On the astronomical forcing of simple conceptual ice age models

2020 ◽  
Author(s):  
Gaëlle Leloup ◽  
Didier Paillard
Keyword(s):  
Conceptual Model ◽  
Climate Model ◽  
Ice Age ◽  
Early Pleistocene ◽  
Model Parameters ◽  
Ice Ages ◽  
Glacial Cycles ◽  
Orbital Parameters ◽  
Ice Volume ◽  
Astronomical Forcing

<p>Variations of the Earth’s orbital parameters are known to pace the ice volume variations of the last million year [1], even if the precise mechanisms remain unknown.<br>Several conceptual models have been used to try to better understand the connection between ice-sheet changes and the astronomical forcing. An often overlooked question is to decide which astronomical forcing can best explain the observed cycles.</p><p>A rather traditional practice was to use the insolation at a some specific day of the year, for instance at mid-july [2] or at the june solstice [3].<br>But it was also suggested that the integrated forcing above some given threshold could be a better alternative [4]. In a more recent paper, Tzedakis et al. [5] have shown that simple rules, based on the original Milankovitch forcing or caloric seasons, could also be used to explain the timing of ice ages.<br>Here we adapt and simplify the conceptual model of Parrenin and Paillard 2003 [6], to first reduce the set of parameters.<br>Like in the original conceptual model from [6], this simplified conceptual model is based on climate oscillations between two states: glaciation and deglaciation. It switches to one another when crossing a defined threshold. While the triggering of glaciations is only triggered by orbital parameters, the triggering of deglaciations is triggered by a combination of orbital parameters and ice volume. <br>Then, we apply the different possible forcings listed above and we try to adapt the model parameters to reproduce the ice volume record, at least in a qualitative way. This allows us to discuss which kind of astronomical forcing better explains the Quaternary ice ages, in the context of such simple threshold-based models.</p><p>[1] Variations in the Earth's Orbit: Pacemaker of the Ice Ages, Hays et al., 1976, Science
</p><p>[2] Modeling the Climatic Response to Orbital Variations, Imbrie and Imbrie, 1980, Science
</p><p>[3] The timing of Pleistocene glaciations from a simple multiple-state climate model, Paillard, 1998, Nature</p><p>[4] Early Pleistocene Glacial Cycles and the Integrated Summer Insolation Forcing, Huybers et al., 2006, Science</p><p>[5] A simple rule to determine which insolation cycles lead to interglacials, Tzedakis et al., 2017, Nature</p><p>[6] Amplitude and phase of glacial cycles from a conceptual model, Parrenin Paillard, 2003, EPSL.</p>

scholarly journals Reconstructing the evolution of ice sheets, sea level, and atmospheric CO<sub>2</sub> during the past 3.6 million years

2021 ◽  
Vol 17 (1) ◽  
pp. 361-377
Author(s):  
Constantijn J. Berends ◽  
Bas de Boer ◽  
Roderik S. W. van de Wal
Keyword(s):  
Sea Level ◽  
Radiative Forcing ◽  
Climate Model ◽  
Ice Sheets ◽  
Early Pleistocene ◽  
Glacial Cycles ◽  
Proxy Data ◽  
Late Pliocene ◽  
Ice Volume ◽  
The Past

Abstract. Understanding the evolution of, and the interactions between, ice sheets and the global climate over geological timescales is important for being able to project their future evolution. However, direct observational evidence of past CO2 concentrations, and the implied radiative forcing, only exists for the past 800 000 years. Records of benthic δ18O date back millions of years but contain signals from both land ice volume and ocean temperature. In recent years, inverse forward modelling has been developed as a method to disentangle these two signals, resulting in mutually consistent reconstructions of ice volume, temperature, and CO2. We use this approach to force a hybrid ice-sheet–climate model with a benthic δ18O stack, reconstructing the evolution of the ice sheets, global mean sea level, and atmospheric CO2 during the late Pliocene and the Pleistocene, from 3.6 million years (Myr) ago to the present day. During the warmer-than-present climates of the late Pliocene, reconstructed CO2 varies widely, from 320–440 ppmv for warm periods to 235–250 ppmv for the early glacial excursion ∼3.3 million years ago. Sea level is relatively stable during this period, with maxima of 6–14 m and minima of 12–26 m during glacial episodes. Both CO2 and sea level are within the wide ranges of values covered by available proxy data for this period. Our results for the Pleistocene agree well with the ice-core CO2 record, as well as with different available sea-level proxy data. For the Early Pleistocene, 2.6–1.2 Myr ago, we simulate 40 kyr glacial cycles, with interglacial CO2 decreasing from 280–300 ppmv at the beginning of the Pleistocene to 250–280 ppmv just before the Mid-Pleistocene Transition (MPT). Peak glacial CO2 decreases from 220–250 to 205–225 ppmv during this period. After the MPT, when the glacial cycles change from 40 to 80 120 kyr cyclicity, the glacial–interglacial contrast increases, with interglacial CO2 varying between 250–320 ppmv and peak glacial values decreasing to 170–210 ppmv.

