Introduction Over the past million years, our Earth displays a rhythmic beat when exiting full glacial cycles and entering interglacial warm periods. The characteristics and duration of these systematic warm periods provide an excellent dataset to help prognoses of future climate patterns. Astronomical Milankovitch cycles play a major role and trigger internal Earth processes that control the rapid onset and gradual cooling of interglacial warm periods. This post examines the duration of these interglacial warm periods as a key analog dataset compared to several published statistical and complex climate model projections. Results indicate climate models where the initiation of glaciation depends strongly on CO₂ concentrations over astronomical controls significantly overpredict the duration of the present-day warm period compared to past interglacial analogs. Glacial Cycles During the past 800 kyrs there are nine glacial cycles with approximately eleven interglacial warm periods including the Holocene present day as shown in Figure 1. The present day is currently within an interglacial warm period and has yet to enter a mild or full glacial period. The length of our current interglacial period and history matching of past glacial cycles has been modeled by many scientists such as (Imbrie, Crucifix and Rougier, Vettoretti and Peltier, Berger and Loutre, Calovet al., Ganopolski, et. al., Archer and Ganopolski, and Tzedakis et. al,). Figure 1: A traverse of the past interglacial-glacial cycles over the past 800 kyrs. Cycles are datumed on the termination of the glacial period and onset of the interglacial warm period. EPICA Dome C isotope temperature estimates are plotted as curves in 1° C increments on the horizontal scale (cold to left and warm to right). The vertical scale is time in 20 kyr increments. Actual age is plotted on each cycle. Interglacial warm periods are highlighted in red (> -2° C) and the coldest portion of the glacial period in blue. Eccentricity cycles are noted on top. Marine isotope stages (MIS) are also noted. These glacial cycles last approximately 100 kyrs. However, they are not exactly 100 kyrs in duration as described by Javier and in my previous post here. Figure 1 shows they range from 76 kyrs in Glacial Cycle IX to 119 kyrs in Glacial Cycle II. While there is error of +/- 3 kyrs on the exact pick of the termination datum, that does not change the observations below. In Figure 1, the 400 kyr eccentricity cycle is clearly evident in the glacial cycle duration and interglacial character. Glacial cycles are shorter in duration during nearly circular orbits which occur every 400 kyrs. The nearly circular orbits occur during Glacial Cycles IX and V which are MIS 19 and 11, respectively, are less than 90 kyrs in duration. They have brief mild glacial periods. Since the current Glacial Cycle I is occurring in a nearly circular orbit, several scientists project this cycle will be short with the next glacial maximum occurring in 55 kyrs to 100 kyrs as suggested by Crucifix, Imbrie, Berger, and in my previous post here. The glacial cycles increase in duration during the 400 kyrs following each nearly circular orbit. Older Glacial Cycles IX to VI increase in duration from 76 kyrs to 102 kyrs and more recent Glacial Cycles V to II increase in duration from 89 kyrs to 119 kyrs. The older glacial cycles last a total of less than 370 kyrs combined while more recent glacial cycles span greater than 400 kyrs. This suggests the eccentricity cycle that started 800 kyrs ago was shorter in duration than the most recent eccentricity cycle that started 400 kyrs ago. Earth is currently in a nearly circular orbit and at the beginning of the next 400 kyr eccentricity cycle. Glacial cycles that occur during predominantly elliptical orbits such as Glacial Cycles VII and III tend to have interglacial doublet periods (MIS 15a and 15c, MIS 7 a/c and 7e). Interestingly, the following 100 kyr cycle after the elliptical orbit tends to be equal to or longer in duration. It also contains a stunted second interglacial warm period such as MIS 13a and a longer mild glacial period. Interglacial Warm Periods Earth is currently in an interglacial period. There have been at least 10 interglacial warm periods during the past 1 million years that serve as analog datasets. The duration of the interglacial warm periods ranges from 5 to 35 kyrs. They are recognized in benthic oxygen isotopes in marine sediments (Lisiecki and Raymo, 2005) and with deuterium isotopes from ice cores in Antarctica (EPICA) as shown in Figure 1. Antarctica dome C isotopes are corrected to temperature and then multiplied by 0.5 to approximate global temperatures. Figure 1 shows interglacial warm periods shaded in red using a global temperature for the Dome C isotope data of a minus 2° C cutoff. This is a lower cutoff than my previous climate traverse which uses a minus 1° C cut-off. The cutoff was lowered in Figure 1 because the older interglacial warm periods are not as warm as the more recent five warm periods and many would not make a minus 1° C limit. The present day warm period is 1 to 2° C cooler than the past four interglacial periods. In a series of workshops of the Past Interglacials Group (PIGS) they defined interglacial duration periods as a time when sea level is greater than minus 20 meters relative to present day and the Northern Hemisphere (NH) is predominantly ice free except for the Greenland ice sheet (Berger, A., et al). These workshops established isotope and CO₂ limits that define an interglacial period