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DOE OSTI2021

Characterization of an electrically conductive proppant for fracture diagnostics

Fracture diagnosis with electromagnetic (EM) and electrical tools requires proppants with high electrical conductivity and mechanical strength. Lab measurements of the electrical and hydraulic conductivity of proppants are critical for selecting the best candidates. Such measurements greatly benefit simulations, field tests, and the ultimate application of such proppants in the field. To that end, a new lab protocol is developed for measuring the electrical and hydraulic conductivity of proppants. The lab setup, which mainly includes a resistivity core holder and a Hassler sleeve core holder, allows for simulation of realistic pressure and temperature conditions when making measurements. Petroleum coke (PC) is proposed as a candidate proppant because of its widespread availability and low cost. Lab measurements show that the effective electrical conductivity of pure PC in a model fracture is approximately 5000 S/m, under a closure stress greater than [Formula: see text] (4000 psi). When PC is mixed with sand, the effective electrical conductivity of the mixture decreases with an increasing weight percentage of sand. Although sand degrades the contact between PC particles, the electrical conductivity stays reasonably high (approximately 1700 S/m) when 50% sand is added. Hydraulic conductivity measurements show that when a fracture is propped with pure PC, the measured fracture conductivity is greater than [Formula: see text] ([Formula: see text]) (dimensionless fracture conductivity greater than 100 for a shale with [Formula: see text] or 100 nD permeability) under a confining pressure of [Formula: see text] (6000 psi). This means that a fracture propped with PC is infinitely conductive in a typical shale formation. When sand is added, the fracture’s hydraulic conductivity becomes even higher, which clearly shows PC’s ability of sustaining high stresses. The proposed protocol provides a robust and effective method that can be generalized for lab testing for other candidate proppants. The data presented clearly show that PC has the potential for field-scale applications in EM hydraulic fracture diagnostics.

Geochemistry & Geophysics↗

DOE OSTI2024

Competitiveness Assessment of Decarbonizing Electricity and Process Heat Supply to a Campus with a Small Nuclear Reactor

This paper analyzes the competitiveness of siting a small nuclear reactor to support decarbonization of sites requiring tens of MW of electricity and/or process heat to support centralized heating and cooling system. This paper focuses on campuses as representative of sites with collections of buildings and research facilities with decarbonization needs represented by buildings heating, and electricity consumption by electrical loads which may include cooling via chilled water (e.g., for air conditioning and to cool down computer clusters). A nuclear reactor can be considered to decarbonize a site’s high-temperature steam generation used mostly for building heating needs, climate control, and hot water, by supplying process heat capabilities, while electricity decarbonization would be achieved mostly by the grid. However, a secondary application can be considered to maximize reactor utilization and avoid ramping down the reactor if the steam demand varies significantly throughout the year. Chilled water generation through steam-driven systems was identified as an attractive secondary option for the site analyzed, due to potential for plant design simplification, while electricity generation could be considered as well to reduce electricity purchases for a wider range of site applications. For a campus with peak 60MW thermal power demand, a small nuclear reactor with similar thermal power rating would almost eliminate CO2 emissions from steam generation and reduce electricity imports for chilled water production. A preliminary techno-economic feasibility study shows that a small nuclear reactor design that is optimized to support process heat can represent an economically feasible option when compared with other decarbonization alternatives.

