A Multivariate Reduced-order Optimal Interpolation Method and its Application
291
tenns of transport streamfunction, temperature and salinity defined on depth levels.
The estimation state vector (our state vector for all practic al means) is
x = {\jf,T,S}
(22)
The EOFs we use below are therefore trivariate in these variables. What this
means is that for instance temperature measurements will influence model temperature, but also salinity and streamfunction, in an empirically coherent manner.
Once the trivariate correction has been calculated, we correct the density, apply
geostrophy on the increments (hence assuming no error on the ageostrophic part -
a very common, robust assumption), and perfonn ancillary restart tasks such as
recalculating the value of streamfunction around islands and applying convective
adjustment. A simple scheme was used to update the model error variances in Di
from one analysis to the next (adding a constant to the previous analysis error variance as in De Mey, 1994), whereas the space-time error correlations and observational error variances were kept fixed, in accordance with standard OI practice. The
guess error correlation (in EOF modal space) derived from a space-time analytical
model with isotropic and homogeneous correlation radii of 100 km and 30 days for
all the modes. The observational errors were assumed to be uncorrelated in space
and time.
We present simulations assimilating separately two kinds of observations: SeaLevel Anomaly (SLA), using fonn (20) ofthe local observation operator, and temperature profiles.
SLA data were real altimeter data processed by CLS
(www.cls.fr). while XBT data were simulated in a twin experiment setup. The difference in surface steric heights between the model and the "truth" observed by the
altimeter was accounted for by removing the average of the innovation vector at
each time step of the filter. The reference or "Mean Sea-Surface Height" (MSSH)
for altimetry was a model annual or multi-year average (depending on the case). In
addition, a special processing was used by CLS to correct the altimeter SLA for the
long-wavelength, high-frequency departures from the inverted barometer effect.
15.3.2 Assimilation of simulated XBT profiles
We first present a multivariate assimilation experiment of XBT profiles as well
as the effect of using regional, regime-dependent EOFs. The twin experiment is
made ofthree simulations:
• The control simulation is initialized on Jan 1, 1998 and is forced by ECMWF
1998 winds and interactive fluxes. Fifty randomly-distributed XBT profiles are
simulated from this run every week at all modellevels between surface layer
(120m) and IOOOm.
• Thefree run is initialized on Jan 1, 1993 (wrong initial conditions) but uses the
correct 1998 forcings. The initial conditions are obtained from a simulation
using ERA (ECMWF Re-analysis, www.ecmwf.int/research/eraJindex.html)
291
tenns of transport streamfunction, temperature and salinity defined on depth levels.
The estimation state vector (our state vector for all practic al means) is
x = {\jf,T,S}
(22)
The EOFs we use below are therefore trivariate in these variables. What this
means is that for instance temperature measurements will influence model temperature, but also salinity and streamfunction, in an empirically coherent manner.
Once the trivariate correction has been calculated, we correct the density, apply
geostrophy on the increments (hence assuming no error on the ageostrophic part -
a very common, robust assumption), and perfonn ancillary restart tasks such as
recalculating the value of streamfunction around islands and applying convective
adjustment. A simple scheme was used to update the model error variances in Di
from one analysis to the next (adding a constant to the previous analysis error variance as in De Mey, 1994), whereas the space-time error correlations and observational error variances were kept fixed, in accordance with standard OI practice. The
guess error correlation (in EOF modal space) derived from a space-time analytical
model with isotropic and homogeneous correlation radii of 100 km and 30 days for
all the modes. The observational errors were assumed to be uncorrelated in space
and time.
We present simulations assimilating separately two kinds of observations: SeaLevel Anomaly (SLA), using fonn (20) ofthe local observation operator, and temperature profiles.
SLA data were real altimeter data processed by CLS
(www.cls.fr). while XBT data were simulated in a twin experiment setup. The difference in surface steric heights between the model and the "truth" observed by the
altimeter was accounted for by removing the average of the innovation vector at
each time step of the filter. The reference or "Mean Sea-Surface Height" (MSSH)
for altimetry was a model annual or multi-year average (depending on the case). In
addition, a special processing was used by CLS to correct the altimeter SLA for the
long-wavelength, high-frequency departures from the inverted barometer effect.
15.3.2 Assimilation of simulated XBT profiles
We first present a multivariate assimilation experiment of XBT profiles as well
as the effect of using regional, regime-dependent EOFs. The twin experiment is
made ofthree simulations:
• The control simulation is initialized on Jan 1, 1998 and is forced by ECMWF
1998 winds and interactive fluxes. Fifty randomly-distributed XBT profiles are
simulated from this run every week at all modellevels between surface layer
(120m) and IOOOm.
• Thefree run is initialized on Jan 1, 1993 (wrong initial conditions) but uses the
correct 1998 forcings. The initial conditions are obtained from a simulation
using ERA (ECMWF Re-analysis, www.ecmwf.int/research/eraJindex.html)