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Tunnel excavation is a three-dimensional (3D) problem. However, despite recent advances in computing resources, 3D models are still computationally inefficient and two-dimensional (2D) simulations are therefore often used. Modelling the tunnelling process in a 2D plane strain analysis requires a specific approach that allows a 3D tunnelling effect to be taken into consideration. As far as the urban tunnels are concerned, most cases reported in the literature have focused on estimating the applicability of these equivalent approaches that are based on the evaluation of the settlement that develops on the ground surface, without considering the influence of segment joints. The main objective of this study was to provide a 2D numerical investigation to highlight the influence of two equivalent approaches, that is, the convergence-confinement method (CCM) and the volume loss method (VLM), on the behaviour of a tunnel built in an urban area, in terms of not only the surface settlement but also the structural lining forces, taking into account the effect of segment joints. A technique that can be used to simulate the tunnel wall displacement process, based on the principles of the VLM, has been developed using the FLAC 3D finite difference program (Itasca in FLAC fast Lagrangian analysis of continua, version 4.0; User’s manual, http.itascacg.com , 2009 ). A comparison with 3D numerical results has been introduced to estimate the precision of these 2D equivalent approaches. The results have shown a significant influence of the tunnel boundary deconfinement technique and segment joints on the tunnel lining behaviour and surface settlements. The structural forces obtained by means of the CCM are often smaller than those determined with the VLM for the same surface settlement. Generally, the structural lining forces determined by the CCM are in better agreement with the 3D numerical results than the ones obtained with the VLM. However, in order to obtain an accurate estimation of the structural forces, the impact of the construction loads during tunnelling should be taken into account.

Many applications in river research and management rely upon two‐dimensional (2D) numerical models to characterize flow fields, assess habitat conditions, and evaluate channel stability. Predictions from such models are potentially highly uncertain due to the uncertainty associated with the topographic data provided as input. This study used a spatial stochastic simulation strategy to examine the effects of topographic uncertainty on flow modeling. Many, equally likely bed elevation realizations for a simple meander bend were generated and propagated through a typical 2D model to produce distributions of water‐surface elevation, depth, velocity, and boundary shear stress at each node of the model's computational grid. Ensemble summary statistics were used to characterize the uncertainty associated with these predictions and to examine the spatial structure of this uncertainty in relation to channel morphology. Simulations conditioned to different data configurations indicated that model predictions became increasingly uncertain as the spacing between surveyed cross sections increased. Model sensitivity to topographic uncertainty was greater for base flow conditions than for a higher, subbankfull flow (75% of bankfull discharge). The degree of sensitivity also varied spatially throughout the bend, with the greatest uncertainty occurring over the point bar where the flow field was influenced by topographic steering effects. Uncertain topography can therefore introduce significant uncertainty to analyses of habitat suitability and bed mobility based on flow model output. In the presence of such uncertainty, the results of these studies are most appropriately represented in probabilistic terms using distributions of model predictions derived from a series of topographic realizations.

