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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Dynamic Inland Propagation of Thinning Due to Ice Loss at the Margins of the Greenland Ice Sheet

Mass-balance analysis of the Greenland ice sheet based on surface elevation changes observed by the European Remote-sensing Satellite (ERS) (1992-2002) and Ice, Cloud and land Elevation Satellite (ICESat) (2003-07) indicates that the strongly increased mass loss at lower elevations (<2000 m) of the ice sheet, as observed during 2003-07, appears to induce interior ice thinning at higher elevations. In this paper, we perform a perturbation experiment with a three-dimensional anisotropic ice-flow model (AIF model) to investigate this upstream propagation. Observed thinning rates in the regions below 2000m elevation are used as perturbation inputs. The model runs with perturbation for 10 years show that the extensive mass loss at the ice-sheet margins does in fact cause interior thinning on short timescales (i.e. decadal). The modeled pattern of thinning over the ice sheet agrees with the observations, which implies that the strong mass loss since the early 2000s at low elevations has had a dynamic impact on the entire ice sheet. The modeling results also suggest that even if the large mass loss at the margins stopped, the interior ice sheet would continue thinning for 300 years and would take thousands of years for full dynamic recovery.

ice dynamics↗
NASA NTRS1992

Learning and tuning fuzzy logic controllers through reinforcements

A new method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system is presented. In particular, our Generalized Approximate Reasoning-based Intelligent Control (GARIC) architecture: (1) learns and tunes a fuzzy logic controller even when only weak reinforcements, such as a binary failure signal, is available; (2) introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; (3) introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and (4) learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward network, which can then adaptively improve performance by using gradient descent methods. We extend the AHC algorithm of Barto, Sutton, and Anderson to include the prior control knowledge of human operators. The GARIC architecture is applied to a cart-pole balancing system and has demonstrated significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing.

Berenji, Hamid R.↗
NASA NTRS1991

Uranus atmospheric dynamics and circulation

The observations, models, and theories relevant to the atmospheric dynamics and meteorology of Uranus are discussed. The available models for the large-scale heat transport and atmospheric dynamics as well as diagnostic interpretations of the Voyager data are reviewed. Some pertinent ideas and questions regarding the global circulation balance are considered, partly in comparison with other planetary atmospheres. The available data indicate atmospheric rotation at midlatitudes nearly 200 m/s faster than that of the planetary magnetic field. Analysis of the dynamical deformation of the shape and size of isobaric surfaces measured by the Voyager radio-occultation experiment suggests a subrotating equator at comparable altitudes. Infrared temperature retrievals above the cloud deck indicate a smaller equator-to-pole contrast than expected for purely radiative-convective equilibrium, but show local variations implying a latitudinally correlated decrease with altitude in the cloud-tracked wind.

Allison, Michael↗
NASA NTRS2021

Surface Melting Over the Greenland Ice Sheet Derived From Enhanced Resolution Passive Microwave Brightness Temperatures (1979–2019)

Surface melting is a major component of the Greenland ice sheet surface mass balance, and it affects sea level rise through direct runoff and the modulation of ice dynamics and hydrological processes, supraglacially, englacially and subglacially. Passive microwave (PMW) brightness temperature observations are of paramount importance in studying the spatial and temporal evolution of surface melting due to their long temporal coverage (1979–present) and high temporal resolution (daily). However, a major limitation of PMW datasets has been the relatively coarse spatial resolution, which has historically been of the order of tens of kilometers. Here, we use a newly released PMW dataset (37 GHz, horizontal polarization) made available through a NASA “Making Earth System Data Records for Use in Research Environments” (MeASUREs) program to study the spatiotemporal evolution of surface melting over the Greenland ice sheet at an enhanced spatial resolution of 3.125 km. We assess the outputs of different detection algorithms using data collected by automatic weather stations (AWSs) and the outputs of the Modèle Atmosphérique Régional (MAR) regional climate model. We found that sporadic melting is well captured using a dynamic algorithm based on the outputs of the Microwave Emission Model of Layered Snowpack (MEMLS), whereas a fixed threshold of 245 K is capable of detecting persistent melt. Our results indicate that, during the reference period from 1979 to 2019 (from 1988 to 2019), surface melting over the ice sheet increased in terms of both duration, up to 4.5 (2.9) d per decade, and extension, up to 6.9 % (3.6 %) of the entire ice sheet surface extent per decade, according to the MEMLS algorithm. Furthermore, the melting season started up to 4.0 (2.5) d earlier and ended 7.0 (3.9) d later per decade. We also explored the information content of the enhanced-resolution dataset with respect to the one at 25 km and MAR outputs using a semi-variogram approach. We found that the enhanced product is more sensitive to local-scale processes, thereby confirming the potential of this new enhanced product for monitoring surface melting over Greenland at a higher spatial resolution than the historical products and for monitoring its impact on sea level rise. This offers the opportunity to improve our understanding of the processes driving melting, to validate modeled melt extent at high resolution and, potentially, to assimilate these data in climate models.

