Werner Schmutz1 and Margit Haberreiter1
One of the natural climate forcings is the so-called orbital forcing, besides others, such as the variation in solar irradiance and volcanic eruptions. The orbital forcing depends on changes in the Earth’s orbit around the Sun and is the result of variations of the following parameters: the orbit’s eccentricity, the obliquity of the Earth’s orbit with respect to the ecliptic plane, and the axial and apsidial precession, i.e., the precession of the Earth’s rotation axis and the precession of the Earth’s orbital ellipse around the Sun. The latter two are often combined into one process. Orbital forcing yields significantly different irradiance values for the two terrestrial hemispheres at high latitudes but has almost no effect on the mean total energy. The dominant forcing determining the ice ages is the one on the northern hemisphere.
1 Milankovi´c cycles
An astronomical influence of the orbital forcing on climate had already been pos-tulated in the 19th century, but a qualitative relationship was only determined at the beginning of the 20th century, mainly by Milutin Milankovi´c. The theory that climate variations are forced by orbital variations is therefore usually referred to as Milankovi´c Cycles. These cycles are schematically shown in Figure1 and are explained in more detail below.
First, the Earth’s orbit is an ellipse. The eccentricity (Figure1a) describes the degree of oblateness (or elongation) of an ellipse. The eccentricity of the Earth’s orbit ranges from 0.000055 to 0.0679, where an eccentricity of zero would indicate a perfect circle. The eccentricity varies with two main periodicities of around 100 kyr and 400 kyr.
Second, the Earth’s equatorial plane is inclined with respect to the ecliptic plane. The angle of inclination is called obliquity or axial tilt, and is indicated as
1Physikalisch-Meteorologisches Observatorium Davos / World Radiation Center, Dorfstrasse 33, 7260 Davos, Switzerland
c
EDP Sciences 2015 DOI: 10.1051/978-2-7598-1733-7.c113
Fig. 1. Schematic illustration of the variation of the eccentricity of the Earth’s orbit (a), the variation of the obliquity or inclination of the terrestrial rotation axis,ε(b), the precession of the Earth’s rotation axis (c), and the apsidial precession (d); illustration courtesy of Stephan Nyeki.
ε in Figure1b. This angle oscillates every 41 kyr from 22.1◦ to 24.5◦. Presently, the obliquity is at 23.44◦.
Third, the Earth’s rotation axis is not fixed in space but describes a cone (Figure1c) with respect to the fixed stars, i.e., it precesses. It takes 26 kyr for the Earth’s rotational axis to complete one full precession cycle. Moreover, the Earth’s elliptical orbit also precesses around the Sun at the rate of 112 kyr (Figure1d), called the apsidial precession. These two precession rates lead to a combined period of∼21 kyr. As a consequence, the occurrence of perihelion, i.e., the point in the Earth’s orbit where the Earth is closest to the Sun, varies from northern summer to northern winter and back to northern summer. Presently, the Earth is closest to the Sun in January, i.e., during the northern winter.
The amount of radiation reaching the Earth depends on the Sun-Earth dis-tance. Due to the varying orbital parameters described above, the smallest Sun-Earth distance occurs at different seasons over the precession time scale. To ac-count for this, the standard representation of the orbital forcing has been defined as theinsolationat high latitude, referring to the radiation reaching Earth during northern summer, i.e., in June at 65◦ North.
Figure2shows the variation in eccentricity, climatic precession, and obliquity, along with the summerinsolationand the CO2 concentration from 200 kyr before the present to 130 kyr into the future relative to the year 1950. The projection of the CO2concentration based on orbital forcing for the future is based on the CO2, i.e., without the anthropogenic CO2contribution, determined from the Vostok ice core (Petit et al.,1999) and the variation of the summerinsolationdetermined by (Berger,1978). In other words, in this analysis, the prediction of CO2for the future is based on the extrapolation of the past CO2 concentration as determined from ice cores using orbital parameters, known for the past as well as for the future, as proxy. The observed CO2 concentration for the present, including anthropogenic
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Fig. 2. Long-term variations of the Earth’s eccentricity (top panel), climatic preces-sion (second panel), obliquity (third panel), summer solstice insolation at 65◦ North (fourth panel), and the corresponding atmospheric CO2 concentration (bottom panel) from 200 kyr before present (BP) to 130 kyr after present (AP). The reference year (0 kyr) is 1950. The variation of the CO2concentration in the lower panel is determined from the historic CO2 concentration fromPetit et al.(1999) and the orbital prediction byBerger (1978). Thus, the variation in CO2 is purely related to the orbital effects. Note, the current CO2 value including anthropogenic CO2 emission is∼400 ppmv as of February 2015. Figure courtesyBerger et al.(2003).