Satellite‐based optical video sensors are poised as the next frontier in remote sensing. Satellite video offers the unique advantage of capturing the transient dynamics of floods with the potential to supply hitherto unavailable data for the assessment of hydraulic models. A prerequisite for the successful application of hydraulic models is their proper calibration and validation. In this investigation, we validate 2D flood model predictions using satellite video‐derived flood extents and velocities. Hydraulic simulations of a flood event with a 5‐year return period (discharge of 722 m3 s−1) were conducted using Hydrologic Engineering Center—River Analysis System 2D in the Darling River at Tilpa, Australia. To extract flood extents from satellite video of the studied flood event, we use a hybrid transformer‐encoder, convolutional neural network (CNN)‐decoder deep neural network. We evaluate the influence of test‐time augmentation (TTA)—the application of transformations on test satellite video image ensembles, during deep neural network inference. We employ Large Scale Particle Image Velocimetry (LSPIV) for non‐contact‐based river surface velocity estimation from sequential satellite video frames. When validating hydraulic model simulations using deep neural network segmented flood extents, critical success index peaked at 94% with an average relative improvement of 9.5% when TTA was implemented. We show that TTA offers significant value in deep neural network‐based image segmentation, compensating for aleatoric uncertainties. The correlations between model predictions and LSPIV velocities were reasonable and averaged 0.78. Overall, our investigation demonstrates the potential of optical space‐based video sensors for validating flood models and studying flood dynamics. Plain Language Summary Videos of the Earth surface recorded by satellites can enable us to observe and characterize dynamic moving features, such as floods, that would otherwise be very difficult or dangerous to investigate from the ground. Hydrologists often rely on using physics‐based computer models to simulate flood events, but require observational data to make sure these reflect reality accurately. We use artificial intelligence techniques to automatically detect flood extents from satellite video, and track surface features from frame to frame in order to measure how fast the water surface is flowing. Satellite video was collected during opportunistically clear skies in January 2022, along a 6.5 km length of the River Darling in Australia. The flood extent and flow velocities were used to improve numerical model predictions of the flood event. Our findings demonstrate the considerable promise of satellite video to complement existing flood mapping and modeling approaches, and to provide insight into the earth's hydrosphere, particularly in remote locations and during extreme conditions. Key Points Satellite video derived flood extents and velocities successfully validate 2D hydraulic model predictions Test‐time augmentation during deep learning inference improved flood extent delineation and enhanced 2D model validation metrics Incorporating characterization of discharge uncertainty into hydraulic model predictions resulted in more accurate model validation

A meaningful solution to an inversion problem should be composed of the preferred inversion model and its uncertainty and resolution estimates. The model uncertainty estimate describes an equivalent model domain in which each model generates responses which fit the observed data to within a threshold value. The model resolution matrix measures to what extent the unknown true solution maps into the preferred solution. However, most current geophysical electromagnetic (also gravity, magnetic and seismic) inversion studies only offer the preferred inversion model and ignore model uncertainty and resolution estimates, which makes the reliability of the preferred inversion model questionable. This may be caused by the fact that the computation and analysis of an inversion model depend on multiple factors, such as the misfit or objective function, the accuracy of the forward solvers, data coverage and noise, values of trade-off parameters, the initial model, the reference model and the model constraints. Depending on the particular method selected, large computational costs ensue. In this review, we first try to cover linearised model analysis tools such as the sensitivity matrix, the model resolution matrix and the model covariance matrix also providing a partially nonlinear description of the equivalent model domain based on pseudo-hyperellipsoids. Linearised model analysis tools can offer quantitative measures. In particular, the model resolution and covariance matrices measure how far the preferred inversion model is from the true model and how uncertainty in the measurements maps into model uncertainty. We also cover nonlinear model analysis tools including changes to the preferred inversion model (nonlinear sensitivity tests), modifications of the data set (using bootstrap re-sampling and generalised cross-validation), modifications of data uncertainty, variations of model constraints (including changes to the trade-off parameter, reference model and matrix regularisation operator), the edgehog method, most-squares inversion and global searching algorithms. These nonlinear model analysis tools try to explore larger parts of the model domain than linearised model analysis and, hence, may assemble a more comprehensive equivalent model domain. Then, to overcome the bottleneck of computational cost in model analysis, we present several practical algorithms to accelerate the computation. Here, we emphasise linearised model analysis, as efficient computation of nonlinear model uncertainty and resolution estimates is mainly determined by fast forward and inversion solvers. In the last part of our review, we present applications of model analysis to models computed from individual and joint inversions of electromagnetic data; we also describe optimal survey design and inversion grid design as important applications of model analysis. The currently available model uncertainty and resolution analyses are mainly for 1D and 2D problems due to the limitations in computational cost. With significant enhancements of computing power, 3D model analyses are expected to be increasingly used and to help analyse and establish confidence in 3D inversion models.

