Calculation of Areal Rainfall Using Finite Element Techniques With Altitudinal Corrections

Abstract

A procedure for calculating areal rainfall, based on recent innovations in finite element analysis, is presented. The procedure involves the use of interpolation functions, allowing an accurate representation of the shape and relief of the catchment, with numerical integration performed by Gaussian quadrature. Each raingauge is allotted two weights, one associated with the rainfall reduced to a datum, and the other with the rainfall-altitude relationship. The latter weight effectively removes any systematic errors due to altitudinal bias of the network.The rainfall-altitude relationship, derived for individual storms and for synoptic situations for a small area, is used to show that errors due to the bias of the network can be considerable. RESUMEUn procede pour Ie calcuI de precipitation-surface, base sur des innovations recentes dans Ie domaine de l'analyse des elements finis est presentee Ce procede comparte l'emploi des fonctions d'interpolation, ce qui permet une representation exacte de la forme et du relief du bassin de captage, avec l'integration numerique qui s'effectue par la quadrature de Gauss. Chaque pluviometre est affecte de deux poids, l'un qui correspond a la precipitation ramenee a une donnee, l'autre qui correspond au rapport entre la precipitation et l'altitude. Ce dernier poids supprime toutes Ie erreurs systematiques caussees par la deviation de I'altitude du reseau.Le rapport entre la precipitation et l'altitude, derive pour Ie cas des averses individuelles et pour les situations synoptiques, pour une petite surface, est utilise pour demontrer que les erreurs causees par la deviation du reseau peuvent ctre considerables.

COMPARING SOME METHODS OF ESTIMATING MEAN AREAL RAINFALL1

“…(1974); Singh andBirsoy (1975a, 1975b); Singh (1976); Kruizinga and Yperlaan (1978); Sanderson and Alimed (1979) RDS McGuiness and Harold (1965); Solomon, et at. (1968); Brooks and McWhorter (1969); Pentland and Cuthbert (1971); Wei and McGuiness (1973); Singh andBirsoy (1975a, 1975b); Dean and Snyder (1977); Simanton and Osborn (1980) TA Bethialimy (1976) MP Pande and Al-Mashidani (1978) FE Akin (1971); Hutchinson and Walley (1972) AV Clarke and Edwards (1972) easiest and fastest methods, provided comparable results. TSA-QUAD and TSA-CUB, the more complex forms of TSA, did not appear to have any particular advantage over TSA-LINa departure from the findings of Mandeville and Rodda (1970).…”