Design of steady state porometers for measuring leaf stomatal conductance

Thomas N Buckley & Matthew E Gilbert

Author Affliations

Buckley: Department of Biology, Sonoma State University

Gilbert: Department of Plant Sciences, University of California, Davis

Overview

Stomatal conductance to water vapour (g_sw, mol m^-2 s^-1) can easily be inferred from measurements of flow rate, humidity and temperature that are not particularly costly or technically difficult. Below we describe the required measurements and calculations, and some practical considerations, for building a steady-state porometer (SSP). Future additions to this protocol will include detailed designs for an SSP that can be built in laboratories for a minimal budget. An SSP infers g_sw from the degree to which leaf transpiration increases the humidity of a steady stream of air passing through a chamber. SSPs typically measure g_sw fairly quickly (~1 min) to ensure stomata do not have enough time to respond to conditions in the porometer chamber. Null-balance SSPs modulate flow rate to seek a chamber humidity setpoint, which requires feedback circuitry or software but permits chamber humidity to be matched to external conditions. A basic flow path diagram for an SSP is shown in Figure 1. (Alternative techniques, not discussed here, include cup porometers, which infer g_sw from the rate at which a leaf humidifies a sealed chamber, and viscous flow porometers, which measure the rate of air effusion through an amphistomatous leaf when pressure is applied at one surface.)

Background

Roughly half the atmosphere’s water vapour transpires through leaf stomata each year (Hetherington & Woodward, 2003). Stomata are the primary biological control on transpiration, and they respond to light, CO₂ and the water status of the leaf, soil and air. Rapid measurements of g_sw are useful in basic and applied research, from crop phenotyping to irrigation scheduling and from guard cell physiology to ecosystem water balance.

Materials/Equipment

– DC powered air pump (~1 – 2 L min^-1 capacity)

– non-adsorptive tubing (teflon or polypropylene; 1/4″ outer and 1/8″ or 3.175mm internal diameter)

– dessicant cell containing drierite or silica gel

– particulate air filter

– mass flow controller

– leaf chamber with neoprene gaskets

– leaf temperature sensor in leaf chamber (fine-wire- or IR-thermocouple)

– miniature fan or blower in leaf chamber

– humidity sensor (or relative humidity/air temperature sensor) in leaf chamber or in outgoing flow path of leaf chamber

– 12V battery

Either:

– (1) Campbell Scientific CR850 datalogger and SDM-AO4A analog output module; or

– (2) Measurement Computing USB-1208LS & USB-2001-TC dataloggers and tablet computer or laptop

Units, terms, definitions

a, leaf area enclosed in chamber (m²)

E, transpiration rate (mol m^_-2 s^-1)

f_in, flow rate into chamber (mol air s^-1)

g_sw, stomatal conductance to water vapour (mol air m^-2 s^-1)

g_tw, total conductance to water vapour (mol air m^_-2 s^-1)

p_tot, atmospheric pressure (Pa)

r_o, non-stomatal leaf resistance to water vapour ((mol air m^-2 s^-1)^-1)

T, temperature of air in Kelvins (K)

T_a, temperature of air in degrees Celsius (^oC)

T_l, temperature of leaf in degrees Celsius (^oC)

w_a, water vapour mole fraction of air above leaf boundary layer (mol water mol^-1air)

w_a*, porometer setpoint for w_a (mol water mol^-1air)

w_i, water vapour mole fraction of air inside leaf (mol water mol^-1air)

w_in, water vapour mole fraction of air entering chamber (mol water mol^-1air)

w_out, water vapour mole fraction of air exiting chamber (mol water mol^-1air)

Sequential assembly of flow path connected by Teflon or polypropylene tubing

1. An air pump capable of pumping approximately 1 – 2 L air min^-1 (~(1 – 2)*10^-5 mol air s^-1).

2. A dessicant cell (typically a 2 x 15 cm cylinder) containing either drierite or silica gel. It is useful to mix a small amount of indicating drierite with non-indicating drierite.

3. A particulate air filter to remove dust from the environment and dessicant before the air contacts the mass flow controller.

4. A mass flow controller. Check that the flow orientation is correct.

5. A leaf chamber that clamps onto a leaf, seals with neoprene gaskets, contains a temperature sensor (either a fine wire thermocouple or an infrared thermocouple) beneath the leaf and has a miniature DC fan or lateral blower that generates very vigorous air mixing.