as shown in Figure 2. Benthic oxygen isotopes δ¹⁸O in marine sediment records, during interglacials, range from 3.5 to 3.73 ⁰/00. Antarctic deuterium isotopes, during interglacials, are minus 403 ⁰/00. Deuterium isotopes of minus 403 ⁰/00 are closely equivalent to the minus 1° C global temperatures used in this post. Both minus 1 and minus 2° C cutoffs are examined in this article. Figure 2: Generalized schematic of interglacial warm periods for MIS 5e and 9e. Note these warm periods are 1 to 2 degrees C warmer than present day (orange dotted line). The color bar on top refers to the different phases of an interglacial period. The horizontal axis is relative time in thousands of years and the vertical axis is global temperature relative to present day (^oC). Direct measurement limits are highlighted in red callout box. The continuous and direct measurement of isotopes provides a robust dataset for interglacial comparisons and evolution. Associating these measurements with relative sea level and lack of Northern Hemisphere ice is a good proxy. Conversely, sea level measurements and the lack of NH ice are indirect and interpretable observations. Sea level curves are relative measurements impacted by many factors including isostatic rebound, tectonic uplift/subsidence and even hurricanes. Importantly, sea level curves are discontinuous and only cover a portion of the record. There are no consistent historical datasets available to confidently measure sea level. This suggests sea level and NH ice presence are less reliable to use for history matching climate models and that isotopes provide a more continuous and reliable dataset. Milankovitch Cycles, notably summer insolation minima and obliquity, are recognized as the key triggers for termination of glacial conditions and initiation of ice sheets (Berger et.al, Tzedakis, Imbrie). Figure 2 summarizes Earth climatic processes associated with the warm onset and eventual cooling after the astronomical trigger. The cooling of warm periods is more gradual than their inception. When cooling occurs, temperatures drop over time with an average slope of m = 0.35 as calculated here. This highly consistent cooling slope suggests that natural temperature decline is repeatable and controlled by similar processes. Once cooling has started, it will take internal oceanic-atmospheric processes 3 to 4 kyrs to initiate ice sheets in the NH, drop sea levels and exit the interglacial period. Interglacial Duration Analogs Berger, et. al established a dataset of the duration of past interglacial warm periods using various methods. In this post, that dataset was expanded to include two EPICA global temperature limits of minus 1 and minus 2° C. Figure 3 is a histogram of the interglacial duration dataset. In general, these warm periods during the past million years range from less than 5 kyrs to 35 kyrs, with MIS 11 being the longest in duration. The present-day Holocene, also referred to MIS 1, is currently longer in duration than MIS 7e and several of the older interglacial periods. It is similar in duration to MIS 5e and 9e, but not as long as MIS 11, so far. Internal characteristics and detailed comparisons of the younger interglacials have been described in a previous post here. Figure 3: Plot of the past interglacial warm period durations from Berger, PIGS dataset. Dome C global temperatures of minus 1 and minus 2° C limits were included. There are notable differences between the older warm periods and the youngest five warm periods during the past million years. The different isotope and CO₂ methods are fairly consistent in defining the younger interglacials (MIS 1 to 11) and less consistent in older interglacials. The LR04 marine isotope (orange) tends to show shorter warm period durations than the Dome C isotopes particularly in the older interglacials. The Dome C minus 2° limit in light blue tends to be the most lenient cutoff and almost always overestimates the duration. Defining interglacials by CO₂ limits (red) is the most inconsistent variable and tends to underestimate the warm period durations. The younger interglacials have CO₂ concentrations higher than the 260-ppm limit except for MIS 7ac. None of the older interglacials have CO₂ greater than 260 ppm except MIS 19. This suggests the presence of CO₂ during recent interglacial warm periods has increased naturally with time and higher CO₂ concentrations are associated with these warmer periods. The warm duration dataset in Figure 3 was plotted on a frequency plot to evaluate probability, or frequency of occurrences, as shown in Figure 4. This graph shows the relative proportion of each duration to the total distribution over the past million years. Fifty percent of the time an interglacial duration lasts approximately 16 kyrs. Ninety percent of the time or a majority of the time an interglacial period lasts at least 10 kyrs. Only ten percent of the time or rarely does an interglacial period last a 32 kyrs or longer. Figure 4: Excel Pareto plot of interglacial durations using various temperature, isotope, and CO₂ limits over the past million years. These past interglacials provide a key analog dataset for the current and future interglacial warm periods. Why does this matter? For scientists, analogs are valuable to increase confidence that concepts, hypotheses and theories are underpinned with historical data. Analogs demonstrate what is known versus unknown. The description of analogs is essential to create a common understanding of Earth and climate models input, output and their limitations.

