The principal elements of the radiative forcing concept are summarised below.

(A) The concept was developed first in the context of the one-dimensional radiative-convective models that investigated the equilibrated global, annual mean surface temperature responses to radiative perturbations caused by changes in the concentrations of radiatively active species (Manabe and Wetherald, 1967; Ramanathan and Coakley, 1978; WMO, 1986). Over the past decade, the concept has been extended to cover different spatial dimensions and seasonal time-scales (IPCC, 1992, 1994).

(B) In the one-dimensional radiative-convective model framework, the surface and troposphere are closely coupled, behaving as a single thermodynamic system under the joint control of radiative and convective processes, with a specified lapse rate determining the thermal structure. The stratospheric state is determined by the radiative equilibrium condition. The stratosphere and troposphere irradiances are together constrained by the requirement that the top of the atmosphere net total irradiance (i.e., radiative energy absorbed minus that emitted by the Earth�s entire climate system) must be zero at equilibrium. In applying the forcing concept to arbitrary spatial and seasonal time-scales, as opposed to the global annual mean, it has been assumed (WMO, 1992; SAR) that the stratosphere is in radiative-dynamical (rather than radiative) equilibrium (see (D) below).

(C) The stratosphere is a fast response system which, in response to an imposed radiative perturbation, comes into equilibrium on a time-scale (about a few months) that is much more rapid than the surface-troposphere system (typically decades) (Hansen et al., 1997a; Shine and Forster, 1999). The latter is a slow response system owing principally to the thermal inertia of the oceans.

(D) When a perturbation is applied (such as increases in well-mixed greenhouse gases), there is an instantaneous change in irradiances that is manifest in general as a radiative imbalance (forcing) at the surface, tropopause and the top of the atmosphere. The rapid thermal re-equilibration of the stratosphere leads to an alteration of the radiative imbalance imposed on the surface-troposphere system (WMO, 1992), thereby yielding an adjusted forcing (SAR). The surface and troposphere, operating in a slow response mode, are still in a process of adjustment while the stratosphere has already reached its new equilibrium state. The SAR points out the clear distinction existing between the instantaneous and adjusted forcings.

For the arbitrary space and time mean stratosphere, there arises the need to evaluate the radiative flux changes with the stratosphere in a radiative-dynamical equilibrium. A classical method to determine this is the �Fixed Dynamical Heating� (FDH; WMO, 1995) in which it is assumed that the dynamical heating rate in the stratosphere is unchanged and that the stratosphere comes to a new thermal equilibrium in response to the perturbation through adjustments in the temperature profile, such that a new radiative-dynamical equilibrium is attained (radiative response; see Ramanathan and Dickinson (1979) and Fels et al. (1980)). The resulting adjustment process in the stratosphere makes an additional contribution to the forcing of the surface-troposphere system. When the stratosphere has adjusted to a new radiative-dynamical equilibrium with resultant changes to its thermal state, the change in flux at the tropopause and at the top of the atmosphere become identical. It is important that the stratosphere be in radiative-dynamical equilibrium and, as shown by Hansen et al. (1997a), it is the adjusted rather than the instantaneous forcing that is a more relevant indicator of the surface temperature response. The adjustment of stratosphere is crucial for some of the forcings, but not for all of them (Shine and Forster, 1999). In the case of some radiative perturbations, the stratosphere is hardly perturbed and the instantaneous and adjusted radiative flux changes thus tend to be similar (SAR). In other cases, there is only a small (20% or less) influence due to the stratospheric adjustment process. However, for the case of ozone depletion in the lower stratosphere, the effect of a strato-spheric adjustment could even yield a change in the sign of the forcing.

(E) As a direct consequence of the above, the forcing definition most appropriate for the response of the surface-troposphere system to a radiative perturbation is the net (down minus up) radiative (solar plus long-wave) change defined at the tropopause after the stratosphere has come to a new thermal equilibrium state. Thus, the level at which the tropopause is assumed in the models is an important aspect for the quantitative determination of the forcing (Forster et al., 1997), as is the model vertical resolution used to resolve the vicinity of the tropopause region (Shine et al., 1995). The classical radiative-convective model definition of the tropopause considers it as a boundary between a region where radiative-convective equilibrium prevails (i.e., troposphere) and a region that is in radiative (or radiative-dynamical, i.e., stratosphere) equilibrium. Such a distinction could be ambiguous in the case of the three-dimensional GCMs or the real world. However, radiative forcing appears to be relatively robust to changes in the definition of the tropopause in a GCM (Christiansen, 1999).

(F) A major motivation for the radiative forcing concept is the ease of climate change analysis when radiative forcing, feedback, and climate response are distinguished from one another. Such a separation is possible in the modelling framework where forcing and feedback can be evaluated separately e.g., for the case of CO₂ doubling effects (see Dickinson, 1982; Dickinson and Cicerone, 1986; Cess and Potter, 1988; Cess et al., 1993). The consideration of forcing, feedback and response as three distinct entities in the modelling framework (see also Charlson, 2000) while originating from the one-dimensional radiative/convective models, has made the transition to GCM studies of climate (Hansen et al., 1981; Wetherald and Manabe, 1988; Chen and Ramaswamy, 1996a).

(G) A critical aspect of the separability mentioned in (F) is holding the surface and troposphere state fixed in the evaluation of the radiative forcing. For example, in the case of a change in the concentration of a radiatively active species, the term �state� implies that all parameters are held at the unperturbed values with only the concerned species� concentration being changed. Thus, in the strictest sense, temperature in the troposphere, water vapour and clouds in the entire atmosphere, and circulation, are held fixed in the computation of the irradiance changes at the tropopause, with only the stratosphere adjusted to a new thermal equilibrium state via the radiative response. In contrast to this prescription for calculating the forcing, the resulting changes in the meteorological and climatic parameters (e.g., tropospheric temperature and water vapour) constitute responses to the imposed perturbation (WMO, 1986; Charlson, 2000). In the IPCC context, the change in a radiative agent�s characteristic has involved anthropogenic (e.g., CO₂) and natural (e.g., aerosols after a volcanic eruption) perturbations.

It is important to emphasise that changes in water vapour in the troposphere are viewed as a feedback variable rather than a forcing agent. However, in the case of the second indirect aerosol forcing, the separation is less distinct. Anthropogenic emissions (e.g., aircraft, fossil fuel) or precursors to water vapour are negligible. The same is true for changes in water vapour in the stratosphere, except in the instance that the oxidation of CH₄ provides an input. Changes in the condensed liquid and solid phases of water (i.e., clouds) are also considered as part of the climate feedback. The strict requirement of no feedbacks in the surface and troposphere demands that no secondary effects such as changes in troposphere motions or its thermodynamic state, or dynamically-induced changes in water substance in the surface and atmosphere, be included in the evaluation of the net irradiance change at the tropopause. (Note: the second indirect effect of aerosols consists of microphysically-induced changes in the water substance.)

(H) The foregoing governing factors reflect the fundamental recognition that, in response to an externally imposed radiative forcing, there is a shift in the equilibrium state of the climate system. This forcing of the climate change in the IPCC parlance is to be distinguished from forcing definitions initiated for other purposes, e.g., cloud forcing (Ramanathan et al., 1989), sea surface temperature related forcing during ENSO periods, etc.

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