Accelerated model-based T1, T2* and proton density mapping using a Bayesian approach with automatic hyperparameter estimation.

PURPOSE: To achieve automatic hyperparameter estimation for the model-based recovery of quantitative MR maps from undersampled data, we propose a Bayesian formulation that incorporates the signal model and sparse priors among multiple image contrasts. THEORY: We introduce a novel approximate message passing framework "AMP-PE" that enables the automatic and simultaneous recovery of hyperparameters and quantitative maps. METHODS: We employed the variable-flip-angle method to acquire multi-echo measurements using gradient echo sequence. We explored undersampling schemes to incorporate complementary sampling patterns across different flip angles and echo times. We further compared AMP-PE with conventional compressed sensing approaches such as the l 1 $$ {l}_1 $$ -norm minimization, PICS and other model-based approaches such as GraSP, MOBA. RESULTS: Compared to conventional compressed sensing approaches such as the l 1 $$ {l}_1 $$ -norm minimization and PICS, AMP-PE achieved superior reconstruction performance with lower errors in T 2 ∗ $$ {\mathrm{T}}_2^{\ast } $$ mapping and comparable performance in T 1 $$ {\mathrm{T}}_1 $$ and proton density mappings. When compared to other model-based approaches including GraSP and MOBA, AMP-PE exhibited greater robustness and outperformed GraSP in reconstruction error. AMP-PE offers faster speed than MOBA. AMP-PE performed better than MOBA at higher sampling rates and worse than MOBA at a lower sampling rate. Notably, AMP-PE eliminates the need for hyperparameter tuning, which is a requisite for all the other approaches. CONCLUSION: AMP-PE offers the benefits of model-based recovery with the additional key advantage of automatic hyperparameter estimation. It works adeptly in situations where ground-truth is difficult to obtain and in clinical environments where it is desirable to automatically adapt hyperparameters to individual protocol, scanner and patient.

Characterizing heterogeneous forest structure in ponderosa pine forests via UAS-derived structure from motion.

Increasingly, dry conifer forest restoration has focused on reestablishing horizontal and vertical complexity and ecological functions associated with frequent, low-intensity fires that characterize these systems. However, most forest inventory approaches lack the resolution, extent, or spatial explicitness for describing tree-level spatial aggregation and openings that were characteristic of historical forests. Uncrewed aerial system (UAS) structure from motion (SfM) remote sensing has potential for creating spatially explicit forest inventory data. This study evaluates the accuracy of SfM-estimated tree, clump, and stand structural attributes across 11 ponderosa pine-dominated stands treated with four different silvicultural prescriptions. Specifically, UAS-estimated tree height and diameter-at-breast-height (DBH) and stand-level canopy cover, density, and metrics of individual trees, tree clumps, and canopy openings were compared to forest survey data. Overall, tree detection success was high in all stands (F-scores of 0.64 to 0.89), with average F-scores > 0.81 for all size classes except understory trees (< 5.0 m tall). We observed average height and DBH errors of 0.34 m and - 0.04 cm, respectively. The UAS stand density was overestimated by 53 trees ha-1 (27.9%) on average, with most errors associated with understory trees. Focusing on trees > 5.0 m tall, reduced error to an underestimation of 10 trees ha-1 (5.7%). Mean absolute errors of bole basal area, bole quadratic mean diameter, and canopy cover were 11.4%, 16.6%, and 13.8%, respectively. While no differences were found between stem-mapped and UAS-derived metrics of individual trees, clumps of trees, canopy openings, and inter-clump tree characteristics, the UAS method overestimated crown area in two of the five comparisons. Results indicate that in ponderosa pine forests, UAS can reliably describe large- and small-grained forest structures to effectively inform spatially explicit management objectives.

Inversion recovery and saturation recovery pulmonary vein MR angiography using an image based navigator fluoro trigger and variable-density 3D cartesian sampling with spiral-like order.