6. A capacitive relative humidity (RH) humidity sensor. If the sensor is not combined with an air temperature sensor, then a separate air temperature sensor must be included as well. This sensor must measure air in the chamber above the leaf boundary layer, or air exiting the leaf chamber.

Calibration of capacitive humidity sensor

1. Zero the sensor:

a. Ensure the dessicant cell contains fresh dessicant.

b. Ensure no leaf is in the chamber and no other water source (e.g. dirt that may have adsorbed moisture) is in the chamber or anywhere else in the system. If the chamber is a single sided chamber, then seal the chamber leaf aperture with a non-adsorptive layer (e.g. glass microscope slide).

c. Flow air through the closed chamber as in a normal measurement. Record the raw relative humidity measurement, which is the zero offset.

d. Use this zero offset to modify the calibration within the porometer program (note: a sample porometer program that demonstrates how to implement this calibration step, and other steps associated with sensor interrogation and data storage and display, will be included in a revision to this protocol).

2. Span the sensor:

a. Remove the dessicant cell and air filter from the system.

b. Replace the air filter with a fresh filter that has not previously been used downstream of dessicant in the flow path.

c. Provide an air source of known humidity (see below).

d. Flow air through the closed chamber as in a normal measurement. Record the raw relative humidity measurement, which is the span value.

e. Use this span value to modify the calibration within the porometer program.

3. Replace the original dessicant cell and air filter.

Generation of air source with known humidity, without a commercial dewpoint generator

1. Fill a large-mouthed Erlenmeyer flask approximately half-way with water.

2. Cap the flask with a stopper that has two holes: one suitable for small diameter tubing (e.g. 1/4″) and one that can receive a water jacketed condenser (e.g. 1/2″).

3. Connect a tube (the inlet tube) leading from the air pump to the smaller stopper hole and run the tube to the base of the flask. Two separate pieces of tubing can be joined in the stopper if necessary.

4. Place the lower end of the condenser into the larger stopper hole.

5. Connect the incoming and outgoing water lines from a recirculating temperature-controlled water bath to the water path of the condenser.

6. Activate the water bath and set the desired dewpoint (see the dewpoint formula under Calculations below; for reference, 50% relative humidity at 25^oC is approximately equivalent to a dewpoint of 13.8^oC).

7. Place a temperature sensor at the downstream (outgoing) end of the condenser gas path to measure the actual temperature of gas exiting the condenser, which will be equal to the dewpoint.

a. Ensure that the temperature sensor is dry and shielded from radiation.

b. Thread the temperature sensor into the condenser through a T-junction inline in the tubing downstream of the condenser, and seal the T-junction with silicone.

8. Connect the downstream tubing from the condenser to the porometer’s air filter.

Making a measurement of stomatal conductance

1. If turning on the instrument let the mass flow controller function for at least 10 minutes before using the porometer.

2. Activate the pump at least 30 seconds prior to a measurement to ensure steady air humidity in the incoming gas stream.

3. Clamp the chamber onto a leaf, ensuring that the leaf completely covers the opening to the chamber.

4. Wait for transpiration rate (E) to reach steady state, and record initial transpiration rate.

5. Instruct the porometer program to adjust flow rate (f_in) to achieve the desired target ambient humidity (w_a*).

6. When transpiration rate has reached steady state once more, record stomatal conductance (g_sw).

Estimation of boundary layer resistance

1. Repeat the steps for a normal measurement of stomatal conductance but use a moistened piece of filter paper in place of a leaf.

2. Instruct the porometer program to store the inverse of the inferred value of stomatal conductance as the non-stomatal resistance (r_o), for future calculations.

Calculations

Stomatal conductance to water vapour, g_sw (mol air m^-2 s^-1), is computed from

(1) ,

where r_o (m² s mol^-1air), total non-stomatal resistance to water vapour, includes (and is typically assumed equal to) boundary layer resistance, and g_tw (mol air m^-2 s^-1), total leaf conductance to water vapour, is computed from

(2) ,

where w_iand w_a (mol water mol^-1air) are the water vapour mole fractions inside the pore (intercellular) and above the leaf boundary layer (ambient), respectively, and E is leaf transpiration rate (mol water m^-2 s^-1). w_i is computed by dividing the saturation vapour pressure at the leaf temperature T_l (^oC) by total pressure (p_tot, Pa):

(3) .

