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Imputation

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  1. Imputation Accounting For Tree Species As Well As Size Differences Projecting tree lists from known points of ground observation to inventory polygons that have not yet been sampled. Ian Moss ForesTree Dynamics Ltd Victoria B.C.

  2. Outline • Study location. • Basic imputation process (stand structure classification). • Two approaches to account for species dominance patterns (rule based vs using empirical evidence). • Some thoughts and conclusions on the relative merits of the two.

  3. Cariboo – 2 Million Hectares North Central – 6 Million Hectares

  4. The Basic Process 1. Ground-plot data: Assess degree of similarity, use distance matrix to develop stand structure classification.

  5. Contrast Plot-Polygon Pairs LN(ODDS) = Assume that two polygons with the same level of attribute expression belong to the same stand structure class.

  6. Imputation 3. Use log odds relationship to: a) Impute k-nearest known plot-polygon pairs. b) Compile stand and stock tables (then classify). or: • Modify stand structure classification plot assignments to account for within class (polygon) variation. • Compile stand and stock tables. • Impute modified stand structure classes.

  7. Adjust Stand & Stock Statistics Adjust trees per hectare to ensure that the stand and stock table total volume (or basal area) by species is equal to the polygon estimates. (Re) classify adjusted statistics based on original classification.

  8. Quick Review • Stand structure classification. • Contrast plot-polygon pairs: calibrate function. • Imputation • Adjustment So what about species?

  9. Species – 2 Scenarios • Stand structure classification independent of species – develop rules to integrate inventory polygon species into stand and stock table estimates. • Develop stand structure classification to explicitly account for species differences; incorporate species into steps 2 (calibrate function), 3 (imputation) & 4 (adjustment). i.e. brute force and ignorance (but feels good) versus: pin the tail on the donkey (includes pain & torture)

  10. Brute Force & Ignorance • Within a given zone assign a maximum dbh to each species. 2. Estimate the proportions (volume or basal area) of species from the inventory polygons. 3. Estimate the proportions (volume or basal area) by diameter class from imputation. 4. Reconcile 1,2 & 3 to estimate the proportions of species by diameter class. Multiply by total polygon volume or basal area. Adjust trees per hectare and related attributes proportionately.

  11. Reconciliation Repeat until convergence or 500 iterations, whichever is first. Multiply by total stand volume … and it is done.

  12. Pin The Tail On The Donkey 1799 Cruise Types 600 + Cruise Strata Sp – Age,Ht,Cc,SI Only a few species and species groups really well (over) represented. Include species explicitly in the stand structure classification … much more complex.

  13. … More On Tail Pinning 250 Stand Structure Classes This figure describes 1 of those classes. Sx – blue Bl – olive green Pl – forest green At - orange A compromise in precision – species vs. size

  14. … & other issues … • Frequent occurrences of weak associations of known polygon-plot pairs with unknown plot-polygon pairs (Log(odds) ratio’s). • Sometimes the k-nearest neighbours do not have all of the species recorded for an inventory polygon – what to do then?

  15. One Alternative Suggestion • Create an open ended, species based classification, with fewer classes (e.g. 25). • Use photo interpretation to apply the classification to a wide variety of stand conditions (census/sub-sample). • Use stratified random sampling to correct for error. • Integrate these steps into the imputation process.

  16. In the meantime … Brute Force and Ignorance … It is tidier … It feels better … Which comes first - tree size distribution, species, neither, both? Current strength … Stand structure classification … similarity on the ground used to calibrate similarity amongst polygons … stand structure classification is key to understanding & good communication. I am looking forward to hearing about other approaches. Thank you.