Contrast enhanced pulmonary vein magnetic resonance angiography (PV CE-MRA) has value in atrial ablation pre-procedural planning. We aimed to provide high fidelity, ECG gated PV CE-MRA accelerated by variable density Cartesian sampling (VD-CASPR) with image navigator (iNAV) respiratory motion correction acquired in under 4 min. We describe its use in part during the global iodinated contrast shortage. VD-CASPR/iNAV framework was applied to ECG-gated inversion and saturation recovery gradient recalled echo PV CE-MRA in 65 patients (66 exams) using .15 mmol/kg Gadobutrol. Image quality was assessed by three physicians, and anatomical segmentation quality by two technologists. Left atrial SNR and left atrial/myocardial CNR were measured. 12 patients had CTA within 6 months of MRA. Two readers assessed PV ostial measurements versus CTA for intermodality/interobserver agreement. Inter-rater/intermodality reliability, reproducibility of ostial measurements, SNR/CNR, image, and anatomical segmentation quality was compared. The mean acquisition time was 3.58 ± 0.60 min. Of 35 PV pre-ablation datasets (34 patients), mean anatomical segmentation quality score was 3.66 ± 0.54 and 3.63 ± 0.55 as rated by technologists 1 and 2, respectively (p = 0.7113). Good/excellent anatomical segmentation quality (grade 3/4) was seen in 97% of exams. Each rated one exam as moderate quality (grade 2). 95% received a majority image quality score of good/excellent by three physicians. Ostial PV measurements correlated moderate to excellently with CTA (ICCs range 0.52-0.86). No difference in SNR was observed between IR and SR. High quality PV CE-MRA is possible in under 4 min using iNAV bolus timing/motion correction and VD-CASPR.

Prospectively accelerated dynamic speech magnetic resonance imaging at 3 T using a self-navigated spiral-based manifold regularized scheme.

This work develops and evaluates a self-navigated variable density spiral (VDS)-based manifold regularization scheme to prospectively improve dynamic speech magnetic resonance imaging (MRI) at 3 T. Short readout duration spirals (1.3-ms long) were used to minimize sensitivity to off-resonance. A custom 16-channel speech coil was used for improved parallel imaging of vocal tract structures. The manifold model leveraged similarities between frames sharing similar vocal tract postures without explicit motion binning. The self-navigating capability of VDS was leveraged to learn the Laplacian structure of the manifold. Reconstruction was posed as a sensitivity-encoding-based nonlocal soft-weighted temporal regularization scheme. Our approach was compared with view-sharing, low-rank, temporal finite difference, extra dimension-based sparsity reconstruction constraints. Undersampling experiments were conducted on five volunteers performing repetitive and arbitrary speaking tasks at different speaking rates. Quantitative evaluation in terms of mean square error over moving edges was performed in a retrospective undersampling experiment on one volunteer. For prospective undersampling, blinded image quality evaluation in the categories of alias artifacts, spatial blurring, and temporal blurring was performed by three experts in voice research. Region of interest analysis at articulator boundaries was performed in both experiments to assess articulatory motion. Improved performance with manifold reconstruction constraints was observed over existing constraints. With prospective undersampling, a spatial resolution of 2.4 × 2.4 mm2/pixel and a temporal resolution of 17.4 ms/frame for single-slice imaging, and 52.2 ms/frame for concurrent three-slice imaging, were achieved. We demonstrated implicit motion binning by analyzing the mechanics of the Laplacian matrix. Manifold regularization demonstrated superior image quality scores in reducing spatial and temporal blurring compared with all other reconstruction constraints. While it exhibited faint (nonsignificant) alias artifacts that were similar to temporal finite difference, it provided statistically significant improvements compared with the other constraints. In conclusion, the self-navigated manifold regularized scheme enabled robust high spatiotemporal resolution dynamic speech MRI at 3 T.

Numerical simulation of variable density and magnetohydrodynamics effects on heat generating and dissipating Williamson Sakiadis flow in a porous space: Impact of solar radiation and Joule heating.

