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94-524: Arithmetically the EROI can be defined as: When the EROI of a source of energy is less than or equal to one, that energy source becomes a net "energy sink", and can no longer be used as a source of energy. A related measure, called energy stored on energy invested ( ESOEI ), is used to analyse storage systems. To be considered viable as a prominent fuel or energy source a fuel or energy must have an EROI ratio of at least 3:1. The energy analysis field of study

188-1086: A , b and c are arc lengths, in radians, of the sides of a spherical triangle. C is the angle in the vertex opposite the side which has arc length c . Applied to the calculation of solar zenith angle Θ , the following applies to the spherical law of cosines: C = h c = Θ a = 1 2 π − φ b = 1 2 π − δ cos ⁡ ( Θ ) = sin ⁡ ( φ ) sin ⁡ ( δ ) + cos ⁡ ( φ ) cos ⁡ ( δ ) cos ⁡ ( h ) {\displaystyle {\begin{aligned}C&=h\\c&=\Theta \\a&={\tfrac {1}{2}}\pi -\varphi \\b&={\tfrac {1}{2}}\pi -\delta \\\cos(\Theta )&=\sin(\varphi )\sin(\delta )+\cos(\varphi )\cos(\delta )\cos(h)\end{aligned}}} This equation can be also derived from

282-477: A 1:2.7 production for oxen). One can then use this to calculate the population of the Roman Empire required at its height, on the basis of about 2,500–3,000 calories per day per person. It comes out roughly equal to the area of food production at its height. But ecological damage ( deforestation , soil fertility loss particularly in southern Spain, southern Italy, Sicily and especially north Africa) saw

376-579: A PhD. Since then he has had a diverse career at Brookhaven Laboratory , The Ecosystems Center at the Marine Biological Laboratory, Woods Hole , Cornell University , University of Montana and, for the last 20 years, at the State University of New York College of Environmental Science and Forestry ( SUNY ESF ). Hall, professor of systems ecology at SUNY-ESF teaches a freshman course called The Global Environment and

470-481: A clear day. When 1361 W/m is arriving above the atmosphere (when the Sun is at the zenith in a cloudless sky), direct sun is about 1050 W/m , and global radiation on a horizontal surface at ground level is about 1120 W/m . The latter figure includes radiation scattered or reemitted by the atmosphere and surroundings. The actual figure varies with the Sun's angle and atmospheric circumstances. Ignoring clouds,

564-525: A collapse in the system beginning in the 2nd century, as EROI began to fall. It bottomed in 1084 when Rome's population, which had peaked under Trajan at 1.5 million, was only 15,000. Evidence also fits the cycle of Mayan and Cambodian collapse too. Joseph Tainter suggests that diminishing returns of the EROI is a chief cause of the collapse of complex societies, which has been suggested as caused by peak wood in early societies. Falling EROI due to depletion of high quality fossil fuel resources also poses

658-464: A consensus of observations or theory, Q ¯ day {\displaystyle {\overline {Q}}^{\text{day}}} can be calculated for any latitude φ and θ . Because of the elliptical orbit, and as a consequence of Kepler's second law , θ does not progress uniformly with time. Nevertheless, θ  = 0° is exactly the time of the March equinox, θ  = 90°

752-421: A day is the average of Q over one rotation, or the hour angle progressing from h = π to h = −π : Q ¯ day = − 1 2 π ∫ π − π Q d h {\displaystyle {\overline {Q}}^{\text{day}}=-{\frac {1}{2\pi }}{\int _{\pi }^{-\pi }Q\,dh}} Let h 0 be

846-404: A decrease thereafter. PMOD instead presents a steady decrease since 1978. Significant differences can also be seen during the peak of solar cycles 21 and 22. These arise from the fact that ACRIM uses the original TSI results published by the satellite experiment teams while PMOD significantly modifies some results to conform them to specific TSI proxy models. The implications of increasing TSI during

940-407: A deep solar minimum of 2005–2010) to be +0.58 ± 0.15 W/m , +0.60 ± 0.17 W/m and +0.85 W/m . Estimates from space-based measurements range +3–7   W/m . SORCE/TIM's lower TSI value reduces this discrepancy by 1   W/m . This difference between the new lower TIM value and earlier TSI measurements corresponds to a climate forcing of −0.8   W/m , which is comparable to

1034-429: A different perspective that mainstream economists do not share. Central to Halls argument is an understanding that the survival of all living creatures is limited by the concept of energy return on investment ( EROEI ): that any living thing or living societies can survive only so long as they are capable of getting more net energy from any activity than they expend during the performance of that activity. "Energy used by

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1128-569: A difficult challenge for industrial economies, and could potentially lead to declining economic output and challenge the concept (which is very recent when considered from a historical perspective) of perpetual economic growth. EROI is calculated by dividing the energy output by the energy input. Measuring total energy output is often easy, especially in the case for an electrical output where some appropriate electricity meter can be used. However, researchers disagree on how to determine energy input accurately and therefore arrive at different numbers for

