Saturday, July 28, 2007

The effect of solar radiation variation on the climate of the Earth

Mikhail I. Budyko's article, "The effect of solar radiation variation on the climate of the Earth," published in 1969 was one of the first theoretical investigation of the ice-albedo feedback mechanism; i.e., the more snow and ice, the more solar radiation is reflected back into space and hence the colder Earth grows and the more it snows. Budyko notes that over the last 200 million years the temperature difference between the poles and the equator was comparatively small compared what it is today. He says that during that time there were no "zones of cold climate."

He and his group at the Main Geophysical Observatory at Leningrad found that over the period from the end of the 19th century until 1940 there was a rise in the average temperature of the Earth of 0.6° C. From 1940 until the mid1950's there a fall in temperature of 0.2° C.

One major purpose of the article was to provide quantitative analysis of how to explain the variation of glaciation in the Quaternary Period. n his analysis Budyko considers some exogenous variations in Qp due to factors such as changes in the characteristics of Earth's orbit or variation in the transparency of the atmosphere due to volcanic dust.and the endogenous changes in the average albedo for the Earth. Here we examine the latter.

A large part of solar energy coming to the Earth from the Sun is reflected by the climatic system and goes back to space. This energy does not heat the Earth. When the reflective capability of climatic system is larger, climate is cooler. The value of albedo A is the ratio of solar energy flux reflected by the climatic system to the total solar irradiation flux.

The value of A changes with time and for the last tens of years it is ~ 0.3. Albedo is dimensionless value but using S one can find flux of solar energy reflected by climatic system.The energy-balance equation for the Earth’s climatic system has the form πr2 •S•(1 - A) + WE = 4πr2σTE4, where r is the Earth’s radius, S is the solar irradiance (constant) at the distance of 1 a.u., A is the spherical albedo of the Earth, WE – the heat-flux power entering the climatic system from the interior of the Earth, σ is the Stefan—Boltzmann constant, and TE is the effective (radiative) temperature of the climatic system. The left-hand side of the equation is the energy flux that heats the climatic system, whereas the right-hand side corresponds to the heat flux escaping from the system into the interplanetary space.The mean power WE of the heat flux coming from the interior of the Earth to the climatic system is on the order of 1013 W This value is lower by, approximately, four orders of magnitude than the energy flux arriving at the Earth from the Sun. Therefore, we may ignore the quantity WE in equation and to write it in the form

S•(1 - A)/4 = σTE 4, πr2 •S•(1 - A) + WE = 4πr2σTE4,

Satellite-based observations performed starting from 1978 have shown that the solar irradiation is S = 1366 W/m2 and negligibly (smaller than by 0.1 %) varies with time (The corresponding variation of TE attains, approximately, 0.07 °C.) Thus, we may assume that S = const. The spherical albedo A is the variable quantity. Its present-day value is assumed to be equal to 0.3 For the indicated values of S and A, the effective temperature is TE = 254 K, or –19 °C. This temperature characterizes the total amount of the thermal energy emitted by the climatic system per unit time into the interplanetary space. The corresponding power of the heat loss by the Earth for the infrared radiation emission into space is 236 W/m2. This value is in good agreement with the results of satellite observations.

The effective temperature TE = −19 °C corresponds to the atmosphere temperature at the altitude of ~ 5.5 km. At this altitude, the atmosphere mass is divided into approximately equal parts. This fact indicates that in the infrared range, the atmosphere is the basic emitter of the climatic system.

The main climatic parameter characterizing the Earth’s climate is the global air temperature Ts near the Earth surface. This temperature determines water evaporation from the Earth’s surface, cloudiness, and rainfall, atmosphere dynamics, ice-cover area, etc.

Using the simple two-layer model of the global radiation balance, we can relate the temperature Ts of the model to the temperature TE. According to this model one of the layers is concentrated in the troposphere at an altitude of h ~ 5.5 km, whereas the other is situated near the Earth surface. The heat is transferred from the more heated layer near the Earth surface, which has the temperature Ts, to the less heated one residing at the altitude of h ~ 5.5 km and having the temperature TE. In accordance with the Stefan—Boltzmann law, we can write the energy-balance equation for this two layer system in the form.

S•(1 – A – k)/4 = σ(Ts 4 − TE4), or S• (1 – A – k)/4 = σTs 4(1 -- TE4/Ts4).

Here, the dimensionless factor k features the mean absorptive capability of the atmosphere with respect to the solar radiation. This factor is not constant, and its present-day value is, approximately, 0.26.

The temperatures TE and Ts vary in phase with each other.Therefore, the dimensionless parameter TE / Ts entering intothe relationship characterizes the structure of the climatic system in itself rather than the energy fluxes circulating within the system. Therefore, we may assume that this parameter is almost invariable with time. In this case and for S = const, the temperature Ts and the Earth climate depend on two variable quantities, namely, on the global albedo A and the mean absorptive capability k of the atmosphere. As the observations show the value of A changes with time and k is practically constant.

From 1985 till 2000 the gradual decrease of global cloud coverage and albedo were observed. The value of this decrease was ~ 6 % and solar energy flux reflected back to space decreased at ΔF ≈ (6) W/m2. Since 2000 the values of global cloud coverage and albedo became to increase slightly.

Therefore we can see the change to Albedo that balances the radiative equations is in the area of 6 w/m2, the forcing response of GHG being 2.4 w/m2.

This Equivalent to 2% increase in solar irradiance, a factor 20 more than typical maxima to minima variations. This brings some interesting questions.

1) Reversibility suggests natural variations.
2) GCM do not show such variations.
3) What is the climatic impact? Recent warming.


Budyko, Mikhail I., "The effect of solar radiation variations on the climate of the Earth," Tellus vol. 21, (1969) pp. 611–619.

E. Palle, P.R. Goode, P. Montanes-Rodriguez, S.F. Koonin, “Can
Earth’s albedo and surface temperature increase together?,” EOS, 2006,
vol. 87, No. 4, pp. 37, 43.

A.S. Monin, A.A. Berestov, “New about climate,” Vestnik RAS, 2005,
vol. 75, No. 2, pp. 126-131 (in Russian).


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