11.4 Complete Energy Budget

By substituting Equation (11.3) into Equation (11.1), and including the expression given by Equation (11.2) in Equation (11.3), one gets for the full expression of the leaf energy budget the following:

\[\begin{equation} Q_a = \varepsilon \sigma [T_l + 273]^4 + k_1 \bigg( \frac{V}{D}\bigg)^{1/2} [T_l - T_a] + L(T_l) \frac{_s d_l (T_l) - [r.h.]_s d_a (T_a)}{r_l + k_2 \big( \frac{D}{V}\big)^{1/2}} \tag{11.4} \end{equation}\]

Here all environmental variables that affect the energy status of the leaf act simultaneously. They are \(Q_a\), \(T_a\), \(\varepsilon\), \(D\), and \(r_l\) while the absorptivity of the leaf surface to radiation is buried in the term \(Q_a\). When all the environmental variables and appropriate leaf properties are known, a unique value of \(T_l\), will balance this equation.

11.4.1 Values of Leaf Parameters

Leaves are of many sizes from 1.0 \(\times\) 10^-3 m by 2.0 \(\times\) 10^-2 m for a Douglas fir needle to 0.3 m by 1.5 m for a banana leaf. Some leaves will have lengths very nearly equal to their widths. Internal diffusion resistances of leaves vary from less than 100 s m^-1 to infinity but with commonly occurring values between 200 and 2000 s m^-1. Most leaves will have an absorptivity to shortwave radiation of about 0.6, but it may vary from 0.4 to 0.8. Longwave absorptivity will equal the longwave emissivity of 0.96. The total amount of radiation absorbed by a leaf will vary from about 400 to 800 W m^-2 but higher and lower amounts may be encountered.

11.4.2 Values of the Environmental Variables

It is relatively easy for any of us to visualize the range of values for air temperature. A leaf is likely to encounter freezing when the air temperature is 0°C. Maximum air temperature for hot desert conditions, for example, would be about 45°C. Relative humidity is also easy to visualize as a result of common experience. For example, humid air would have a relative humidity of about 70% or greater and for very dry air r.h. = 30% or less. It is easy for one to look up in tables the water vapor density of saturated air at any particular temperature. Values range from 1.289 kg m^-3 at 0°C to 1.068 kg m^-3 at 45°C. Wind speeds are a part of common experience. Still air usually has very slight air movement which we arbitrarily put at 0.1 m s^-1. A gentle breeze is 1.0 m s^-1 (2.2 mph) and a moderate wind is 10 m s^-1 (22 mph). Radiation is the least familiar of all of the environmental variables and yet it is the most significant of them.

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