AOSN-II August 2003

ESSE Uncertainty Forecasts

ESSE uncertainty initialization and forecast procedure

The forecast issued today (on Aug 27th) is a 1-day extension of the ESSE forecast issued yesterday (on Aug 26th). It is a 2-day error forecast for Aug 28, 0000GMT.

The ESSE forecast for August 28, 0000 GMT was initialized from an error nowcast for August 26, 0000 GMT. The background ocean field on August 26, 0000 GMT is a HOPS forecast simulation which assimilates all available and calibrated data up to August 25, 10GMT (several R/V Pt Sur and gliders profiles were still being processed for Aug22-25 and could not be utilized).

The dominant 275 eigenvectors of the posterior error covariance estimate for August 26, 0000 GMT were utilized to perturb the ocean fields on August 26, 0000 GMT. 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 1-day forecast simulations, each forced by forecast COAMPS atmospheric fluxes issued for Aug 25, was then carried out.

A total of 500 ensemble 2-day forecasts were carried out during the night of Aug 25 (EDT). The corresponding error standard deviation forecast for August 28, 000GMT are shown in the table below.

Error Subspace Statistical Estimation (ESSE) Results
Full Domain
Temperature Salinity U velocity component V velocity component
Monterey Bay Zoom
Temperature Salinity U velocity component V velocity component
Barotropic Streamfunction (including Monterey Bay)

U and V velocities are the two components of the internal velocity (i.e. total velocity - vertically averaged velocity) along the domain coordinate system (zonal is 29.4 degrees northeast from a latitude, meridional is 29.4 degrees northwest from a longitude)

The ESSE uncertainty forecasts are a function of: the posterior (initial condition) uncertainties, the dynamical evolution of these initial uncertainties, the impacts of model error estimates which are compounded during this evolution and the COAMPS forcings. One of this process, the dynamical evolution of uncertainties, is strongly dependent on the local properties of the kinetic energy, potential energy and enstrophy (square of vorticity) fields.

The first 2 dominant singular vectors of the normalized ensemble of 2-day forecasts are shown in the table below. They explain 18.5 and 7.5 percent of the total normalized variance explained by all 500 members, respectively. They are described in the Analyses section below.

Dominant singular vectors of the ESSE ensemble (ESSE modes 1-2)
Singular vector 1
Temperature Salinity U velocity component V velocity component
Singular vector 2
Temperature Salinity U velocity component V velocity component
Barotropic Streamfunction (including Monterey Bay)

The forecast of the covariance of the surface temperature at 36.75,-122.08 with the whole state vector (the 3D fields of T, S, U and V) is illustrated in the table below. Together, these covariances fields correspond to a row of the covariance matrix. They are described in the Analyses section below.

ESSE covariance fields of surface T at 36.75,-122.08 with all other state variables
Full Domain
Temperature Salinity U velocity component V velocity component
Monterey Bay Zoom
Temperature Salinity U velocity component V velocity component
Barotropic Streamfunction (including Monterey Bay)

Analyses of ESSE Results

Dynamics and uncertainties. In Monterey Bay, the the re-establishment of a cyclonic circulation is forecast, mainly in response to upwelling favorable atmospheric forcings. The upwelling at Pt Ano Nuevo is forecast to be advected across the mouth of the Bay, leading to high shear and high mixing, hence a source of uncertainty.

For the Monterey Bay zoom, the most interesting uncertainty features relate to the structure of the coastal current across the mouth of Monterey Bay. This coastal current mixes and advects the warm and fresh meander/eddy southward. This leads to large expected standard deviations in T and S, in surface near the center of the mouth of the Bay and at depth (e.g. 30m) just offshore of the Monterey Bay Peninsula (where the coastal current meanders at these depths). The corresponding velocity uncertainties are largest along the whole mouth of the Bay (edge of the Monterey Bay zoom domain in the Table above). The barotropic stream function errors remain the largest west of the Peninsula above the deepest/steepest bathymetry.

