Ice Ages and Climate Change

KEY WORDS: ice ages, climate change, solar energy, ice, snow

THIS WEB PAGE IS PRIMARILY CONCERNED WITH WHY AND WHEN ICE AGES BEGIN AND WHY AND WHEN ICE AGES END.

The Earth is about 4.5 billion years old and during that time it has passed through many variations in climate ranging from very warm to very cold. The climate is strongly affected by the arrangement of the oceans and the continents which have varied widely over billions of years due to continental drift. This website is concerned with a tiny portion of that history over the past couple of million years when the placement of the continents did not vary much, although the isthmus of Panama closed about 3 million years ago.  The Earth acquires energy from the Sun and loses energy by radiation to space. A large amount of the energy from the Sun is absorbed in the tropics ( a band of latitude from about 20S to 20N) and energy is distributed within the Earth system by convection and radiation, and flows of air and water carry energy widely across the globe.  Energy from the Sun is absorbed everywhere on Earth but to a lesser degree than the tropics. While significant variations in local climate occur on Earth, the overall average of climate ultimately depends on the difference between the rate at which energy is absorbed, lee the rate at which energy is rejected to space. 

 If one region of the Earth experiences a period when it absorbs less energy than usual, it will become cooler, but it will not affect the climate of the entire Earth significantly very much unless it is a large region and the cooling is great. 

A system is defined by a quantity that describes the system. In our case, the system is the Earth at high northern latitudes (50N to 70N) and the quantity is the average extent of coverage by ice and snow in that region per year. A positive feedback process is one where if the quantity varies up or down due to external influences, the system will tend to amplify the change in the quantity in either direction. In our case, if external factors tend to increase the spread of snow and ice, the system will increase it further by positive feedback. That ius caused by the fact that snow and ice reflect incoming sunlight causing less local warming, and as the local area cools, the ice spreads, causing less solar absorption, etc.

Links to other documents

Revisiting Ice Ages (short version) 

Imbries Model for Ice Ages

Ice Ages in Brief

Short course in Ice Ages

Book on Ice Ages  (at Amazon)

Future Climate Change  (a projection of future warming vs, future emissions)

How greenhouse gases warm the Earth  LINK

Estimates of warming in the 21st century LINK

The Hockey Stick: Bad Science LINK

Editorial:

There is ample data to assure that over the past 2.7 million years, there have been large quasi-periodic variations in the amount of snow and ice stored in the upper Northern Hemisphere. The high points are called "ice ages" and the low points are called "interglacials". Geological evidence demonstrates at least the last ice age, some 20,000 years ago, while ocean sediment data and Arctic and Antarctic ice core data demonstrate multiple ice ages. The extent of this last ice age can be seen by the fact that there was so much snow and ice stored in the upper Northern Hemisphere that the oceans were about 370 feet lower than they are today.

There are valid reasons to believe that quasi-periodic variations in solar input to high northern latitudes are mainly involved in the quasi-periodic variations of snow and ice stored in the upper Northern Hemisphere, and these solar variations can be attributed to quasi-periodic variations in the Earth's orbit about the Sun. All ice ages begin at a downturn in solar and ice ages terminate at an upturn in solar. When the time series of ice volume (from ocean sediment data) is analyzed for frequencies, the time constants of solar variation appear.

So far, so good.

Ooops. However, while all ice ages begin at a downturn in solar, not every downturn starts an ice age. While ice ages terminate at an upturn in solar, not every upturn produces a termination. So, the outstanding question is why do some downturns start an ice age (and some don't), and why do some upturns produce a termination (and some don't)?

A second question is why the timing of ice ages changed around 1 million years ago.

There are various papers in the literature that claim to answer some of these questions, but I don't find them very satisfactory. I believe that I constructed the best explanation available to date. It is posted here on my website below.

Revisiting Ice Age Cycles   by   Donald Rapp 2024

Link to published paper

Highlights

It is widely accepted that variations in insolation to high latitudes is the driving force for the observed periodic occurrence and termination of ice ages. This paper provides rationalizations for why some increases in insolation to high northern latitudes produce terminations and some do not, and why some deceases in insolation to high northern latitudes induce ice ages, and some do not. It also provides a rationale for why the spacing of ice ages changes across the Mid-Pleistocene Transition (MPT).

