Geog595 Ecological Modeling
Spring 2010
Due: 5pm Jan 26, 2010
Lab 1 Calculating Incoming Solar Radiation with C
1. Objectives
(1) Learning programming in ecological modeling in C.
(2) Development a module that calculates solar radiation arriving at the Earth surface at any place any day and any time.
2. Input Data
Latitude and longitude
Measured total photosynthetically active radiation (PAR)
Month, Date and Hour of measurements
Air Pressure
3. Theory
Solar radiation is the ultimate source of energy that drives all ecosystem process. It is essential to modelers to know how much solar radiation arriving at the Earth surface in order to model other ecological processes. At the very top of the atmosphere, the solar radiation flux density is usually considered a constant, “Solar Constant” (S0=1367.0 W/m2). However, for scientific computation, it can no longer be considered as constant, it actually varies as a result of Sun-Earth distance changes through the year.
,
where J is Julian date. The amount of solar radiation arriving at the Earth surface changes because of the change in atmospheric conditions and position of the Sun in the sky. The total radiation at the top of the atmosphere is composed of ultraviolet (SU), visible (SV) and near-infrared (SN) as in the following:
Due to the lack of account for SU in the literature, let assume ultraviolet has the same optical properties as the Visible and combine them into a single component of SUV. Then we will separate Visible light out from SVU when modeling photosynthesis. For convenience we will call SVU as SV.
According to (Weiss and Norman, 1985), the potential U and V direct radiation is
Where P is air pressure, and P0 is standard air pressure (P0=101,325Pa). m is the atmospheric optical depth as
The potential diffuse Visible reaching the horizontal surface is considered 40% of the scattered radiation:
The potential direct NIR reaching the horizontal surface is
And the potential diffuse NIR radiation on the horizontal surface is
ω is the water absorption in the near infrared for 10 mm of precipitation water
Then, the fraction of direct beam in PAR and NIR are
Where A=0.9, B=0.7, C=0.88, and D=0.68. RATIO is the measured to potential solar radiation, i.e. RATIO=RT/(RV+RN). Often we do not have RT measure, but RV only, we can convert RV to RT as RT=RV/0.439.
Calculating solar zenith angle by time of day:
Where τ is local time hour angle. τ=15×(t-12) degrees, t is in hours; φ is latitude; δ is sun declination angle.
The Goudriaan and Van Laar (1994) model, as given in Leuning et al. (1995) for fractions of diffuse radiation for total radiation based on atmospheric transmittance (τa):
The Spitters et al (1986) model for fractions of diffuse radiation for total radiation:
Where R=0.847-1.61cos(θ)+1.04cos2(θ), and K=(1.47-R)/1.66.
4. Lab Report
(1) Run your program to get the diffuse fraction of total radiation for the three approaches and make a time-series plot for them. Compare the difference.
(2) Modify the model so that the program only runs the Weiss and Norman (1985) model with direct and diffuse radiation (not fractions) for PAR and NIR, delete all unnecessary statements and add programs as needed, save the new program as Weiss_Norman.c.
(3) Plot the four components of radiation you produced in (2) above as a function of time of day with excel. Explain the seasonal and diurnal patterns you see.