The diurnal cycle is a fundamental time scale in the climate system, at which the upper ocean and atmosphere are routinely observed to vary. Current climate models, however, are not configured to resolve the diurnal cycle in the upper ocean or the interaction of the ocean and atmosphere on these time scales. This study examines the diurnal cycle of the tropical upper ocean and its climate impacts. In the present paper, the first of two, a high vertical resolution ocean general circulation model (OGCM), with modified physics, is developed which is able to resolve the diurnal cycle of sea surface temperature (SST) and current variability in the upper ocean. It is then validated against a satellite derived parameterization of diurnal SST variability and in-situ current observations. The model is then used to assess rectification of the intraseasonal SST response to the Madden–Julian oscillation (MJO) by the diurnal cycle of SST. Across the equatorial Indo-Pacific it is found that the diurnal cycle increases the intraseasonal SST response to the MJO by around 20%. In the Pacific, the diurnal cycle also modifies the exchange of momentum between equatorially divergent Ekman currents and the meridionally convergent geostrophic currents beneath, resulting in a 10% increase in the strength of the Ekman cells and equatorial upwelling. How the thermodynamic and dynamical impacts of the diurnal cycle effect the mean state, and variability, of the climate system cannot be fully investigated in the constrained design of ocean-only experiments presented here. The second part of this study, published separately, addresses the climate impacts of the diurnal cycle in the coupled system by coupling the OGCM developed here to an atmosphere general circulation model.