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At least 343 records · Page 19

Climate Impacts of Convective Cloud Microphysics in NCAR CAM5

Here we improved the treatments of convective cloud microphysics in the NCAR Community Atmosphere Model version 5.3 (CAM5.3) by 1) implementing new terminal velocity parameterizations for convective ice and snow particles, 2) adding graupel microphysics, 3) considering convective snow detrainment, and 4) enhancing rain initiation and generation rate in warm clouds. Furthermore, we evaluated the impacts of improved microphysics on simulated global climate, focusing on simulated cloud radiative forcing, graupel microphysics, convective cloud ice amount, and tropical precipitation. Compared to CAM5.3 with the default convective microphysics, the too-strong cloud shortwave radiative forcing due primarily to excessive convective cloud liquid is largely alleviated over the tropics and midlatitudes after rain initiation and generation rate is enhanced, in better agreement with the CERES-EBAF estimates. Geographic distributions of graupel occurrence are reasonably simulated over continents; whereas the graupel occurrence remains highly uncertain over the oceanic storm-track regions. When evaluated against the CloudSat–CALIPSO estimates, the overestimation of convective ice mass is alleviated with the improved convective ice microphysics, among which adding graupel microphysics and the accompanying increase in hydrometeor fall speed play the most important role. The probability distribution function (PDF) of rainfall intensity is sensitive to warm rain processes in convective clouds, and enhancement in warm rain production shifts the PDF toward heavier precipitation, which agrees better with the TRMM observations. Common biases of overestimating the light rain frequency and underestimating the heavy rain frequency in GCMs are mitigated.

54 ENVIRONMENTAL SCIENCES↗

Use of satellite data in a diagnostic parameterization of convective heating

Heating estimates derived from a diagnostic technique using observed rainfall and GOES IR digital imagery were completed and evaluated for accuracy. A sensitivity analysis was done to examine assumptions regarding shape of the normalized mass flux profile, cloud precipitation efficiency, and existence of convective scale downdrafts. The results, which were derived using what are felt to be bounding limits of the assumptions, indicate that the heating estimates are reliable for use in diagnostic available potential energy (APE) budgets. Comparison to heating estimates derived as residuals in the thermodynamic equation show the level of maximum heating (near 300 mb) to be the same on a time averaged basis. Heating estimates were used to study the response of the large scale environment to the cumulus scale thermodynamic forcing. An analysis of the thermally forced component of vertical motion through the omega equation showed that a significant fraction of the total grid scale upward motion results from the heating provided by the condensation and vertical eddy heat transport in the convective cells.

Robertson, F. R.↗

Remote sensing of water vapor convergence, deep convection, and precipitation over the tropical Pacific Ocean during the 1982-1983 El Nino

Using data collected by SMMR on board the Nimbus 7 satellite, estimates of atmospheric water vapor were obtained over the tropical Pacific Ocean during the 1982-1983 El Nino. A parameterization that physically relates the synoptic and convective scales was employed, making it possible to explicitly resolve convective elements and rain cells for poorly resolvable measurements. The derived water vapor flux convergences were analyzed during the El Nino episode to map the inferred deep convection and estimated rainfall over regions impacted by the event, and the inferred monthly rainfall amounts were compared with observations for 14 island and coastal stations in the Pacific Ocean.

Ardanuy, Philip E.↗

Facile Metal Release from Pore-Lining Phases Enables Unique Carbonate Zonation in a Basalt Carbon Mineralization Demonstration

Carbon-negative strategies such as geologic carbon sequestration in continental flood basalts offers a promising route to the removal of greenhouse gases, such as CO 2 , via safe and permanent storage as stable carbonates. This potential has been successfully demonstrated at a field scale at the Wallula Basalt Carbon Storage Pilot Project where supercritical CO 2 was injected into the Columbia River Basalt Group (CRBG). Here, we analyze recovered post-injection sidewall core cross-sections containing carbonate nodules using μ-XRF chemical mapping techniques that revealed compositional zonation within the nodules. The unique nature of the subsurface anthropogenic carbonates is highlighted by the near absence of Mg in an ankerite-like composition. Furthermore, a comparison between pre- and post-injection sidewall cores along with an in-depth chemical mapping of basalt pore lining cements provides a better understanding into the source and fate of critical cationic species involved in the precipitation of carbon mineralization products. Collectively, these results provide crucial insights into carbonate growth mechanisms under a time-dependent pore fluid composition. Finally, as such, these findings will enable parameterization of predictive models for future CO 2 sequestration efforts in reactive reservoirs around the world.

