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• A model was proposed to evaluate irradiance in irregularly built urban environments. • The proposed model interprets the circumsolar sky radiance by the simple data. • Accuracies of various models were evaluated by data under irregular obstructions. • The proposed model outperformed the classical models in urban environments for HK. The diffuse radiation on building envelopes can be essential to the thermal environment and the energy study of buildings. Because a part of the skydome can be obstructed irregularly in city environments, the diffuse radiance distribution over the skydome should be determined to evaluate the radiation accurately. In this study, this distribution is described by several representative sky directions to specifying the radiance variation features over the skydome, especially the attenuation around the sun. The irradiance of each sky element (normalized by the horizontal diffuse) is correlated to the routine global radiation and the solar altitude as an all-sky model for simple engineering uses. According to two sets of one-month field measurements (in different sites) of the vertical irradiance under irregular obstructions in the hot and humid Hong Kong, the coefficient of determination (R 2) is 0.041 and 0.142 higher than the classical single-direction anisotropic diffuse model that is adopted by many simulation tools, and the R 2 difference can be up to 0.38 for partly cloudy days. When compared to the distribution models, the R 2 outperformance of the proposed model can still be 0.057. The proposed approach is thus effective to the solar radiation studies in the city environments. [ABSTRACT FROM AUTHOR]