## Acadian Variant Height Model

The current default (recommended) tree height model is a non-linear (Weibull) function of Zone (NS, NB, PE, ME), BGI, Species, DBH, basal area, QMD, and basal area of larger trees. Each species model was fit independently and not all variables were used in each model depending on available data. Each species model was also assessed for extrapolation issues, and where issues were found, the model was constrained where possible. Individual height predictions can be boosted if a sub-sample of height trees are available in the survey data. This boosting occurs automatically on loading of the tree list if heights are present.

Fit by C.R. Hennigar, NB ERD 2017.

### Height Calculation Procedure

Tree height is predicted first using the current height model described above that includes species-specific tree height equations. When height observations are available in the plot or stand, the predictions are progressively boosted using:

1) A Lorey’s height estimate from observed heights when height samples are > 5 in the plot, and

2) Species-level bias correction multipliers derived from least squared analysis of differences between observed and predicted heights when height samples per species are > 5 in the plot.

Height equations vary in form and parameters by species and Zone and most equations require Biomass Growth Index (BGI), stand basal area per hectare (BA; >= 1 cm DBH), and BA of trees thicker than the subject tree (BAL). Stand and tree structural metrics like BAL are calculated internally by OSM.

#### Step 1: Tree height prediction

Equation forms and number of parameters (b0-b5) vary by species. The equation example below is for balsam fir. This result would be used ‘as is’ if there are < 5 trees measured for height in the plot.

This step is implemented by the Variant Model.

#### Step 2: Tree height prediction adjustment with estimated Lorey’s height.

If number of height samples from a plot is ≥ 5, then the HT1 prediction above is boosted (accuracy improved on average) using estimated Lorey’s height (LHT):

Note that in this case, LHT is calculated only from tree height observations; i.e., no individual height predictions for trees with missing tree heights are used. Proper weighting of height samples in the OSM_TreeList is important to yield accurate LHT estimates for purposes of height model boosting. See OSM.AcadianModel.InputTables.OSM_TreeList.Weight and OSM.Simulation.Model.HeightModel to understand how to set weights on individual tree heights in the input tree list in order to properly calculate Lorey’s height (LHT) for alternative plot designs (fixed area, point sampling, or hybrid approaches).

If no weights are provided by the user, the model assumes the heights were collected with point sampling and an average of sampled heights is computed. It is impossible for the program to know if the plot is fixed or variable radius, or whether height is expressed as an average in a DBH class tally. Here we assume that heights are measured with individual tree resolution with sample probability proportional to tree size (basal area). This is the most common sampling procedure for timber cruises using height sub-sampling.

This step is implemented by the Variant Model.

As of June 2nd 2019

· Issues with tree agitation artificially inflating height sample size were fixed.

As of August 16th 2019

· LHT prediction boosting was omitted when LHT < 4 m or > 20 m, or when DBH < 5 cm or > 50 cm. LHT adjustment can result in very odd height predictions in these extreme cases, under some circumstances. These extremes are also at the upper and lower end of data used to fit the model, so this constraint avoids erroneous extrapolation (doing more harm than good).

As of November 20th 2019

· When weights are user-defined in OSM_TreeList, any weights that equal zero will now be ignored (not included in sample size calculations) during local height calibration.

· Updated default weighting (when no user-defined weights exist) to simply average the height samples, rather than weight by basal area factor.

#### Step 3: Species height prediction adjustment with least squares error analysis

If number of height samples within a plot is ≥ 5 for an individual species, then species observed heights (obs) are compared against predicted heights (prd) from step 2 using basal area weighted least-squares to determine a basal area weighted bias correction factor to be applied to trees with missing heights of the same species.

If the multiplier is between 0.5 and 1.5, the multiplier is accepted and the species height is adjusted using:

, otherwise, the multiplier is ignored and HT2 is used as is.

As above for LHT, see OSM.AcadianModel.InputTables.OSM_TreeList.Weight and OSM.Simulation.Model.HeightModel, to understand how to set weights on individual tree heights in the input tree list in order to properly weight individual trees for this self-calibration step for alternative plot designs (fixed area, point sampling, or hybrid approaches).

This step is implemented by the OSM Base Model.

As of June 2nd 2019

· Issues with tree agitation artificially inflating height sample size were fixed.

As of November 19th 2019

· When weights are user-defined in OSM_TreeList, any weights that equal zero will now be ignored (not included in sample size calculations) during local height calibration.