Geoscience Reference
In-Depth Information
S
cw
e
−
ift
S
ccw
e
ift
D
cw
e
−
i
ω
t
D
ccw
e
i
ω
t
V
(
t
)=
V
0
+
+
+
+
(2.23)
where
is diurnal tidal frequency.A complex function for position is obtained by
integration:
ω
)
S
cw
e
−
ift
1
+
S
ccw
1
e
ift
X
(
t
)=
X
0
+
V
0
t
+(
i
/
f
−
−
(2.24)
/
ω
)
D
cw
e
−
i
ω
t
1
+
D
ccw
1
e
i
ω
t
+
···
(
i
−
−
Other natural frequenciesmay be consideredas well, but at high latitudes overrel-
atively short time intervals, the frequency separation between inertial motion and
semidiurnaltidesistoosmalltohavemuchimpactonthecomputedvelocityfields.
Givenatimeseriesofpositionfixesoveratimeperiodcomparabletothelongest
period in the frequency array (24h), solving for the coefficients in (2.24) becomes
a linear algebra problem using standard least-squares analysis and Gaussian elimi-
nation (McPhee 1988). In a typical application, the vector of complex coefficients
([
is calculated every 3h over a window 24h wide,
withvelocitythencalculatedatanyparticulartimevia(2.23)bylinearinterpolation
ofthecoefficients.Acomplex-demodulationtrajectorycalculatedfromtheposition
data in Fig. 2.3 is drawn offset for comparison. An expanded view of the velocity
fieldduringSeptember1998(Fig.2.4)showsthatingeneral,theinertialcomponent
isgenerallylargerthandiurnalexceptduringtimesofrapidacceleration(changein
inertia).
Before “undithered”global positioningsatellite capability,estimating ice veloc-
ity from navigationdata was hamperedby relatively sparse position data or by rel-
atively large errors in individual fixes. By complex demodulation, it was possible
toobtainrealisticvelocityestimatesfromsuchdata,becausethetechniqueincorpo-
rates the physical constraint of the inherent inertia in the coupled ice/upper ocean
system. With the advent of frequent, highly accurate GPS data, other techniques
provide good velocity data; nevertheless, complex demodulation offers consider-
able insight into the physical system. Relatively sudden accelerations or decelera-
tions in ice drift (e.g., day 263) can set off persistent trains of inertial oscillations,
withstrengthdependingnotonlyonwind(drift)speedbutchangesindirectionwith
respecttotheexistinginertiaoftheice/upperoceansystem.Borrowingfromelectri-
cal engineering terminology, the oscillating coefficients are like “phasors” that de-
scribe the amplitude and phase of the inertial or tidal oscillation. Figure 2.5 shows
a time-seriesvector representationof the two leadingcoefficientsin (2.23).For the
firstpartoftheperiodthereisrapiddrifttothenorthwestwithrelativelysmalliner-
tialcontent.Thenbeginningaboutmidday(UT)onday262,themeanmotionveers
rapidlynorthward,andapparentlythisclockwise“kick”excitesastrongtrainofin-
ertialphasorsthatpersistswithlittlephasechange(changeinvectororientation)for
several inertial periods with relatively small mean velocity, hence the pronounced
cycloidalmotionapparentin thedrifttrajectory(Fig.2.3).
X
0
,
V
0
,
S
cw
,
S
ccw
,
D
cw
,
D
ccw
])
