Section: New Results

Calibration of the TRANUS Land Use Module

The setting up of a LUTI model requires, like most numerical models, at least one phase of parameter estimation. This is concisely referred to here as calibration, although the calibration of a LUTI model also entails other aspects such as the definition of spatial zones, of economic sectors, etc. The TRANUS LUTI model plus software, like many other existing models, come along with a relatively simple calibration methodology. Most LUTI models indeed perform parameter estimation in a piecewise fashion, by sequentially estimating subsets of parameters. While this reduces the mathematical and computational complexity of calibration, neglecting the interactions across different modules and their parameters, may result in a significant loss of a model's quality. A second issue is that TRANUS, like several other LUTI softwares, employs rudimentary numerical routines for parameter estimation. We aim at reducing these weaknesses.

To do so, we first defined a particular parameter estimation problem for TRANUS properly as an optimisation problem, based on an explicit cost function that is to be minimised (something lacking in many articles on LUTI calibration). Next, we developed a series of numerical estimation schemes to solve this optimisation problem. The main difficulty here was that the model is dynamic; by delving into the model's equations and structure, we were able to unwind the model's dynamics and to make it amenable to standard numerical optimisation by gradient descent type methods [4] . This was first done for the estimation of a particular subset of model parameters (the so-called shadow prices). We have recently started to work on the simultaneous estimation of these and other model parameters.

This work is done in collaboration with Arthur Vidard from the MOISE Inria project-team and Brian Morton from the University of North Carolina at Chapel Hill.