at all. We propose that it requires a novel approach to describe these structures that focuses on the work done to build and maintain these structures, and the feedbacks.
Ralf Loritz, Axel Kleidon, Conrad Jackisch, Martijn Westhoff, Uwe Ehret, Hoshin Gupta, and Erwin Zehe
Hydrol. Earth Syst. Sci., 23, 3807–3821, https://doi.org/10.5194/hess-23-3807-2019, https://doi.org/10.5194/hess-23-3807-2019, 2019
Short summary
Short summary
In this study, we develop a topographic index explaining hydrological similarity within a energy-centered framework, with the observation that the majority of potential energy is dissipated when rainfall becomes runoff.
Malte Neuper and Uwe Ehret
Hydrol. Earth Syst. Sci., 23, 3711–3733, https://doi.org/10.5194/hess-23-3711-2019, https://doi.org/10.5194/hess-23-3711-2019, 2019
Short summary
Short summary
In this study, we apply a data-driven approach to quantitatively estimate precipitation using weather radar data. The method is based on information theory concepts. It uses predictive relations expressed by empirical discrete probability distributions, which are directly derived from data rather than the standard deterministic functions.
Stephanie Thiesen, Paul Darscheid, and Uwe Ehret
Hydrol. Earth Syst. Sci., 23, 1015–1034, https://doi.org/10.5194/hess-23-1015-2019, https://doi.org/10.5194/hess-23-1015-2019, 2019
Short summary
Short summary
We present a data-driven approach created to explore the full information of data sets, avoiding parametric assumptions. The evaluations are based on Information Theory concepts, introducing an objective measure of information and uncertainty. The approach was applied to automatically identify rainfall-runoff events in discharge time series, however it is generic enough to be adapted to other practical applications.
Erwin Zehe, Ralf Loritz, Conrad Jackisch, Martijn Westhoff, Axel Kleidon, Theresa Blume, Sibylle K. Hassler, and Hubert H. Savenije
Hydrol. Earth Syst. Sci., 23, 971–987, https://doi.org/10.5194/hess-23-971-2019, https://doi.org/10.5194/hess-23-971-2019, 2019
Miguel de la Varga, Alexander Schaaf, and Florian Wellmann
Geosci. Model Dev., 12, 1–32, https://doi.org/10.5194/gmd-12-1-2019, https://doi.org/10.5194/gmd-12-1-2019, 2019
Short summary
Short summary
GemPy is an open-source Python-based 3-D structural geological modeling software, which allows the implicit (i.e. automatic) creation of complex geological models from interface and orientation data. GemPy is implemented in the programming language Python, making use of a highly efficient underlying library, Theano, for efficient code generation that performs automatic differentiation. This enables the link to probabilistic machine-learning and Bayesian inference frameworks.
Mirko Mälicke, Sibylle K. Hassler, Markus Weiler, Theresa Blume, and Erwin Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2018-396, https://doi.org/10.5194/hess-2018-396, 2018
Manuscript not accepted for further review
Short summary
Short summary
In this study we use time dependent variograms to identify periods of organized soil moisture during drying. We could identify emerging spatial patterns which imply periods of terrestrial control on soil moisture organization. The coupling of time dependent variograms with density based clustering is a new approach to detect similarity in spatial patterns. The presented method is useful to describe states of organization and improve kriging workflows by extending their prerequisites.
Ralf Loritz, Hoshin Gupta, Conrad Jackisch, Martijn Westhoff, Axel Kleidon, Uwe Ehret, and Erwin Zehe
Hydrol. Earth Syst. Sci., 22, 3663–3684, https://doi.org/10.5194/hess-22-3663-2018, https://doi.org/10.5194/hess-22-3663-2018, 2018
Short summary
Short summary
In this study we explore the role of spatially distributed information on hydrological modeling. For that, we develop and test an approach which draws upon information theory and thermodynamic reasoning. We show that the proposed set of methods provide a powerful framework for understanding and diagnosing how and when process organization and functional similarity of hydrological systems emerge in time and, hence, when which landscape characteristic is important in a model application.
Raphael Schneeberger, Miguel de La Varga, Daniel Egli, Alfons Berger, Florian Kober, Florian Wellmann, and Marco Herwegh
Solid Earth, 8, 987–1002, https://doi.org/10.5194/se-8-987-2017, https://doi.org/10.5194/se-8-987-2017, 2017
Short summary
Short summary
Structural 3-D modelling has become a widely used technique within applied projects. We performed a typical modelling workflow for a study site with the occurrence of an underground facility. This exceptional setting enabled us to test the surface-based extrapolation of faults with the mapped faults underground. We estimated the extrapolation-related uncertainty with probabilistic 2-D interpolation. This research was conducted to improve structural 3-D modelling in less-constrained areas.
Simon Paul Seibert, Conrad Jackisch, Uwe Ehret, Laurent Pfister, and Erwin Zehe
Hydrol. Earth Syst. Sci., 21, 2817–2841, https://doi.org/10.5194/hess-21-2817-2017, https://doi.org/10.5194/hess-21-2817-2017, 2017
Short summary
Short summary
Runoff production mechanisms and their corresponding physiographic controls continue to pose major research challenges in catchment hydrology. We propose innovative data-driven diagnostic signatures for overcoming the prevailing status quo in inter-comparison studies. Specifically, we present dimensionless double mass curves which allow us to infer information on runoff generation at the seasonal and annual timescales. The method is based on commonly available data.
Ralf Loritz, Sibylle K. Hassler, Conrad Jackisch, Niklas Allroggen, Loes van Schaik, Jan Wienhöfer, and Erwin Zehe
Hydrol. Earth Syst. Sci., 21, 1225–1249, https://doi.org/10.5194/hess-21-1225-2017, https://doi.org/10.5194/hess-21-1225-2017, 2017
Short summary
Short summary
In this study we examine whether we can step beyond the qualitative character of perceptual models by using them as a blueprint for setting up representative hillslope models. Thereby we test the hypothesis of whether a single hillslope can represent the functioning of an entire lower mesoscale catchment in a spatially aggregated way.
Simon Paul Seibert, Uwe Ehret, and Erwin Zehe
Hydrol. Earth Syst. Sci., 20, 3745–3763, https://doi.org/10.5194/hess-20-3745-2016, https://doi.org/10.5194/hess-20-3745-2016, 2016
Short summary
Short summary
While the assessment of "vertical" (magnitude) errors of streamflow simulations is standard practice, "horizontal" (timing) errors are rarely considered. To assess their role, we propose a method to quantify both errors simultaneously which closely resembles visual hydrograph comparison. Our results reveal differences in time–magnitude error statistics for different flow conditions. The proposed method thus offers novel perspectives for model diagnostics and evaluation.
