Increasing Summer Insolation of the Northern Hemisphere Trends Towards Reduced Ice Volume; Coupled by a 400,000 year Eccentricity Cycle Extending the Holocene Interglacial
Januray 21, 2019
Januray 21, 2019
Currently it is widely believed that the world is warming due to increase temperature trends caused by elevated levels of Carbon Dioxide levels. There is validity in these claims; based on mathematic modeling, temperature observations, abnormalities observed in temperature extremes, and unusual warming in the Oceans. However in previous articles, prepared by MOTM staff, we compared the current interglacial to three previous interglacials; Eemian, Anglian, and Penultimate Interglacial Complex. Within these interglacials we compared orbital variations, Ice Volume in the Chukchi and East Siberian Seas, temperatures fluctuations, ice volume trends, sea levels, and duration of interglacials. Furthermore, we made a historical comparison of the rapid rise of the seas and loss of glaciers in the late Pleistocene and early Holocene 18,000 to 5,000 years ago to current climate changes. We also took a look at major paleohydrological droughts and floods and discussed controversial subjects in the climate change science. Current controversial subjects include and not limited to deforestation albedo, Global warming data bias, CLOUD research on aerosol particles, and etc. Then we compared current Carbon Dioxide Levels and Ice Volume to 500 million years of Climate Change and Early Pleistocene.
Orbital Variations Effects on Interglacial Behavior and Paleohydrological Events during the Quaternary Ice Age: A Compilation of MOTM editorial pieces
I. Glaciers or Rising Oceans; Damned if you do, damned if don’t, And maybe both
II. Paleohydrological events from the late Pleistocene to the Holocene 30kya to 1500AD
III. NOAA shows a modest 3.2 mm sea level rise over the last year. How significant is the current sea level raise from a geological perspective?
IV. A Climate Change Perspective-Relating Things to the Early Holocene and the Eemian
V. A Solar Forcing Comparison Between the Holocene and Anglian Interglacial Periods Related by Eccentricity
Though warming temperatures continue to trend upward we want to point out that there appears to be a warming hiatus between 1998 and 2013. This observation is commonly used by Climate Change Skeptics but is believed by many in the science community the hiatus was caused by an exceptionally warm El Niño year in 1998 that was an outlier that affected the temperature trend. Recent temperature measurements continue to trend upward, but as we would like to point out they also seem to follow the lower range of global warming predictions.
This graph shows the major temperature sets compared to CMIP5 model projections.
Orbital Variations Effects on Interglacial Behavior and Paleohydrological Events during the Quaternary Ice Age: A Compilation of MOTM editorial pieces
I. Glaciers or Rising Oceans; Damned if you do, damned if don’t, And maybe both
II. Paleohydrological events from the late Pleistocene to the Holocene 30kya to 1500AD
III. NOAA shows a modest 3.2 mm sea level rise over the last year. How significant is the current sea level raise from a geological perspective?
IV. A Climate Change Perspective-Relating Things to the Early Holocene and the Eemian
V. A Solar Forcing Comparison Between the Holocene and Anglian Interglacial Periods Related by Eccentricity
Though warming temperatures continue to trend upward we want to point out that there appears to be a warming hiatus between 1998 and 2013. This observation is commonly used by Climate Change Skeptics but is believed by many in the science community the hiatus was caused by an exceptionally warm El Niño year in 1998 that was an outlier that affected the temperature trend. Recent temperature measurements continue to trend upward, but as we would like to point out they also seem to follow the lower range of global warming predictions.
This graph shows the major temperature sets compared to CMIP5 model projections.
This graph shows the temperature set using the HadCRUT4.6 temperature set.
One problem with these global temperature measurements is skillfully point out by Clive West,
“In 2012 all the major temperature sets (HadCRUT, GISS,NCDC) showed no consequent year warmer than the El Nino year 1998. Furthermore the trend was dropping below model predictions. Since then a huge effort has been made to add new weather stations in Arctic regions where warming is fastest and to improve the spatial coverage averaging.
HadCRUT4.6 has about 2000 more stations than HadCRUT3 had in 2012, but also dropped some stations in S. America (they were cooling). Temperature homogenisation on land and oceans has also had a net warming effect, although quite why seems to be a bit of a mystery.