Equation 3 (WMO, 2008) gives w_iin mol water mol^-1air. It assumes that air in the leaf is saturated with water vapour, which is supported by experiment (Farquhar & Raschke, 1978; Sharkey et al., 1982; Mott & O’Leary, 1984). E is computed as

(4) ,

where a (m²) is the leaf area enclosed in the chamber, f_in(mol air s^-1) is the flow rate of air into the chamber, and w_outand w_in (mol water mol^-1air) are the water vapour mole fractions of gas exiting and entering the chamber, respectively. w_ais typically assumed equal to w_out, the water vapour mole fraction of the air leaving the chamber. Equations 2 and 4 were given by von Caemmerer and Farquhar (1981). Note that Eqns 1-4 ignore cuticular transpiration. If the gradient for cuticular transpiration is the same as that for stomatal transpiration, then g_sw as calculated above is in fact the sum of cuticular and stomatal conductances.

Other resources

Notes and troubleshooting tips

Practical considerations

Porometry calculations require seven quantities: f_in, w_in, w_out, a, T_l, p_tot and r_o. At least three of these must be directly measured during each measurement in any SSP: f_in, w_out and T_l. The others can in some cases be assumed or measured only periodically. For instance, w_incan be assumed zero if the incoming air is desiccated, p_tot can be inferred from altitude, and a can be calculated from chamber dimensions if the leaf occupies the entire chamber. r_ois often estimated using wet filter paper to model a leaf with zero stomatal resistance (so that r_o= g_tw^-1), though this practice has been questioned (Grace, 1989). Error due to uncertainty in r_o is greatest when r_o or g_sw are large, and can be minimised by using strong chamber fans to reduce boundary layer resistance. Thin blowers are now available that allow chambers to be mixed from the side rather than underneath, which permits a thinner chamber design.

Gas flow

Gas flow is measured by a mass flow meter (MFM) or controller (MFC), which are widely available and cost ca. USD$300-$1000 for reasonably accurate and reliable units. They can be recalibrated by the manufacturer, or in the lab by inverting a graduated cylinder filled with water in a larger vessel, flowing air into the cylinder through a tube and recording the time needed to elevate the cylinder by a given volume. Null-balance SSPs use an MFC to produce a target value of ambient humidity, w_a*, by modulating f_in. The setpoint flow rate f_in* that produces w_a* is found by solving Eqn 4 for f_in (and assuming w_out = w_a):

(5) ,

where E’ is the transpiration rate measured at some initial value of f_in. If evaporative gradient (Dw = w_i – w_a) is the specified target, then w_a* = w_i – Dw*. The accuracy of this algorithm is reduced to the extent that changes in Dw affect T_l, and thus w_i, via evaporative cooling. A pressure source, typically a small pump, is needed to drive flow through the chamber. Inexpensive aquarium air pumps (~USD$10-20) are adequate. For reference, if ambient relative humidity is 50% and leaf and air temperatures are both 25^oC, then a flow rate of 1 L min^-1 will keep chamber and ambient humidity equal in a 6 cm² chamber fed with desiccated air if g_tw = 1.16 mol m^-2 s^-1.

Desiccation

Indicating silica gel or drierite of fine size (10-20 mesh) are typically used as desiccants. Commercially available tubes (~15 cm long and 2 cm wide) are sufficient for a few hours of measurements, but should be replaced often. Desiccant tubes should be placed vertically so that the desiccant granules settle and avoid creating a preferential flow path. An air filter should be placed between the desiccant and leaf chamber and before the MFC. The state of the desiccant can be tested periodically by closing the porometer chamber and using the chamber humidity sensor to test for any deviation from close to 0% relative humidity. Note that drierite and silica gel both adsorb CO₂, so measurement time must be minimised to avoid inducing stomatal response to changed CO₂ partial pressure.