J. Florian Wellmann, Sam T. Thiele, Mark D. Lindsay, and Mark W. Jessell
Geosci. Model Dev., 9, 1019–1035, https://doi.org/10.5194/gmd-9-1019-2016, https://doi.org/10.5194/gmd-9-1019-2016, 2016
Short summary
Short summary
We often obtain knowledge about the subsurface in the form of structural geological models, as a basis for subsurface usage or resource extraction. Here, we provide a modelling code to construct such models on the basis of significant deformational events in geological history, encapsulated in kinematic equations. Our methods simplify complex dynamic processes, but enable us to evaluate how events interact, and finally how certain we are about predictions of structures in the subsurface.
E. Zehe, U. Ehret, L. Pfister, T. Blume, B. Schröder, M. Westhoff, C. Jackisch, S. J. Schymanski, M. Weiler, K. Schulz, N. Allroggen, J. Tronicke, L. van Schaik, P. Dietrich, U. Scherer, J. Eccard, V. Wulfmeyer, and A. Kleidon
Hydrol. Earth Syst. Sci., 18, 4635–4655, https://doi.org/10.5194/hess-18-4635-2014, https://doi.org/10.5194/hess-18-4635-2014, 2014
U. Ehret, H. V. Gupta, M. Sivapalan, S. V. Weijs, S. J. Schymanski, G. Blöschl, A. N. Gelfan, C. Harman, A. Kleidon, T. A. Bogaard, D. Wang, T. Wagener, U. Scherer, E. Zehe, M. F. P. Bierkens, G. Di Baldassarre, J. Parajka, L. P. H. van Beek, A. van Griensven, M. C. Westhoff, and H. C. Winsemius
Hydrol. Earth Syst. Sci., 18, 649–671, https://doi.org/10.5194/hess-18-649-2014, https://doi.org/10.5194/hess-18-649-2014, 2014
E. Zehe, U. Ehret, T. Blume, A. Kleidon, U. Scherer, and M. Westhoff
Hydrol. Earth Syst. Sci., 17, 4297–4322, https://doi.org/10.5194/hess-17-4297-2013, https://doi.org/10.5194/hess-17-4297-2013, 2013
A. Kleidon, E. Zehe, U. Ehret, and U. Scherer
Hydrol. Earth Syst. Sci., 17, 225–251, https://doi.org/10.5194/hess-17-225-2013, https://doi.org/10.5194/hess-17-225-2013, 2013
Related subject area
Subject: Catchment hydrology | Techniques and Approaches: Stochastic approaches
Monthly new water fractions and their relationships with climate and catchment properties across Alpine rivers
Technical note: Two-component electrical-conductivity-based hydrograph separation employing an exponential mixing model (EXPECT) provides reliable high-temporal-resolution young water fraction estimates in three small Swiss catchments
Flood frequency analysis using mean daily flows vs. instantaneous peak flows
On the regional-scale variability in flow duration curves in Peninsular India
Towards a conceptualization of the hydrological processes behind changes of young water fraction with elevation: a focus on mountainous alpine catchments
A mixed distribution approach for low-flow frequency analysis – Part 2: Comparative assessment of a mixed probability vs. copula-based dependence framework
A mixed distribution approach for low-flow frequency analysis – Part 1: Concept, performance, and effect of seasonality
Significant regime shifts in historical water yield in the Upper Brahmaputra River basin
A geostatistical spatially varying coefficient model for mean annual runoff that incorporates process-based simulations and short records
Low-flow estimation beyond the mean – expectile loss and extreme gradient boosting for spatiotemporal low-flow prediction in Austria
Impact of bias nonstationarity on the performance of uni- and multivariate bias-adjusting methods: a case study on data from Uccle, Belgium
A space–time Bayesian hierarchical modeling framework for projection of seasonal maximum streamflow
Parsimonious statistical learning models for low-flow estimation
Development of a Wilks feature importance method with improved variable rankings for supporting hydrological inference and modelling
Technical Note: Improved partial wavelet coherency for understanding scale-specific and localized bivariate relationships in geosciences
Effects of climate anomalies on warm-season low flows in Switzerland
Estimation of annual runoff by exploiting long-term spatial patterns and short records within a geostatistical framework
A methodology to estimate flow duration curves at partially ungauged basins
The role of flood wave superposition in the severity of large floods
Contribution of low-frequency climatic–oceanic oscillations to streamflow variability in small, coastal rivers of the Sierra Nevada de Santa Marta (Colombia)
Stochastic reconstruction of spatio-temporal rainfall patterns by inverse hydrologic modelling
An assessment of trends and potential future changes in groundwater-baseflow drought based on catchment response times
More frequent flooding? Changes in flood frequency in the Pearl River basin, China, since 1951 and over the past 1000 years
Topography significantly influencing low flows in snow-dominated watersheds
A discrete wavelet spectrum approach for identifying non-monotonic trends in hydroclimate data
Evaluating climate change impacts on streamflow variability based on a multisite multivariate GCM downscaling method in the Jing River of China
Estimating unconsolidated sediment cover thickness by using the horizontal distance to a bedrock outcrop as secondary information
On the probability distribution of daily streamflow in the United States
The European 2015 drought from a hydrological perspective
Heterogeneity measures in hydrological frequency analysis: review and new developments
ENSO-conditioned weather resampling method for seasonal ensemble streamflow prediction
Ordinary kriging as a tool to estimate historical daily streamflow records
Trends in floods in West Africa: analysis based on 11 catchments in the region
Implementation and validation of a Wilks-type multi-site daily precipitation generator over a typical Alpine river catchment
Spatial controls on groundwater response dynamics in a snowmelt-dominated montane catchment
Is bias correction of regional climate model (RCM) simulations possible for non-stationary conditions?
Data compression to define information content of hydrological time series
Topological and canonical kriging for design flood prediction in ungauged catchments: an improvement over a traditional regional regression approach?
Regionalised spatiotemporal rainfall and temperature models for flood studies in the Basque Country, Spain
Exploring the physical controls of regional patterns of flow duration curves – Part 1: Insights from statistical analyses
Land cover and water yield: inference problems when comparing catchments with mixed land cover
An elusive search for regional flood frequency estimates in the River Nile basin
Interannual hydroclimatic variability and its influence on winter nutrient loadings over the Southeast United States
Variational assimilation of streamflow into operational distributed hydrologic models: effect of spatiotemporal scale of adjustment
Contrasting trends in floods for two sub-arctic catchments in northern Sweden – does glacier presence matter?
