Lorraine Lisiecki's Home Page Dissertation Appendices

Dissertation Appendices

Lorraine E. Lisiecki
Table of Contents

Table of Contents

1. Appendix A, Orbital Forcing

1.1. Milankovitch Theory

Milankovitch theory in its purest form states that the size of northern hemisphere ice sheets is controlled by the amount of insolation in summer months at 65oN [Milankovitch, 1930]. High northern latitudes are used because changes in northern ice sheets are assumed to be driven by local insolation. The summer months are singled out because at high latitudes it always cold enough to snow in the winter, so the year-to-year accumulation of snow necessary to build a large ice sheet is likely to be controlled by the amount of melting in summer.

The main argument in favor of Milankovitch theory is the dominance of precession, obliquity, and eccentricity frequencies in both insolation changes and the climate record. [For opposing viewpoints, see Winograd et al., 1992; Muller and MacDonald, 1997; Wunsch, 2004]. The main challenge is that high-latitude summer insolation is dominated by 19- and 23-kyr precession cycles, but late Pleistocene glacial cycles are 100 kyr and early Pleistocene glacial cycles are 41 kyr. The many variations of Milankovitch theory created to account for this discrepancy are collectively known as theories of orbital forcing, due to their emphasis on the role that Earth's orbital configuration plays in controlling insolation. However, the specific mechanisms by which insolation changes produce observed climate responses are still poorly understood; some recent theories are presented in Section 1.3.

1.2. Orbital Cycles

The seasonal and spatial distributions of insolation vary with time due to cyclic variations in the orbital configuration of the Earth, resulting from the gravitational influences of the other planets in the solar system. The solution of orbital variations is chaotic and thus has only been calculated back to 20 Ma [Laskar et al., 1993]. The phases of these cycles become susceptible to uncertainty beginning only a few million years ago [Laskar et al., 1993; Lourens et al., 1996], but the periods of some cycles are considered relatively stable and have been observed in climate records from before 20 Ma [e.g., Zachos et al., 2001]. Provided below are the basic characteristics of the orbital parameters thought to be most important in controlling climate.

Obliquity is the angle of the equator relative the ecliptic plane, which primarily affects the seasonal and latitudinal distribution of insolation. High obliquity results in more high-latitude summer insolation at the expense of low-latitude summer insolation, and its effect is symmetric in the northern and southern hemispheres. Obliquity also produces a small net change in annual insolation as a function of latitude. The range of Earth's obliquity over the last 6 Myr is 22 - 24.5o [Laskar et al., 1993]. Its primary periodicity is 41 kyr, but it experiences significant amplitude modulation with a quasi-periodicity of ~1.2 Myr [Hinnov, 2000].

Precession changes the direction of the planet's axis of rotation, which affects where in the Earth's orbit each season occurs. Precession is frequently measured as the angle between the longitude of perihelion (the orbital position closest to the sun) and the moving vernal equinox and has dominant periods of 19 and 23 kyr. Precession affects the seasonality of all latitudes by altering the Earth-sun distance during each season. For example, northern hemisphere summer is warmest when it occurs at perihelion; this configuration also results in warm southern winters, cold southern summers, and cold northern winters. Precession has no net effect on annual insolation at any latitude, and the strength of its seasonal effect is modulated by the eccentricity of the planet's orbit. When eccentricity is high, seasonal differences in Earth-sun distance are large, but net annual insolation only changes by ~0.1%. Eccentricity varies primarily at periodicities near 100 and 400 kyr; its range over the last 6 Myr is 0 - 0.06 [Laskar et al., 1993].

1.3. Orbital Tuning Targets

Orbital tuning (see Section 1.2.2) requires the selection of a particular forcing function. In agreement with Milankovitch theory, the most commonly considered forcing function is insolation at 65oN on the summer solstice, June 21. Selecting an alternate time of year affects the phase of precession in the insolation curve. Selecting the particular latitude of insolation affects the relative influence of 41-kyr obliquity cycles and 23-kyr precession cycles. Insolation at 65oN is commonly thought to drive climate records at all latitudes because northern hemisphere insolation/ice volume appears to exert a strong global influence through meachanisms such as albedo changes, atmospheric temperature gradients, greenhouse gas concentrations, and thermohaline circulation. However, some surface processes at equatorial or high southern latitudes could be driven by local insolation curves.

Each aspect of the climate system experiences and reacts to an entire annual cycle of insolation and interacts with parts of the climate at other latitudes and with different response times. Insolation targets generally represent an author's best guess at the dominant forcing function and response time of a climate variable. Tuning targets could be constructed as the sum of several insolation curves with different response times, but the physics of the climate system are rarely understood well enough to justify such precision.

Another alternative is to construct a tuning target from orbital parameters instead of insolation curves. This allows one to control the relative magnitude and phase of the factors affecting insolation without necessarily finding that combination at a specific season and location on Earth. Some orbital targets, such as ETP (the sum of normalized eccentricity, tilt, and precession) include eccentricity explicitly in an attempt to model a nonlinear climate response to the eccentricity modulation of precession. Orbital targets are most commonly chosen based on the spectral properties of a time series rather than the physical processes involved in its generation, usually because these processes are poorly understood.

2. Appendix B, The d18O of Foraminifera

Time series of the d18O of foraminiferal calcite tests provide an important record of climate change, reflecting changes in global ice volume and sea water temperature and salinity. The notation d18O is a measure of the abundance of the 18O isotope relative to a chosen standard, in this case standard mean ocean water (SMOW). The isotopic ratio of foraminiferal carbonate (d18Oc) is determined by the isotopic composition of the surrounding water (d18Ow) with a temperature-dependent offset.

A large portion change in d18Oc records is thought to result of the sequestration of isotopically light oxygen (16O) in large continental ice sheets, resulting in ocean water that has a larger proportion of 18O. The scaling between d18Ow and global ice volume depends on the average d18O of the ice, which is a function of evaporation and precipitation patterns. Because ocean mixing times are only ~1 kyr and ice sheet response times are at least several kiloyears, the ice volume signal in d18O should be nearly synchronous throughout the ocean.

Water temperature is another significant source of variability in d18Oc because it affects the degree of isotopic fractionation between foraminiferal carbonate and sea water. The empirical equation to convert between the carbonate-water offset and temperature is

T=16.98 - 4.52(d18Oc - d18Ow) + 0.028 (d18Oc - d18Ow)2

[Erez and Luz, 1982]. However, a small, constant offset is sometimes present in the d18Oc values of different species [Shackleton and Hall, 1984].

Finally, interpretation of d18Oc is complicated a little more by the fact that the d18O of sea water is not completely uniform. Evaporation increases d18Ow by preferentially leaving behind the heavier isotope 18O in much the same way that evaporation leaves behind salt ions and increases salinity. Zahn and Mix [1991] examine the d18Ow and salinity, S, of sites below 2 km depth in the modern Atlantic to derive the following empirical relationship between d18Ow and S,


The slope of this equation for the deep Atlantic is steeper than the one for Atlantic surface water because brine rejection during sea-ice formation increases the salinity of Antarctic Bottom Water (AABW) without affecting its d18Ow. The scaling between d18Ow and salinity can vary with time due to changes in patterns of sea ice formation, evaporation, and precipitation.

Due to the observed similarity of most marine d18O records and the global nature of the ice volume signal, d18O measurements serve as the primary means for placing marine climate records on a common timescale. The major difficulty in interpretting d18Oc is that it is impossible to distinguish between temperature change and ice volume change.

Copyright 2005 by Lorraine E. Lisiecki. Do not reproduce without permission.