Abstract

The astronomical theory of ice ages is widely accepted. Periodic variations in the Earth’s orbit produce variations in the insolation at high latitudes and ice ages begin on down lobes of insolation and terminate on up lobes of insolation. However, not all down lobes create ice ages and not all up lobes produce terminations. The ice ages change character at the so-called mid-Pleistocene transition, about a million years ago. The actual amount of solar power absorbed depends on insolation and the absorptivity of the surface. The absorptivity is particularly affected by the obliquity in the pre-MPT era, and by dust deposits late in the post-MPT era. When these are included, we can rationalize why some down lobes produce ice ages, and some up lobes produce terminations in both eras. In the pre-MPT era, ice ages originate when the insolation enters a down lobe and the obliquity is minimal (higher reflectivity) and ice ages terminate at a coincidence of high insolation and high obliquity (lower reflectivity). These links between SIHL and obliquity tends to be repetitive with approximately 41,000-year spacing. Later in the post-MPT era, ice ages also originate at a down lobe of SIHL. However, once an ice age is started, each successive up lobe in SIHL might cause a slight decrease in ice volume but doesn’t bring about a termination. After several precession cycles, high dust levels increase absorptivity, and the next up lobe produces a termination.

1. Introduction

1.1 Background

Rapp (2018) provided an extensive summary of experimental data and modeling of ice ages. The character of ice ages changed across the mid-Pleistocene transition (MPT) about one million years ago. Prior to the MPT, ice ages did not accumulate as much ice and were spaced at roughly 41,000-year intervals. After the MPT, ice ages accumulated more ice and were spaced at wider intervals ranging from 88,000 years to 110,000 years. A large body of experimental data and analysis has clearly shown that variations in insolation at high northern latitudes plays an important role in determining the timing of ice ages in both eras. Spectral analysis of ice volume variability data displays the cadence of insolation. There is a good correlation of growth and decay of ice ages with the ups and downs of insolation at high latitudes. Nevertheless, a challenge remains to explain why ice ages in each era begin and terminate at specific turns of the oscillating insolation. [1]

In this article, we define the insolation falling on unit area (above the atmosphere) at a high northern latitude (typically 65°N) as the “solar input to high latitudes” (SIHL). Variations in the Earth’s orbit about the Sun produce periodic oscillations in SIHL. The SIHL oscillates in time due to precession with a period of about 21,000 to 22,000 years. The amplitude of these oscillations is determined by the variable obliquity (41,000 year period) and eccentricity (~ 100,000 year period) of the earth’s orbit. A plot of SIHL vs. time shows primary oscillations with the period due to precession, with amplitude of the oscillations determined by obliquity and eccentricity at any time point.

The major challenge in explaining the timing of ice ages driven by variability of SIHL is the fact that SIHL oscillates up and down with a period of 21,000 to 22,000 years due to precession, while the pattern of ice volume vs. time shows much longer periods and does not display the oscillations of precession. What is observed (both pre-MPT and post-MPT) is that every initiation of an ice age occurs in sync with a down lobe of SIHL, and every termination of an ice age occurs in sync with an up lobe of SIHL. The problem is that not every down lobe initiates an ice age and not every up lobe terminates an ice age. And it is not clear a priori why that is so? [1]

The purpose of this paper is to examine the relationship between SIHL and the ice age cycles (separately for pre-MPT and post-MPT) and to thereby provide a rationalization for how up lobes and down lobes of SIHL affect the ice age cycles in each era.

Several investigators have attempted to explain at least partially why the pattern of ice volume vs. time does not reflect the timing of the rapidly varying SIHL. A few key papers are reviewed next.

1.2 Simplest Model (1980)

Imbrie and Imbrie (1980) proposed a simple formula for modeling the effect of variations of SIHL on ice volume. [2] They proposed the equation:

dV/dt = – {(1 ± B)/t} {S + V}

where S is a measure of SIHL and V is meant to be a measure of the ice volume, to be determined by integration over time. B and t are constants. The ± sign in front of B requires that we use the + sign when dV/dt is negative, and the – sign when dV/dt is positive. That allows the rate of change of V with time to be slower when the ice is building up, and faster when ice is diminishing.

