i Detection of Smoke and Dust Aerosols Using Multi-sensor Satellite ...

7.2.2.1 Theoretical impact analysis of science data products by mis-registration
The normalized indices (NI) are the normalization of two or more spectral bands.
They are usually used for the scene identification with general formula shown in Eq. (7.6),
where Ra and Rb are responses of bands a and b respectively. Commonly, one band in NI
is sensitive to a given matter class and the other band is insensitive to it, such as
Normalized Difference Vegetation Index (NDVI) (Rouse et al., 1973; Huete et al., 1994),
Normalized Difference Snow Index (NDSI) (Hall et al., 2002), Normalized Difference
Water Index (NDWI) (Gao, 1996), and Normalized Difference Dust Index (NDDI) (Qu et
al., 2006). In some indices, Ra or Rb can be the response combination of several spectral
bands, such as Normalized Multi-band Drought Index (NMDI) (Wang et al., 2007).
R R
NI
R R
a b
a b
114
(7.6)
If there is a small response deviation of two bands, ΔRa and ΔRb, the change of NI
value, ΔNI, is approximately equal to the first order partial derivative with respect to two
variables, Ra and Rb. Practically, one of bands is designated as reference band in most
cases to simplify the calculation by setting ΔRa=0 (or ΔRb=0). The ΔNI can be computed
with Eq. (7.7)
2Ra
NI R
2
( R R )
a b
'
b
(7.7)
where ΔRb’is the minute response change of band b caused by its spatial mis-registration
relative to band a.