54 ENVIRONMENTAL SCIENCES↗

Learning to Correct Climate Projection Biases

The fidelity of climate projections is often undermined by biases in climate models due to their simplification or misrepresentation of unresolved climate processes. While various bias correction methods have been developed to post-process model outputs to match observations, existing approaches usually focus on limited, low-order statistics, or break either the spatiotemporal consistency of the target variable, or its dependency upon model resolved dynamics. We develop a Regularized Adversarial Domain Adaptation (RADA) methodology to overcome these deficiencies, and enhance efficient identification and correction of climate model biases. Instead of pre-assuming the spatiotemporal characteristics of model biases, we apply discriminative neural networks to distinguish historical climate simulation samples and observation samples. The evidences based on which the discriminative neural networks make distinctions are applied to train the domain adaptation neural networks to bias correct climate simulations. We regularize the domain adaptation neural networks using cycle-consistent statistical and dynamical constraints. An application to daily precipitation projection over the contiguous United States shows that our methodology can correct all the considered moments of daily precipitation at approximately $1^\circ$ resolution, ensures spatiotemporal consistency and inter-field correlations, and can discriminate between different dynamical conditions. Our methodology offers a powerful tool for disentangling model parameterization biases from their interactions with the chaotic evolution of climate dynamics, opening a novel avenue toward big-data enhanced climate predictions.

58 GEOSCIENCES↗

Land surface hydrology parameterization for atmospheric general circulation models including subgrid scale spatial variability

Parameterizations are developed for the representation of subgrid hydrologic processes in atmospheric general circulation models. Reasonable a priori probability density functions of the spatial variability of soil moisture and of precipitation are introduced. These are used in conjunction with the deterministic equations describing basic soil moisture physics to derive expressions for the hydrologic processes that include subgrid scale variation in parameters. The major model sensitivities to soil type and to climatic forcing are explored.

Entekhabi, D.↗

Extratropical Cyclone Clouds in the GFDL Climate Model: Diagnosing Biases and the Associated Causes

The clouds in southern hemisphere extratropical cyclones generated by the GFDL climate model are analyzed against MODIS, CloudSat and CALIPSO cloud and precipitation observations. Two model versions are used: one is a developmental version of AM4, a model GFDL will utilize for CMIP6, the other is the same model with a different parameterization of moist convection. Both model versions predict a realistic top-of-atmosphere cloud cover in the southern oceans, within 5% of the observations. However, an examination of cloud cover transects in extratropical cyclones reveals a tendency in the models to overestimate high-level clouds (by differing amounts) and underestimate cloud cover at low-levels (again by differing amounts), especially in the post-cold frontal (PCF) region, when compared to observations. Focusing on only the models, their differences in high and mid-level clouds are consistent with their differences in convective activity and relative humidity (RH), but the same is not true for the PCF region. In this region, RH is higher in the model with less cloud fraction. These seemingly contradictory cloud and RH differences can be explained by differences in the cloud parameterization tuning parameters that ensure radiative balance. In the PCF region, the model cloud differences are smaller than either of the model biases with respect to observations, suggesting other physics changes are needed to address the bias. The process-oriented analysis used to assess these model differences will soon be automated and shared.

Catherine M Naud↗

Rainbows and Climate Change: A tutorial on climate model diagnostics and parameterization