In the center of Monterey Bay, some uncertainties are also present, in relation with the strength and position of the re-establishing cyclonic circulation, and on the corresponding mesoscale eddies.

For the full domain, uncertainties remain large along the meanders of the coastal current. The upper-layer eddy field (10-40m depth) which feeds on the available energy in the surface thermocline also has a strong influence on the error field (e.g. see eddy hot-spots at 30m). Corresponding properties can be seen in the velocity and transport error standard deviations. In particular, the northward barotropic transport by the California under-current (about 1.5 to 2.5Sv) has a maximum forecast uncertainty of about 0.35Sv (i.e. 10-15 percent).

ESSE modes 1 and 2. All modes are non-dimensional. The first ESSE mode (singular vector 1) can be related to two filaments of the coastal current. This can be seen by comparing the salinity component of this first mode with the salinity forecast for Aug 28. For T and S, the dominant amplitudes are within the upper 40 m (below, modal amplitudes decay). Note that the largest T amplitudes are a bit further offshore than the largest S amplitudes, in accord with the mean T and S fields/fronts, respectively. In the downstream (southward) direction, the T and S patterns show a succession of positive/negative and negative/positive lobes, respectively. This may indicate that the filaments tend to vary in opposition of phase. The U, V and Psi components also relate to the variability of the same two filaments of the coastal current. The double T and S lobes lead to quadrants in the U and V modes, reflecting the relatively geostrophic equilibrium.

The second ESSE mode mainly relates to the most northern of the two filaments and to the corresponding eddying/meandering field. Comments similar to these made for the first mode also apply to this second mode.

Sample ESSE covariances. The covariance of the surface temperature at 36.75,-122.08 with the whole state vector is given as an example (see table above). The specific location "at 36.75,-122.08" was simply chosen because it is in front of Monterey Bay, slightly offshore. It is important to note that should T data be sampled at 36.75,-122.08 in the surface, the covariance fields illustrated by the Table indicate the multivariate impact of this T data.

Focusing on the full domain, it is interesting to note that the tracer covariance fields somewhat indicate the presence of 2 scales, the mesoscale and a large-scale. At the large scale, T-T covariances are positive downstream and negative upstream. Opposite signs holds for T-S covariances. Large-scale effects are also visible in the T-Psi covariances (barotropic effects), but less so in the T-U and T-V covariances (internal effects). These properties are likely due to the large-scale influence of the California Current System.

Looking at the T-T covariances, the mesoscale correlation scales are slightly elongated in the along-slope direction at this 36.75,-122.08 location (about 15km along and 7km across). They are also slightly longer in the downstream than in the upstream direction. The T-S covariances show a double lobe pattern, centered near 36.75,-122.08 (this relates to the non-similar T and S properties in the region). Analogous remarks can be made for the T-U and T-V covariances. The covariances at depth indicate the dynamical relationships/correlations between the surface T at 36.75,-122.08 and the other variables at depth. It is clear that this surface T has a very limited impact at 200m: excepted on the barotropic velocity and a little bit on the internal velocities, the impact is in fact close to null.

Computations. For information purposes, the total elapsed time necessary to:

  • carry-out the 500 2-day forecasts of the ensemble and
  • compute 3 singular value decomposition of that ensemble as its size was increasing to check for convergence
    was: 17 hours, using 18 cpus. This shows that ESSE can be utilized in real-time

    Adaptive sampling recommendations

  • The clarification of the structure of the coastal current across the mouth of Monterey Bay and the associated region of anticyclonic vorticity should be investigated. In Monterey Bay, this is the region of highest forecast uncertainty across all state variables. A specific question that the adaptive sampling could focus on is: is it an eddy interacting with the coastal current or is it a meander of the current itself? Suggested locations for the sampling were given during the RTOC presentation.
  • The first two esse modes indicate that sampling the region around 36o 45' N and 122o 20' W would likely be very useful since it corresponds to one of the modal centers.



    Return to the Harvard AOSN-II home page