Mathematically, V is a quantity that obeys the above differential equation. The greater V is, the more it acts to make dV/dt less positive (or equivalently, more negative). If one believes a priori that the rate of accumulation of snow/ice is inhibited by increased snow/ice, one might interpret V as being related to ice volume, although exactly what that relationship is, is not clear at the outset.

One can then tabulate S year by year for hundreds of thousands of years and integrate the above equation to determine how V varies with time. We have done this for numerous cases.

The term t was included supposedly as a time-delay term, under the belief that as the driving force S changes, it takes thousands of years for the ice volume to approach a new equilibrium due to changes in S. Note that t is measured in thousands of years, and the integration of the differential equation takes place typically over several hundred thousand years. But is t actually a time-delay term in the equation? Not really. The term t mainly affects the magnitude of dV/dt relative to (V + S), but the timing of the ups and downs of V(t) vs. time is dictated primarily by the time-dependence of S which is the forcing equation. Since V(t) is given in arbitrary numbers, the value chosen for t seems to be somewhat irrelevant to the model. In fact, integration of the equation proves that t does not produce a time delay. [1]

There are three problems with this model:

(1) In the pre-MPT era the experimental pattern of V vs. t found in the LR–04 stack of ocean sediment data of is that of a series of trapezoid-like patterns, and the rate of increase of ice volume when ice growth is rapid is about the same as the rate of diminution of ice volume when decay is rapid, across any ice age in that era. So, one would think that B should be close to zero in the pre-MPT period.

(2) In the post-MPT era, particularly over the four most recent ice ages, the actual pattern of V vs. t is not really a slow buildup, followed by a rapid decrease (as is often assumed). The actual pattern of V(t) is a rapid buildup to perhaps half of the ultimate maximum V in 5,000 to 10,000 years, followed by a long, slow buildup to the maximum V, followed by a rapid decrease.

(3) The discontinuous change in the differential equation where dV/dt changes sign is not physical. It would be more reasonable to make B a continuous function of V. A hyperbolic tangent might work well.

The author carried out multiple integrations of the Imbries’ equation in the post-MPT period and it produces a pattern of V(t) that varies with a ~ 22,000 year period due to precession. The calculated V(t) does not resemble the actual ice ages. In plain words, it doesn’t work.

There are fundamental reasons why the Imbries’ equation doesn't work well. One is that there is no reason to think that the response to S and V should be linear. It is sometimes believed that ice accumulates slowly and terminates rapidly, following a "sawtooth" pattern. The Imbries’ equation is based on that notion. However, inspection of the actual ice volume patterns in both the pre-MPT and post-MPT era shows that the actual patterns do not follow that simple notion. In both eras, ice accumulates very rapidly in the first several thousand years. After that, the ice volume reaches a plateau in the pre-MPT era and slowly increases in the post-MPT era. The Imbries’ equation can't possibly account for that. See Figures 1 and 2. Furthermore, there is no evidence that the value of V inhibits dV/dt in the early stages of glaciation. The rate of ice accumulation is high for several thousand years and seeming independent of V. From a longer point of view in the pre-MPT, the variables S and obliquity determine dV/dt and V does not enter.

Figure 1. Typical pattern of ice ages in the pre-MPT era. [1]

Figure 2. Typical pattern of ice ages in the post-MPT era. [1]

1.3 More Complex Model (1998)

Paillard (1998) presented a model in which depending on the values of insolation and ice volume, the climate system would respond in three different regimes: i (interglacial), g (mild glacial) and G (full glacial) and the differential equations that govern transitions between them are constrained by rules. [3] This approach is an improvement over the Imbries’ model and further development of this approach might provide good insights. Rapp (2018) suggested an increase to four regimes, adding a termination regime and he analyzed how that might work. However, this approach requires further analysis with realistic data for SIHL.

