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# The transient climatic response and the detection of anthropogenic effects on climate

DOI link for The transient climatic response and the detection of anthropogenic effects on climate

The transient climatic response and the detection of anthropogenic effects on climate book

# The transient climatic response and the detection of anthropogenic effects on climate

DOI link for The transient climatic response and the detection of anthropogenic effects on climate

The transient climatic response and the detection of anthropogenic effects on climate book

## ABSTRACT

To illustrate the factors governing the transient climatic response to an external forcing change, consider a planet that consists of an infinitely mixed, isothermal reservoir of thermal inertia R (J m-2 K-1) and temperature T, governed by

(11.1)

where Q is the global mean absorption of solar radiation and F is the emission of infrared radiation to space. The thermal inertia R is the amount of heat that needs to be added per square metre of horizontal area to raise the temperature of the reservoir by 1 K; the larger it is, the more slowly temperature will change. For a mixed layer of depth h, R is given by pcPh, where pis the density of seawater (1027kg/m3) and c is the specific heat of water ( 4.186 x 103 J kg-1 K-1).lr the planet is initially in a balanced state (Q = F), and a radiative forcing of magnitude !:lF is applied, the equation governing the change in temperature, !:lT, is

(11.2)

where A= dF!dT - dQ/dT is the radiative damping parameter (first introduced in Section 3.3, and extensively discussed in Section 9.1). The solution to this equation is

( 11.3) where !:lTeq is the equilibrium or steady-state temperature change, and 1 = RIA. A detailed derivation of Eqs (11.2) and (11.3) is presented in Box 11.1. When t = 1, the temperature has changed by I - e-1 = 0.632 of the final change, when t = 21 the temperature warms by another 0.632 of the change that still had to occur at t = 1, and so on, as !:lT asymptotically approaches !:lTcq · 1 is referred to as the e~folding time, and it depends on the thermal inertia and the radiative damping parameter. For a 70 m deep mixed layer and A = 2 W m-2 K-1 (corresponding to about 2 K warming for a C02 doubling), 1"" 5 years.