Long-range forecasting of intermittent streamflow
Applying sequential Monte Carlo methods into a distributed hydrologic model: lagged particle filtering approach with regularization
Low-frequency variability of European runoff
Comparison of catchment grouping methods for flow duration curve estimation at ungauged sites in France
Regional flow duration curves for ungauged sites in Sicily
Marius G. Floriancic, Michael P. Stockinger, James W. Kirchner, and Christine Stumpp
Hydrol. Earth Syst. Sci., 28, 3675–3694, https://doi.org/10.5194/hess-28-3675-2024, https://doi.org/10.5194/hess-28-3675-2024, 2024
Short summary
Short summary
The Alps are a key water resource for central Europe, providing water for drinking, agriculture, and hydropower production. To assess water availability in streams, we need to understand how much streamflow is derived from old water stored in the subsurface versus more recent precipitation. We use tracer data from 32 Alpine streams and statistical tools to assess how much recent precipitation can be found in Alpine rivers and how this amount is related to catchment properties and climate.
Alessio Gentile, Jana von Freyberg, Davide Gisolo, Davide Canone, and Stefano Ferraris
Hydrol. Earth Syst. Sci., 28, 1915–1934, https://doi.org/10.5194/hess-28-1915-2024, https://doi.org/10.5194/hess-28-1915-2024, 2024
Short summary
Short summary
Can we leverage high-resolution and low-cost EC measurements and biweekly δ18O data to estimate the young water fraction at higher temporal resolution? Here, we present the EXPECT method that combines two widespread techniques: EC-based hydrograph separation and sine-wave models of the seasonal isotope cycles. The method is not without its limitations, but its application in three small Swiss catchments is promising for future applications in catchments with different characteristics.
Anne Bartens, Bora Shehu, and Uwe Haberlandt
Hydrol. Earth Syst. Sci., 28, 1687–1709, https://doi.org/10.5194/hess-28-1687-2024, https://doi.org/10.5194/hess-28-1687-2024, 2024
Short summary
Short summary
River flow data are often provided as mean daily flows (MDF), in which a lot of information is lost about the actual maximum flow or instantaneous peak flows (IPF) within a day. We investigate the error of using MDF instead of IPF and identify means to predict IPF when only MDF data are available. We find that the average ratio of daily flood peaks and volumes is a good predictor, which is easily and universally applicable and requires a minimum amount of data.
Pankaj Dey, Jeenu Mathai, Murugesu Sivapalan, and Pradeep P. Mujumdar
Hydrol. Earth Syst. Sci., 28, 1493–1514, https://doi.org/10.5194/hess-28-1493-2024, https://doi.org/10.5194/hess-28-1493-2024, 2024
Short summary
Short summary
This study explores the regional streamflow variability in Peninsular India. This variability is governed by monsoons, mountainous systems, and geologic gradients. A linkage between these influencing factors and streamflow variability is established using a Wegenerian approach and flow duration curves.
Alessio Gentile, Davide Canone, Natalie Ceperley, Davide Gisolo, Maurizio Previati, Giulia Zuecco, Bettina Schaefli, and Stefano Ferraris
Hydrol. Earth Syst. Sci., 27, 2301–2323, https://doi.org/10.5194/hess-27-2301-2023, https://doi.org/10.5194/hess-27-2301-2023, 2023
Short summary
Short summary
What drives young water fraction, F*yw (i.e., the fraction of water in streamflow younger than 2–3 months), variations with elevation? Why is F*yw counterintuitively low in high-elevation catchments, in spite of steeper topography? In this paper, we present a perceptual model explaining how the longer low-flow duration at high elevations, driven by the persistence of winter snowpacks, increases the proportion of stored (old) water contributing to the stream, thus reducing F*yw.
Gregor Laaha
Hydrol. Earth Syst. Sci., 27, 2019–2034, https://doi.org/10.5194/hess-27-2019-2023, https://doi.org/10.5194/hess-27-2019-2023, 2023
Short summary
Short summary
In seasonal climates with a warm and a cold season, low flows are generated by different processes so that return periods used as a measure of event severity will be inaccurate. We propose a novel mixed copula estimator that is shown to outperform previous calculation methods. The new method is highly relevant for a wide range of European river flow regimes and should be used by default.
Gregor Laaha
Hydrol. Earth Syst. Sci., 27, 689–701, https://doi.org/10.5194/hess-27-689-2023, https://doi.org/10.5194/hess-27-689-2023, 2023
Short summary
Short summary
Knowing the severity of an extreme event is of particular importance to hydrology and water policies. In this paper we propose a mixed distribution approach for low flows. It provides one consistent approach to quantify the severity of summer, winter, and annual low flows based on their respective annualities (or return periods). We show that the new method is much more accurate than existing methods and should therefore be used by engineers and water agencies.
Hao Li, Baoying Shan, Liu Liu, Lei Wang, Akash Koppa, Feng Zhong, Dongfeng Li, Xuanxuan Wang, Wenfeng Liu, Xiuping Li, and Zongxue Xu
Hydrol. Earth Syst. Sci., 26, 6399–6412, https://doi.org/10.5194/hess-26-6399-2022, https://doi.org/10.5194/hess-26-6399-2022, 2022
Short summary
Short summary
This study examines changes in water yield by determining turning points in the direction of yield changes and highlights that regime shifts in historical water yield occurred in the Upper Brahmaputra River basin, both the climate and cryosphere affect the magnitude of water yield increases, climate determined the declining trends in water yield, and meltwater has the potential to alleviate the water shortage. A repository for all source files is made available.
Thea Roksvåg, Ingelin Steinsland, and Kolbjørn Engeland
Hydrol. Earth Syst. Sci., 26, 5391–5410, https://doi.org/10.5194/hess-26-5391-2022, https://doi.org/10.5194/hess-26-5391-2022, 2022
Short summary
Short summary
The goal of this work was to make a map of the mean annual runoff for Norway for a 30-year period. We first simulated runoff by using a process-based model that models the relationship between runoff, precipitation, temperature, and land use. Next, we corrected the map based on runoff observations from streams by using a statistical method. We were also able to use data from rivers that only had a few annual observations. We find that the statistical correction improves the runoff estimates.
