Geoscience Reference
In-Depth Information
Fig. 3.6
Covariance samples from Fig. 3.5 multiplied by ρc
p
to convert to sensible heat flux,
along with confidence limits derived from the modified bootstrap method described in the text.
The dashed line is the mean of four realizations (1h) with the shaded box indicating the 95%
confidence limitsfor the1-h mean
where
X
n
is the sample mean of n realizations for the covariance, and
σ
n
is the
averageofthebootstrapstandarddeviations.ThedashedlineinFig.3.6isthesam-
ple mean of the four covariance heat flux estimates, with the corresponding 95%
confidencelimitsindicatedbytheshadedbox.
The aboveprocedurecan be applied as well to evaluate confidence intervals for
thecovarianceestimateofturbulentstress
u
w
+
v
w
.Inthiscasethereare
two dimensions, and the confidence limits trace a square in the complex plane, as
depictedinFig.3.7.
Caution must be exercised in assigning a confidence interval for the covariance
of two deviatory time series to the corresponding turbulent fluxes, mainly because
of uncertainty in applying Taylor's hypothesis, which rigorously pertains only to
steady flows. In practice, vary few natural IOBLs are steady for more than a few
hours at a time, and the choice of averaging time for the “turbulent realizations”
may significantly affect the mean fluxes estimated from the covariance measure-
ments. An examplefrom a 6-h period duringthe MaudNESS driftdiscussed above
illustratesthis.From0300to0900on10August2005,icedriftwasrelativelysteady
with moderate stress. The data set was broken into 14 different sets of realizations
of the product time series,
w
τ
=
i
T
, with averaging times ranging from 1min (360
×
