The noise waveform of atmospheric radio noise below 100 MHz is typically impulsive in nature. The impulses are caused by atmospheric events, mainly lightning strokes, that create electromagnetic emissions known as sferics. Sferic impulses in the noise waveform are seen to cluster in groups, indicating an underlying clustering process related to the physical characteristics of the lightning mechanism. The objective of this work is the statistical modeling of the clustering of noise impulses in atmospheric radio noise in the range 10 Hz to 60 kHz (denoted low-frequency noise). Based on hundreds of hours of impulse interarrival time measurements made by the Stanford Radio Noise Survey System on such noise, a new Clustering Poisson atmospheric noise model is developed to describe the clustering process. This new statistical model is based on several previously known statistical-physical models of atmospheric radio noise, but in addition to these models it takes into account the clustering of sferic impulses. It is shown that the clustering model accurately characterizes the impulse interarrival time distributions found in low-frequency radio noise data.