What is interesting though is that the flat trend prior to 2014 has now disappeared in HadCRUT4.6 which uses the same averaging procedure throughout. So this must be due to ongoing data corrections and to all the new stations added consequently. Each new monthly release of data shows that earlier values of global temperatures also get updated. Data homogenisation is a continuing process updating past measurements as well as new ones. Note however that temperatures have been falling for the last two years following the the 2016 El Nino peak. If 2019 continues this cooling trend then the pause or hiatus in warming could well return.”
As we pointed out in an earlier editorial piece, there is some concern about adding 2,000 temperature stations in the arctic and removing stations in South America that showed cooling. Adding that many new stations in the Arctic will no doubt produce a more accurate temperature average, but as MOTM pointed out earlier it might create hyper sensitivity to temperature changes, which would be hard to compare to historical temperature averages that do not enjoy that level of sensitivity. Furthermore, MOTM has made the observation that within the Climate Change debate the most common interglacial period used for comparison to the current one is the Eemian. One of the problems with the Eemian interglacial period is that it warmed faster, temperatures were greater then current temperatures, and the interglacial was shorter then the current interglacial.
“In 2012 all the major temperature sets (HadCRUT, GISS,NCDC) showed no consequent year warmer than the El Nino year 1998. Furthermore the trend was dropping below model predictions. Since then a huge effort has been made to add new weather stations in Arctic regions where warming is fastest and to improve the spatial coverage averaging.
HadCRUT4.6 has about 2000 more stations than HadCRUT3 had in 2012, but also dropped some stations in S. America (they were cooling). Temperature homogenisation on land and oceans has also had a net warming effect, although quite why seems to be a bit of a mystery.
What is interesting though is that the flat trend prior to 2014 has now disappeared in HadCRUT4.6 which uses the same averaging procedure throughout. So this must be due to ongoing data corrections and to all the new stations added consequently. Each new monthly release of data shows that earlier values of global temperatures also get updated. Data homogenisation is a continuing process updating past measurements as well as new ones. Note however that temperatures have been falling for the last two years following the the 2016 El Nino peak. If 2019 continues this cooling trend then the pause or hiatus in warming could well return.”
As we pointed out in an earlier editorial piece, there is some concern about adding 2,000 temperature stations in the arctic and removing stations in South America that showed cooling. Adding that many new stations in the Arctic will no doubt produce a more accurate temperature average, but as MOTM pointed out earlier it might create hyper sensitivity to temperature changes, which would be hard to compare to historical temperature averages that do not enjoy that level of sensitivity. Furthermore, MOTM has made the observation that within the Climate Change debate the most common interglacial period used for comparison to the current one is the Eemian. One of the problems with the Eemian interglacial period is that it warmed faster, temperatures were greater then current temperatures, and the interglacial was shorter then the current interglacial.
Some people believe these differences between Eemian and the Holocene are due to 400,000 year cycles in eccentricity. The last interglacial to have a shared a similar eccentricity as the Holocene was the Anglian Interglacial 420,000 years ago.
MOTM in earlier article showed that Anglian interglacial is a better comparison for the current one. This was also skillfully pointed out by Clive West.
“Interglacials usually average ~10,000 years, so is our luck about to run out? It turns out that the answer is no, because we are very fortunate that human society has developed during an interglacial when the earth’s orbit has very low eccentricity. Eccentricity is important because it regulates the strength of polar maximum summer insolation caused by precession of the equinoxes every 21,000 years. Precession determines the distance from the sun during a Polar summer. If summer coincides with the earth’s perihelion then summer insolation can be up to 20% higher than average. However if the earth’s orbit is nearly circular, as it is today, then precession has little effect at all. That is why we have about 12000 years left before cooling begins. However, the alignment of precession is not perfect, and the north-south precession cycle is inverted. Despite this, at very low eccentricity, it is only obliquity that really counts. We conclude that within 12000 years the earth would naturally be returning to a new ice age lasting 100,000 years. The earth then enters another long period of high eccentricity lasting a further 400,000 years. Future Interglacials will last only ~10,000 years, before the cycle repeats.”
