Environmental fluctuation effects on the global energy balance

Abstract

Much effort has been devoted to developing simple energy-balance climatic models. Although consideration of latitudinal energy transfer^1–4 gives more complete answers it has become clear that global, ‘zero dimensional’ models may also provide much useful information^5,6. These models have the form: T is the surface temperature, C the thermal inertia coefficient, Q the solar constants, σ the Stefan constant, a (T) the (generally temperature-dependent) albedo, and ε the emissivity of the Earth–atmosphere system. The variability of the climate system rests, therefore, on certain types of change experienced by the solar output, or by such planetary factors as emissivity, albedo, cloudiness and so forth. In addition to some long-term trends of the solar constant⁷, it has been suggested that the Sun is in an almost-intransitive state^8,9. Hence, it may generate large fluctuations around some mean value of its output, which will be perceived by the Earth–atmosphere system as an ‘external noise’ affecting Q. The fact that the terrestrial atmosphere is likely to be in an almost intransitive state¹⁰ can also generate appreciable fluctuations in factors influencing the albedo and the emissivity. In the absence of precise knowledge of the mechanism of these fluctuations, one is again tempted to regard them as an ‘external noise’ affecting a (T) and ε. We explore here the qualitative effect of such environmental fluctuations in the thermal regime¹³, at the level of a zero-dimensional planetary model. Previous analyses of nonlinear systems of chemical and biological interest^11,12 have shown that external noise can dramatically affect the macroscopic behaviour predicted by the deterministic equations of evolution, if coupled to these equations in a multiplicative way.