Study of the Continuous Parametric Fields Theory applyed to variables without agregation

The Theory of the Continuous Parametric Fields has been developed by the engineer Mario Silber in the year 1985 to model the areal distribution of continuous variables, such as rainfalls, temperatures, pressures, starting from the determination of a space correlations field.

The suppositions adopted in the original theory make that it appropiately fits if the work is done with variables of high aggregation level, that is to say, monthly values, seasonal and annual means. In this case the space correlation field may be assumed as isotropic.

When the variables under study don't present any aggregation, as for example in the study of the rainfall corresponding to a storm, the isotropic supposition is no longer valid. The form of the field will not depend only on the properties of the network of data acquisition but also of the peculiar characteristics of the event that it is simulated, those that are not softened when the aggregation of the variables do not exist.

It becomes necessary then to study the behavior of the model in this situation, looking for to show the behavior of their parameter in relation with the variations on the characteristics of the event, in order to obtain a tool that allows the estimate of data in points without capture of information or the fullfilment of data lack.

Associating theoretical fields to precipitation events and through the adjustment of the results of the model with these perfectly controlled fields, that is to say of those with known generating function, it can be defined a behavior of the model parameter.

The present work proposes a way of estimation of this parameter, keeping in mind the structure of the network of data acquisition, its density and scatter, and a storm pattern, through the adjustment of empiric functions.

Through the overlapping of surfaces defined by planes, normal cylinders and binormal distributions, on a ideal basin the rainfall fields corresponding to different types of events are obtained. These surfaces are simulated then with the model for different structures of the network, verifying the variations suffered by the model parameter in each case.

Starting from these obtained data, empiric relationships that facilitate their estimate may be found, depending on simpler characteristics.