“Interglacials usually average ~10,000 years, so is our luck about to run out? It turns out that the answer is no, because we are very fortunate that human society has developed during an interglacial when the earth’s orbit has very low eccentricity. Eccentricity is important because it regulates the strength of polar maximum summer insolation caused by precession of the equinoxes every 21,000 years. Precession determines the distance from the sun during a Polar summer. If summer coincides with the earth’s perihelion then summer insolation can be up to 20% higher than average. However if the earth’s orbit is nearly circular, as it is today, then precession has little effect at all. That is why we have about 12000 years left before cooling begins. However, the alignment of precession is not perfect, and the north-south precession cycle is inverted. Despite this, at very low eccentricity, it is only obliquity that really counts. We conclude that within 12000 years the earth would naturally be returning to a new ice age lasting 100,000 years. The earth then enters another long period of high eccentricity lasting a further 400,000 years. Future Interglacials will last only ~10,000 years, before the cycle repeats.”
Eccentricity of the orbit has becoming more important for predicting glaciation and interglacial periods the last one million years. The observable reason for this is the first half the Pleistocene interglacial were more dominated by Obliquity variations in the earth tilt. During this time period the interglacials occurred on average every 41,000 years. Over time the glaciation cycles gradually become longer and more severe as the interglacial events become more dominated by a 100,000 years cycle involving Obliquity, Eccentricity, and Precession. As Eccentricity has becoming more important for predicting timing, duration, and intensity of a interglacial period this has made the comparison between the Anglian and Holocene interglacials more fitting then the Penultimate Complex and Eemian interglacials.
Here we would like to backstep and take a closer look at Orbital Eccentricity, Obliquity, and Precession. Right now it is currently believed that the Milankovitch cycles is the largest driver on paleohydrological weather patterns and glacial/interglacial cycles. It is believed that we would not have discernible seasons without the tilt of earth. However, these cycles are broken down into Eccentricity, Obliquity (tilt), and Precession. Eccentricity can be described by changing of the shape; Eccentricity is, simply, the shape of the Earth's orbit around the Sun. This constantly fluctuating, orbital shape ranges between more and less elliptical (0 to 5% ellipticity) on a cycle of about 100,000 years. These oscillations, from more elliptic to less elliptic, are of prime importance to glaciation in that it alters the distance from the Earth to the Sun, thus changing the distance the Sun's short wave radiation must travel to reach Earth, subsequently reducing or increasing the amount of radiation received at the
Right now it is currently believed that the Milankovitch cycles is the largest driver on paleohydrological weather patterns, length of days during the seasons, and glacial/interglacial cycles. It is believed that we would not have discernible seasons without the tilt of earth. However, these cycles are broken down into Eccentricity, Obliquity (tilt), and Precession. Eccentricity can be described by changing of the shape; Eccentricity is, simply, the shape of the Earth's orbit around the Sun. This constantly fluctuating, orbital shape ranges between more and less elliptical (0 to 5% ellipticity) on a cycle of about 100,000 years. These oscillations, from more elliptic to less elliptic, are of prime importance to glaciation in that it alters the distance from the Earth to the Sun, thus changing the distance the Sun's short wave radiation must travel to reach Earth, subsequently reducing or increasing the amount of radiation received at the
Right now it is currently believed that the Milankovitch cycles is the largest driver on paleohydrological weather patterns, length of days during the seasons, and glacial/interglacial cycles. It is believed that we would not have discernible seasons without the tilt of earth. However, these cycles are broken down into Eccentricity, Obliquity (tilt), and Precession. Eccentricity can be described by changing of the shape; Eccentricity is, simply, the shape of the Earth's orbit around the Sun. This constantly fluctuating, orbital shape ranges between more and less elliptical (0 to 5% ellipticity) on a cycle of about 100,000 years. These oscillations, from more elliptic to less elliptic, are of prime importance to glaciation in that it alters the distance from the Earth to the Sun, thus changing the distance the Sun's short wave radiation must travel to reach Earth, subsequently reducing or increasing the amount of radiation received at the
Today a difference of only about 3 percent occurs between aphelion (farthest point) and perihelion (closest point). This 3 percent difference in distance means that Earth experiences a 6 percent increase in received solar energy in January than in July. This 6 percent range of variability is not always the case, however. When the Earth's orbit is most elliptical the amount of solar energy received at the perihelion would be in the range of 20 to 30 percent more than at aphelion. Most certainly these continually altering amounts of received solar energy around the globe result in prominent changes in the Earth's climate and glacial regimes. At present the orbital eccentricity is nearly at the minimum of its cycle. The eccentricity of the Earth's orbit is currently about 0.0167; the Earth's orbit is nearly circular.