Johannes Laimighofer, Michael Melcher, and Gregor Laaha
Hydrol. Earth Syst. Sci., 26, 4553–4574, https://doi.org/10.5194/hess-26-4553-2022, https://doi.org/10.5194/hess-26-4553-2022, 2022
Short summary
Short summary
Our study uses a statistical boosting model for estimating low flows on a monthly basis, which can be applied to estimate low flows at sites without measurements. We use an extensive dataset of 260 stream gauges in Austria for model development. As we are specifically interested in low-flow events, our method gives specific weight to such events. We found that our method can considerably improve the predictions of low-flow events and yields accurate estimates of the seasonal low-flow variation.
Jorn Van de Velde, Matthias Demuzere, Bernard De Baets, and Niko E. C. Verhoest
Hydrol. Earth Syst. Sci., 26, 2319–2344, https://doi.org/10.5194/hess-26-2319-2022, https://doi.org/10.5194/hess-26-2319-2022, 2022
Short summary
Short summary
An important step in projecting future climate is the bias adjustment of the climatological and hydrological variables. In this paper, we illustrate how bias adjustment can be impaired by bias nonstationarity. Two univariate and four multivariate methods are compared, and for both types bias nonstationarity can be linked with less robust adjustment.
Álvaro Ossandón, Manuela I. Brunner, Balaji Rajagopalan, and William Kleiber
Hydrol. Earth Syst. Sci., 26, 149–166, https://doi.org/10.5194/hess-26-149-2022, https://doi.org/10.5194/hess-26-149-2022, 2022
Short summary
Short summary
Timely projections of seasonal streamflow extremes on a river network can be useful for flood risk mitigation, but this is challenging, particularly under space–time nonstationarity. We develop a space–time Bayesian hierarchical model (BHM) using temporal climate covariates and copulas to project seasonal streamflow extremes and the attendant uncertainties. We demonstrate this on the Upper Colorado River basin to project spring flow extremes using the preceding winter’s climate teleconnections.
Johannes Laimighofer, Michael Melcher, and Gregor Laaha
Hydrol. Earth Syst. Sci., 26, 129–148, https://doi.org/10.5194/hess-26-129-2022, https://doi.org/10.5194/hess-26-129-2022, 2022
Short summary
Short summary
This study aims to predict long-term averages of low flow on a hydrologically diverse dataset in Austria. We compared seven statistical learning methods and included a backward variable selection approach. We found that separating the low-flow processes into winter and summer low flows leads to good performance for all the models. Variable selection results in more parsimonious and more interpretable models. Linear approaches for prediction and variable selection are sufficient for our dataset.
Kailong Li, Guohe Huang, and Brian Baetz
Hydrol. Earth Syst. Sci., 25, 4947–4966, https://doi.org/10.5194/hess-25-4947-2021, https://doi.org/10.5194/hess-25-4947-2021, 2021
Short summary
Short summary
We proposed a test statistic feature importance method to quantify the importance of predictor variables for random-forest-like models. The proposed method does not rely on any performance measures to evaluate variable rankings, which can thus result in unbiased variable rankings. The resulting variable rankings based on the proposed method could help random forest achieve its optimum predictive accuracy.
Wei Hu and Bing Si
Hydrol. Earth Syst. Sci., 25, 321–331, https://doi.org/10.5194/hess-25-321-2021, https://doi.org/10.5194/hess-25-321-2021, 2021
Short summary
Short summary
Partial wavelet coherency method is improved to explore the bivariate relationships at different scales and locations after excluding the effects of other variables. The method was tested with artificial datasets and applied to a measured dataset. Compared with others, this method has the advantages of capturing phase information, dealing with multiple excluding variables, and producing more accurate results. This method can be used in different areas with spatial or temporal datasets.
Marius G. Floriancic, Wouter R. Berghuijs, Tobias Jonas, James W. Kirchner, and Peter Molnar
Hydrol. Earth Syst. Sci., 24, 5423–5438, https://doi.org/10.5194/hess-24-5423-2020, https://doi.org/10.5194/hess-24-5423-2020, 2020
Short summary
Short summary
Low river flows affect societies and ecosystems. Here we study how precipitation and potential evapotranspiration shape low flows across a network of 380 Swiss catchments. Low flows in these rivers typically result from below-average precipitation and above-average potential evapotranspiration. Extreme low flows result from long periods of the combined effects of both drivers.
Thea Roksvåg, Ingelin Steinsland, and Kolbjørn Engeland
Hydrol. Earth Syst. Sci., 24, 4109–4133, https://doi.org/10.5194/hess-24-4109-2020, https://doi.org/10.5194/hess-24-4109-2020, 2020
Short summary
Short summary
Annual runoff is a measure of how much water flows through a river during a year and is an important quantity, e.g. when planning infrastructure. In this paper, we suggest a new statistical model for annual runoff estimation. The model exploits correlation between rivers and is able to detect whether the annual runoff in the target river follows repeated patterns over time relative to neighbouring rivers. In our work we show for what cases the latter represents a benefit over comparable methods.
Elena Ridolfi, Hemendra Kumar, and András Bárdossy
Hydrol. Earth Syst. Sci., 24, 2043–2060, https://doi.org/10.5194/hess-24-2043-2020, https://doi.org/10.5194/hess-24-2043-2020, 2020
Short summary
Short summary
The paper presents a new, simple and model-free methodology to estimate the streamflow at partially gauged basins, given the precipitation gauged at another basin. We show that the FDC is not a characteristic of the basin only, but of both the basin and the weather. Because of the dependence on the climate, discharge data at the target site are here retrieved using the Antecedent Precipitation Index (API) of the donor site as it represents in a streamflow-like way the precipitation of the basin.
Björn Guse, Bruno Merz, Luzie Wietzke, Sophie Ullrich, Alberto Viglione, and Sergiy Vorogushyn
Hydrol. Earth Syst. Sci., 24, 1633–1648, https://doi.org/10.5194/hess-24-1633-2020, https://doi.org/10.5194/hess-24-1633-2020, 2020
Short summary
Short summary
Floods are influenced by river network processes, among others. Flood characteristics of tributaries may affect flood severity downstream of confluences. The impact of flood wave superposition is investigated with regard to magnitude and temporal matching of flood peaks. Our study in Germany and Austria shows that flood wave superposition is not the major driver of flood severity. However, there is the potential for large floods at some confluences in cases of temporal matching of flood peaks.
