Global sensitivity analysis is an important step in the process of developing and analyzing hydrological models. Measured data of different variables are used to identify the number of sensitive ...model parameters and to better constrain the model output. However, data scarcity is a common issue in hydrology. Since in hydrology we are dealing with multi‐scale time dependent problems, we want to overcome that issue by exploiting the potential of using the decomposed wavelet temporal scales of the discharge signal for the identification of sensitive model parameters. In the proposed methodology, we coupled the discrete wavelet transform with a technique for model parameter dimension reduction, that is, the active subspace method. We apply the proposed methodology to the LuKARS model, a lumped karst aquifer model for the Kerschbaum spring in Waidhofen/Ybbs (Austria). Our results demonstrate that the temporal scale dependency of hydrological processes affects the structure and dimension of the active subspaces. The results reveal that the dimensionality of an active subspace increases with the increasing number of hydrologic processes affecting a temporal scale. As a consequence, different parameters are sensitive on different temporal scales. Finally, we show that the total number of sensitive parameters identified at different temporal scales is larger than the number of sensitive parameters obtained using the complete spring discharge signal. Hence, instead of using multiple time series to determine the number of sensitive parameters, we can also obtain more information about parameter sensitivities from one single, decomposed time series.
Key Points
The dimension and structure of a hydrological models' active subspace are temporal scale‐dependent
Hydrological processes that are dominant on different temporal scales can be derived from the active subspace structure
Methodology provides information on temporal scale‐dependent parameter sensitivities
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
In this paper, we derive the time-fractional Cahn–Hilliard equation from continuum mixture theory with a modification of Fick's law of diffusion. This model describes the process of phase separation ...with nonlocal memory effects. We analyze the existence, uniqueness, and regularity of weak solutions of the time-fractional Cahn–Hilliard equation. In this regard, we consider degenerating mobility functions and free energies of Landau, Flory–Huggins and double-obstacle type. We apply the Faedo–Galerkin method to the system, derive energy estimates, and use compactness theorems to pass to the limit in the discrete form. In order to compensate for the missing chain rule of fractional derivatives, we prove a fractional chain inequality for semiconvex functions. The work concludes with numerical simulations and a sensitivity analysis showing the influence of the fractional power. Here, we consider a convolution quadrature scheme for the time-fractional component, and use a mixed finite element method for the space discretization.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Subsurface flows, particularly hyporheic exchange fluxes, driven by streambed topography, permeability, channel gradient and dynamic flow conditions provide prominent ecological services such as ...nitrate removal from streams and aquifers. Stream flow dynamics cause strongly nonlinear and often episodic contributions of nutrient concentrations in river‐aquifer systems. Using a fully coupled transient flow and reactive transport model, we investigated the denitrification potential of hyporheic zones during peak‐flow events. The effects of streambed permeability, channel gradient and bedform amplitude on the spatio‐temporal distribution of nitrate and dissolved organic carbon in streambeds and the associated denitrification potential were explored. Distinct peak‐flow events with different intensity, duration and hydrograph shape were selected to represent a wide range of peak‐flow scenarios. Our results indicated that the specific hydrodynamic characteristics of individual flow events largely determine the average positive or negative nitrate removal capacity of hyporheic zones, however the magnitude of this capacity is controlled by geomorphological settings (i.e., channel slope, streambed permeability and bedform amplitude). Specifically, events with longer duration and higher intensity were shown to promote higher nitrate removal efficiency with higher magnitude of removal efficiency in the scenarios with higher slope and permeability values. These results are essential for better assessment of the subsurface nitrate removal capacity under the influence of flow dynamics and particularly peak‐flow events in order to provide tailored solutions for effective restoration of interconnected river‐aquifer systems.
