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This paper describes a computerized physical model that predicts both horizontally and vertically polarized noise in the ELF to LF band (10 Hz to 60 kHz). Since naturally occurring radio noise in this band is produced by lightning and propagates to the receiver via the Earth-ionosphere waveguide, the model starts with average lightning flash density data from which it calculates radiated power for horizontal and vertical noise. Adjustments are made to the radiated power to account for seasonal and latitudinal differences in the lightning processes. The noise power is then integrated over fairly large geographic areas to formulate horizontal and vertical equivalent noise transmitters. The power radiated from each of these transmitters is propagated to the receiver location using standard anisotropic long wave propagation algorithms and well-known models of the Earth-ionosphere waveguide. From the received power the model predicts RMS noise, standard deviation, voltage deviation VD, and the amplitude probability distribution of the noise for both polarizations. Since the model is based on theory, it can also predict these parameters under disturbed ionospheric conditions. The model's generally good agreement with RMS noise data is demonstrated.