Surface Current Mapping off California with Radiometry and Altimetry

1
XBT Fall Rate Problem A Historical
Perspective Bill Emery, Univ. of Colorado Bob
Heinmiller (deceased 2005)
2

• In the early 1980s the XBT probes in widest use
  were
• The T4 probe which went to about 500 m and
• The T7 probe which went to about 700 m.
• The latter become the deep-blue probe which has
  seen the widest use in oceanography.
• Much of this material is taken from a paper by
  Bob Heinmiller, Curt Ebbesmeyer, Bruce Taft, Don
  Olson and Oleg Nikitin published in Deep-Sea Res.
  in 1983.

3
T7 XBT probe
4
Proof that I actually did collect XBT data in
the past.
5
This was the era of MODE and POLYMODE so many of
these XBT - CTD comparisons were made on US and
then USSR research vessels.
6
Previous Comparisons As part of the INDOPAC
expedition Arnold Mantyla dropped 11 T4 probes
with coincident Nansen casts reporting a linear
decrease in isotherm depth difference from 0 at
the surface to -16 m at 450 m depth. A series
of XBT-CTD comparisons were made in the
mid-1970s (Flierl, 1974 Flierl and Robinson,
1977 McDowell, 1977 Federov et al., 1978 and
Seaver and Kuleshov, 1979,82) which all noted
systematic differences between T7 XBT and
corresponding CTD depths. As shown in table 1
there were a total of 178 comparisons of which
35 were taken at the same time as the CTD
profile while the rest were taken half way
between the CTD stations.
7
T4 and T7 comparisons As part of NORPAX in data
set 11 all of the T4 XBTs were dropped
immediately after the CTD profiles. It should be
noted that during this time comparisons between
CTD temperatures and coincident reversing
thermometer data yielded a mean difference of
0.006 C and a standard deviation of 0.02 C
which should be taken as an upper limit on the
accuracy of the CTD temperature measurements.
Between 1976 and 1978 data sets 12-15 were
collected using T7 probes dropped during or
immediately after a Niel-Brown CTD cast. In most
of these profiles coincident reversing
thermometers were used to provide corrections for
the CTD temperatures (Iselin 0.0026 C, Gyre
0.0034 C)
8
10 of the 15 available data sets were edited as
follows for data sets 6 to 11 the 2 CTD
temperature profiles adjacent to the XBT
temperature were linearly interpolated to the
position of the XBTcast. Means and standard
deviations were computed for the T4 XBT - CTD
temperatures (data sets 6 - 11) and for the T7
XBT - CTD (data sets 12 - 15).
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A T4 XBT profile was rejected if at any depth
the temperature difference with the CTD profile
exceeded 3 times the standard deviation (again
only for data sets 6 - 11). This resulted in a
rejection of about 8 - 16 of the XBT
profiles. A T7 XBT profile was rejected if
this same difference exceeded 1.5 X standard
deviation which resulted in a rejected of about
18 - 21 of the XBT temperature profiles being
eliminated.
11
This analysis is based on the assumption that
we can have both systematic errors that are
independent of depth and depth dependent
errors. Sources of the systematic errors are
temperature offsets due to incorrect balancing of
the thermistor (see next slides), incorrect
weight of the probe (next slides), etc.
Sources of the latter are the changing mass with
the outlay of copper wire, the changing water
density and hence friction, etc.
12
Balancing thermistor circuit in the probe by hand.
13
Weighing the individual spools of copper wire.
14
To account for temperature errors the profiles
were first examined in regions where the vertical
temperature gradients were very small
(thermostads) and the XBT profiles were corrected
for any offsets observed in these layers before
the depth dependent errors were calculated.
15
Thermostads were found in the 50 m mixed layer
(T4s in 6-11), in the 125 m mixed layer near a
Gulf Stream ring (T7 12) and in the 18C water
(T7 13-15). The mean temperature gradient in
the 25 m Pacific mixed layer was taken to be
-0.01 C/m (sets 6-11) which in the North
Atlantic thermostads was -0.006 C/m.
Previous studies suggested that XBT depth errors
in the thermostads were about 3 m resulting in a
temperature error of -0.03 which about half of
the 0.05 C resolution possible with an XBT
profile.
16
Since this is much smaller than the mean
temperature differences between the XBT and CTD
in Table 3 we conclude that we dont need to
include the depth-dependent error in the
thermostads and we can use them for temperature
calibration. Georgi et al. (1980) carefully
calibrated XBT probes in a constant thermal bath
and found that temperature errors varied between
-0.011 and 0.014 C over a range of 0 to 30 C.
These differences are small relative to the
0.17 C mean temperature difference in Table 3
which means that the XBT temperature errors are
not significant in calculating the depth errors.
17
Returning to Table 3 we note that for data set
11 the XBT and CTD casts were nearly coincident
and that the s.d. of 0.18 C is close to the mean
