Spectral mismatch models are part of the translation from broadband plane-of-array (POA) irradiance to effective irradiance. Generally, the translation takes the form

$E_e&space;=&space;M&space;\times&space;\{&space;IAM_B&space;\times&space;E_b&space;+&space;E_{diff}&space;\}&space;\times&space;SF$

where $M$ is the spectral mismatch modifier, $IAM_B$ is the reflection losses for the beam irradiance $E_b$  (i.e., $DNI&space;\times&space;\cos(AOI)$) , $E_{diff}$ is the diffuse POA irradiance and $SF$ is the soiling factor.  Models for $IAM_B$ are found here.

Air mass model for M

A polynomial may be fit to concurrent measurements of effective irradiance $E_e$ and absolute air mass $AM_a$ to model $M$. The polynomial model has the advantage of simplicity: air mass $AM_a$ can be modeled from ephemeris. However, care should be taken when applying this model outside the range of data used to fit the model.

In the SAPM, a 4th degree polynomial $f_1(AOI)$ is fit to data and the coefficients are normalized so that $f_1(AM_a&space;=&space;1.5)&space;=&space;1$:

$f_1&space;(AM_a)&space;=&space;\alpha_0&space;+&space;\alpha_1&space;\times&space;AM_a&space;+&space;\alpha_2&space;\times&space;AM_a^2&space;+&space;\alpha_3&space;\times&space;AM_a^3&space;+&space;\alpha_4&space;\times&space;AM_a^4$

This approach is adopted in the De soto et al. performance model , and is illustrated here for a c-Si module.

Model for M using air mass and precipitable water

An alternative model is presented by M. Lee and A. Panchula (2016), where $M$ is modeled using air mass and estimated precipitable water:

$M&space;=&space;b_0&space;+&space;b_1&space;\times&space;AM_a&space;+&space;b_2&space;\times&space;p_{wat}&space;+&space;b_3&space;\times&space;\sqrt{AM_a}&space;+&space;b_4&space;\times&space;\sqrt{p_{wat}}&space;+&space;b_5&space;\times&space;\frac{AM_a}{\sqrt{p_{wat}}}$

where $p_{wat}$ is precipitable water (cm) which can be estimated from ambient temperature and relative humidity using an appropriate model (e.g., pvl_calcPwat). Coefficients for this model are found in PVLib function pvl_FSspeccorr.m.