# Stomatal conductance

By definition, stomatal conductance, usually measured in mmol m⁻² s⁻¹, is the measure of the rate of passage of carbon dioxide (CO2) entering, or water vapor exiting through the stomata of a leaf. Stomata are small pores on the top and or bottom of a leaf that are responsible for taking in CO2 and expelling water vapour. The rate of stomatal conductance, or its inverse, stomatal resistance, is directly related to the boundary layer resistance of the leaf and the absolute concentration gradient of water vapor from the leaf to the atmosphere. It is under direct biological control of the leaf through the use of guard cells, which surround the stomatal pore [1] (Taiz/Zeiger 1991). The turgor pressure and osmotic potential of guard cells is directly related to the stomatal conductance.[2] Stomatal conductance is a function of stomatal density, stomatal aperture, and stomatal size.[3] Stomatal conductance is integral to leaf level calculations of transpiration (E). Multiple studies have shown a direct correlation between the use of herbicides and changes in physiological and biochemical growth processes in plants, particularly non-target plants, resulting in a reduction in stomatal conductance and turgor pressure in leaves.[4] [5][6]

## Light-dependent stomatal opening

Light-dependent stomatal opening occurs in many species and under many different conditions. Light is a major stimulus involved in stomatal conductance, and has two key elements that are involved in the process: the stomatal response to blue light, and photosynthesis in the guard cell's chloroplast. The stomata open when there is an increase in light, and they close when there is a decrease in light. This is because the blue light activates a receptor on the guard cell membrane which induces the pumping of protons of the cells, which creates an electrochemical gradient. This causes free floating potassium and other ions to enter the guard cells via a channel. The increase in solutes within the guard cells leads to a decrease in the osmotic potential of the cells, causing water to flood in, the guard cell's to become enlarged, and therefore open.The second key element involved in light-dependent stomatal opening is the photosynthesis in the guard cell's chloroplast. This event also increases the amount of solutes within the guard cell. Carbon Dioxide enters the chloroplasts which increases the amount of photosynthesis. This increases the amount of solutes that are being produced by the chloroplast which are then released into the cytosol of the guard cell. Again, this causes a decrease in osmotic potential, water floods into the cells, the cells swell up with water, and the stomate is opened[7].

Recent studies have looked at the stomatal conductance of fast growing tree species to identify the water use of various species. Through their research it was concluded that the predawn water potential of the leaf remained consistent throughout the months while the midday water potential of the leaf showed a variation due to the seasons. For example, canopy stomatal conductance had a higher water potential in July than in October. The studies conducted for this experiment determined that the stomatal conductance allowed for a constant water use per unit leaf area[8]. Other studies have explored the relationship between drought stress and stomatal conductance. Through these experiments, researchers have found that a drought resistant plant regulates it's transpiration rate via stomatal conductance. This minimizes water loss and allows the plant to survive under low water conditions[9].

## Methods for measuring

Stomatal conductance can be measured in several ways: Steady-state porometers: A steady state porometer measures stomatal conductance using a sensor head with a fixed diffusion path to the leaf. It measures the vapor concentration at two different locations in the diffusion path. It computes vapor flux from the vapor concentration measurements and the known conductance of the diffusion path using the following equation:

${\displaystyle {\frac {C_{vL}-C_{v1}}{R_{vs}+R_{1}}}={\frac {C_{v1}-C_{v2}}{R_{2}}}}$

Where ${\displaystyle C_{vL}}$ is the vapor concentration at the leaf, ${\displaystyle C_{v1}}$ and ${\displaystyle C_{v2}}$ are the concentrations at the two sensor locations, ${\displaystyle R_{vs}}$ is the stomatal resistance, and ${\displaystyle R_{1}}$ and ${\displaystyle R_{2}}$ are the resistances at the two sensors. If the temperatures of the two sensors are the same, concentration can be replaced with relative humidity, giving

${\displaystyle R_{vs}={\frac {1-h_{1}}{h_{2}-h_{1}}}R_{2}-R_{1}}$

Stomatal conductance is the reciprocal of resistance, therefore

${\displaystyle g_{vs}={\frac {1}{R_{vs}}}}$ .

A dynamic porometer measures how long it takes for the humidity to rise from one specified value to another in an enclosed chamber clamped to a leaf. The resistance ${\displaystyle R}$ is then determined from the following equation:

${\displaystyle \Delta t={\frac {\left(R+A\right)l\Delta h}{1-h}}}$

where ∆${\displaystyle t}$ is the time required for the cup humidity to change by ∆${\displaystyle h}$, ${\displaystyle h}$ is the cup humidity, ${\displaystyle l}$ is the cup “length,” and ${\displaystyle A}$ is an offset constant.

Null balance porometers maintain a constant humidity in an enclosed chamber by regulating the flow of dry air through the chamber and find stomatal resistance from the following equation:

${\displaystyle R_{vs}={\frac {A}{f}}\left({\frac {1}{h}}-1\right)-R_{va}}$

where ${\displaystyle R_{vs}}$ is the stomatal resistance, ${\displaystyle R_{va}}$ is the boundary layer resistance, ${\displaystyle A}$ is the leaf area, ${\displaystyle f}$ is the flow rate of dry air, and ${\displaystyle h}$ is the chamber humidity.

The resistance values found by these equations are typically converted to conductance values.

## Models

A number of models of stomatal conductance exist.

### Ball-Berry-Leuning model

The Ball-Berry-Leuning model was formulated by Ball, Woodrow and Berry in 1987, and improved by Leuning in the early 90s.[10] The model formulates stomatal conductance, ${\displaystyle g}$ as

${\displaystyle g=g_{0}+{\frac {a_{1}A_{n}}{(c_{s}-\Gamma )(1+{\frac {D_{s}}{D_{0}}})}}}$

where ${\displaystyle g}$ is the stomatal conductance for CO
2
diffusion, ${\displaystyle g_{0}}$ is the value of ${\displaystyle g}$ at the light compensation point, ${\displaystyle A_{n}}$ is CO
2
assimilation rate of the leaf, ${\displaystyle D_{s}}$ is the vapour pressure deficit, ${\displaystyle c_{s}}$ is the leaf-surface CO2 concentration, ${\displaystyle \Gamma }$ is the CO2 compensation point. ${\displaystyle a_{1}}$ and ${\displaystyle D_{0}}$ are empirical coefficients.