1222-635: A falling EROI in the Later Roman Empire was one of the reasons for the collapse of the Western Empire in the fifth century CE. In "The Upside of Down" he suggests that EROI analysis provides a basis for the analysis of the rise and fall of civilisations. Looking at the maximum extent of the Roman Empire , (60 million) and its technological base the agrarian base of Rome was about 1:12 per hectare for wheat and 1:27 for alfalfa (giving

1316-490: A high-entropy wake, it spews degraded matter and energy, that is... waste heat, waste gases, toxic byproducts, the molecules of iron lost to rust and abrasion. Low entropy emissions include trash and pollution in all their forms. Matter taken up into the economy can be recycled, using energy; but energy, used once, is forever unavailable to us at that level again. The law of entropy commands a one-way flow downward from more to less useful forms. Thus, Georgescu-Roegen, paraphrasing

1410-469: A meta-study from 2013. Regarding output, it obviously depends on the local insolation , not just the system itself, so assumptions have to be made. Some studies (see below) include in their analysis that photovoltaic produce electricity, while the invested energy may be lower grade primary energy . A 2015 review in Renewable and Sustainable Energy Reviews assessed the energy payback time and EROI of

1504-1331: A more general formula: cos ⁡ ( Θ ) = sin ⁡ ( φ ) sin ⁡ ( δ ) cos ⁡ ( β ) + sin ⁡ ( δ ) cos ⁡ ( φ ) sin ⁡ ( β ) cos ⁡ ( γ ) + cos ⁡ ( φ ) cos ⁡ ( δ ) cos ⁡ ( β ) cos ⁡ ( h ) − cos ⁡ ( δ ) sin ⁡ ( φ ) sin ⁡ ( β ) cos ⁡ ( γ ) cos ⁡ ( h ) − cos ⁡ ( δ ) sin ⁡ ( β ) sin ⁡ ( γ ) sin ⁡ ( h ) {\displaystyle {\begin{aligned}\cos(\Theta )=\sin(\varphi )\sin(\delta )\cos(\beta )&+\sin(\delta )\cos(\varphi )\sin(\beta )\cos(\gamma )+\cos(\varphi )\cos(\delta )\cos(\beta )\cos(h)\\&-\cos(\delta )\sin(\varphi )\sin(\beta )\cos(\gamma )\cos(h)-\cos(\delta )\sin(\beta )\sin(\gamma )\sin(h)\end{aligned}}} where β

1598-497: A source of continued controversy is the creation of a different methodology endorsed by certain members of the IEA which for example most notably in the case of photovoltaic solar panels , controversially generates more favorable values. In the case of photovoltaic solar panels, the IEA method tends to focus on the energy used in the factory process alone. In 2016, Hall observed that much of

1692-426: A spectral graph as function of wavelength), or per- Hz (for a spectral function with an x-axis of frequency). When one plots such spectral distributions as a graph, the integral of the function (area under the curve) will be the (non-spectral) irradiance. e.g.: Say one had a solar cell on the surface of the earth facing straight up, and had DNI in units of W/m^2 per nm, graphed as a function of wavelength (in nm). Then,

1786-445: A standard practice for the supply chain energy input can be adopted. For example, consider the steel, but don't consider the energy invested in factories deeper than the first level in the supply chain. It is in part for these fully encompassed systems reasons, that in the conclusions of Murphy and Hall's paper in 2010, an EROI of 5 by their extended methodology is considered necessary to reach the minimum threshold of sustainability, while

1880-401: A surface is largest when the surface directly faces (is normal to) the sun. As the angle between the surface and the Sun moves from normal, the insolation is reduced in proportion to the angle's cosine ; see effect of Sun angle on climate . In the figure, the angle shown is between the ground and the sunbeam rather than between the vertical direction and the sunbeam; hence the sine rather than

1974-879: A time series for a Q ¯ d a y {\displaystyle {\overline {Q}}^{\mathrm {day} }} for a particular time of year, and particular latitude, is a useful application in the theory of Milankovitch cycles. For example, at the summer solstice, the declination δ is equal to the obliquity  ε . The distance from the Sun is R o R E = 1 + e cos ⁡ ( θ − ϖ ) = 1 + e cos ⁡ ( π 2 − ϖ ) = 1 + e sin ⁡ ( ϖ ) {\displaystyle {\frac {R_{o}}{R_{E}}}=1+e\cos(\theta -\varpi )=1+e\cos \left({\frac {\pi }{2}}-\varpi \right)=1+e\sin(\varpi )} For this summer solstice calculation,

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2068-417: A tool often used to understand well-being in a society. According to this calculation, the amount of energy a society has available to them increases the quality of life for the people living in that country, and countries with less energy available also have a harder time satisfying citizens' basic needs. This is to say that societal EROI and overall quality of life are very closely linked. The following table