The second function is tilt; axial tilt, the second of the three Milankovitch Cycles, is the inclination of the Earth's axis in relation to its plane of orbit around the Sun. Oscillations in the degree of Earth's axial tilt occur on a periodicity of 41,000 years from 21.5 to 24.5 degrees.
Today the Earth's axial tilt is about 23.5 degrees, which largely accounts for our seasons. Because of the periodic variations of this angle the severity of the Earth's seasons changes. With less axial tilt the Sun's solar radiation is more evenly distributed between winter and summer. However, less tilt also increases the difference in radiation receipts between the equatorial and polar regions.
The third and final of the Milankovitch Cycles is Earth's precession. Precession is the Earth's slow wobble as it spins on axis. This wobbling of the Earth on its axis can be likened to a top running down, and beginning to wobble back and forth on its axis. The precession of Earth wobbles from pointing at Polaris (North Star) to pointing at the star Vega. When this shift to the axis pointing at Vega occurs, Vega would then be considered the North Star. This top-like wobble, or precession, has a periodicity of 23,000 years.
The third and final of the Milankovitch Cycles is Earth's precession. Precession is the Earth's slow wobble as it spins on axis. This wobbling of the Earth on its axis can be likened to a top running down, and beginning to wobble back and forth on its axis. The precession of Earth wobbles from pointing at Polaris (North Star) to pointing at the star Vega. When this shift to the axis pointing at Vega occurs, Vega would then be considered the North Star. This top-like wobble, or precession, has a periodicity of 23,000 years.
This means that the Northern Hemisphere will experience winter when the Earth is furthest from the Sun and summer when the Earth is closest to the Sun. This coincidence will result in greater seasonal contrasts. At present, the Earth is at perihelion very close to the winter solstice.
It was pointed out above the eccentricity and obliquity is decreasing. This means the tilt of the earth is moving closer to angle of 21.5 degrees and the eccentricity of the orbit of earth is moving closer to a circular path. Due to precession the Earth’s winter solstice of the Northern Hemisphere is moving further away from the sun over the next 5,000 years. The later will be negated by the fact the eccentricity is decreasing, the Obliquity is decreasing, and the Northern Hemisphere will be moving closer to the sun during summer solstice. As the obliquity decreases the earth’s surface at the North Pole will have an increase solar energy per unit of surface areas.
It was pointed out above the eccentricity and obliquity is decreasing. This means the tilt of the earth is moving closer to angle of 21.5 degrees and the eccentricity of the orbit of earth is moving closer to a circular path. Due to precession the Earth’s winter solstice of the Northern Hemisphere is moving further away from the sun over the next 5,000 years. The later will be negated by the fact the eccentricity is decreasing, the Obliquity is decreasing, and the Northern Hemisphere will be moving closer to the sun during summer solstice. As the obliquity decreases the earth’s surface at the North Pole will have an increase solar energy per unit of surface areas.
The MOTM staff is very interested in the effects of solar forcing in the Northern Hemisphere for several reasons. The first reason is that the Northern Hemisphere is warming faster than the Southern Hemisphere; the most rapid warming rates on earth are located in the Arctic.
“In Warming, Northern Hemisphere is Outpacing the South. If global warming were a race, the Northern Hemisphere would be winning. It is warming faster than the Southern Hemisphere, with some of the most rapid warming rates on Earth located in the Arctic, where sea and land ice is shrinking and thinning. Apr 9, 2013”
The Second reason we are interested in Solar Insolation of the Northern Hemisphere, particularity the 65N, is because the insolation cycle is very similar to the Anglian Interglacial that occurred 420,000 years ago.
“In Warming, Northern Hemisphere is Outpacing the South. If global warming were a race, the Northern Hemisphere would be winning. It is warming faster than the Southern Hemisphere, with some of the most rapid warming rates on Earth located in the Arctic, where sea and land ice is shrinking and thinning. Apr 9, 2013”
The Second reason we are interested in Solar Insolation of the Northern Hemisphere, particularity the 65N, is because the insolation cycle is very similar to the Anglian Interglacial that occurred 420,000 years ago.