Stauff, Nicolas E.↗

DOE OSTI2023

High-pressure electrical conductivity and elasticity of iron-bearing δ-AlOOH

Abstract The electrical conductivity and elasticity of deep hydrous phases are essential to constraining water distribution, as well as deciphering the origins of conductivity anomalies in the lower mantle. To uncover the impact of iron-bearing δ-AlOOH on the geophysical properties of the lower mantle, we carried out synchrotron X-ray diffraction and electrical conductivity measurements on δ-(Al0.52Fe0.48)OOH and (Al0.95Fe0.05)OOH in diamond-anvil cells at pressures up to 75 GPa at room temperature. A sharp volume reduction of ~6.5% was observed in δ-(Al0.52Fe0.48)OOH across the spin transition at 40.8–43.3 GPa, where its electrical conductivity increases steadily without abrupt changes. The electrical conductivity of δ-(Al0.52Fe0.48)OOH is greater than that of pure δ-AlOOH at high pressure, suggesting that both small polaron and proton conduction mechanisms dominate in iron-bearing δ-AlOOH. Furthermore, the high-pressure electrical conductivity profiles are comparable between δ-(Al0.95Fe0.05)OOH and δ-(Al0.52Fe0.48)OOH, indicating that high-iron content only marginally influences the conductivity of iron-bearing δ-AlOOH. Notably, the electrical conductivity of iron-bearing δ-AlOOH along the North Philippine geotherm is greater than the average 1D electrical conductivity profile in the mantle (Ohta et al. 2010a). This result suggests that δ-(Al,Fe)OOH is a promising candidate to account for high conductivity in some subducting slabs.

Geochemistry & Geophysics↗

DOE OSTI2020

Dual Phase Soft Magnetic Laminates for Low-cost, Non/Reduced-Rare-Earth Containing Electrical Machines

To accelerate the mass market adoption of electric drive vehicles, the key technology barriers in electric motors are (1) magnet cost and rare-earth element price volatility; (2) non-rare-earth electric motor performance; and (3) materials property optimization. The goal of this project was to address these barriers by advancing a unique and innovative dual phase soft magnetic material technology and demonstrating the material in a 30-kW synchronous reluctance motor without using any permanent magnet for electric vehicles. Dual phase magnetic materials offer the electric motor designer the ability to locally control the magnetic saturation level in a motor laminate, while at the same time enhancing the mechanical strength of the laminate material, resulting in an enhancement in motor performance and efficiency. Scalable dual phase soft magnetic laminates manufacturing technologies were developed in collaboration with multiple US manufacturers. 1000 lbs of alloy sheet with a thickness of 0.25mm and width of 280 mm was manufactured within the specifications. Batch sizes of up to 240 laminates per run were produced from the alloy sheet. Two prototype motors with dual phase soft magnetic laminates were designed, built, and tested. The major goal of building the subscale prototype as a pathway to develop scalable manufacturing technologies for the dual phase soft magnetic laminates was met. The additional goal of building and testing the subscale prototype in order to validate the calculated performance with the tested motor performance was also met. For the full-scale 30kW continuous power synchronous reluctance motor prototype, the tested performance met the targets in terms of continuous power at the operating speeds up to 8000 rpm. Post-test studies were conducted and the root causes for the discrepancy between the predicted and tested peak power, continuous power at high speed range, and efficiency were identified. Further modeling study showed that the dual phase rotor machine has a 27% higher torque to active weight ratio than an equivalent performance silicon steel rotor machine. Application space and multiple discussions with traction motor and electric vehicle manufacturers for commercialization of the dual phase soft magnetic material technology were identified and conducted. An initial cost model was established based on the developed manufacturing technologies with the US manufacturers. Future paths for further cost reduction were identified, including increasing the market volume by broadening the applications of the dual phase soft magnetic laminate technology for electric machines in other energy sections such as oil & gas, heating, ventilation, and air conditioning (HVAC), and power generation.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2021

Competitiveness Metrics for Electricity System Technologies

The relative economic competitiveness of power generation technologies is a topic of much interest to diverse electric industry participants. However, assessing competitiveness can be challenging as it requires considering both total costs and total system value of each technology, which are complicated by the (1) numerous and diverse grid services needed to operate a reliable power system; (2) variations in the economic value of the grid services with system state and location, and over multiple timescales, due to the challenges of transporting and storing electricity; and (3) the unique characteristics of different electric system assets. Ideally, metrics designed or used to convey technology competitiveness must consider these complexities, but existing metrics often fall short. For example, the levelized cost of energy does not consider the system economic value of the various technologies nor does it consider services beyond electricity production. Various other metrics have been designed with the purpose of more-accurately communicating the economic viability of electric system technologies. In this report, we summarize the primary sources and components of costs and value and review the known competitiveness metrics by presenting their definitions, applications, advantages, and disadvantages. We also introduce a new set of competitiveness metrics, which we refer to as System Profitability metrics, that more-directly applies the economic principles of return-on-investment to electric system technologies. We use conceptual examples to show how the System Profitability metrics better reflect economic viability and relative technology competitiveness compared with existing metrics. We also describe how competitiveness metrics can be quantified using optimization-based models and demonstrate this capability using a U.S. electric sector capacity expansion model.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

Electric Field Measurements at the Surface of a Piezoelectric Transformer for Plasma Jet Formation using the Plasma Research Facility at Sandia National Laboratory (Final Report)

The overall goal of this research is to understand how low-temperature non-equilibrium plasmas form directly off the surface of piezoelectric crystals. Specifically, this project aims to temporally and spatially resolve how the electric field evolves on and near the surface of a piezoelectric transformer (PT) at conditions that produce an atmospheric-pressure air plasma jet emanating from the corner of the PT. In this work, we used the Plasma Research Facility (PRF) at Sandia National Laboratory to conduct temporally- and spatially-resolved electric field induced second harmonic (E-FISH) measurements of the electric field at and near the surface of a piezoelectric transformer, providing a fundamental understanding of how piezoelectric crystals can be used for plasma generation. We carried out two Objectives: Objective 1 – The first objective was to measure the temporal and spatial evolution of the electric field along the surfaces approaching the corner of a rectangular PT just below conditions that lead to plasma jet formation. Such a measurement can be used to explain when and where the electric field peaks, leading to plasma formation; Objective 2 – The second objective was to measure the temporal and spatial evolution of the electric field along the surfaces approaching the corner of a rectangular PT just at conditions of plasma jet formation. This, in principle, gives a more accurate determination of how the electric field leads to plasma formation but is more difficult due to the relatively stochastic plasma jet behavior of a PT. This work was complemented by an award from the Sandia PRF, and we worked with Dr. Edward Barnat at the Sandia PRF to carry out these objectives.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

The Role of Innovation in the Electric Utility Sector

Innovation is essential for future power systems to be safe and secure, clean and sustainable, affordable and equitable, and reliable and resilient, according to a recent National Academies report. But state regulatory reforms are needed to encourage adoption of new technologies to support evolution of the nation’s power systems.1 Berkeley Lab's report, The Role of Innovation in the Electric Utility Sector, provides consumer, labor, utility, third-party provider, and clean technology consultant perspectives on this theme. To achieve state targets for clean energy and greenhouse gas emissions, some state regulatory utility commissions are exploring new approaches to spur innovation: -For utilities, regulatory and marketing flexibility, increased funding for demonstration projects, and performance-based ratemaking including multi-year rate plans -For third parties, ways to provide utility customers with innovative products and services directly Among the questions the report addresses: 1. How are consumer advocate views evolving with respect to innovative regulatory and ratemaking approaches? 2. How can utility decarbonization and grid modernization initiatives provide opportunities for local communities and workers to receive tangible benefits and facilitate community support for siting electricity infrastructure? 3. How are electric utilities partnering with technology companies to provide innovative energy management services and sustainable energy solutions for utility customers? 4. What regulatory innovations are public utility commissions exploring to enable third-party providers to participate in the transition to a modern electric system? 5. What regulatory changes are needed to enable innovative solutions from utilities and third parties at the necessary speed and scale to meet state decarbonization goals? The report is the 13th in the Future Electric Utility Regulation series, which taps leading thinkers to tackle complex regulatory issues for electricity. 1 National Academies of Sciences, Engineering, and Medicine. 2021. The Future of Electric Power in the United States. The National Academies Press.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Exploration of a Novel Technique for Waste Heat Recovery Through Molecular Dynamics: Influence of Wettability and Electric Field on Water and Water-Based Nanofluids

Most of the energy produced globally comes by way of a heat engine. The Carnot principle places a limit as to how thermodynamically efficient a heat engine can be. There is no heat engine that can be 100% thermodynamically efficient and as such a substantial proportion of all heat supplied to a heat engine is lost as waste heat. Waste heat therefore is a large energy source ready to be properly utilized. Herein, a novel approach for converting waste heat to electricity is discussed. It involves the use of the liquid to vapor phase change of a material dielectric (water) or electrolyte (nanofluid) in the embodiment of a capacitor for direct thermal to electrostatic energy conversion. While this method of waste heat recovery could potentially be added to the ever expanding portfolio of energy conversion techniques, a number of aspects must be addressed before it can be brought into practice. Water was seen as an ideal dielectric phase change material given its high relative permittivity ratio when in the liquid form as compared to its vapor form. However, given its short voltage holdoff time the phase change of water would need to occur rapidly. This brings up concerns of explosive boiling. Herein, molecular dynamics analysis into the explosive boiling behavior of thin water films gave more insight into how the interaction between the surface and liquid affected explosive boiling onset time. A Lennard-Jones potential with one interaction site and a Morse potential with three interaction sites between water and solid substrate were used. It was found generally that a stronger interaction between water film and substrate led to faster explosive boiling onset times but an increase in the number of interaction sites delayed explosive boiling, even at the same wettability (contact angle). Understanding changes in the density and enthalpy of vaporization of a liquid dielectric such as water in the presence of an electric field is of importance due to the electrostatic nature of the waste heat conversion method under consideration. Specifically, if both density and enthalpy of vaporization are increased, the thermodynamic efficiency of the waste heat conversion method under consideration is decreased. Electric field effects are explored herein via molecular dynamics using two water models, the TIP4P-Ew and SWM4-NDP. The SWM4-NDP model is polarizable while the TIP4P-Ew model is not, which allows for a determination of the importance of model polarizability (i.e. variation in water model dipole moment) on these two properties of water when subjected to an electric field. Herein it was found that both water models respond similarly in terms of density and vaporization enthalpy variance upon the introduction of an electric field. Comparison was also made to the pressure induced by the electric field (electrostriction pressure) by way of a density comparison and it was found that the predicted electrostriction pressure overestimates the pressure experienced by water. Water by itself has a high enthalpy of vaporization, which limits the efficiency of the newly proposed conversion method. Research both experimental and through simulation has shown that the vaporization enthalpy of nanofluids can be engineered via nanoparticle size and material selection. An avenue less explored is manipulating the enthalpy of vaporization by altering the interaction strength between the nanoparticles and the base fluid. In practice this could be achieved through the addition of coatings to the nanoparticles to alter their wettability to the base fluid. This was explored by using a Lennard-Jones potential and Morse potential to model the interaction between base fluid (water) and the nanoparticle. For nanoparticles 2nm in diameter and at weight percentages up to 6%, the change in vaporization enthalpy due to alterations of the interaction strength between nanoparticle and base fluid was not significant (less than a 1% difference) when compared to the effect of altering the weight percentage of nanoparticles in the nanofluid or introducing an electric field. However, the effect of wettability may still become important at other nanoparticle concentrations and sizes. In all, the studies presented here further the understanding of phase change and thermodynamic properties of water and water based nanofluids under an electrostatic field which will help inform the development of a novel approach to waste heat conversion. The reduction of waste heat will improve energy sustainability outlooks.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2023

PR100: Estimated Medium- and Heavy-Duty Electric Vehicle Adoption and Load Estimation in Puerto Rico through 2050

The 2-year Puerto Rico Grid Resilience and Transition to 100% Renewable Energy Study analyzed stakeholder-driven pathways to Puerto Rico’s clean energy future. Outputs relating to electricity demand modeling were partially informed by estimates of electric vehicle adoption across all classes of medium- and heavy-duty vehicles (MHDVs), and the ensuing charging loads. To create these estimates, the team developed a transportation model for MHDVs in Puerto Rico to estimate the amount and geospatial distribution of energy used. Charging schedules for the different end uses of MHDVs were then used to construct electric load shapes assuming a portion of those vehicles would be replaced by battery electric counterparts. Study results showed that, by 2050, electric vehicles may constitute roughly 50% of the MHDV population in Puerto Rico. The resulting electrical demand curve attributable to MHDV charging showed that, for solar energy-based electrical systems with limited energy storage, this demand may create challenges unless appropriately managed either on the demand or supply side.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

Retail Electricity Price and Cost Trends: 2024 Update [Slides]