2162-399: A value of 12–13 by Hall's methodology is considered the minimum value necessary for technological progress and a society supporting high art. Richards and Watt propose an Energy Yield Ratio for photovoltaic systems as an alternative to EROI (which they refer to as Energy Return Factor ). The difference is that it uses the design lifetime of the system, which is known in advance, rather than

2256-636: A variety of PV module technologies. In this study, which uses an insolation of 1700 kWh/m/yr and a system lifetime of 30 years, mean harmonized EROIs between 8.7 and 34.2 were found. Mean harmonized energy payback time varied from 1.0 to 4.1 years. In 2021, the Fraunhofer Institute for Solar Energy Systems calculated an energy payback time of around 1 year for European PV installations (0.9 years for Catania in Southern Italy, 1.1 years for Brussels) with wafer-based silicon PERC cells. In

2350-1003: Is sin ⁡ ( δ ) = sin ⁡ ( ε ) sin ⁡ ( θ ) {\displaystyle \sin(\delta )=\sin(\varepsilon )\sin(\theta )} . ) The conventional longitude of perihelion ϖ is defined relative to the March equinox, so for the elliptical orbit: R E = R o ( 1 − e 2 ) 1 + e cos ⁡ ( θ − ϖ ) {\displaystyle R_{E}={\frac {R_{o}(1-e^{2})}{1+e\cos(\theta -\varpi )}}} or R o R E = 1 + e cos ⁡ ( θ − ϖ ) 1 − e 2 {\displaystyle {\frac {R_{o}}{R_{E}}}={\frac {1+e\cos(\theta -\varpi )}{1-e^{2}}}} With knowledge of ϖ , ε and e from astrodynamical calculations and S o from

2444-457: Is π r , in which r is the radius of the Earth. Because the Earth is approximately spherical , it has total area 4 π r 2 {\displaystyle 4\pi r^{2}} , meaning that the solar radiation arriving at the top of the atmosphere, averaged over the entire surface of the Earth, is simply divided by four to get 340   W/m . In other words, averaged over

2538-411: Is a function of distance from the Sun, the solar cycle , and cross-cycle changes. Irradiance on the Earth's surface additionally depends on the tilt of the measuring surface, the height of the Sun above the horizon, and atmospheric conditions. Solar irradiance affects plant metabolism and animal behavior. The study and measurement of solar irradiance have several important applications, including

2632-461: Is a compilation of sources of energy. The minimum requirement is a breakdown of the cumulative energy expenses according to material data. Frequently in literature harvest factors are reported, for which the origin of the values is not completely transparent. These are not included in this table. The bold numbers are those given in the respective literature source, the normal printed ones are derived (see Mathematical Description). ESOEI (or ESOI e )

2726-447: Is a number of a day of the year. Total solar irradiance (TSI) changes slowly on decadal and longer timescales. The variation during solar cycle 21 was about 0.1% (peak-to-peak). In contrast to older reconstructions, most recent TSI reconstructions point to an increase of only about 0.05% to 0.1% between the 17th century Maunder Minimum and the present. However, current understanding based on various lines of evidence suggests that

2820-461: Is a photovoltaic panel manufacturing plant which can be made energy-independent by using energy derived from its own roof using its own panels. Such a plant becomes not only energy self-sufficient but a major supplier of new energy, hence the name solar breeder. Research on the concept was conducted by Centre for Photovoltaic Engineering, University of New South Wales, Australia. The reported investigation establishes certain mathematical relationships for

2914-403: Is a primary cause of the higher irradiance values measured by earlier satellites in which the precision aperture is located behind a larger, view-limiting aperture. The TIM uses a view-limiting aperture that is smaller than the precision aperture that precludes this spurious signal. The new estimate is from better measurement rather than a change in solar output. A regression model-based split of

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3008-438: Is absorbed and the remainder reflected. Usually, the absorbed radiation is converted to thermal energy , increasing the object's temperature. Humanmade or natural systems, however, can convert part of the absorbed radiation into another form such as electricity or chemical bonds , as in the case of photovoltaic cells or plants . The proportion of reflected radiation is the object's reflectivity or albedo . Insolation onto

3102-519: Is an American systems ecologist and ESF Foundation Distinguished Professor at State University of New York in the College of Environmental Science & Forestry. Hall was born near Boston , and received a B.A. in biology from Colgate University , and an M.A. from Penn State University . He trained as systems ecologist by Howard Odum at the University of North Carolina , where he received

3196-916: Is an angle from the horizontal and γ is an azimuth angle . The separation of Earth from the Sun can be denoted R E and the mean distance can be denoted R 0 , approximately 1 astronomical unit (AU). The solar constant is denoted S 0 . The solar flux density (insolation) onto a plane tangent to the sphere of the Earth, but above the bulk of the atmosphere (elevation 100 km or greater) is: Q = { S o R o 2 R E 2 cos ⁡ ( Θ ) cos ⁡ ( Θ ) > 0 0 cos ⁡ ( Θ ) ≤ 0 {\displaystyle Q={\begin{cases}S_{o}{\frac {R_{o}^{2}}{R_{E}^{2}}}\cos(\Theta )&\cos(\Theta )>0\\0&\cos(\Theta )\leq 0\end{cases}}} The average of Q over

