[Mitgcm-support] Combined Kalman filter (kf025) and control (c20000630)

Wed Jul 9 15:56:29 EDT 2003

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Comparison of XBT data with combined Kalman filter results (kf025) and
control integration (c20000630):

This[1] is a map of 1993-1997, Pacific, XBT locations. A histogram
showing number of casts per 10-deg-latitude by 10-deg-longitude by 100-m
box is shown here[2] . In general terms, the temporal coverage is very
good in the equatorial Pacific because of TAO moorings and the spatial
coverage is good along major ship routes but rather sparse elsewhere.

Last week I showed results which reproduced figures 13-15 in ECCO Report
Number 5:

Figure 13[3] : time and basin averaged RMS differences,

Figure 14[4] : RMS differences within various 100-m thick depth levels,
and

Figure 15[5] : 0-800-m heat content estimates over 20 deg regions.

The first two figures are dominated by time-mean differences which we do
not correct with the Kalman filter at this time. Therefore they will not
be part of routine analysis. More on third figure later.

One question raised last week concerned Kalman filter influence outside
region of baroclinic Kalman filter (north of 20 deg N and south of 20
deg S). I did not find any obvious bugs in the analysis so these
differences are presumed real. Maps of RMS temperature difference
between KF025 assimilation and GCM simulation are shown here[6] .
Although largest "corrections" occur in equatorial region, large
differences exist at higher latitudes, especially in Kuroshio region and
near Australia and Tasmania.

To emphasize changes in the variability rather than the time mean, the
following analysis was carried out. XBT casts were bined in
10-deg-latitude by 10-deg-longitude by 100-m boxes and the following
statistical quantities were computed for XBT data, GCM equivalent, and
Kalman-filter equivalent: means, standard deviations, standard deviation
differences, and correlation coefficients. Vertical profiles[7] for the
various statistical quantities were constructed using an average over
the Pacific basin and the 1993-1997 assimilation period weighted by the
number of available measurements in each box. Overall the
simulation/assimilation results display the sharper, shallower
thermocline, that was also evident in earlier comparisons with TAO data[8]
. On a basin-average, assimilation standard deviation difference and
correlation coefficient relative to XBT data are only marginally
improved from the simulation. But as the next few figures show there is
a lot of regional variability in the simulation/assimilation/data
comparisons.

A map of standard deviation difference between KF025 assimilation and
XBT data is shown here[9] . Largest differences (2-4 deg C) are in the
Kuroshio and East Australian Current regions at all depths and at the
thermocline in the Equatorial region. As a measure of skill of the
Kalman filter estimates relative to simulation, the next figure[10]
displays difference fields of standard deviation misfits:
std(GCM-XBT)-std(KF-XBT). The way to interpret this figure is that
positive areas (yellows and reds) indicate regions where the
assimilation varibility is closer to the XBT data than the simulation
while negative areas (dark greens and blues) indicate regions where the
simulation is closer to the XBT data. The assimilation improves
temperature variability estimates in the Equatorial Pacific near the
thermocline, a conclusion consistent with that from earlier comparisons
with TAO data. Elsewhere, results are mixed.

Correlation coefficient[11] maps between simulation or assimilation and
XBT data show rather good correlation (>5) over most of the domain for
depths shallower than 400 m. A measure of skill of the Kalman filter
estimates relative to simulation is the difference[12] between the
Kalman filter and GCM correlation coefficients to the XBT data. Once
again, positve values, red and yellows, indicate that the Kalman filter
estimates improve upon GCM simulation. Overall, this analysis shows
mostly improvements above 200 m and below 400 m near the Equator, with
results being mixed to negative outside the equatorial band and in the
200-400-m depth range.

A further comparison is in terms of seasonal heat content estimates in
the top 800-m for 20-deg by 20-deg boxes. Typical time series[13] show
good correlation between simulation or assimilation results and the XBT
data, as expected from the earlier[14] analysis, but there is a cold
bias in the GCM at most locations. Statistical analysis of the heat
content time series is summarized in the following figure[15] . Top
panel shows standard deviation of XBT heat content estimates. Second row
panels show simulation and assimilation heat content standard deviation,
respectively. Third and fourth row panels show standard deviation
difference and correlation coefficient analyses, as labeled. Overall
estimates of heat content variability are improved after assimilation in
the Eastern Equatorial Pacific but results elsewhere are mixed.
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[1] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/LOC1.ps
[2] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/LOC2.ps
[3] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/RMS1.ps
[4] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/RMS2.ps
[5] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/HEAT1.ps
[6] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/RMS4.ps
[7] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/STD1.ps
[8] http://escher:2000/hosts/triton/dm1/dimitri/data/tao/matlab/FIGS/TempStats/global.ps
[9] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/STD2.ps
[10] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/STD3.ps
[11] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/COR1.ps
[12] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/COR2.ps
[13] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/HEAT1.ps
[14] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/COR1.ps
[15] http://escher:2000/hosts/triton/dm1/dimitri/data/xbt/FIGS/HEAT2.ps