Tree Water Use Model Development

Tree models: What are they?

A “model” is a system of data and theories, presented mathematically to represent a “state of affairs”.  A popular and well known equation is one proposed by Albert Einstein, E = mc2 where E = energy, m = mass, and c2 = the square of the speed of light.  Einstein’s equation showed that very small amounts of mass might be converted into a very large amount of energy and vice versa.

Mathematical equations are common in numerous fields of science, including plant physiology.  In plant physiology, there are two primary types of models or equations 1) empirical and 2) mechanistic.

  • Empirical models are fit to data (measurements) and once the fit is complete, they allow us to predict within that range of data, time span, and environmental conditions. 
  • Mechanistic models rely on information that characterizes the underlying biological response of the tree organs.  Permitting dynamic predictions outside of the data that was collected to parameterize the original process-based model. 


Mechanistic models can predict how the plant will respond to a given set of environmental values based on the founding principals of the tree’s biology.  Mechanistic models can be used to help resolve water management issues in the nursery and landscape industries.

Tree Models and the Nursery Industry?

Once we have plant measurement values, the model parameters can be defined.  Once the models are parameterized, they can be used to predict nursery tree water use.  The equation below illustrates the stomatal conductance (transpiration or water use) model.

gs = ((m * Anet * Hs)/Cs) + b

Although the ultimate answer for this equation is the volume of tree transpiration, we first have to determine the trees photosynthetic rate because a linear relationship exists between the photosynthetic rate and transpiration volume.  We measure photosynthesis and plug the value into the equation; all other values of the stomatal conductance equation are derived from atmospheric and weather station data.

Models such as the one illustrated in the equation above are well founded in the world of plant physiology and have been proven time and time again.  This and many other equations are used to arrive at accurate estimates of whole tree, nursery, and landscape water use.  In fact the equation requires only simple multiplication and division for computation.

More than one model or equation can be parameterized from collected data and once parameterized, the models interact with each other.  They interact because calculations from one model may be required to solve a second model and so on.  The models are easily programmed into software and run on a computer.  The computer software removes the cumbersome nature of calculator type computation.

cartoon tree with cubes  representing canopy volumes.  Sub   volume  calculations are computed for  each cubic volume of crown and  then   added together for a whole crown  estimate.

The figure to the right illustrates how a computer applies the models to an individual tree crown.  Because light and other environmental parameters vary from the top of a tree crown to the bottom, model calculations must be repeated for discrete sub volumes of a crown.  By calculating estimates for each sub volume of crown, environmental variation is taken into account, greatly improving the accuracy of the water use estimate.  Crown sub volumes are simply added together for a whole crown estimate.

Mechanistic models are a powerful and robust means to estimate tree water use in both nurseries and landscape trees.  The models provide a realistic method of quantifying tree water use under almost any imaginable nursery or landscape environmental or substrate moisture condition.  Furthermore, the models we developed are capable of estimating values on a genotype-by-genotype basis (this component is important given the amount of cultivars and species in the trade).

All questions and comments can be e-mailed to Dr. Bill Bauerle. Bill.Bauerle@colostate.edu