In the paper (10.1016/j.renene.2022.11.056) Quality control procedure for 1-minute pyranometric measurements of global and shadowband-based diffuse solar irradiance by F. Nollas, G. Salazar, & C. Gueymard, a new minimum value for GHI is introduced. The authors write:

Filter 2 is used here to establish a low GHI limit corresponding to heavily overcast or thunderstorm conditions, which lead to very low, albeit valid, values. To establish this limit, a dataset from 14 high-quality BSRN stations, mostly in equatorial or tropical regions, has been selected and analyzed because cloudiness can there be substantial over a large range of SZA. The following envelope for the minimum acceptable GHI is found, and can be considered “universal”:

(2) GHImin = (6.5331–0.065502•SZA+1.8312E-4•SZA^2) / (1 + 0.01113•SZA).

Note, however, that because the corresponding GHI values are very low (e.g., 1.1 W/m2 for SZA = 90°), it is imperative that the GHI observations are first corrected for the inherent thermal offset of thermopile pyranometers, as discussed in Section 2.

EDIT: The paper also defines a minimum limit for the diffuse irradiance (DIF/DHI):

Filter 7 is a test whose purpose is to determine physically-possible minimum values for DIF. Under cloudless conditions, the minimum possible DIF corresponds to the ideal situation of an aerosol-free atmosphere, when the only scattering process is caused by molecules. This is referred to as the “Rayleigh limit” RL, for which Long and Shi [15] provided a simple function, used here:
(3)RL = μ0 (209.3 + 0.046725 P −708.3 μ0 + 1128.7 μ02 –911.2 μ03 +287.85 μ04)
where μ0 = cos(SZA) and P is surface pressure in mbar. In the case of thick overcast or thunderstorm situations, however, it is common observation that the sky becomes dark, indicating that DIF can be noticeably lower than RL. No quantitative evaluation of the minimum possible DIF under such conditions could be found in the literature. A simple fix is readily found by considering that under such sky conditions, DNI≈0 and therefore DIF ≈ GHI. Hence the minimum acceptable DIF can be taken as GHImin from Eq. (2). That limit is much lower than RL for essentially any SZA. This confirms that RL is not appropriate under all-sky conditions, contrarily to what was assumed by Long and Shi [15], among others. In what follows, the Diffuse limit, DL, is considered to be RL if the estimated DNI is > 10 W/m2, or GHImin otherwise.

I think it would be great to add the proposed empirical equation and the Rayleigh limit to the growing number of QA irradiance algorithms.