Geoscience Reference
In-Depth Information
measurement is not very widely available and is mainly used in developed countries.
Furthermore, the measurements recorded only provide information about a short
period of time. On a long-term basis, operational hydrology will be used to deal
with specific data relating to rainfall. There are two different types of problems that
can be associated with networks of rain gauges:
- estimating rainfall in a particular point for which there is no actual
measurement available;
- evaluating average rainfall on a basin.
In order to solve the problems associated with the estimation methods, it is
necessary to formalize the way in which rainfall is represented mathematically.
Geostatistics were developed in France by G. Matheron [MAT 71] and his team at
the École des Mines in Paris [DEL 78; JOU 80]. The École des Mines is a
prestigious French engineering school in Paris. Some time later this idea of
geostatistic modeling was successfully used in the analysis of precipitation
fields [MAL 74; LAB 82; LEM 86]. Unlike geological data where only one
observation is available, rainfall is a phenomenon that can be observed many times.
According to the geostatistic vocabulary, rainfall is said to be a “climatologic data”.
Before going into further detail on the practical uses of the different estimation
methods that exist, it is necessary to consider the theory behind them. This theory
stems from research carried out by Obled [OBL 87], and from the works published
by his team at the Institute of Mechanics in Grenoble, France [CRE 79] [TOU 81;
LEB 84]. The research carried out by Obled may, at first, seem to be quite complex
and may also seem to have little to do with the world of physics. This research has
played an essential role in helping people effectively use the computing tools widely
available today.
7.2.1.1.
Rainfall: a random function of order 2
Where:
- R is a numerical value at a point
x
G
in a given domain D;
-
ω
is an event taken from a set
Ω
;
- P is a measurement of probability so that:
P
(
Ω
)
=
∫
Ω
P
(
d
ω
)
=
1
.
Rx
G
is the total amount of rainfall
that has been recorded by a rain gauge located at a point
x
G
in a particular region
being investigated, noted as D. The period of investigation is noted as t and begins
with an instantωrecorded during the nighttime Ω .
G
is a random function. For example
Rxω
(, )
(, )
G
=
G
If an event
ω is fixed, then the function
f
(
x
)
R
(
x
,
ω
)
is a trajectory of
k
k
f
k
G
can be represented by
isohyetal curves measured between the instants of
ω
and
ω
+ t.
R
G
. As far as rainfall is concerned, the function
(
x
)
( ω
)