Berkeley Lab’s "Retail Electricity Price and Cost Trends" summarizes recent trends in retail electricity price levels and price drivers in the United States. This report is intended to serve as a reference document for the diverse set of decision-makers impacted by changes in retail electricity prices and to provide a factual basis for assessing recent changes in retail electricity prices and key underlying drivers. National, regional, and state trends are reported for 2019 through 2023 using publicly-available data for: -Average retail electricity prices, retail sales, and utility revenues -Utility capital expenditures, operations and maintenance costs, and fuel and purchased power costs -Retail electricity sales impacts from behind-the-meter resources The report also includes qualitative case studies highlighting recent and/or regionally-specific issues contributing significantly to retail electricity price trends

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

Electricity Rate Designs for Large Loads: Evolving Practices and Opportunities

Electricity demand from large load customers such as data centers is projected to grow significantly in the near term. While data centers play an important role in advancing technology innovation and economic growth in the United States, data center energy needs present challenges and opportunities for electricity supply and infrastructure. This technical brief serves as a foundation for the discussion of issues and sharing of perspectives among utilities, regulators, large load customers, and other stakeholders. As utilities and regulators explore rate structures to address growing data center electricity demand, several issues have emerged: -Fair allocation of electricity system costs to large-load customers without unfair shifting of costs to other customers -Appropriate mitigation of the financial risks associated with stranded assets from underutilized utility system investments -Mitigation of operational and resource adequacy risks if electricity demand exceeds supply -Appropriate risk-sharing in commercializing newer electricity technologies such as advanced geothermal, small modular reactors, and long duration energy storage -Accommodating the diverse needs of large-load customers, such as having the option to match electricity consumption with output from carbon-free resources or using onsite generation to provide system capacity The technical brief also identifies key design elements that aim to address these issues and uses leading examples from pending and approved rate structures, agreements, and special contracts to ground the elements in practice.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Multi-Year Electric Field Study at the North Slope of Alaska (OYESNSA) Field Campaign Report

The Global Electric Circuit (GEC) of the atmosphere provides a unique perspective on Earth’s changing climate. Monitoring this global electrical signature provides details of the global nature of electrified clouds and thunderstorms. The North Slope of Alaska (NSA) is a unique location for collecting these electric field measurements. Besides being at the opposite pole from many previous electric field measurements taken at Russia’s Vostok station in Antarctica, this site provides a rare opportunity to use other instruments at the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) User Facility’s NSA observatory at Utqiaġvik (formerly known as Barrow), such as the Ka-band ARM Zenith Radar (KAZR), upward-facing micropulse lidar (MPL), vertical profile of meteorological measures, and other aerosol measurements. Since 2017, Texas A&M University at Corpus Christi (TAMUCC) has established an observational instrument package, including CS110 electric fields and anemometer, at ARM’s NSA observatory at Utqiaġvik. This enabled the unique opportunity to not only provide information about the global signature of the GEC, but also the physical inputs to the local electric field, by analyzing the physical properties of the simultaneous cloud, wind, and aerosol properties occurring with the vertical electric field.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Multi-Year Electric Field Study at the North Slope of Alaska (OYESNSA) Field Campaign Report

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Environmental and Economic Assessment of Portable Systems: Production of Wood-Briquettes and Torrefied-Briquettes to Generate Heat and Electricity

This study assessed the environmental impacts and economic feasibility of generating heat using wood-briquettes (WBs), and heat and electricity using torrefied-wood-briquettes (TWBs). WBs and TWBs were manufactured from forest residues using portable systems and delivered to either residential consumers or power plants in the United States. An integrated cradle-to-grave life-cycle assessment (LCA) and techno-economic analysis (TEA) approach was used to quantify environmental impacts and minimum-selling prices (MSPs) of heat and electricity, respectively. Results illustrated that 82% and 59% of the cradle-to-grave global warming (GW) impact of producing heat resulted from the feedstock preparation in WBs and torrefaction in TWBs, respectively. About 46–54% of total cost in the production of heat were from labor and capital costs only. The GW impact of electricity production with TWBs was dominated by the torrefaction process (48% contribution). Capital cost (50%) was a major contributor to the total cost of electricity production using TWBs. The GW impacts of producing heat were 7–37 gCO₂eq/MJ for WBs, and 14–51 gCO₂eq/MJ for TWBs, whereas producing electricity using TWBs was 146–443 gCO₂eq/kWhe. MSPs of generating heat from WBs and TWBs were €1.09–€1.73 and €1.60–€2.26/MJ, respectively, whereas the MSP of electricity from TWBs was €20–€25/kWhe. Considering carbon and pile-burn credits, MSPs of heat and electricity were reduced by 60–90% compared to the base-case.