3290-484: Is credited with being popularized by Charles A. S. Hall , a Systems ecology and biophysical economics professor at the State University of New York . Hall applied the biological methodology, developed at an Ecosystems Marine Biological Laboratory, and then adapted that method to research human industrial civilization. The concept would have its greatest exposure in 1984, with a paper by Hall that appeared on

3384-409: Is energy-dense and transportable, while wind is variable), when the EROI of the main sources of energy for an economy fall that energy becomes more difficult to obtain and its relative price may increase. In regard to fossil fuels, when oil was originally discovered, it took on average one barrel of oil to find, extract, and process about 100 barrels of oil. The ratio, for discovery of fossil fuels in

3478-680: Is exactly the time of the June solstice, θ  = 180° is exactly the time of the September equinox and θ  = 270° is exactly the time of the December solstice. A simplified equation for irradiance on a given day is: Q ≈ S 0 ( 1 + 0.034 cos ⁡ ( 2 π n 365.25 ) ) {\displaystyle Q\approx S_{0}\left(1+0.034\cos \left(2\pi {\frac {n}{365.25}}\right)\right)} where n

3572-408: Is expected to decrease from 44.4 in 1950 to a plateau of 6.7 in 2050. The standard EROI for natural gas is estimated to decrease from 141.5 in 1950 to an apparent plateau of 16.8 in 2050. The EROI for nuclear plants ranges from 20 to 81. The natural or primary energy sources are not included in the calculation of energy invested, only the human-applied sources. For example, in the case of biofuels

3666-456: Is known as Milankovitch cycles . Distribution is based on a fundamental identity from spherical trigonometry , the spherical law of cosines : cos ⁡ ( c ) = cos ⁡ ( a ) cos ⁡ ( b ) + sin ⁡ ( a ) sin ⁡ ( b ) cos ⁡ ( C ) {\displaystyle \cos(c)=\cos(a)\cos(b)+\sin(a)\sin(b)\cos(C)} where

3760-2450: Is nearly constant over the course of a day, and can be taken outside the integral ∫ π − π Q d h = ∫ h o − h o Q d h = S o R o 2 R E 2 ∫ h o − h o cos ⁡ ( Θ ) d h = S o R o 2 R E 2 [ h sin ⁡ ( φ ) sin ⁡ ( δ ) + cos ⁡ ( φ ) cos ⁡ ( δ ) sin ⁡ ( h ) ] h = h o h = − h o = − 2 S o R o 2 R E 2 [ h o sin ⁡ ( φ ) sin ⁡ ( δ ) + cos ⁡ ( φ ) cos ⁡ ( δ ) sin ⁡ ( h o ) ] {\displaystyle {\begin{aligned}\int _{\pi }^{-\pi }Q\,dh&=\int _{h_{o}}^{-h_{o}}Q\,dh\\[5pt]&=S_{o}{\frac {R_{o}^{2}}{R_{E}^{2}}}\int _{h_{o}}^{-h_{o}}\cos(\Theta )\,dh\\[5pt]&=S_{o}{\frac {R_{o}^{2}}{R_{E}^{2}}}{\Bigg [}h\sin(\varphi )\sin(\delta )+\cos(\varphi )\cos(\delta )\sin(h){\Bigg ]}_{h=h_{o}}^{h=-h_{o}}\\[5pt]&=-2S_{o}{\frac {R_{o}^{2}}{R_{E}^{2}}}\left[h_{o}\sin(\varphi )\sin(\delta )+\cos(\varphi )\cos(\delta )\sin(h_{o})\right]\end{aligned}}} Therefore: Q ¯ day = S o π R o 2 R E 2 [ h o sin ⁡ ( φ ) sin ⁡ ( δ ) + cos ⁡ ( φ ) cos ⁡ ( δ ) sin ⁡ ( h o ) ] {\displaystyle {\overline {Q}}^{\text{day}}={\frac {S_{o}}{\pi }}{\frac {R_{o}^{2}}{R_{E}^{2}}}\left[h_{o}\sin(\varphi )\sin(\delta )+\cos(\varphi )\cos(\delta )\sin(h_{o})\right]} Let θ be

3854-492: Is often integrated over a given time period in order to report the radiant energy emitted into the surrounding environment ( joule per square metre, J/m ) during that time period. This integrated solar irradiance is called solar irradiation , solar exposure , solar insolation , or insolation . Irradiance may be measured in space or at the Earth's surface after atmospheric absorption and scattering . Irradiance in space

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3948-443: Is rare, and in practice it is often excluded in EROI analysis of energy sources. In a 2010 paper by Murphy and Hall, the advised extended ["Ext"] boundary protocol, for all future research on EROI, was detailed. In order to produce, what they consider, a more realistic assessment and generate greater consistency in comparisons, than what Hall and others view as the "weak points" in a competing methodology. In more recent years, however,