Currently, the Southern Hemisphere receives about 7% more radiance then the Northern Hemisphere. However, it is noticed that the Northern Hemisphere has higher surface temperature. Below we present a broad range of reasons the Southern Hemisphere is warmer,
“One of the most fundamental features of the Earth’s climate is that the Northern Hemisphere (NH) is warmer than the Southern Hemisphere (SH) (Fig. 1). There are several possible reasons for this. An informal poll of members of the public and some scientists often produces the answer that it is because the NH has more land and, therefore, heats up more in summer because of the lesser heat capacity. On the other hand, many scientists argue that it is because the ocean transports heat northward across the equator. We have also encountered more subtle arguments such as continental geometry that results in upwelling and equatorward sea ice export in the Antarctic Circumpolar Current (ACC) and Southern Ocean (SO) cooling the SH. Also, it could be argued that the impact of continental geometry on subtropical coastal upwelling preferentially cools the south (Philander et al. 1996). Finally, it could be a transient response to greenhouse gas forcing because the NH has the larger land fraction and heats up faster than the more oceanic SH. While the inter-hemispheric temperature asymmetry is interesting in and of itself, it is also of practical importance because of the influence it exerts on the position of the Intertropical Convergence Zone (ITCZ) (Kang et al. 2008) whose rains are relied upon many tropical societies for their water and food production.”
The take home message is that what happens in the Northern Hemisphere in regard to the Orbital Variations plays a larger role in determining the super glacial and interglacial cycle in the Northern Hemisphere. Right now decreasing obliquity and eccentricity is estimated to have a net decrease in total insolation on earth. However, as you look at the graph below you see that there is a small increase in summer insolation in the Northern Hemisphere in the near term future. Is it possible that the increased summer insolation can have a net warming effect on the glaciers and Arctic ice in the Northern Hemisphere? Could adding 2,000 new weather stations increase the hyper sensitivity to measuring these subtle changes?
“One of the most fundamental features of the Earth’s climate is that the Northern Hemisphere (NH) is warmer than the Southern Hemisphere (SH) (Fig. 1). There are several possible reasons for this. An informal poll of members of the public and some scientists often produces the answer that it is because the NH has more land and, therefore, heats up more in summer because of the lesser heat capacity. On the other hand, many scientists argue that it is because the ocean transports heat northward across the equator. We have also encountered more subtle arguments such as continental geometry that results in upwelling and equatorward sea ice export in the Antarctic Circumpolar Current (ACC) and Southern Ocean (SO) cooling the SH. Also, it could be argued that the impact of continental geometry on subtropical coastal upwelling preferentially cools the south (Philander et al. 1996). Finally, it could be a transient response to greenhouse gas forcing because the NH has the larger land fraction and heats up faster than the more oceanic SH. While the inter-hemispheric temperature asymmetry is interesting in and of itself, it is also of practical importance because of the influence it exerts on the position of the Intertropical Convergence Zone (ITCZ) (Kang et al. 2008) whose rains are relied upon many tropical societies for their water and food production.”
The take home message is that what happens in the Northern Hemisphere in regard to the Orbital Variations plays a larger role in determining the super glacial and interglacial cycle in the Northern Hemisphere. Right now decreasing obliquity and eccentricity is estimated to have a net decrease in total insolation on earth. However, as you look at the graph below you see that there is a small increase in summer insolation in the Northern Hemisphere in the near term future. Is it possible that the increased summer insolation can have a net warming effect on the glaciers and Arctic ice in the Northern Hemisphere? Could adding 2,000 new weather stations increase the hyper sensitivity to measuring these subtle changes?
Though total solar insolation is decreasing, could there be a positive feedback loop that is pushing the Northern Hemisphere in a warming trend. We raised a few questions why the climate might have a net warming effect even though total solar insolation is decreasing. For one, the Southern Hemisphere is still colder than the Northern Hemisphere due to greater water surface. Land areas are distributed predominantly in the Northern Hemisphere (68%) relative to the Southern Hemisphere (32%) as divided by the equator. Second, due to small increase in summer insolation in the Northern Hemisphere would this have a noticeable impact? As you can see in the graph below, it shows the significant reduced ice in Chukchi and East Siberian Seas 10-8kya. This reduction in ice may be influenced by the summer insolation in the Northern Hemisphere. You can also see in the graph as the NHSI decreases with seasonal ice cover that was formed around 8.5 to 7kya. And as the NHSI continued to decline seasonal and perennial ice cover started to form about 4.5 kya.
