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DOE OSTI2021

Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations

Advection-dispersion equations (ADEs) are commonly used to describe transport phenomena in porous media. Even though mature discretization-based numerical methods for ADEs exist, some challenges still remain, especially when it comes to solving advection-dominated forward ADEs and diffusion-dominated backward ADEs. The latter problem usually arises in the source identification context and leads to numerically unstable grid-based solutions that require a form of regularization or should be treated as an inverse problem that is computationally more expensive because it requires solving the forward problem multiple times. In this study, we propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled ADE and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward ADE problems, where its performance for various P\'{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1\% and outperforms some conventional discretization-based methods for $Pe$ larger that 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5\% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50\% in the considered cases) the accuracy of the PINN solution of the backward ADE.

He, Qizhi↗

DOE OSTI2026

Advected carbon younger than the sediment fuels microbial metabolism in a pumped deep aquifer

Ever deeper wells are drilled worldwide to pump potable groundwater. Recent studies argue that overpumping compresses clays and releases reactive dissolved organic carbon (DOC), which in turn drives a series of microbial reactions that affect groundwater potability including arsenic concentrations. Here, we use a novel method to measure the radiocarbon ages of microbial RNA to determine the source of reactive or metabolizable DOC and argue against the compression of clays as the sole source of carbon. We show that microbial RNA (5,230; 5,550; 6,250 yr; n = 3 wells), DOC (280-10,800 yr; n = 13), and methane (modern to 6,240 yr; n = 3), from an overpumped deep aquifer in Bangladesh are much younger than the overlying clay layers deposited during the Pleistocene over 12,000 years ago. Mass-balance indicates that at least half of the carbon incorporated into RNA has to come from reactive DOC or methane that is advected downward via vertical recharge. This metabolism of advected organic carbon could have implications for the quality of water pumped from deep aquifers.

Biological and medical sciences↗

DOE OSTI2022

Geological activity shapes the microbiome in deep-subsurface aquifers by advection

Subsurface environments host diverse microorganisms in fluid-filled fractures; however, little is known about how geological and hydrological processes shape the subterranean biosphere. Here, we sampled three flowing boreholes weekly for 10 mo in a 1478-m-deep fractured rock aquifer to study the role of fracture activity (defined as seismically or aseismically induced fracture aperture change) and advection on fluid-associated microbial community composition. We found that despite a largely stable deep-subsurface fluid microbiome, drastic community-level shifts occurred after events signifying physical changes in the permeable fracture network. The community-level shifts include the emergence of microbial families from undetected to over 50% relative abundance, as well as the replacement of the community in one borehole by the earlier community from a different borehole. Null-model analysis indicates that the observed spatial and temporal community turnover was primarily driven by stochastic processes (as opposed to deterministic processes). We, therefore, conclude that the observed community-level shifts resulted from the physical transport of distinct microbial communities from other fracture(s) that outpaced environmental selection. Given that geological activity is a major cause of fracture activity and that geological activity is ubiquitous across space and time on Earth, our findings suggest that advection induced by geological activity is a general mechanism shaping the microbial biogeography and diversity in deep-subsurface habitats across the globe.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Idealized Large-Eddy Simulations of Stratocumulus Advecting over Cold Water. Part I: Boundary Layer Decoupling

