Advancing ocean science has a significant impact to the development of the world, from operating a safe navigation for vessels to maintaining a healthy and diverse ocean ecosystem. Various ocean software systems have been extensively adopted for different purposes, for instance, predicting hourly sea level elevation across shorelines, simulating large-scale ocean circulations, as well as integrating into Earth system models for weather forecasts and climate projections. Regardless of their significance, guaranteeing the trustworthiness of ocean software and modelling systems is a long-standing challenge. The testing of ocean software suffers a lot from the so-called oracle problem, which refers to the absence of test oracles mainly due to the nonlinear interactions of multiple physical variables and the high complexity in computation. In the ocean, observed tidal signals are distorted by non-deterministic physical variables, hindering us from knowing the "true" astronomical tidal constituents existing in the timeseries. In this paper, we present how to test tidal analysis and prediction (TAP) software based on metamorphic testing (MT), a simple yet effective testing approach to the oracle problem. In particular, we construct metamorphic relations from the periodic property of astronomical tide, and then use them to successfully detect a real-life defect in an open-source TAP software. We also conduct a series of experiments to further demonstrate the applicability and effectiveness of MT in the testing of TAP software. Our study not only justifies the potential of MT in testing more complex ocean software and modelling systems, but also can be expanded to assess and improve the quality of a broader range of scientific simulation software systems.