Geog 595 Ecological modeling

Spring 2010

Due: Feb 17, 2010

Lab 3 Modeling Net Radiation for Vegetation Canopies

Objectives:

(1)  Implement the models for canopy radiation interception for both shortwave and longwave radiation.

(2)  Gain skills in C programming for Ecological Modeling with multiple computation modules

Theory

(1) Shortwave Radiation

According to Lab 2, the absorbed shortwave radiation for PAR by a vegetated canopy can be modeled as:

Thus the total absorbed PAR by the vegetated canopy is

Similarly, the total absorbed radiation for NIR by the vegetated canopy can be modeled as

Thus the total absorbed NIR by the canopy is

The total shortwave radiation absorbed by the canopy is

The shortwave radiation entering the forest floor from canopy includes direct PAR, diffuse PAR, direct NIR and diffuse NIR. Given the reflectance of forest floor, ρs, the absorbed shortwave radiation on the forest floor is

Where

2. Longwave Radiation

Any object with temperature greater than 0oK emits radiation. The total amount of energy emitted by a blackbody is given by Stefean-Boltzman’s law:

For vegetation canopy, εcanopy=0.98; for forest floor, εfloor=0.95. However, the emissivity for atmosphere is more complicated as it varies with cloud cover and water vapor. For clear skies, the emissivity of the atmosphere can be estimated as (Brustaert, 1975):

Where ea is the vapor pressure of the air in mb (1 mb =100 Pa), and Tair is in degrees Kelvin. For cloudy skies, the emissivity of the air is a function of cloud cover as (Unsworth and Monteith, 1975):

Where c is the fraction of cloud cover of the sky [0,1]. Cloud cover is often not recorded. Song et al. (2009) developed an approach estimating the cloud cover during the day time based on the total transmittance, τ.

Based on our work separating radiation into direct and diffuse component, we know that for a clear day, τ=0.7, i.e. c=0. When τ =0.3, the total radiation is 100% diffuse, i.e. c =1.0, thus

Because the longwave radiation from the atmosphere arrives in all direction, it can be treated as diffuse radiation. Leaves are highly absorptive to the longwave radiation, thus they can be treated as black leaves. The average longwave radiation plant canopy absorb is

At the same time, canopy also absorb longwave radiation from the forest floor, which can be modeled similarly,

The total absorbed longwave radiation by the canopy per unit LAI is

In the meantime, canopy itself is emitting longwave radiation both upward and downward.

Therefore, the net longwave radiation in the plant canopy is

The net canopy radiation is

The total canopy net radiation by both sunlit and shaded leaves is

For the forest floor, it receives longwave radiation from the air through the gaps and from the canopy that is not gap. In the meantime, it emit longwave radiation. Thus, the net long wave radiation for the forest floor is

The net radiation for the forest floor considering both shortwave and longwave radiation is

The total net radiation for the who stand is

Integration of Multiple Modeling Modules in C

1.  Scope of variables

2.  Nominal variables and variable address in C

3.  Structures and pointers to structure and memory allocation

4.  Functions in C

5.  Header Files in C

6.  Makefile

Modeling Exercises

1.  Compile the program and run it as

Geog595 –f TdrTsoilWindLaiPrecParTaVpdMay2001-Daytime.txt > netradiation.txt

The last column of the output is the net radiation at the stand level. Please compare the output with the last column in the file “PSN-ET-RnetMay2001-Daytime.txt” which is observed net radiation for the same stand. Please use a scatter plot to do the comparison with x-axis being the modeled data and y-axis being the measured data.

Please add trend line on the graph, and force the intercept to zero and adding R2 on the graph. Please also calculate the root mean squared error between the modeled and measured net radiation.

2.  Write a function for Kb(θ) called “compute_direct_extinction_coefficient.c”, and modified the main program, the header and the Makefile. Please compile and run the program. You should get the exact output as in netradiation.txt

3.  Write a header file, a Makefile named Makefile2, to integrate your Kb(θ) function above (compute_direct_extinction_coefficient.c) and a new main program main.c into a program called Extinctco. Once you have all these files written, you can compile them to create Extinctco by typing “make –f Makefile2”. Please include all these programs in your lab report.