1.4 Consideration of North and South (2005, 2006)

Lisiecki and Raymo (2005) and Raymo et al. (2006) provided an analysis of ice age patterns in the pre-MPT period as derived from SIHL. [4, 5]

In a landmark achievement, Lisiecki and Raymo (2005) published details from the LR-04 stack of ocean sediment data that provides estimates of global ice volume over the past several million years. That stack represents arguably the best representation of the ebb and flow of global glaciation over an extended time. The raw stack data provides estimates of d18O vs. depth in the sediments, and is equivalent to global ice volume. [4]

Perhaps the most challenging aspect of this impressive work was converting depth to a timescale for the sedimentary data. The procedure used by L&R involved a combination of several contributing approaches. One part of this analysis involved use of the Imbries’ model. When the Imbries’ model was applied to their data in the pre-MPT era, the result was as shown in Figure 3. I performed the integration which duplicated the result provided by L&R. The Imbries’ equation produces negative values for V(t). Note that L&R converted their V(t) to a vertical scale of d18O ranging from 3.0 to 4.4, but it is not clear how they did that, or even whether than makes sense physically. Obviously, this result looks nothing like the actual data for ice volume.

Figure 3. Calculated relative ice volume using the Imbries’ equation for the north.

Raymo et al. (2006) pointed out that the ocean sediment data measured global ice volume, rather than northern ice volume. [5] Prior to the MPT, global ice volume during ice ages didn’t reach the high levels of the post-MPT era. They made a crucial assumption that seems credible. Here, I paraphrase their argument in my own terms:

It was suggested that the ice volume in the North in the pre-MPT was not sufficient to control the global climate. Unlike the post-MPT, the growth and decay of Antarctic ice responded to the changes in solar intensity at Antarctica. According to this concept, the Antarctic ice sheets became land-limited after the MPT. Albedo changes in the south were minimal and albedo feedback from the northern ice sheets controlled the global climate in the post-MPT.

The model of Raymo et al. (2006) suggests that in the pre-MPT:

(i) The annual cycle of ice/snow in both the North and South varied according to local SIHL. The ice/snow in the North never reached the extent needed to control the global climate.

(ii) In the South, ice/snow rose and fell in response to the local solar input.

(iii) The change in global ice volume in a precessional cycle is the result of gains and losses in the North and the South. The increase in ice the North during a down lobe in a precession cycle is partly balanced by a loss of ice in the South where there is a solar up lobe. This partly cancels the higher frequency component of precession and the global ice volume follows a predominantly obliquity cycle. 

(iv) In the pre-MPT, the global ice volume in the North and the South typically maximized at 50-60 percent of levels attained in the post-MPT.

Raymo et al. (2006) applied the Imbries’ model to the North and the South in the pre-MPT period. Following Raymo et al. (2006), I utilized the Imbries' equation to model the combination of North ice volume and 0.3 times South ice volume as shown in Figure 4. Note that V(t) is negative. The LR-04 data was scaled to fit on the graph. As Raymo et al. (2006) pointed out, the agreement of the cadence is remarkable. Despite the fit of model to data, this writer remains a bit skeptical. How can the Imbries’ model represent reality with it's negative V(t), its linear response to an obviously non-linear system, and its gross failure in the post-MPT era? The results seem enigmatic?

Figure 4. Comparison of modeled ice volume vs. time based on North and South (red curve) to the scaled LR-04 ice volume data (blue curve).

1.5 Sophisticated Model for the Pre-MPT (2023)

Watanabe et al. (2023) employed a three-dimensional dynamic ice-sheet model to estimate changes in ice volume for a portion of the pre-MPT. [6] They claimed their model provided good correlation to the observed variation of ice volume (as represented by changes in sea level) from about 1,550 to 1,200 thousand years ago. However, the model is too complex to infer the timing of the cycles in simple terms.

2. Materials and Methods

In this study, the materials were data on insolation, ice volume and temperature over the past 2 million years. The methods used were inspection and interpretation of the data, and where appropriate, modeling by integration of differential equations. The purpose was to return to fundamental data and examine the relationships between insolation (SIHL) and ice volume in the pre-MPT and post -MPT eras, to discern the connections between up lobes of SIHL and terminations, and the connections between down lobes in SIHL and starts of ice ages.