This study is confined to the numerical evaluation of variable density and magnetohydrodynamics influence on Williamson Sakiadis flow in a porous space. In this study, Joule heating, dissipation, heat generation effect on optically dense gray fluid is encountered. The inclined moving surface as flow geometry is considered to induce the fluid flow. A proposed phenomenon is given a mathematical structure in partial differential equations form. These partial differential equations are then made dimensionless using dimensionless variables. The obtained dimensionless model in partial differential equations is then changed to ordinary differential equations via stream function formulation. A set of transformed equations has been solved with bvp4c solver. The numerical fallout of velocity field, temperature field, skin friction, and heat transfer rate are illustrated in graphs and tables with flow parametric variations. Conclusion is drawn that mounting values of density variation parameter confirm the reduction in velocity field and augmentation in temperature of the fluid. When Williamson fluid parameter enhances, both fluid velocity and temperature are rising correspondingly. Growing magnitudes of the magnetic number, radiation parameter, heat generation, and Eckert number rise the temperature of the fluid. A rise in a porous medium parameter weakens the fluid velocity. Skin friction is reducing as radiation parameter and density variation parameter are increased. The present solutions are compared to those that have already been published in order to validate the current model. The comparison leads to the conclusion that the two outcomes are in excellent agreement, endorsing the veracity of the current answers.

Topology Optimization of Turbulent Flow Cooling Structures Based on the k-ε Model.

Topology optimization (TO) is an effective approach to designing novel and efficient heat transfer devices. However, the TO of conjugate heat transfer has been essentially limited to laminar flow conditions only. The present study proposes a framework for TO involving turbulent conjugate heat transfer based on the variable density method. Different from the commonly used and oversimplified Darcy model, this approach is based on the more accurate and widely accepted k-ε model to optimize turbulent flow channels. We add penalty terms to the Navier-Stokes equation, turbulent kinetic energy equation, and turbulent energy dissipation equation, and use interpolation models for the thermal properties of materials. A multi-objective optimization function, aiming to minimize the pressure drop and the average temperature, is set up to balance the thermal and hydraulic performance. A case study is conducted to compare various optimization methods in the turbulent regime, and the results show that the present method has substantially higher optimization effectiveness while remaining computationally inexpensive.

Highly accelerated dynamic acquisition of 3D grid-tagged hyperpolarized-gas lung images using compressed sensing.

PURPOSE: To develop and test compressed sensing-based multiframe 3D MRI of grid-tagged hyperpolarized gas in the lung. THEORY AND METHODS: Applying grid-tagging RF pulses to inhaled hyperpolarized gas results in images in which signal intensity is predictably and sparsely distributed. In the present work, this phenomenon was used to produce a sampling pattern in which k-space is undersampled by a factor of approximately seven, yet regions of high k-space energy remain densely sampled. Three healthy subjects received multiframe 3D 3 He tagging MRI using this undersampling method. Images were collected during a single exhalation at eight timepoints spanning the breathing cycle from end-of-inhalation to end-of-exhalation. Grid-tagged images were used to generate 3D displacement maps of the lung during exhalation, and time-resolved maps of principal strains and fractional volume change were generated from these displacement maps using finite-element analysis. RESULTS: Tags remained clearly resolvable for 4-6 timepoints (5-8 s) in each subject. Displacement maps revealed noteworthy temporal and spatial nonlinearities in lung motion during exhalation. Compressive normal strains occurred along all three principal directions but were primarily oriented in the head-foot direction. Fractional volume changes displayed clear bilateral symmetry, but with the lower lobes displaying slightly higher change than the upper lobes in 2 of the 3 subjects. CONCLUSION: We developed a compressed sensing-based method for multiframe 3D MRI of grid-tagged hyperpolarized gas in the lung during exhalation. This method successfully overcomes previous challenges for 3D dynamic grid-tagging, allowing time-resolved biomechanical readouts of lung function to be generated.

Kz-accelerated variable-density stack-of-stars MRI.

