Combining auxiliary variables and field inventory data of forest parameters using the model-based approach is frequently used to produce synthetic estimates for small areas. These small areas arise when it may not be financially feasible to take ground measurements or when such areas are inaccessible. Until recently, these estimates have been calculated without providing a measure of the variance when aggregating multiple pixel areas. This paper uses a Random Forest algorithm to produce estimates of quadratic mean diameter at breast height (QMDBH) (cm), basal area (m${}^2$ ha${}^{-1}$), stem density (n/ha${}^{-1}$), and volume (m${}^3$ ha${}^{-1}$), and subsequently estimates the variance of multiple pixel areas using a k-NN technique. The area of interest (AOI) is the state owned commercial forests in the Slieve Bloom mountains in the Republic of Ireland, where the main species are Sitka spruce (Picea sitchensis (Bong.) Carr.) and Lodgepole pine (Pinus contorta Dougl.). Field plots were measured in summer 2018 during which a lidar campaign was flown and Sentinel 2 satellite imagery captured, both of which were used as auxiliary variables. Root mean squared error (RMSE%) and R${}^2$ values for the modelled estimates of QMDBH, basal area, stem density, and volume were 19% (0.70), 22% (0.67), 28% (0.62), and 26% (0.77), respectively. An independent dataset of pre-harvest forest stands was used to validate the modelled estimates. A comparison of measured values versus modelled estimates was carried out for a range of area sizes with results showing that estimated values in areas less than 10–15 ha in size exhibit greater uncertainty. However, as the size of the area increased, the estimated values became increasingly analogous to the measured values for all parameters. The results of the variance estimation highlighted: (i) a greater value of k was needed for small areas compared to larger areas in order to obtain a similar relative standard deviation (RSD) and (ii) as the area increased in size, the RSD decreased, albeit not indefinitely. These results will allow forest managers to better understand how aspects of this variance estimation technique affect the accuracy of the uncertainty associated with parameter estimates. Utilising this information can provide forest managers with inventories of greater accuracy, therefore ensuring a more informed management decision. These results also add further weight to the applicability of the k-NN variance estimation technique in a range of forests landscapes.

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.