Energy Balance of Leaves

The energy balance of a leaf is discussed here as an example, as it represents any organ or surface of a plant. The thermodynamic laws applicable to a leaf are basically the same as described for the atmosphere. However, additional parameters need to be considered for a leaf, namely exchange resulting from reflection of short- and long-wave light at the upper and lower side of the leaf and outgoing re-radiation from the soil to the leaf (Fig. 2.1.10; Jones 1994).

In as far as Is represents the radiation flux to a surface at right angles to the incoming radiation and IL the net radiation flux to a surface oriented in any direction, then Longwave radiation (heat flux)

Fig. 2.1.10. Radiation balance of a leaf. Is Radiation from the sun as direct and diffuse radiation; <r(TatnJ4 heat radiation of the atmosphere; a(Tjf heat radiation of the upper surface of the leaf; a(TB)4 heat radiation from the soil (from Jones 1994)

Longwave radiation (heat flux)

Fig. 2.1.10. Radiation balance of a leaf. Is Radiation from the sun as direct and diffuse radiation; <r(TatnJ4 heat radiation of the atmosphere; a(Tjf heat radiation of the upper surface of the leaf; a(TB)4 heat radiation from the soil (from Jones 1994)

IL = Sintis

where /> the angle between solar ray and object (i.e. the equation describes the energy gain on slopes, see also Fig. 2.1.6). Neglecting possible outgoing heat and storage, the following equation describes the energy gain of a leaf from absorption of short-wave radiation or from IR radiation out from the upper and lower surfaces, from the sensible and latent heat transport, and from metabolism:

Energy balance = short- and long-wave absorption -heat loss - sensible and latent heat transport - metabolism = 0

Symbols and indices are explained in Eqs. (2.1.1)—(2.1.3). The sensible heat flux for a leaf is:

Cp (Tleaf Tatm)

whereby the boundary layer resistance, rb, is proportional to the length of the leaf (1) and inversely proportional to wind speed (u):

Neglecting the boundary layer of the leaf, the latent heat flux is proportional to the vapour pressure deficit between leaf and atmosphere (Dl) and to the stomatal conductance (gs):

and gs is dependent on DL. So far, this relation may only be shown as a physiologically regulated, empirical function:

where DL1/2 corresponds to the vapour pressure deficit at which the stomata are half closed; gs is measured in ventilated cuvettes. The conductivity of a non-ventilated leaf depends on the boundary layer [Eq. (2.1.8)] and is lower than gs.

The equations for the leaf energy balance show that leaf temperature, although measur able, cannot be directly calculated (perhaps it may be interpolated as part of the energy balance), as temperature depends both on the laws of physics relating to the energy balance as well as a physiological reaction. Plants have many possibilities of regulating leaf temperature to avoid extremes and to keep it in the optimal range for physiological activity (see Chap. 1.3.2). These possibilities are:

• Short-term (modulated) responses: change of leaf position, and regulation of stomata, and thus cooling by transpiration;

• Modified responses: changes in leaf size (e.g. slitting of banana leaves with high irradiation) and LAI;

• Evolutionary (genotypic) responses: changes in the reflective characteristics of the leaf, e.g. hairs and pigment composition.