Environmental Engineering Reference
In-Depth Information
5.6.3 Afrequency-distributionfunctionfor scaling
vegetationcover
be scaled up. Therefore, the slope
s
is scaled down to
the plot scale using Equation 5.14. The vegetation cover
is represented as the subpixel frequency distribution by
using Equation 5.15 with 101 levels from 0% to 100%.
The monthly overland flow is scaled to a rain day by using
the exponential frequency distribution similar to rainfall
distribution described by Carson andKirkby (1972). Thus
the scaled erosion model becomes:
The entire information required for environmental mod-
elling is saved in distribution functions. Instead of assum-
ing a Gaussian distribution, different distribution modes
are discovered after analyzing multi-scale data of vegeta-
tion cover (Zhang
et al
., 2002). The Polya distribution, a
mixture distribution of a beta and a binomial distribution,
is very effective in simulating the distribution of vegeta-
tion cover at numerous measurement scales (Zhang
et al
.,
2002).
d
1
−
D
)
1
.
67
100
2
kl OF
0
(
f
(
v
,
d
)
e
−
0
.
07
v
E
=
γ
(5.17)
v
=
0
)
n
−
x
1
(
α
+
β
)
where
E
is monthly erosion (mm),
k
is a soil erodibility
coefficient,
OF
is average daily overland flow (mm),
l
is
the monthly rainfall events (days),
D
is local topographic
fraction dimension,
n
C
x
x
(1
f
(
x
)
=
θ
−
θ
(
α
)
(
β
)
0
×
θ
α
−
1
(1
)
β
−
1
d
−
θ
θ
is a local topographic parameter,
v
is percent vegetation cover (%),
f
(
v
,
d
) is a Polya mass
function,
d
represents original modelling scale,
s
is the
slope (m m
-1
).
This upscaled model is employed to calculate monthly
global erosion in Eurasia and North Africa based on a
dataset of 1 km resolution (Figure 5.11). The required
dataset includes monthly overland flow calculated using a
modified Carson and Kirkby (1972) model (Zhang
et al
.,
2002), monthly vegetation cover estimated in terms of
AVHRR-NDVI (Zhang
et al
., 1997), and a DEM selected
from LP DAAC (2011). The resultant spatial pattern of
soil erosion suggests that high rates of soil erosion can be
accounted for in terms of the steep unstable terrain, highly
erodible soil, high monthly precipitation, and vegetation
removal by human activity or seasonal factors. Con-
versely, low soil-erosion rates reflect the lower relief, the
greater density of the vegetation canopy, and the areas of
lowprecipitation. Erosion is serious in southern East Asia,
India, along the Himalayas and Alps, and in west Africa.
In seasonal terms, the erosion rate is high from spring to
autumn in southern east China, summer and autumn in
India, and fromApril to October in west Africa. Relatively
high erosion rates occur in western Europe during the
winter months while very low soil loss occurs in summer.
γ
0
≤
x
≤
n
≤
N
(5.15)
where
n
is the number of events,
α
and
β
are the parame-
ters defined by variance and expected value,
x
represents
a random variable between 0 and
n
,and
θ
is a variable
that ranges between 0 and 1.
Both the expected value and the variance in this func-
tion have to be calculated for the determination of
parameters
α
β
. When changing the spatial reso-
lution of vegetation cover, it is seen that the expectation
is stable across scales while the variance is reduced at con-
tinually smaller scales. Therefore a method of predicting
this reduction in variance is needed in order to employ the
Poyla function to predict the frequency distribution at the
fine scales from coarse resolution data. When a multiscale
dataset degrading the high-resolution vegetation cover
(0.55m) derived from aerial photography is analyzed, it
can be seen that a logarithmic function between variance
and scale in all the subimages can effectively describe
the decline of subimage variance with increasing spatial
resolution (Zhang
et al
., 2002):
and
2
σ
=
a
+
b
ln(
d
)
(5.16)
2
represents variance,
d
represents measurement
scale, and
a
and
b
are coefficients.
After the subimage variance is calculated, the distri-
bution of vegetation cover in a subimage (or a pixel)
can be estimated across (up or down) scales. Using this
technique, the frequency distributions of vegetation cover
at a measurement scale of 30m are predicted on the basis
of vegetation cover derived from AVHRR-NDVI at a
resolution of 1 km (Figure 5.10).
where
σ
5.7 Conclusion
It is widely recognized that spatial environmental mod-
elling is always impacted by scaling issues because of
the nature of environmental heterogeneity. A number
of techniques have been developed to reduce the scaling
effects on modelling outputs. A very effective approach
is to identify scalable parameters that characterize the
relevant intrinsic environmental processes. When scaling
5.6.4 Upscaledsoil-erosionmodel
It is clear that, to calculate soil erosion at the global
scale accurately, the Thornes erosion model needs to
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