14.5.2 Energy emission (reradiation)

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All bodies possessing energy emit radiant energy in proportion to the fourth power of their absolute temperature:

Radiation emitted (energy flux density) = σT4 (14.3)

where σ is a coefficient of proportionality (Stefan–Boltzmann constant) and equals 5.670 ×10–8 J m–2 s–1 K–4

True black bodies have an emissivity (e) of 1, and Equation 14.3 holds (providing a basis for remote sensing of surface temperature). However, plants are only imperfect blackbodies (e ≥0.9), and an additional term has to be introducted to Equation 14.3 to cover this minor departure from ideal conditions. As an aside, the laws of conservation of energy show that absorptivity = emissivity, so that good absorbers are also good emitters.

Radiation emitted by the sun and earth may be approximated by black body radiators at temperatures around 6000 K and 250 K respectively. This large contrast in surface temperature means that spectral curves for sunlight do not overlap those for reemission of radiation from the earth back to space. Incoming radiation is commonly referred to as shortwave solar radiation (0–3.0 µm) and outgoing radiation as long-wave radiation (3.0–100 µm). The earth’s atmosphere is a good absorber in the 3–100 µm waveband (Figure 12.1) due to the combined actions of CO2, ozone and organic molecules, but most of all to H2O vapour. Most long-wave radiation lost from earth to space occurs via a gap in the solar spectrum between about 8 and 12 µm (the atmospheric ‘window’).

Net radiation absorbed by a leaf is thus a balance between incoming shortwave radiation and outgoing shortwave plus long-wave radiation. Incoming shortwave radiation includes direct-beam solar radiation, diffuse sky radiation and reflections from surroundings. Outgoing radiation includes reflected shortwave plus re-emitted long-wave radiation from both leaf surfaces.

Combining all of these terms, a leaf will have a positive energy balance in daytime due to incoming radiation, and a negative balance at night-time due especially to long-wave radiation from leaf to sky (and other cold objects nearby). On clear cold winter nights with a sky temperature of around –50°C and a leaf temperature initially of around 10°C, radiant heat loss from leaf to sky will be prodigious. If calm con-ditions prevail on such nights, exchange of sensible heat is restricted by a thick boundary layer and leaves will fail to draw much warmth from that source. As a consequence, leaf temperature will continue to fall below air temperature, and chilling injury or frost damage will result (Sections 14.4, 14.6 and Case study 14.1). Large leaves, which have thicker boundary layers than small leaves, are especially vulnerable, and because boundary layers are thicker away from the leaf edges, dew or frost generally forms first on leaf centres.