Although it has been more than two decades since the discovery of the modulation lanes in the dynamic spectra of Jupiter's decametric radiation by Riihimaa, a realistic model accounting for them has not yet been published. We present such a model for modulation lanes observed during Io-A and Io-B storms. A grid-like interference screen composed of field-aligned columns of enhanced plasma density downstream from Io is assumed. The screen is located at the inner edge of the Io plasma torus, the

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... lumns crossing Io's orbit. The column spacing is on the order of 100 km. Radiation from the source near the northern foot of the Io-activated flux tube passes through the screen on its way to Earth. Interference between rays that are scattered on passing through the columns with the relatively unscattered rays passing between columns produces a multilobed radiation intensity pattern that rotates with slightly less than Jupiter's angular velocity. Emission at different frequencies is produced at different altitudes above the foot of the activated flux tube, and because of its slope, at slightly different longitudes. Within a received bandwidth at Earth, some frequency components will have arrived from intensity lobe maxima and others from lobe minima. The frequency-time plot is thus in the form of characteristically sloping modulation lanes. Our model provides remarkably close fits to the best available modulation lane observations, and also yields values of both the lead angle of the radio-emitting flux tube ahead of Io and the cone half-angle of the assumed hollow-cone emission beam.