Abstract
The boreal tree line is in many places expected to advance upwards into the mountains due to climate change. This study aimed to develop a general method for estimation of vegetation height change in general, and change in tree height more specifically, for small geographical domains utilizing bi-temporal airborne laser scanner (ALS) data. The domains subject to estimation may subsequently be used to monitor vegetation and tree height change with detailed temporal and geographical resolutions. A method was developed with particular focus on statistically rigorous estimators of uncertainty for change estimates. The method employed model-dependent statistical inference. The method was demonstrated in a 12 ha study site in a boreal–alpine tree line in southeastern Norway, in which 316 trees were measured on the ground in 2006 and 2012 and ALS data were acquired in two temporally coincident campaigns. The trees ranged from 0.11 m to 5.20 m in height. Average growth in height was 0.19 m. Regression models were used to predict and estimate change. By following the area-based approach, predictions were produced for every individual 2 m2 population element that tessellated the study area. Two demonstrations of the method are provided in which separate height change estimates were calculated for domains of size 1.5 ha or greater. Differences in height change estimates among such small domains illustrate how change patterns may vary over the landscape. Model-dependent mean square error estimates for the height change estimators that accounted for (1) model parameter uncertainty, (2) residual variance, and (3) residual covariance are provided. Findings suggested that the two latter sources of uncertainty could be ignored in the uncertainty analysis. The proposed estimators are likely to work well for estimation of differences in height change along a gradient of small monitoring units, like the 1.5 ha cells used for demonstration purposes, and thus may potentially be used to monitor tree line migration over time.
Highlights
The world’s climate will undergo distinct alterations over the coming decades, leading to rapid changes in basic growth factors, such as temperature and precipitation
Because the montane and northern forests found in the transition zones between the boreal forest and the alpine and tundra regions appear in areas where trees exist close to their tolerance limit in terms of temperature, these areas are characterized by steep temperature–productivity gradients
Because trees measured in the field on both occasions were required for constructing the model of height change using the airborne laser scanner (ALS) data, only trees that had laser recordings within their crown periphery at both points in time could be used for height change modeling
Summary
The world’s climate will undergo distinct alterations over the coming decades, leading to rapid changes in basic growth factors, such as temperature and precipitation. Numerous recent studies (e.g., [16,17,18]) have shown that ALS data with point densities of 7–11 points m−2 may be applied to detect individual pioneer trees in the alpine tree line With such pulse densities, about 90–100% of the trees with heights greater than 1 m are likely to be hit by laser pulses, resulting in echoes with height values greater than zero, i.e., located above the terrain surface. Næsset and Nelson [11] proposed a statistical sampling approach by which the mean difference (net change) in height for all echoes in a defined minimum monitoring unit, for example, 1 ha, is followed over time. Under such an approach, identification of individual trees is not a concern. The bi-temporal data used in the current study covered a time span of six years
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