Geoscience Reference
In-Depth Information
- V
2
Y. R
2
= the variance explained by the regression model,,
- V
2
Y (1- R
2
) = variance of the residuals.
As is the case for a simple regression, each regression coefficient measures the
change that takes place within the dependent variable Y, whenever an independent
variable x
1
, x
2
..., x
n
varies by one unit, the other variables remain constant.
In addition to the search for other variables, one of the keys behind the
improvements that have been made to the model in case of a poor correlation, is the
delinearization of the relationship that we want to obtain. The correlation can be
improved by the use of a power law (for example, taking square roots), or by using
a logarithmic law. The easiest way to improve the correlation is to keep the
traditional calculation used to calculate the linear correlation coefficient , which was
developed by Bravais-Pearson, and to transform the data by anamorphosis. As a
result of the calculations carried out, a data matrix is created, in which, for instance,
the variable “distance from the sea” does not relate to the total distance from the sea
but rather to the square root of the total distance.
This approach, which is focused on geography, requires some previous
knowledge on the topic, which is based on experience [CAR 94”]. The equation
generated as a result is all the more representative of the statistical relationships that
exist between climate and the environment so as correlation coefficient is high.
Resolving the equation for each value of Y for which the independent X variables
are known, makes it possible to provide data for the entire area in question.
At this point for each regression a choice needs to be made between the quest for
the best regressors (independent variables), and to use a list that has been created
containing a weak number of X variables which are always the same. It is also a
very good idea to monitor the influence that altitude and distance from the sea have
on these variables, in other words, to check whether the effects of altitude and
distance from the sea are constant or whether they change on a daily, weekly, or
monthly basis, etc.
The formal separation of the determinist and empirical approaches is not so clear
cut: the choice of independent variables used is linked to the world of physics.
Altitude decreases the effect that the ground roughness has on the wind, and it
expresses a decrease in air pressure that influences air temperature. Distance from
the sea influences the frequency and intensity of sea air advection currents. Relative
altitude (which compares the location of an area to a base level) controls the
nocturnal thermal inversion, which is linked to a strong level of terrestrial radiation
at night-time etc.
Other possibilities also exist, such as those that are part of the NUATMOS
model [ROS 88], which combines the advantages of both the empirical approach
(using data generated by a network) and the advantages associated with fluid