Sahoo, Kamalakanta (ORCID:0000000277635296)↗

NASA NTRS1973

Direct comparison between satellite electric field measurements and the visual aurora

Electric field data from two passes of the Injun 5 satellite, one corresponding to magnetically quiet conditions and one corresponding to substorm conditions, are compared with simultaneous all-sky camera data from College, Alaska. In each case, a significant deviation of the electric field from the expected V x B field (where V is the satellite velocity) was evident, and a distinct electric field reversal could be identified. In the region of substantial electric field equatorward of the electric field reversal, a diffuse auroral arc was observed during the magnetically quiet pass, and auroral patches were observed during the substorm pass. In the substorm case, the electric field reversal occurred very near a discrete auroral arc at the poleward side of the diffuse arcs and patches. Comparison of the quiet time and substorm cases suggests that the convection electric field penetrates deeper into the magnetosphere during a substorm.

Swift, D. W.↗

NASA NTRS1975

Magnetotail electric fields observed from lunar orbit

Direct observations of convection electric fields in the earth's magnetotail are reported. The electric fields have been measured from lunar orbit by detection of the E x B/B-squared drift displacement of low-energy electrons at the limb of the moon. It is found that electric fields range in magnitude from a value less than or equal to 0.02 mV/m, the limit of sensitivity of the method, to 2 mV/M. The typical value is 0.15 mV/M, and the corresponding convection velocity is 15 km/s. The sense of the electric field is almost always dawn to dusk. The electric field is often variable on a time scale of hours and sometimes minutes. The observations indicate that the electric field is not uniform across the magnetotail. If it is assumed that the typical measured electric-field value represents an average over the inhomogeneities, the potential drop across the entire tail is of the order of 40 kV.

Mccoy, J. E.↗

NASA NTRS1977

The influence of convection electric fields on thermal proton outflow from the ionosphere

The continuity, momentum and energy hydrodynamic equations for an O(+)-H(+) ionosphere have been solved self-consistently for steady state conditions when a perpendicular (convection) electric field is present. Comparison of the H(+) temperature profiles obtained with and without the electric field show that the effect of the electric field is to enhance the H(+) temperature at high altitudes from about 3600 to 6400 K. Due to ion heating by the electric field, there is a net reduction of O(+) in the F2-region as compared with the case of a nonconvecting ionosphere. When the reduction of O(+) is neglected, the electric field acts to increase the H(+) outward flux. However, when the reduction of O(+) is included, there is a net reduction in the outward H(+) flux. Nevertheless, the convection electric field still results in an increase in the rate of depletion of the F-region ionization due to H(+) outflow, by a factor of 2.2 for a 100 mV/m electric field.

Raitt, W. J.↗

NASA NTRS1979

Solar-terrestrial coupling through atmospheric electricity

There are a number of measurements of electrical variations that suggest a solar-terrestrial influence on the global atmospheric electrical circuit. The measurements show variations associated with solar flares, solar magnetic sector boundary crossings, geomagnetic activity, aurorae, differences between ground current and potential gradients at high and low latitudes, and solar cycle variations. The evidence for each variation is examined. Both the experimental evidence and the calculations made with a global model of atmospheric electricity indicate that there is solar-terrestrial coupling through atmospheric electricity which operates by altering the global electric current and field distribution. A global redistribution of currents and fields can be caused by large-scale changes in electrical conductivity, by alteration of the columnar resistance between thunderstorm cloud tops and the ionosphere, or by both. If the columnar resistance is altered above thunderstorms, more current will flow in the global circuit, changing the ionospheric potential and basic circuit variables such as current density and electric fields. The observed variations of currents and fields during solar-induced disturbances are generally less than 50% of mean values near the earth's surface.

Roble, R. G.↗