1.1 shortwave.aml

This is a routine to calculate direct clears-sky short-wave radiation, originating from Lalit Kumar (Kumar et al., 1997), and available at ftp://fatboy.geog.unsw.edu.au. This AML is very parsimonious, and generates similar output as solarflux.aml. However, it is at least 3x faster. Other than solarflux.aml, this routine does not allow to calculate grids for time periods shorter than a single day. The routine enables the user to generate daily (to many days) grids of clear-sky direct radiation. The user is prompted for: If the user wants to calculate the radiation for a single day, the same Julian day has to be submitted for start and end of calculations. Southern latitudes have to be indicated as negative values. The time interval (submitted in minutes) to increment the solar path determines how often the sun position is calculated during a day. The program then integrates the energy linearly over time. 30 to 120 minutes are reasonable intervals depending on the size of the DEM (# of pixels).

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 by:

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° .

General specifications of the AML:

Command: &r shortwave (at GRID or ARC prompt)
Required input: DEM
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
Corrections shortwavc.aml
Programmer L. Kumar
Available @: fatboy.geog.unsw.edu.au
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.

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.

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Last Updated: 9/14/00
By Niklaus E. Zimmermann