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We set up a tunneling approach to the analogue Hawking effect in the case ofmodels of analogue gravity which are affected by dispersive effects. Aneffective Schroedinger-like equation for the basic scattering phenomenonIN->P+N*, where IN is the incident mode, P is the positive norm reflected mode,and N* is the negative norm one, signalling particle creation, is derived,aimed to an approximate description of the phenomenon. Horizons and barrierpenetration play manifestly a key-role in giving rise to pair-creation. Thenon-dispersive limit is also correctly recovered. Drawbacks of the model arealso pointed out and a possible solution ad hoc is suggested.

Tunneling approach and thermality in dispersive models of analogue gravity