Theory of operation

The LI-600 is equipped to measure two different aspects of leaf photosynthesis. The porometer uses a mass balance for water vapor flux from the leaf to compute stomatal conductance. The fluorometer uses optical techniques to probe the quantum yield of photosystem II.

The LI-600 also has a GPS receiver and an accelerometer/magnetometer that measures the pitch, roll, and heading of a leaf. Those measurements, along with GPS information, are used by the LI-600 software to calculate a leaf's angle of incidence.

This section describes the theory and equations behind these measurements and provides an overview of other sensors in the LI-600.

Leaf porometer

The LI-600 porometer is an open system. Stomatal conductance (gsw) is computed from transpiration (E) in a leaf cuvette and leaf temperature (Tleaf) is measured by a non-contact infrared thermometer. Transpiration is computed from the difference in H2O in an air-stream flowing through a leaf cuvette (Figure 9‑1).

Figure 9‑1. Air flow measured before and after interaction with a leaf.

Relative humidity (RH) sensors on the cuvette measure the air stream before and after it interacts with a leaf. Flow rates are measured before and after passing through the cuvette; leaf temperature is measured in the cuvette.

Derivation of equations

The mass balance of water vapor in an open system at steady-state is given by

9‑1

where s is leaf area (m2), E is transpiration (mol m-2 s-1), ui, uo (µmol s-1) are flow rates into and out of the leaf cuvette, respectively, Wref, Wsam are water vapor mole fractions into and out of the leaf cuvette (mol H2O mol air-1). Since

9‑2

we can substitute equation 9‑2 into equation 9‑1 to write

9‑3

Solving equation 9‑3 for E gives

9‑4

Total conductance to water vapor is given by

9‑5

where gtw is total conductance to water vapor (mol H2O m-2 s-1), and Wleaf is the calculated molar concentration of water vapor within the leaf inter-cellular air-space (mol H2O mol air-1). Wleaf is calculated from measured leaf temperature and pressure (equations 9‑7 and 9‑9).

Calculation of stomatal conductance (gsw) requires removal of the contribution from the boundary layer (gbw)

9‑6

where (gsw) is the one-sided stomatal conductance to water vapor, and (gbw) is the one-sided boundary layer conductance, both in (mol H2O m-2 s-1).

Boundary layer conductance in the LI-600 cuvette is a function of the flow rate (equation 9‑10).

The actual measurements for water vapor being made in the LI-600 are done using relative humidity sensors on the inlet and outlets of the cuvette. In order to calculate the mass balance as described above, the relative humidities must be converted to molar fractions, requiring additional measurements for the temperature of the sensors (Tref) and the atmospheric pressure (Press).

The vapor pressures are calculated from the relative humidity measurement and a saturation vapor function from Buck (1981):

9‑7

where satvap(T) is the saturation vapor pressure (kPa) at the given temperature T (°C)

9‑8

where VPx is the calculated vapor pressure (kPa) with x is 'cham','ref' or 'leaf', rhx is the relative humidity (%) measured by the LI-600 sensors and Tref (°C) is the temperature read by a thermistor in the block adjacent to the RH sensors. For calculation of leaf vapor pressure, it is assumed that the internal air-space is at saturation, i.e., relative humidity within the leaf is 100%, which reduces the equation to equation 9‑7.

Water vapor concentrations are dependent on the atmospheric pressure and must be calculated in order to solve the mass balance

9‑9

where H2Ox is the water vapor concentration in reference, sample cuvette and leaf (mmol H2O mol air-1) VPx is the vapor pressure from equation 9‑8 and Press is atmospheric Pressure (kPa).

Boundary layer conductance

The portion of the leaf in the cuvette has the boundary layer stripped by the air flow across the leaf surface. The conductance of the boundary layer is measured using a source of temperature-controlled water vapor where total conductance = boundary layer conductance.

9‑10gbw = flow2 × -6.755E-5 + 0.0292302 × flow

where flow is the cuvette flow rate in (µmol s-1).

Implementation of equations in the LI-600

The equations implemented in the LI-600 are shown below.

Sensor calculations

The following equations convert the sensor read-out in volts to the appropriate units. The RH and flow sensor equations currently take the following form to allow for factory calibration and user-adjustable zero and span settings:

9‑11

where V is the voltage read from the sensor, Z is a user-settable zero parameter and S is a user-settable span parameter and f(x) is a 3rd or 4th order polynomial.

