An Extended Fourier Approach to Improve the Retrieved Leaf Area Index (LAI) in a Time Series from an Alpine Wetland

An extended Fourier approach was presented to improve the retrieved leaf area index (LAIr) of herbaceous vegetation in a time series from an alpine wetland. The retrieval was performed from the Aqua MODIS 8-day composite surface reflectance product (MYD09Q1) from day of year (DOY) 97 to 297 using a look-up table (LUT) based inversion of a two-layer canopy reflectance model (ACRM). To reduce the uncertainty (the ACRM inversion is ill-posed), we used NDVI and NIR images to reduce the influence of the soil background and the priori information to constrain the range of sensitive ACRM parameters determined using the Sobol’s method. Even so the uncertainty caused the LAIr versus time curve to oscillate. To further reduce the uncertainty, a Fourier model was fitted using the periodically LAIr results, obtaining LAIF. We note that the level of precision of the LAIF potentially may increase through removing singular points or decrease if the LAIr data were too noisy. To further improve the precision level of the LAIr, the Fourier model was extended by considering the LAIr uncertainty. The LAIr, the LAI simulated using the Fourier model, and the LAI simulated using the extended Fourier approach (LAIeF) were validated through comparisons with the field measured LAI. The R2 values were 0.68, 0.67 and 0.72, the residual sums of squares (RSS) were 3.47, 3.42 and 3.15, and the root-mean-square errors (RMSE) were 0.31, 0.30 and 0.29, respectively, on DOY 177 (early July 2011). In late August (DOY 233), the R2 values were 0.73, 0.77 and 0.79, the RSS values were 38.96, 29.25 and 27.48, and the RMSE values were 0.94, 0.81 and 0.78, respectively. The results OPEN ACCESS Remote Sens. 2014, 6 1172 demonstrate that the extended Fourier approach has the potential to increase the level of precision of estimates of the time varying LAI

An Extended Fourier Approach to Improve the Retrieved Leaf Area Index (LAI) in a Time Series from an Alpine Wetland

An extended Fourier approach was presented to improve the retrieved leaf areaindex (LAIr) of herbaceous vegetation in a time series from an alpine wetland. The retrievalwas performed from the Aqua MODIS 8-day composite surface reflectance product(MYD09Q1) from day of year (DOY) 97 to 297 using a look-up table (LUT) based inversionof a two-layer canopy reflectance model (ACRM). To reduce the uncertainty (the ACRMinversion is ill-posed), we used NDVI and NIR images to reduce the influence of the soilbackground and the priori information to constrain the range of sensitive ACRM parametersdetermined using the Sobol"s method. Even so the uncertainty caused the LAIr versus timecurve to oscillate. To further reduce the uncertainty, a Fourier model was fitted using theperiodically LAIr results, obtaining LAIF. We note that the level of precision of the LAIFpotentially may increase through removing singular points or decrease if the LAIr data weretoo noisy. To further improve the precision level of the LAIr, the Fourier model wasextended by considering the LAIr uncertainty. The LAIr, the LAI simulated using the Fouriermodel, and the LAI simulated using the extended Fourier approach (LAIeF) were validatedthrough comparisons with the field measured LAI. The R2 values were 0.68, 0.67 and 0.72,the residual sums of squares (RSS) were 3.47, 3.42 and 3.15, and the root-mean-squareerrors (RMSE) were 0.31, 0.30 and 0.29, respectively, on DOY 177 (early July 2011). In lateAugust (DOY 233), the R2 values were 0.73, 0.77 and 0.79, the RSS values were 38.96,29.25 and 27.48, and the RMSE values were 0.94, 0.81 and 0.78, respectively. The resultsOPEN ACCESSRemote Sens. 2014, 6 1172demonstrate that the extended Fourier approach has the potential to increase the level ofprecision of estimates of the time varying LAI