scholarly journals A theory of glacial cycles: resolving Pleistocene puzzles

2021 ◽  
Author(s):  
Hsien-Wang Ou
Keyword(s):  
Freezing Point ◽  
Surface Air Temperature ◽  
Climate System ◽  
Ice Age ◽  
Early Pleistocene ◽  
Polar Ice ◽  
Glacial Cycles ◽  
Convective Flux ◽  
Ice Volume ◽  
Ice Cap

Abstract. Since the summer surface air temperature that regulates the ice margin is anchored on the sea surface temperature, we posit that the climate system constitutes the intermediary of the orbital forcing of the glacial cycles. As such, the relevant forcing is the annual solar flux absorbed by the ocean, which naturally filters out the precession effect in early Pleistocene but mimics the Milankovitch insolation in late Pleistocene. For a coupled climate system that is inherent turbulent, we show that the ocean may be bistable with a cold state defined by the freezing point subpolar water, which would translate to ice bistates between a polar ice cap and an ice sheet extending to mid-latitudes, enabling large ice-volume signal regardless the forcing amplitude so long as the bistable thresholds are crossed. Such thresholds are set by the global convective flux, which would be lowered during the Pleistocene cooling, whose interplay with the ice-albedo feedback leads to transitions of the ice signal from that dominated by obliquity to the emerging precession cycles to the ice-age cycles paced by eccentricity. Through a single dynamical framework, the theory thus may resolve many long-standing puzzles of the glacial cycles.

scholarly journals Reconstructing the Evolution of Ice Sheets, Sea Level and Atmospheric CO<sub>2</sub> During the Past 3.6 Million Years

2020 ◽  
Author(s):  
Constantijn J. Berends ◽  
Bas de Boer ◽  
Roderik S. W. van de Wal
Keyword(s):  
Sea Level ◽  
Climate Model ◽  
Ice Sheets ◽  
Early Pleistocene ◽  
Geological Time ◽  
Glacial Cycles ◽  
Proxy Data ◽  
Late Pliocene ◽  
Ice Volume ◽  
The Past

Abstract. Understanding the evolution of, and the interactions between, ice sheets and the global climate over geological time is important for being able to constrain earth system sensitivity. However, direct observational evidence of past CO2 concentrations only exists for the past 800 000 years. Records of benthic δ18O date back millions of years, but contain signals from both land ice volume and ocean temperature. In recent years, inverse forward modelling has been developed as a method to disentangle these two signals, resulting in mutually consistent reconstructions of ice volume, temperature and CO2. We use this approach to force a hybrid ice-sheet – climate model with a benthic δ18O stack, reconstructing the evolution of the ice sheets, global mean sea level and atmospheric CO2 during the late Pliocene and the Pleistocene, from 3.6 million years (Myr) ago to the present day. During the warmer-than-present climates of the Late Pliocene, reconstructed CO2 varies widely, from 320–440 ppmv for warm periods such as Marine Isotope Stage (MIS) KM5c, to 235–250 ppmv for the MIS M2 glacial excursion. Sea level is relatively stable during this period, with a high stand of 6–14 m, and a drop of 12–26 m during MIS M2. Both CO2 and sea level are within the wide ranges of values covered by available proxy data for this period. Our results for the Pleistocene agree well with the ice-core CO2 record, as well as with different available sea-level proxy data. During the early Pleistocene, 2.6–1.2 Myr ago, we simulate 40 kyr glacial cycles, with interglacial CO2 decreasing from 280–300 ppmv at the beginning of the Pleistocene, to 250–280 ppmv just before the Mid-Pleistocene Transition (MPT). Peak glacial CO2 decreases from 220–250 ppmv to 205–225 ppmv during this period. After the MPT, when the glacial cycles change from 40 kyr to 80/120 kyr cyclicity, the glacial-interglacial contrast increases, with interglacial CO2 varying between 250–320 ppmv, and peak glacial values decreasing to 170–210 ppmv.

scholarly journals Why could ice ages be unpredictable?