Surface melting↗
NASA NTRS1984

Dynamics of coupled ice-ocean system in the marginal ice zone: Study of the mesoscale processes and of constitutive equations for sea ice

This study is aimed at the modelling of mesoscale processed such as up/downwelling and ice edge eddies in the marginal ice zones. A 2-dimensional coupled ice-ocean model is used for the study. The ice model is coupled to the reduced gravity ocean model (f-plane) through interfacial stresses. The constitutive equations of the sea ice are formulated on the basis of the Reiner-Rivlin theory. The internal ice stresses are important only at high ice concentrations (90-100%), otherwise the ice motion is essentially free drift, where the air-ice stress is balanced by the ice-water stress. The model was tested by studying the upwelling dynamics. Winds parallel to the ice edge with the ice on the right produce upwilling because the air-ice momentum flux is much greater that air-ocean momentum flux, and thus the Ekman transport is bigger under the ice than in the open water. The upwelling simulation was extended to include temporally varying forcing, which was chosen to vary sinusoidally with a 4 day period. This forcing resembles successive cyclone passings. In the model with a thin oceanic upper layer, ice bands were formed.

Hakkinen, S.↗
DOE OSTI2026

Ensemble Kalman filter for data assimilation coupled with low-resolution computations techniques applied in fluid dynamics

This paper presents an innovative Reduced-order model (ROM) for merging experimental and simulation data using data assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our methodology introduces a novel approach by implementing the ensemble Kalman filter (EnKF) within a reduced-dimensional framework, grounded in a robust theoretical foundation and applied to fluid dynamics. To address the substantial computational demands of DA, the proposed ROM employs low-resolution (LR) techniques to drastically reduce computational costs. This innovative approach involves downsampling datasets for DA computations, followed by an advanced reconstruction technique based on low-cost singular value decomposition (lcSVD). The lcSVD method, a key innovation in this paper, has never been applied to DA before and offers a highly efficient way to enhance resolution with minimal computational resources. Our results demonstrate significant reductions in both computation time and RAM usage through these LR techniques without compromising the accuracy of the estimations. For instance, in a turbulent test case, for a data compression rate of 15.9, the LR approach can achieve a speed-up of 13.7 and a RAM compression of 90.9% while maintaining a low relative root mean square error (RRMSE) of 2.6%, compared to 0.8% in the high-resolution (HR) reference. Furthermore, we highlight the effectiveness of the EnKF in estimating and predicting the state of fluid flow systems based on limited observations and given low-fidelity numerical data. This paper highlights the potential of the proposed DA method in fluid dynamics applications, particularly for improving computational efficiency in CFD and related fields. Its ability to balance accuracy with low computational and memory costs makes it especially suitable for large-scale and real-time applications, such as environmental monitoring or engineering design. This method will be incorporated into ModelFLOWs-app.

