Geoscience Reference
In-Depth Information
The phenomena of a time delay of the ocean/atmosphere system brightness
temperature response in the resonant spectral domains 5.9 and 13.5 mm on the
variations of surface heat
fl
fluxes is described by the Duamel
'
is integral equation:
Z
t
T
b
ð
t
; kÞ
¼
q
ðsÞ
r
ð
t
sÞ
d
s
ð
2
:
23
Þ
0
were T
b
(t,
ʻ
) is radiobrightness temperature for wavelength
ʻ
(K), q(t) is heat
fl
ux on
the ocean-atmosphere interface (W/m
2
/h),
˄
is time delay (hours), r(t) is response
delay function (K/(W/m
2
/h)).
Solution of Eq. (
2.23
) can be theoretically realized by traditional methods which
are used for solution of inverse tasks in the form of integral equation of the
rst
type. But in real case, functions T
b
(t,
ʻ
) and q(t) have discrete form as restricted in
the time numerical sets. Therefore, traditional methods such as Laplace transfor-
mation or iterative procedure (Tricomi 1960) lead to large errors. More effective
method for solution of Eq. (
2.23
) was proposed by Grankov and Soldatov (2005). It
consists in the use of exponential approximation:
r
ð
t
Þ
¼
X
N
a
i
exp
ð
b
i
t
Þ
i¼1
where coef
cients a
i
and b
i
are de
ned from condition:
n
2
a
i
,b
i
}
(
)
[
]
=
M
=
min
1
n
T
(
)
t
−
F
(
t
)
,
{
i
1
where t
i
=i
ʔ
t,
F
ð
t
i
Þ
¼
X
q
ð
t
i
t
s
Þ
X
i
1
N
ð
a
k
=
b
k
Þ
exp
b
k
t
s
ð
Þ
1
exp
b
k
D
½
ð
t
Þ
s¼0
k¼0
Numerical calculations in Fig.
2.37
show that such approach to solution of
Eq. (
2.23
) gives errors no more 5
7 %. We see that time delay exists between
radiobrightness temperature and heat
-
flux. This is important for calibration of
satellite measurements. Calculation of the function r(t) of the brightness tempera-
ture T
b
response (sensitivity) to the total heat fluxes q the variation is clearly
demonstrated. In this case, brightness temperatures were calculated from the
oceanographic, meteorological, and aerological data, observed in the experiment
with ATLANTEX-90 synchronized with use of the DMSP F-08 heat
fl
fl
uxes data
q obtained from the vessel Victor Bugaev during the cyclone of 9
13 April 1990.
-
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