CO2 emission, is considerably higher, i.e.,∼400 ppmv as of February 2015. The panels illustrate that the summerinsolationis determined by the superposition of the first three parameters. Also, it is obvious that the variation of the eccentricity (top panel), on time scales of roughly 100 kyr, dominates the peaks in the summer insolation(fourth panel), and, as a consequence, leads to an increase of the CO2
concentration (bottom panel). The latter is, to a first approximation, in phase with the variation of the temperature on the Earth.
Theinsolation in northern summer is strongly modulated by the movement of the perihelion, precessing, as discussed above, on the combined 21-kyr time scale (Figure1c,d). In addition, the variation in obliquity (Figure1b) introduces an additional 41-kyr variability. Moreover, due to the multitude of planetary perturbations on the terrestrial orbit, there are many periods present in each of the variations of the three orbital parameters. The interplay of all the periods yields a seemingly chaotic picture of the combined effect of the orbital forcing on the insolation in northern summer. However, the periods are all mechanistic perturbations, and can therefore be determined precisely for the past as well as for the future; see e.g. (Berger, 1978). Based on the orbital influence alone, i.e., without the anthropogenic CO2emission, it is predicted that the Earth would be entering its next ice age within a 50-kyr time scale, when the northern summer insolationreaches its next minimum (see Figure2, fourth panel).
The present CO2gas concentration (not illustrated in Figure2), including the anthropogenic emission, has reached a value of∼400 ppmv as of February 2015. In fact the total CO2gas concentration has increased over the last 250 years by more than 100 ppmv, i.e., roughly the same amount it has increased over the last 10 kyr due to the orbital forcing. Thus, to obtain the total future CO2gas concentration, the value given the fourth panel of Figure2 would need to be corrected by the increase in anthropogenic CO2emissions.
2 Correlation with climate indicators from ice cores and benthic rock The influence of the Earth’s varying orbit around the Sun on climate is established beyond reasonable doubt by the correlation between climate indicators and the orbital forcing. As already mentioned, the latter is usually represented by the insolation, i.e., solar irradiation, in the northern summer, i.e., in June at latitude 65◦ North.
The standard measurements to reconstruct the climate for the past are the following. First, the CO2 gas concentration, which is archived in the Arctic and Antarcitc ice sheet, is a direct measurement of the greenhouse gas concentration at the time the corresponding ice layer formed.
Second, the oxygen isotope ratio (δ18O) in O2reflects changes in the global ice volume and the hydrological cycle. Third, the deuterium content of the ice (δDice) is aproxyof the local temperature change. The age of the ice is determined accord-ing to its depth in the ice core. Even though the correspondaccord-ing date of an ice layer and thus the date of the climate indicators it contains, can only be determined
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Fig. 3.Time series of climate indicators (first to forth line) determined from ice cores at Vostok station, and northern summerinsolation(bottom line). The lowerx-axis gives the glaciological timescale and the top x-axis the corresponding depths of the ice for:
a) CO2 (blue); b)δDice isotopic temperature of the atmosphere (red); c) CH4 (green line); d)δ18Oatm (brown); and e) mid-June insolation at 65◦ North (in Wm2, bottom line). The mean resolution of the CO2 (CH4) profile is about 1 500 (950) years. It goes up to about 6 000 years for CO2 in the fractured zones and in the bottom part of the record, whereas the CH4 time resolution ranges from a few tens of years to 4 500 years. The overall accuracy for CH4 and CO2measurements are 20 ppbv and 2–3 ppmv, respectively; CourtesyPetit et al.(1999).
within uncertainties, they are sufficiently well known to conclude from ice cores obtained in Greenland and compared to antarctic cores, that warm and cold peri-ods on the northern and southern hemisphere have developed in phase – at least during the last 800 kyr.
Figure3 shows the CO2 concentration (blue line), the temperature recon-structed fromδDice(red line), CH4gas concentration (green line), and the oxygen isotope ratio δ18O (upper brown line) from the Vostok ice core records, covering the last 400 kyr, i.e., the last four glacial–interglacial cycles. The data show that there are periods with high peak temperatures, which develop relatively quickly from a cold stage. After the temperature reaches the maximum of a warm pe-riod, it gradually decreases until the onset of the next high-temperature peak.
This saw-tooth pattern repeats about every 100 kyr. At the onset of the warming there is, within the uncertainty of ice-dating, always a strong maximum of summer
insolationin the northern hemisphere. This is, as discussed above, the result of a maximum in forcing resulting from a coherent positive combination of eccentricity, precession, and obliquity of the Earth’s orbit, with the key drivers being a large eccentricity along with a perihelion in the northern summer. Most importantly, the repetition period of the glacial–interglacial cycles is in synchronisation with the occurrence of high eccentricity.
