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Abstract Internal tides (ITs) play a critical role in ocean mixing, and have strong signatures in ocean observations. Here, global IT sea surface height (SSH) in nadir altimetry is compared with an ocean forecast model that assimilates de‐tided SSH from nadir altimetry. The forecast model removes IT SSH variance from nadir altimetry at skill levels comparable to those achieved with empirical analysis of nadir altimetry. Accurate removal of IT SSH is needed to fully reveal lower‐frequency mesoscale eddies and currents in altimeter data. Analysis windows of order 30–120 days, made possible by the frequent (hourly) outputs of the forecast model, remove more IT SSH variance than longer windows. Forecast models offer a promising new approach for global internal tide mapping and altimetry correction. Because they provide information on the full water column, forecast models can also help to improve understanding of the underlying dynamics of ITs.