The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
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3. ESTIMATION METHODS
Firstly, the canopy height datasets were normalized with a
square root transformation (SQRTHT); afterwards, all estimated
SQRTHT values were backtransformed before comparing to
measured height values (Hudak et al. 2002).
3.1 Ordinary Least Squares(OLS) regression
The OLS multiple regression model takes the general form:
Z = a + j>,(Jr,) + e <T>
¡=1
Where, Z is the forest canopy height, Xj is the i explanatory
variable (SVIs, LAI, forest cover and X and Y location), (f. is
the linear slope coefficient corresponding to X„ £ is the
residual error (Kleinbaum et al.1998).
3.2 Ordinary Kriging(OK)
Kriging interpolates the sample data to estimate values at
unsampled locations, based solely on a linear model of
regionalization. The linear model of regionalization essentially
is a weighting function required to krig and can be graphically
represented by a semivariogram. The semivariance /(h) is the
following equations.
Where, Z * (p) is the primary variable and X a and fl a are the
weights and locations of n neighboring samples respectively.
The kriging
weights was forced to sum to one:
(ll)
a=1
3.3 Ordinary CoKriging (OCK)
Cokriging is a multivariate extension of kriging and relies on a
linear model of co-regionalization that exploits not only the
autocorrelation in the primary variable, but also the cross
correlation between the primary variable and a secondary
variable. Cokriging can be graphically represented by the cross-
semivariogram, defined as:
1 N(h) ,
r ^ = 2N(h)^ Zi( ' Ma ^~ Zi( ' Ma+h ^ (12)
x (zj(M a )-Zj(ju a +h))
Where, y..{h) is the cross-semivariance between variables I and
j, Z- and Z • is the data value of variable i and j at locations
J 5 Z J J
jU a and p + h respectively. The OCK estimator of Z * at
location p takes the form:
1 N(h)
rW = Wff^lL( Z ^a)- Z ^a +h )) 2 (8)
2N(h)
Where /(h) is semivariance as a function of lag distance h,
N(h) is the number of pairs of data locations separated by h,
and Z is the data value at locations jU a and p a +h
(Goovaerts, 1997). And in this study, the exponential models
was used to simulate the nugget, sill, range and the shape of the
sample semivariogram:
The traditional OCK operates under two nonbias constraints:
«|=1 OT 2 =l
/(h) = c
, ,-3 h.
1 ~ exp( )
a
(9)
Where, a is the practical range of the semivariogram, c is sill.
3.4 Integrated
Residuals from the OLS regression models were exported and
imported into ARCGIS software for kriging/cokriging. The
same rules and procedures were followed for modelling the
residuals as for modelling the SQRTHT data.
The OK model estimates a value Z * at each location p and
takes the general form:
z*(//) = "|/IWh)
a=1
(10)
4. RESULTS AND DISCUSSION
In this paper, the needle forest and broadleaf forest were
classified for estimation of the canopy height. The accuracy of
classification was validation by our fieldwork.