arXiv subjects

Mohammad Afzal Shadab

Publications and source records attributed to Mohammad Afzal Shadab.

7 recordsLinked to original sources

arXiv2026

HydroFirn: A numerical model for large-scale multidimensional firn hydrology

Observations show the multidimensional dynamics of meltwater and distribution of ice layers in the firn on the Greenland Ice Sheet. However, state-of-the-art large-scale models for firn hydrology are essentially one-dimensional, limiting their ability to explain observed datasets and failing to reduce uncertainty in surface mass balance and sea-level rise estimates. Here, we present a large-scale, multidimensional, multiphase, and thermomechanical model to simulate firn hydrology. The model is highly efficient due to a novel algorithm in which an extra equation for pressure is solved only in saturated regions. Furthermore, the model can apply spatially heterogeneous boundary conditions to the unsaturated-saturated domain and allows for the dynamic formation of fully impermeable ice layers. The numerical results show excellent comparisons against analytic solutions to one- and two-dimensional problems that involve coupled unsaturated-saturated flows, thermodynamics, and phase change. We further apply the model to investigate field data from southwest Greenland and find that lateral heterogeneities strongly influence the depth of melt percolation and ice layer formation. Improved understanding of these local, multidimensional processes will provide physics-based constraints on firn densification, reduce uncertainty in converting altimetric elevation change to mass change, and improve estimates of freshwater fluxes to the ocean under a warming climate.

physics.geo-ph↗

arXiv2026

A vertically integrated model with phase change for aquifers in cold firn

Surface meltwater from glaciers and ice sheets contributes significantly to sea-level rise, yet the processes governing its transport and retention within cold firn remain poorly constrained, particularly in multiple dimensions. Here we present a multidimensional, vertically integrated modeling framework for aquifers in cold firn that incorporates phase change and residual trapping of liquid water. This mathematical framework, together with its numerical implementation, extends terrestrial groundwater models to describe aquifers expanding within otherwise cold firn, highlighting the analogous physics governing both systems. We derive semi-analytical solutions for finite-volume aquifers and validate them against numerical simulations and higher-fidelity model results. These solutions elucidate key features of meltwater dynamics and provide benchmarks for firn hydrologic models. We further demonstrate the three-dimensional expansion of an aquifer in cold, heterogeneous firn. Both the semi-analytical and numerical results show that lateral aquifer propagation slows at lower initial firn temperatures due to porosity reduction and associated loss of liquid water from freezing. Overall, this framework provides new insights into the formation and expansion of firn aquifers in percolation zones and helps clarify how subsurface meltwater storage modulates meltwater fluxes, surface mass loss, and contributes to global sea-level rise.

physics.flu-dyn↗

arXiv2024

History and Habitability of the LP 890-9 Planetary System

We present numerous aspects of the evolution of the LP 890-9 (SPECULOOS-2/TOI-4306) planetary system, focusing on the likelihood that planet c can support life. We find that the host star reaches the main sequence in 1 Gyr and that planet c lies close to the inner boundary of the habitable zone. We find the magma ocean stage can last up to 50 Myr, remove 8 Earth-oceans of water, and leave up to 2000 bars of oxygen in the atmosphere. However, if the planet forms with a hydrogen envelope as small as 0.1 Earth-masses, no water will be lost during the star's pre-main sequence phase from thermal escape processes. We find that the planets are unlikely to be in a 3:1 mean motion resonance and that both planets tidally circularize within 0.5 Gyr when tidal dissipation is held constant. However, if tidal dissipation is a function of mantle temperature and rheology, then we find that planet c's orbit may require more than 7 Gyr to circularize, during which time tidal heating may reach hundreds of terawatts. We thus conclude that the habitability of planet c depends most strongly on the initial volatile content and internal properties, but no data yet preclude the viability of an active biosphere on the planet.

astro-ph.EP↗

arXiv2024

A hyperbolic-elliptic PDE model and conservative numerical method for gravity-dominated variably-saturated groundwater flow

Richards equation is often used to represent two-phase fluid flow in an unsaturated porous medium when one phase is much heavier and more viscous than the other. However, it cannot describe the fully saturated flow for some capillary functions without specialized treatment due to degeneracy in the capillary pressure term. Mathematically, gravity-dominated variably saturated flows are interesting because their governing partial differential equation switches from hyperbolic in the unsaturated region to elliptic in the saturated region. Moreover, the presence of wetting fronts introduces strong spatial gradients often leading to numerical instability. In this work, we develop a robust, multidimensional mathematical model and implement a well-known efficient and conservative numerical method for such variably saturated flow in the limit of negligible capillary forces. The elliptic problem in saturated regions is integrated efficiently into our framework by solving a reduced system corresponding only to the saturated cells using fixed head boundary conditions in the unsaturated cells. In summary, this coupled hyperbolic-elliptic PDE framework provides an efficient, physics-based extension of the hyperbolic Richards equation to simulate fully saturated regions. Finally, we provide a suite of easy-to-implement yet challenging benchmark test problems involving saturated flows in one and two dimensions. These simple problems, accompanied by their corresponding analytical solutions, can prove to be pivotal for the code verification, model validation (V&V) and performance comparison of simulators for variably saturated flow. Our numerical solutions show an excellent comparison with the analytical results for the proposed problems. The last test problem on two-dimensional infiltration in a stratified, heterogeneous soil shows the formation and evolution of multiple disconnected saturated regions.

