The simplest approach to estimating $$IAM_B\left (\theta_{AOI} \right)$$  was developed by Souka and Safat (1966) and later adopted by the American Society of Heating, Refrigeration, and Air Conditioning (ASHRAE), and is known as the “ASHRAE incidence modifier.”

$$IAM_B= 1-b_{0} \left (\frac{1}{\cos \left (\theta_{AOI} \right)} -1\right)$$

This function has the benefit of needing only one parameter, $$b_0$$ , but suffers from a discontinuity at $$\theta_{AOI}=90^{\circ}$$  and low accuracy at high incident angles.  Some authors suggest not applying this function for incident angles where $$\theta_{AOI} \gt 80^{\circ}$$  (Abella et al., 2003).  Figure 1 compares ASHRAE model results for two values of $$b_O$$  .

Image of ASHRE_Figure1

Figure 1. IAM Model Results for the ASHRAE model.


[1] Souka A.F., Safwat H.H., "Determination of the optimum orientations for the double exposure flat-plate collector and its reflections". Solar Energy vol .10, pp 170-174. 1966.

[2] M. A. Abella, E. Lorenzo and F. Chenlo, "Effective irradiance estimation for PV applications," Proceedings of 3rd World Conference on Photovoltaic Energy Conversion, 2003. Osaka, Japan, 2003, pp. 2085-2089 Vol.2.