Geoscience Reference
In-Depth Information
3.2.4 Estimating Confidence Limits for Covariance Calculations
A variation on the bootstrap method (Efron and Gong 1983; EmeryandThomson
2001) provides estimates of confidence limits for the covariance statistics used
to derive turbulent fluxes. The procedure is illustrated for the
w
T
covariance
from 1h of turbulence data collected near the ice/ocean interface during one of
the MaudNESS drift experiments. The data were separated into 15-min realiza-
tions, for which ADV velocities were rotated into a reference frame aligned with
the mean streamline so that
0, and with a linear trend removed from
temperature leaving the deviatory value
T
. Time series for the first realization are
shown in Fig. 3.4, including the product series
w
w
=
v
=
T
. Arrows indicate opposite
conditionsofdownwardvelocitycarryingatemperaturedeficitandupwardvelocity
with a temperature surplus, each contributing positively to the instantaneous prod-
ucttime series. The average of the productdeviatorytime series (covariance)com-
prisesbothpositiveandnegativecontributionswithfairlylargeexcursionsfromthe
mean, which is 6
×
10
−
6
Kms
−
1
. With the sample mean so much smaller than
the large-scale excursions (i.e., the standard deviation of the product time series is
largerelativetothemean),thequestionis:howrepresentativeofthetruecovariance
isthemeanoftheproducttime series?
.
4
×
Deviatory Temperature
x 10
-
3
4
2
0
-
2
0
5
10
15
Vertical Velocity
0.05
0
-
0.05
0
5
10
15
w x T
9
x 10
-
5
15
10
5
0
-
5
0
5
10
15
minutes
Fig. 3.4
Fifteen-min sample of
T
and vertical velocity, and the product series centered at time
222.510of2005duringMaudNESS,Phase2,Drift1.Arrowsmarktimeswhendownwardvelocity
carrying atemperature deficit and upward velocity carrying asurplus bothcontribute positively to
thecovariance
w
T