RH sensors

The RH Sensors have a small sensitivity to temperature that must be accounted for. A temperature correction occurs both in the zero setting and in the calibration function. The sample RH sensor also must be corrected for a match offset, as shown in Additional calculations for porometry. We will use the terminology of RHr and RHs to indicate sensors before the cuvette (reference) and sensors after the cuvette (sample). Note that a match offset is applied to the RHs value (equation 9‑16).

9‑12a

9‑12b

where mx and bxz are factory-determined coefficients and Tref is a thermistor embedded in the block adjacent to the RH sensors.

Converting RH sensor voltage to RH (%) requires 4 factory-determined coefficients and the zero and span setting for each sensor.

9‑13a

9‑13b

where subscript r and s represent the reference and sample RH sensors, respectively. is the sensor voltage, is the user-settable sensor zero, is the user-settable span (nominally 1.0).

RH (%) is then computed from y with a 3rd order polynomial

9‑14a

9‑14b

where ax, bx, cx and dx are factory-determined coefficients for each RH sensor.

Matching RH sensors

The above equations describe calculations for the RH sensors. Any offset between the two sensors must be accounted for by matching them.

9‑15

9‑16

Flow sensors

Converting flow sensor voltage to a flow rate (µmol s-1) requires 4 factory-determined coefficients and a zero and span setting for each flow sensor.

9‑17a

9‑17b

where subscript In or Out are for the flow sensors entering and exiting the cuvette, respectively, VflowX is the sensor voltage, ZflowX is the user-settable sensor zero (nominally 0.6), SflowX is the user-settable span (nominally 1.0).

Flow (µmol s-1) is then computed from y with a 4th order polynomial

9‑18a

9‑18b

where ax, bx, cx and dx are factory-determined coefficients for each flow sensor.

Infrared temperature sensor

Leaf temperature (°C) is computed as a function of the reference temperature and the IRT sensor response

9‑19

where Vleaf is the voltage from the IRT target, Tref is the reference temperature and atl to gtl are factory coefficients.

PAR sensor

Photosynthetically active radiation (µmol m-2 s-1) is computed from a factory-calibrated photodiode response.

9‑20

where Vpar is the voltage measured from the sensor, Zquantum is a user-settable offset for when no light reaches the sensor, and Qcoeff is a factory calibration with units of .

Additional calculations for porometry

9‑21

9‑22

9‑23

9‑24

9‑25

9‑26

9‑27

9‑28

9‑29

9‑30gbw = flow2 × -6.755E-5 + 0.0292302 × flow

9‑31

9‑32

Stability criteria in auto mode

In Auto mode, the user does not manually log a measurement; the LI-600 automatically logs the data point when the stability criteria set in the configuration are met. The software provides flexibility in allowing a user to choose when a measurement is considered stable (see Automode Setup). A measurement is considered stable based on monitoring changes over time to both the computed stomatal conductance gsw, and the de-modulated fluorescence signal F if the fluorometer is used. In a given configuration, a user selects which variables to monitor (gsw, F or both) and a stability limit, and the periods over which to calculare the change. Since the LI-600 is designed for rapid survey measurements, the time period is limited to 1, 2, or 4 seconds.

The LI-600 retains up to 4 seconds of 2 Hz data to calculate stability criteria as follows:

9‑33

9‑34

9‑35

where X is either the computed stomatal conductance gsw, or the de-modulated fluorescence signal F if a fluorometer is used, and t is the time for a given measurement.

Since a limited number of data points (2, 4 or 8) are used, the stability criteria is not a regression slope, but represents the amount of change in the parameter over the selected time period. The LI-600 continuously computes the stability criteria, and compares the value to the slope limit. When two consecutive data points are below the threshold, then the measurement is considered stable and is logged.

User calibration procedures

Users can adjust calibrations for the flow sensors (zero only) and the RH sensors (zero and 1-point span). See also Calibrating the sensors.

RH sensor zero

Resetting the zero set-point on an RH sensor will alter the offset parameter for a given sensor (brhr or brhs in equations 9‑12a and 9‑12b). A prerequisite to starting a calibration is access to tank air or a column of chemical to scrub H2O from the airstream. Ensure dry conditions prior to resetting a zero, which can take 30 minutes or more of flowing dry air across the sensors.

Upon initiation, the calibration routine averages 10 seconds of data for Tref and Vx and then recalculate the zero intercept:

9‑36

After calculating bxnew, the user must confirm the new setpoint. The new value will then stored to memory.