4042-422: Is run for about 100 years. Because much of the energy required for producing oil from oil sands (bitumen) comes from low value fractions separated out by the upgrading process, there are two ways to calculate EROI, the higher value given by considering only the external energy inputs and the lower by considering all energy inputs, including self generated. One study found that in 1970 oil sands net energy returns

4136-416: Is studying material and energy flows referred to as Industrial ecology , and applying this perspective, to attempting to understand human economies from a biophysical rather than just social perspective. Hall, and other biophysical economic thinkers are trained in ecology and evolutionary biology , fields that break down the natural world as done also by physicists. These views hold the global economy in

4230-542: Is used when EROI is below 1. "ESOI e is the ratio of electrical energy stored over the lifetime of a storage device to the amount of embodied electrical energy required to build the device." One of the notable outcomes of the Stanford University team's assessment on ESOI, was that if pumped storage was not available, the combination of wind energy and the commonly suggested pairing with battery technology as it presently exists, would not be sufficiently worth

4324-472: The signal-to-noise ratio , respectively. The net effect of these corrections decreased the average ACRIM3 TSI value without affecting the trending in the ACRIM Composite TSI. Differences between ACRIM and PMOD TSI composites are evident, but the most significant is the solar minimum-to-minimum trends during solar cycles 21 - 23 . ACRIM found an increase of +0.037%/decade from 1980 to 2000 and

4418-451: The solar insolation driving photosynthesis is not included, and the energy used in the stellar synthesis of fissile elements is not included for nuclear fission . The energy returned includes only human usable energy and not wastes such as waste heat . Nevertheless, heat of any form can be counted where it is actually used for heating. However the use of waste heat in district heating and water desalination in cogeneration plants

4512-631: The ACRIM III data that is nearly in phase with the Sun-Earth distance and 90-day spikes in the VIRGO data coincident with SoHO spacecraft maneuvers that were most apparent during the 2008 solar minimum. TIM's high absolute accuracy creates new opportunities for measuring climate variables. TSI Radiometer Facility (TRF) is a cryogenic radiometer that operates in a vacuum with controlled light sources. L-1 Standards and Technology (LASP) designed and built

4606-557: The EROIs of all the fuels used in a society or nation. A societal EROI has never been calculated and researchers believe it may currently be impossible to know all variables necessary to complete the calculation, but attempted estimates have been made for some nations. Calculations are done by summing all of the EROIs for domestically produced and imported fuels and comparing the result to the Human Development Index (HDI),

4700-1040: The Earth Radiometer Budget Experiment (ERBE) on the Earth Radiation Budget Satellite (ERBS), VIRGO on the Solar Heliospheric Observatory (SoHO) and the ACRIM instruments on the Solar Maximum Mission (SMM), Upper Atmosphere Research Satellite (UARS) and ACRIMSAT . Pre-launch ground calibrations relied on component rather than system-level measurements since irradiance standards at the time lacked sufficient absolute accuracies. Measurement stability involves exposing different radiometer cavities to different accumulations of solar radiation to quantify exposure-dependent degradation effects. These effects are then compensated for in

4794-463: The Earth moving between its perihelion and aphelion , or changes in the latitudinal distribution of radiation. These orbital changes or Milankovitch cycles have caused radiance variations of as much as 25% (locally; global average changes are much smaller) over long periods. The most recent significant event was an axial tilt of 24° during boreal summer near the Holocene climatic optimum . Obtaining

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4888-569: The Evolution of Human Culture and graduate-level courses in Systems Ecology , Ecosystems , Energy systems , Tropical Development and Biophysical Economics. Hall retired from full-time teaching in June 2012, and he now works to consolidate his life work into a format that will continue to be useful for future research. Hall's research interests are in the field of Systems ecology with strong interests in biophysical economics , and

4982-473: The TRF in both optical power and irradiance. The resulting high accuracy reduces the consequences of any future gap in the solar irradiance record. The most probable value of TSI representative of solar minimum is 1 360 .9 ± 0.5 W/m , lower than the earlier accepted value of 1 365 .4 ± 1.3 W/m , established in the 1990s. The new value came from SORCE/TIM and radiometric laboratory tests. Scattered light

5076-646: The TSI record is not sufficiently stable to discern solar changes on decadal time scales. Only the ACRIM composite shows irradiance increasing by ~1   W/m  between 1986 and 1996; this change is also absent in the model. Recommendations to resolve the instrument discrepancies include validating optical measurement accuracy by comparing ground-based instruments to laboratory references, such as those at National Institute of Science and Technology (NIST); NIST validation of aperture area calibrations uses spares from each instrument; and applying diffraction corrections from

5170-495: The United States, has declined steadily over the last century from about 1000:1 in 1919 to only 5:1 in the 2010s. Since the invention of agriculture, humans have increasingly used exogenous sources of energy to multiply human muscle-power. Some historians have attributed this largely to more easily exploited (i.e. higher EROI) energy sources, which is related to the concept of energy slaves . Thomas Homer-Dixon argues that

