Application of the Expectation Maximization Algorithm to Estimate Missing Values in Gaussian Bayesian Network Modeling for Forest Growth

The leaf area index (LAI) is a biophysical variable related to atmosphere-biosphere exchange of CO
₂
. One way to obtain LAI value is by the Moderate Resolution Imaging Spectroradiometer (MODIS) biophysical products. In this paper, we use this product to improve the physiological principles predicting growth model within a Gaussian Bayesian network (GBN) setup. The MODIS time series, however, contains gaps caused by persistent clouds, cloud contamination, and other technique problems. We used the Expectation Maximization (EM) algorithm to estimate these missing values. During a period of 26 successive months, the EM algorithm is applied to four different cases: successively and not successively missing values during two different winter seasons, successively and not successively missing values during one spring season, and not successively missing values during the full study. Results show that the maximum value of the averaged absolute error between the original values and those estimated equals 0.16. This low value indicates that the estimated values well represent the original values. Moreover, the root mean square error of the GBN output reduces from 1.57 to 1.49 when performing the EM algorithm to estimate the not successively missing values. We conclude that the EM algorithm within a GBN can adequately handle missing MODIS LAI values and improves the estimation of the LAI.