‘[Intellectual] Growth comes through analogy: through seeing how things connect, rather than only seeing how they might be different’. —Albert Einstein

History of Climate Model Projections This section is a brief historical overview of climate model projections for the duration of the present-day interglacial warm period. It is not intended as a discussion of various models or computational algorithms of the models. The intent is to compare model projections of the present day warm period to historical analog data. Figure 5 shows various published authors’ model projections for the current warm period duration compared to the paleoclimate analog dataset. Figure 5: Climate model projections compared to the mean (blue) and mode (orange) of past interglacial durations after Berger, et. al. Model durations for present day (MIS 1) are shown in green (low side) and red (high side). Past analogs means/mode range from 5 to 30 kyrs while models project the present-day warm to extend from 20 kyrs up to 100 kyrs. All model projections were adjusted by 12 kyrs to include the existing MIS 1 warm duration to date. Early projections for the Holocene interglacial cooling by scientists such as Imbrie in 1980 were statistically derived and used relatively simple models based on past interglacial analog data. These projections suggest cooling begins in about 25 kyrs from present day and glaciation in about 55 kyrs. The influence of CO₂ was not included. Climate models became more sophisticated as computing power increased. They included ice-sheet models, coupled oceanic-atmospheric models as well as orbital and insolation (solar radiation) influences. Anthropogenic CO₂ emissions increasingly came into the spotlight during the 1980’s and climate models began running sensitivities on the impact of various CO₂ concentrations. In 2002, Berger and Loutre estimated that the present day warm period will have a duration of 50,000 years with the next glacial maximum in 100,000 years. They point out eccentricity will be nearly circular within the next 25,000 years which reduces the influence of precession. Consequently, insolation variations will be suppressed over the next 100,000 years. Their models begin to use CO₂ concentrations in addition to insolation controls which defers initiation of glacial conditions. Concentrations of human induced CO₂ ranging from 750 ppm to 220 ppm were modeled. Berger and Loutre state, “Only for CO₂ concentrations less than 220 ppmv was an early entrance into glaciation simulated.” In 2004, Vettoretti and Peltier’s complex 3D fully coupled atmosphere-ocean general circulation model (GCM) challenged that observation. They concluded in the absence of modern anthropogenic GHG influence that the next glacial inception is less than 10 kyrs and at most 20 kyrs into the future when obliquity is at a minimum and insolation is reduced in the Northern Hemisphere. They present a schematic for the evolution of CO₂ with orbital parameters to explain the time lapse of CO₂ to decreasing temperatures. They conclude, “Our analyses suggest that insolation forcing is by far the most significant driver of the glacial inception process with GHG concentration playing a secondary role.” In 2005, Archer and Ganopolski, using a coupled climate-ice sheet model conclude that insolation minima are tightly correlated with ice sheet nucleation and growth. Also, an increase in baseline pCO₂ will require a deeper minimum insolation. Therefore, the nucleation threshold for initiation of glaciation depends strongly on CO2 concentrations in their model. As a result, the present day warm period is predicted to last 50 to over 100 yrs. Modeled future pCO2 trajectories for anthropogenic CO₂ of 300, 1000, and 5000 Gton C releases were evaluated. Constant CO₂ concentrations do not decrease naturally below 280 ppm as observed in past analog data to allow for initiation of the next glaciation. Crucifix and Rougier’s 2009 model was a 3D stochastic system bounded by a Bayesian framework. This model focused primarily on variations of internal Earth processes; ice volume, atmospheric CO₂ and deep ocean temperature. It appears astronomical insolation and obliquity factors were not included in the model. They note a weak predictability of CO₂ in the model and the CO₂ dynamics during interglacial periods was not satisfactorily reproduced. Their figure 8 shows a wide distribution in the input parameters during the present day and near future as shown by spaghetti chaos. Parameters were trained based on the preceding interglacial period which improved the deviation in the data (their figure 9). The model projected the next glacial inception in 40 to 50 kyrs from the present with peak glacial conditions in 60 kyrs. In 2016, using a model of intermediate complexity, Ganopolski, et. al. continued promoting CO₂ relationship to insolation in their history matching of ice volume and sea level and subsequent projections. Their publication states,

