Geoscience Reference
In-Depth Information
This equation is very similar to the one that was generated by the Ministry of
Agriculture [GAL 82], which was drawn up to measure rainfall levels that were
recorded over a 10 year period in the region of Paris:
S
K
(
S
,
t
)
=
1
−
0
.
33
30
t
This equation was developed empirically, after having examined K values by
using traditional methods for all types of surfaces and for all durations of time. As
can be seen in Figure 7.13, there is a strong correlation between the duration of
observation from 1 hour to 20 hours and drainage basins with an area of 1 to
100 km
2
.
7.3.1.3.
Perspectives
The geostatistic modeling of rainfall has paved the way for research to be carried
out on reduction coefficients. Factors that were once difficult to integrate into
research, such as time, frequency, or shape of the drainage basin, can now be
integrated into this new research. More research still needs to be carried out in this
field, even though it is now a commonly used method to measure rainfall levels.
7.3.2.
Average spatial rainfall
The aim here is to evaluate the rainfall that falls within a drainage basin as a
whole. This is made possible by studying the spatial average for each period of
rainfall without having to apply the process of interpolation to rainfall recorded at
each different measuring site located in the drainage basin. This is a very old
problem that different generations of geographers and hydrologists have had to
resolve by using Thiessen polygons or isohyetal methods. In the next section we
will see how the geostatistic approach for measuring rainfall is used to help
geographers and hydrologists overcome this problem.
7.3.2.1.
Rainfall can be derived
This derivation process can only occur under conditions where stationarity is not
possible. We have already seen in this chapter that it is possible to interpolate
R
G
∗
rainfall
at any given point in a drainage basin without having to rely on
measurements of autocorrelation by using the equation:
( ω
)
G
G
∗
n
R
(
x
,
ω
)
=
a
+
=
λ
R
(
x
,
ω
)
o
o
i
i
i
1
G
G
n
a
=
m
(
x
)
−
=
λ
m
(
x
)
o
o
i
i
i
1
[ ]
[ ] [ ]
−
1
λ
=
C
C
i
,
j
i
,
o
i
