Modeling Transpiration of Leaves

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Transpiration is the transport of water vapor through plant stomatal apertures. This water loss is a necessary requirement for vascular plants as they take up carbon dioxide for photosynthesis. The two main factors that determine transpiration are the conductance of water vapor from inside the leaf to the atmosphere and the gradient of water vapor from inside to outside the leaf. It is generally assumed that the water vapor in the leaf is saturating, thus the gradient is determined by the leaf temperature and water vapor concentration in air. Here, relative humidity is used to determine the atmospheric water vapor ( axis), and leaf conductance to water vapor ( axis) represents all diffusive conductances associated with the leaf. Transpiration is modeled based on leaf energy budget and a Fick's law analogy.

Contributed by: Carl Bernacchi and Andy VanLoocke (October 2014)
Open content licensed under CC BY-NC-SA



This Demonstration uses a leaf energy balance equation [1]:


where is the leaf temperature (°C), is air temperature (°C), is the apparent psychrometer constant (), is the slope of the saturation mole fraction function (, with being the slope of the saturation vapor pressure function and () being air pressure), is absorbed total radiation (), is emissivity of the surface (leaf), is the Stefan–Boltzmann constant (), is convective-radiative conductance (), is specific heat of air (), and is vapor pressure deficit ).

Transpiration () is calculated using an analogy to Fick's law:


where , on the axis, is leaf conductance to water vapor (), is saturated vapor partial pressure in the leaf based on , and is the actual partial pressure of water vapor in air based on relative humidity, on the axis.


[1] G. S. Campbell and J. M. Norman, An Introduction to Environmental Biophysics, 2nd ed., New York: Springer, 1998.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.