Error Budget of Inverse Box Models: The North Atlantic

Linear inverse box models based on hydrographic data are widely used to estimate the ocean circulation and associated transports of heat and of other important quantities. The inverse method permits calculation of a circulation that is consistent with basic conservation laws such as those for mass or salt along with uncertainties. Both uncertainties and solution depend upon assumptions about noise and the limitations of linear models. Internal waves introduce noise into the measurements, while ocean variability sets bounds on the linear model skills when time average circulation is sought. Observations of internal wave spectra and sensitivity experiments on hydrographic data suggest estimates for measurement errors in transport calculations of ±3 Sv (1 Sv ≐ 106 m3 s−1 ≃ 109 kg s−1) at midlatitudes, with dependence on latitude. The output of a realistic numerical ocean model is used to quantify the impact of ocean variability on one-time hydrographic sections. The implied error is of order ±8 Sv in net mass balance and ±100 kmol s−1 in net silica balance. (The estimates are a priori errors.) Net mass balance has often been assumed more accurate with errors in individual layers compensating. While this may be true instantaneously, it is shown here that such an assumption leads to incorrect estimation of the time mean transports and diapycnal transfers.