Solar Radiation Modeling:

Don Cline



The models TOPORAD and TOPQUAD are for computing the spatial distribution of solar radiation throughout an area of interest. TOPORAD computes the instantaneous solar radiation distribution, i.e. computes the distribution for one instant in time. TOPQUAD integrates the solar radiation inputs over the course of a day, to yield the total solar radiation loading. TOPQUAD calls TOPORAD several times for one day, then performs the integration.

To run TOPORAD and TOPQUAD, you must use IPW: the Image Processing Workbench, written by Jim Frew and Jeff Dozier at UC Santa Barbara. IPW utilizes UNIX primitives to perform a variety of image processing functions. This tutorial and the subsequent exercises will get you started in IPW, but only far enough to run the models and perform some basic IPW functions.

Digital Elevation Models

The basic data required to run TOPORAD and TOPQUAD is a digital elevation model (DEM). A DEM is a matrix, or grid of elevations, with one elevation for each element of the matrix. The spatial resolution of the DEM refers to the dimension, in ground units, of each side of the grid element (elements are usually square, but don't have to be). For example, USGS standard product DEMs come in different spatial resolutions, depending on their source: DEMS produced from data related to 7.5 min quadrangles is nominally 30 m x 30 m, while other USGS DEM products have resolutions of ~90 m x 90 m, etc.

To do much with DEMs, we have to know the "address" of each element in the grid. Usually, we do this with row/column addresses. If the origin of the DEM is the upper left corner, then the top row is row one, and the left-most column is column one. Then the address of the upper-left cell is (1,1). The terms ith row, jth column are used to refer to generic cell addresses, especially in coding. In remote sensing, it is more common to refer to rows as "lines" and columns as "samples".

We also have to be aware of the range of elevations in a DEM, and how that range can be represented in digital values. 256 values from 0-255 can be coded as 8-bit data, but that is not enough for most places. In Colorado, where elevations may range from 2000-4000 m in the same DEM, we need at least 2000 values. 12-bit data can represent 4096 values, which is sufficient for most places.

For this exercise in using TOPQUAD and TOPORAD, we'll be using a DEM for Niwot Ridge in the Colorado Front Range. It has a spatial resolution of 20 m x 20 m, and has 175 lines (rows) and 423 samples (columns). Elevations in the DEM range from 3107 m to 4095 m. The data comes to you as an ASCII file with 1 field (elevations) and 74025 lines (175 x 423 = 74025). The origin of the DEM is the upper left corner, and the ASCII file lists each element starting with 1,1, 1,2, 1,3... 2,1, 2,2, 2,3... etc.

Atmospheric Parameters

To run either TOPORAD or TOPQUAD, you have to know (or guess) something about the atmosphere. Obviously, whether it's clear or overcast significantly affects the radiation regime. But, perhaps less obviously, the gaseous constituents, particulates, etc. also affect the radiation regime, and must be accounted for even under clear skies.

The three atmospheric parameters needed for these models are called tau, omega, and gamma (t,w,g).

Modeling Exercise

There are four components to this lab. The first two are tutorials to demonstrate how to import data into IPW, and how to run TOPORAD and TOPQUAD. The third component is a set of exercises to perform. Follow the links below to each of these components.

1. Tutorial: Converting ASCII elevation data to IPW format.

2. Tutorial: Viewing IPW images using xv2.

3. Tutorial: Running TOPORAD and TOPQUAD

4. Exercises