Juan Camilo Restrepo, Aldemar Higgins, Jaime Escobar, Silvio Ospino, and Natalia Hoyos
Hydrol. Earth Syst. Sci., 23, 2379–2400, https://doi.org/10.5194/hess-23-2379-2019, https://doi.org/10.5194/hess-23-2379-2019, 2019
Short summary
Short summary
This study evaluated the influence of low-frequency oscillations that are linked to large-scale oceanographic–atmospheric processes, on streamflow variability in small mountain rivers of the Sierra Nevada de Santa Marta, Colombia, aiming to explore streamflow variability, estimate the net contribution to the energy of low-frequency oscillations to streamflow anomalies, and analyze the linkages between streamflow anomalies and large-scale, low-frequency oceanographic–atmospheric processes.
Jens Grundmann, Sebastian Hörning, and András Bárdossy
Hydrol. Earth Syst. Sci., 23, 225–237, https://doi.org/10.5194/hess-23-225-2019, https://doi.org/10.5194/hess-23-225-2019, 2019
Jost Hellwig and Kerstin Stahl
Hydrol. Earth Syst. Sci., 22, 6209–6224, https://doi.org/10.5194/hess-22-6209-2018, https://doi.org/10.5194/hess-22-6209-2018, 2018
Short summary
Short summary
Due to the lack of long-term observations, insights into changes of groundwater resources are obscured. In this paper we assess past and potential future changes in groundwater drought in headwater catchments using a baseflow approach. There are a few past trends which are highly dependent on the period of analysis. Catchments with short response times are found to have a higher sensitivity to projected seasonal precipitation shifts, urging for a local management based on response times.
Qiang Zhang, Xihui Gu, Vijay P. Singh, Peijun Shi, and Peng Sun
Hydrol. Earth Syst. Sci., 22, 2637–2653, https://doi.org/10.5194/hess-22-2637-2018, https://doi.org/10.5194/hess-22-2637-2018, 2018
Qiang Li, Xiaohua Wei, Xin Yang, Krysta Giles-Hansen, Mingfang Zhang, and Wenfei Liu
Hydrol. Earth Syst. Sci., 22, 1947–1956, https://doi.org/10.5194/hess-22-1947-2018, https://doi.org/10.5194/hess-22-1947-2018, 2018
Short summary
Short summary
Topography plays an important role in determining the spatial heterogeneity of ecological, geomorphological, and hydrological processes. Topography plays a more dominant role in low flows than high flows. Our analysis also identified five significant TIs: perimeter, slope length factor, surface area, openness, and terrain characterization index. These can be used to compare watersheds when low flow assessments are conducted, specifically in snow-dominated regions.
Yan-Fang Sang, Fubao Sun, Vijay P. Singh, Ping Xie, and Jian Sun
Hydrol. Earth Syst. Sci., 22, 757–766, https://doi.org/10.5194/hess-22-757-2018, https://doi.org/10.5194/hess-22-757-2018, 2018
Zhi Li and Jiming Jin
Hydrol. Earth Syst. Sci., 21, 5531–5546, https://doi.org/10.5194/hess-21-5531-2017, https://doi.org/10.5194/hess-21-5531-2017, 2017
Short summary
Short summary
We developed an efficient multisite and multivariate GCM downscaling method and generated climate change scenarios for SWAT to evaluate the streamflow variability within a watershed in China. The application of the ensemble techniques enables us to better quantify the model uncertainties. The peak values of precipitation and streamflow have a tendency to shift from the summer to spring season over the next 30 years. The number of extreme flooding and drought events will increase.
Nils-Otto Kitterød
Hydrol. Earth Syst. Sci., 21, 4195–4211, https://doi.org/10.5194/hess-21-4195-2017, https://doi.org/10.5194/hess-21-4195-2017, 2017
Short summary
Short summary
The GRANADA open-access database (NGU, 2016a) was used to derive point recordings of thickness of sediment above the bedrock D(u). For each D(u) the horizontal distance to nearest outcrop L(u) was derived from geological maps. The purpose was to utilize L(u) as a secondary function for estimation of D(u). Two estimation methods were employed: ordinary kriging (OK) and co-kriging (CK). A cross-validation analysis was performed to evaluate the additional information in the secondary function L(u).
Annalise G. Blum, Stacey A. Archfield, and Richard M. Vogel
Hydrol. Earth Syst. Sci., 21, 3093–3103, https://doi.org/10.5194/hess-21-3093-2017, https://doi.org/10.5194/hess-21-3093-2017, 2017
Short summary
Short summary
Flow duration curves are ubiquitous in surface water hydrology for applications including water allocation and protection of ecosystem health. We identify three probability distributions that can provide a reasonable fit to daily streamflows across much of United States. These results help us understand of the behavior of daily streamflows and enhance our ability to predict streamflows at ungaged river locations.
Gregor Laaha, Tobias Gauster, Lena M. Tallaksen, Jean-Philippe Vidal, Kerstin Stahl, Christel Prudhomme, Benedikt Heudorfer, Radek Vlnas, Monica Ionita, Henny A. J. Van Lanen, Mary-Jeanne Adler, Laurie Caillouet, Claire Delus, Miriam Fendekova, Sebastien Gailliez, Jamie Hannaford, Daniel Kingston, Anne F. Van Loon, Luis Mediero, Marzena Osuch, Renata Romanowicz, Eric Sauquet, James H. Stagge, and Wai K. Wong
Hydrol. Earth Syst. Sci., 21, 3001–3024, https://doi.org/10.5194/hess-21-3001-2017, https://doi.org/10.5194/hess-21-3001-2017, 2017
Short summary
Short summary
In 2015 large parts of Europe were affected by a drought. In terms of low flow magnitude, a region around the Czech Republic was most affected, with return periods > 100 yr. In terms of deficit volumes, the drought was particularly severe around S. Germany where the event lasted notably long. Meteorological and hydrological events developed differently in space and time. For an assessment of drought impacts on water resources, hydrological data are required in addition to meteorological indices.
Ana I. Requena, Fateh Chebana, and Taha B. M. J. Ouarda
Hydrol. Earth Syst. Sci., 21, 1651–1668, https://doi.org/10.5194/hess-21-1651-2017, https://doi.org/10.5194/hess-21-1651-2017, 2017
Short summary
Short summary
The notion of a measure to quantify the degree of heterogeneity of a region from which information is required to estimate the magnitude of events at ungauged sites is introduced. These heterogeneity measures are needed to compare regions, evaluate the impact of particular sites, and rank the performance of delineating methods. A framework to define and assess their desirable properties is proposed. Several heterogeneity measures are presented and/or developed to be assessed, giving guidelines.