Humidity measurement

Chilled mirror dewpoint hygrometers are highly accurate and rarely require numerical calibration (particularly if mirror temperature is measured with a platinum resistance temperature detector or PRTD, which has little drift), but have slow response times and are expensive, somewhat large and prone to mirror fouling by dust or airborne oils. Capacitive sensors (e.g. Vaisala or Sensirion) are generally less precise and require periodic calibration, but they are small and relatively inexpensive. These typically measure relative humidity (RH, %) and air temperature (T_a, ^oC) separately; w_a is computed by applying T_a to Eqn 3 and multiplying by 0.01*RH. OEM capacitance humidity sensors are far cheaper, so data from several sensors can be pooled to reduce effects of noise and drift.

Mixing and pressurisation

Chamber air should be thoroughly mixed with miniature fans (from underneath the leaf) or blowers (from the side) (e.g. Sunon) to ensure uniform gas composition and a small and consistent boundary layer that does not vary with flow rate. Pressure should be positive with respect to surroundings to ensure any gas leaks are advective rather than diffusive. Together these steps justify the assumption that w_a= w_out and help to ensure that any leaks across the chamber gasket do not alter the composition of gas sampled in the outgoing stream. Leaks are minimized by using ~4 mm wide neoprene foam gaskets. The leaf clamp portion of the porometer should be disengaged during storage to allow the gaskets to decompress.

Leaf temperature

Leaf temperature (T_l) is typically measured with a fine wire thermocouple appressed to the lower leaf surface. This actually measures a weighted average of leaf and air temperature, but the weights are unknown and probably vary with surface features and thermocouple construction. Leaf-air temperature difference can be minimised by shading the leaf and using strong fans to maximise convective coupling, although some decoupling due to evaporative cooling is unavoidable. Alternatively, T_l can be estimated using an infrared thermocouple. This eliminates the leaf-air averaging problem, but IR thermocouple accuracy is limited by uncertainty in leaf emissivity and by lag or error in measurement of the reference temperature in the IR sensor body (Bugbee et al., 1998).

Chamber

The chamber and any tubing should be minimally adsorptive of water vapour; Bloom et al. (1980) discuss adsorptive properties of construction materials. High density polyethylene (HDPE) and aluminum are easy to machine into chambers. Aluminum’s high heat capacity can reduce leaf-air decoupling, but aluminum is heavy and must be nickel plated to prevent adsorption. Teflon or polypropylene tubing are both ideal and widely available; Bev-A-Line tubing, a flexible material that is familiar to users of the Li-Cor Li-6400 gas exchange system, is highly adsorptive and should therefore be avoided for use with humidified gas streams. Chambers with windows allow radiation to enter, which affects temperature as discussed above but also allows continuous monitoring of g_sw, which is of interest in some applications. During measurement it may not be necessary to expose the leaf to the natural light intensity as stomatal responses to the light change should occur over a greater period than the measurement time (~1 minute).

The entire unit can be designed in modular fashion to allow different chambers to be used for different leaf types. Ideally the humidity sensor(s) and blower could be housed in the handheld chamber module, in close association with a leaf chamber that can be removed, thus avoiding removing anything but the leaf temperature sensor when changing chambers. It is only necessary to measure one surface of non-amphistomatous leaves; if both leaf surfaces are to be measured using the same sensors, then care should be taken to ensure adequate and equal mixing at both surfaces.

Sensor interrogation, interface and power

Many suitable dataloggers are available. When choosing dataloggers, bear in mind that some RH/T_a sensors require digital measurement, and MFCs are often controlled using an analog output voltage. Products by Campbell Scientific Inc. are widely used in demanding field applications; their CR850 (USD$1295) includes a small LCD screen that can serve as a primary interface, and it can also communicate with mobile phone apps if IP-enabled with a network link interface (NL-200, USD$295). Analog output for MFC control would require a separate module (SDM-AO4A, USD$495). A less expensive alternative is to combine USB i/o boards (e.g., analog output and digital i/o using USB-1208LS (USD$129), and thermocouple measurement using USB-2001-TC (USD$99); Measurement Computing Inc.) with a small tablet PC (~USD$200-$500) programmed to provide a flexible interface. When porometer designs are added to this page, sample porometer programs to operate those designs will also be made available. Suitable batteries to operate sensors and dataloggers can be obtained at any electronic hobby shop or online for minimal cost.

