Errors in dynamical fields inferred from oceanographic cruise data: Part I. The impact of observation errors and the sampling distribution

Diagnostic studies of ocean dynamics based on the analysis of oceanographic cruise data are usually quite sensitive to observation errors, to the station distribution and to the synopticity of the sampling. Here we present an error analysis of the first two sources. The third one is evaluated in Part II of this work (J. Mar. Sys. (2005), this issue). For observed variables and those linearly related to them, we use the Optimal Statistical Interpolation (OI) formulation. For variables which are not linearly related to observed variables (e.g., the vertical velocity), we carry out numerical experiments in a consistent way with OI statistics. Best results are obtained when some kind of scale selection or spatial filtering is applied in order to suppress small scales that cannot be properly resolved by the station distribution.The formulation is first applied to a high resolution (SeaSoar) sampling aimed to the recovery of mesoscale features in a region of large spatial variability (noise-to-signal fraction of the order of 0.002). Fractional errors (rms error divided by the standard deviation of the field) are estimated in about 2% for dynamic height and between 4% and 20% for geostrophic vorticity and vertical velocity. For observed variables, observation errors and sampling limitations are shown to contribute in similar amounts to total errors. For derived variables, sampling errors are by far the dominant contribution. For less dense samplings (e.g., equally spaced CTD stations), fractional errors are about 6% for dynamic height and between 15% and 30% for geostrophic vorticity and vertical velocity. For this sampling strategy, errors of all variables are mostly associated with sampling limitations.