Box inverse models, altimetry and the geoid: Problems with the omission error

When one combines satellite altimetry and a geoid model to improve estimates of the ocean general circulation from hydrographic data with a box inverse model, there arises a problem of different resolution and representation of the data types involved. Here we show how this problem can lead to an artificial leakage of the error estimates of short‐scale (high degree) spherical harmonic functions into long wavelength (low wave number) Fourier functions. A similar paradox effect can be seen in an idealized box inverse model constrained by additional sea‐surface topography data of low, medium, and high resolution: When more information is added in the form of additional smaller scales, the error of a transport estimate eventually increases. Consequently, including the large geoid omission errors associated with smaller scales in a box inverse model of the Southern Ocean increases the posterior errors of transport estimates over those of a model that does not include the geoid omission error. We do not claim that including or excluding the geoid omission error is correct. Instead, we juxtapose two different ways of estimating the geoid errors to demonstrate the effect that the omission error might have on the long, supposedly well‐known, scales. How (or if) to properly account for the geoid omission error must be the topic of further research. A proper treatment of the geoid model errors is demanded when one evaluates the errors of absolute sea‐surface topography data.