Data Assimilation↗
NASA NTRS2010

Comet Gas and Dust Dynamics Modeling

This software models the gas and dust dynamics of comet coma (the head region of a comet) in order to support the Microwave Instrument for Rosetta Orbiter (MIRO) project. MIRO will study the evolution of the comet 67P/Churyumov-Gerasimenko's coma system. The instrument will measure surface temperature, gas-production rates and relative abundances, and velocity and excitation temperatures of each species along with their spatial temporal variability. This software will use these measurements to improve the understanding of coma dynamics. The modeling tool solves the equation of motion of a dust particle, the energy balance equation of the dust particle, the continuity equation for the dust and gas flow, and the dust and gas mixture energy equation. By solving these equations numerically, the software calculates the temperature and velocity of gas and dust as a function of time for a given initial gas and dust production rate, and a dust characteristic parameter that measures the ability of a dust particle to adjust its velocity to the local gas velocity. The software is written in a modular manner, thereby allowing the addition of more dynamics equations as needed. All of the numerical algorithms are added in-house and no third-party libraries are used.

Von Allmen, Paul A.↗
DOE OSTI2021

Full Vorticity Budget of the Arabian Sea from a 0.1° Ocean Model: Sverdrup Dynamics, Rossby Waves, and Nonlinear Eddy Effects

Abstract The Arabian Sea, influenced by the Indian monsoon, has many unique features, including its basin-scale seasonally reversing surface circulation and the Great Whirl, a seasonal anticyclonic system appearing during the southwest monsoon close to the western boundary. To establish a comprehensive dynamical picture of the Arabian Sea, we utilize numerical model output and design a full vorticity budget that includes a fully decomposed nonlinear term. The ocean general circulation model has 0.1° resolution and is mesoscale eddy-resolving in the region. In the western boundary current system, we highlight the role of nonlinear eddies in the life cycle of the Great Whirl. The nonlinear eddy term is of leading-order importance in this feature’s vorticity balance. Specifically, it contributes to the Great Whirl’s persistence in boreal fall after the weakening of the southwesterly winds. In the open ocean, Sverdrup dynamics and annual Rossby waves are found to dominate the vorticity balance; the latter is considered as a key factor in the formation of the Great Whirl and the seasonal reversal of the western boundary current. In addition, we discuss different forms of vertically integrated vorticity equations in the model and argue that the bottom pressure torque term can be interpreted analogously as friction in the western boundary and vortex stretching in the open ocean.

58 GEOSCIENCES↗
NASA NTRS1994

Dynamics of binary-disk interaction. 1: Resonances and disk gap sizes

We investigate the gravitational interaction of a generally eccentric binary star system with circumbinary and circumstellar gaseous disks. The disks are assumed to be coplanar with the binary, geometrically thin, and primarily governed by gas pressure and (turbulent) viscosity but not self-gravity. Both ordinary and eccentric Lindblad resonances are primarily responsible for truncating the disks in binaries with arbitrary eccentricity and nonextreme mass ratio. Starting from a smooth disk configuration, after the gravitational field of the binary truncates the disk on the dynamical timescale, a quasi-equilibrium is achieved, in which the resonant and viscous torques balance each other and any changes in the structure of the disk (e.g., due to global viscous evolution) occur slowly, preserving the average size of the gap. We analytically compute the approximate sizes of disks (or disk gaps) as a function of binary mass ratio and eccentricity in this quasi-equilibrium. Comparing the gap sizes with results of direct simulations using the smoothed particle hydrodynamics (SPH), we obtain a good agreement. As a by-product of the computations, we verify that standard SPH codes can adequately represent the dynamics of disks with moderate viscosity, Reynolds number R approximately 10(exp 3). For typical viscous disk parameters, and with a denoting the binary semimajor axis, the inner edge location of a circumbinary disk varies from 1.8a to 2.6a with binary eccentricity increasing from 0 to 0.25. For eccentricities 0 less than e less than 0.75, the minimum separation between a component star and the circumbinary disk inner edge is greater than a. Our calculations are relevant, among others, to protobinary stars and the recently discovered T Tau pre-main-sequence binaries. We briefly examine the case of a pre-main-sequence spectroscopic binary GW Ori and conclude that circumbinary disk truncation to the size required by one proposed spectroscopic model cannot be due to Linblad resonances, even if the disk is nonviscous.

