Imputation

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.

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Cariboo 2 Million Hectares North Central 6
Million Hectares
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The Basic Process
1. Ground-plot data Assess degree of
similarity, use distance matrix to develop stand
structure classification.
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Contrast Plot-Polygon Pairs
LN(ODDS)
Assume that two polygons with the same level of
attribute expression belong to the same stand
structure class.
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Imputation
3. Use log odds relationship to
a) Impute k-nearest known plot-polygon pairs.
b) Compile stand and stock tables (then classify).
or

1. Modify stand structure classification plot
   assignments to account for within class
   (polygon) variation.
2. Compile stand and stock tables.
3. Impute modified stand structure classes.

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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.
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Quick Review

1. Stand structure classification.
2. Contrast plot-polygon pairs calibrate function.
3. Imputation
4. Adjustment

So what about species?
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Species 2 Scenarios

1. Stand structure classification independent of
   species develop rules to integrate inventory
   polygon species into stand and stock table
   estimates.
2. Develop stand structure classification to
   explicitly account for species differences
   incorporate species into steps 2 (calibrate
   function), 3 (imputation) 4 (adjustment).

brute force and ignorance (but feels good)
i.e.
pin the tail on the donkey (includes pain
torture)
versus
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Brute Force Ignorance

1. 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.
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Reconciliation
Repeat until convergence or 500 iterations,
whichever is first. Multiply by total stand
volume and it is done.
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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.
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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
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other issues

• Frequent occurrences of weak associations of
  known polygon-plot pairs with unknown
  plot-polygon pairs (Log(odds) ratios).
• Sometimes the k-nearest neighbours do not have
  all of the species recorded for an inventory
  polygon what to do then?

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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.

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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.