This work aimed to develop a modified stack-of-stars golden-angle radial sampling scheme with variable-density acceleration along the slice (kz) dimension (referred to as VD-stack-of-stars) and to test this new sampling trajectory with multi-coil compressed sensing reconstruction for rapid motion-robust 3D liver MRI. VD-stack-of-stars sampling implements additional variable-density undersampling along the kz dimension, so that slice resolution (or volumetric coverage) can be increased without prolonging scan time. The new sampling trajectory (with increased slice resolution) was compared with standard stack-of-stars sampling with fully sampled kz (with standard slice resolution) in both non-contrast-enhanced free-breathing liver MRI and dynamic contrast-enhanced MRI (DCE-MRI) of the liver in volunteers. For both sampling trajectories, respiratory motion was extracted from the acquired radial data, and images were reconstructed using motion-compensated (respiratory-resolved or respiratory-weighted) dynamic radial compressed sensing reconstruction techniques. Qualitative image quality assessment (visual assessment by experienced radiologists) and quantitative analysis (as a metric of image sharpness) were performed to compare images acquired using the new and standard stack-of-stars sampling trajectories. Compared to standard stack-of-stars sampling, both non-contrast-enhanced and DCE liver MR images acquired with VD-stack-of-stars sampling presented improved overall image quality, sharper liver edges and increased hepatic vessel clarity in all image planes. The results have suggested that the proposed VD-stack-of-stars sampling scheme can achieve improved performance (increased slice resolution or volumetric coverage with better image quality) over standard stack-of-stars sampling in free-breathing DCE-MRI without increasing scan time. The reformatted coronal and sagittal images with better slice resolution may provide added clinical value.

Numerical modeling investigations of colloid facilitated chromium migration considering variable-density flow during the coastal groundwater table fluctuation.

Fluctuation of the groundwater table in the coastal zone influences the migration of colloids in vadose zone, which can further carry contaminants to transport. To capture the variable-density water flow and the migration processes, this study developed a colloid-facilitated migration model by adjusting the adsorption coefficient and considering the relationship between colloid and salinity based on the experimental observations. This model was further applied to explore the effects of freshwater and seawater fluctuations on the migration and transformation of colloids and Cr in coastal vadose zones. The greater the hydraulic conductivity of the saturated aquifer was, the more Cr were discharged into the ocean by submarine groundwater discharge. Furthermore, the increase in the freshwater fluctuation amplitude expanded the pollution ranges of colloidal Cr and dissolved Cr. The rise of the seawater fluctuation amplitude had a more obvious reduction effect on the total solid retained Cr in the contaminant source, compared with that of the freshwater fluctuation. As the seawater fluctuation amplitude increased from 0.1 m to 0.8 m, the ratio of total solid retained Cr reduction in the contaminant source to the initial value increased from 1.8 % to 7.8 %. The results obtained from this study deepens our understanding of how colloids and contaminants migrate across a coastal area from vadose zone induced by the groundwater table fluctuation.

Tidal fluctuations relieve coastal seawater intrusion caused by groundwater pumping.

Coastal aquifers are vulnerable to seawater intrusion and salinization due to groundwater pumping. Most research on salinization vulnerability and pumping rate optimization considers constant seaside boundary. However, tidal fluctuations may propagate through aquifers and affect pumping-induced seawater intrusion. We numerically tested the combined effects of tidal fluctuations and groundwater pumping on the variable-density groundwater flow and salt transport in aquifers with pumping wells close to the coast. The simulations showed that tidal fluctuations relieved seawater intrusion due to groundwater extraction. Stronger tidal fluctuation created larger upper saline plume which inhibited the seawater intrusion in the lower aquifer. Compared with those without tides, the tidal fluctuations with a tidal amplitude of 1 m could increase maximum pumping rate by 35.2 % and 28.7 % in flux- and head-controlled systems, respectively. These results suggest that combined impacts of tides and pumping should be considered in assessing seawater intrusion and designing more sophisticated pumping optimization.

Changes in the salt concentration distribution in surface water (seawater) due to seawater recirculation in a porous medium under tidal fluctuations.

