# Annualmeeting:2017 CSDMS meeting-109

# Rapid algorithm for convolution integral-like flux formulations

**Tyler Doane**,

*Vanderbilt University Nashville Tennessee, United States*. 1218 Villa Place, Apt B

- David Furbish,
*Vanderbilt University Nashville Tennessee, United States*. david.j.furbish@vanderbilt.edu

[[Image:|300px|right|link=File:]]Recent research has highlighted the idea that long distance particle motions can be a significant component of the hillslope sediment flux. In this situation, mathematical descriptions of hillslope sediment transport must be nonlocal. That is, the flux at a position x, is a weighted function of conditions around x. This contrasts with local conditions which state that the flux is only a function of conditions at x. There are several ways to incorporate nonlocality into a mathematical description of sediment transport. Here, we focus on implementing and testing a convolution integral-like formulation. In this case, the flux is a convolution integral of a volumetric entrainment rate and a kernel that is related to the probability distribution of particle travel distance. Computation of convolution integrals is typically done by taking advantage of the convolution theorem for Fourier transforms, where a convolution integral becomes multiplication in wavenumber domain. However, in our case, the kernel is a function of position, and therefore precludes us from taking advantage of this method. Here, we apply a method that can reduce the problem back to a proper convolution integral and therefore allows for rapid computation (Gilad and von Hardenberg, 2006). We use this method to demonstrate nonlocal transport on lateral moraines on the east side of the Sierra Nevada. This method has applications in all convolution integral-like formulations including nonlinear filtering.