Joost V. L. Beckers, Albrecht H. Weerts, Erik Tijdeman, and Edwin Welles
Hydrol. Earth Syst. Sci., 20, 3277–3287, https://doi.org/10.5194/hess-20-3277-2016, https://doi.org/10.5194/hess-20-3277-2016, 2016
Short summary
Short summary
Oceanic–atmospheric climate modes, such as El Niño–Southern Oscillation (ENSO), are known to affect the streamflow regime in many rivers around the world. A new method is presented for ENSO conditioning of the ensemble streamflow prediction (ESP) method, which is often used for seasonal streamflow forecasting. The method was tested on three tributaries of the Columbia River, OR. Results show an improvement in forecast skill compared to the standard ESP.
William H. Farmer
Hydrol. Earth Syst. Sci., 20, 2721–2735, https://doi.org/10.5194/hess-20-2721-2016, https://doi.org/10.5194/hess-20-2721-2016, 2016
Short summary
Short summary
The potential of geostatistical tools, leveraging the spatial structure and dependency of correlated time series, for the prediction of daily streamflow time series at unmonitored locations is explored. Simple geostatistical tools improve on traditional estimates of daily streamflow. The temporal evolution of spatial structure, including seasonal fluctuations, is also explored. The proposed method is contrasted with more advanced geostatistical methods and shown to be comparable.
B. N. Nka, L. Oudin, H. Karambiri, J. E. Paturel, and P. Ribstein
Hydrol. Earth Syst. Sci., 19, 4707–4719, https://doi.org/10.5194/hess-19-4707-2015, https://doi.org/10.5194/hess-19-4707-2015, 2015
Short summary
Short summary
The region of West Africa is undergoing important climate and environmental changes affecting the magnitude and occurrence of floods. This study aims to analyze the evolution of flood hazard in the region and to find links between flood hazards pattern and rainfall or vegetation index patterns.
D. E. Keller, A. M. Fischer, C. Frei, M. A. Liniger, C. Appenzeller, and R. Knutti
Hydrol. Earth Syst. Sci., 19, 2163–2177, https://doi.org/10.5194/hess-19-2163-2015, https://doi.org/10.5194/hess-19-2163-2015, 2015
R. S. Smith, R. D. Moore, M. Weiler, and G. Jost
Hydrol. Earth Syst. Sci., 18, 1835–1856, https://doi.org/10.5194/hess-18-1835-2014, https://doi.org/10.5194/hess-18-1835-2014, 2014
C. Teutschbein and J. Seibert
Hydrol. Earth Syst. Sci., 17, 5061–5077, https://doi.org/10.5194/hess-17-5061-2013, https://doi.org/10.5194/hess-17-5061-2013, 2013
S. V. Weijs, N. van de Giesen, and M. B. Parlange
Hydrol. Earth Syst. Sci., 17, 3171–3187, https://doi.org/10.5194/hess-17-3171-2013, https://doi.org/10.5194/hess-17-3171-2013, 2013
S. A. Archfield, A. Pugliese, A. Castellarin, J. O. Skøien, and J. E. Kiang
Hydrol. Earth Syst. Sci., 17, 1575–1588, https://doi.org/10.5194/hess-17-1575-2013, https://doi.org/10.5194/hess-17-1575-2013, 2013
P. Cowpertwait, D. Ocio, G. Collazos, O. de Cos, and C. Stocker
Hydrol. Earth Syst. Sci., 17, 479–494, https://doi.org/10.5194/hess-17-479-2013, https://doi.org/10.5194/hess-17-479-2013, 2013
L. Cheng, M. Yaeger, A. Viglione, E. Coopersmith, S. Ye, and M. Sivapalan
Hydrol. Earth Syst. Sci., 16, 4435–4446, https://doi.org/10.5194/hess-16-4435-2012, https://doi.org/10.5194/hess-16-4435-2012, 2012
A. I. J. M. van Dijk, J. L. Peña-Arancibia, and L. A. (Sampurno) Bruijnzeel
Hydrol. Earth Syst. Sci., 16, 3461–3473, https://doi.org/10.5194/hess-16-3461-2012, https://doi.org/10.5194/hess-16-3461-2012, 2012
P. Nyeko-Ogiramoi, P. Willems, F. M. Mutua, and S. A. Moges
Hydrol. Earth Syst. Sci., 16, 3149–3163, https://doi.org/10.5194/hess-16-3149-2012, https://doi.org/10.5194/hess-16-3149-2012, 2012
J. Oh and A. Sankarasubramanian
Hydrol. Earth Syst. Sci., 16, 2285–2298, https://doi.org/10.5194/hess-16-2285-2012, https://doi.org/10.5194/hess-16-2285-2012, 2012
H. Lee, D.-J. Seo, Y. Liu, V. Koren, P. McKee, and R. Corby
Hydrol. Earth Syst. Sci., 16, 2233–2251, https://doi.org/10.5194/hess-16-2233-2012, https://doi.org/10.5194/hess-16-2233-2012, 2012
H. E. Dahlke, S. W. Lyon, J. R. Stedinger, G. Rosqvist, and P. Jansson
Hydrol. Earth Syst. Sci., 16, 2123–2141, https://doi.org/10.5194/hess-16-2123-2012, https://doi.org/10.5194/hess-16-2123-2012, 2012
F. F. van Ogtrop, R. W. Vervoort, G. Z. Heller, D. M. Stasinopoulos, and R. A. Rigby
Hydrol. Earth Syst. Sci., 15, 3343–3354, https://doi.org/10.5194/hess-15-3343-2011, https://doi.org/10.5194/hess-15-3343-2011, 2011
S. J. Noh, Y. Tachikawa, M. Shiiba, and S. Kim
Hydrol. Earth Syst. Sci., 15, 3237–3251, https://doi.org/10.5194/hess-15-3237-2011, https://doi.org/10.5194/hess-15-3237-2011, 2011
L. Gudmundsson, L. M. Tallaksen, K. Stahl, and A. K. Fleig
Hydrol. Earth Syst. Sci., 15, 2853–2869, https://doi.org/10.5194/hess-15-2853-2011, https://doi.org/10.5194/hess-15-2853-2011, 2011
E. Sauquet and C. Catalogne
Hydrol. Earth Syst. Sci., 15, 2421–2435, https://doi.org/10.5194/hess-15-2421-2011, https://doi.org/10.5194/hess-15-2421-2011, 2011
F. Viola, L. V. Noto, M. Cannarozzo, and G. La Loggia
Hydrol. Earth Syst. Sci., 15, 323–331, https://doi.org/10.5194/hess-15-323-2011, https://doi.org/10.5194/hess-15-323-2011, 2011
Cited articles
Allard, D., Comunian, A., and Renard, P.: Probability aggregation methods in
geoscience, Math. Geosci., 44, 545–581, https://doi.org/10.1007/s11004-012-9396-3, 2012.
