As discussed in the SAR, the change in the net irradiance at the tropopause, as defined in Section 6.1.1, is, to a first order, a good indicator of the equilibrium global mean (understood to be globally and annually averaged) surface temperature change. The climate sensitivity parameter (global mean surface temperature response T_s to the radiative forcing F) is defined as:

T_s / F = (6.1)

(Dickinson, 1982; WMO, 1986; Cess et al., 1993). Equation (6.1) is defined for the transition of the surface-troposphere system from one equilibrium state to another in response to an externally imposed radiative perturbation. In the one-dimensional radiative-convective models, wherein the concept was first initiated, is a nearly invariant parameter (typically, about 0.5 K/(Wm^-2); Ramanathan et al., 1985) for a variety of radiative forcings, thus introducing the notion of a possible universality of the relationship between forcing and response. It is this feature which has enabled the radiative forcing to be perceived as a useful tool for obtaining first-order estimates of the relative climate impacts of different imposed radiative perturbations. Although the value of the parameter “” can vary from one model to another, within each model it is found to be remarkably constant for a wide range of radiative perturbations (WMO, 1986). The invariance of has made the radiative forcing concept appealing as a convenient measure to estimate the global, annual mean surface temperature response, without taking the recourse to actually run and analyse, say, a three-dimensional atmosphere-ocean general circulation model (AOGCM) simulation.

In the context of the three-dimensional AOGCMs, too, the applicability of a general global mean climate sensitivity parameter (i.e., global mean surface temperature response to global mean radiative forcing) has been explored. The GCM investigations include studies of (i) the responses to short-wave forcing such as a change in the solar constant or cloud albedo or doubling of CO₂, both forcing types being approximately spatially homogeneous (e.g., Manabe and Wetherald, 1980; Hansen et al., 1984, 1997a; Chen and Ramaswamy, 1996a; Le Treut et al., 1998), (ii) responses due to different considered mixtures of greenhouse gases, with the forcings again being globally homo-geneous (Wang et al., 1991, 1992), (iii) responses to the spatially homogeneous greenhouse gas and the spatially inhomogeneous sulphate aerosol direct forcings (Cox et al., 1995), (iv) responses to different assumed profiles of spatially inhomogeneous species, e.g., aerosols and O₃ (Hansen et al., 1997a), and (v) present-day versus palaeoclimate (e.g., last glacial maximum) simulations (Manabe and Broccoli, 1985; Rind et al., 1989; Berger et al., 1993; Hewitt and Mitchell, 1997).

Overall, the three-dimensional AOGCM experiments performed thus far show that the radiative forcing continues to serve as a good estimator for the global mean surface temperature response but not to a quantitatively rigorous extent as in the case of the one-dimensional radiative-convective models. Several GCM studies suggest a similar global mean climate sensitivity for the spatially homogeneous and for many but not all of the spatially inhomogeneous forcings of relevance for climate change in the industrial era (Wang et al., 1992; Roeckner et al., 1994; Taylor and Penner, 1994; Cox et al., 1995; Hansen et al., 1997a). Paleoclimate simulations (Manabe and Broccoli, 1985; Rind et al., 1989) also suggest the idea of similarities in climate sensitivity for a spatially homogeneous and an inhomogeneous forcing (arising due to the presence of continental ice sheets at mid- to high northern latitudes during the last glacial maximum). However, different values of climate sensitivity can result from the different GCMs which, in turn, are different from the l values obtained with the radiative-convective models. Hansen et al. (1997a) show that the variation in l for most of the globally distributed forcings suspected of influencing climate over the past century is typically within about 20%. Extending considerations to some of the spatially confined forcings yields a range of about 25 to 30% around a central estimate (see also Forster et al., 2001). This is to be contrasted with the variation of 15% obtained in a smaller number of experiments (all with fixed clouds) by Ramaswamy and Chen (1997b). However, in a general sense and considering arbitrary forcing types, the variation in l could be substantially higher (50% or more) and the climate response much more complex (Hansen et al., 1997a). It is noted that the climate sensitivity for some of the forcings that have potentially occurred in the industrial era have yet to be comprehensively investigated.

While the total climate feedback for the spatially homo-geneous and the considered inhomogeneous forcings does not differ significantly, leading to a near-invariant climate sensitivity, the individual feedback mechanisms (water vapour, ice albedo, lapse rate, clouds) can have different strengths (Chen and Ramaswamy, 1996a,b). The feedback effects can be of considerably larger magnitude than the initial forcing and govern the magnitude of the global mean response (Ramanathan, 1981; Wetherald and Manabe, 1988; Hansen et al., 1997a). For different types of perturbations, the relative magnitudes of the feedbacks can vary substantially.

