Abstract. Atmospheric turbidity is an important parameter for assessing the air pollution in local areas, as well as being the main parameter controlling the attenuation of solar radiation reaching the Earth's surface under cloudless sky conditions. Among the different turbidity indices, the Ångström turbidity coefficient β is frequently used. In this work, we analyse the performance of three methods based on broad-band solar irradiance measurements in the estimation of β. The evaluation of the performance of the models was undertaken by graphical and statistical (root mean square errors and mean bias errors) means. The data sets used in this study comprise measurements of broad-band solar irradiance obtained at eight radiometric stations and aerosol optical thickness measurements obtained at one co-located radiometric station. Since all three methods require estimates of precipitable water content, three common methods for calculating atmospheric precipitable water content from surface air temperature and relative humidity are evaluated. Results show that these methods exhibit significant differences for low values of precipitable water. The effect of these differences in precipitable water estimates on turbidity algorithms is discussed. Differences in hourly turbidity estimates are later examined. The effects of random errors in pyranometer measurements and cloud interferences on the performance of the models are also presented. Examination of the annual cycle of monthly mean values of β for each location has shown that all three turbidity algorithms are suitable for analysing long-term trends and seasonal patterns.