Bayesian maximum entropy data fusion of field-observed leaf area index (LAI) and Landsat Enhanced Thematic Mapper Plus-derived LAI

Accurate high-resolution leaf area index (LAI) reference maps are necessary for the validation of coarser-resolution satellite-derived LAI products. In this article, we propose an efficient method based on the Bayesian Maximum Entropy (BME) paradigm to combine field observations and Landsat Enhanced Thematic Mapper Plus (ETM+)-derived LAI surfaces in order to produce more accurate LAI reference maps. This method takes into account the uncertainties associated with field observations and with the regression relationship between ETM+-derived LAI and field measurements to perform a non-linear prediction of LAI, the variable of interest. In order to demonstrate the difference by soft data and hard data, we estimate the LAI reference maps by three BME interpolation methods, BME1, BME2, and BME3. BME1 and BME2 perform maximum estimation and mean estimation, respectively, by taking the ETM+-derived LAI as interval soft data and the field LAI measurements as hard data. BME3 is utilized when ETM+-derived LAI surfaces are processed as uniform probability soft data and field measurements are processed as Gaussian probability soft data. Three study sites are selected from the BigFoot project (NASA's Earth Observing System validation programme) (http://www.fsl.orst.edu/larse/bigfoot/index.html). In regard to the mean and standard deviation of LAI surfaces, standard deviation predicted by BME methods has lower values than that derived by ETM+. The mean value of the BME-predicted LAI, which takes into account the uncertainties of field measurements, is lower than that of ETM+-derived LAI at each study site. A comparison with field measurements shows that BME1, BME2, and BME3 have root mean square errors (RMSE) of 0.455, 0.485, and 0.517 and average biases of −0.017, −0.010, and −0.304, respectively. The RMSEs and biases of the predicted LAI surfaces are less when compared to the ETM+-derived LAI, which has the average RMSE and bias of 0.642 and −0.080. When the field measurements are processed as soft data, the predicted LAI by BME3 has more bias than those of the predictions by BME1 and BME2, but has less RMSE than that of the ETM+-derived LAI by 0.125. In summary, BME is capable of incorporating the spatial autocorrelation and the uncertainties in the field LAI measurements into the LAI surface estimation to produce a more accurate LAI surface with less RMSE in validation. The maximum estimation has relatively better accuracy than the mean estimation. The results indicate that the BME is a promising method for fusing point-scale and area-scale data.