s.d. of 0.23 C. This mean s.d. is twice as
large as that for the T7 probes. Thus, we
conclude that this variability is characteristic
of these two types of XBT probes.
18
After all the XBT profiles were adjusted for
the thermostad calibration differences in XBT
and CTD isotherm depths (dz) were computed along
with the mean difference ( ) and the
standard deviation of the differences (sdz).
Note depth values were linearly interpolated for
sets 2, 4 and 5, 6 m was subtracted from depths
given by Seaver and Kuleshov to correct for the
offset reported, Federov et al. reported depth
differences only as a function of temperature so
data set 3 was not considered in the comparisons,
and a reported correction of 8 m was added to
data set 12.
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20
Both T4 and T7 difference profiles start
positive near the surface and then turn negative.
This inflection point is at 150 m for the T4s
and 400 m for the T7s. In general the T4s
have larger differences beneath the inflection
point and also show larger variability between
the different data sets. We now turn to the
standard deviations of these differences which
show a surprising similarity for all of the T4
data sets and some very marked variability in the
upper 400 m of the T7 profiles.
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22
Note data sets 6 - 10 were those T4 profiles
separated by 30 km while in data set 11 the XBT
and CTD profiles were nearly coincident.
Thus, while the 6-10 profiles show a similar but
increasing variability with depth data set 11
shows a rapid decrease from the surface down to
100 m below which the variability is nearly
constant at 10 m. A very similar variability
limit of about 10 m is seen for the T7 profiles
in data set 12 which was close to a Gulf Stream
ring. Data sets 13-15 were collected from Feb.
to July, 1978 in the area of the 18 C mode
water. It is the presence of the mode water
in these profiles that causes the large
variations in depth difference in the upper
layers not the performance of the XBT probes.
23
Below the 18 C mode water the T7 XBT depth
difference variability is nearly constant again
at about 10 m. This suggests that the error is
not depth-dependent and has a mean value of 10 m
for both types of XBT probes. To test this
conclusion statistically we carried out an F-test
analysis of our results. We used for our
F-test where m is the number of data sets, n is
the number in data set i, is the mean of
data set i, si is the standard deviation of
xi, is the equally weighted overall mean
of the data .
24
We have modified the F-test to use only means
and standard deviations and to apply the test to
data sets of differing size. To apply the
tests the depth differences in Table 1 were
interpolated to common depths at 25 m (T4 probes)
and 125 m (T7 probes) intervals. For the T4
probes the F-test results exceeded the 5
critical level for most depths, which indicated
that the six mean curves are not homogeneous.
For the T7 probes the F-test indicates that all
depths except between 150 and 250 m the mean
values of depth differences were statistically
similar at the 5 critical level.
25
Because of the F-test results we determined
that we could not develop a correction for the T4
profiles and thus concentrated only on the T7
data. The next figure is a plot of the T7 mean
differences obtained by averaging the T7 profiles
in Fig. 2b. Each data set was equally
weighted. We also include the dotted lines
shown in Fig. 2 which can be used to represent
different portions of the T7 profiles.
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27
This figure suggests that the differences can
be approximated by 2 straights line segments.
So we fitted the data in the following table to
two straight line segments using a least-squares
fit. The resulting equations are Where zx
is the XBT depth and zc is the CTD depth in
meters.
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29
The maximum deviation from this linear fit is
1.9 at 550 m depth. The RMS deviation from the
curve fit is 0.75 m. The mean deviations are
in general lt 1/10 of the standard deviations of
the differences. We conclude that the linear
fits are a good approximations to the depth
differences. Attempts to use other difference
formulations resulted in larger RMS differences.
30
In these equations XBT depth is defined in
terms of the CTD depth which is not known. For
practical use the CTD depth should be expressed
in terms of the XBT depth as Only for T7
probes.
31
It should be emphasized that this analysis was
based on older analog XBT data which suffers from
additional recording errors not found in modern
digital systems. This in part was our
motivation for the termostad calibration. We
also note that while the given precision of the
XBT even in these older systems was given as 0.1
C but our comparisons demonstrated T7 mean
differences of 0.19 C with a standard deviation
of 0.11 C.
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