C. Tricot

Insolation and Earth's orbital periods

Solar irradiance received on a horizontal surface depends on the solar output, the semimajor axis of the elliptical orbit of the Earth around the sun (a), the distance from the Earth to the sun (r), and the zenith distance (z). The spectrum of the distance, r, for a given value of the true longitude, lambda, displays mainly the precessional periods and, with much less power, half precession periods, eccentricity periods, and some combination tones. The zenith distance or its equivalent, the elevation angle (E), is only a function of obliquity (epsilon) for a given latitude, phi, true longitude, and hour angle, H. Therefore the insolation at a given constant value of z is only a function of precession and eccentricity. On the other hand, the value of the hour angle, H, corresponding to this fixed value of z varies with epsilon, except for the equinoxes, where H corresponding to a constant z also remains constant through time. Three kinds of insolation have been computed both analytically and numerically: the instantaneous insolation (irradiance) at noon, the daily irradiation, and the irradiations received during particular time intervals of the day defined by two constant values of the zenith distance (diurnal irradiations). Mean irradiances (irradiations divided by the length of the time interval over which they are calculated) are also computed for different time intervals, like the interval between sunrise and sunset, in particular. Examples of these insolations are given in this paper for the equinoxes and the solstices. At the equinoxes, for each latitude, all insolations are only a function of precession (this invalidates the results obtained by Cerveny [1991)). At the solstices, both precession and obliquity are present, although precession dominates for most of the latitudes. Because the lengths of the astronomical seasons are secularly variable (in tenus of precession only), a particular calendar day does not always correspond to the same position relative to the sun through geological time. Similarly, a given longitude of the Sun on its orbit does not correspond to the same calendar day. For example, 103 kyr ago, assuming arbitrarily that the spring equinox is always on March 21, autumn began on September 13, and 114 kyr ago, it began on September 27, the length of the summer season being 85 and 98 calendar days, respectively, at these remote times in the past.

Testing the Astronomical Theory With a Coupled Climate Ice-sheet Model

Ice, land and deep-sea cores have provided strong evidence that orbital perturbations are of primary importance in the timing of the waxing and waning of Pleistocene continental ice sheets. Spectral analyses of climatic records have shown that, at least near the frequencies of variation in obliquity and precession, a considerable fraction of the climate variance is driven in some way by insolation changes accompanying changes in the Earths orbit. The exceptional strength of the dominating 100,000-year cycle needs a non-linear amplification of the eccentricity-precession cycles from the ice sheets themselves and related mechanisms. Now that the astronomical model has passed both severe statistical tests and some tests of physical plausibility, the influence of orbital variations is thought to be real enough to be tested with numerical climate models. In addition to the calculation of the Earths climate which is in equilibrium with a particular insolation pattern and boundary conditions, the simulation of the transient response of the climate system to orbital variations is important since it will lead to better understanding of the physical mechanisms involved in the relationship between the astronomical forcing and climate. It has been suggested that the time evolution of the latitudinal distribution of the seasonal pattern of insolation is the key factor driving the climate system on the 1000-year time scale. In this paper, a 2.5-D time-dependent climate model taking into account the feedbacks between the atmosphere, the upper ocean, the sea ice, the ice sheets and the lithosphere, is used to confirm this thesis. The model results produce long-term variations of the global ice volume over the past 125,000 years that are in general agreement with the most recent geological reconstructions. A comparison with the sea-level curve of Chappell and Shackleton and with the δ18O curve of Duplessy-Labeyrie-Blanc shows that our early stage 3 is a few thousands of years younger than dated by Chappell and Shackleton, and our stage 3 high-sea level itself is 20 meters lower than their value (i.e., 50 m below present sea level instead of 30 m).

Entering the Glaciation With a 2-d Coupled Climate Model

A 2-dimensional model which links the atmosphere, the mixed layer of the ocean, the sea-ice, the continents, the ice sheets and their underlying lithosphere has been used to test the Milankovitch theory over the last glacial-interglacial cycle. Sensitivity tests have shown that the orbital variations can induce, in such a system, feedbacks sufficient to generate the low frequency part of the climatic variations over the last 122 ka BP. These variations at the astronomical time scale are broadly in agreement with ice volume and sea level reconstruction independently obtained from geological data. At the beginning of the integration during isotopic Substage 5e when there was no northern american nor eurasian ice sheets, June insolation at high latitudes seemed to correlate well with summer temperature at the surface of the ice sheets and with the ablation rate. The relation is more complicated when large ice sheets exist. Broadly, the June-July insolation from 60 to 70-degrees-N. leads the ice volume by roughly 5000 years over the last glacial-interglacial cycle. The simulated climate was shown to be sensitive to the ice albedo-temperature feedback, to the precipitation-altitude negative feedback over the ice sheets, to the ice sheet slope and continentality effects, and to the albedo of the ice sheets as a function of the snowfall frequency at their surface. The formation and waxing of the ice sheets are particularly sensitive to ablation, more than to snowfalls. Imperfections in the simulated climate were recognized, in particular at the last glacial maximum when the cooling was not large enough and the northern hemisphere ice sheets did not extend far enough to the south, weaknesses which are partly solved in a further experiment (Gallee et al., 1989) by using the proper CO2 atmospheric concentration given by the Vostok ice core in addition to the astronomical forcing.