Many studies have used numerical simulations and experiments to simulate saltwater intrusion in a nearshore aquifer. Thus, it is known that seawater recirculation occurs in a porous medium just below a sloping beach, and a saltwater wedge occurs in the medium below where the slope intersects the water level at low tide. This study investigated the salt distribution in the surface water when subterranean recirculation of seawater is occurring and there is a saltwater wedge in an underlying porous medium, along with the relationships between the seawater recirculation and the tidal amplitude and beach gradient. The salt distribution in a subterranean aquifer and in surface seawater where the shore sloped gently seaward with a constant slope of 1/10 or 1/5 under tidal amplitudes of 0.5, 1.0, or 2.0 m was numerically simulated by the ASGMF method, which couples water pressure and water flow in a porous medium with those in the overlying surface water and can simulate variable-density flows and the salt concentration distribution in both the porous medium and the surface water. The results showed that the recirculation of seawater depended on the tidal amplitude, being greater when the amplitude exceeded 1.0 m, but that it was unlikely to occur when the beach gradient was steep. Thus, the aspect ratio (width to depth) of the seawater recirculation decreased as the tidal amplitude increased above 1.0 m. Furthermore, the simulated surface water level was often lower than the tidal water level; thus, the surface water level was not consistent with the tidal water level imposed at the right boundary of the simulation domain but varied slightly under the influence of water flow in the surface water and gas flow in the atmosphere. The salt concentration in the surface water was not always the same as the seawater salt concentration because a thin freshwater layer and a brackish water layer of mixed freshwater and saltwater overlay the seawater.

Estimating the self-thinning boundary line for oak mixed forests in central China by using stochastic frontier analysis and a proposed variable density model.

A suitable self-thinning model is fundamental to effective density control and management. Using data from 265 plot measurements in oak mixed forests in central China, we demonstrated how to estimate a suitable self-thinning line for oak mixed forests from three aspects, i.e., self-thinning models (Reineke's model and the variable density model), statistical methods (quantile regression and stochastic frontier analysis), and the variables affecting stands (topography and stand structure factors). The proposed variable density model, which is based on the quadratic mean diameter and dominant height, exhibited a better goodness of fit and biological relevance than Reineke's model for modeling the self-thinning line for mixed oak forests. In addition, the normal-truncated normal stochastic frontier model was superior to quantile regression for modeling the self-thinning line. The altitude, Simpson index, and dominant height-diameter ratio ( H d /D) also had significant effects on the density of mixed forests. Overall, a variable density self-thinning model may be constructed using stochastic frontier analysis for oak mixed forests while considering the effects of site quality and stand structure on density. The findings may contribute to a more accurate density management map for mixed forests.

Trading off spatio-temporal properties in 3D high-speed fMRI using interleaved stack-of-spirals trajectories.

PURPOSE: Highly undersampled acquisitions have been proposed to push the limits of temporal resolution in functional MRI. This contribution is aimed at identifying parameter sets that let the user trade-off between ultra-high temporal resolution and spatial signal quality by varying the sampling densities. The proposed method maintains the synergies of a temporal resolution that enables direct filtering of physiological artifacts for highest statistical power, and 3D read-outs with optimal use of encoding capabilities of multi-coil arrays for efficient sampling and high signal-to-noise ratio (SNR). METHODS: One- to four-shot interleaved spherical stack-of-spiral trajectories with repetition times from 96 to 352 ms at a nominal resolution of 3 mm using different sampling densities were compared for image quality and temporal SNR (tSNR). The one- and three-shot trajectories were employed in a resting state study for functional characterization. RESULTS: Compared to a previously described single-shot trajectory, denser sampled trajectories of the same type are shown to be less prone to blurring and off-resonance vulnerability that appear in addition to the variable density artifacts of the point spread function. While the multi-shot trajectories lead to a decrease in tSNR efficiency, the high SNR due to the 3D read-out, combined with notable increases in image quality, leads to superior overall results of the three-shot interleaved stack of spirals. A resting state analysis of 15 subjects shows significantly improved functional sensitivity in areas of high off-resonance gradients. CONCLUSION: Mild variable-density sampling leads to excellent tSNR behavior and no increased off-resonance vulnerability, and is suggested unless maximum temporal resolution is sought.

Improved 3D real-time MRI of speech production.