“Our analysis suggests that even in the absence of human perturbations no substantial build-up of ice sheets would occur within the next several thousand years and the current interglacial would probably last for another 50,000 years.”

Even more interesting, Ganopolski, et. al claim that,

“Moderate anthropogenic cumulative CO₂ emissions of 1,000 to 1,500 gigatonnes of carbon will postpone the next glacial inception by at least 100,000 years.“

An interglacial duration exceeding 100,000 years would skip three obliquity cycles. This would make our current Glacial Cycle 1 the longest glacial cycle as well as the longest interglacial period observed during the past million years. In stark contrast, the past glacial cycles that include both interglacial and glacial conditions during nearly orbital eccentricity cycles are all shorter than 90 kyrs (Figure 1). In 2017, Javier and Tzedakis, et al. used new and different methods to evaluate astronomical controls on interglacial onset and pacing for the past million years. Tzedakis developed a statistical model using orbital forcing and elapsed time to correctly classify all but two interglacials during the past 2.6 million years. Both Javier and Tzedakis conclude that obliquity is the dominant astronomical parameter driving ice volume changes. As Tzedakis states,

“The phasing of precession and obliquity influences the duration of interglacial periods over one or two insolation peaks, leading to shorter (~ 13 kyr) and longer (~28 kyr) interglacials.”

