## Abstract

A physically modeled method is presented to obtain accurate turbidity determinations from broadband direct irradiance measurements. The method uses parameterizations of various extinction processes affecting the transfer of shortwave radiation in a cloudless atmosphere. The integration over the shortwave solar spectrum is performed with a more realistic weighting function than is conventionally used. The calculation and properties of the broadband aerosol optical depth are discussed in detail as a function of the aerosol optical characteristics. The method is general, as it can predict any one of the four turbidity coefficients currently used in climatological studies as defined by Ångström, Linke, Unsworth–Monteith, and Schüepp. Formal interrelationships are proposed so that climatological data based on different coefficients can be consistently intercompared without recourse to empirical formulas. The new parameterizations are more detailed than those of the literature, particularly regarding the optical depth of the clean dry atmosphere that now depends explicitly on the stratospheric ozone and nitrogen dioxide amounts. This inevitably induces changes in the prediction of the broadband turbidity coefficients (Linke and Unsworth–Monteith), particularly at small zenith angles when compared to older calculations. These coefficients are also shown to depend on zenith angle and precipitable water, causing parasitic variations of turbidity during a day or the year even if the aerosol characteristics do not vary. The masking effect of tropospheric nitrogen dioxide is presented, as well as a method to correct the predicted turbidity for circumsolar radiation. A detailed error analysis is discussed, showing that the instrumental error and the estimation error on precipitable water are the main limiting factors of the method. Although smaller potential error is obtained at larger zenith angles, accurate estimates of precipitable water are necessary for valid turbidity predictions when applied to clean dry atmospheres. A limited test of the method is presented, using spectral radiative data from five different sites as the reference. The method performs well, provided that accurate precipitable water data can be obtained. In contrast, the older Louche’s method is shown to produce unrealistic negative values under clean dry conditions. Monthly average turbidity over 3–4 years was also obtained from hourly irradiance at two sites with widely different aerosol regimes. Compared to the present results, Louche’s method is found to overpredict the Unsworth–Monteith coefficient at both sites, while simultaneously underpredicting the Ångström coefficient at the clearest site.

*Corresponding author address:* Dr. Christian Gueymard, 2959 Ragis Rd., Edgewater, FL 32132.