PURPOSE: To provide 3D real-time MRI of speech production with improved spatio-temporal sharpness using randomized, variable-density, stack-of-spiral sampling combined with a 3D spatio-temporally constrained reconstruction. METHODS: We evaluated five candidate (k, t) sampling strategies using a previously proposed gradient-echo stack-of-spiral sequence and a 3D constrained reconstruction with spatial and temporal penalties. Regularization parameters were chosen by expert readers based on qualitative assessment. We experimentally determined the effect of spiral angle increment and kz temporal order. The strategy yielding highest image quality was chosen as the proposed method. We evaluated the proposed and original 3D real-time MRI methods in 2 healthy subjects performing speech production tasks that invoke rapid movements of articulators seen in multiple planes, using interleaved 2D real-time MRI as the reference. We quantitatively evaluated tongue boundary sharpness in three locations at two speech rates. RESULTS: The proposed data-sampling scheme uses a golden-angle spiral increment in the kx -ky plane and variable-density, randomized encoding along kz . It provided a statistically significant improvement in tongue boundary sharpness score (P < .001) in the blade, body, and root of the tongue during normal and 1.5-times speeded speech. Qualitative improvements were substantial during natural speech tasks of alternating high, low tongue postures during vowels. The proposed method was also able to capture complex tongue shapes during fast alveolar consonant segments. Furthermore, the proposed scheme allows flexible retrospective selection of temporal resolution. CONCLUSION: We have demonstrated improved 3D real-time MRI of speech production using randomized, variable-density, stack-of-spiral sampling with a 3D spatio-temporally constrained reconstruction.

Design Optimization of Lattice Structures under Compression: Study of Unit Cell Types and Cell Arrangements.

Additive manufacturing enables innovative structural design for industrial applications, which allows the fabrication of lattice structures with enhanced mechanical properties, including a high strength-to-relative-density ratio. However, to commercialize lattice structures, it is necessary to define the designability of lattice geometries and characterize the associated mechanical responses, including the compressive strength. The objective of this study was to provide an optimized design process for lattice structures and develop a lattice structure characterization database that can be used to differentiate unit cell topologies and guide the unit cell selection for compression-dominated structures. Linear static finite element analysis (FEA), nonlinear FEA, and experimental tests were performed on 11 types of unit cell-based lattice structures with dimensions of 20 mm × 20 mm × 20 mm. Consequently, under the same relative density conditions, simple cubic, octahedron, truncated cube, and truncated octahedron-based lattice structures with a 3 × 3 × 3 array pattern showed the best axial compressive strength properties. Correlations among the unit cell types, lattice structure topologies, relative densities, unit cell array patterns, and mechanical properties were identified, indicating their influence in describing and predicting the behaviors of lattice structures.

Design and topology optimization of air conditioning suspension bracket for metro.

During the operation of subway vehicles, the vibration of air conditioning units is mainly transmitted to the vehicle body through the suspension support, which seriously affects the stability and comfort of the vehicle during operation. Therefore, the design and optimization of the suspension support of air conditioning units has become a hot topic in the research of the dynamic characteristics of subway vehicles. In this paper, the rigid and flexible coupling dynamic model of metro is firstly calculated to simulate the stress of the suspension point of air conditioning of the vehicle body when the vehicle is running. The initial structure design of the suspension support is carried out, and the stress of the air conditioning suspension point is taken as the load input to analyze the stiffness and strength of the initial structure of the suspension support. Then, the fatigue life is taken as the topology constraint, and the variable density method (SIMP) is used to optimize the topology of the suspension bracket. Finally, the optimized suspension support is validated. The results show that after topological optimization, the maximum displacement and maximum stress of the suspension support under vertical, horizontal, and vertical loads are reduced by 80%, 93%, and 99%, respectively, compared with the original structure model, and the maximum stress under vertical loads is reduced by 50%.

Modeling variable density flow in subsurface and surface water in the vicinity of the boundary between a surface water-atmosphere system and the subsurface.