2013 ◽  
Vol 9 (1) ◽  
pp. 1053-1098 ◽  
Author(s):  
M. Crucifix
Keyword(s):  
Structural Stability ◽  
Ice Age ◽  
Ice Ages ◽  
Periodic Forcing ◽  
Glacial Cycles ◽  
Climatic Fluctuations ◽  
Know How ◽  
Astronomical Forcing ◽  
Random Fluctuations ◽  
Periodic Components

Abstract. It is commonly accepted that the variations of Earth's orbit and obliquity control the timing of Pleistocene glacial-interglacial cycles. Evidence comes from power spectrum analysis of palaeoclimate records and from inspection of the timing of glacial and deglacial transitions. However, we do not know how tight this control is. Is it, for example, conceivable that random climatic fluctuations could cause a delay in deglaciation, bad enough to skip a full precession or obliquity cycle and subsequently modify the sequence of ice ages? To address this question, seven previously published conceptual models of ice ages are analysed by reference to the notion of generalised synchronisation. Insight is being gained by comparing the effects of the astronomical forcing with idealised forcings composed of only one or two periodic components. In general, the richness of the astronomical forcing allows for synchronisation over a wider range of parameters, compared to periodic forcing. Hence, glacial cycles may conceivably have remained paced by the astronomical forcing throughout the Pleistocene. However, all the models examined here also show a range of parameters for which the structural stability of the ice age dynamics is weak. This means that small variations in parameters or random fluctuations may cause significant shifts in the succession of ice ages if the system were effectively in that parameter range. Whether or not the system has strong structural stability depends on the amplitude of the effects associated with the astronomical forcing, which significantly differ across the different models studied here. The possibility of synchronisation on eccentricity is also discussed and it is shown that a high Rayleigh number on eccentricity, as recently found in observations, is no guarantee of reliable synchronisation.

scholarly journals Reconstructing the evolution of ice sheets, sea level and atmospheric CO2 during the past 3.6 million years

2020 ◽  
Author(s):  
Tijn Berends ◽  
Bas de Boer ◽  
Roderik van de Wal
Keyword(s):  
Sea Level ◽  
Climate Model ◽  
Ice Sheets ◽  
Early Pleistocene ◽  
Geological Time ◽  
Glacial Cycles ◽  
Late Pliocene ◽  
Ice Volume ◽  
The Past ◽  
And Sea Level

&lt;p&gt;Understanding the evolution of, and the interactions between, ice sheets and the global climate over geological time is important for being able to constrain earth system sensitivity. However, direct observational evidence of past CO&lt;sub&gt;2&lt;/sub&gt; concentrations only exists for the past 800,000 years. Records of benthic d&lt;sup&gt;18&lt;/sup&gt;O date back millions of years, but contain signals from both land ice volume and ocean temperature. In recent years, inverse forward modelling has been developed as a method to disentangle these two signals, resulting in mutually consistent reconstructions of ice volume, temperature and CO&lt;sub&gt;2&lt;/sub&gt;. We use this approach to force a hybrid ice-sheet &amp;#8211; climate model with a benthic d&lt;sup&gt;18&lt;/sup&gt;O stack, reconstructing the evolution of the ice sheets, global mean sea-level and atmospheric CO&lt;sub&gt;2&lt;/sub&gt; during the late Pliocene and the Pleistocene, from 3.6 Myr ago to the present day. The resulting reconstructions of CO&lt;sub&gt;2&lt;/sub&gt; and sea level agree well with the ice core record and different sea-level proxies, indicating that this model set-up yields useful information for colder-than-present climates. For the warmer-than-present climates of the Late Pliocene, different proxies for both CO&lt;sub&gt;2&lt;/sub&gt; and sea level are contradictory, making model validation difficult. During the early Pleistocene, 2.6 &amp;#8211; 1.2 Myr ago, we simulate 40 kyr glacial cycles with CO&lt;sub&gt;2 &lt;/sub&gt;ranging between 270 &amp;#8211; 280 ppmv during interglacials and 210 &amp;#8211; 240 ppmv during glacial maxima. After the Mid-Pleistocene Transition (MPT), when the glacial cycles change from 40 kyr to 80/120 kyr cyclicity, these values change to 260 to 280 ppmv during interglacials, and 180 &amp;#8211; 200 ppmv during glacial maxima.&lt;/p&gt;

scholarly journals Ice thickness and volume of the Renland Ice Cap, East Greenland