3. Results

3.1. The Pre-MPT Era

Figure 5 shows a comparison of SIHL, obliquity and sea level (as an inverse measure of global ice) across a segment of the pre-MPT. [6] This figure shows that sharp drops in sea level (increases in ice volume) occur only at SIHL down lobes. However, not all SIHL down lobes cause a drop in sea level. Furthermore, the SIHL down lobes that produce a drop in sea level are not always the down lobes with the greatest amplitude.

The solar power absorbed by the surface depends on the product of insolation (SIHL) and the absorptivity of the surface. The absorptivity is greater, the more the solar rays approach the vertical to the surface. The greater the obliquity, the greater is the angle between the solar rays and the normal to the surface, so the absorptivity is less at higher obliquity.

It can be seen in Figure 5 that when the obliquity down lobe occurs in the same time regime as a solar down lobe – sea level drops sharply indicating the beginning of an ice age (see vertical green lines). These occurrences appear to be spaced roughly regularly at approximately 41,000 year intervals (same as spacing of obliquity). There is an approximate resonance between the 41,000 year spacing of variations of obliquity and the 21,000-22,000 year spacing of precession so that almost every other precession down lobe occurs when there is an obliquity down lobe, resulting in minimum solar power absorbed by the surface, producing glaciation. The data indicates that start of an ice age requires solar and obliquity down lobes to occur in the same time regime. To get a best fit, the solar curves were shifted to the right a few thousand years. This might be due to a time lag between changes in solar and changes in ice volume, or possibly the sea level time scale is off, or some combination of the two.

Figure 5. Obliquity, solar power, and sea level in a segment of the pre-MPT era. Green lines show onsets of ice ages. Data from Watanabe et al. (2023). [6]

Figure 6 shows a comparison of SIHL, obliquity and sea level (as an inverse measure of global ice) across a segment of the pre-MPT. [6] This figure shows that sharp increases in sea level (decreases in ice volume) occur only at SIHL up lobes. However, not all SIHL up lobes cause a rise in sea level. Furthermore, the up lobes in SIHL that produce an increase in sea level are not always the up lobes with the greatest amplitude. The green lines show the starts of ice ages, and the red lines show terminations of ice ages. Dashed lines show lesser changes than solid lines.

Figure 6. Obliquity, solar power, and sea level in a segment of the pre-MPT era. Green lines show onsets of ice ages and red lines show terminations of ice ages. Data from Watanabe et al. (2023). [6]

We conclude that approximately every 41,000 years, the obliquity and SIHL undergo down lobes in the same time regimes, resulting in an ice age building up over very roughly 10,000 years. As time progresses, SIHL and obliquity run out of phase and the ice volume decreases slightly but the ice age remains. Finally, very roughly 20,000 years after start of the ice age, the obliquity and SIHL both enter the same time regimes and up lobes bringing about a termination of the ice age. The ensuing interglacial lasts very roughly 10,000 years. This cycle repeats itself with very roughly 30,000-year ice ages and very roughly 10,000-year interglacials. The ice ages appear to be very roughly 41,000 years apart. The exact timing varies from these round numbers.

3.2. The Post-MPT Era

3.2.1 Post-MPT Data

In the post-MPT era, the earth was colder than it was in the pre-MPT era, and the ice sheets were more extensive and more robust, and once started, they reached sufficient extent that they were better able to withstand up lobes in SIHL that occurred afterward. The ice age cycles were quite different from those in the pre-MPT period; yet variation of the solar parameters was essentially the same.

Figure 7 shows a comparison of the SIHL to the Antarctic temperature anomaly in the post-MPT era. [7] Each start of a major ice age (green dashed lines) occurs as a SIHL down lobe begins. All the sharp increases in temperature (terminations – red dashed lines) occur as a SIHL up lobe begins.

Not every SIHL down lobe produces glaciation. Not every SIHL up lobe produces a termination. Why?

