## Y WfT V15

164 9 Global Dynamics of the Ice Sheets Table 9-1 Scaling Notation for Ice-Sheet Variables Horizontal distance (summit to edge) Vertical and horizontal temperature difference Advective time scale (surface to base) where y ixid (pg)nJ1 4. Thus, for example, if n 1, H ( ia pg)1 4 A 4. It also follows from Eqs. (9.6) and (9.7) that U (p g)nHln+X L. To discuss the scaling of thermal processes in an ice sheet, particularly at its base where melting may lead to liquid water formation and surging, we...

## Q [q v pcrnc

Where we have invoked the Boussinesq approximation, p p. Thus, SDMs must include parameterizations not only of the effects of fluctuations of frequencies less than about an hour (x ), as in the GCMs, but also the effects of all frequencies up to the 100-y climatic averaging period (x*). This can include the diurnal and seasonal cycles, mesoscale phenomena, synoptic weather waves, and even interannual and decadal variations. In view of the complexity and high energy level of all this subclimatic...

## Toward A More Complete Theory

The ultimate goal of climatic theory is to account not only for the global ice mass and thermal evolution we have emphasized here, but to account for the full three-dimensional geographical distributions of all the climatic variables describing the atmosphere, oceans, and terrestrial biosphere, as well as the location and topography of the ice sheets. These aspects will require the explicit use of atmospheric, biospheric, and oceanic general circulation models coupled with three-dimensional...

## Simplified Dynamics Of The Thermohaline Ocean State

The fundamental equations governing the behavior of the ocean were given in Chapter 4. Based on simplifications of these equations many models have now been formulated with the aim of predicting and accounting for the main circulations and other properties of the ocean see reviews by Niiler (1992) and Haidvogel and Bryan (1992) as examples . These models have ranged from full three-dimensional ocean general circulation models such as that of Semtner and Chervin (1992), to highly simplified...

## Techniques For Climate Reconstruction

The nature and reliability of climatic information available for any earlier time period are highly dependent on the techniques available for climatic reconstruction. In this chapter we present a brief survey of these techniques, ranging from those applicable on the shortest time scales, when quantitative and qualitative human inferences are possible, to the longest scales, which depend heavily on isotopic analysis of core material obtained from stratified sedimentary rocks and ice sheets. We...

## The Slowresponse Control Variables

Whereas studies of the equilibrium response of the combined atmosphere and surface boundary layer to both external forcing and prescribed slow-response variables might be able to give an adequate account of the climatic state of the fast-response domains, they cannot account for the evolution of the slow-response variables themselves. To a large degree it is these slowly varying domains that provide the main signals of the longer term climatic change of our planet. As noted, because of their...

## Nw rii nv nn

So that to first-order ice mass changes can be assumed to imply nearly opposite ocean mass changes dU di dUj dt. As described in greater detail by Saltzman (1978), if we integrate the climatic-averaged form of the energy equation, Eq. (4.4), through the depth of the atmosphere, and through the depth of the subsurface medium (whether it is land, ocean, or ice, or some combination thereof), neglecting small terms, we obtain the following pair of equations for the rates of change of sensible heat...

## Bibliography

Faure-Denard, J. M. McGlade, and F. I. Woodward (1990). Increases in terrestrial carbon storage from the last glacial maximum to the present. Nature 348, 711-714. Adh mar, J. F. (1842). Les Revolutions de la Mer Deluges P riodiques, Paris. Agassiz, L. (1840). Etudes Sur les Glaciers. Privately published, Neuchatel. Algeo, T. J., R. A. Berner, J. B. Maynard, and S. E. Scheckler (1995). Late Devonian oceanic anoxic events and biotic crises Rooted in the evolution of...

## Survey Of Global Paleoclimatic Variations

We now present an overview of the findings obtained by the use of the techniques described in the previous chapter. This summary will start with the more poorly known, long-term variations extending over about one-half billion years (the Phanero-zoic Eon) and will proceed with increasing time resolution to the better known recent variations. As one might surmise from our discussion of the proxy techniques for past climate reconstruction, only a crude estimate of global climate changes,...

## FerioOol2 J j4fto0bUdO

Figure 6-9 Sample deterministic solution near the stable equilibrium (1q of Fig. 6-8 in units of departure from the equilibrium (r ', 9') (a) time evolution of t ' (full curve) and 9' (dashed curve) (b) trajectory (c) trajectory speed (dots are spaced at every 60 years). Figure 6-9 Sample deterministic solution near the stable equilibrium (1q of Fig. 6-8 in units of departure from the equilibrium (r ', 9') (a) time evolution of t ' (full curve) and 9' (dashed curve) (b) trajectory (c)...

## Dynamical Analysis A Simple Heinrich Scale Oscillator

In the previous section it was shown that there is some degree of consistency between diagnostic calculations of 7b in relation to 7m and the observed Heinrich events that are presumed to occur only when 7b 7m. In order to account for the quasi-cyclical evolution of these events, however, we must explicitly introduce the physics of the melting process that occurs when 7b 7m, as represented by Eq. (9.66), in a closed dynamical model. The simplest such model can be obtained by specializing the...

## Forced Evolution Of The Tectonicmean Climatic State

As noted in Section 12.5, the determination of the ultra-long-term variations of the tectonic-mean climatic state depends on a knowledge of all the astronomical and solid Earth changes with which they are equilibrated. These include changes in the solar constant (S) as it affects external radiative forcing R(S), the rate of rotation of the Earth ( 2), the long-term exposure to bolides and cosmic dust (U), tectonic changes in continental topography and oceanic bathymetry (h), changes in the...

## Millennialscale Variations

In Sections 3.4-3.6 we provided an overview of some of the variability that occurred on 1- to 10-ky time scales, the most notable of which have been identified as Heinrich (H) oscillations (6- to 10-ky period) and Dansgaard-Oeschger (D-O) oscillations (1- to 3-ky period) (see Figs. 3-7 and 3-9). The H-oscillations are clearly associated with the presence of ice sheets, their main signature being the ice-rafted debris in sediment cores derived from icebergs that are massively discharged from the...

## Prototypical Climatic Applications

It is appropriate at this point to discuss in a more general way aspects of dynamical systems theory that are relevant for analyzing a system like that given by Eq. (5.11), discussed in the previous chapter (e.g., Section 5.3). We begin by describing the formalism for determining the stability of an equilibrium of such a system. For generality, let us consider the stability properties of any equilibrium (steady state) of a system of equations of the form where x denotes a set of variables....

## P p [int r tMss s

Where we have expressed the viscous terms in Eqs. (11.27) and (11.28) by a Rayleigh friction (k const.). From the continuity Eq. (11.29) we can define a stream function, ty, for the TH circulation, Cross-differentiating Eqs. (11.27) and (11.28) with respect to z and v, respectively, to eliminate V, then subtracting Eq. (11.28) from Eq. (11.27), and applying Eq. (11.31), we obtain the vorticity equation for the TH circulation, The Coriolis term ( du dz) is probably small compared to the density...

## T XV[C02S[C02ml

Where cm is the mass flux of carbon in the form of CO2, and a square-bracketed quantity x denotes the mole concentration of x in units of mol m3. Figure 10-2 Schematic portrayal of the main carbon reservoirs and annual mean fluxes of carbon for the present day. Units are GtC for reservoirs, and GtC y l for fluxes. After Watson et al. (1990). The surface water layer concentration CC ls is determined by the partial pressure of CO2 in the atmosphere at the interface, (pC02)atm, and the solubility...