5264-435: The actual lifetime. This also means that it can be adapted to multi-component systems where the components have different lifetimes. Another issue with EROI that many studies attempt to tackle is that the energy returned can be in different forms, and these forms can have different utility. For example, electricity can be converted more efficiently than thermal energy into motion, due to electricity's lower entropy. In addition,

5358-406: The calculation to include the cost of refining and transporting the fuel during the refining process. Since this expands the bounds of the calculation to include more production process EROI will decrease. Extended EROI includes point of use expansions as well as including the cost of creating the infrastructure needed for transportation of the energy or fuel once refined. Societal EROI is a sum of all

5452-442: The cavity, electronic degradation of the heater, surface degradation of the precision aperture and varying surface emissions and temperatures that alter thermal backgrounds. These calibrations require compensation to preserve consistent measurements. For various reasons, the sources do not always agree. The Solar Radiation and Climate Experiment/Total Irradiance Measurement ( SORCE /TIM) TSI values are lower than prior measurements by

5546-407: The cavity. This design admits into the front part of the instrument two to three times the amount of light intended to be measured; if not completely absorbed or scattered, this additional light produces erroneously high signals. In contrast, TIM's design places the precision aperture at the front so that only desired light enters. Variations from other sources likely include an annual systematics in

5640-451: The conventional polar angle describing a planetary orbit . Let θ  = 0 at the March equinox . The declination δ as a function of orbital position is δ = ε sin ⁡ ( θ ) {\displaystyle \delta =\varepsilon \sin(\theta )} where ε is the obliquity . (Note: The correct formula, valid for any axial tilt,

5734-428: The cover of the journal Science . Global PV market by technology in 2013. The issue is still subject of numerous studies, and prompting academic argument. That's mainly because the "energy invested" critically depends on technology, methodology, and system boundary assumptions, resulting in a range from a maximum of 2000 kWh/m of module area down to a minimum of 300 kWh/m with a median value of 585 kWh/m according to

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5828-426: The daily average insolation for the Earth is approximately 6 kWh/m = 21.6 MJ/m . The output of, for example, a photovoltaic panel, partly depends on the angle of the sun relative to the panel. One Sun is a unit of power flux , not a standard value for actual insolation. Sometimes this unit is referred to as a Sol, not to be confused with a sol , meaning one solar day . Part of the radiation reaching an object

5922-501: The economist Alfred Marshall , said: “Biology, not mechanics, is our Mecca.” Solar insolation Solar irradiance is the power per unit area ( surface power density ) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Solar irradiance is measured in watts per square metre (W/m ) in SI units . Solar irradiance

6016-565: The economy is a proxy of the amount of real work done in our economy," according to Charles A. Hall. In the 1980s, Hall and others hypothesised, "Over time, the Dow Jones should snake about the real amount of work." Twenty years later, a century's market and energy data shows that whenever the Dow Jones Industrial Average spikes faster than US energy consumption, it crashes: 1929, 1970s, the dot.com bubble, and now with

6110-499: The electrical heating needed to maintain an absorptive blackened cavity in thermal equilibrium with the incident sunlight which passes through a precision aperture of calibrated area. The aperture is modulated via a shutter . Accuracy uncertainties of < 0.01% are required to detect long term solar irradiance variations, because expected changes are in the range 0.05–0.15   W/m per century. In orbit, radiometric calibrations drift for reasons including solar degradation of

6204-409: The energy imbalance. In 2014 a new ACRIM composite was developed using the updated ACRIM3 record. It added corrections for scattering and diffraction revealed during recent testing at TRF and two algorithm updates. The algorithm updates more accurately account for instrument thermal behavior and parsing of shutter cycle data. These corrected a component of the quasi-annual spurious signal and increased

6298-414: The energy input of the roads which are used to ferry the goods be taken into account? What about the energy used to cook the steelworkers' breakfasts? These are complex questions evading simple answers. A full accounting would require considerations of opportunity costs and comparing total energy expenditures in the presence and absence of this economic activity. However, when comparing two energy sources

6392-453: The final data. Observation overlaps permits corrections for both absolute offsets and validation of instrumental drifts. Uncertainties of individual observations exceed irradiance variability (~0.1%). Thus, instrument stability and measurement continuity are relied upon to compute real variations. Long-term radiometer drifts can potentially be mistaken for irradiance variations which can be misinterpreted as affecting climate. Examples include

6486-483: The form of energy of the input can be completely different from the output. For example, energy in the form of coal could be used in the production of ethanol. This might have an EROI of less than one, but could still be desirable due to the benefits of liquid fuels (assuming the latters are not used in the processes of extraction and transformation). There are three prominent expanded EROI calculations, they are point of use, extended and societal. Point of Use EROI expands

