Geoscience Reference
In-Depth Information
a pilot study of applying GWR in water resources research, the temporal discrepancy
won't distort the results.
9.4 Methods
Because most of the urbanization and water quality indicators were not normally
distributed checked by the Kolmogorov-Smirnov test and visual interpretation of
histogram and Q-Q plots, appropriate methods such as natural log and square
root were applied to transform the non-normally distributed variables to meet the
condition of normal distribution for further analyses.
The spatially varying relationships between urbanization and water quality indi-
cators were analyzed by using GWR. In a GWR model, a water quality indicator was
dependent variable, and either PDLU or PD was independent variable. There were
two urbanization indicators and fourteen water quality indicators. Therefore, the
relationships for 28 pairs of water quality and urbanization indicators were analyzed.
GWR analyses were conducted using GWR 3 software package (Fotheringham et al.
2002
).
Afterwards, the outputs from the GWR models, including the values of
t
-test on
the local parameter estimates and the local
R
2
values, were mapped to give a clear
visualization of the spatial variations in the relationships between urbanization and
water quality and the abilities of the urbanization indicators to explain water quality.
All mappings and GIS analyses were performed using ArcGIS 9.2.
The detailed description of the model design in this study can be found in Tu and
Xia (
2008
). Detailed description of GWR technique can be found in some literatures
(Brunsdon et al.
1998
; Fotheringham et al.
2002
). Thus, theoretical background of
GWR is only briefly introduced here.
GWR is an extension of the traditional standard regression framework (e.g. OLS)
by allowing local rather than global parameters to be estimated (Fotheringham et al.
2001
). A GWR model can be stated as:
p
y
j
=
β
0
(
u
j
,
v
j
)
+
1
β
i
(
u
j
,
v
j
)
x
ij
+
ε
j
(9.1)
i
=
where u
j
and
v
j
are the coordinates for each location (spatial data point)
j
,
β
0
(
u
j
,
v
j
)is
the intercept for location
j
,
β
i
(
u
j
,
v
j
) is the local parameter estimate for independent
variable
x
i
at location
j
,
is the error term.
GWR assumes that every data point is more affected by nearby data points
than those further away. Thus, GWR is calibrated by weighting all data points
around a regression point using a distance decay function to produce local parameter
estimates.
The weighting function is an exponential distance decay form:
ε
d
ij
/
b
2
)
w
ij
=
exp(
−
(9.2)
