Accuracy Near The Horizon
The above approximation overlooks the curvature of the Earth, and is reasonably accurate for values of up to around 75°. A number of refinements have been proposed to more accurately model the path thickness towards the horizon, such as that proposed by Kasten and Young (1989):
-
(A.2)
A more comprehensive list of such models is provided in the main article Airmass, for various atmospheric models and experimental data sets. At sea level the air mass towards the horizon ( = 90°) is approximately 38.
Modelling the atmosphere as a simple spherical shell provides a reasonable approximation:
-
(A.3)
where the radius of the Earth = 6371 km, the effective height of the atmosphere ≈ 9 km, and their ratio ≈ 708.
These models are compared in the table below:
| Flat Earth | Kasten & Young | Spherical shell | |
|---|---|---|---|
| degree | (A.1) | (A.2) | (A.3) |
| 0° | 1.0 | 1.0 | 1.0 |
| 60° | 2.0 | 2.0 | 2.0 |
| 70° | 2.9 | 2.9 | 2.9 |
| 75° | 3.9 | 3.8 | 3.8 |
| 80° | 5.8 | 5.6 | 5.6 |
| 85° | 11.5 | 10.3 | 10.6 |
| 88° | 28.7 | 19.4 | 20.3 |
| 90° | 37.9 | 37.6 |
This implies that for these purposes the atmosphere can be considered to be effectively concentrated into around the bottom 9 km, i.e. essentially all the atmospheric effects are due to the atmospheric mass in the lower half of the Troposphere. This is a useful and simple model when considering the atmospheric effects on solar intensity.
Read more about this topic: Air Mass (solar Energy)
Famous quotes containing the words accuracy and/or horizon:
“U.S. international and security policy ... has as its primary goal the preservation of what we might call “the Fifth Freedom,” understood crudely but with a fair degree of accuracy as the freedom to rob, to exploit and to dominate, to undertake any course of action to ensure that existing privilege is protected and advanced.”
—Noam Chomsky (b. 1928)
“The world of the egotist is, inevitably, a narrow world, and the boundaries of self are limited to the close horizon of personality.... But, within this horizon, there is room for many attributes that are excellent....”
—Ellen Glasgow (1873–1945)