Puulajeittainen estimointi ja ei-parametriset menetelmät Multi-scale Geospatial Analysis of Forest Ecosystems Tahko Petteri Packalén Faculty of Science and Forestry

How to consider tree species? Stratification Inventory area is stratified as a separate step by main tree species Is this species-specific estimation at all? Estimation by tree species Individual tree approach Area based method Note: here the term species-specific growing stock refers to attributes obtained by tree species

Species-specific estimation by ALS data The estimation by tree species is rather difficult Species-specific estimates are substantially less accurate than the estimates of total characteristics Species-specific estimation may be practically impossible if the number of tree species is high or stand is multilayered by species How to relate ALS data to tree species – height or density does not correlate very well with tree species? Lidar intensity? Fusion of optical images and ALS point cloud Compatible stand description

Species-specific estimation by individual tree approach Detect and delineate individual trees Classify detected canopies by tree species Several classification methods have been tested Estimate tree attributes by tree species Aggregate to desired level

Species-specific estimation by individual tree approach Well-defined case – classify each tree Final error in species-specific stand attribute is an accumulated error in each processing step It may be difficult to trace back what is the reason for certain error at aggregated level Simultaneous NN imputation of all required tree attributes

Species-specific estimation by area based method Instead of classifying individual trees all stand attributes are estimated by tree species In mixed forests several tree species may or may not occur in the same estimation unit (e.g. plot or grid cell). Two principles: –First estimate whether a particular tree species occur or not. If occur estimate required attributes, if not set to zero or null. –Estimate attributes always for all tree species. For non-existing species prediction should be zero or null, i.e. rely on the capability of the estimation procedure to discover the non-existing tree species.

Compatibility in area based method Compatibility is important in practical applications. This means that: –estimator does not predict negative values –the sum of species-specific estimates is equal to the total estimate –attribute relations are logical; if mean diameter of pine is 7 cm mean height must be realistic, not e.g. 25 m Above requirements are difficult to fulfill by regression modeling, compatibility may be obtained e.g. by non-parametric methods

Accuracy Based on current knowledge it is impossible to state which approach is better in terms of species-specific estimates Aggregation improves the accuracy in both approaches (not related to species-specific estimation) It is very difficult – or at least expensive – to validate accuracy at the stand level since it requires separate validation measurements from trees to stand from cells to stand

Validity of accuracy assessment in terms of species-specific predictions RMSE is not always the best metric to assess the accuracy of species-specific attributes From the silvicultural point of view minority tree species are often less important –if there are 250m 3 /ha pine in a stand it is quite irrelevant whether the volume of spruce is estimated to be 5m 3 /ha or 10m 3 /ha RMSE of dominant tree species, RMSE of minor tree species, ignore “near zero” observations

Which one makes more sense?

Nearest Neighbor imputation Measure n predictor variables and one or more dependent variables on a set of observation units (Reference obs) Dependent variables are assigned to locations in an n-dimensional prediction space; dimensions are formed by the ranges of values of the n predictor layers Values of the dependent variables then can be imputed to other locations in the prediction space (Target obs) Numerous distance metrics, e.g. Euclidean, Manhattan, Minkowsky, Mahalanobis, MSN, RF etc.

Nearest Neighbor imputation Issues to consider –Distance metric, how to calculate weight matrix? Exhaustive search, heuristic algorithms, … In Mahalanobis and MSN weights are solved analytically –What is the optimal value of k? –How to weight NNs in order to obtain the estimate? Multiple dependent variables may be estimated simultaneously  often utilized in forestry applications

NN development in Kärkihanke Nearest Neighbor Imputation in Airborne Laser Scanning Based Forest Inventory –Visit at Oregon State University Two topics –Heuristic optimization in NN imputation –Tree list estimation in complex stands

Heuristic optimization in NN imputation A selection of an appropriate set of independent variables to the NN imputation is difficult and laborious taks There are several distance metrics used to define neighborhood  Use heuristic optimization to solve both tasks Select minimized goodness-of-fit criterion (e.g. weighted RMSE) Distance metric: weighted Euclidean distance Minimize goodness-of-fit criterion by SA, GA, …

Tree list estimation in complex stands

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