better than the time independent maps. Since the number of degrees of freedom in the model (1160) is comparable to the number of data (1200), it is possible that a good fit might be obtained even with incorrect dynamics. One way to rule this out is to use longer durations for the fit, which would increase the number of data, and so provide a better test of the dynamics, but the longer durations encounter more nonlinearity and require more iterations.
As a simple check of the quality of the dynamical model, and the effects of the initialization proceedure, the initializations estimated by the iterative fitting were forecast forward to predict data not used in the fit, to provide an independent cross-validation of the model dynamics.
Figure 5a shows a comparison of the rms error (in milliseconds) for three different predictions of about 450 AMODE travel times, and rms error in degrees (Fig. 5b) for 18 moored thermistors (3 on each mooring). The larger the values, the poorer the predictions. The solid line gives the rms misfit for the‘climatological’prediction, guessing zero for the ocean perturbation state at all times. The long-dashed line shows the error results from a QG model forecast from an optimized initialization using 12 days of travel time data (the moored thermistor data were not used). The short-dashed line is a persistence forecast from the same initialization. Using 12 days of moored travel time data to initialize the model, the travel time variability caused by eddies can be predicted for at least 60 days before the model prediction is worse than a climatological guess of zero (persistence alone becomes worse than climatology after about 25 days), consistent with prior estimates of an“eddy turnover time”. Even at the start, the model predictions have rms errors of about 25% of the total data rms, due to ocean variability not included in the QG model, such as surface processes and water mass interleaving.
