- Name of the DEM of the study site
- Name of the radiation output grid
- Latitude in degrees of the study site
- Julian day for day to start calculation
- Julian day for day to end calculation
- Time interval for incrementing daily solar path

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/m^{2} 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/m^{2});
*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) |

Required input: | DEM |

Output units: | kJ/m^{2}/time period |

Solar constant used: | 1.367 kW/m^{2} |

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; can’t 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 |

**References**:

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.