Earth System Models (ESMs) must represent processes below the grid scale of a model using representations (parameterizations) of physical and chemical processes. As a tutorial exercise to understand diagnostics and parameterization, this work presents a representation of rainbows for an ESM: the Community Earth System Model version 2 (CESM2). Using the 'state' of the model, basic physical laws, and some assumptions, we generate a representation of this unique optical phenomena as a diagnostic output. Rainbow occurrence and it's possible changes are related to cloud occurrence and rain formation which are critical uncertainties for climate change prediction. The work highlights issues which are typical of many diagnostics parameterizations such as assumptions, uncertain parameters and the difficulty of evaluation against uncertain observations. Results agree qualitatively with limited available global 'observations' of Rainbows. Rainbows are seen in expected locations in the sub-tropics over the ocean where broken clouds and frequent precipitation occurs. The diurnal peak is in the morning over ocean and in the evening over land. The representation of rainbows is found to be quantitatively sensitive to the assumed amount of cloudiness and the amount of stratiform rain. Rainbows are projected to have decreased, mostly in the Northern Hemisphere, due to aerosol pollution effects increasing cloud coverage since 1850. In the future, continued climate change is projected to decrease cloud cover, associated with a positive cloud feedback. As a result the rainbow diagnostic projects that rainbows will increase in the future, with the largest changes at mid-latitudes. The diagnostic may be useful for assessing cloud parameterizations, and is an exercise in how to build and test parameterizations of atmospheric phenomena.

54 ENVIRONMENTAL SCIENCES↗

Assessing climate change impacts on live fuel moisture and wildfire risk using a hydrodynamic vegetation model

Abstract. Live fuel moisture content (LFMC) plays a critical role in wildfire dynamics, but little is known about responses of LFMC to multivariate climate change, e.g., warming temperature, CO2 fertilization, and altered precipitation patterns, leading to a limited prediction ability of future wildfire risks. Here, we use a hydrodynamic demographic vegetation model to estimate LFMC dynamics of chaparral shrubs, a dominant vegetation type in fire-prone southern California. We parameterize the model based on observed shrub allometry and hydraulic traits and evaluate the model's accuracy through comparisons between observed and simulated LFMC of three plant functional types (PFTs) under current climate conditions. Moreover, we estimate the number of days per year of LFMC below 79 % (which is a critical threshold for wildfire danger rating of southern California chaparral shrubs) from 1960 to 2099 for each PFT and compare the number of days below the threshold for medium and high greenhouse gas emission scenarios (RCP4.5 and 8.5). We find that climate change could lead to more days per year (5.2 %–14.8 % increase) with LFMC below 79 % between the historical (1960–1999) and future (2080–2099) periods, implying an increase in wildfire danger for chaparral shrubs in southern California. Under the high greenhouse gas emission scenario during the dry season, we find that the future LFMC reductions mainly result from a warming temperature, which leads to 9.1 %–18.6 % reduction in LFMC. Lower precipitation in the spring leads to a 6.3 %–8.1 % reduction in LFMC. The combined impacts of warming and precipitation change on fire season length are equal to the additive impacts of warming and precipitation change individually. Our results show that the CO2 fertilization will mitigate fire risk by causing a 3.5 %–4.8 % increase in LFMC. Our results suggest that multivariate climate change could cause a significant net reduction in LFMC and thus exacerbate future wildfire danger in chaparral shrub systems.

54 ENVIRONMENTAL SCIENCES↗

Convection-Permitting Simulations With the E3SM Global Atmosphere Model

This paper describes the first implementation of the Δx = 3.25 km version of the Energy Exascale Earth System Model (E3SM) global atmosphere model and its behavior in a 40-day prescribed-sea-surface-temperature simulation (January 20 through February 28, 2020). This simulation was performed as part of the DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains (DYAMOND) Phase 2 model intercomparison. Effective resolution is found to be ~ 6x the horizontal dynamics grid resolution despite using a coarser grid for physical parameterizations. Despite this new model being in an immature and untuned state, moving to 3.25 km grid spacing solves several long-standing problems with the E3SM model. In particular, Amazon precipitation is much more realistic, the frequency of light and heavy precipitation is improved, agreement between the simulated and observed diurnal cycle of tropical precipitation is excellent, and the vertical structure of tropical convection and coastal stratocumulus look good. In addition, the new model is able to capture the frequency and structure of important weather events (e.g., tropical cyclones, extratropical cyclones including atmospheric rivers, and cold air outbreaks). Interestingly, this model does not get rid of the erroneous southern branch of the intertropical convergence zone nor the tendency for strongest convection to occur over the Maritime Continent rather than the West Pacific, both of which are classic climate model biases. Several other problems with the simulation are identified, underscoring the fact that this model is a work in progress.

