Geoscience Reference
In-Depth Information
In these equations the parameters of a and λ are independent of the
observations that are made during a particular event (period of rainfall) ω. At
each measurement site within the drainage basin, rainfall is treated as being a
linear combination of the observations that have been made. This means that
average spatial rainfall is also a linear combination of the observations that have
been made in the drainage basin. In order to evaluate the accuracy of each
measurement site as far as the estimation of spatial averages in the drainage basin
are concerned, the values of the field averages
x G
( m G , the field variances
2
)
σ
(
)
and
the correlogram
)
must be known.
G
G
G
G
G
G
(with
C
(
x
,
x
)
=
σ
(
x
σ
(
x
)
ρ
(
x
x
)
).
i
j
i
)
j
i
j
x G ,
which are part of a regular grid and which can be found inside the contours of a
drainage basin. When the averages of these parameters are known it is then possible
to calculate the amount of rainfall that falls in the drainage basin
The parameters
a
and
λ are then calculated for a total of n points
k
(ω for an
R
)
BV
event ω .
1
n
1
n
a
=
a
,
λ
=
λ
o
i
i
o
k
k
n
n
k
=
1
k
=
1
n
G
=
R
(
ω
)
=
a
+
λ
R
(
x
,
ω
)
o
i
i
BV
k
1
This approach is very useful for carrying out gradex calculations within the
drainage basin. The Gradex method [GUI 67] assumes that the gradex of the rainfall
recorded in the drainage basin is equal to the gradex of the rainfall that is recorded
in the local area. By using the two equations, it becomes very easy to calculate the
amount of rainfall that has fallen in a drainage basin on a daily basis, and it then
becomes possible to work out the gradex from these values. Figure 7.14 illustrates
how this method can be adopted by using the example of the Ardèche drainage
basin [BER 05]. The simplicity of the calculations makes it possible to calculate the
exact amount of rainfall recorded in the basin on a daily basis by combining the
values recorded in the drainage basin with daily rainfall values that are recorded by
the network of rain gauges. Table 7.3 clearly shows that the average gradex of daily
rainfall that is recorded by the rain gauges is at least 20% greater than the average
gradex of daily rainfall that is recorded in the drainage basin.
This result clearly shows the advantage of using geostatistic tools when it comes
to estimating rainfall levels in the drainage basin. The traditional methods used tend
to produce systematic errors that cannot be corrected.
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