Geoscience Reference
In-Depth Information
2. At the first visited N nodes u
1
:
A. Model, using either a parametric or nonparametric approach, the local ccdf
of Z(u
1
) conditional on n original data {Z (u
α
), α = 1,Λ, n} F
Z
(u
1
; z
1
|(n)) = prob
{Z (u
1
) ≤ z
1
|(n)}
B. Generate, via the Monte Carlo drawing relation, a simulated value z
(l)
(u
1
)
from this ccdf F
Z
(u
1
: z
1
|(n)), and add it to the conditioning data set, now of
dimension n + 1, to be used for all subsequent local ccdf determinations.
3. At the i
th
node u
i
along the random path:
A. Model the local ccdf of Z(u
i
) conditional on n original data and the i -1
near previously simulated values { z
(l)
(u
i
), j = 1,Λ, i -1}:
Z
(u
1
; z
i│
(n + i 1)) = prob{Z (u
i
) ≤ z
i
(n + i 1)} (8)
B. Generate a simulated value z
(l)
(u
i
) from this ccdf and add it to the condition-
ing data set, now of dimension n + i.
4. Repeat step 3 until all N nodes along the random path are visited.
The SGS assumes a Gaussian random fi eld, such that the mean value and covari-
ance completely characterize the ccdf (Press et al., 1998). During the SGS process,
Gaussian transformation of available measurements is simulated, such that each simu-
lated value is conditional on original data and all previously simulated values (Deutsch
and Journel, 1992; Lin et al., 2001). A value simulated at a one location is randomly
selected from the normal distribution function defi ned by the kriging mean and vari-
ance based on neighborhood values. Finally, simulated normal values are back-trans-
formed into simulated values to yield the original variable. The simulated value at
the new randomly visited point value depends on both original data and previously
simulated values. This process is repeated until all points have been simulated.
RESULTS AND DISCUSSION
Statistics and Spatial Structures of NDVI Images
Statistics of remotely sensed images can be used as a basic tool to characterize land-
scape changes (Akiwumi and Butler, 2008; Fox et al., 2008; Giriraj et al., 2008; Ward
et al., 2000; Zomeni et al., 2008). Table 1 summarizes the statistics for seven actual
NDVI images of areas A and B before and after disturbances. The lowest mean and
minimum NDVI values in 1996-2004 occurred on March 6, 1999, after the Chi-Chi
earthquake in both areas A and B areas. Moreover, the largest range between minimum
and maximum NDVI values also occurred on March 6, 1999, after the Chi-Chi earth-
quake in both areas A and B. The most negative minimum NDVI values occurred on
November 27, 2000, and December 17, 2003, in both areas A and B. On these dates,
the standard deviations of NDVI values were slightly larger than those on other dates.
These statistical results illustrate that the Chi-Chi earthquake had the largest impact on
all landscapes represented by NDVI images for areas A and B. The second and third
greatest impacts on all landscapes are from typhoons Xangsane (November, 2000) and
Dujuan (September, 2003) in areas A and B, respectively (Figures 2 and 3 and Table
1). Particularly, typhoon Xangsane right after the Chi-Chi earthquake was the second
disturbance to impact landscape changes in the study areas. Numerous extension cracks,