The18O and13C isotopes are also measured in benthic rock sediments dating back several millions of years. The synchronization between northern hemispheric summer forcing and the climatic modulations is well established down to the 41-kyr oscillation of the obliquity of the Earth’s orbital axis relative to the ecliptic.
Moreover, the climatic changes in the past, beyond the dating limit of ice cores, can be assessed from oxygen isotope ratios (δ18O) in calcium carbonate of benthic foraminifera. These data reveal that a switch occurred from intermediate warm periods every 100 kyr – as during the last one million years – to 41 kyr, the latter being the dominant period of the Earth’s obliquity variations. The transition be-tween the two modes took place in the mid-Pleistocene, about 0.8 to 1.2 million years ago. Even though some mechanisms that are at play are only partially un-derstood, the current understanding is that inter-glacial warm periods within the last ice ages were forced by irradiance variations resulting from the varying orbit of the Earth around the Sun.
3 Global influence of northern summer orbital forcing
Given the good correlation between orbital forcing and climatic variations, it seems obvious that the solar irradiance arriving at the terrestrial surface indeed drives the Earth’s climate. However, it turns out that this relation is far from easy to understand or straightforward to model. The reasons are as follows. First, the eccentricity of the Earth’s orbit varies from∼0 to∼0.07. Integrating the radiation energy over the year, however, it turns out that the annual energy received at the Earth does not depend on the Earth’s eccentricity to first order. Only to second order does the annual energy reaching the Earth increase by a small amount for larger eccentricity. Indeed, for large eccentricity, the difference in insolation between perihelion and aphelion can be very large, i.e., up to 23 %. At the same time, the current view is that if perihelion occurs during the northern summer, the climate is forced towards a warmer global climate. Thus, the orbital forcing is not a matter of the total energy but rather its redistribution over the seasons. We note that if the correlation between climate and theinsolationforcing for summer in the northern hemisphere is positive, then it has to be anti-correlated with southern summer insolation. As the warm and cold periods of the two hemispheres are varying synchronously – at least within the last 1 Mio years – it is the northern hemisphere climate which dominates over the counter-actinginsolationforcing of the southern hemisphere. Most likely, this can be attributed to the much larger fractional area covered by land in the northern hemisphere with respect to the southern hemisphere.
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4 The role of historic CO2 concentration
Presently, the Earth is at perihelion in January. Thus, the positive forcing that has brought Earth into the present warm period, theHolocene, is understood to have happened half a precession period (i.e., about 10 kyr) ago, when perihelion ocurred during the northern summer. Indeed this time interval coincides with the start of the Holocene. However the question arises, why does the temperature curve (Figure3, red curve) show this saw-tooth pattern, i.e., why does the temperature decrease relatively slowly after each sudden warming? One hypothesis is that the orbital forcing is only the trigger that releases a climate process. It appears that a thousand years of exceptionally high summer insolation in the northern hemi-sphere, with a negative yearly mass balance of the northern glaciers, is sufficient to completely remove the glaciation of the northern hemisphere, except for very high latitudes. Feedback mechanisms keep the land free of ice during the sum-mer. Additionally, the warm temperatures trigger the release of CO2, stored in the deep ocean. In principle, in this scenario of orbital forcing, the development of the Earth’s climate could be completely controlled by the concentration of CO2
and other greenhouse gases in theatmosphere. In this case, it would be the carbon cycle time scale, which is responsible for the slow temperature decline after a warm peak.
However, there are indications that this picture of the orbital forcing is not fully complete. Climate modeling, including the behavior of ice sheets reacting to orbital forcing and the understanding of the alternation between warm periods and ice ages have only recently advanced to a stage of moderate understanding of the many complicated and inter-related processes at play. Interestingly, model results suggest that limiting the orbital forcing to the trigger mechanism, as de-scribed above, is only part of the story (see e.g. Stap et al. (2014)). In fact, during the time between the inter-glacial peaks, occurring every 100 kyr, δ18O, theproxyfor the ice volume and the hydrological cycle obtained from Antarctica, i.e., the southern hemisphere, closely follows the northern hemisphere summer forcing (see Figure3, fourth and fifth line, respectively). It is suggested that the CO2gas concentration might be responsible for this global link between the north-ern summer orbital forcing and its correspondingδ18O signal in the southern ice sheet. Thus, there are many aspects of orbital forcing, which still need to be fully understood.