Geoscience Reference
In-Depth Information
1.07 < u
*
< 1.14 cm s
-
1
4
Mean
3
2
1
28
8
10
4
m
2
s
-
2
Fig. 3.7
Four15-minrealizationcovariance estimatesofstress: τ
=
u
w
+
i
v
w
where shaded
boxes show the individual confidence intervals for
u
w
and
v
w
, respectively, along with the
mean value and associated CI box. The real axis (horizontal) isaligned withthe direction of mean
flow in each case, with the average deflection of the stress vector about 28
◦
counterclockwise.
Also listed is a confidence interval for friction velocity magnitude, taken from the minimum and
maximum limitsof themean stress
w
T
realizations) to 1h (six realizations), and with the covariances,
, for each
realization averaged for the entire period. Results with error bars representing the
confidence intervals for the resulting mean covariances (multiplied by
ρ
c
p
)are
shown in Fig. 3.8. When the realization interval is too short (
5min)muchofthe
covariance captured at the longer realization times is missed, because the interval
is comparable to the time scales of the energy containing eddies. For sets with re-
alization intervals in the range from about 6 to 20min, the mean values lie within
or near the confidenceintervalforthe standard15-minrealization set (indicatedby
thedashedlines).Yetforlongerrealizationintervals(30-60min),themeanvalueis
lowerbyasmuchasa wattpersquaremeter.
This exercise is intended to drive home the point that calculating fluxes from
covariancestatisticsoftimeseriesisonlyanapproximationtotheensembleaverage
and depends on several somewhat subjective factors, including a tradeoff between
realization interval and longer term temporal changes in the environment. Based
mainly on experience from numerous exercises like these, we typically use 15min
for the realization averaging interval, and further average these for a minimum of
1h (four realizations) for stable flux estimates. A notable exception was LeadEX,
where the scale of the energy containing turbulent eddies in the statically unstable
conditionswassignificantlylargerthaninnearneutrallystableconditions(McPhee
andStanton1996).Inthatcase thechosenrealizationintervalwas1h.
<