Artymowicz, Pawel↗
NASA NTRS2018

Low-Latency Teleoperations: Operational Implications for Human Space Exploration

Low-latency teleoperations (LLT) is envisioned to be an element of human exploration missions in a number of different applications. LLT can be broadly considered to encompass any remote operation of an asset with a communication delay that is less than the human response time to allow for what is effectively "real-time" or "near real-time" operations. This paper will explore motivations and operational implications for why and how LLT might be used for human exploration space missions. LLT analyses have been performed under the auspices of the NASA Human Spaceflight Architecture Team (HAT) and Evolvable Mars Campaign (EMC). The EMC created a flexible, evolvable, capability-driven architectural strategy to enable a sustainable long-term human presence at Mars. LLT is envisioned to be part of that strategy for both in-space and on-surface applications, and this paper will expand on operational considerations within that broader strategic context, as well additional contexts. Some operational implications explored in this paper, derived largely from previous work, are: (1) crew mission support, for which we will address roles for Mission Control on earth, balanced with the capability for crew and robotic assets to operate independently, (2) science operations, with a focus on "backroom" support, highly dynamic science, and enhanced science return and efficiency, and (3) operational efficiency at a deep-space destination such as Mars, including implications for communications infrastructures and how to leverage and balance system autonomy with crew operations, both of which can inform the overall operational "choreography" between crew members, multiple shifts, and exploration assets.

human spaceflight↗
DOE OSTI2021

Model based co-simulation platform for integrated building system control and design optimization

Both steady-state and dynamic simulations have been widely used by HVAC&R industry to support product/equipment development for decades. Steady-state simulation focuses on the system mass, energy and momentum balance of an equilibrium state. It is based on high-fidelity components models, and thus is suitable for system and component design optimization. Dynamic simulation studies the system transient response and is generally used for controls development and verification. It usually does not require rigorous component models of high accuracy because 1) the commonly used PID control is feedback control whose control performance evaluation doesn’t require high fidelity system/plant model; 2) high-fidelity dynamic model significantly increases the number of equations and variables and creates tremendous challenge for math solver. For supervisory control, transactive control or optimization of an integrated building system, the HVAC&R equipment is often one of the sub-components to be controlled. High-fidelity equipment models are required for accurately evaluating control strategies. In addition, building equipment manufacturers have developed a lot of high-fidelity steady-state equipment/component models per their expertise. Thus, a platform that can integrate OEM high-fidelity steady-state model with dynamic building simulation and/or electric power system & grid simulation to support the development and verification of supervisory control for integrated building systems is necessary. In this study, ORNL’s heat pump design tool (HPDM) is utilized to develop a co-simulation platform for supervisory control and optimization in integrated building systems. It is based on a model that integrates high-fidelity steady-state simulation equipment models with dynamic building simulation. A practical case of using the proposed co-simulation platform to develop and evaluate the supervisory control and optimization is presented and discussed.

Sun, Jian↗
DOE OSTI2020

Dynamic stability of active sites in hydr(oxy)oxides for the oxygen evolution reaction

The poor activity and stability of electrode materials for the oxygen evolution reaction are the main bottlenecks in the water-splitting reaction for H 2 production. In this work, by studying the activity–stability trends for the oxygen evolution reaction on conductive M 1 O x H y , Fe–M 1 O x H y and Fe–M 1 M 2 O x H y hydr(oxy)oxide clusters (M 1 = Ni, Co, Fe; M 2 = Mn, Co, Cu), we show that balancing the rates of Fe dissolution and redeposition over a MO x H y host establishes dynamically stable Fe active sites. Together with tuning the Fe content of the electrolyte, the strong interaction of Fe with the MO x H y host is the key to controlling the average number of Fe active sites present at the solid/liquid interface. We suggest that the Fe–M adsorption energy can therefore serve as a reaction descriptor that unifies oxygen evolution reaction catalysis on 3 d transition-metal hydr(oxy)oxides in alkaline media. Thus, the introduction of dynamically stable active sites extends the design rules for creating active and stable interfaces.

