LiDAR_&Satellite_Application

Except for the approaches discussed in the previous sections, another approach of modelling thermal transfer associated with leaf is based on thermodynamics at a macro level (see Figure 1). In this case, most parameters used in modelling are the ones of state they are used to describe how they are affected by a process that energy exchanges between internal and external system. Those parameters such as Gibbs free energy has intensive properties. Similarly, the size of system is arbitrarily selected and designed. The derived equation is based on the 2nd law of thermodynamics. The water in leaf is treated as solvent and other molecules such as chlorophylls and including ions are handled as solutes. The former is certainly able to be evaporated through phase transition, and the later appears immobile thus remains in system (leaf). In fact, water potential different (thus water potential gradient) in leaf is a driving force to evaporate water. However, from angle of thermodynamics, those internal factors (parameters) is not required to take them into account. They are useful in the detailed research in plant physiology. This approach is to bridge the data gained by remote sensing between the parameters associated with leaf. Such as the concentration of chlorophyll in leaf. In this practice, the following points should be noticed:

1. The temperature used in modelling is selected at 25℃, the difference of temperature at each possible state is kept at 1℃. Therefore, if the temperature is dropped, it is considered as cooling; if the temperature is raised, such process is treated as heating. Of course, the selected temperature is adjustable according to local temperature.

2. Enthalpy of phase transition can be selected from radiance at senor and ground. That means the temperature of system is being dropped as soon as the evaporation starts. The reason is shown in the following points.

3. It may be unnecessary to use the latent heat of vaporization of pure water (44 kJ/mole at 25℃ gained from textbook or handbook because this obtained value is measured at a constant pressure without other factors disturbing pure solvent in lab. Nevertheless, as the matter of fact, the latent heat of vaporization of water in leaf could be much different. It is a variable due to a fact that

• the process of evaporation is affected by several factors such as gravitational force, magnetic force from each field.

• It also employs the fluctuation of pressure owing to the solutes diffusing with water flowing into cell. In order to maintain chemical potential balance, the extra pressure must be added onto a cell. That causes water flow into and out cell at all time.

• Therefore, in thermodynamics use the term of the partial molar properties indicates how an extensive property of a solution or mixture varies with changes in the molar composition of the mixture at constant temperature and pressure.

• As seen, during the period of respiration of leaf, varieties of many parameters respond to it. This includes the latent heat of vaporization of water. That is the reason why we should select measured radiance at sensor and ground to be the latent heat of vaporization of water, then effectively estimate the dynamic concentration of chlorophyll in the process of photosynthesis by means of calculation (see section 55).

4. All of processes in plant occur simultaneously other than step by step so as to continuously maintain life of plant without any broken points. It is same as the case that human’s breathing is for continuously surviving. Accordingly, separately modelling this complex process is only for seeking for understanding in detail rather than pulling the life of plant apart.