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\begin{document}

\title{Application of small area variance estimates of forest parameters using
earth observation auxiliary variables and a k-Nearest Neighbours
technique.}



\author[1]{Dylan Walshe}%
\author[1]{Daniel McInerney}%
\author[1]{Joao Paulo Pereira}%
\author[2]{Kenneth A. Byrne}%
\affil[1]{Coillte}%
\affil[2]{University of Limerick}%


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  \date{June 13, 2024}


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\begin{abstract}
Combining auxiliary variables and ground data of forest parameters using
the model-based approach has become a frequently used methodology to
produce synthetic estimates for small areas. These small areas arise as
it may not be financially feasible to take ground measurements or some
areas may be inaccessible to ground-based personnel. Until recently,
these estimates have been calculated without providing a measure of the
variance or in large homogeneous forested areas where the variability
would be minimal. This paper uses a Random Forest algorithm to produce
estimates of QMDBH (cm) and volume (m3 ha-1) and a k-nn technique to
produce variance estimates in a previously unproven heterogeneous forest
environment. The area of interest (AOI) was the commercial forest in the
Slieve Bloom Mountains in the Republic of Ireland, where the majority
species are Sitka spruce (Picea sitchensis (Bong.) Carr.) and Lodgepole
pine (Pinus contorta Dougl.). Field plots were measured during the
Summer in 2018 during which a LiDAR campaign was flown and Sentinel 2
satellite imagery captured, which were both used as auxiliary variables.
Root mean squared errors (rmse) for the modeled estimates of QMDBH and
volume were 4.4 cm and 111 m3 ha-1 and the r2 values were 0.65 and 0.76
respectively. An independent dataset of pre-harvest forest stands was
used to validate the modeled variance estimates. The results showed that
73\% of QMDBH measurements and 60\% of volume measurements were within
the confidence intervals of the estimated values. The mean percentage
standard deviation for QMDBH and volume were 17\% and 21\% respectively.
This application of variance estimation in such a heterogeneous forest
landscape adds further weight to the applicability of the methodology in
a range of forest landscapes. This finding is extremely important as it
highlights the benefits of using earth observation data to produce
estimates and confidence intervals for small areas in heterogeneous
forest landscape.%
\end{abstract}%



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