Propriedades fundamentais dos splines cúbicos uni e bidimensionais: aplicações em hidrologia

Abstract

The growing need for a better use of the waters of the reservoirs of the Northeast Region has given us a challenge: to provide the specialists with mathematical methods that allow them to know more deeply the mechanisms that act on these reservoirs. One of the mechanisms that hydrologists consider important to study is the phenomenon of sedimentation of a pond bed. For this, we constructed an algorithm capable of providing a surface, corresponding to the bed of the pond, and that can be visualized. Another study that is wished to do is more immediate: to determine the volume of the reservoir at a given moment from the height of the water slide, provided by a limnimetric ruler, and a graph of height versus volume. How to build such a chart was another of our tasks. This monograph presents the main properties of the cubic and bicubic splines to support two methods: the first uses cubic spline integrals to calculate volumes under surfaces of which we only know a finite number of points (arranged according to a rectangular mesh). The second uses bicubic splines to represent such surfaces.