RH sensor span

Resetting the span setpoint is an adjustment of the parameter Sx in equations 9‑13a and 9‑13b for each sensor, respectively. A prerequisite to starting a calibration is access to a known H2O source, such as a dewpoint generator. The known quantity might be in a dewpoint temperature, or potentially in mole fraction units. The software will accept either unit and convert to the correct relative humidity at the sensor using equations 9‑7, 9‑21, and 9‑25, with Press coming from the LI-600 pressure sensor and Tref coming from the LI-600 reference thermistor.

The span setting requires all calibration parameters for a given sensor from equations 9‑12a, 9‑12b, 9‑13a, 9‑13b, 9‑14a, and 9‑14b, as well as rhtrue, current reference temperature Tref and the voltage of the sensor Vx.

Upon initiation, the calibration routine averages 10 seconds of data for Tref and Vx and then re-calculate the span

9‑37

where is inverse of equations 9‑14a and 9‑14b, Tref and Vx are the current values read by the RH and Temperature sensors and mx and other parameters are the current calibration values for the sensor from equations 9‑14a, and 9‑14b. After calculating Sxnew, the new value is stored to memory.

Flow sensors zero

Resetting the zero setpoint on a flow sensor will alter the offset parameter for a given sensor (Zflowx in equations 9‑17a and 9‑17b). If you select the option to zero the flow sensors, the software powers down the pump and the blower before resetting the zero. The calibration procedure will need the current zero parameters (Zx from equations 9‑17a and 9‑17b) and current values for the voltage reading on the flow sensor (Vflowx) with the pump/blower OFF.

The calibration routine averages 10 seconds of data for Vflowx and then resets the zero:

9‑38a

9‑38b

After calculating Zflowx, the new value is stored to memory:

9‑39

Fluorometer

The LI-600 fluorometer is a Pulse-Amplitude Modulated (PAM) fluorometer with a measuring beam provided by two LEDs focused on the portion of leaf in the porometer cuvette. Fluorescence is detected via a single detector located between the LED measuring beams, filtered by a 750 ± 40 nm band-pass filter. Fluorescence is detected then from ~700 to 780 nm, which gathers the majority of fluorescence from PSII but is also contaminated with PSI florescence in a similar fashion to the LI-6800 Portable Photosynthesis System fluorometer (Genty et al., 1989, Pfundel et al., 2013).

Actinic light is not provided by the LI-600 fluorometer but rather by ambient light which could be natural sun-light or any number of artificial light sources. The two LEDs are both modulated at a constant frequency and provide both the measuring beam and saturating flash. One unique aspect of the design is that the saturating flash is not delivered as a constant output but is modulated at high frequencies to achieve the necessary high light intensity. The use of both LEDs for providing the measuring beam and saturating flash has a few advantages over using a single LED for each purpose, including 1) improved light uniformity from light reaching the leaf from multiple angles and 2) increased peak intensity for the measuring beam, leading to 3) improved signal-to-noise ratio.

The peak intensities of the measuring beam necessarily are quite high in order to receive enough signal and are factory set to ~10,000 µmol m-2 s-1. Pulse width has been set to 667 ns. Total integrated light intensity incident on the leaf from the LEDs is calculated as

9‑40

where Pfreq is the current pulse frequency (2 to 750,000 Hz), Pwidth is the pulse width (667 ns) and Qpeakx is the peak intensity of the left and right LEDs, set by a factory calibration.

The peak intensity is ~10,000 µmol m-2 s-1 and is calculated from a calibration coefficient set at the factory. Frequencies for steady-state measurements will be very low (4 to 8 Hz), while frequencies during the flash will be much higher (250 to 750 kHz).

Implementation on the LI-600

TheLI-600 calculates parameters as described.

Calculating light intensity from LED calibration coefficients

Each LED has two calibration coefficients: a DAC set point (DACx) and a parameter relating DAC setting to light intensity (Qcalx). The peak intensity of each LED is calculated from these coefficients:

9‑41a

9‑41b

A given configuration provides a steady-state modulation frequency Modrate in Hz and a desired flash intensity for rectangular and phases 1 and 3 of multi-phase flashes flash_intensity in µmol m-2 s-1. The instrument will determine the flash modulation frequency based on desired user intensity and calculated peak intensity (assuming both LEDs have the same intensity) from:

9‑42

where Pwidth is 667E-9 seconds

The total amount of light incident on the leaf from the LEDs is then calculated from

9‑43

Freqset will be either the steady-state modulation frequency Modrate if not during a flash, Freqflash during a rectangular flash or Phases 1 and 3 of an MPF or the calculated frequency based on ramp rate during Phase 2 of an MPF. PARflr is written to flash files during each log point.

