LiDAR_&Satellite_Application

In order for readers to comfortably understand some complex process and hidden theories, the additional explanations following up the last ones given in the last page are supplied as follows.

The information of sampling including reflectance and radiance profile is shown in Figure 7 respectively. However, more detailed information inclusive of the results from calculations should be displayed and explained. They are given in Figure 8 and 9 respectively.

The investigated wavelength in Figure 8 is located within VIS region. Because the thermodynamical transfer is a part of cycles in leaf, for the sake of easily understanding, which may be compared to a well-known Carnot cycle. Reading states in Figure 8 should follow up the order of the indicated letters thus starting from up-case letter: A. Some additional points are given as follows

1. In the state of A, it can be considered that the solar energy absorbed by chlorophyll-a is used to heat water in leaf, the temperature is then raised from the lower temperature (e.g. 24℃/or 25℃) to 26℃, a higher temperature. Assume that 25℃ is an optimum temperature for a kind of investigate plant to maintain its normal metabolism. Therefore, the extra energy residing inside leaf must be released. The releasing process is that of evaporation by means of cell squeezing water out of cell.

2. The negative radiance measured by a sensor (B in Figure 8) indicates that

• In terms of concept of thermodynamics, the enthalpy (a state variable) is changed. However, the negative enthalpy difference is impossible to happen in the process of evaporation being used as a latent of evaporation to heat water. Therefore, only approach and explanation for the matters happening in leaf is that temperature is reduced from high level to low owing to evaporation. Consequently, the process of thermodynamical calculation is that treating measured radiance as a positive latent of evaporation by remaining its negative sign, and inserting temperature from high to low into the equation given in the section 41 produces the positive concentration of chlorophyll-a at that time of chlorophyll-a being measured.

• It should be further emphasized that the measured negative radiance is a record measured by a device installed in sensor at one-time point. However, on the basis of this fact, a very common explanation in remote sensing in the world is “water adsorption” against measured negative radiance at one wavelength —a very abstract concept without quantitatively connecting it to real world in leaf.

• Furthermore, the thermodynamical calculation is performed in an arbitrarily designed state system. Such a treatment is strictly consistent with the principle of thermodynamics. The value assigned to each state variable is arbitrary, but input and output of mass and energy must be balanced for a given system. Accordingly, the outcomes of calculation must meet and have real physicochemical and physical, (bio-) chemical meaning. Through practice in scientific calculation based on measured data, a lot of unclear phenomena and assumptions can be explained in detail and corrected respectively.

3. Once water is evaporated from a system (leaf). Of course, chlorophyll-a is regarded as a solute being remained in the solution (leaf), Its concentration is being increased with the reducing amount of water (solvent) being evaporated out of solution (leaf). Refer to the concentration change of chlorophyll-a form state of B to that of D.

4. Once the temperature of system is dropping to one desired temperature (e.g. 25℃ is assumed as an optimum temperature). At this point (state), the evaporation is terminated. Hence, phase equilibrium of system is reached to. In other words, chemical potential of gaseous water molecules (vapour) is equal to that of liquid water molecules in the solution. The enthalpy difference then becomes zero. Therefore, a time-point-based radiance is equal to zero as well (see E in Figure 8). But, it does not mean that concentration of chlorophyll-a in solution equals zero! At this point (state), its concentration is temporally kept as a constant, which could be ± 0.1209 μg/cm2.s.sr thus the value is gained from its last state (D).

5. From the state of F, it can be proved that another thermodynamic cycle is already started. Then, the similar situation restarts from the state of A.

6. Making use of measured data of radiance at sensor and the same thermodynamical principle, the concentration of chlorophyll-a within SWIR region is capable of being calculated as well (see Figure 9). Except for that, some gaseous mixture diffusing around leaf is also detected (see D and H Figure 9) at wavelength over 2.0 μm. These gaseous mixtures are formed during respiration of leaf, and come from its surroundings such as air as well as soil. They are also able to be calculated. But it needs much knowledge of molecular diffusion. It is another big topic.