Geoscience Reference
In-Depth Information
how it is possible to record average spatial rainfall in a drainage basin, two different
observations can be made: first, the random function is stationary (which is the case
for small urban drainage basins), and second, rainfall levels generally vary and this
is the case for larger drainage basins.
7.3.1.
Reduction coefficient
7.3.1.1.
Definition and traditional methods
In order to evaluate the volume of water flowing on a surface, it is necessary to
know the exact amount of rainfall that has fallen and has generated this flow of
water. The level of isolated rainfall for a particular area tends to be known (by the
use of a rain gauge), and not the average rainfall that has fallen on the surface of the
drainage basin. The term
K
will be used to refer to the reduction coefficient.
K
is
used to represent the relationship between the average rainfall that has fallen on a
surface
P
BV
, and the isolated rainfall that has fallen with the same frequency
F
.
The value of the coefficient
K
depends on the surface of the drainage basin, on
the frequency of rainfall, on the rain itself, as well as on the spatial distribution of
the rainfall.
K
is only valid if the isolated rainfall with frequency
F
is the same at
each point in the drainage basin. We have made the assumption that rain is a random
stationary function. This means that the frequential distribution of the isolated
rainfall is the same at each point in the drainage basin being investigated.
For many years now, studies that have been carried out on a regional basis to
elucidate
K
coefficient have remained too empirical. One of the first solutions
resulting from all this research was that developed by Brunet-Moret and Roche
[BRU 66]. Their solution takes into consideration measurements recorded over both
short and long periods of time.
This technique, and others developed after it, evaluate and examine the spatial
average rainfall for the drainage basin for all recorded rainfall. These were long and
tedious processes, and they could not be used to extrapolate results that provided
information on the surface area of the drainage basin, duration of rainfall, and the
frequency of rainfall.
7.3.1.2.
Geostatistic approaches
The geostatistic approach, which was developed by Laborde [LAB 86] and then
Lebel [LEB 88], relies on the simple geostatistic observations that were mentioned
earlier in this section. The advantage of using this method is that it is no longer
necessary to calculate average rainfall. If the statistical distribution of the rainfall
and its structure can be worked out by using a variogram or a correlogram, it then
becomes possible to evaluate the reduction coefficients for all frequencies of rainfall
and for all drainage basins.
Rainfall that falls in the drainage basin needs to be considered as being the result
of a random stationary function with an order of 2:
