COAMPS Wind Stress at Ocean Surface ("CO"
in tables)
The COAMPS control forecast, issued by the Naval Research Laboratory,
Monterey is given for 0h, 24h, 48h and 72h.
A phase-shift method based on Autoregressive functions is used to perturb
the COAMPS wind stress fields in space and time. The phase shift functions
"lx" and "ly" are shown in the top panels for each time, for each of the
8 ensemble members (there is a similar phase shift "tau" in time, not shown)
The wind stress fields u_s and v_s are perturbed in the following manner:
u_s (x,y,t) --> u_s (x+lx,y+ly,t+tau)
v_s (x,y,t) --> v_s (x+lx,y+ly,t+tau)
Using this technique, it is expected that realistic atmospheric features
are preserved, and that ensemble variance is largest in areas where the
gradient is highest. The ensemble generation technique still need to be
refined considerably, but the first attempt is encouraging.
ROMS Ocean Model
The ROMS model (labeled
"ctrl") was run each day at JPL, with all available and quality-checked
AOSN-II data being assimilated using a 3d-Var scheme. The model consists
of 3 nested grids, with resolution 15, 5 and 1.67 km. The innermost domain
covers Monterey Bay.
Each of the 8 ROMS ensemble members was run to 2-3 days on the JPL
Supercomputer, with the corresponding perturbed COAMPS atmospheric
forcing, and initial condition derived from breeding. The forecast ocean
currents, temperature and salinity fields are shown for depths of 0m, 10m,
30m, 50m and 200m in the Monterey Bay region.
ETKF Summary Maps
Based on the ROMS ensembles, the ETKF adaptive sampling (or "targeting")
strategy was tested near the end of AOSN-II. Some maps are linked from
the lower frame. The "summary map" gives the predicted reduction in forecast
error variance as a function of the location in which a targeted observation
is taken. Hence, the best location to take an observation is where the
value is highest (red shading). Unlike our atmospheric targeting to date,
these summary maps are 3-dimensional fields. Only horizontal and vertical
cross-sections are shown here. In principle, one can draw a hypothetical
glider track through the maxima of the ETKF result. Alternatively, the
ETKF calculations can be computed for any combination of prescribed observational
paths, over a series of times. This is the direction in which we'd like
to head, but first the ETKF needs to be evaluated before taking this ambitious
step. Currently, I don't have tremendous faith in the ETKF results since
the number of ensemble members (8 at most) is far too small, and the ensemble
perturbation technique above needs more development. Improved computing
power over the next few years will alleviate the small-ensemble problem
considerably.
For more details on the adaptive sampling using the ETKF, click
here.
The Near Future
1. The Error Subspace Statistical Estimation approach of Lermusiaux
and Robinson (1999) has some theoretical similarities with the ETKF. A
theoretical inter-comparison between the two strategies in data assimilation,
ensemble generation, and adaptive sampling will be performed in the very
near future. The relative strengths of the two techniques can be exploited
to produce an improved ensemble-based strategy for adaptive sampling.
2. The breeding technique for ensemble initialization will be replaced
by the ETKF technique of Wang and Bishop (2003), once the observation operators
and error variance estimates for the myriad of observation types are available.
3. One of the primary mechanisms for producing an upwelling event is
strong sustained winds, that last for several days. Typically, these winds
prevail from the north-west during the California summer. The sensitivity
of the ROMS ocean model to changes in atmospheric wind fields needs investigation.
The development of a fully coupled atmosphere-ocean model requires considerable
research and is probably some time away, but the simple sensitivity studies
using prescribed forcings and fluxes may still shed valuable light on how
the atmospheric fields are affecting the oceanic state.
4. The ETKF targeting strategy needs to be evaluated. First, the ability
of the ETKF to predict the variance of "signals" will be assessed. A signal
represents the difference in two ocean state estimates; one of which has
assimilated the targeted observations, whereas the other has ignored the
targeted observations. The techniques of Majumdar et al. (2001) and Bishop
et al. (2003) will be used to test whether the ETKF is making reliable
predictions. As mentioned above, there are several different applications
of the ETKF that can be developed and evaluated. However, large, reliable
ensembles are necessary (although by no means sufficient) for the ETKF
to make trustworthy predictions of the effects of targeted observations.
Longer-Term Goal
A reliable adaptive sampling strategy can in principle be used to deploy
autonomous vehicles along any path, at any time, to improve forecast skill.
The development of such a strategy that is consistent with a state-of-the-art
data assimilation scheme that assimilates observations nearly continuously
in time is the ultimate goal. The intelligent deployment of autonomous
vehicles in the ocean (and atmosphere) is likely to lead to improved forecasts
and understanding of key physical processes of interest.
Links