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Water ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 110
Author(s):  
Raphael Schneider ◽  
Simon Stisen ◽  
Anker Lajer Højberg

About half of the Danish agricultural land is drained artificially. Those drains, mostly in the form of tile drains, have a significant effect on the hydrological cycle. Consequently, the drainage system must also be represented in hydrological models that are used to simulate, for example, the transport and retention of chemicals. However, representation of drainage in large-scale hydrological models is challenging due to scale issues, lacking data on the distribution of drain infrastructure, and lacking drain flow observations. This calls for more indirect methods to inform such models. Here, we investigate the hypothesis that drain flow leaves a signal in streamflow signatures, as it represents a distinct streamflow generation process. Streamflow signatures are indices characterizing hydrological behaviour based on the hydrograph. Using machine learning regressors, we show that there is a correlation between signatures of simulated streamflow and simulated drain fraction. Based on these insights, signatures relevant to drain flow are incorporated in hydrological model calibration. A distributed coupled groundwater–surface water model of the Norsminde catchment, Denmark (145 km2) is set up. Calibration scenarios are defined with different objective functions; either using conventional stream flow metrics only, or a combination with hydrological signatures. We then evaluate the results from the different scenarios in terms of how well the models reproduce observed drain flow and spatial drainage patterns. Overall, the simulation of drain in the models is satisfactory. However, it remains challenging to find a direct link between signatures and an improvement in representation of drainage. This is likely attributable to model structural issues and lacking flexibility in model parameterization.


Abstract In this part II paper we present a fully consistent analytical derivation of the ‘dry’ isentropic 1½-layer shallow water model described and used in part I of this study, with no convection and precipitation. The mathematical derivation presented here is based on a combined asymptotic and slaved Hamiltonian analysis which is used to resolve an apparent inconsistency arising from the application of a rigid-lid approximation to an isentropic two-layer shallow water model. Real observations based on radiosonde data are used to justify the scaling assumptions used throughout the paper, as well as in part I. Eventually, a fully consistent isentropic 1½-layer model emerges from imposing fluid at rest (v1 = 0) and zero Montgomery potential (M1 = 0) in the upper layer of an isentropic two-layer model.


Abstract An isentropic 1½-layer model based on modified shallow water equations is presented, including terms mimicking convection and precipitation. This model is an updated version of the isopycnal single-layer modified shallow water model presented in Kent et al. (2017). The clearer link between fluid temperature and model variables together with a double-layer structure make this revised, isentropic model a more suitable tool to achieve our future goal: to conduct idealized experiments for investigating satellite data assimilation. The numerical model implementation is verified against an analytical solution for stationary waves in a rotating fluid, based on Shrira’s methodology for the isopycnal case. Recovery of the equivalent isopycnal model is also verified, both analytically and numerically. With convection and precipitation added, we show how complex model dynamics can be achieved exploiting rotation and relaxation to a meridional jet in a periodic domain. This solution represents a useful reference simulation or “truth” in conducting future (satellite) data-assimilation experiments, with additional atmospheric conditions and data. A formal analytical derivation of the isentropic 1½-layer model from an isentropic 2-layer model without convection and precipitation is shown in a companion paper (Part II).


Water ◽  
2021 ◽  
Vol 13 (24) ◽  
pp. 3633
Author(s):  
Reed M. Maxwell ◽  
Laura E. Condon ◽  
Peter Melchior

While machine learning approaches are rapidly being applied to hydrologic problems, physics-informed approaches are still relatively rare. Many successful deep-learning applications have focused on point estimates of streamflow trained on stream gauge observations over time. While these approaches show promise for some applications, there is a need for distributed approaches that can produce accurate two-dimensional results of model states, such as ponded water depth. Here, we demonstrate a 2D emulator of the Tilted V catchment benchmark problem with solutions provided by the integrated hydrology model ParFlow. This emulator model can use 2D Convolution Neural Network (CNN), 3D CNN, and U-Net machine learning architectures and produces time-dependent spatial maps of ponded water depth from which hydrographs and other hydrologic quantities of interest may be derived. A comparison of different deep learning architectures and hyperparameters is presented with particular focus on approaches such as 3D CNN (that have a time-dependent learning component) and 2D CNN and U-Net approaches (that use only the current model state to predict the next state in time). In addition to testing model performance, we also use a simplified simulation based inference approach to evaluate the ability to calibrate the emulator to randomly selected simulations and the match between ML calibrated input parameters and underlying physics-based simulation.


2021 ◽  
Vol 90 (1) ◽  
Author(s):  
E. Guerrero Fernández ◽  
M. J. Castro Díaz ◽  
M. Dumbser ◽  
T. Morales de Luna

AbstractIn this work, we present a novel numerical discretization of a variable pressure multilayer shallow water model. The model can be written as a hyperbolic PDE system and allows the simulation of density driven gravity currents in a shallow water framework. The proposed discretization consists in an unlimited arbitrary high order accurate (ADER) Discontinuous Galerkin (DG) method, which is then limited with the MOOD paradigm using an a posteriori subcell finite volume limiter. The resulting numerical scheme is arbitrary high order accurate in space and time for smooth solutions and does not destroy the natural subcell resolution inherent in the DG methods in the presence of strong gradients or discontinuities. A numerical strategy to preserve non-trivial stationary solutions is also discussed. The final method is very accurate in smooth regions even using coarse or very coarse meshes, as shown in the numerical simulations presented here. Finally, a comparison with a laboratory test, where empirical data are available, is also performed.


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