For spatially homogeneous forcings of opposite signs, the responses are somewhat similar in magnitude, although the ice albedo feedback mechanism can yield an asymmetry in the high latitude response with respect to the sign of the forcing (Chen and Ramaswamy, 1996a). Even if the forcings are spatially homo-geneous, there could be changes in land surface energy budgets that depend on the manner of the perturbation (Chen and Ramaswamy, 1996a). Furthermore, for the same global mean forcing, dynamic feedbacks involving changes in convective heating and precipitation can be initiated in the spatially inhomogeneous perturbation cases that differ from those in the spatially homogeneous perturbation cases.

The nature of the response and the forcing-response relation (Equation 6.1) could depend critically on the vertical structure of the forcing (see WMO, 1999). A case in point is O₃ changes, since this initiates a vertically inhomogeneous forcing owing to differing characteristics of the solar and long-wave components (WMO, 1992). Another type of forcing is that due to absorbing aerosols in the troposphere (Kondratyev, 1999). In this instance, the surface experiences a deficit while the atmosphere gains short-wave radiative energy. Hansen et al. (1997a) show that, for both these special types of forcing, if the perturbation occurs close to the surface, complex feedbacks involving lapse rate and cloudiness could alter the climate sensitivity substantially from that prevailing for a similar magnitude of perturbation imposed at other altitudes. A different kind of example is illustrated by model experiments indicating that the climate sensitivity is considerably different for O₃ losses occurring in the upper rather than lower stratosphere (Hansen et al., 1997a; Christiansen, 1999). Yet another example is stratospheric aerosols in the aftermath of volcanic eruptions. In this case, the lower stratosphere is radiatively warmed while the surface-troposphere cools (Stenchikov et al., 1998) so that the climate sensitivity parameter does not convey a complete picture of the climatic perturbations. Note that this contrasts with the effects due to CO₂ increases, wherein the surface-troposphere experiences a radiative heating and the stratosphere a cooling. The vertical partitioning of forcing between atmosphere and surface could also affect the manner of changes of parameters other than surface temperature, e.g., evaporation, soil moisture.

Zonal mean and regional scale responses for spatially inhomogeneous forcings can differ considerably from those for homogeneous forcings. Cox et al. (1995) and Taylor and Penner (1994) conclude that the spatially inhomogeneous sulphate aerosol direct forcing in the northern mid-latitudes tends to yield a significant response there that is absent in the spatially homogeneous case. Using a series of idealised perturbations, Ramaswamy and Chen (1997b) show that the gradient of the equator-to-pole surface temperature response to spatially homogeneous and inhomo-geneous forcings is significantly different when scaled with respect to the global mean forcing, indicating that the more spatially confined the forcing, the greater the meridional gradient of the temperature response. In the context of the additive nature of the regional temperature change signature, Penner et al. (1997) suggest that there may be some limit to the magnitude of the forcings that yield a linear signal.

A related issue is whether responses to individual forcings can be linearly added to obtain the total response to the sum of the forcings. Indications from experiments that have attempted a very limited number of combinations are that the forcings can indeed be added (Cox et al., 1995; Roeckner et al., 1994; Taylor and Penner, 1994). These investigations have been carried out in the context of equilibrium simulations and have essentially dealt with the CO₂ and sulphate aerosol direct forcing. There tends to be a linear additivity not only for the global mean temperature, but also for the zonal mean temperature and precipitation (Ramaswamy and Chen, 1997a). Haywood et al. (1997c) have extended the study to transient simulations involving greenhouse gases and sulphate aerosol forcings in a GCM. They find the linear additivity to approximately hold for both the surface temperature and precipitation, even on regional scales. Parameters other than surface temperature and precipitation have not been tested extensively. Owing to the limited sets of forcings examined thus far, it is not possible as yet to generalise to all natural and anthropogenic forcings discussed in subsequent sections of this chapter.

One caveat that needs to be reiterated (see IPCC, 1994 and SAR) regarding forcing-response relationships is that, even if there is a cancellation in the global mean forcing due to forcings that are of opposite signs and distributed spatially in a different manner, and even if the responses are linearly additive, there could be spatial aspects of the responses that are not necessarily null. In particular, circulation changes could result in a distinct regional response even under conditions of a null global mean forcing and a null global mean surface temperature response (Ramaswamy and Chen, 1997a). Sinha and Harries (1997) suggest that there can be characteristic vertical responses even if the net radiative forcing is zero.

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