Bárdossy, A.: Copula-based geostatistical models for groundwater quality
parameters, Water Resour. Res., 42, 1–12, https://doi.org/10.1029/2005WR004754, 2006.
Batty, M.: Spatial Entropy, Geogr. Anal., 6, 1–31,
https://doi.org/10.1111/j.1538-4632.1974.tb01014.x, 1974.
Bell, G., Hey, T., and Szalay, A.: Computer science: Beyond the data deluge,
Science, 323, 1297–1298, https://doi.org/10.1126/science.1170411, 2009.
Bianchi, M. and Pedretti, D.: An entrogram-based approach to describe spatial heterogeneity with applications to solute transport in porous media, Water Resour. Res., 54, 4432–4448, https://doi.org/10.1029/2018WR022827, 2018.
Branch, M. A., Coleman, T. F., and Li, Y.: A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization
problems, SIAM J. Sci. Comput., 21, 1–23, https://doi.org/10.1137/S1064827595289108,
1999.
Brunsell, N. A.: A multiscale information theory approach to assess spatial-temporal variability of daily precipitation, J. Hydrol., 385, 165–172, https://doi.org/10.1016/j.jhydrol.2010.02.016, 2010.
Chapman, T. G.: Entropy as a measure of hydrologic data uncertainty and model performance, J. Hydrol., 85, 111–126, https://doi.org/10.1016/0022-1694(86)90079-X, 1986.
Chicco, D.: Ten quick tips for machine learning in computational biology,
BioData Min., 10, 1–17, https://doi.org/10.1186/s13040-017-0155-3, 2017.
Cover, T. M. and Thomas, J. A.: Elements of information theory, 2nd Edn.,
John Wiley & Sons, New Jersey, USA, 2006.
Darscheid, P.: Quantitative analysis of information flow in hydrological
modelling using Shannon information measures, Karlsruhe Institute of
Technology, Karlsruhe, 73 pp., 2017.
Darscheid, P., Guthke, A., and Ehret, U.: A maximum-entropy method to estimate discrete distributions from samples ensuring nonzero probabilities,
Entropy, 20, 601, https://doi.org/10.3390/e20080601, 2018.
Fix, E. and Hodges Jr., J. L.: Discriminatory analysis, non-parametric
discrimination, Project 21-49-004, Report 4, USA School of Aviation Medicine, Texas, https://doi.org/10.2307/1403797, 1951.
Gneiting, T. and Raftery, A. E.: Strictly proper scoring rules, prediction,
and estimation, J. Am. Stat. Assoc., 102, 359–378, https://doi.org/10.1198/016214506000001437, 2007.
Gong, W., Yang, D., Gupta, H. V., and Nearing, G.: Estimating information
entropy for hydrological data: one dimensional case, Water Resour. Res., 1,
5003–5018, https://doi.org/10.1002/2014WR015874, 2014.
Good, I. J.: Rational decisions, J. Roy. Stat. Soc., 14, 107–114, 1952.
Goovaerts, P.: Geostatistics for natural resources evaluation, Oxford Univers., New York, 1997.
Hristopulos, D. T. and Baxevani, A.: Effective probability distribution
approximation for the reconstruction of missing data, Stoch. Environ. Res.
Risk A., 34, 235–249, https://doi.org/10.1007/s00477-020-01765-5, 2020.
Journel, A. G.: Nonparametric estimation of spatial distributions, J. Int.
Assoc. Math. Geol., 15, 445–468, https://doi.org/10.1007/BF01031292, 1983.
Journel, A. G.: Combining knowledge from diverse sources: an alternative to
traditional data independence hypotheses, Math. Geol., 34, 573–596,
https://doi.org/10.1023/A:1016047012594, 2002.
Journel, A. G. and Huijbregts, C. J.: Mining geostatistics, Academic Press, London, UK, ISBN 0-12-391050-1, 1978.
Kazianka, H. and Pilz, J.: Spatial Interpolation Using Copula-Based
Geostatistical Models, in: geoENV VII – Geostatistics for Environmental
Applications, Springer, Berlin, 307–319, https://doi.org/10.1007/978-90-481-2322-3_27, 2010.
Kitanidis, P. K.: Introduction to geostatistics: applications in hydrogeology, Cambridge University Press, Cambridge, UK, 1997.
Knuth, K. H.: Optimal data-based binning for histograms, online preprint: arXiv:physics/0605197v2 [physics.data-an], 2013.
Krige, D. G.: A statistical approach to some mine valuation and allied problems on the Witwatersrand, Master's thesis, University of Witwatersrand, Witwatersrand, 1951.
Krishnan, S.: The tau model for data redundancy and information combination in earth sciences: theory and application, Math. Geosci., 40, 705–727,
https://doi.org/10.1007/s11004-008-9165-5, 2008.
Leopold, L. B. and Langbein, W. B.: The concept of entropy in landscape
evolution, US Geol. Surv. Prof. Pap. 500-A, US Geological Survey, Washington, 1962.
Li, J. and Heap, A. D.: A review of spatial interpolation methods for
environmental scientists, 2008/23, Geosci. Aust., Canberra, 137 pp., 2008.
Li, J. and Heap, A. D.: A review of comparative studies of spatial interpolation methods in environmental sciences: Performance and impact factors, Ecol. Inform., 6, 228–241, https://doi.org/10.1016/j.ecoinf.2010.12.003, 2011.
Li, J. and Heap, A. D.: Spatial interpolation methods applied in the
environmental sciences: A review, Environ. Model. Softw., 53, 173–189,
https://doi.org/10.1016/j.envsoft.2013.12.008, 2014.
Liu, D., Wang, D., Wang, Y., Wu, J., Singh, V. P., Zeng, X., Wang, L., Chen,
Y., Chen, X., Zhang, L., and Gu, S.: Entropy of hydrological systems under
small samples: uncertainty and variability, J. Hydrol., 532, 163–176, https://doi.org/10.1016/j.jhydrol.2015.11.019, 2016.
Loritz, R., Gupta, H., Jackisch, C., Westhoff, M., Kleidon, A., Ehret, U., and Zehe, E.: On the dynamic nature of hydrological similarity, Hydrol. Earth Syst. Sci., 22, 3663–3684, https://doi.org/10.5194/hess-22-3663-2018, 2018.