Abstract We explore the decoupling physics of a stratocumulus-topped boundary layer (STBL) moving over cooler water, a situation mimicking warm-air advection (WADV). We simulate an initially well-mixed STBL over a doubly periodic domain with the sea surface temperature decreasing linearly over time using the System for Atmospheric Modeling large-eddy model. Due to the surface cooling, the STBL becomes increasingly stably stratified, manifested as a near-surface temperature inversion topped by a well-mixed cloud-containing layer. Unlike the stably stratified STBL in cold-air advection (CADV) that is characterized by cumulus coupling, the stratocumulus deck in the WADV is unambiguously decoupled from the sea surface, manifested as weakly negative buoyancy flux throughout the subcloud layer. Without the influxes of buoyancy from the surface, the convective circulation in the well-mixed cloud-containing layer is driven by cloud-top radiative cooling. In such a regime, the downdrafts propel the circulation, in contrast to that in CADV regime for which the cumulus updrafts play a more determinant role. Such a contrast in convection regime explains the difference in many aspects of the STBLs including the entrainment rate, cloud homogeneity, vertical exchanges of heat and moisture, and lifetime of the stratocumulus deck, with the last being subject to a more thorough investigation in Part II. Finally, we investigate under what conditions a secondary stratus near the surface (or fog) can form in the WADV. We found that weaker subsidence favors the formation of fog whereas a more rapid surface cooling rate does not. Significant Statement The low-lying blanketlike clouds, called stratocumulus (Sc), reflect much incoming sunlight, substantially modulating Earth’s temperature. While much is known about how the Sc evolves when it moves over warmer water, few studies examine the opposite situation of Sc moving over colder water. We used a high-resolution numerical model to simulate such a case. When moving over cold water, the Sc becomes unambiguously decoupled from the water surface, distinctive from its warm counterpart in which the Sc interacts with the water surface via intermittent cauliflower-like clouds called cumulus clouds. Such decoupling influences many aspects of the Sc–sea surface system, which combine to alter the ability of the Sc to reflect sunlight, thereby influencing the climate. This work laid the foundation for future work that quantifies the contribution of such a decoupled Sc regime to Earth’s radiative budget and climate change.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Development of a forced advection sampling technique (FAST) for quantification of methane emissions from orphaned wells

Abstract. Orphaned wells, meaning unplugged and non-producing wells lacking responsible owners, pose a significant and undersampled environmental challenge due to their vast number and unknown associated emissions. We propose, develop and test an alternative method for estimating emissions from orphaned wells using a forced advection sampling technique (FAST) that can overcome many of the limitations in current methods (cost, accuracy, safety). In contrast to existing ambient Gaussian plume methods, our approach uses a fan-generated flow to force advection between the emission source and a point methane (CH4) sensor. The fan flow field is characterized using a colocated sonic anemometer to measure the 3D wind profile generated by the fan. Using time-series measurements of CH4 concentration and wind, a simple estimate of the CH4 emission rate of the source can be inferred. The method was calibrated using outdoor controlled-release experiments and then tested on four orphaned wells in Lufkin, TX, and Osage County, OK. Our results suggest that the FAST method can provide a low-cost, portable, fast and safe alternative to existing methods with reasonable estimates of orphaned well emissions over a range of leak rates below 40 g h−1 and within certain geometric and atmospheric constraints.

Dubey, Mohit L↗

NASA NTRS1975

Sasaki's variational optimization analysis of temperature and moisture advection in a severe storm environment

Temperature and moisture advection patterns of dry air intrusion were analyzed by a variational optimization method to relate mesoscale advection to a severe thunderstorm environment. The analysis results presented here were obtained from a case study, May 26, 1973, when a tornado squall line developed in Oklahoma in conjunction with a clearly delineated dry air intrusion. Observations from the synoptic upper air network were used for inputs of horizontal wind components, potential temperature, and mixing ratio at each 50 mb increment from 950 to 100 mb. An objective analysis was performed to assign values of the variables to grid points of a 15 x 14 horizontal grid with approximate 125 km grid spacing at each pressure level. After the analysis the data fields were smoothed using a variational formalism.

Mcfarland, M. J.↗

NASA NTRS1976

Numerical problems in the advection of pollutants

Prediction of pollutant transport involves solution of the advection equation numerically. Truncation errors arising from integrating the advection equation by using finite difference schemes are discussed. Numerical errors manifest themselves in artificial dissipation and dispersion of pollutants. Criteria for measuring the dissipation and dispersion are presented, and minimization of those errors is discussed. An alternative procedure by integration in the wavenumber space is examined. Examples illustrating quantitative discrepancy in actual forecasting are also shown.

Liu, C. Y.↗

NASA NTRS1979

Aerosol particles and the formation of advection fog

A study of numerical simulation of the effects of concentration, particle size, mass of nuclei, and chemical composition on the dynamics of warm fog formation, particularly the formation of advection fog, is presented. This formation is associated with the aerosol particle characteristics, and both macrophysical and microphysical processes are considered. In the macrophysical model, the evolution of wind components, water vapor content, liquid water content, and potential temperature under the influences of vertical turbulent diffusion, turbulent momentum, and turbulent energy transfers are taken into account. In the microphysical model, the supersaturation effect is incorporated with the surface tension and hygroscopic material solution. It is shown that the aerosol particles with the higher number density, larger size nuclei, the heavier nuclei mass, and the higher ratio of the Van't Hoff factor to the molecular weight favor the formation of the lower visibility advection fogs with stronger vertical energy transfer during the nucleation and condensation time period.

