Application of the EM-algorithm for Bayesian Network Modelling to Improve Forest Growth Estimates

Leaf area index (LAI) is a biophysical variable that is related to atmosphere-biosphere exchange of CO2. One way to obtain LAI value is by the Moderate Resolution Imaging Spectroradiometer (MODIS) biophysical products (LAI MODIS). The LAI MODIS has been used to improve the physiological principles predicting growth (3-PG) model within a Bayesian Network (BN) set-up. The MODIS time series, however, contains gaps caused by persistent clouds, cloud contamination, and other retrieval problems. We therefore formulated the EM-algorithm to estimate the missing MODIS LAI values. The EM-algorithm is applied to three different cases: successive and not successive two winter seasons, and not successive missing MODIS LAI during the time study of 26 successive months at which the performance of the BN is assessed. Results show that the MODIS LAI is estimated such that the maximum value of the mean absolute error between the original MODIS LAI and the estimated MODIS LAI by EM-algorithm is 0.16. This is a low value, and shows the success of our approach. Moreover, the BN output improves when the EM-algorithm is carried out to estimate the inconsecutive missing MODIS LAI such that the root mean square error reduces from 1.57 to 1.49. We conclude that the EM-algorithm within a BN can handle the missing MODIS LAI values and that it improves estimation of the LAI.