Loritz, R., Kleidon, A., Jackisch, C., Westhoff, M., Ehret, U., Gupta, H., and Zehe, E.: A topographic index explaining hydrological similarity by accounting for the joint controls of runoff formation, Hydrol. Earth Syst. Sci., 23, 3807–3821, https://doi.org/10.5194/hess-23-3807-2019, 2019.
Mälicke, M. and Schneider, H. D. Scikit-GStat 0.2.6: A scipy flavored
geostatistical analysis toolbox written in Python (Version v0.2.6), Zenodo,
https://doi.org/10.5281/zenodo.3531816, 2019.
Mälicke, M., Hassler, S. K., Blume, T., Weiler, M., and Zehe, E.: Soil moisture: variable in space but redundant in time, Hydrol. Earth Syst. Sci., 24, 2633–2653, https://doi.org/10.5194/hess-24-2633-2020, 2020.
Manchuk, J. G. and Deutsch, C. V.: Robust solution of normal (kriging)
equations, available at: http://www.ccgalberta.com (last access: 10 September 2020), 2007.
Mishra, A. K., Özger, M., and Singh, V. P.: An entropy-based investigation into the variability of precipitation, J. Hydrol., 370, 139–154, https://doi.org/10.1016/j.jhydrol.2009.03.006, 2009.
Myers, D. E.: Spatial interpolation: an overview, Geoderma, 62, 17–28, https://doi.org/10.1016/0016-7061(94)90025-6, 1993.
Naimi, B.: On uncertainty in species distribution modelling, Doctoral
thesis, University of Twente, Twente, 2015.
Nearing, G. S. and Gupta, H. V.: Information vs. Uncertainty as the Foundation for a Science of Environmental Modeling, available at: http://arxiv.org/abs/1704.07512 (last access: 10 September 2020), 2017.
Oliver, M. A. and Webster, R.: A tutorial guide to geostatistics: Computing
and modelling variograms and kriging, Catena, 113, 56–69,
https://doi.org/10.1016/j.catena.2013.09.006, 2014.
Pechlivanidis, I. G., Jackson, B., Mcmillan, H., and Gupta, H. V.: Robust
informational entropy-based descriptors of flow in catchment hydrology, Hydrolog. Sci. J., 61, 1–18, https://doi.org/10.1080/02626667.2014.983516, 2016.
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Blondel, M., Thirion, B., Grisel, O., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, É.: Scikit-learn: Machine Learning in Python, J. Mach. Learn. Res., 12, 2825–2830, 2011.
Pham, T. D.: GeoEntropy: A measure of complexity and similarity, Pattern
Recognit., 43, 887–896, https://doi.org/10.1016/j.patcog.2009.08.015, 2010.
Putter, H. and Young, G. A.: On the effect of covariance function estimation
on the accuracy of kriging predictors, Bernoulli, 7, 421–438, 2001.
Rasmussen, C. E. and Williams, C. K. I.: Gaussian processes for machine
learning, MIT Press, London, 2006.
Roodposhti, M. S., Aryal, J., Shahabi, H., and Safarrad, T.: Fuzzy Shannon
entropy: a hybrid GIS-based landslide susceptibility mapping method, Entropy, 18, 343, https://doi.org/10.3390/e18100343, 2016.
Roulston, M. S. and Smith, L. A.: Evaluating probabilistic forecasts using
information theory, Mon. Weather Rev., 130, 1653–1660,
https://doi.org/10.1175/1520-0493(2002)130<1653:EPFUIT>2.0.CO;2,
2002.
Ruddell, B. L. and Kumar, P.: Ecohydrologic process net- works: 1. Identification, Water Resour. Res., 45, 1–23, https://doi.org/10.1029/2008WR007279, 2009.
Scott, D. W.: Scott bin width, Biometrika, 66, 605–610,
https://doi.org/10.1093/biomet/66.3.605, 1979.
Shannon, C. E.: A mathematical theory of communication, Bell Syst. Tech. J.,
27, 379–423, 623–656, 1948.
Shepard, D.: A two-dimensional interpolation function for irregularly-spaced
data, in: Proceedings of the 1968 23rd ACM National Conference, 27–29 August 1968, New York, 517–524, 1968.
Singh, V. P.: Entropy theory and its application in environmental and water engineering, 1st Edn., John Wiley & Sons, West Sussex, UK, ISBN 978-1-119-97656-1, 2013.
Solomatine, D. P. and Ostfeld, A.: Data-driven modelling: some past experiences and new approaches, J. Hydroinform., 10, 3–22,
https://doi.org/10.2166/hydro.2008.015, 2008.
Tarantola, A.: Inverse problem theory and methods for model parameter
estimation, Siam, Philadelphia, 2005.
Tarantola, A. and Valette, B.: Inverse problems = quest for information,
J. Geophys., 50, 159–170, 1982.
Thiesen, S., Darscheid, P., and Ehret, U.: Identifying rainfall-runoff events in discharge time series: A data-driven method based on Information Theory, Hydrol. Earth Syst. Sci., 23, 1015–1034, https://doi.org/10.5194/hess-23-1015-2019, 2019.
Thiesen, S., Vieira, D. M., and Ehret, U.: KIT-HYD/HER: version v1.4), Zenodo, https://doi.org/10.5281/zenodo.3614718, 2020.
Weijs, S. V.: Information theory for risk-based water system operation, Technische Universiteit Delft, Delft, 210 pp., 2011.
Weijs, S. V., van Nooijen, R., and van de Giesen, N.: Kullback–Leibler
divergence as a forecast skill score with classic reliability–resolution–uncertainty decomposition, Mon. Weather Rev., 138, 3387–3399, https://doi.org/10.1175/2010mwr3229.1, 2010.
Wellmann, J. F.: Information theory for correlation analysis and estimation of uncertainty reduction in maps and models, Entropy, 15, 1464–1485,
https://doi.org/10.3390/e15041464, 2013.
Yakowitz, S. J. and Szidarovszky, F.: A comparison of kriging with nonparametric regression methods, J. Multivar. Anal., 16, 21–53, 1985.
Short summary
A spatial interpolator has been proposed for exploring the information content of the data in the light of geostatistics and information theory. It showed comparable results to traditional interpolators, with the advantage of presenting generalization properties. We discussed three different ways of combining distributions and their implications for the probabilistic results. By its construction, the method provides a suitable and flexible framework for uncertainty analysis and decision-making.
A spatial interpolator has been proposed for exploring the information content of the data in...