54 ENVIRONMENTAL SCIENCES↗

X-Band Radar and Surface-Based Observations of Cold-Season Precipitation in Western Colorado’s Complex Terrain

Abstract Hydrologic processes associated with intermountain cold-season precipitation in the Upper Colorado River basin have important impacts on avalanche forecasting and water resource management. However, traditional weather radar networks struggle with observations in this complex terrain. Data collected during the Study of Precipitation, the Lower Atmosphere, and the Surface for Hydrometeorology (SPLASH) and its sister campaign, Surface Atmosphere Integrated Field Laboratory (SAIL) in the East River watershed of western Colorado, are used to examine a multistorm period from 23 December 2021 to 1 January 2022 that contributed 35% of the total winter precipitation in this watershed. Dual-polarization X-band radar and disdrometer measurements show ∼30-mm differences in precipitation amount at two sites in proximity over four distinct storm events within the period. Wind patterns, synoptic forcings, microphysical characteristics of precipitation, and surface meteorology are analyzed to explain the observed spatial variability of cold-season precipitation in complex mountainous terrain. Analysis shows that differences over time within this event are mainly accounted for by synoptic forcings, such as frontal passages; differences between sites are accounted for by the impact of variations in local wind patterns on precipitation microphysics. Patterns of surface precipitation intensity are compared and found to be correlated with X-band radar signatures; a relationship between a strong dendritic growth stage and intense low-density surface precipitation is reinforced by this study. This relationship demonstrates the importance of particle growth mechanisms on surface snowfall patterns in high-altitude complex terrain, underscoring the importance of realistic microphysical parameterizations. Significance Statement The amount and density of snowpack from western Colorado winter storms have significant impacts on water resources in the Upper Colorado River basin. Snowpack characteristics are affected by small-scale differences in how snow forms in the atmosphere. These differences are hard to study in the complex terrain of the Rockies, but data from the SPLASH and SAIL field campaigns allows us to investigate how snow crystal formation and mountain-driven wind patterns affect snow near the surface. Our study finds that snow crystal growth varies over small space and time scales and is likely controlled by the terrain beneath a given location and resultant local wind patterns. These results imply that predicting snowpack in the Rockies requires properly representing local wind patterns and crystal growth processes in models.

Heflin, Stella↗

Prediction of convective activity using a system of parasitic-nested numerical models

A limited area, three dimensional, moist, primitive equation (PE) model is developed to test the sensitivity of quantitative precipitation forecasts to the initial relative humidity distribution. Special emphasis is placed on the squall-line region. To accomplish the desired goal, time dependent lateral boundaries and a general convective parameterization scheme suitable for mid-latitude systems were developed. The sequential plume convective parameterization scheme presented is designed to have the versatility necessary in mid-latitudes and to be applicable for short-range forecasts. The results indicate that the scheme is able to function in the frontally forced squallline region, in the gently rising altostratus region ahead of the approaching low center, and in the over-riding region ahead of the warm front. Three experiments are discussed.

Perkey, D. J.↗

Initialization and assimilation of cloud and rainwater in a regional model

The initialization and assimilation of cloud and rainwater quantities in a mesoscale regional model was examined. Forecasts of explicit cloud and rainwater are made using conservation equations. The physical processes include condensation, evaporation, autoconversion, accretion, and the removal of rainwater by fallout. These physical processes, some of which are parameterized, represent source and sink in terms in the conservation equations. The question of how to initialize the explicit liquid water calculations in numerical models and how to retain information about precipitation processes during the 4-D assimilation cycle are important issues that are addressed.

Raymond, William H.↗

Tracking Aerosol Convection Interactions Experiment (TRACER) Field Campaign Report