6580-533: The global warming of the last two decades of the 20th century are that solar forcing may be a marginally larger factor in climate change than represented in the CMIP5 general circulation climate models . Average annual solar radiation arriving at the top of the Earth's atmosphere is roughly 1361   W/m . The Sun's rays are attenuated as they pass through the atmosphere , leaving maximum normal surface irradiance at approximately 1000   W/m at sea level on

6674-844: The hour angle when Q becomes positive. This could occur at sunrise when Θ = 1 2 π {\displaystyle \Theta ={\tfrac {1}{2}}\pi } , or for h 0 as a solution of sin ⁡ ( φ ) sin ⁡ ( δ ) + cos ⁡ ( φ ) cos ⁡ ( δ ) cos ⁡ ( h o ) = 0 {\displaystyle \sin(\varphi )\sin(\delta )+\cos(\varphi )\cos(\delta )\cos(h_{o})=0} or cos ⁡ ( h o ) = − tan ⁡ ( φ ) tan ⁡ ( δ ) {\displaystyle \cos(h_{o})=-\tan(\varphi )\tan(\delta )} If tan( φ ) tan( δ ) > 1 , then

6768-412: The investment, suggesting instead curtailment. A related recent concern is energy cannibalism where energy technologies can have a limited growth rate if climate neutrality is demanded. Many energy technologies are capable of replacing significant volumes of fossil fuels and concomitant green house gas emissions . Unfortunately, neither the enormous scale of the current fossil fuel energy system nor

6862-574: The issue of the irradiance increase between cycle minima in 1986 and 1996, evident only in the ACRIM composite (and not the model) and the low irradiance levels in the PMOD composite during the 2008 minimum. Despite the fact that ACRIM I, ACRIM II, ACRIM III, VIRGO and TIM all track degradation with redundant cavities, notable and unexplained differences remain in irradiance and the modeled influences of sunspots and faculae . Disagreement among overlapping observations indicates unresolved drifts that suggest

6956-508: The lower values for the secular trend are more probable. In particular, a secular trend greater than 2 Wm is considered highly unlikely. Ultraviolet irradiance (EUV) varies by approximately 1.5 percent from solar maxima to minima, for 200 to 300 nm wavelengths. However, a proxy study estimated that UV has increased by 3.0% since the Maunder Minimum. Some variations in insolation are not due to solar changes but rather due to

7050-410: The mortgage collapse. Nicholas Georgescu-Roegen (a Romanian-born economist whose work in the 1970s began to define this new approach) models the economy as a living system. Like all life, it draws from its environment valuable (or “low entropy”) matter and energy, for animate life, food; for an economy, energy, ores, the raw materials provided by plants and animals. And like all life, an economy emits

7144-494: The necessary growth rate of these technologies is well understood within the limits imposed by the net energy produced for a growing industry. This technical limitation is known as energy cannibalism and refers to an effect where rapid growth of an entire energy producing or energy efficiency industry creates a need for energy that uses (or cannibalizes) the energy of existing power plants or production plants. The solar breeder overcomes some of these problems. A solar breeder

7238-437: The prediction of energy generation from solar power plants , the heating and cooling loads of buildings, climate modeling and weather forecasting, passive daytime radiative cooling applications, and space travel. There are several measured types of solar irradiance. Spectral versions of the above irradiances (e.g. spectral TSI , spectral DNI , etc.) are any of the above with units divided either by meter or nanometer (for

7332-431: The published work in this field is produced by advocates or persons with a connection to business interests among the competing technologies, and that government agencies had not yet provided adequate funding for rigorous analysis by more neutral observers. EROI and Net energy (gain) measure the same quality of an energy source or sink in numerically different ways. Net energy describes the amounts, while EROI measures

7426-444: The ratio or efficiency of the process. They are related simply by or For example, given a process with an EROI of 5, expending 1 unit of energy yields a net energy gain of 4 units. The break-even point happens with an EROI of 1 or a net energy gain of 0. The time to reach this break-even point is called energy payback period (EPP) or energy payback time (EPBT). Although many qualities of an energy source matter (for example oil

7520-630: The reference radiometer and the instrument under test in a common vacuum system that contains a stationary, spatially uniform illuminating beam. A precision aperture with an area calibrated to 0.0031% (1 σ ) determines the beam's measured portion. The test instrument's precision aperture is positioned in the same location, without optically altering the beam, for direct comparison to the reference. Variable beam power provides linearity diagnostics, and variable beam diameter diagnoses scattering from different instrument components. The Glory/TIM and PICARD/PREMOS flight instrument absolute scales are now traceable to

7614-549: The relation of energy to society . His work has involved streams, estuaries and tropical forests but focused increasingly on human-dominated ecosystems in the US and Latin America. His research reflects his interest in understanding and developing analyses and computer simulation models of the complex systems of nature and humans and their interactions. Halls focus has been on energy as it relates to economics and environment. His focus

7708-497: The relative proportion of sunspot and facular influences from SORCE/TIM data accounts for 92% of observed variance and tracks the observed trends to within TIM's stability band. This agreement provides further evidence that TSI variations are primarily due to solar surface magnetic activity. Instrument inaccuracies add a significant uncertainty in determining Earth's energy balance . The energy imbalance has been variously measured (during

