Assimilation of SPOT/VEGETATION NDVI data into a sahelian vegetation dynamics model

This paper presents a method to monitor the dynamics of herbaceous vegetation in the Sahel. The approach is based on the assimilation of Normalized Difference Vegetation Index (NDVI) data acquired by the VEGETATION instrument on board SPOT 4/5 into a simple sahelian vegetation dynamics model. The study region is located in the Gourma region of Mali. The vegetation dynamics model is coupled with a radiative transfer model (the SAIL model). First, it is checked that the coupled models allow for a realistic simulation of the seasonal and interannual variability of NDVI over three sampling sites from 1999 to 2004. The data assimilation scheme relies on a parameter identification technique based on an Evolution Strategies algorithm. The simulated above-ground herbage mass resulting from NDVI assimilation is then compared to ground measurements performed over 13 study sites during the period 1999-2004. The assimilation scheme performs well with 404 kg DM/ha of average error (n = 126 points) and a correlation coefficient of r = 0.80 (to be compared to the 463 kg DM/ha and r = 0.60 of the model performance without data assimilation). Finally, the sensitivity of the herbage mass model estimates to the quality of the meteorological forcing (rainfall and net radiation) is analyzed thanks to a stochastic approach.     

Using hash tables to manage the time-storage complexity in a point location problem: Application to explicit model predictive control

The online computational burden of linear model predictive control (MPC) can be moved offline by using multi-parametric programming, so-called explicit MPC. The solution to the explicit MPC problem is a piecewise affine (PWA) state feedback function defined over a polyhedral subdivision of the set of feasible states. The online evaluation of such a control law needs to determine the polyhedral region in which the current state lies. This procedure is called point location; its computational complexity is challenging, and determines the minimum possible sampling time of the system. A new flexible algorithm is proposed which enables the designer to trade off between time and storage complexities. Utilizing the concept of hash tables and the associated hash functions, the proposed method solves an aggregated point location problem that overcomes prohibitive complexity growth with the number of polyhedral regions, while the storage–processing trade-off can be optimized via scaling parameters. The flexibility and power of this approach is supported by several numerical examples.