Convective clouds serve a critical role in the Earth’s energy and water cycles through their transport of heat, moisture, momentum, and chemical species through the troposphere driving the global circulation (e.g., Hartmann et al. 1984, Del Genio et al. 2012, Su et al. 2014). On more local scales, convective clouds impact the atmospheric heating profile through diabatic heating effects, removal of water from the atmospheric column through precipitation, and conditioning of the local environment impacting further development of clouds (e.g., Sullivan and Voigt 2021). These critical roles underscore the importance of realistic representation of convective processes across scales of models from large-eddy simulation (LES), to convection-permitting models (CPM; e.g., Kendon et al. 2020, Marinescu et al. 2021), to numerical weather prediction (NWP) models used for operational weather forecasting, to Earth system models used to predict climate sensitivity (Sanderson et al. 2011, Sherwood et al. 2014, Tomassini et al. 2014, Zhao et al. 2016, Cronin et al. 2017). A key component of improving model representation of convective clouds is better quantification and parameterization of updraft microphysics and dynamics, including their interactions with the surrounding environment and storm organization (Bony et al. 2015, Hagos and Houze 2016, Donner et al. 2016, Morrison et al. 2020). Aerosol is an important environmental factor that could affect convective clouds and precipitation since cloud droplet and ice formation processes are initiated by it. Andrae et al. (2004) hypothesized that aerosols associated with increased biomass burning particles acting as cloud condensation nuclei (CCN) result in smaller and more monodisperse cloud droplets leading to suppression of warm rain formation, ultimately leading to more cloud water being lofted above the freezing level based on observations in the Amazon region. The subsequent increase in latent heat release increases the buoyancy of rising convective parcels invigorating the deep convection. This work was followed by a description of the theoretical basis for this “cold-phase invigoration” by Rosenfeld et al. (2008), who argued that it could have a significant effect for deep convective clouds with warm cloud-bases. Several modeling studies (e.g., Khain et al. 2005, 2009, van den Heever et al. 2006, Fan et al. 2007, 2009, 2012, Lee et al. 2008, Storer et al. 2010, Lebo et al. 2012, Storer and van den Heever 2013, Chen et al. 2020, Dagan et al. 2022) have investigated these aerosol-convection interactions and the environmental factors that influence their relative importance and magnitude. More recently, several studies have indicated that “warm-phase invigoration”, the enhancement of convection through condensational heating, also appears to play a role in enhancing both shallow cumuli (Seiki and Nakajima 2014, Saleeby et al 2015) and deeper tropical convection (Lebo and Seinfeld 2011, Khain et al. 2012, Sheffield et al 2015, Fan et al. 2018, Igel and van den Heever 2021), as well as Houston thunderstorms (Fan et al. 2007, 2020). However, still other studies have provided additional evidence of systematic biases in simulated convective outflow ice size distribution properties, which are consistent with a lack of poorly understood secondary ice production within convective updrafts (e.g., Fridlind et al. 2017). To help address these critical gaps in our understanding of cloud processes, aerosol processes and aerosol-cloud interactions, the Tracking Aerosol Convection Interactions Experiment was designed building upon efforts by the Aerosol, Cloud, Precipitation and Climate (ACPC) Initiative (http://acpcintiative.org/), a joint effort of the International Geosphere-Biosphere Programme (IGBP) and the World Climate Research Program (WCRP) that focused on resolving uncertainties in the interactions between aerosol and clouds towards better understanding the role that these interactions play in the climate system. The TRACER campaign was motivated by recommendations from a number of pilot studies undertaken by ACPC (van den Heever et al. 2017, Fridlind et al. 2019, Hu et al. 2019, Fan et al. 2020, Marinescu et al. 2021, Hernandez-Deckers et al. 2022) that pointed towards the southeastern Texas region as a locale where aerosol-convection interactions could be studied owing to the copious occurrence of isolated convection during the summer months accompanied by diverse and significant sources of aerosols from both anthropogenic and natural sources. The TRACER campaign began on 01 October 2021 and extended through 30 September 2022 with an intensive operational period (IOP) during June-September 2022. Three main sites (Table 1) were managed by the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) user facility.

54 ENVIRONMENTAL SCIENCES↗

Scrutinizing entrainment and mass flux closures in shallow cumulus parameterizations using cloud-radar observations and large-eddy simulation (Final Report)

Representing warm, shallow clouds is a challenge for Global Climate Models, which leads to uncertainty in model projections of future climate. Our study was particularly concerned with how climate models represent the effects of shallow, non-precipitating cumulus clouds. Climate models must make certain assumptions when representing low clouds such as how much dry air from outside the cloud is mixed into the warm, moist cloud updraft. This process is called “entrainment” and tends to weaken the cloud updraft and dry out the cloud, compared to a theoretical cloud with no mixing. This project was a joint observational and modeling study to derive estimates of entrainment from field observations and use high-resolution modeling to evaluate the assumptions used in climate model representations of shallow cumulus. Our research took advantage of a wide variety of Department of Energy measurements from fixed climate-monitoring locations over the Southern Great Plains of the U.S. and the in the Eastern North Atlantic, along with short-term field projects (MAGIC, CAP–MBL, ACE–ENA). During the project, the PI maintained regular collaborations with Department of Energy Scientists at Brookhaven and Argonne National Laboratories. The project funded two students, who both obtained their M.S. in Atmospheric Science and are currently in the Atmospheric Science Ph.D. program. Both were lead authors on research papers funded by this grant.

