ESSE Uncertainty Forecasts

ESSE Uncertainty Forecasts, Data Assimilation and Adaptive Sampling

Uncertainties were initialized for August 21, GMT00, using the ESSE initialization approach. The background ocean field on August 21, GMT00 is based on a HOPS forecast simulation which assimilated all calibrated data up to GMT06 on August 20. Using the error subspace estimate for August 21 (the prior uncertainties), data collected during August 21 are assimilated using ESSE. During this process, T and S data correct the T and S fields, but also the velocities since the ESSE error covariances are multivariate. Uncertainties are reduced and the output is an corrected ocean field estimate (an analysis) and an updated error estimate (the posterior error subspace). Starting from these posterior uncertainties, a ESSE ensemble error forecast is computed for August 23 GMT00. Adaptive sampling sampling patterns are then recommended based on these predicted errors and dynamical evolution of oceanic features. All of these are illustrated and briefly discussed below.

ESSE uncertainty initialization procedure and results

To initialize uncertainties, the differences between the background simulation and the T and S data collected prior to August 20 are first utilized to compute multivariate T and S vertical empirical functions (EOFs). To obtain three-dimensional EOFs for T and S, the vertical EOFs are combined with horizontal eigenmodes. These modes are based on a "Mexican hat", (second derivative of a Gaussian) covariance function, whose parameters were set to 5km decorrelation (decay) scale (km) and 12.5km zero crossing. To compute velocity uncertainties, the background field on August 20, GMT00 is perturbed with each three-dimensional EOFs for T and S. The dynamical ocean model equations, forced by the COAMPS atmospheric fluxes, are then numerical integrated for one-day. The final result is an ensemble of adjusted T,S,u,v anomalies for August 21, GMT00. The singular value decomposition of normalized T, S, u and v anomalies is then computed to lead a complete error subspace (dominant error singular vectors/EOFS). Presently, 500 three-dimensional, multivariate singular vectors are retained to determine this prior (before data assimilation) error subspace on August 21.

These prior uncertainties for August 21 are illustrated in the Table below.

An interesting feature is these error standard deviation estimates are the uncertainties that corresponds to the filament out of the Monterey Bay Peninsula (see surface U and T errors in both the full and zoom domain for example. See also the ocean fields and satellite SST as shown in a 22 August presentation. This filament forms during the upwelling stage, based on cold and salty waters mainly from Pt Sur, but also with waters advected across the mouth of the Bay from the Pt AN upwelling center. During the relaxation period, winds subside and then reverse to weak northward forcings. The internal ocean dynamics then mainly drives the motions of the filament, thinning it and extending it further west, with the weak winds favoring some north-northeastward advection in the Ekman Layer. All of these processes lead to uncertainties which are locally largest where fronts are the strongest (e.g. a change of frontal position or strength is a high relative uncertainty). This is why the most visible errors for this filament are in the upper-layer T, in the bottom-of-Ekman-layer S, and along-filament velocities, the U-velocity. Of course, several other features and fronts are clearly identified by the ESSE error fields, e.g. overlay the T and S error fields onto the corresponding ocean fields.

ESSE assimilation procedure and results

During August 21, the ocean measurements included T/S data from the WHOI gliders, T/S data from the SIO gliders, NPS aircraft SST and some Martin CTD data?

All of these data are assimilated using ESSE. The resulting posterior uncertainties for August 21 are illustrated below.

It is first interesting to look at the T/S posterior error fields and to compare them to the prior T/S error fields, using the location of the data (see the 22 August presentation). The error reduction in ESSE is non-isotropic, non-homogeneous, following the ocean dynamics and features. Secondly, the velocity errors are also reduced. An important point to stress is that the aircraft SST is extended naturally at depths and across the T, S, u and v fields, in accord with the multivariate ESSE error covariances and the underlying ocean primitive equation dynamical model and its local error estimates. There is in principle no need for specific extension schemes.

The ESSE forecast for August 24, 0000 GMT was initialized from the above error nowcast for August 21, 0000 GMT (error after ESSE data assimilation). The dominant 250 eigenvectors of the posterior error covariance estimate are utilized to perturb the ocean field analysis. A white noise of an amplitude proportional to the estimated absolute and relative errors in the observations is added to this random combination, in part to represent the errors truncated by the error subspace. An ensemble of 2-day forecast simulations, each forced by forecast COAMPS atmospheric fluxes, was then carried out. Presently, 264 of such forecast simulations are utilized to forecast the uncertainties on August 24.

ESSE forecast procedure and results

For Monterey Bay, an interesting feature in these standard deviations is the high error line in the surface T error field. It is located just west and north of the Monterey Bay Peninsula, and oriented towards the northeast. The U error field also shows higher errors there.

These error features are related to the return of upwelling favorable conditions on top of an almost relax ocean state offshore of Monterey Bay. Around the Peninsula, the relax state correspond to an inflow from the south into the Bay. As the forecast winds reverse back to a upwelling favorable condition, especially near Pt AN, the southward ocean flow across the mouth of the Bay strengthens, advecting the relatively warm waters from the relaxed state at Pt AN. These two currents converge just north of the Peninsula and lead to an inflowing jet of warmer waters into the Bay (clearly visible in the ocean forecast). The position of this jet and its strength are uncertain, hence the high error lines.

For the full modeling domain, interesting areas continue to correspond to the meanders of the coastal current and to its eddies. It is actually very interesting to superpose the T and S errors maps onto the corresponding ocean fields (again see the 22 August presentation).

Adaptive sampling recommendations

The WHOI adaptive gliders should focus on the inflow of warmer waters into the Bay and to the corresponding frontal jet just north of the Monterey Bay Peninsula.