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All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Comments on the Diffusive Behavior of Two Upwind Schemes

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Wood, William A.↗
NASA NTRS1998

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

Wood, William A.↗
NASA NTRS2005

North Pacific Cloud Feedbacks Inferred from Synoptic-Scale Dynamic and Thermodynamic Relationships

This study analyzed daily satellite cloud observations and reanalysis dynamical parameters to determine how mid-tropospheric vertical velocity and advection over the sea surface temperature gradient control midlatitude North Pacific cloud properties. Optically thick clouds with high tops are generated by synoptic ascent, but two different cloud regimes occur under synoptic descent. When vertical motion is downward during summer, extensive stratocumulus cloudiness is associated with near surface northerly wind, while frequent cloudless pixels occur with southerly wind. Examinations of ship-reported cloud types indicates that midlatitude stratocumulus breaks up as the the boundary level decouples when it is advected equatorward over warmer water. Cumulus is prevalent under conditions of synoptic descent and cold advection during winter. Poleward advection of subtropical air over colder water causes stratification of the near-surface layer that inhibits upward mixing of moisture and suppresses cloudiness until a fog eventually forms. Averaging of cloud and radiation data into intervals of 500-hPa vertical velocity and advection over the SST gradient enables the cloud response to changes in temperature and the stratification of the lower troposphere to be investigated independent of the dynamics.

Norris, Joel R.↗
NASA NTRSDate not supplied

Explicit Discontinuous Galerkin Methods for Conservation Laws

The two explicit DG methods in this study are based on a ‘predictor-corrector’ formulation, the first introduced by Lörcher, Gassner, and Munz (2007, 2008) called space–time expansion discontinuous Galerkin or STE-DG scheme, and the second, introduced independently by the author (Huynh 2006, 2013) called the upwind moment scheme. The predictor step of the two methods is essentially identical using a Cauchy-Kovalevsky (CK) procedure, which involves no interaction of the data among neighboring cells. The corrector step also shares the same space-time integration formulation and is where interaction of the data among neighboring cells takes place; the difference, however, is in how the resulting space-time volume integral is estimated. As a consequence of the different estimates, for the case of advection in one spatial dimension (1D), the moment scheme has a CFL (Courant-Friedrichs-Lewy) condition of 1 for all p and is accurate to order 2p+1, i.e., it possesses the super accuracy property, whereas the STE-DG method has a more restrictive CFL condition and is accurate to the expected order of p+1. For 1D advection, compared with the CFL conditions of 1/(2p+1) of standard RK-DG (Runge-Kutta) scheme where space and time discretization are of the same order, the moment scheme allows a significantly larger time step size. It also turns out that the scheme yields a result identical to Van Leer’s scheme III (1977), which amounts to shifting the data a distance of advection corresponding to the time step and projecting the result onto the space of polynomial solutions. Contrary to Van Leer’s approach, however, the space-time ‘predictor-corrector’ formulation facilitates extensions to the case of systems of equations. Concerning 2D extensions, in the case of advection, when the flow is along the diagonal direction, the CFL conditions for the moment schemes become restrictive as will be shown by Fourier (Von Neumann) stability and accuracy analyses. Since the moment scheme employs the right Radau points as collocation points in time, the method is closely related to the implicit Radau IIA scheme, which is stable for any time step size. The role of Radau IIA in relieving stability restriction for these explicit DG schemes remains to be explored

Discontinuous Galerkin↗
DOE OSTI2023

Eulerian finite element implementations of a dislocation density-based continuum model

In Eulerian finite element simulations, the mesh moves relative to the material. After every change of position between the mesh and the material, the state variables are interpolated to the new mesh position, which is referred to as advection. Large strain crystal plasticity models are based on the multiplicative decomposition of the total deformation gradient. Further, the stress is evaluated as a function of the thermoelastic strain, temperature, and other state variables. Advection of tensor quantities, such as the strain, is coupled with possibly significant advection errors. In an effort to reduce the advection errors, we develop two rate forms of an established dislocation density-based continuum model. To that end, we replace the multiplicative decomposition of the deformation gradient with the additive decomposition of the velocity gradient, and define the stress rate instead of the total stress. The Eulerian implementation is compared with Lagrangian calculations, and two numerical examples with severe deformation levels are presented.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Dynamics of ENSO Phase–Locking and Its Biases in Climate Models