physics.comp-ph↗

arXiv2024

A unified kinematic wave theory for melt infiltration into firn

Motivated by the refreezing of melt water in firn we revisit the one-dimensional percolation of liquid water and non-reactive gas in porous ice. We analyze the dynamics of infiltration in the absence of capillary forces and heat conduction to understand the coupling between advective heat and mass transport in firn. In this limit, we formulate a kinematic wave theory that results in a 2X2-system of hyperbolic partial differential equations (PDEs) corresponding to the conservation of composition and enthalpy. For simple initial conditions (Riemann problems) this system admits self-similar solutions that illuminate the structure of melting/refreezing fronts and analytical solutions are provided for 12 basic cases of physical relevance encountered in the literature. Further we develop an extended kinematic theory that encompasses the cases when the firn saturates completely to form a perched water table governed by elliptic PDE so that the model is no longer fully hyperbolic (local). These solutions provide benchmarks for numerical models of melt infiltration into firn. They also provide insight into important physical processes such as the formation of frozen fringes, the perching of meltwater on pre-existing low porosity layers and the conditions required for impermeable ice lens formation. Lastly, these analytic solutions can be utilized to improve and compare the performance of the firn hydrology, ice-sheet and Earth system models. Our analysis provides a theoretical framework to understand these important processes in firn which affect the partitioning between meltwater infiltration and surface runoff and therefore determine the surface mass loss from ice sheets and its contribution to sea level rise.

physics.flu-dyn↗

arXiv2021

Investigating Steady Unconfined Groundwater Flow using Physics Informed Neural Networks

A novel deep learning technique called Physics Informed Neural Networks (PINNs) is adapted to study steady groundwater flow in unconfined aquifers. This technique utilizes information from underlying physics represented in the form of partial differential equations (PDEs) alongside data obtained from physical observations. In this work, we consider the Dupuit-Boussinesq equation, which is based on the Dupuit-Forchheimer approximation, as well as a recent more complete model derived by Di Nucci (2018) as underlying models. We then train PINNs on data obtained from steady-state analytical solutions and laboratory based experiments. Using PINNs, we predict phreatic surface profiles given different input flow conditions and recover estimates for the hydraulic conductivity from the experimental observations. We show that PINNs can eliminate the inherent inability of the Dupuit-Boussinesq equation to predict flows with seepage faces. Moreover, the inclusion of physics information from the Di Nucci and Dupuit-Boussinesq models constrains the solution space and produces better predictions than solely the training data. PINNs based predictions are very robust and show little effect from added noise in the training data. Further, we compare the PINNs obtained using the two different flow models to examine the effects of higher order flow terms, which are neglected by the Dupuit Forchheimer approximation. We found a dimensionless parameter $Π$, which is the ratio of vertical to horizontal flow effects. For $Π\leq 0.1$, Dupuit-Boussinesq approximation is found to be applicable but not otherwise. Lastly, we discuss the effectiveness of using PINNs for examining groundwater flow.

physics.geo-ph↗

arXiv2018

Fifth order finite volume WENO in general orthogonally-curvilinear coordinates

High order reconstruction in the finite volume (FV) approach is achieved by a more fundamental form of the fifth order WENO reconstruction in the framework of orthogonally-curvilinear coordinates, for solving the hyperbolic conservation equations. The derivation employs a piecewise parabolic polynomial approximation to the zone averaged values to reconstruct the right, middle, and left interface values. The grid dependent linear weights of the WENO are recovered by inverting a Vandermode-like linear system of equations with spatially varying coefficients. A scheme for calculating the linear weights, optimal weights, and smoothness indicator on a regularly- and irregularly-spaced grid in orthogonally-curvilinear coordinates is proposed. A grid independent relation for evaluating the smoothness indicator is derived from the basic definition. Finally, the procedures for the source term integration and extension to multi-dimensions are proposed. Analytical values of the linear and optimal weights, and also the weights required for the source term integration and flux averaging, are provided for a regularly-spaced grid in Cartesian, cylindrical, and spherical coordinates. Conventional fifth order WENO reconstruction for the regularly-spaced grids in the Cartesian coordinates can be fully recovered in the case of limiting curvature. The fifth order finite volume WENO-C (orthogonally-curvilinear version of WENO) reconstruction scheme is tested for several 1D and 2D benchmark test cases involving smooth and discontinuous flows in cylindrical and spherical coordinates.

physics.comp-ph↗