Calibration

As the SSP determines g_sw from first principles there is no need to calibrate the porometer for g_sw per se. However, the humidity and temperature sensors and flow meters may drift from factory specifications. The chamber humidity sensor should be re-zeroed whenever desiccant is replaced – ideally at least daily. The span of the humidity sensor can be checked periodically using a commercial dew point generator, or by generating air of known dewpoint by saturating it by bubbling through warm water and then lowering it to a known dewpoint by passing it through a condenser regulated to a controlled temperature. Typically a dew point temperature 5^oC below ambient will provide a good span, while preventing any condensation on the cool metal or plastic surfaces of the porometer. Humidity sensors are often precalibrated and fit in sockets, and thus may be rapidly replaced in the field.

Limitations to porometry

Commercially available porometers vary widely in theoretical basis, and numerous authors have discussed porometer designs and their limitations (Parkinson & Legg, 1972; Pearcy, Schulze & Zimmermann, 1989; McDermitt, 1990). It is important to recognise that porometers measure a brief snapshot of g_sw – in one leaf, at one point in time – and the difficulties of scaling this snapshot to larger spatiotemporal scales are great. Other techniques, including weighing lysimetry, sap flow and eddy covariance, can measure in situ and whole plant transpiration more directly. At a minimum, porometry should be directly coupled to measurements of local environmental conditions to provide context; to this end, we note that an SSP with its chamber open is an excellent humidity and temperature sensor.

Appendix

Molar vs volumetric conductance units

Two sets of dimensions are commonly used for stomatal conductances: molar units (e.g. mol m^-2 s^-1) are now standard in plant sciences, whereas volumetric units (e.g. m s^-1, which is equivalent to m³ m^-2 s^-1) were common in the older plant literature and remain so in the atmospheric sciences. Volumetric units were deprecated by plant scientists in the 1970s (Cowan, 1977; Farquhar & Raschke, 1978) to eliminate dependence on temperature and atmospheric pressure, which often differ among experimental treatments. Thus, temperature and pressure should be reported when m s^-1 are used. To convert a volumetric conductance to a molar one, divide the former by the molar volume of air; this equals RT/p_tot from the ideal gas law, where R is the gas constant (8.314 m³ Pa mol^-1 K^-1), T is the air temperature of the air in the stomatal pore in Kelvins and p_totis atmospheric pressure in Pascals (~10⁵). For volumetric units in mm s^-1, first convert to m s^-1 by multiplying by 10^-3.

Chemical species identity in conductance units

Conductances are sometimes given with the chemical identity of the diffusing species, e.g. mol H₂O m^-2 s^-1. This is motivated by the fact that the diffusivity of H₂O in still air is 1.6 times that of CO₂, so stomatal conductances to CO₂ and H₂O are not numerically equal. However, the correct chemical identity for the “mol” in molar conductance units is “air,” rather than the diffusing species. This can be seen by deriving g_sw from Fick’s First Law of Diffusion. The latter can be derived from first principles of geometry and kinetics (e.g. Atkins, 1990) as

(6) ,

where j_x is the number flux of species x (molecules of x per unit area, per unit time), {lambda}_x (m) and c_x (m s^-1) are the mean free path and mean velocity of x, respectively, and dN_x/dz is the gradient in the number density of x (N_x, molecules of x m^-3air) along the diffusion axis (dN_x/dz has units of {molecules of x m^-3air} m^-1). The quantity {lambda}_xc_x/3 is the diffusivity of x (D_x , m² s^-1). For transpiration we define x as w (water). To convert j_w to molar units with a leaf area basis (E, mol w m^-2_leaf s^-1), multiply by the number of moles of water per molecule of water (the inverse of Avogadro’s number, n_A, molecules w mol^-1w) and by the total pore area per unit leaf area (the product of stomatal density, {rho}_s, stomata m^-2_leaf, and area per pore, a_p, m²_pore stoma^-1). Note also that N_w/n_A = C_w, the molar concentration of water (mol w m^-3air). Thus,

(7) .

Now we approximate dC_w/dz as the ratio of finite molar concentration difference ({delta}C_w) to a finite effective diffusion pathlength (l, m), and convert {delta}C_w to a mole fraction difference, {delta}X_w (mol w mol^-1air) by noting that C_w equals X_w divided by the molar volume of air (RT/p_tot, m³air mol^-1air). Thus, with units spelled out,

(8) .

Total conductance (g_tw) comprises everything in Eqn 8 except the mole fraction gradient {delta}X_w:

(9) .

