Amplitude and phase of glacial cycles from a conceptual model

Abstract

The astronomical theory of climate, in which the orbital variations of the Earth are taken to drive the climate changes, explains many features of the paleoclimatic records. Nevertheless, the precise link between insolation variations and climatic changes during the Quaternary remains mysterious in several aspects. In particular, the largest sea level changes of the past million years occurred when insolation variations were minimal, like during stage 11, and vice versa like during stage 7. Moreover, recent data from terminations II and III show surprising phase lead and lag between insolation and sea level variations. To explain these paradoxical amplitude and phase modulations, we suggest here that deglaciations started when a combination of insolation and ice volume was large enough. To illustrate this new idea, we present a simple conceptual model that simulates the sea level curve of the past million years with very realistic amplitude modulations, and with good phase modulations.

Introduction

Although we find astronomical frequencies in almost all paleoclimatic records [1], [2], it is clear that the climatic system does not respond linearly to insolation variations [3]. The first well-known paradox of the astronomical theory of climate is the ‘100 kyr problem’: the largest variations over the past million years occurred approximately every 100 kyr, but the amplitude of the insolation signal at this frequency is not significant. Although this problem remains puzzling in many respects, multiple equilibria and thresholds in the climate system seem to be key notions to explain this paradoxical frequency. In particular, the ice volume critical size is a good candidate to trigger the threshold [3], [4]. Indeed, terminations occurred only after considerable build-up of ice volume; beyond this point, the next northern latitude summer insolation maximum, even a relatively weak one, will cause a deglaciation [5]. This simple idea allowed Paillard [4] to construct a conceptual model that successfully simulates the 100 kyr terminations.

Another intriguing paradox is the relation between the amplitudes of the insolation extrema and the corresponding ice volume extrema. There is no simple relation between these two extrema. For example, transition V (from stage 12 to stage 11), which was probably the largest one over the past million years [6], [7], [8], occurred when insolation variations were very weak. This is known as the ‘stage 11 problem’. Similarly, transition III (from stage 8 to stage 7) was rather small, whereas insolation variations during this time period were important [9]. The very small ice volume during stage 11 could be explained by its exceptional duration, two precessional cycles against only one for the other interglacial [4]. But what is the explanation for MIS 12.2, a stage with a weak minimum of insolation but probably the largest ice volume of the past 600 kyr [8]? (see Fig. 1) The same question also exists for MIS 16.2 and 2.2. A related paradox is the ‘400 kyr problem’. The amplitude of summer high latitude insolation variations is maximum every 400 kyr, due to the dominance of this periodicity in the eccentricity modulation of the precessional forcing. The 400 kyr problem is often presented as the absence of such a frequency in paleoclimatic records [10]. For the last 400 kyr, it is even the contrary: an amplitude modulation in the sea level curve does exist, but is opposite to the 400 kyr cycle of insolation. Sea level transitions were maximal when insolation variations were minimal, and vice versa (see Fig. 1). However, this inverse relationship is not so clear for the rest of the record all along the last million years.

Moreover, the phase relationship between a termination and the corresponding insolation extremum may not be constant through time. Termination II has been in advance with respect to the insolation maximum [11], [12], whereas new U–Th datings seem to show the contrary for termination III [13].

To solve these amplitude and phase paradoxes, we suggest here that ice volume and insolation together play a role in the triggering of deglaciations. We suppose that the climatic system has two main states of variation: g (glaciation) and d (deglaciation), and that the g-to-d transition occurs when a combination of insolation and ice volume is large. More precisely, a deglaciation can occur when insolation forcing is moderate if ice volume is very large, or reciprocally when ice volume is moderate if insolation forcing is very large. We propose here a conceptual model based on this simple idea. It is driven by changes in the June Solstice insolation at 65°N and by obliquity. This simple model not only reproduces sea level transitions at the correct time, but also sea level extrema with the right amplitude. In addition, despite high latitude northern insolation being the only external forcing, we obtain significant phase variations between climatic transitions and insolation, in agreement with chronologies for terminations II and III. This proves that, in contrast to some previously published ideas [14], [15], an astronomical theory of glacial cycles can easily accommodate for such phase variations. Furthermore, it proposes a conceptual explanation of how phase and amplitude variations are linked together.