Inverting a canopy re ̄ ectance model using a neural network

An o-nadir canopy re¯ ectance model, the Liang and Strahler algorithm for the Coupled Atmosphere and Canopy (CAC) model, was used to simulate multi-angle re¯ ectances based on various combinations of canopy bio-physical parameters. Biophysical parameters such as leaf angle distribution (LAD) and leaf area index (LAI) were input to the CAC model along with re¯ ectances of leaf and soil and aerosol optical depth. The CAC model, however, can only be inverted through numerical iterations and it is extremely di cult to use for retrieval of those biophysical parameters with ordinary inversion methods. In order to retrieve those biophysical parameters, we employed an error back-propagation feed-forward neural network program. We constructed a number of neural network models based on the simulated results from the CAC model. In this paper, we report the results obtained from retrieving any individual parameter from multi-angle re¯ ectances and results obtained from simultaneously retrieving some combinations of two parameters and ® ve parameters. We tested the use of a di erent number of multi-angle re¯ ectances as input to the neural networks. This number varied in the range 1± 64. The test results showed that a relative error between 1 and 5% or better was achievable for retrieving one parameter at a time or two parameters simultaneously. The relative errors for two of the ® ve simultaneously retrieved parameters were less than 17%. The amount of computation required by simultaneous retrieval of ® ve parameters was prohibitively high for a regular workstation.