A mathematical model with a physical basis is introduced to describe the first return strokes in lightning flashes. It needs four variable input parameters and, once they are specified, the model describes how the current, speed and the electromagnetic fields of the first return strokes vary in space and time. The four input parameters can also be extracted from the channel base current if it is available. The model predicted electromagnetic fields do agree well with the features of the measured first return stroke fields. Model simulations show that the peak radiation field and the peak radiation field time derivative vary almost linearly with the corresponding current parameters. Equations which can be used to extract current parameters from the fields are also given.
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