Publication

Erosion of soils due to rainfall impact – An interpolation method

David Andrew Barry, Marc Parlange, Alessandro Brovelli, Seifeddine Jomaa
2012
Journal Articles

Abstract

An approximate analytical solution of the Hairsine-Rose model of erosion is obtained by interpolation of asymptotic expressions for large times and great distances. The solution, when erosion is initiated by rainfall impact, is both simple and accurate. The results are illustrated by comparison with a numerical solution.

Official source

https://infoscience.epfl.ch/entities/publication/69741e1d-9bda-4030-8aee-398d15a6ec70

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David Andrew Barry, Marc Parlange, Alessandro Brovelli, Seifeddine Jomaa
2012
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/69741e1d-9bda-4030-8aee-398d15a6ec70

About this result

Ontological neighbourhood

Mathematics

Analysis: Numerical analysis

Related concepts (28)

Interpolation

In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.

Polynomial interpolation

In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each . There is always a unique such polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials.

Multivariate interpolation

In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable (multivariate functions); when the variates are spatial coordinates, it is also known as spatial interpolation. The function to be interpolated is known at given points and the interpolation problem consists of yielding values at arbitrary points . Multivariate interpolation is particularly important in geostatistics, where it is used to create a digital elevation model from a set of points on the Earth's surface (for example, spot heights in a topographic survey or depths in a hydrographic survey).

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