Figure 7. Comparison of Antarctic temperature (from ice cores) to variations in SIHL. The red dashed lines show onsets of termination of ice ages at solar up lobes. The green dashed lines show onset of glaciation at solar down lobes. [7]

The ocean sediment data for d18O over the last 500,000 years is shown in Figure 8. The faint red lines show that a large expansion of ice takes place in the first down lobe of SIHL, spreading ice so far that the next up lobe in SIHL cannot terminate the ice age, but only slow its growth temporarily. The ice age continues to expand with further accumulation of ice for typically 4 or 5 cycles of precession. Eventually, rapid termination occurs at a down lobe of SIHL.

Figure 8. d18O as measured by ocean sediments in the last 500,000 years. Rapid spread of ice in the initial several thousand years is emphasized by faint vertical red lines. [1]

3.2.2 Model for Post-MPT

The post-MPT data tells us that coming out of an interglacial, an ice age starts at the next down lobe of SIHL. Once an ice age starts in the post-MPT era, the extent of glaciation expands rapidly over several thousand years. Each successive down lobe of SIHL adds to the ice volume and each successive up lobe of SIHL temporarily slows down ice accumulation but does not necessarily terminate the ice age. The ice volume continues to grow until a particular up lobe of SIHL brings about a termination. This is illustrated schematically in Figure 9.

The question is why does termination occur at this up lobe of SIHL? The answer might be that accumulation of dust on the ice late in an ice age increases its absorptivity and when that builds up sufficiently, the next up lobe in SIHL brings about a termination. Figure 10 shows that the major terminations late in the post-MPT era all occurred at SIHL up lobes accompanied by high dust levels.

Ellis and Palmer (2016) provided extensive evidence that deposition of dust on the ice sheets provided a decrease in ice-albedo that acted as a trigger to enable the next precession up-lobe to melt the ice sheets. [8] Only at the depth of an ice age (at the lowest temperature and the lowest CO2 concentration) after 4 or 5 precession cycles had evolved, would sufficient dust be deposited on the ice sheets to cause albedo reductions and glacial termination. There is good evidence that Antarctic dust levels peaked prior to each termination, but we only have Arctic dust data for the last termination. But since this limited Arctic dust data agrees so well with the Antarctic dust record, it is not unreasonable to assume that Arctic dust flux was closely correlated with Antarctic dust since the MPT. It seems likely that the effects of SIHL variations were being masked by the albedo-feedback driven tendency toward glaciation in the North, until dust deposition decreased the albedo, thus allowing a SIHL up-lobe to produce a termination. The pattern during the period from 800,000 years ago to 450,000 years ago was not as regular as that after 45,000 years ago, but the spacing of major glacial-interglacial periods tended to be very roughly 4 precessional cycles. The data for the past five ice ages indicate that the heat balance of higher northern latitudes favored glaciation, and lacking any unusual internal Earth factor, the ice sheets at higher northern latitudes would have continued to grow unabated. The data indicate that precessional up-lobes in SIHL in the North might have produced temporary slowdowns in the expansion of the ice sheets, but the long-term trend through at least four precessional periods was a continuing expansion of the ice sheets. The data also show that after 4 or 5 precessional cycles, the growth of the ice sheets came to a rather sudden halt, and a termination ensued in which the ice sheets melted in a period of roughly 7,000 years.

We surmise from the work of Peltoniemi, et al. (2015) that the solar elevation is a crucial parameter for bringing about a glacial termination resulting in an interglacial. [9] The solar elevation at solar noon at mid-summer is {90° – (latitude) + (obliquity)}. At 65°N latitude, the solar elevation at solar noon at mid-summer is {25° + (obliquity)}. As the obliquity ranges from about 22° to 24°, the sine of the solar elevation at solar noon at mid-summer ranges from 0.258 to 0.269, an increase of 4%.

These observations lend some credence to the idea that terminations originate at a precessional upswing in SIHL immediately after major dust deposition. 

Figure 9. Model for ice ages in the post-MPT era.

Figure 10. Dust levels at an overlapping time scale as SIHL and temperature in Antarctic ice cores. [1, 8]

4. Discussion

There is little doubt that oscillations in SIHL, induced by variations in the Earth’s orbit, are the main drivers for the recurrent cycles of glacial and interglacial periods. Spectral analysis demonstrates participation of the orbital parameters. [1] We have demonstrated here that essentially all terminations of ice ages occur on up lobes of SIHL, while ice ages begin on down lobes of SIHL. The big questions are why some up lobes produce terminations while others do not, and why some down lobes originate ice ages while other do not. The answer to these questions is subdivided into pre-MPT and post-MPT eras.