54 ENVIRONMENTAL SCIENCES↗

Evaluating and Improving Convective Parameterization for GCMs Using ARM Observations. Final report

This technical report summarizes the achievements during the project period funded by the Atmospheric System Research (ASR) program. The general goal of the project is to improve the representation of atmospheric deep convection in global climate models. By using DOE Atmospheric Radiation Measurement (ARM) program observations and a hierarchy of models from cloud-resolving to global climate models, we evaluated and improved many aspects of convection parameterization schemes, such as the trigger function for convection and closure condition to determine the amount of convection. We also incorporated the stochasticity of convection into a convection scheme. These improvements, when implemented into the National Center for Atmospheric Research (NCAR) Community Earth System Model (CESM) and the DOE Exascale Energy Earth System Model (E3SM), led to improved simulation of precipitation characteristics, including precipitation intensity, Intertropical Convergence Zone, and Madden-Julian oscillation. The project also improved the representation of microphysical processes in convective clouds. It enables the interaction of cloud microphysics with aerosols in weather and climate models.

54 ENVIRONMENTAL SCIENCES↗

Potential of GPM IMERG Precipitation Estimates to Monitor Natural Disaster Triggers in Urban Areas: the Case of Rio deJaneiro, Brazil

Extreme rainfall can be a catastrophic trigger for natural disaster events at urban scales. However, there remains large uncertainties as to how satellite precipitation can identify these triggers at a city scale. The objective of this study is to evaluate the potential of satellite-based rainfall estimates to monitor natural disaster triggers in urban areas. Rainfall estimates from the Global Precipitation Measurement (GPM) mission are evaluated over the city of Rio de Janeiro, Brazil, where urban floods and landslides occur periodically as a result of extreme rainfall events. Two rainfall products derived from the Integrated Multi-satellite Retrievals for GPM (IMERG), the IMERG Early and IMERG Final products, are integrated into the Noah Multi-Parameterization (Noah-MP) land surface model in order to simulate the spatial and temporal dynamics of two key hydrometeorological disaster triggers across the city over the wet seasons during 2001-2019. Here, total runoff (TR) and rootzone soil moisture (RZSM) are considered as flood and landslide triggers, respectively. Ground-based observations at 33 pluviometric stations are interpolated, and the resulting rainfall fields are used in an in-situ precipitation-based simulation, considered as the reference for evaluating the IMERG-driven simulations. The evaluation is performed during the wet seasons (November-April), when average rainfall over the city is 4.4mm/day. Results show that IMERG products show low spatial variability at the city scale, generally overestimate rainfall rates by 12-35%, and impacts on TR and RZSM vary spatially mostly as a function of land cover and soil types. Results based on statistical and categorical metrics show that IMERG skill in detecting extreme events is moderate, with IMERG Final performing slightly better for most metrics. By analyzing two recent storms, we observe that IMERG detects mostly hourly extreme events, but underestimates rainfall rates, resulting in underestimated TR and RZSM. An evaluation of normalized time series using percentiles shows that both satellite products have significantly improved skill in detecting extreme events when compared to the evaluation using absolute values, indicating that IMERG precipitation could be potentially used as a predictor for natural disasters in urban areas.

IMERG↗

Parameterized study of the ionospheric modification associated with sun-aligned polar cap arcs

The local ionospheric modification that is due to a generalized steady state solar aligned (SA) arc structure is addressed. For a representative set of SA arc parameters which includes both convection and precipitation, emphasis is placed on the modification by SA polar cap arcs upon the F region electron density and the height integrated conductivity. At low fluxes and low characteristic energies, SA polar cap arcs have the most pronounced relative effect at F region altitudes in darkness for winter solar minimum conditions. The absolute enhancement in summer solar minimum and winter solar maximum is equivalent to that of winter solar minimum, but the higher ambient densities make the relative enhancement less. The TEC enhancement associated with an SA arc may be used to indicate the degree of plasma cross flow across the arc.

Crain, D. J.↗