Odyssée- versus hand- differentiation of a terrain-modelling application
by
Bernard Cappelaere
IRD - UMR 5569 , Montpellier, France
Coauthors: David Elizondo (IRD), Christele Faure (INRIA)

Modeling of earth surface processes such as land-water interactions at the hillslope and catchment scales, requires efficient procedures for parameter adjustment against sparse and diverse data. To this end, the Odyssée software has been tested on a sample application that solves a 2D non-linear diffusion-type equation for terrain modeling. Both the forward and the reverse differentiation modes have been implemented. A comparison is made with a manually-produced differentiated code (MD) for this application, obtained by solving the adjoint equations associated with the model's discrete state equations. The performances of the codes produced by the manual and automatic methods are compared, in terms of accuracy and of computing efficiency (CPU and memory needs). The perturbation method (finite-difference approximation of derivatives) is used as a reference. Based on the test of Taylor, the accuracy of the two AD modes proves to be excellent and as high as machine precision permits. Comparatively, the manually-produced derivatives (MD) sometimes appear to be slightly biased, which is likely due to the fact that a theoretical model (state equations) and a practical model (computer program) do not exactly coincide; the accuracy of the perturbation method is very uncertain. The MD code largely outperforms all other methods in computing efficiency.

http://homepages.feis.herts.ac.uk/~comqun/AD2000/Ext_Abstracts/cappelear.ps

Date received: February 11, 2000