36 MATERIALS SCIENCE↗
NASA NTRS1995

Studies of the draping and flaring angles of the Mars and Earth magnetotails

Observations of the Mars tail by the spacecraft have been used to estimate the draping angle of the magnetic field within the tail and the boundary flaring angle. The boundary of the tail is defined by the sudden disappearance of the proton flux by the TAUS ion spectrometer. Solar wind measurements by the TAUS instrument are used to calculate the approximate solar wind dynamic pressure when the spacecraft is within the tail boundary. The average draping angle (Acrsin((square root of (B(sub y)(exp 2) + B(sub z)(exp 2)))/B(sub T))) is found to be 27.2 deg +/- 1.4 deg. The draping angle magnitude depends on the solar wind dynamic pressure, but is quite variable. The flaring angle of the tail boundary at X = -2.5 R(sub M) has also been calculated from the balance of pressure between the lobe of the Martian tail and the component pressures of the solar wind. The flaring angle depends strongly on the solar wind dynamic pressure, and this dependence is identical to that obtained at the Earth by Petrinec and Russell. However, the magnitude of the flaring angle at Mars X = -2.5 R(sub M) is one-half the value obtained at Earth for -22.5 R(sub E) is less than or equal to X -10 R(sub E).

Zhang, T.-L.↗
DOE OSTI2020

Differential effects of drought on nonstructural carbohydrate storage in seedlings and mature trees of four species in a subtropical forest

Nonstructural carbohydrates (NSC) play important roles in forest vulnerability to climate change, especially under increasing drought intensity and frequency. Understanding NSC dynamics is essential for accurately predicting the resistance and resilience of forests in response to drought. However, our knowledge of NSC re-sponses to drought is still limited due to the lack of research in trees of di?erent life stages. In this study, we conducted a throughfall exclusion experiment (TFE) with four subtropical evergreen tree species to examine drought e?ects on NSC in mature trees and understory seedlings. Our results showed the differential effects of drought on NSC dynamics of understory seedlings and mature trees. In the TFE experiment, mature trees of all four species were relatively homoeostatic with the insigni?cantly changed NSC pools, photosynthesis, and growth under the drought treatment compared to the control. In contrast, understory seedlings displayed sig-ni?cant decreases in total NSC and soluble sugars (-14.70 ± 3.66% and -16.93 ± 3.85%, respectively) with the exception of Lithocarpus glaber (L. glaber). The seedlings of L. glaber with the highest hydraulic resistance maintained or slightly increased NSC and its components in response to drought. Our study highlights the im-portance of life stage in assessing drought e?ects of trees on NSC storage and then forest C cycling, which could be incorporated into the dynamic global vegetation models (DGVMs) to better understand drought effects on forest C balance in the future.

Zhang, Peipei↗
DOE OSTI2026

Pinned Clouds over Industrial Sources of Heat during TRACER

An analysis of stereo-camera data from the Tracking Aerosol Convection Interactions Experiment (TRACER) campaign in Houston, Texas, reveals the existence of pinned clouds sitting atop industrial heat sources. These are not plumes of vapor and condensate emanating from stacks: The pinned shallow cumuli have cloud bases at about the lifting condensation of near-surface air. On many mornings, the pinned clouds are the only shallow cumuli in the field of view of the stereo cameras, persisting by themselves for at least an hour. On those mornings, the lower atmosphere straddles the boundary between stable and unstable, and the waste heat from industrial facilities is able to pin moist convection overhead. When solar heating of the surface becomes sufficient later in the morning, those mornings transition to having widespread shallow moist convection. Occurring within the field of view of the stereo cameras and other TRACER instruments, these pinned clouds represent steady plume-like moist convection triggered by known heat sources in a well-characterized atmosphere, making them a rich target for further study. Significance Statement This article introduces steady-state cumulus clouds observed during the Tracking Aerosol Convection Interactions Experiment (TRACER) campaign that were pinned to industrial heat sources. These pinned clouds were present in the early morning only when conditions were primed for moist convection, but for which there was not yet enough solar heating to trigger widespread convection. They persist in a statistical steady state and therefore provide a natural setting to explore the mechanisms controlling convective dynamics, which play a central role in Earth’s atmospheric circulation and radiative balance.

