How do trees grow? The science of stand growth

This article is based on our podcast episode released on 26th of November 2024. [Listen to the full episode here.]

In a serene Danish forest, foresters used to rely on simple paper tables to predict how trees grow. 

But as climate changes and forestry gets more complicated, these traditional methods are being replaced by advanced mathematical models. These new tools, combined with data from satellites, drones, and other modern technologies, are changing how we understand tree growth and could revolutionise the future of forestry.

Let’s explore how.

The math behind tree growth

Modern growth models use differential equations – a type of math that helps us understand how things change over time. 

Rasmus explains this concept using a simple car analogy: "If you have a car's speed and differentiate that, you get its acceleration."

These dynamic models work by looking at how forests change over time. Starting with what we know about a forest today - things like tree height, diameter, and number of trees - the models help us predict what the forest will look like next year. Once we have those predictions, we can use them to look even further ahead, building up a picture of how the forest might develop over many years.

Today, foresters use these principles to understand how trees grow and influence each other over time. But what exactly do these models measure? Let's look at the key factors that determine forest growth.

Modern growth models, like the VIDAR system from the University of Copenhagen, focus on three main parameters:

• Height
• Basal area (the ground space covered by tree trunks)
• Number of trees in practice

“The models show how height, basal area and number of trees affect each other," Rasmus explains. "For example, when the height of the trees increase so does the mortality, indicating increase in competition among the trees"

The “site index” challenge

One of the key factors in growth models is the "site index" – a number that shows how well trees are expected to grow in a specific area. This single number cleverly combines many different factors that affect tree growth, such as soil quality, wind exposure, and water availability. 

Instead of trying to model each factor separately (which would be extremely complex), foresters have traditionally used this simplified approach, often basing the number on how well previous trees have grown in the area.

This practical approach has been widely used for decades because it provides a quick way to estimate growth potential. But as our climate changes at an unprecedented rate, a crucial question emerges: can we still rely on historical growth patterns to predict the future?

Some researchers argue we need better ways to measure this.

When old models meet new climate realities

The old ways of measuring forests may no longer be good enough in today’s rapidly changing climate: 

"A lot of what we consider 'ground truth' in forestry comes from data collected nearly 100 years ago," Rasmus points out. "We need to verify if this still reflects reality today. Modern technology like satellites could help us collect new data over large areas and update our understanding."

This shift raises an important question: "What would be a reasonable time frame for a model to be valid – five years, ten years?" Jens asks. 

As climate patterns change faster than ever, the reliability of tree growth predictions becomes increasingly uncertain. Regular model updates and shorter time frames between revisions are important - but that's not all. 

By utilizing new data sources from satellites, drones and other modern technology, we can verify and tune our existing models to become more accurate. This might even lead to the development of completely new models that better reflect today's reality.

From models to new possibilities

Traditional growth models were designed for even-aged forests managed in conventional ways. But, as Rasmus points out, "These models can't really describe uneven-aged forest and continuous cover." 

With changing forest practices, we need models that can adapt to these new realities.

"We need to move away from traditional forestry models to more scenario-based thinking," Rasmus reflects. This approach could help foresters better prepare for whatever the future might bring.

These models help foresters predict timber value, plan thinning operations, understand how trees compete for resources, and support long-term decision-making. 

As climate and management practices evolve, these tools become increasingly important for making smarter, more sustainable choices for our forests.

Want to learn more about tree growth models? Check out these resources:

• Forest Vegetation Simulator (FVS) – US Forest Service
• University of Copenhagen Forest Research