Hung, R. J.↗

NASA NTRS1981

Estimation and correction of advection effects with single and multiple, conventional and Doppler radars

The laws of fluid motion are invariant under a Gallilean transformation. For a perfect observing system, the data analysis should, therefore, also be invariant under a Gallilean transformation. This invariance is often not preserved in practical observing systems. In this connection, it is often advisable to perform mesoscale analysis in a frame moving with respect to the earth's surface. In the present investigation the velocity of such a frame is referred to as an advection velocity. The investigation is concerned with remaining problems regarding the Gallilean transformation. The establishment of a frame of reference for the achievement of maximum coherence is considered, taking into account the case of given nonsimultaneous observations of scalars or Cartesian vectors. It is found that advection speed can be estimated objectively if a scalar or Cartesian vector can be observed directly and if, in addition, the time and position of each observation is approximately known.

Gal-Chen, T.↗

NASA NTRS1984

Empirically derived second order schemes for the advection equations with minimum dissipation and dispersion errors

Two second-order advection schemes of the Lax-Wendroff type are empirically derived which have accuracy and phase characteristics similar to that of a third-order scheme. The new schemes are compared with other currently used methods, and are shown to have superior behavior in simulating the advection of localized disturbances. The schemes are derived for constant flow and generalized to two-dimensional non-uniform flow.

Takacs, L. L.↗

NASA NTRS1985

A two-step scheme for the advection equation with minimized dissipation and dispersion errors

A two-step advection scheme of the Lax-Wendroff type is derived which has accuracy and phase characteristics similar to that of a third-order scheme. The scheme is exactly third-order accurate in time and space for uniform flow. The new scheme is compared with other currently used methods, and is shown to simulate well the advection of localized disturbances with steep gradients. The scheme is derived for constant flow and generalized to two-dimensional nonuniform flow.

Takacs, L. L.↗

NASA NTRS1985

Effects of upstream-biased third-order space correction terms on multidimensional Crowley advection schemes

The impact of upstream-biased corrections for third-order spatial truncation error on the stability and phase error of the two-dimensional Crowley combined advective scheme with the cross-space term included is analyzed, putting primary emphasis on phase error reduction. The various versions of the Crowley scheme are formally defined, and their stability and phase error characteristics are intercompared using a linear Fourier component analysis patterned after Fromm (1968, 1969). The performances of the schemes under prototype simulation conditions are tested using time-dependent numerical experiments which advect an initially cone-shaped passive scalar distribution in each of three steady nondivergent flows. One such flow is solid rotation, while the other two are diagonal uniform flow and a strongly deformational vortex.

Schlesinger, R. E.↗

NASA NTRS1987

Numerical advection algorithms and their role in atmospheric transport and chemistry models

During the last 35 years, well over 100 algorithms for modeling advection processes have been described and tested. This review summarizes the development and improvements that have taken place. The nature of the errors caused by numerical approximation to the advection equation are highlighted. Then the particular devices that have been proposed to remedy these errors are discussed. The extensive literature comparing transport algorithms is reviewed. Although there is no clear cut 'best' algorithm, several conclusions can be made. Spectral and pseudospectral techniques consistently provide the highest degree of accuracy, but expense and difficulties assuring positive mixing ratios are serious drawbacks. Schemes which consider fluid slabs bounded by grid points (volume schemes), rather than the simple specification of constituent values at the grid points, provide accurate positive definite results.

Rood, Richard B.↗

NASA NTRS1988

The role of gravity wave generated advection and diffusion in transport of tracers in the mesosphere

The roles of advection and turbulent diffusion in controlling tracer transport in the meridional plane of the mesosphere are compared using a version of the global primitive equation model for the middle atmosphere developed by Holton and Wehrbein (1980). The results of model sensitivity tests demonstrated that transport in the mesosphere for long-lived species with large-scale heights, such as H2O, CO, and NO(x), is primarily an advective process; on a global scale, small-scale turbulent diffusion produced by gravity wave breaking plays a secondary role. It is concluded that, for such tracers, the eddy diffusion coefficient used in one-dimensional chemical models of the mesosphere should be regarded as a parameterization of the transport by the meridional circulation, not as a parameterization of mixing by small-scale diffusion.

