## Energy Flows in the Biosphere

Y M Svirezhev, Potsdam Institute for Climate Impact Research, Potsdam, Germany © 2008 Elsevier B.V. All rights reserved.

Introduction

Incoming and Outgoing Radiations and the Planetary

Energy Balance Transformation of Solar Energy Inside the EAS Greenhouse Effect Albedo

Equations of Radiative Balance

Energetics of Photosynthesis and Vegetation

Photosynthesis

Efficiency of Vegetation

Energy Transfers, Trophic Chains, and Trophic

Networks Conclusion Further Reading

### Introduction

Life on Earth is a product of so-called 'photon's mill', which has started to function when our solar system was in the form of matter's 'clots' embedded into the ocean of 'cold' photons with temperature T = 2.7 K. Evolution and self-organization of planets (including life on our planet) is a result of this mill's functioning, which is happening due to the fact that Sun's surface irradiates the 'hot photons' at T = 5800 K, and these photons reach the cold planet's surfaces. Then they cool down to the temperature of the surface and irradiate back into the space. For the Earth, this temperature is equal to 253 K; it is the temperature, which could be measured by an observer at the top of atmosphere. Formally, the photon's mill is a typical 'heat machine' that is functioning by Carnot cycle, but its working body is the photon gas (for details see Entropy and Entropy Flows in the Biosphere).

Incoming and Outgoing Radiations and the Planetary Energy Balance

A parallel flow of solar radiation at the Earth's mean distance from the Sun is equal to 1368 Wm"2; this is an irradiation of blackbody with T = 5800 K (see Figure 1). Since the Sun's flow is parallel its effective section is ^rErth, where rErth is the Earth's radius. An area of the Earth's surface is 4^rErth, that is, four times larger than the section's area; therefore, only one-fourth of the total flow, 342 W m"2, is coming to the area unit of the upper boundary of the 'Earth + atmosphere system' (EAS). It is obvious that specific flow is varying from point to point on the globe and in time within 1-year interval, so that these and other local values connected with energy flows are averaged over the globe and the year.

Incoming radiation is described by the energy spectrum E in(A, x, y, t), where A is a wavelength, x and y are geographic coordinates, and t is a time. By interacting

Figure 1 Spectra of incoming and outgoing solar radiation. (a) Standard spectrum of solar radiation at the top of the atmosphere. (b) Typical spectrum of the Earth's thermal radiation.

Figure 1 Spectra of incoming and outgoing solar radiation. (a) Standard spectrum of solar radiation at the top of the atmosphere. (b) Typical spectrum of the Earth's thermal radiation.

with a surface, it is transformed onto the energy spectrum of outgoing radiation, E out(À, x, y, t):

where F(A, x,y, t) is the transition operator. The spectrum of outgoing radiation is close to the blackbody spectrum with T = 253 K.

Really, we have information only about these two spectra measured sufficiently frequently, sufficiently densely, in sufficiently big number of spectral bands (today up to 120), in the course of sufficiently long time. Outside of the EAS, satellites are carrying out these measurements today. At the level of the Earth's surface (the ground), it is performed also by satellites, and when they are corrected by data of the ground measurements. Note that outgoing radiation contains a lot of information about a surface, interacting with incoming radiation. Spectra of incoming and outgoing radiations are shown in Figure 1.

The simplest form of F(A, x, y, t) is a shift operator R(A, x, y, t) = Em(A, x, y, t) -Eout(A, x, y, t); a convolution R(x, y, t) = JnR(A, x, y, t)dA over all wavelengths is named a local 'radiative (radiation) balance'. Convolutions Em(x, y, t) = /nEm(A, x, y, t)dA and £out(x, y, t) = / nEout(A, x, y, t)dA are the total energy of incoming and outgoing radiation at the given point and in the given moment. If we average R(x, y, t) over the EAS surface, SEAs, and 1-year interval, t1, we get the 'annual planetary radiative balance'

SEAS?t1 J G JT

is equal to zero. This is a typical 'empirical generalization'.

The wavelengths A is usually measured in the band ft,: (0.2, 50 mm), which contains almost 100% of the total energy of incoming and outgoing radiations. Its most part (~99%) is a shortwave radiation (SWR) with wavelengths A lying within the spectral band S: (0.2, 5.0 mm), where 53.5% constitutes a radiation with Ae(0.4, 0.7 mm), so-called photosynthetically active radiation (PAR). This spectral band is called 'visible'. The radiation with ApL (5, 50 mm), the long-wave radiation, LWR, constitutes only 0.45% of the total radiation. About 0.5% constitutes an ultraviolet radiation, A < 0.2 mm, that is, fortunately, almost completely detained by ozone layer. Note that other divisions of the total spectral band are often used, for instance, S: (0.3, 3.0 mm), etc.

Later on we shall operate with values of energy integrated over these two spectral bands and averaged on the total EAS' surface and 1-year interval: Es , EL and Es , E™ . In accordance with observed data we have with sufficient accuracy that for the EAS: (E™)EAS = 340 Wm-2, (ELm)EAS = 0, and (Er)eas = 102 Wm-2, (4°™)eas = 238 Wm-2, so that (Em )eas = (Eou )eas . Earth on the whole gets 238 Wm -2 x 5 x 1014m2= 1.2 x 1017W of the SWR, and irradiates as much LWR again.

The relation between these values can also be presented as

where aEAS = (E^Oeas/ÎE™^ = 0.3 is so-called planetary 'albedo' (from LASin whiteness'), that is, a coefficient of reflectance of the EAS with respect to incoming radiation.

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