Intermediate models of the coupled tropical atmosphere–ocean system have been used to illuminate the physics of interannual climate phenomenon such as El Niño Southern Oscillation (ENSO) in the tropical Pacific and to explore how the tropics might respond to a forcing such as changing insolation (Milankovitch) or atmospheric carbon dioxide. Importantly, most of the intermediate models are constructed as anomaly models: models that evolve on a prescribed climatological mean state, which is typically prescribed and done so on a rather ad hoc basis. Here we show how the observed climatological mean state fields [ocean currents and upwelling, sea surface temperature (SST) and atmospheric surface winds] can be incorporated into a linearized intermediate model of the tropical coupled atmosphere–ocean system: called Linear Ocean–Atmosphere Model (LOAM), it is a linearized version of the Zebiak and Cane model. With realistic, seasonally varying mean state fields, we find that the essential physics of the ENSO mode is very similar to that in the original model and to that in the observations and that the observed mean fields support an ENSO mode that is stable to perturbations. Thus, our results provide further evidence that ENSO is generated and maintained by stochastic (uncoupled) perturbations. The method that we have outlined can be used to assimilate any set of ocean and atmosphere climatological data into the linearized atmosphere–ocean model. In a companion paper, we apply this same method to incorporate mean field output from two global climate models into the linearised model. We use the latter to diagnose the physics of the leading coupled mode (ENSO) that is supported by the climate models, and to illuminate why the structure and variance in the ENSO mode changes in the models when they are forced by early Holocene and Last Glacial Maximum boundary conditions.