Holton, James R.↗

NASA NTRS1990

Two-dimensional atmospheric transport and chemistry model - Numerical experiments with a new advection algorithm

Extensive testing of the advective scheme proposed by Prather (1986) has been carried out in support of the California Institute of Technology-Jet Propulsion Laboratory two-dimensional model of the middle atmosphere. The original scheme is generalized to include higher-order moments. In addition, it is shown how well the scheme works in the presence of chemistry as well as eddy diffusion. Six types of numerical experiments including simple clock motion and pure advection in two dimensions have been investigated in detail. By comparison with analytic solutions, it is shown that the new algorithm can faithfully preserve concentration profiles, has essentially no numerical diffusion, and is superior to a typical fourth-order finite difference scheme.

Shia, Run-Lie↗

NASA NTRS1990

Waves, advection, and cloud patterns on Venus

The stable layers adjacent to the nearly neutral layer within the Venus clouds are found to be capable of supporting vertically trapped, horizontally propagating waves with horizontal wavelengths of about 10 km and speeds of a few meters per second relative to the mean wind in the neutral layer. These waves may possibly be excited by turbulence within the neutral layer. Here, the properties of the waves, and the patterns which they might produce within the visible clouds if excited near the subsolar point are examined. The patterns can be in agreement with many features in images. The waves are capable of transferring momentum latitudinally to help maintain the general atmospheric spin, but at present we are not able to evaluate wave amplitudes. We also examine an alternative possibility that the cloud patterns are produced by advection and shearing by the mean zonal and meridional flow of blobs formed near the equator. It is concluded that advection and shearing by the mean flow is the most likely explanation for the general pattern of small scale striations.

Schinder, Paul J.↗

NASA NTRS1991

LIMS (Limb Infrared Monitor of the Stratosphere) observation of traveling planetary waves and potential vorticity advection in the stratosphere and mesosphere

Eastward and westward traveling waves were observed by the Nimbus 7 Limb Infrared Monitor of the Stratosphere (LIMS) during the northern winter 1978-1979. Eastward waves were prevalent in early winter and were involved in a minor Canadian warming in December 1978. A large westward traveling wave, as described by previous authors, was observed in January 1979 during a series of minor warmings. By comparing these two events, it is shown that in both cases the superposition of traveling and quasi-stationary waves led to constructive interference that was responsible for the warmings. However, there was significant asymmetry between eastward and westward traveling components. A local Eulerian analysis of potential vorticity (PV) transport indicates that adiabatic, geostrophic advection by the resolvable scales of motion explains qualitatively (but not quantitatively) the observed potential vorticity tendencies in the LIMS Northern Hemisphere winter. In particular, calculated advection explains the eastward rotation of the main vortex, intrusion of low PV air into the polar cap, and formation of high PV filaments at the vortex periphery.

Dunkerton, Timothy J.↗

NASA NTRS1991

Mantle viscosity - A comparison of models from postglacial rebound and from the geoid, plate driving forces, and advected heat flux

Models of the radial variation of effective viscosity inferred from the earth's response to surface loads associated with Pleistocene deglaciation are compared to structures inferred from models of geodynamic phenomena associated with convection: the geoid, plate-driving forces, and advected heat flux. While observations of the earth's response to surface loads do not have sufficient resolution to justify more than two viscous layers, adequately matching the observed long-wavelength geoid anomalies associated with density contrasts in the lower mantle (inferred from seismic tomography) and in the upper mantle (inferred from a model of subducted slabs) requires more structure. It is possible to explain the geoid, observed plate velocities, the advected heat flux in the lower mantle, and relative sea-level variations in oceanic regions, all with a mantle with a high-viscosity/elastic lid, an asthenospheric channel of 2 x 10 exp 19 Pa s from 100 to 400-km depth, a 6 x 10 exp 20 Pa s transition zone, and a lower mantle of 6 x 10 exp 21 Pa s. The uplift history of Australia, Fennoscandia, and Laurentia can be explained with an asthenospheric viscosity less than a factor of 10 higher. Lateral variations in lower mantle viscosity are not required. Transient creep appears to be unimportant for the recent response-to-surface loads from Pleistocene deglaciation.

Hager, Bradford H.↗