Javier also recognized a 6.5 kyr lag between interglacials and obliquity cycles. Of note, neither scientist used CO₂ concentration to drive interglacial pacing. Discussion Several modelers conclude that decreasing insolation and obliquity are primary triggers for glacial inception with CO₂ playing a secondary role (Vettoretti and Peltier, and Calovet et.al.). Their projections of the current warm period ranges from 20 to 30 kyrs and fits within the range of past analog warm duration data. Tzedakis classified interglacials statistically using external astronomical data only and CO₂ was not included. Other modelers allow CO2 concentrations during this weak eccentricity cycle to be a critical driver in the initiation of glaciation. In the cases where CO₂ concentrations require a stronger insolation trigger, the present day warm period is extended by 50 to 100 kyrs (Berger and Loutre, Archer and Ganopolski, Ganopolski, et. al). Constant CO₂ concentrations are incorporated into their models and do not vary naturally as seen in past interglacial coolings. Berger states, “…the relationship between astronomical parameters and CO₂ trends is expected to be indirect and complex.” Figure 6 illustrates past glacial-interglacial cycles compared to interglacial model projections of 20 kyrs, 50 kyrs, and 100 kyrs for the present day. Figure 6: Climate projections in vertical red bars for present-day warm duration shown in Glacial Cycle 1. See Figure 1 for label descriptions. The model projections are from present day and are added on top of the existing 12 kyrs of present day (MIS 1) duration. Projections of 50 to 100 kyrs interglacial durations are well outside the range of past analog data as shown in figures 4, 5 and 6. The 100 kyr model projection for present day warm duration far exceeds the range of past analog data during the last million years. The 100 kyr projection suggested by Ganopolski et. al. extends the current warm period as long as an entire glacial cycle. Such a large deviation from the last million years of historical analog data and interruption of the natural rhythm of Earth’s glacial cycles warrants further scrutiny. Crucifix and Rougier believe that the evaluation of paleoclimates is a multi-disciplinary process and should include field scientists, mathematicians, climate modelers, complex systems experts and statisticians. Further, climate modeling is not merely a technological problem that can be solved with more complicated models and faster computers. Finally, climate models have two basic building blocks; Earth’s climate history and a projection of the future. History during the past million years is reasonably verified by scientific data and proxy information. The future is an interpretive blend of conjecture and science. It is imperative that any climate model be rigorously history matched and only a successful history-match should be used as a base case. The natural base case needs to be clearly defined and presented before adding assumptions and projecting into the future. Unfortunately, several climate modelers have a singular focus on using CO₂ concentrations to trigger initiation of glaciation over astronomical processes resulting in extended projections that conflict with paleoclimate analogs. CO₂ dominated model projections should not be considered a base case for decision making, but merely an unproven sensitivity in overall climate model studies. Conclusions Over the past million years, glacial-interglacial cycles range from 76 kyrs to 119 kyrs in duration. The 400 kyr eccentricity cycle is evident in the glacial cycle duration and interglacial pattern. Glacial cycles are shorter than 90 kyrs in duration during nearly circular orbits every 400 kyrs. Glacial cycles contain interglacial doublet periods during more elliptical orbits every 400 kyrs. Earth is currently in a nearly circular orbit with analog data indicating the current glacial cycle will be less than 90 kyrs long. The past ten warm interglacial periods range from 5 to 35 kyrs in duration. Cumulative probabilistic evaluation using different variables including CO₂ concentration limits for interglacials demonstrates that only ten percent of the time or rarely does an interglacial warm period last 32 kyrs or longer. Fifty percent of the time an interglacial warm period lasts 16 kyrs. Earth has been in an interglacial warm period for approximately the past 12 kyrs. Climate model projections for the extent of Earth’s warm period range from 10 kyrs to over 100 kyrs beyond present day. Models that emphasize astronomical controls such as insolation and obliquity show glacial inception in the next 10 to 30 kyrs. These projections fit within the range of paleoclimate analogs and should be considered the base case. Models that project glacial inception in the next 50 to over 100 kyrs suggest that CO₂ concentration affects climate more than astronomical variables. These projections are outside the range of past interglacial analogs and even exceed the duration of the entire interglacial-glacial cycle. They far exceed the analog datasets and should not yet be considered reliable as a base case scenario.

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality – Albert Einstein, Address to the Prussian Academy of Sciences (1921)

Acknowledgements: Special thanks to Andy May and Donald Ince for reviewing and editing the article.   This article appeared on the Watts Up With That? website at https://wattsupwiththat.com/2017/09/21/climate-model-projections-significantly-diverge-from-paleoclimate-analogs/]]>