Quoted from:[1]H. Ögelman and A. Ecevit and E. Tasdemiroǧlu. A new method for estimating solar radiation from bright sunshine data[J]. Solar Energy, 1984.

https://www.sci-hub.ren/10.1016/0038-092x(84)90018-5

INTRODUCTION

At the present, due to its simplicity, the most commonly used correlation is the modified Angstrom type relation; however, difficulty exists in determining what values of a and b should be used. In this paper, in an attempt to find a simple relationship, we examine the correlation of 1841 daily values of H/Ho and s/S for the locations of Adana and Ankara in Turkey and fit a quadratic relation to the measurements. We then proceed to show that this fit to the daily data lends itself to a simple calculation of monthly averages (H/Ho), from the value of (s/S) and its standard deviations, G/s. A further quadratic correlation of gs2/s with (s/S) allows us to write a single quadratic relationship between (H/Ho) and (s/S). We examine the accuracy of these estimations by applying it to a set of measurements from 6 climatologically different regions of Turkey. We discuss the possible global validity of this relationship by demonstrating that it predicts the correlation of a and b parameters of the modified Angstrom equation for different locations on the globe.

Öelman et al. have developed second-order polynomial equation to estimate global solar radiation:

\( H/H_0 =0.195+0.676 S/S_0 −0.083(S/S_0) ^2. \)

The rate of change of (H/Ho) with respect to (s/S) is 0.676 for (s/S) = 0 and decreases to 0.392 for (s/S) = 1. This may mean that as the atmosphere changes from total cloud to no cloud cover situation, the rate of change of increase in the contribution of the bright sunshine and the rate of change of decrease of the forward scattering and multiple reflection by the clouds both decrease at a constant rate.

By putting (s/S) as unity the turbidity index t is obtained as (H/Ho) = 0.729. Angstrom[4] suggests a value for atmospheric turbidity around 0.80 for lower latitudes where the mean atmospheric thickness for the sun is less. However, for mid latitudes the turbidity index is expected to have a lower value.