7802-660: The role of the elliptical orbit is entirely contained within the important product e sin ⁡ ( ϖ ) {\displaystyle e\sin(\varpi )} , the precession index, whose variation dominates the variations in insolation at 65°   N when eccentricity is large. For the next 100,000 years, with variations in eccentricity being relatively small, variations in obliquity dominate. The space-based TSI record comprises measurements from more than ten radiometers and spans three solar cycles. All modern TSI satellite instruments employ active cavity electrical substitution radiometry . This technique measures

7896-400: The same source of energy. How deep should the probing in the supply chain of the tools being used to generate energy go? For example, if steel is being used to drill for oil or construct a nuclear power plant, should the energy input of the steel be taken into account? Should the energy input into building the factory being used to construct the steel be taken into account and amortized? Should

7990-463: The scientific literature EROIs wind turbines is around 16 unbuffered and 4 buffered. Data collected in 2018 found that the EROI of operational wind turbines averaged 19.8 with high variability depending on wind conditions and wind turbine size. EROIs tend to be higher for recent wind turbines compared to older technology wind turbines. Vestas reports an EROI of 31 for its V150 model wind turbine. The EROI for hydropower plants averages to about 110 when it

8084-678: The solar breeder which clearly indicate that a vast amount of net energy is available from such a plant for the indefinite future. The solar module processing plant at Frederick, Maryland was originally planned as such a solar breeder. In 2009 the Sahara Solar Breeder Project was proposed by the Science Council of Japan as a cooperation between Japan and Algeria with the highly ambitious goal of creating hundreds of GW of capacity within 30 years. Charles A. S. Hall Charles A. S. Hall (born 1943)

8178-392: The sun does not set and the sun is already risen at h = π , so h o = π . If tan( φ ) tan( δ ) < −1 , the sun does not rise and Q ¯ day = 0 {\displaystyle {\overline {Q}}^{\text{day}}=0} . R o 2 R E 2 {\displaystyle {\frac {R_{o}^{2}}{R_{E}^{2}}}}

8272-625: The system, completed in 2008. It was calibrated for optical power against the NIST Primary Optical Watt Radiometer, a cryogenic radiometer that maintains the NIST radiant power scale to an uncertainty of 0.02% (1 σ ). As of 2011 TRF was the only facility that approached the desired <0.01% uncertainty for pre-launch validation of solar radiometers measuring irradiance (rather than merely optical power) at solar power levels and under vacuum conditions. TRF encloses both

8366-409: The top of the Earth's atmosphere is about 1361   W/m . This represents the power per unit area of solar irradiance across the spherical surface surrounding the Sun with a radius equal to the distance to the Earth (1   AU ). This means that the approximately circular disc of the Earth, as viewed from the Sun, receives a roughly stable 1361   W/m at all times. The area of this circular disc

8460-546: The underground layers of shale to produce oil from the kerogen. Resulting EROI is typically around 1.4-1.5. Economically, oil shale might be viable due to the effectively free natural gas on site used for heating the kerogen, but opponents have debated that the natural gas could be extracted directly and used for relatively inexpensive transportation fuel rather than heating shale for a lower EROI and higher carbon emissions. The weighted average standard EROI of all oil liquids (including coal-to-liquids, gas-to-liquids, biofuels, etc.)

8554-443: The unit of the integral (W/m^2) is the product of those two units. The SI unit of irradiance is watts per square metre (W/m = Wm ). The unit of insolation often used in the solar power industry is kilowatt hours per square metre (kWh/m ). The Langley is an alternative unit of insolation. One Langley is one thermochemical calorie per square centimetre or 41,840   J/m . The average annual solar radiation arriving at

8648-471: The view-limiting aperture. For ACRIM, NIST determined that diffraction from the view-limiting aperture contributes a 0.13% signal not accounted for in the three ACRIM instruments. This correction lowers the reported ACRIM values, bringing ACRIM closer to TIM. In ACRIM and all other instruments but TIM, the aperture is deep inside the instrument, with a larger view-limiting aperture at the front. Depending on edge imperfections this can directly scatter light into

8742-469: The year and the day, the Earth's atmosphere receives 340   W/m from the Sun. This figure is important in radiative forcing . The distribution of solar radiation at the top of the atmosphere is determined by Earth's sphericity and orbital parameters. This applies to any unidirectional beam incident to a rotating sphere. Insolation is essential for numerical weather prediction and understanding seasons and climatic change . Application to ice ages

8836-504: Was about 1.0 but by 2010 had increased to about 5.23. Conventional sources of oil have a rather large variation depending on various geologic factors. The EROI for refined fuel from conventional oil sources varies from around 18 to 43. Due to the process heat input requirements for oil shale harvesting, the EROI is low. Typically natural gas is used, either directly combusted for process heat or used to power an electricity generating turbine, which then uses electrical heating elements to heat

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