When seawater intrudes into a subterranean estuary, there is interaction between groundwater and surface water, and ocean tides and waves can influence the salt concentration distribution in subsurface of the estuary. However, numerical simulations of seawater intrusion into a subterranean estuary often neglect the atmosphere and surface water and simply specify hydrostatic pressure and a constant seawater salt concentration. This study examined the influence of fluid flow and pressure in a surface water-atmosphere system consisting of both atmosphere and surface water on the salt distribution in subsurface and in the surface water by a numerical simulation that couples fluid flows in the surface water-atmosphere system and groundwater. This study first confirmed the precision of the simulation method by comparing experimentally determined salt concentration distributions in silica beads unsaturated with water. This study then conducted an experiment in a two-dimensional tank filled with seawater and glass beads (mean diameter 0.2 mm) and carried out two simulations of this tank experiment: one of a limited system consisting of the porous medium and surface water only, and the other of a full system, consisting of the porous medium, surface water, and atmosphere. Darcy's law has frequently been applied in limited system simulations by assigning extremely high permeability to the surface water. This study therefore also conducted a third, simpler numerical simulation of the limited system that used only Darcy's law. The salt concentration distribution obtained by the full system simulation was closer to the experimental distribution than that obtained by the limited system simulation. This result implies that fluid flow and pressure in both the atmosphere and surface water influence water flow and water pressure in the porous medium. Furthermore, the third simulation using Darcy's law only could not precisely reproduce flow in the surface water. Therefore, when variable-density flow in surface water and a shallow subsurface are numerically simulated, the simulation system needs to include atmosphere and surface water to take account of the influence of fluid flow and fluid pressure in both the atmosphere and surface water on the fluid flow and transport of salt in a shallow subsurface.

A steady stratified purely azimuthal flow representing the Antarctic Circumpolar Current.

We construct an explicit steady stratified purely azimuthal flow for the governing equations of geophysical fluid dynamics. These equations are considered in a setting that applies to the Antarctic Circumpolar Current, accounting for eddy viscosity and forcing terms.

Uncertainty analysis for precipitation and sea-level rise of a variable-density groundwater simulation model based on surrogate models.

Effective coastal aquifer management typically relies on numerical models to analyze the seawater intrusion (SI) process. Before using groundwater simulation models to predict the extent of SI in the future, preparing input data is an extremely necessary and important step. For precipitation and sea-level rise (SLR), which are two of the most influential factors for SI, it is difficult to precisely forecast their variations. Current studies of using numerical models to predict future SI often overlook the uncertainty of these two factors. This can result in compromised predictions of SI. In this study, a three-dimensional variable-density groundwater simulation model was established for a coastal area in Longkou, China. Then, the Monte Carlo method was applied to perform uncertainty analysis for the input data of precipitation and SLR of the SI model. In order to reduce the huge computational load brought by repeated invocation of the SI model during the process of Monte Carlo simulation, a surrogate model based on a multi-gene genetic programming (MGGP) method was developed to replace the SI simulation model for calculation. A comparison between the MGGP surrogate model and the Kriging surrogate model was carried out, and the results show that the MGGP surrogate model has a distinct advantage over the Kriging surrogate model in approximating the excitation-response relationship of the variable-density groundwater simulation model. Through statistical analysis of Monte Carlo simulation results, an object and reasonable risk assessment of SI for the study area was obtained. This study suggests that it is essential to take the uncertainty of precipitation and SLR into account when modeling and predicting the extent of SI.

Development of a robust ensemble meta-model for prediction of salinity time series under uncertainty (case study: Talar aquifer).

The aim of this study is to develop an accurate and reliable numerical model of the coastal Talar aquifer threatened by seawater intrusion by developing an ensemble meta-model (MM). In comparison with previous methodologies, the developed model has the following superiority: (1) Its performance is enhanced by developing ensemble MMs using four different meta-modelling frameworks, i.e., artificial neural network, support vector regression, radial basis function, genetic programing and evolutionary polynomial regression; (2) The accuracy of different MMs based on 16 integration of four meta-modeling frameworks is compared; and (3) the effect of aquifer heterogeneity on the MM. The performance of the proposed MM was assessed using an illustrative case aquifer subject to seawater intrusion. The obtained results indicate that the ensemble MM that combines all four meta-modeling frameworks outperformed the GP and ANN models, with a correlation coefficient of 0.98. Moreover, the proposed MM using nonlinear-learning ensemble of SVR-EPR achieves a better and robust forecasting performance. Therefore, it can be considered as an accurate and robust simulator to predict salinity levels under different abstraction patterns in variable density flow. The result of uncertainty analyses reveals that robustness value and pumping rate are inversely proportional and scenarios with a robustness measure of about 12% are more reliable.