Here, the contributions of different oceanic feedbacks to the El Niño–Southern Oscillation (ENSO) phase-locking are examined by deriving ENSO dynamics based on the recharge-discharge framework. In observations, the significant winter preference of the ENSO peak is determined by a strong seasonal modulation of SST growth rate, which is controlled by the zonal advective and thermodynamic feedbacks. However, the majority of climate models fail to simulate ENSO phase-locking because the contribution of zonal advective feedback to the seasonal modulation of the SST growth rate is much smaller compared to observations. The weak annual cycle of the SST-current coupling coefficient and small annual mean of the negative climatological zonal SST gradient are two factors contributing to the weak-biased seasonality of zonal advective feedback. Further analysis shows that the Niño3.4 SSTA has better phase-locking performance than Niño3 SSTA in the climate models due to the better simulation of zonal advection feedback in the Niño3.4 region.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Large-Scale Forcing Impact on the Development of Shallow Convective Clouds Revealed From LASSO Large-Eddy Simulations

Real-world large-eddy simulations (LES) are driven by time-varying large-scale forcings (LSF) - e.g., temperature advection, moisture advection, and subsidence - derived from large-scale weather models. This study investigates the impact of the uncertainty in LSF on real-world LES in terms of the development of shallow convection at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) atmospheric observatory for the 11 June 2016 case using LES provided by the U.S. Department of Energy's LES ARM Symbiotic Simulation and Observation (LASSO) activity. The LASSO dataset provides an ensemble of LES for the selected case, which consists of LES runs that were driven by different LSF. The two contrasting LES runs investigated here generate different types of convective clouds, i.e., nonprecipitating shallow clouds and precipitating cumulus congestus, mainly due to the difference of LSF in temperature advection in the free troposphere. The temperature advection modulates the strength of the capping inversion and therefore the buoyancy of the air parcels rising from the atmospheric boundary layer (ABL). The inversion, together with large-scale updrafts, controls the penetration of the ABL thermals into the free troposphere, leading to cumulus congestus in the case of a weaker inversion. In contrast, clouds remain shallow in the case of a strong inversion. Differences between the two simulations are amplified over time, as mixed-phase clouds are formed near the top of the congestus in the weaker inversion case. Furthermore, this high dependency of LES results to LSF stresses the importance of accurate LSF by large-scale models to real-world LES simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Investigating Inherent Numerical Stabilization for the Moist, Compressible, Non‐Hydrostatic Euler Equations on Collocated Grids

This study investigates inherent numerical dissipation due to upwind fluxes and reconstruction strategies for collocated Finite-Volume integration of the Euler equations. Idealized supercell simulations are used without any explicit dissipation. Flux terms are split into: mass flux, pressure, and advected quantities. They are computed with the following upwind strategies: central, advectively upwind, and acoustically upwind. This is performed for third and ninth-order-accurate reconstructions with and without Weighted Essentially Non-Oscillatory limiting. Acoustic-only upwinding for pressure and mass flux terms and advective-only upwinding for advected quantities is the most flexible simplification found. It reduces data movement and computations. Assuming a constant speed of sound in acoustic upwinding gives similar results to using the true speed of sound. Dissipation from upwind adapts automatically to grid spacing, time step, reconstruction accuracy, and flow smoothness. While stability is maintained even at 21st-order spatial accuracy, there is a limit to the spatial order of accuracy for which upwinding alone can create a realizable solution in the conditions of this study. Convex combinations of upwind and central solutions for flux terms also reduced dissipation, but as the central proportion grows, solutions become physically unrealizable. The range of length scales of the kinetic energy spectra can be extended along k −5/3 to smaller spatial scales by reducing dissipation either with higher-order reconstructions or using convex combinations of upwind and central fluxes. However, not all extensions of the length scale range along k −5/3 exhibit physically realizable solutions, even though the spectra appear to be physical.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A Scale‐Dependent Analysis of the Barotropic Vorticity Budget in a Global Ocean Simulation