2021 ◽  
pp. 1-13
Author(s):  
Iben Koldtoft ◽  
Aslak Grinsted ◽  
Bo M. Vinther ◽  
Christine S. Hvidberg
Keyword(s):  
Surface Topography ◽  
Climate Model ◽  
Thickness Distribution ◽  
High Elevation ◽  
Surface Velocity ◽  
Ice Thickness ◽  
Model Parameters ◽  
East Greenland ◽  
Ice Volume ◽  
Ice Cap

Abstract To assess the amount of ice volume stored in glaciers or ice caps, a method to estimate ice thickness distribution is required for glaciers where no direct observations are available. In this study, we use an existing inverse method to estimate the bedrock topography and ice thickness of the Renland Ice Cap, East Greenland, using satellite-based observations of the surface topography. The inverse approach involves a procedure in which an ice dynamical model is used to build-up an ice cap in steady state with climate forcing from a regional climate model, and the bedrock is iteratively adjusted until the modelled and observed surface topography match. We validate our model results against information from airborne radar data and satellite observed surface velocity, and we find that the inferred ice thickness and thereby the stored total volume of the ice cap is sensitive to the assumed ice softness and basal slipperiness. The best basal model parameters for the Renland Ice Cap are determined and the best estimated total ice volume of 384 km3 is found. The Renland Ice Cap is particularly interesting because of its location at a high elevation plateau and hence assumed low sensitivity to climate change.

Emergence of critical climate states during the Pleistocene

2021 ◽  
Author(s):  
Nicholas Golledge
Keyword(s):  
Dynamical Systems ◽  
Late Pleistocene ◽  
Dominant Frequency ◽  
Climate System ◽  
Ice Age ◽  
Early Pleistocene ◽  
Glacial Cycles ◽  
Pleistocene Climate ◽  
System Nodes ◽  
Systems Framework

&lt;p&gt;During the Pleistocene (approximately 2.6 Ma to present) glacial to interglacial climate variability evolved from dominantly 40 kyr cyclicity (Early Pleistocene) to 100 kyr cyclicity (Late Pleistocene to present). Three aspects of this period remain poorly understood: Why did the dominant frequency of climate oscillation change, given that no major changes in orbital forcing occurred? Why are the longer glacial cycles of the Late Pleistocene characterised by a more asymmetric form with abrupt terminations? And how can the Late Pleistocene climate be controlled by 100 kyr cyclicity when astronomical forcings of this frequency are so much weaker than those operating on shorter periods? Here we show that the decreasing frequency and increasing asymmetry that characterise Late Pleistocene ice age cycles both emerge naturally in dynamical systems in response to increasing system complexity, with collapse events (terminations) occuring only once a critical state has been reached. Using insights from network theory we propose that evolution to a state of criticality involves progressive coupling between climate system 'nodes', which ultimately allows any component of the climate system to trigger a globally synchronous termination. We propose that the climate state is synchronised at the 100 kyr frequency, rather than at shorter periods, because eccentricity-driven insolation variability controls mean temperature change globally, whereas shorter-period astronomical forcings only affect the spatial pattern of thermal forcing and thus do not favour global synchronisation. This dynamical systems framework extends and complements existing theories by accomodating the differing mechanistic interpretations of previous studies without conflict.&lt;/p&gt;

scholarly journals The waxing and waning of the Northern Hemisphere ice sheets

1995 ◽  
Vol 21 ◽  
pp. 96-102 ◽  
Author(s):  
I. Marsiat
Keyword(s):  
Mass Balance ◽  
Northern Hemisphere ◽  
Land Surface ◽  
Climate Models ◽  
Climate Model ◽  
Ice Sheet ◽  
Ice Age ◽  
Surface Model ◽  
Glacial Cycle ◽  
Ice Volume