In the pre-MPT era, we find that ice ages originate at time periods when the SIHL is entering a down lobe and the obliquity is minimal, resulting in a combination of low SIHL and higher reflectivity (at lower obliquity which makes the solar angle at high latitude more glancing). Ice ages terminate at a coincidence of high SIHL and high obliquity. Because the timing of variations in obliquity is almost double that of precession, the occurrence of these links between SIHL and obliquity tends to be repetitive with approximately 41,000 year spacing. 

Later in the post-MPT era, we find that ice ages originate at a down lobe of SIHL. Because the Earth is now cooler than in the pre-MPT era, once an ice age is started, there is a rapid increase in the spread of ice, so that each successive up lobe in SIHL might cause a slight decrease in ice volume but is unable to bring about a termination. Each down lobe that follows adds to the ice volume. The ice age continues to expand as up lobes and down lobes of SIHL continue. After several precession cycles, the effect of global cooling creates a very dusty atmosphere, and when high dust levels and an up lobe become coincident in time, a termination occurs.

5. Conclusion

The astronomical theory of ice ages is widely accepted. Periodic changes in key parameters of the Earth’s orbit produce variations in the solar input to high latitudes (SIHL) and ice ages begin on down lobes of SIHL and terminate on up lobes of SIHL. However, not all down lobes create ice ages and not all up lobes produce terminations. The ice ages change character at the so-called mid-Pleistocene transition, about a million years ago. The actual amount of solar power absorbed depends on SIHL and the absorptivity of the surface. The absorptivity is affected by the obliquity in the pre-MPT era, and by dust deposits late in the post-MPT era. When these are included, we can rationalize why some down lobes produce ice ages, and some up lobes produce terminations in both eras. In the pre-MPT era, ice ages originate when the SIHL enters a down lobe and the obliquity is minimal (higher reflectivity) and ice ages terminate at a coincidence of high SIHL and high obliquity. These links between SIHL and obliquity tends to be repetitive with approximately 41,000-year spacing. Later in the post-MPT era, ice ages originate at a down lobe of SIHL. Once an ice age is started, each successive up lobe in SIHL might cause a slight decrease in ice volume but doesn’t bring about a termination. After several precession cycles, high dust levels increase absorptivity, and the next up lobe produces a termination.

The uncertainty is now resolved.

6. Author Contributions

Donald Rapp carried out the entire study.

7. Funding

No funding was provided by any agency.

8. References

[1] Rapp, D. (2018) Ice Ages and Interglacials, Springer-Praxis Books, Heidelberg, Germany.

[2] John Imbrie and John Z. Imbrie published an influential paper “Modeling the Climatic Response to Orbital Variations” in Science 207, 943-953

[3] Paillard, Didier (1998) “The timing of Pleistocene glaciations from a simple multiple-state climate model,” Nature 391, 378-381.

[4] Lisiecki, L. E. and M. E. Raymo 2005. A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O records Paleoceanography 20, PA1003-PA1019.

[5] Raymo, M. E. et al. (2006) Plio-Pleistocene Ice Volume, Antarctic Climate, and the Global d18O Record Science 313, 492-495.

[6] Watanabe, Y., Abe-Ouchi, A., Saito, F., et al. (2023) “Astronomical forcing shaped the timing of early Pleistocene glacial cycles” Communications Earth & Environment 4, Article number: 113.

[7] Rapp (2018), loc cit., Section 8.6.4

[8] Ellis, Ralph and Michael Palmer (2016) “Modulation of Ice Ages via precession and dust-albedo feedbacks” Geoscience Frontiers http://www.sciencedirect.com/science/article/pii/S1674987116300305

[9] Peltoniemi, J. I., M. Gritsevich, T. Hakala, et al. (2015) “Soot on Snow experiment: bidirectional reflectance factor measurements of contaminated snow” The Cryosphere 9, 2323–2337.