Predicting offshore temperatures in Monterey Bay based on coastal observations using linear forecast models

The linear systems approach is used to forecast offshore near-surface and subsurface temperatures in Monterey Bay and further offshore based on coastal sea surface temperatures (SSTs) at Pacific Grove. SST from Pacific Grove provided the input to the system and the forecast parameters or outputs were temperature at 1 m and 100 m at the M1 buoy located 20 km from Pacific Grove near the center of Monterey Bay, and temperature at 1 m at the M2 buoy located 55 km from Pacific Grove. To forecast temperatures at the M1 and M2 buoys, Box-Jenkins, State-Space, ARX, and ARMAX models were employed. Model formulation, implementation, forecasting procedures, and methods of evaluation are presented. Seven and 30-day forecasts were routinely made for the daily observations although other forecast horizons were employed. For all models and variables, RMS differences between the forecasts and the observations increased rapidly between 1 and 15 days. Beyond about 30 days, RMS differences tended to remain almost constant with increasing forecast horizon. Overall, model forecasts were best for temperature at 100 m at the M1 buoy, due to the fact that temperature is well conserved at depth. Differences in performance between the models were small but the ARMAX model often produced forecasts that were slightly better than the rest, a result that we attribute to a more complete specification of the noise. Although the Box-Jenkins and State-Space models have the potential to produce better forecasts, because more terms must be specified to implement them, the opportunity to produce less-than-optimal results is also greater. Finally, because of seasonal changes in the circulation of Monterey Bay, it is possible that causality was violated, upon occasion, placing certain constraints on the results. Models based on the linear systems approach, where they can be implemented, could serve as a useful adjunct to hydrodynamic ocean circulation models by providing additional information for model initialization, evaluation, and data assimilation. Using the same approach, operational forecasts of the coastal circulation could be made by including forecast winds and the predicted tides as inputs, and CODAR-observed surface currents as the output. In a less glamorous but still useful role, they could be used to fill significant gaps in offshore records where data continuity and quality are important.