Assessing spatial variability and estimating mean crown diameter in boreal forests using variograms and amplitude spectra of very-high-resolution remote sensing data

The retrieval of forest variables from optical remote sensing data using physically-based models is an ill-posed problem and does not make full use of the high spatial resolution imagery that is becoming available globally. A possible solution to this is to use prior information about the retrieved variables, which constrains the possible solutions and reduces uncertainty in forest variable estimation. Therefore, we tried to quantify physically-based parameters that could be retrieved using the second-order statistics of measured and simulated very-high-resolution (pixel size less than 1 m) images of Finnish boreal forests. These forests have a well-defined structure and are usually not closed, i.e. the reflected signal has a considerable contribution from a green forest floor. We retrieved the second-order statistics using variograms and Fourier amplitude spectra. We found, in line with previous studies, that the range of variograms correlates well (r = 0.83) with the mean crown diameter for spatially homogeneous forest patches, and it can be used to estimate crown diameters with reasonable accuracy (RMSE = 0.42 m). We present a novel approach, which uses the Fourier amplitude spectrum to study the spatial structure of a forest. The approach provided encouraging results with the measured data: despite the lower accuracy (RMSE = 0.67 m) compared with variograms, we found that it could also be used to estimate mean crown diameters for heterogeneous forest areas. The Fourier amplitude spectrum approach did not work with the simulated images. Our results highlight the possibility to obtain further information from very-high-resolution images of forests to solve the ill-posed problem of forest variable estimation from optical remote sensing data using physically-based models.