Past modelling studies have shown that the energy balance of the ice-sheet surface is of primary importance in representing the 100 000 year glacial cycle. In particular, modelling of the net mass-balance function is an important part of coupled ice-sheet/climate models. We conduct a series of palaeoclimatic simulations with a vertically integrated ice-flow model coupled to the two-dimensional statistical-dynamical LLN (Louvain-la-Neuve) climate model. The models are coupled through a land-surface model which computes seasonal cycles of surface temperature and precipitation at the real altitude of the surface and evaluates the annual snow and/or ice-mass budget. The present-day climate of the Northern Hemisphere, the Greenland mass balance and the snowfield characteristics are quite well represented despite the relative simplicity of the model. Total ice-volume and sea-level variations during the last glacial cycle are well simulated. This suggests that the physical mechanisms included in the models are sufficient to explain the most striking features of the ice-age cycle. Introducing an improved and more detailed topography improves the simulation of the total ice volume but fails to correct inadequacies in the simulated ice distribution on the surface of the Earth.

scholarly journals The waxing and waning of the Northern Hemisphere ice sheets

1995 ◽  
Vol 21 ◽  
pp. 96-102
Author(s):  
I. Marsiat
Keyword(s):  
Mass Balance ◽  
Northern Hemisphere ◽  
Land Surface ◽  
Climate Models ◽  
Climate Model ◽  
Ice Sheet ◽  
Ice Age ◽  
Surface Model ◽  
Glacial Cycle ◽  
Ice Volume

Past modelling studies have shown that the energy balance of the ice-sheet surface is of primary importance in representing the 100 000 year glacial cycle. In particular, modelling of the net mass-balance function is an important part of coupled ice-sheet/climate models. We conduct a series of palaeoclimatic simulations with a vertically integrated ice-flow model coupled to the two-dimensional statistical-dynamical LLN (Louvain-la-Neuve) climate model. The models are coupled through a land-surface model which computes seasonal cycles of surface temperature and precipitation at the real altitude of the surface and evaluates the annual snow and/or ice-mass budget. The present-day climate of the Northern Hemisphere, the Greenland mass balance and the snowfield characteristics are quite well represented despite the relative simplicity of the model. Total ice-volume and sea-level variations during the last glacial cycle are well simulated. This suggests that the physical mechanisms included in the models are sufficient to explain the most striking features of the ice-age cycle. Introducing an improved and more detailed topography improves the simulation of the total ice volume but fails to correct inadequacies in the simulated ice distribution on the surface of the Earth.

scholarly journals Bispectra of climate cycles show how ice ages are fuelled

2019 ◽  
Vol 15 (6) ◽  
pp. 1959-1983 ◽  
Author(s):  
Diederik Liebrand ◽  
Anouk T. M. de Bakker
Keyword(s):  
Complex Dynamics ◽  
Ice Age ◽  
Early Pleistocene ◽  
Oceanic Circulation ◽  
Ice Ages ◽  
Cycle Frequency ◽  
Climate Cycles ◽  
Middle And Late Pleistocene ◽  
Heat And Moisture ◽  
Earth’S System

Abstract. The increasingly nonlinear response of the climate–cryosphere system to insolation forcing during the Pliocene and Pleistocene, as recorded in benthic foraminiferal stable oxygen isotope ratios (δ18O), is marked by a distinct evolution in ice-age cycle frequency, amplitude, phase, and geometry. To date, very few studies have thoroughly investigated the non-sinusoidal shape of these climate cycles, leaving precious information unused to further unravel the complex dynamics of the Earth's system. Here, we present higher-order spectral analyses of the LR04 δ18O stack that describe coupling and energy exchanges among astronomically paced climate cycles. These advanced bispectral computations show how energy is passed from precession-paced to obliquity-paced climate cycles during the Early Pleistocene (from ∼2500 to ∼750 ka) and ultimately to eccentricity-paced climate cycles during the Middle and Late Pleistocene (from ∼750 ka onward). They also show how energy is transferred among many periodicities that have no primary astronomical origin. We hypothesise that the change of obliquity-paced climate cycles during the mid-Pleistocene transition (from ∼1200 to ∼600 ka), from being a net sink into a net source of energy, is indicative of the passing of a land-ice mass loading threshold in the Northern Hemisphere (NH), after which cycles of crustal depression and rebound started to resonate with the ∼110 kyr eccentricity modulation of precession. However, precession-paced climate cycles remain persistent energy providers throughout the Late Pliocene and Pleistocene, which is supportive of a dominant and continuous fuelling of the NH ice ages by insolation in the (sub)tropical zones, and the control it exerts on meridional heat and moisture transport through atmospheric and oceanic circulation.

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