Multiple-point statistics (MPS) has shown promise in representing complicated subsurface structures. For a practical three-dimensional (3-D) application, however, one of the critical issues is the difficulty in obtaining a credible 3-D training image. However, bidimensional (2-D) training images are often available because established workflows exist to derive 2-D sections from scattered boreholes and/or other samples. In this work, we propose a locality-based MPS approach to reconstruct 3-D geological models on the basis of such 2-D cross sections (3DRCS), making 3-D training images unnecessary. Only several local training subsections closer to the central uninformed node are used in the MPS simulation. The main advantages of this partitioned search strategy are the high computational efficiency and a relaxation of the stationarity assumption. We embed this strategy into a standard MPS framework. Two probability aggregation formulas and their combinations are used to assemble the probability density functions (PDFs) from different subsections. Moreover, a novel strategy is adopted to capture more stable PDFs, where the distances between patterns and flexible neighborhoods are integrated on multiple grids. A series of sensitivity analyses demonstrate the stability of the proposed approach. Several hydrogeological 3-D application examples illustrate the applicability of the 3DRCS approach in reproducing complex geological features. The results, in comparison with previous MPS methods, show better performance in portraying anisotropy characteristics and in CPU cost.

This study assesses the effects of topography and land cover data resolutions on the estimates of flood extent, inundation depths, flow velocities, and arrival times of a two-dimensional (2D) hydrodynamic HEC-RAS model under differently sized mesh structures, with the example of the urban floodplain of Kilicozu Creek (Kirsehir, Turkey). To analyse these effects under a wide range of data conditions, seven different resolution digital surface models (DSMs) (from 0.0432 to 10 m/pixel) and Manning’s roughness layers (MRLs) (from 2 to 25 m/pixel) are produced for the subject floodplain by processing the high-quality DSM and orthophoto of the Kirsehir city centre. Additionally, seven different computational point spacings (CPSs) (from 2 m × 2 m to 25 m × 25 m) are tested to evaluate changes in the model outputs depending on the dimensions of mesh grids. Simulations are carried out for 19 different DSM, MRL, and CPS configurations under the 500-year flood scenario. The simulation performed for the most detailed model configuration is utilised as the base model simulation to compare the performances of other simulations. The model simulation configurated with the 2 m cell size DSM, 10 m cell size MRL, and 10 m × 10 m CPS shows comparable performance to the base model simulation with a small loss in the accuracy of the estimates, indicating that very-fine-resolution (less than 2 m) topography and high-resolution (less than 10 m) land cover data may not be indispensable to produce reliable simulations with 2D urban flood modelling using HEC-RAS software.

A novel two-dimensional mixed fracture–pore seepage model for fluid flow in fractured porous media is presented based on the computational framework of finite-discrete element method (FDEM). The model consists of a porous seepage model in triangular elements bonded by unbroken joint elements, as well as a fracture seepage model in broken joint elements. The principle for determining the fluid exchange coefficient of the unbroken joint element is provided to ensure numerical accuracy and efficiency. The mixed fracture–pore seepage model provides a simple but effective tool for solving fluid flow in fractured porous media. In this paper, examples of 1D and 2D seepage flow in porous media and porous media with a single fracture or multiple fractures are studied. The simulation results of the model match well with theoretical solutions or results obtained by commercial software, which verifies the correctness of the mixed fracture–pore seepage model. Furthermore, combining FDEM mechanical calculation and the mixed fracture–pore seepage model, a coupled hydromechanical model is built to simulate fluid-driven dynamic propagation of cracks in the porous media, as well as its influence on pore seepage and fracture seepage.

Analysis of the effect of the resolution and quality of terrain data, as the most sensitive input to 2D hydrodynamic modeling, has been one of the main research areas in flood modeling. However, previous studies have lacked discussion on (1) the limitations of the target area and the data source and (2) the underlying causes of simulation bias due to different resolutions. This study first discusses the performance of a high-resolution digital terrain model (DTM), acquired using a drone, for flood modeling in a mountainous riverine city; analyses the effect of the DTM resolution on the results using grid resolutions from 6 cm to 30 m; and then investigates the root causes of the effect based on topographic attributes. Xuanhan, a riverine city in the mountainous region of Southwestern China, was used as the study area. The Hydrologic Engineering Center's River Analysis System (HEC-RAS) 2D model was used for all simulations, and the results generated using a 6 cm DTM acquired by drone were used as a benchmark. The results indicate that flood characteristic simulations exhibit noticeable stepwise changes as the DTM resolution varies. DTMs with a resolution better than 10 m are more effective with respect to capturing the terrain's undulating features in the study area, which is crucial for accurately modeling the inundation area. However, to accurately capture topographic features related to elevation differences, the resolution should preferably be better than 5 m, as this directly affects the accuracy of flood depth simulation. The analysis of topographic attributes provides theoretical support for determining the optimal resolution to meet simulation requirements.

