## Newfoundland and Labrador Variant Height Model

Black spruce and balsam fir allometric tree height models were developed from NL permanent sample plot (PSP) data using a non-linear Weibull function of Species, DBH, basal area, QMD, basal area of larger trees (BAL), and Mean Annual Temperature (MAT). In the fall of 2023, MAT was extracted for each plot x, y, z coordinates using Climate NA Normals for 1961-1990. 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. Fit by C.R. Hennigar, FORUS Research, 2024.

There were insufficient tree height samples from the PSP data to fit custom NL height models for species other than black spruce and fir; so, for now, Nova Scotia (NS) height models were used from the Acadian Variant. Future efforts could leverage the larger NL temporary sample plot (TSP) network to fit other species like white birch, poplar, white spruces, etc. The NS height models require Biomass Growth Index (BGI), as a predictor, which is not an available site predictor in NL. Where NS models were leveraged, the BGI default value used by the NL variant was lowered to 3,000 kg/ha/year from a default value of 3,500 kg/ha/year in the Acadian model, as this BGI value reduced mean bias from about 5% overpredicted to between +/-3% bias. Further reducing to 2,500 kg/ha/year resulted in under prediction of tree heights by about 5%. This 3,000 kg/ha/year value reduced average mean bias across most species tree models during testing so much so that additional bias corrections were deemed unnecessary.

In general, NL observed heights were very similar to NS heights when BGI was set to 3,000 kg/ha/year for the same species, DBH, and competitive position in the stand. OSM self-calibration of these NS models for fir and black spruce did nearly as well as refitting these height models with NL data, baring some additional reduction in absolute height error (Table 1).

Accuracy of these models could be further corrected by using the self-calibration features of OSM with available observations from the NL TSP network, which contains more height tree observations than the PSP program – this was not undertaken here. Individual height predictions can be boosted if a sub-sample of height trees are available in the survey data during simulation. This boosting occurs automatically by the OSM API on loading of the tree list if enough height samples are present.

See also Acadian Variant calibration.

Table 1. Height imputation model performance, comparing Acadian to NL, with and without bias correction.

Species and prediction model* | r2 | Mean Bias (m) Predicted – Observed | Mean Absolute Error (m) | DBHI Observations
Black Spruce |  |  |  |
Acadian NS BGI=3000 | 91% | -0.019 | 0.66 | 134,632
Acadian w Self. Calib. | 92% | 0.100 | 0.66 | 134,632
NL Variant | 92% | 0.086 | 0.65 | 134,632
NL Variant w Bias Corr. | 92% | 0.014 | 0.65 | 134,632
Balsam Fir |  |  |  |
Acadian NS BGI=3000 | 91% | 0.205 | 0.75 | 164,045
Acadian w Self. Calib. | 92% | -0.077 | 0.74 | 164,045
NL Variant | 92% | 0.099 | 0.72 | 164,045
NL Variant w Bias Corr. | 92% | 0.002 | 0.72 | 164,045
White Birch |  |  |  |
Acadian NS BGI=3000 | 79% | 0.319 | 1.11 | 14,810
Acadian w Self. Calib. | 79% | 0.201 | 1.10 | 14,810
White Spruce |  |  |  |
Acadian NS BGI=3000 | 90% | 0.194 | 0.82 | 7,950
Acadian w Self. Calib. | 91% | -0.015 | 0.80 | 7,950
Tamarack |  |  |  |
Acadian NS BGI=3000 | 89% | 0.084 | 0.99 | 1,702
Acadian w Self. Calib. | 89% | 0.042 | 0.99 | 1,702
Red Pine |  |  |  |
Acadian NS BGI=3000 | 93% | 0.128 | 0.61 | 834
Acadian w Self. Calib. | 93% | 0.057 | 0.60 | 834
Red Maple |  |  |  |
Acadian NS BGI=3000 | 91% | -0.042 | 0.65 | 741
Acadian w Self. Calib. | 91% | -0.024 | 0.65 | 741
Trembling Aspen |  |  |  |
Acadian NS BGI=3000 | 89% | 0.034 | 0.98 | 719
Acadian w Self. Calib. | 89% | 0.115 | 0.99 | 719

* Acadian NS BGI=3000 – Acadian Variant version 2.0.0.0, NS zone, BGI = 3,000 kg/ha/y.

Acadian with Self. Calib. – same as Acadian default, but with OSM self-calibration (simple scaling multiplier to correct mean bias).

NL Variant – models fit for NL with only NL data, June 2024.

NL Variant with Bias Corr. Equ. – same as NL Variant default, but with linear bias corrections as a function of DBH and stand basal area.

### 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. Stand and tree structural competition metrics like BAL are calculated internally by OSM. Mean annual temperature is extracted from Climate NA and input by the user when loading plots or stands for simulation.

#### 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.

#### 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.