Environmental Engineering Reference
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biases in Level-1c radiances. The SNOmatchups, accumulated using Cao et al. (
2004
)
algorithm, contain simultaneous observations over the polar regions that are less than
2 min apart and within 111 km ground distance apart for the nadir pixels from any
NOAA satellite pairs. The SNO method leverages the SNO matchups to ensure they
do not contain sampling errors such as the diurnal drift errors. Therefore, the statistical
differences in the SNO matchups represent instrument calibration errors in the
satellite pairs.
Applying the calibration equation (
8.1
) to the SNO matchups between two
satellites, represented by
k
and
j
, a radiance error between them is derived as
(Zou et al.
2006
)
Δ
R ¼
Δ
R
L
Δ
δR þ μ
k
Z
k
μ
j
Z
j
þ E;
(8.2)
where
Δ
δR ¼ δR
k
δR
j
.
E
is a residual term related to the
spatial and time differences between the satellites
k
and
j
and is ignored. In (
8.2
),
Δ
R
L
,
Z
k
, and
Z
j
are a function of the measurements, while
Δ
R
L
¼ R
L
;k
R
L
;j
and
μ
j
are
unknown coefficients. Regression methods were used to solve for these coefficients
from the SNOs in which the summation of
Δ
δR
,
μ
k
, and
2
is minimized. However, because
there is a high degree of colinearity between
Z
k
and
Z
j
for the SNOs, only
ð
Δ
RÞ
Δ
δR
and
the difference between
μ
k
μ
j
), can be determined from regressions
(Zou et al.
2006
). By definition, the regression procedure resulted in zero mean
inter-satellite biases in the SNO matchups. In addition, scene temperature depen-
dency in biases between the two satellites was also significantly reduced with
appropriate regression solutions of (
μ
k
μ
j
). Figure
8.4
shows an example of the
brightness temperature differences in the SNO matchups between NOAA-10 and
NOAA-11 before and after the application of the SNO regression coefficients in the
calibration equation (
8.1
). It is clearly seen that the SNO regressions removed mean
inter-satellite biases in the satellite pairs and the scene temperature dependency in
the biases.
Based on these SNO regression characteristics, a sequential procedure was
developed to solve for coefficients for all NOAA satellites (Zou et al.
2006
,
2009
). In the sequential procedure, the calibration coefficient,
μ
k
and
μ
j
,(
,ofan
arbitrarily selected reference satellite was assumed to be known first, and then
coefficients of all other satellites were determined sequentially (one by one) from
regressions of the SNO matchups between satellite pairs, starting from the satellite
closest to the reference satellite. NOAA-10 was arbitrarily selected as the reference
satellite for MSU instrument, and its offset was assumed to be zero. The sequential
procedure reduced the problem to the determination of the nonlinear coefficient,
μ
N10
, of the reference satellite; since once
Δ
δR
and
μ
μ
N10
is known, calibration coefficients of
all other satellites are solved from the SNOs. This reference satellite problem was
tied to the removal of the solar heating-related instrument temperature variability in
the Level-1c radiance data.
An end-to-end approach was developed to determine the root-level calibration
coefficient by minimizing instrument temperature signals in the end-level inter-satellite
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