Abstract The climatological mean barotropic vorticity budget is analyzed to investigate the relative importance of surface wind stress, topography, planetary vorticity advection, and nonlinear advection in dynamical balances in a global ocean simulation. In addition to a pronounced regional variability in vorticity balances, the relative magnitudes of vorticity budget terms strongly depend on the length‐scale of interest. To carry out a length‐scale dependent vorticity analysis in different ocean basins, vorticity budget terms are spatially coarse‐grained. At length‐scales greater than 1,000 km, the dynamics closely follow the Topographic‐Sverdrup balance in which bottom pressure torque, surface wind stress curl and planetary vorticity advection terms are in balance. In contrast, when including all length‐scales resolved by the model, bottom pressure torque and nonlinear advection terms dominate the vorticity budget (Topographic‐Nonlinear balance), which suggests a prominent role of oceanic eddies, which are of km in size, and the associated bottom pressure anomalies in local vorticity balances at length‐scales smaller than 1,000 km. Overall, there is a transition from the Topographic‐Nonlinear regime at scales smaller than 1,000 km to the Topographic‐Sverdrup regime at length‐scales greater than 1,000 km. These dynamical balances hold across all ocean basins; however, interpretations of the dominant vorticity balances depend on the level of spatial filtering or the effective model resolution. On the other hand, the contribution of bottom and lateral friction terms in the barotropic vorticity budget remains small and is significant only near sea‐land boundaries, where bottom stress and horizontal viscous friction generally peak.

Khatri, Hemant↗
DOE OSTI2026

An implicit-explicit time splitting strategy for the far SOL plasma fluid model with DG-FEM discretization

We consider a far scrape-off layer (SOL) plasma fluid model of ions that is governed by a Braginskiitype model: a one-dimensional, nonlinear system of advection-diffusion equations coupled with a diffusion equation for neutral particles. Our motivation for studying this system arises from the coupling between the edge plasma and radio-frequency (RF) heating, where solving a far SOL plasma fluid model provides critical insights into edge plasma dynamics. Numerical simulations of plasma fluid models require advanced computational techniques to achieve both efficiency and accuracy, especially when resolving the boundary layer in magnetically confined plasmas. In this work, we propose an implicit-explicit time operator splitting strategy that allows for an efficient solution algorithm, where the diffusive terms are treated semi-implicitly requiring only a linear solve, while the advection part is handled explicitly using a strong-stability-preserving Runge-Kutta (SSP-RK3) scheme. This leads to a fully decoupled system in which the diffusion and advection sub-problems can be solved separately, simplifying the overall solution procedure and allowing for efficient parallelization, which is particularly relevant for exploring the impact of RF heating on the SOL plasma. The main challenge of the discretization is due to the strong coupling between diffusion and advection, particularly through the boundary conditions. This makes implementation of such a scheme in an accurate and stable manner nontrivial. We discuss in detail how to split the equations and manage boundary conditions to maintain stability and well-posedness for each subsystem. We also describe a spatial discretization approach, based on the discontinuous Galerkin finite element method (DG-FEM) and present numerical results for a one-dimensional system.

Burkovska, Olena [ORNL] (ORCID:0000000163101130)↗
DOE OSTI2025

Matrix Diffusion Controls Mountain Hillslope Groundwater Ages and Inferred Storage Dynamics

Groundwater age distributions provide fundamental insights on coupled water and biogeochemical processes in mountain watersheds. Field-based studies have found mixtures of young and old-aged groundwater in mountain catchments underlain by bedrock; yet, the processes that dictate these groundwater age distributions are poorly understood. In this work, we use the coupled ParFlow-CLM integrated hydrologic and EcoSLIM particle tracking models to simulate groundwater age distributions on a lower montane hillslope in the East River Watershed, Colorado (USA). We develop a convolution-based approach to propagate fracture-matrix diffusion processes to the EcoSLIM advection-dominated age distributions. We compare observed 3 H and 4 He concentrations from two groundwater wells against model predictions that have varying advective transport times and matrix diffusion magnitudes. Based on a Monte Carlo analysis that considers uncertain matrix and fracture parameters, we find that matrix diffusion is needed to jointly predict 3 H and 4 He observations at both wells. The advection-dominated age distributions lack adequate mixing of young and old-aged water to capture the observed co-occurrence of 3 H and 4 He. The model scenario that best matches the 3 H, 4 He, and water level observations when considering both advective flowpath and matrix diffusion mixing processes has a dynamic bedrock groundwater reservoir that is susceptible to considerable storage losses during low-snow periods. This dynamic groundwater system amplifies the need to assimilate deeper bedrock groundwater into watershed hydro-biogeochemical predictions. This work further highlights the importance of considering matrix diffusion when interpreting environmental tracers in bedrock groundwater systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Observed Sensitivity of Low-Cloud Radiative Effects to Meteorological Perturbations over the Global Oceans