Key Points
Reactive transport model predicts stream geomorphological impacts on hyporheic denitrification potential
High frequency observations of nutrient fluxes improve predictions of denitrification potential
Controls of duration and intensity of peak‐flow events on denitrification potential vary between geomorphological settings
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
Manufactured materials usually contain random imperfections due to the fabrication process, e.g., the 3D-printing, casting, etc. These imperfections affect significantly the effective material ...properties and result in uncertainties in the mechanical response. Numerical analysis of the effects of the imperfections and the uncertainty quantification (UQ) can be often done by use of digital stochastic surrogate material models. In this work, we present a new flexible class of surrogate models depending on a small number of parameters and a calibration strategy ensuring that the constructed model fits to the available observation data, with special focus on two-phase materials. The surrogate models are constructed as the level-set of a linear combination of an intensity field representing the topological shape and a Gaussian perturbation representing the imperfections, allowing for fast sampling strategies. The mathematical design parameters of the model are related to physical ones and thus easy to interpret. The calibration of the model parameters is performed using progressive batching sub-sampled quasi-Newton minimization, using a designed distance measure between the synthetic samples and the data. Then, employing a fast sampling algorithm, an arbitrary number of synthetic samples can be generated to use in Monte Carlo type methods for prediction of effective material properties. In particular, we illustrate the method in application to UQ of the elasto-plastic response of an imperfect octet-truss lattice which plays an important role in additive manufacturing. To this end, we study the effective material properties of the lattice unit cell under elasto-plastic deformations and investigate the sensitivity of the effective Young’s modulus to the imperfections.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
We construct locally supported basis functions which are biorthogonal to conforming nodal finite element basis functions of degree p in one dimension. In contrast to earlier approaches, these basis ...functions have the same support as the nodal finite element basis functions and reproduce the conforming finite element space of degree p-1. Working with Gauß--Lobatto nodes, we find an interesting connection between biorthogonality and quadrature formulas. One important application of these newly constructed biorthogonal basis functions are two-dimensional mortar finite elements. The weak continuity condition of the constrained mortar space is realized in terms of our new dual bases. As a result, local static condensation can be applied which is very attractive from the numerical point of view. Numerical results are presented for cubic mortar finite elements.
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BFBNIB, INZLJ, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK, ZRSKP
As a mean to assess the risk dam structures are exposed to during earthquakes, we employ an abstract mathematical, three dimensional, elasto-acoustic coupled wave-propagation model taking into ...account (i) the dam structure itself, embedded into (ii) its surrounding topography, (iii) different material soil layers, (iv) the seismic source as well as (v) the reservoir lake filled with water treated as an acoustic medium. As a case study for extensive numerical simulations we consider the magnitude 7 seismic event of the 30th of October 2020 taking place in the Icarian Sea (Greece) and the Tahtalı dam around 30 km from there (Turkey). A challenging task is to resolve the multiple length scales that are present due to the huge differences in size between the dam building structure and the area of interest, considered for the propagation of the earthquake. Interfaces between structures and highly non-conforming meshes on different scales are resolved by means of a discontinuous Galerkin approach. The seismic source is modeled using inversion data about the real fault plane. Ultimately, we perform a real data driven, multi-scale, full source-to-site, physics based simulation based on the discontinuous Galerkin spectral element method, which allows to precisely validate the ground motion experienced along the Tahtalı dam, comparing the synthetic seismograms against actually observed ones. A comparison with a more classical computational method, using a plane wave with data from a deconvolved seismogram reading as an input, is discussed.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Alpine permafrost environments are highly vulnerable and sensitive to changes in regional and global climate trends. Thawing and degradation of permafrost has numerous adverse environmental, ...economic, and societal impacts. Mathematical modeling and numerical simulations provide powerful tools for predicting the degree of degradation and evolution of subsurface permafrost as a result of global warming. A particularly significant characteristic of alpine environments is the high variability in their surface geometry which drives large lateral thermal and fluid fluxes along topographic gradients. The combination of these topography-driven fluxes and unsaturated ground makes alpine systems markedly different from Arctic permafrost environments and general geotechnical ground freezing applications, and therefore, alpine permafrost demands its own specialized modeling approaches. In this work, we present a multi-physics permafrost model tailored to subsurface processes of alpine regions. In particular, we resolve the ice–water phase transitions, unsaturated conditions, and capillary actions, and account for the impact of the evolving pore space through freezing and thawing processes. Moreover, the approach is multi-dimensional, and therefore, inherently resolves the topography-driven horizontal fluxes. Through numerical case studies based on the elevation profiles of the Zugspitze (DE) and the Matterhorn (CH), we show the strong influence of lateral fluxes in 2D on active layer dynamics and the distribution of permafrost.
•A new numerical model for permafrost in alpine regions.•Importance of lateral fluxes in mountain permafrost modeling.•Influence of unsaturated conditions on freezing processes.•Development of mountain permafrost during warming scenario.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Two commonly used problem formulations for the description of acoustic wave propagation are investigated; one is based on fluid displacement, and the other one is based on the velocity potential as ...the primary variable. Their equivalence under general Neumann boundary conditions is shown on both the continuous and the discrete level. To obtain the equivalence in the discrete setting, a nonstandard mixed finite element formulation is introduced. Thus, the transfer of an already available analysis for coupled elasto-acoustic problems in the displacement formulation to the potential formulation can be achieved. For the applications, the potential formulation is of special interest because it allows the use of standard Lagrangian elements in both the structure and the fluid subdomain. Moreover, the approach does not require any conformity of the subdomain meshes at the interface, which considerably simplifies the physics-adapted mesh generation. Several engineering examples demonstrate the applicability and efficiency of the resulting numerical scheme.
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CEKLJ, DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
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