The routine takes into account overshadowing by high peaks, meaning that the routine detects pixels that are in the shadow of adjacent higher terrain for a given sun position. This can result in no direct solar radiation over the whole day for specific areas in a DEM, especially when calculating radiation for the winter solstice in northern latitudes when the maximum daily sun-altitude angle is generally low. The original coding of L. Kumar has an error inherent when calculating the over-shadowing by adjacent terrain (using the HILSHADE function in GRID). The solar path is not corrected for N/S latitudes, resulting in wrong sun azimuth values when hillshading a DEM in northern latitudes. See shortwavc.aml for a corrected version.
The routine is based on the assumption that the transmittance of a clear
sky is 0.8 (measured vertically through the atmosphere), and it calculates
the attenuation of the beam radiation due to lower sun-altitude angles
(reduction of transmittivity due to a longer path through the atmosphere).
The equation used to calculate attenuation of beam radiation is derived
from Kreith & Kreider (1978):
where Tau = the transmittance of the atmosphere; and M = the air mass (mass of the atmosphere) for a given sun-altitude angle:
where a = sun-altitude angle for a given sun position (depending on latitude, date, local time). The factor 0.56 governs the asymptotic maximum of a transmittance of 0.8 at a sun-altitude angle of 90° .
Furthermore, the AML uses a value of 1367 W/m2 for the solar
constant (= yearly average of extraterrestrial direct normal radiation),
and adjusts seasonal value of the extraterrestrial direct normal radiation
where Io = extraterrestrial direct normal radiation (in W/m2); JD = Julian day. The factor 0.56 governs the asymptotic maximum of a transmittance of 0.8 at a sun-altitude angle of 90° .
|Command:||&r shortwave (at GRID or ARC prompt)|
|Output units:||kJ/m2/time period|
|Solar constant used:||1.367 kW/m2|
|Transmittance used:||0.8 (max for vertical beam)|
|Minimum calculation step:||1 day|
|Speed of calculations:||Very fast due to parsimonious programming|
|Flexibility of the routine:||Medium; canít go beyond 1 day|
|User interface:||Limited, but simple and easy|
|Known errors:||Hillshading in N-latitudes|
|or download here:||shortwave.aml (use: "save link as")|
|Contact:||niklaus.zimmermann @ wsl.ch|
Kreith, F., and Kreider, J.F. 1978. Principles of Solar Engineering. McGraw-Hill, New York, NY.Last Updated: 9/14/00
Kumar, L., Skidmore, A.K. and Knowles, E., 1997. Modelling topographic variation in solar radiation in a GIS environment. International Journal for Geographical Information Science, 11(5): 475-497.
[top] [back] [home]