index

Context & motivation

Forest carbon accounting requires information on how biomass and volume change with stand age
Yield curves provide this information, but existing models do not cover Canada’s forests consistently
Over 100 Mha of forest have no available yield curves, limiting national-scale assessment

Remote Sensing Yield Curves (RSYC)

Tile-level RSYC

Spatial units: eco-stratification

Here’s an example for black spruce and total volume.

I want to use this slide mainly to illustrate how the hierarchy works.

On the left we start at the ecozone level. Within the Boreal Plains, for example, we have one broad-scale curve.

Then we move down one level and look at ecoprovinces within that ecozone. Here I’ve highlighted the Boreal Foothills.

We can continue down to the ecoregion level — here the Western Alberta Upland — and finally to the individual ecodistricts within that region.

As we move from left to right, the models become increasingly spatially specific.

You can also see that the curves begin to separate more at the finer levels. That gives us the ability to represent regional variation in growth rather than forcing one national trajectory everywhere.

But an important point, which I’ll return to later, is that more detailed does not automatically mean better.

Model library overview

Forest attribute: AGB, total volume
Species-specific or multi-species (Generic → Conifer / Broadleaf → Species)
Spatial representation: Tile, Ecozone → Ecoprovince → Ecoregion → Ecodistrict
Model formulation: National, Regional
Uncertainty

National RSYC model library

	Ecosystem strata	Tiles
AGB	8,191	2,016
Volume	8,260	2,016

Altogether, the current library contains 35,450 fitted yield curves.

I’m not going to read all of these numbers, but the table shows how that total is distributed between AGB and volume, national and regional formulations, and ecosystem strata versus tiles.

The heatmap gives another perspective on the AGB models.

At the top are our multi-species models, and below are the individual species. Common and widely distributed species — black spruce is the clearest example — can support hundreds of models at the finer spatial levels.

For rarer or more geographically restricted species, the library is naturally smaller.

So the main message is not the precise number 35,450. It’s that we now have a large set of candidate curves spanning different levels of biological and spatial specificity.

And that creates the next question: which one should a user choose?

Validation approach

Independent validation with national field plot data (MAGPlot)
Over 50,000 plots across Canada
Comparison by 20-year age classes

To evaluate the curves independently, we use MAGPlot, our harmonized national field-plot database.

It contains more than 50,000 plots assembled from multiple jurisdictions across Canada.

The map shows that this is a very large reference data set, but it also shows an important limitation: the observations aren’t distributed uniformly. They’re much denser in some regions than in others.

That’s why we can validate many of the models very well, while some species-by-region combinations have little or no independent reference data.

For the comparison, we summarize observations in 20-year age classes. This helps prevent the most heavily sampled portions of the age distribution from dominating the overall assessment.

So this gives us a genuinely independent test of how well the remote-sensing yield curves reproduce field-observed growth patterns.

Validation results

Validation - overall performance

	AGB	Volume
Median R²	0.63	0.62
Median RMSE	37.1 Mg ha⁻¹	67.6 m³ ha⁻¹
Median bias	−12.2 Mg ha⁻¹	−10.7 m³ ha⁻¹

Best species-specific models: subalpine fir, eastern white-cedar, and trembling aspen; black spruce
Weakest models yellow birch, Sitka spruce, and tamarack

These are the overall validation results across the model library.

For AGB, the median R-squared is 0.63, and for volume it is 0.62. So the strength of the relationship with the independent observations is remarkably similar for the two attributes.

Median RMSE is about 37 megagrams per hectare for AGB and 68 cubic metres per hectare for volume.

Bias is relatively modest and negative for both — about minus 12 megagrams per hectare for AGB and minus 11 cubic metres per hectare for volume.

There is substantial variation among species.

Subalpine fir, eastern white-cedar and trembling aspen are among the strongest species-specific models. Black spruce also performs very well and is especially important because it has an exceptionally large validation sample.

At the other end, yellow birch, Sitka spruce and tamarack are among the weaker performers. Those cases also remind us why validation matters when choosing which curves to use.

Overall, I’m encouraged by the consistency of the results for both AGB and volume.

Summary

Nationally consistent, RS-derived yield curves for AGB and volume
Extends coverage to managed and unmanaged forests
Demonstrates consistent performance against independent field observations
Supports carbon accounting and national-scale forest assessment

Resources

Website + R package:
ptompalski.github.io/RSYC
this presentation: ptompalski.github.io/RSYC-IBFRA2026
Publications: Tompalski et al., 2024, Tompalski et al., 2025

Let me finish with four main points.

First, RSYC provides a nationally consistent way of deriving yield curves for both aboveground biomass and total volume directly from remote-sensing information.

Second, it allows us to extend growth information beyond the areas and species covered by conventional growth models, including large areas of unmanaged forest.

Third, the independent field validation shows consistent overall performance, while also identifying where individual species or regions are stronger or weaker.

And finally, the model library gives us flexibility — from national to local, and from generic to species-specific — which makes it useful for national-scale forest and carbon assessment.

The curves, parameter tables and R package are all publicly available at the website shown here, and this presentation is online as well.

Thank you.