Understanding how marine low clouds and their radiative effects respond to changing meteorological conditions is crucial to constrain low-cloud feedbacks to greenhouse warming and internal climate variability. In this paper, we use observations to quantify the low-cloud radiative response to meteorological perturbations over the global oceans to shed light on physical processes governing low-cloud and planetary radiation budget variability in different climate regimes. We assess the independent effect of perturbations in sea surface temperature, estimated inversion strength, horizontal surface temperature advection, 700-hPa relative humidity, 700-hPa vertical velocity, and near-surface wind speed. Stronger inversions and stronger cold advection greatly enhance low-level cloudiness and planetary albedo in eastern ocean stratocumulus and midlatitude regimes. Warming of the sea surface drives pronounced reductions of eastern ocean stratocumulus cloud amount and optical depth, and hence reflectivity, but has a weaker and more variable impact on low clouds in the tropics and middle latitudes. By reducing entrainment drying, higher free-tropospheric relative humidity enhances low-level cloudiness. At low latitudes, where cold advection destabilizes the boundary layer, stronger winds enhance low-level cloudiness; by contrast, wind speed variations have weak influence at midlatitudes where warm advection frequently stabilizes the marine boundary layer, thus inhibiting vertical mixing. These observational constraints provide a framework for understanding and evaluating marine low-cloud feedbacks and their simulation by models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Tropical Cyclone Wind Shear-Relative Asymmetry in Reanalyses

Abstract While tropical cyclones (TCs) are axisymmetric vortices to the first order, they often exhibit noteworthy structural asymmetries. These often result from environmental vertical wind shear, which tilts the vortex and induces a wavenumber 1 pattern in the circulation and precipitation fields. Reanalyses and climate models have improved in representing the TC structure and climatology, but their relatively coarse resolution and dependence on parameterized physics cast doubt on their ability to capture the asymmetric TC structure. We perform the most comprehensive process-oriented assessment of TC asymmetry to date in reanalyses. Specifically, we analyze the composite shear-relative TC structure in ERA5 and Climate Forecast System Reanalysis (CFSR), which vary in their resolutions, physical parameterization suites, and data assimilation techniques. These structures are compared with aircraft reconnaissance radar observations. In agreement with the observations, the strongest tangential winds are usually found left-of-shear, while inner core rainfall, ascent, vortex tilt, and low-level inflow are favored directly downshear or in the downshear-left quadrant. Outer rainband convection generally peaks in the downshear-right quadrant. Thermodynamic asymmetries are also apparent, with anomalous low-level moisture right-of-shear, midlevel warmth in the upshear-right quadrant (uptilt), and cloud properties suggestive of a realistic precipitation life cycle from growth to fallout. We also decompose rainfall contributions from the convective parameterization and large-scale cloud schemes and highlight the roles of vorticity advection, buoyancy advection, and diabatic processes in driving asymmetric vertical motions in the inner core and outer rainband regions. Our results suggest that process-level studies of TC asymmetry and TC–wind shear interaction under future warming are viable using climate models. Significance Statement Asymmetries are common in tropical cyclones (TCs), influencing their intensity, track, and hazards. Vertical wind shear often plays a leading-order role in causing these asymmetries. It is uncertain how well asymmetric structures and processes are captured in reanalyses and global climate models (GCMs) with grid spacings of 0.25° and coarser. In this study, we first evaluate TC asymmetry in reanalyses, which have the benefit of being forced by observations. This helps to assess whether the resolutions associated with GCMs sufficiently capture asymmetric structures and processes and motivates upcoming work with free-running GCMs to study how TC asymmetry may change in a warming climate.