Could this have ramifications for temperature bias in the future? Another thing we would like to look at is the irradiance reflection effect or albedo. A typical ocean albedo is approximately 0.06, while bare sea ice varies from approximately 0.5 to 0.7. This means that the ocean reflects only 6 percent of the incoming solar radiation and absorbs the rest, while sea ice reflects 50 to 70 percent of the incoming energy. Snow and Ice have albedo ranging from .7 to .9. As everybody knows the arctic ice has dramatically decreased through the years. As solar insolation increases would we see a decrease in arctic ice and a rise of temperature in the North Hemisphere. First we might see just enough solar forcing to melt ice in the arctic ocean, once this happens you can see that it enters into a feedback loop in the sense that open water only reflects 6% of the solar radiation, while the ice reflects 50-70 % solar radiation. Since there is significantly less ice compared to 13,000 years ago, can a modest increase in NHSI force reduction in the Northern Hemisphere Arctic Ice? Perhaps there is a global warming holding pattern due to the insignificant amount of ice in the seas and on the land to drive the climate in the Northern Hemisphere to cooling. In other words; is the Northern Hemisphere trapped in a warming cycle much like the Anglian Interglacial. We also know that land surfaces have an albedo of 0.0 to 0.4, hence they collect more heat faster. Could this explain a magnified warming trend in the Northern Hemisphere? The colors in this image emphasize the albedo over the earth’s land surfaces, ranging from 0.0 to 0.4. Areas colored red show the brightest, most reflective regions; yellows and greens are intermediate values; and blues and violets show relatively dark surfaces.
“There is a clear tendency that with Milankowitz increases in summer insolation at the North Pole induces decreases in Ice volume. However it can’t explain why 100,000 year interglacial periods have prevailed for the last 600,000 years.”
Due to a decreasing eccentricity and increasing summer insolation in the Northern Hemispere; is it possible that in the Northern Hemisphere might have slightly higher temperatures, reduced ice volume, and continued warming trends? Will this feedback loop be fed by accelerated albedo intensification from shrinking summer ice in the Arctic sea? Will this warming cycle feedback loop continue until the eventually the earth eccentricity increases and earths Northern Hemisphere reaches the furthermost point from the sun during the winter solstice called the apehelion, about 10,000 years from now. At this time will the earth have the cooling inertia to enter glaciation cycle and exit the currently low eccentricity induced warming feedback loop?
Thank you again from the MOTM Staff. If you made it this far we would like to thank you for reading all the way through the article. Our aim to cultivate discussion and debate about Interglacials. In the future we would like to discuss the dust impact on inducing glaciation/interglacials, micro glaciation/interglacial cycles, 2.8 million year eccentricity cycle, continental shift the next 50 million years in the future, and the Late Pliocene.
As a disclaimer we do not deny that global warming isn't happening or that Carbon Dioxide levels aren't rising. We are just curious to how much of the current warming trend can be attributed to background noise such as deforestation albedo, hyper sensitive data measurement, and natural orbital variation cycles, and etc.
Due to a decreasing eccentricity and increasing summer insolation in the Northern Hemispere; is it possible that in the Northern Hemisphere might have slightly higher temperatures, reduced ice volume, and continued warming trends? Will this feedback loop be fed by accelerated albedo intensification from shrinking summer ice in the Arctic sea? Will this warming cycle feedback loop continue until the eventually the earth eccentricity increases and earths Northern Hemisphere reaches the furthermost point from the sun during the winter solstice called the apehelion, about 10,000 years from now. At this time will the earth have the cooling inertia to enter glaciation cycle and exit the currently low eccentricity induced warming feedback loop?
Thank you again from the MOTM Staff. If you made it this far we would like to thank you for reading all the way through the article. Our aim to cultivate discussion and debate about Interglacials. In the future we would like to discuss the dust impact on inducing glaciation/interglacials, micro glaciation/interglacial cycles, 2.8 million year eccentricity cycle, continental shift the next 50 million years in the future, and the Late Pliocene.
As a disclaimer we do not deny that global warming isn't happening or that Carbon Dioxide levels aren't rising. We are just curious to how much of the current warming trend can be attributed to background noise such as deforestation albedo, hyper sensitive data measurement, and natural orbital variation cycles, and etc.