Dark-adapted vs light-adapted measurements

With the LI-600 fluorometer, the actinic light source is provided by external sources unknown to the instrument. The instrument cannot know if a given measurement being made is on a dark-adapted leaf or not. The user must decide which type of measurement is being made. Table 9‑1 shows the values being used for each configuration type. The calculated yield uses the same equation in either case, as shown here.

9‑44

9‑45

Table 9‑1. Dark and light adapted measurement parameters.
Type Pre-flash F Flash F Calculated Yield
Dark-adapted Fo Fm Fv/Fm
Light-adapted Fs Fm’ ΦPSII

Steady-state fluorescence

Steady-state fluorescence logged is the final value received prior to the onset of the flash. A zero offset is applied to the de-modulated fluorescence that removes small artifacts that arise from imperfect discrimination or electronic noise. The offset is stored as a calibration constant and can be re-set by the user. Steady-state fluorescence removes the zero offset following.

9‑46

where vF is read from the ADC and Zflr is a factory coefficient. The measurement frequency is set in the configuration.

Rectangular flash

A rectangular flash delivers a user-selectable flash intensity (µmol m-2 s-1) for a user-selectable amount of time (ms). The LI-600 converts that to a frequency during the flash using the factory calibration value.

Multiphase flash

The LI-600 can perform multiphase flashes for conditions where it is difficult to fully saturate with rectangular flashes (Loriaux et al, 2013). A multiphase flash delivers a flash in three phases and requires inputs of the length of each phase (P1_dur, P2_dur, P3_dur) in msec, and the amount to reduce the intensity (P2_Ramp Dept).

The Phase2 F data is regressed vs. 1E4/Q using only Phase 2 data. The resulting slope is captured and the intercept is logged to Fm'.

Values that are captured or calculated and logged during an MPF only are:

  • P1_dur: Phase 1 Duration (msec)
  • P2_dur: Phase 2 Duration (msec)
  • P3_dur: Phase 3 Duration (msec)
  • P1_FMax: Max F during Phase 1
  • P2_slp: Slope of F vs 1/Q during Phase 2
  • P3_Fmax: Measured Fmax during Phase 3
  • P3_Pred: Predicted Phase 3 F using Phase 2 regression
  • P3_DeltaF: Difference between measured and predicted Phase 3 F (P3_Fmax - P3_Pred)

Additional fluorometer calculations

Electron Transport Rate (ETR) is also calculated from all light-adapted flashes from

9‑47

where φPSII comes from the flash as shown above, Qamb is from the ambient PAR sensor (equation 9‑20), abs and PS2/1 are constants given by the user in the configuration.

Logged Variables

The LI-600 logs variables into two groups: porometry and fluorometry.

Porometry group

The porometry group includes variables in Table 9‑2.

Table 9‑2. Variables logged in the porometry group.
Description Label Units Equation
Stomatal conductance gsw mol m−2 s−1 9‑6
Boundary layer conductance gbw mol m−2 s−1 9‑10
Total conductance gtw mol m−2 s−1 9‑5
Transpiration E mol m−2 s−1 9‑4
Chamber vapor pressure VPcham kPa 9‑21
Leaf vapor pressure VPleaf kPa 9‑23
Reference H2O mole fraction H2O_r mmol mol−1 9‑25
Sample H2O mole fraction H2O_s mmol mol−1 9‑26
Leaf H2O mole fraction H2O_leaf mmol mol−1 9‑27
Leaf Area leaf_area cm2 NA

Fluorometry group

The fluorometry group includes variables in Table 9‑3.

Table 9‑3. Variables logged in the fluorometry group.
Description Label Units Equation
FlashID flashID NA NA
Minimum Fluorescence in Dark Fo NA NA
Maximum Fluorescence in Dark Fm NA
Quantum Efficiency in Dark Fv/Fm NA 9‑44
Minimum Fluorescence in Light Fs NA NA
Maximum Fluorescence in Light Fm’ NA NA
Quantum Efficiency in light phiPSII NA 9‑45
Leaf absorptance abs NA 9‑47
Ratio of PSII to PSII absorptance PS2/1 NA 9‑47
Electron Transport Rate ETR μmol m−2 s−1 9‑47