Thus, the “mol” in molar conductance units represents moles of air, not those of the diffusing species. (The remaining units balance because the generic spatial dimensions in the numerator, which arose from pore area, diffusivity and diffusion pathlength, define a volume of space filled with air, so they cancel the m³ air in the denominator, leaving mol air m^-2_leaf s^-1.)

Links to resources and suppliers

Campbell Scientific, Inc. (stand-alone dataloggers/controllers): http://www.campbellsci.com

Measurement Computing, Inc. (USB dataloggers/controllers): http://www.mccdaq.com

Sensirion (humidity sensors): http://www.sensirion.com

Omega Engineering (mass flow controllers, thermocouple wire, tubing): http://www.omega.com

Literature references

Atkins P.W. (1990) Physical chemistry. (4 ed.). Oxford University Press, Oxford, UK.

Bloom A.J., Mooney H.A., Bjorkman O. & Berry J.A. (1980) Materials and methods for carbon dioxide and water exchange analysis. Plant, Cell & Environment, 3, 371-376.

Bugbee B., Droter M., Monje O. & Tanner B. (1998) Evaluation and modification of commercial infra-red transducers for leaf temperature measurement. Advances in Space Research, 22, 1425-1434.

Caemmerer S. & Farquhar G.D. (1981) Some relationships between the biochemistry of photosynthesis and the gas exchange of leaves. Planta, 153, 376-387.

Cowan I.R. (1977) Stomatal behaviour and environment. Advances in Botanical Research, 4, 117-228.

Farquhar G.D. & Raschke K. (1978) On the Resistance to Transpiration of the Sites of Evaporation within the Leaf. Plant Physiology, 61, 1000-1005.

Grace J. (1989) Measurement of wind speed near vegetation. In: Plant physiological ecology: field methods and instrumentation (eds R.W. Pearcy, J.R. Ehleringer, H.A. Mooney, & P.W. Rundel). Chapman Hall, London.

Hetherington A.M. & Woodward F.I. (2003) The role of stomata in sensing and driving environmental change. Nature, 424, 901-908.

Jones H.G. (1992) Plants and microclimate. (2nd ed.). Cambridge University Press, Cambridge.

McDermitt D.K. (1990) Sources of error in the estimation of stomatal conductance and transpiration from porometer data. Horticultural Science, 25, 1538-1548.

Mott K.A. & O’Leary J.W. (1984) Stomatal Behavior and CO2 Exchange Characteristics in Amphistomatous Leaves. Plant Physiology, 74, 47-51.

Nobel P.S. (1991) Physicochemical and environmental plant physiology. Academic Press, London.

Organization W.M. (2008) Guide to Meteorological Instruments and Methods of Observation. WMO, Geneva, Switzerland.

Parkinson K.J. & Legg B.J. (1972) A continuous flow porometer. Journal of Applied Ecology, 9, 669-699.

Pearcy R.W., Schulze E.D. & Zimmermann R. (1989) Measurement of transpiration and leaf conductance. In: Plant physiological ecology: field methods and instrumentation (eds R.W. Pearcy, J.R. Ehleringer, H.A. Mooney, & P.W. Rundel). Chapman Hall, London.

Sharkey T.D., Imai K., Farquhar G.D. & Cowan I.R. (1982) A Direct Confirmation of the Standard Method of Estimating Intercellular Partial Pressure of CO2. Plant Physiology, 69, 657-659.

Health, safety & hazardous waste disposal considerations

Silica gel and drierite can both cause skin and eye irritation, and respiratory irritation if dust is inhaled. Use gloves and eye protection and avoid generating dust. Disposal of spills does not require special procedures. Material Safety Data Sheets for both products are available from manufacturers and suppliers (e.g., http://www.sigmaaldrich.com; http://www.fishersci.com; http://www.drierite.com).

Figure 1: Block diagram of a steady state porometer console and chamber head. Description: air flows from the console to chamber head (solid arrows), power is supplied via a 12V battery (dashed lines). A datalogger/controller measures the infrared leaf temperature sensor (ir), the relative humidity/air temperature sensor (RH and T_a) and the mass flow meter (dotted lines). In this configuration the porometer can measure g_sw using either a constant flow or a constant chamber humidity; the latter requires a feedback algorithm to regulate the mass flow controller (thick solid line).