A method is proposed which, through the monitoring and modeling of the diurnal variation of α-radioactivity in the air near the ground, appears with a potential in enhancing the measurement of low radioactivity unexpected peaks over the natural background. Portable field instrumentation was used for the monitoring which further included the total γ-radiation at ground level, the relative humidity and temperature. The variation of the α-radioactivity follows a periodic form with peaks in the morning and in the afternoon. The applicability of a mathematical model to describe this variation of the α-radioactivity in terms of the meteorological variables and the γ-radiation was tested positive. This could reduce the difference between the measured and modeled periodic variation to an almost flat one, above which sudden unexpected peaks of radioactivity from possible undeclared nuclear activities could be easier identified.