Physical Interactions Within a Coupled Climate Model Over the Last Glacial Interglacial Cycle

A two-dimensional (2-D) seasonal model has been developed for stimulating the transient response of the climate system to the astronomical forcing. The atmosphere is represented by a zonally averaged quasi-geostrophic model which includes accurate treatment of radiative transfer. The atmospheric model interacts with the other components of the climate system (ocean, sea-ice and land surface covered or not by snow and ice) through vertical fluxes of momentum, heat and humidity. The model explicitly incorporates surface energy balances and has snow and sea-ice mass budgets. The vertical profile of the upper-ocean temperature is computed by an interactive mixed-layer model which takes into account the meridional turbulent diffusion of heat. This model is asynchronously coupled to a model which simulates the dynamics of the Greenland, the northern American and the Eurasian ice sheets. Over the last glacial-interglacial cycle, the coupled model simulates climatic changes which are in general agreement with the low frequency part of the deep-sea, ice and sea-level records. However, after 6000 yBP, the remaining ice volume of the Greenland and northern American ice sheets is overestimated in the simulation. The simulated climate is sensitive to the initial size of the Greenland ice sheet, to the ice-albedo positive feedback, to the precipitation-altitude negative feedback over the ice sheets, to the albedo of the aging snow and to the insolation increase, particularly at the southern edge of the ice sheets, which is important for their collapse or surge.

Glaciation and Deglaciation Mechanisms in a Coupled 2-dimensional Climate-ice-sheet Model

A two-dimensional model which links the atmosphere, the mixed layer of the ocean, the sea ice, the continents, the ice sheets and their underlying bedrock has been used to test the Milankovitch theory over the last glacial-interglacial cycle. It was found that the orbital variations alone can induce, in such a system, feed-backs sufficient to generate the low-frequency part of the climatic variations over the last 122 kyear. These simulated variations at the astronomical time-scale are broadly in agreement with ice volume and sea-level reconstructions independently obtained from geological data. Imperfections in the simulated climate were the insufficient southward extent of the ice sheets and the too small hemispheric cooling during the last glacial maximum. These deficiencies were partly remedied in a further experiment (Gallee and others, in press) by using the time-dependent CO2 atmospheric concentration given by the Vostok ice core in addition to the astronomical forcing. For this second experiment, the main mechanisms and feedbacks responsible for the glaciation and the deglaciation in the model are discussed here.

The last two glacial-interglacial cycles simulated by the LLN model

A 2-dimensional model which links the atmosphere, the mixed layer of the ocean, the sea ice, the continents, the ice sheets and their underlying bedrock has been used to test the Milankovitch theory over the last two glacial-interglacial cycles. A series of sensitivity analyses have allowed us to better understand the internal mechanisms which drive the simulated climate system and in particular the feedbacks related to surface albedo and water vapour.

Climate Studies with a Coupled Atmosphere--Upper-Ocean--Ice-Sheet Model

A two-dimensional zonally averaged model has been developed for simulating the seasonal cycle of the climate of the Northern Hemisphere. The atmospheric component of the model is based on the two-level quasi-geostrophic potential vorticity system of equations. At the surface, the model has land—sea resolution and incorporates detailed snow and sea-ice mass budgets. The upper ocean is represented by an integral mixed-layer model that takes into account the meridional advection and turbulent diffusion of heat. Comparisons between the computed present-day climate and climatological data show that the model does reasonably well in simulating the seasonal cycle of the temperature field. In response to a projected CO2 trend based on the scenario of Wuebbles et al. (DOE/ NBB-0066 Technical Report 15 (1984)), the modelled annual hemispheric mean surface temperature increases by 2 °C between 1983 and 2063. In the high latitudes, the response undergoes significant seasonal variations. The largest surface warmings occur during autumn and spring. The model is then asynchronously coupled to a model that simulates the dynamics of the Greenland, the Eurasian and the North American ice sheets in order to investigate the transient response of the climate to the long-term insolation anomalies caused by orbital perturbations. Over the last interglacial-glacial cycle, the coupled model produces continental ice-volume changes that are in general agreement with the low-frequency part of palaeoclimatic records.

The Greenhouse-effect

The greenhouse effect on the Earth is identified by the difference between the effective radiating temperature of the planet and its surface temperature. The difference between the energy emitted by the surface and that emitted upward to space by the upper atmosphere quantifies it; it can therefore be defined as the long wave energy trapped in the atmosphere. Climate forcing and the response of the climate system within which climate feedback mechanisms are contained, will be defined in this review. Quantitative examples will illustrate what could happen if the greenhouse effect is perturbed by the human activities, in particular if atmospheric CO2 concentrations would double in the future. Recent measurements by satellites of the greenhouse effect will be given. The net cooling effect of clouds on the Earth and whether or not there will be less cooling by clouds as the planet warms, are discussed following a series of papers recently published by Ramanathan and his collaborators.

Ice sheets and sea-level changes as a response to climatic change at the astronomical time scale

Understanding how and why global climate is changing is investigated at the astronomical time scale related to the glacial-interglacial cycles of the Quaternary Ice Age.