Carstens, Jacob D.↗
DOE OSTI2022

Tethered balloon-borne profile measurements of atmospheric properties in the cloudy atmospheric boundary layer over the Arctic sea ice during MOSAiC: Overview and first results

The tethered balloon-borne measurement system BELUGA (Balloon-bornE moduLar Utility for profilinG the lower Atmosphere) was deployed over the Arctic sea ice for 4 weeks in summer 2020 as part of the Multidisciplinary drifting Observatory for the Study of Arctic Climate expedition. Using BELUGA, vertical profiles of dynamic, thermodynamic, aerosol particle, cloud, radiation, and turbulence properties were measured from the ground up to a height of 1,500 m. BELUGA was operated during an anomalously warm period with frequent liquid water clouds and variable sea ice conditions. Three case studies of liquid water phase, single-layer clouds observed on 3 days (July 13, 23, and 24, 2020) are discussed to show the potential of the collected data set to comprehensively investigate cloud properties determining cloud evolution in the inner Arctic over sea ice. Simulated back-trajectories show that the observed clouds have evolved within 3 different air masses (“aged Arctic,” “advected over sea ice,” and “advected over open ocean”), which left distinct fingerprints in the cloud properties. Strong cloud top radiative cooling rates agree with simulated results of previous studies. The weak warming at cloud base is mostly driven by the vertical temperature profile between the surface and cloud base. In-cloud turbulence induced by the cloud top cooling was similar in strength compared to former studies. From the extent of the mixing layer, it is speculated that the overall cloud cooling is stronger and thus faster in the warm oceanic air mass. Larger aerosol particle number concentrations and larger sizes were observed in the air mass advected over the sea ice and in the air mass advected over the open ocean.

Arctic↗
DOE OSTI2022

Islet: interpolation semi-Lagrangian element-based transport

Abstract. Advection of trace species, or tracers, also called tracer transport, in models of the atmosphere and other physical domains is an important and potentially computationally expensive part of a model's dynamical core. Semi-Lagrangian (SL) advection methods are efficient because they permit a time step much larger than the advective stability limit for explicit Eulerian methods without requiring the solution of a globally coupled system of equations as implicit Eulerian methods do. Thus, to reduce the computational expense of tracer transport, dynamical cores often use SL methods to advect tracers. The class of interpolation semi-Lagrangian (ISL) methods contains potentially extremely efficient SL methods. We describe a finite-element ISL transport method that we call the interpolation semi-Lagrangian element-based transport (Islet) method, such as for use with atmosphere models discretized using the spectral element method. The Islet method uses three grids that share an element grid: a dynamics grid supporting, for example, the Gauss–Legendre–Lobatto basis of degree three; a physics parameterizations grid with a configurable number of finite-volume subcells per element; and a tracer grid supporting use of Islet bases with particular basis again configurable. This method provides extremely accurate tracer transport and excellent diagnostic values in a number of verification problems.

58 GEOSCIENCES↗
NASA NTRS1973

A field investigation and numerical simulation of coastal fog

A field investigation of the microphysical and micrometeorological features of fogs occurring near Los Angeles and Vandenberg, California was conducted. Observations of wind speed and direction, temperature, dew point, vertical wind velocity, dew deposition, drop-size distribution, liquid water content, and haze and cloud nucleus concentration were obtained. These observations were initiated in late evening prior to fog formation and continued until the time of dissipation in both advection and radiation fogs. Data were also acquired in one valley fog and several dense haze situations. The behavior of these parameters prior to and during fog are discussed in detail. A two-dimensional numerical model was developed to investigate the formation and dissipation of advection fogs under the influence of horizontal variations in surface temperature. The model predicts the evolution of potential temperature, water vapor content, and liquid water content in a vertical plane as determined by vertical turbulent transfer and horizontal advection. Results are discussed from preliminary numerical experiments on the formation of warm-air advection fog and dissipation by natural and artificial heating from the surface.

Mack, E. J.↗
NASA NTRS1982

The effects of random errors in rawinsonde data on derived kinematic quantities

The sensitivity of kinematic parameters to random errors contained in rawinsonde data is assessed. Parameters under consideration include relative vorticity, vorticity advection, horizontal divergence, kinematic vertical motion, and temperature advection. It is shown that horizontal divergence is the most affected, with reliability a function of height. Vorticity advection is the next most altered by random error, and in this case, the effects of wind errors are greater on the gradient of vorticity than on the vorticity itself. Vertical motions are most affected by random perturbations at 300 mb and above, and temperature advection is found to be the least sensitive to random perturbations.

Belt, C. L.↗
NASA NTRS1991

Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime

Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.

Malevsky, A. V.↗