Gaussian Equation to Describe the Percent of Shadow Length in Satellite Image

TL;DR

This paper introduces an empirical Gaussian equation to accurately estimate the shadow length percentage in satellite images based on the day of the year, simplifying complex astronomical calculations for practical engineering and architectural applications.

Contribution

The study proposes a novel Gaussian-based empirical model that predicts shadow length percentage using only the day number, reducing reliance on complex astronomical equations.

Findings

The Gaussian equation accurately estimates shadow length percentage.

The model simplifies shadow calculations for urban and architectural planning.

It requires only the day number and building height for predictions.

Abstract

The shadow is a separated feature in the satellite images specially high resolution images. It may be looked as a problem when it causes a loss in the ground ray response to the shaded area, and may be, from other view, considered as an indication to the height of the bodies or buildings, when it hidden due to top view of the satellite image usually. The location of the object on the earth affects its shadow length, direction and darkness. The ostensible sun path in the sky also affects the shadow length and direction, it is depending on the change of the rotation axis of planet about its center during the year. And it is clear that the shadow is changing with the sun transmission in the day times. The sun location needs complex equations, because there are several angles describing its location with taking into consideration the location of the shaded body on the earth spatially the latitude, and the shadow direction and length depend on the sun location so it need more equations. Some engineering purposes, and some engineers and designer can not process these complex astronomy equations every time they need to calculate the shadow effect on the urban region or garden for examples, or other architectural purposes, it is unpractical process to estimate the shadow direction and length for civil from these equation. So, we derived in this study a high accurate empirical Gaussian equation to find shadow length percent in the limits of the study area depends on single parameter which is the number of day during the year, and calculating the percent of shadow, so we can calculate the shadow length percent accurately in any day number by the suggested equation after knowing the real building height.