Sustain Our Nation's Forests and Grasslands

The tree height-diameter relationship


Environmental conditions – especially water availability affect the height-diameter relationship. USDA Forest Service photo.

NORTH CAROLINA – The taller a tree grows, the wider its trunk becomes. It’s a fundamental relationship.

Southern Research Station scientists use math to describe the tree height-diameter relationship in their recent study, published in the Journal of Plant Studies. But one of the mathematical constants – a scaling exponent of 2/3 – is not always so constant according to lead author Xiongwen Chen and research ecologist Dale Brockway.

“In many scenarios, the 2/3 or 0.67 scaling exponent is valid,” says Brockway. “However, environmental conditions can influence the scaling exponents observed in the field.”

The researchers measured hundreds of trees across six locations in Alabama and Florida. They measured longleaf pine at the southern, central, and northern parts of the species’ natural range. The three locations receive different amounts of precipitation.

“Water availability affects the height-diameter relationship in longleaf pine,” says Brockway. “Water favors a higher exponent, 0.71 for example – which means tree height is greater, relative to the diameter.” In the drier forest, the exponent was 0.42. Lower exponents indicate a shorter height, relative to the diameter.

Like all organisms, trees respond to their environment. Trees may have the capacity to adjust to spatial and temporal variation in local environments. The results of this study are an example of species adaptation.

The scientists also measured height-diameter relationships for water tupelo, bald cypress, red maple, and river birch. All four species are adapted to swampy conditions.

Red maple and river birch had the expected height-diameter relationships, close to 0.67.

However, scaling exponents for water tupelo and bald cypress were significantly less than 0.67.

Both the red maple and river birch species develop buttresses. Buttresses help trees acquire oxygen in flooded soils and may protect from toppling. Buttresses affect the height-diameter relationship by diverting internal carbohydrate resources away from height growth.

In many cases, the 2/3 scaling exponent describes tree growth very well. “There appears to be substantial variability,” says Brockway. “The scaling exponent is a metric that helps us describe how trees are responding to their environment. It may also help us understand how tree species are adapting to varied and changing conditions.”

Foresters use scaling metrics to estimate growth, productivity, and yield.