The local‐inertial approximations of the shallow water equations (SWEs) have been used for flood forecasting at larger spatial scales owing to the improved computational efficiency and similar accuracy compared to the full 2D SWEs. With the availability of high‐resolution elevation data, the complex terrain of urban areas with various small‐scale features is represented well. Even for a local‐inertial model, utilizing such high‐resolution elevation data in flood simulations of urbanized areas increases the computational cost. A subgrid‐based local‐inertial formulation that permits large numerical grid size for computations while preserving the within‐grid topography is proposed to circumvent this. The subgrid topography can be incorporated into the coarse numerical grid computations by estimating the hydraulic properties, namely, volume and face area, based on water surface elevation variations of the associated high‐resolution terrain. The pre‐stored hydraulic properties are then used to dynamically update the hydraulic variables during the execution of the local‐inertial model. Idealized and real‐world test cases were simulated to illustrate the advantages of the proposed model. The proposed subgrid model performs better in capturing flood depth around subgrid‐scale features such as streets, highways, minor canals, etc., than the simple grid‐averaged local‐inertial models of the same grid size. The proposed model is faster than the existing local‐inertial model (e.g., LISFLOOD‐FP) (∼21–34 times) and the full 2D model (e.g., HEC‐RAS 2D) (∼361–660 times) of similar accuracy in the slow‐rising flood applications. Thus, the subgrid local‐inertial model holds promise in real‐time flood inundation forecasting, resolving smaller urban features. Plain Language Summary Quick and accurate flood forecasting is crucial in highly populated urban areas with several small terrain features like roads, streets, highways, canals, etc. The simulation of flood depth and extent can be made faster by using simplified equations or dividing the domain into larger grids. The equations will be solved over each grid, generating flood depth and flow. However, opting for a large grid will not capture smaller within‐grid terrain elements. Therefore, this paper proposes a novel subgrid‐based local‐inertial model that uses simplified equations and operates at a large grid while still representing the within‐grid terrain. The subgrid‐inertial model simulates flooding around the smaller features of urban areas with less time than finer grid full 2D models. Meanwhile, the existing local‐inertial models operating at large grids often fail to resolve urban terrain features. Thus, using limited computing facilities, the proposed subgrid‐inertial model is highly suited for real‐time riverine flood forecasting in urbanized floodplains. Key Points A subgrid‐based local‐inertial formulation that makes computations at coarse grids while capturing the within‐grid terrain is proposed It is faster than a full 2D model and can resolve complex urban terrain (streets, canals, roads) where existing coarse grid models fail It improves mass flux estimation of coarse grids and holds promise in real‐time forecasting of slow‐rising urban floods

Floods greatly impact human settlements in flood risk areas, such as floodplains and coastal lowlands, following heavy rainfall. The Alto Guadalentin valley, an orogenic tectonic depression, experiences extreme flash floods and land subsidence due to groundwater withdrawal, rendering it one of Europe's fastest subsiding regions. In this study, we compared two 2D flood event models representing different land subsidence scenarios for 1992 and 2016. To determine the flooded area and water depth variations due to land subsidence, the Hydrologic Engineering Centre River Analysis System 2D (HEC-RAS 2D) model was used to simulate flood inundation by the Alto Guadalentin River and its tributaries. Synthetic aperture radar (SAR) satellite (ERS, ENVISAT, and Cosmo-SkyMED) images were employed, along with the interferometric SAR (InSAR) technique, to calculate the magnitude and spatial distribution of land subsidence. By analysing the accumulated subsidence distributions obtained from InSAR, the original topography of the valley in 1992 and 2016 was reconstructed. These digital surface models (DSMs) were then used to generate 2D hydraulic models, simulating flood scenarios in the unsteady mode. The results demonstrated significant changes in the water surface elevation over the 14-year period, with a 2.04 km2 increase in areas with water depths exceeding 0.7 m. These findings were utilized to create a flood risk map and assess the economic flood risk. The data highlight the crucial role of land subsidence in determining the inundation risk in the Alto Guadalentin valley, providing valuable insights for emergency management and civil protection against future potential flooding events.