Assessing Error Correlations in Remote Sensing-Based Estimates of Forest Attributes for Improved Composite Estimation

Abstract

Today, non-expensive remote sensing (RS) data from different sensors and platforms can be obtained at short intervals and be used for assessing several kinds of forest characteristics at the level of plots, stands and landscapes. Methods such as composite estimation and data assimilation can be used for combining the different sources of information to obtain up-to-date and precise estimates of the characteristics of interest. In composite estimation a standard procedure is to assign weights to the different individual estimates inversely proportional to their variance. However, in case the estimates are correlated, the correlations must be considered in assigning weights or otherwise a composite estimator may be inefficient and its variance be underestimated. In this study we assessed the correlation of plot level estimates of forest characteristics from different RS datasets, between assessments using the same type of sensor as well as across different sensors. The RS data evaluated were SPOT-5 multispectral data, 3D airborne laser scanning data, and TanDEM-X interferometric radar data. Studies were made for plot level mean diameter, mean height, and growing stock volume. All data were acquired from a test site dominated by coniferous forest in southern Sweden. We found that the correlation between plot level estimates based on the same type of RS data were positive and strong, whereas the correlations between estimates using different sources of RS data were not as strong, and weaker for mean height than for mean diameter and volume. The implications of such correlations in composite estimation are demonstrated and it is discussed how correlations may affect results from data assimilation procedures.

Potential of Bayesian formalism for the fusion and assimilation of sequential forestry data in time and space

“…To gain benefits, the estimates from the different time points or data sources must be properly weighted, which is typically caried out by assigning weightings (inversely) proportional to the variance of the different estimates. Work by Lindgren et al (2017) assimilating multiple time points (and the follow-up by Ehlers et al, (2018) that was based on analyzing the correlations of the non-independent errors of these estimates) provide ideas and "rules-of-thumb" as to the value of the weightings. In Lindgren et al (2017), the predictions that used past data received a greater weighting than the new data after 2-3 assimilations (depending on the forest attributes), and the weighting placed on new acquisitions was < 10% after ≈7 acquisitions.…”

“…Although the performance varied in estimating forest attributes based on single data acquisitions, the variation associated with the assimilated result decreased and stabilized after the first iterations. Yet, all benefits of assimilating past data were not necessarily visible due to an underestimation in the variances of inter-correlated estimates (Ehlers et al, 2018). According to Ehlers et al (2018), independent observations based on a different acquisition technique or estimation method should receive a greater weighting as they are less correlated.…”

“…Yet, all benefits of assimilating past data were not necessarily visible due to an underestimation in the variances of inter-correlated estimates (Ehlers et al, 2018). According to Ehlers et al (2018), independent observations based on a different acquisition technique or estimation method should receive a greater weighting as they are less correlated. A graphical analysis of the values in Ehlers et al (2018) suggests that even two time-points based on independent sensors or modeling should not be treated equally, i.e., combined with the same weighting, but that the correlation of the errors should be accounted for in the variance estimates.…”

“…According to Ehlers et al (2018), independent observations based on a different acquisition technique or estimation method should receive a greater weighting as they are less correlated. A graphical analysis of the values in Ehlers et al (2018) suggests that even two time-points based on independent sensors or modeling should not be treated equally, i.e., combined with the same weighting, but that the correlation of the errors should be accounted for in the variance estimates. In cases of availability and the use of accurate auxiliary data, the resulting overall error might not be significantly lowered compared to the use of prior inventory data or accurate auxiliary data (Nyström et al, 2015;Kangas et al, 2020), although the internal consistency of the estimates could be improved to a degree that is beneficial for later applications.…”