Atmosphere↗
DOE OSTI2024

Understanding aerosol–cloud interactions using a single-column model for a cold-air outbreak case during the ACTIVATE campaign

Marine boundary layer clouds play a critical role in Earth's energy balance. Their microphysical and radiative properties are highly impacted by ambient aerosols and dynamic forcings. In this study, we evaluate the representation of these clouds and related aerosol–cloud interaction processes in the single-column version of the E3SM climate model (SCM) against field measurements collected during the NASA ACTIVATE campaign over the western North Atlantic, as well as intercompare results with high-resolution process level models. We show that E3SM SCM reproduces the macrophysical properties of post-frontal boundary layer clouds in a cold-air outbreak (CAO) case well. However, it generates fewer but larger cloud droplets compared to aircraft measurements. Further sensitivity tests show that the underestimation of both aerosol number concentration and vertical velocity variance contributes to this bias. Aerosol–cloud interactions are examined by perturbing prescribed aerosol properties in E3SM SCM with fixed dynamics. Higher aerosol number concentration or hygroscopicity leads to more numerous but smaller cloud droplets, resulting in a stronger cooling via shortwave cloud forcing. This apparent Twomey effect is consistent with prior climate model studies. The cloud liquid water path shows a weakly positive relation with cloud droplet number concentration due to precipitation suppression. This weak aerosol effect on cloud macrophysics may be attributed to the dominant impact of strong dynamical forcing associated with the CAO. Our findings indicate that the SCM framework is a key tool to bridge the gap between climate models, process level models, and field observations to facilitate process level understanding.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

SNICAR-ADv4: a physically based radiative transfer model to represent the spectral albedo of glacier ice

Abstract. Accurate modeling of cryospheric surface albedo is essential for our understanding of climate change as snow and ice surfaces regulate the global radiative budget and sea-level through their albedo and mass balance. Although significant progress has been made using physical principles to represent the dynamic albedo of snow, models of glacier ice albedo tend to be heavily parameterized and not explicitly connected with physical properties that govern albedo, such as the number and size of air bubbles, specific surface area (SSA), presence of abiotic and biotic light absorbing constituents (LACs), and characteristics of any overlying snow. Here, we introduce SNICAR-ADv4, an extension of the multi-layer two-stream delta-Eddington radiative transfer model with the adding–doubling solver that has been previously applied to represent snow and sea-ice spectral albedo. SNICAR-ADv4 treats spectrally resolved Fresnel reflectance and transmittance between overlying snow and higher-density glacier ice, scattering by air bubbles of varying sizes, and numerous types of LACs. SNICAR-ADv4 simulates a wide range of clean snow and ice broadband albedo (BBA), ranging from 0.88 for (30 µm) fine-grain snow to 0.03 for bare and bubble-free ice under direct light. Our results indicate that representing ice with a density of 650 kg m−3 as snow with no refractive Fresnel layer, as done previously, generally overestimates the BBA by an average of 0.058. However, because most naturally occurring ice surfaces are roughened “white ice”, we recommend modeling a thin snow layer over bare ice simulations. We find optimal agreement with measurements by representing cryospheric media with densities less than 650 kg m−3 as snow and larger-density media as bubbly ice with a Fresnel layer. SNICAR-ADv4 also simulates the non-linear albedo impacts from LACs with changing ice SSA, with peak impact per unit mass of LACs near SSAs of 0.1–0.01 m2 kg−1. For bare, bubble-free ice, LACs actually increase the albedo. SNICAR-ADv4 represents smooth transitions between snow, firn, and ice surfaces and accurately reproduces measured spectral albedos of a variety of glacier surfaces. This work paves the way for adapting SNICAR-ADv4 to be used in land ice model components of Earth system models.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1987

Solar cycle changes in the ionization sources of the nightside Venus ionosphere

Using new and previous experimental evidence, it is argued that the height-integrated flux of O(+) ions transported from the dayside Venus ionosphere into the nightside ionosphere is strongly reduced (shut off) at solar cycle minimum (SCmin) and that the electron impact source becomes the predominant nightside ionization source during this phase of the solar cycle. The height-integrated transterminator O(+) flux, which is probably the dominant nightside ionization source at solar cycle maximum (SCmax), is shut off at SCmin by compression of the dayside ionopause to low altitude. It is suggested that the ionopause is depressed because the dayside ionospheric kinetic pressure field is reduced by a factor of approximately 3 from its SCmas value and that the typical SCmin solar wind dynamic pressure, which is not less than the typical SCmax value, cannot be balanced by the ionospheric pressure field at altitudes above approximately 250 km.

Knudsen, William C.↗