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 (g_{sw}) is computed from transpiration (E) in a leaf cuvette and leaf temperature (T_{leaf}) is measured by a non-contact infrared thermometer. Transpiration is computed from the difference in H_{2}O in an air-stream flowing through a leaf cuvette (Figure 9‑1).
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
where s is leaf area (m^{2}), E is transpiration (mol m^{-2} s^{-1}), u_{i}, u_{o} (µmol s^{-1}) are flow rates into and out of the leaf cuvette, respectively, W_{ref}, W_{sam} are water vapor mole fractions into and out of the leaf cuvette (mol H_{2}O mol air^{-1}). Since
we can substitute equation 9‑2 into equation 9‑1 to write
Solving equation 9‑3 for E gives
Total conductance to water vapor is given by
where g_{tw} is total conductance to water vapor (mol H_{2}O m^{-2} s^{-1}), and W_{leaf} is the calculated molar concentration of water vapor within the leaf inter-cellular air-space (mol H_{2}O mol air^{-1}). W_{leaf} is calculated from measured leaf temperature and pressure (equations 9‑7 and 9‑9).
Calculation of stomatal conductance (g_{sw}) requires removal of the contribution from the boundary layer (g_{bw})
where (g_{sw}) is the one-sided stomatal conductance to water vapor, and (g_{bw}) is the one-sided boundary layer conductance, both in (mol H_{2}O 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 (T_{ref}) and the atmospheric pressure (Press).
The vapor pressures are calculated from the relative humidity measurement and a saturation vapor function from Buck (1981):
where satvap(T) is the saturation vapor pressure (kPa) at the given temperature T (°C)
where VP_{x} is the calculated vapor pressure (kPa) with x is 'cham','ref' or 'leaf', rh_{x} is the relative humidity (%) measured by the LI-600 sensors and T_{ref} (°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
where H_{2}O_{x} is the water vapor concentration in reference, sample cuvette and leaf (mmol H_{2}O mol air^{-1}) VP_{x} 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.
9‑10g_{bw} = flow^{2} × -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:
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 RH_{r} and RH_{s} to indicate sensors before the cuvette (reference) and sensors after the cuvette (sample). Note that a match offset is applied to the RH_{s} value (equation 9‑16).
where m_{x} and b_{xz} are factory-determined coefficients and T_{ref} 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.
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
where a_{x}, b_{x}, c_{x} and d_{x} 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
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.
where subscript In or Out are for the flow sensors entering and exiting the cuvette, respectively, V_{flowX} is the sensor voltage, Z_{flowX} is the user-settable sensor zero (nominally 0.6), S_{flowX} 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 a_{x}, b_{x}, c_{x} and d_{x} 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 V_{leaf} is the voltage from the IRT target, T_{ref} is the reference temperature and a_{tl} to g_{tl} are factory coefficients.
PAR sensor
Photosynthetically active radiation (µmol m^{-2} s^{-1}) is computed from a factory-calibrated photodiode response.
where V_{par} is the voltage measured from the sensor, Z_{quantum} is a user-settable offset for when no light reaches the sensor, and Q_{coeff} is a factory calibration with units of .
Additional calculations for porometry
9‑22
9‑24
9‑28
9‑29
9‑30g_{bw} = flow^{2} × -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 g_{sw}, 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 (b_{rhr} or b_{rhs} 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 H_{2}O 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 T_{ref} and V_{x} and then recalculate the zero intercept:
9‑36
After calculating b_{xnew}, 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 S_{x} in equations 9‑13a and 9‑13b for each sensor, respectively. A prerequisite to starting a calibration is access to a known H_{2}O 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 T_{ref} 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 rh_{true}, current reference temperature T_{ref} and the voltage of the sensor V_{x}.
Upon initiation, the calibration routine averages 10 seconds of data for T_{ref} and V_{x} and then re-calculate the span
9‑37
where is inverse of equations 9‑14a and 9‑14b, T_{ref} and V_{x} are the current values read by the RH and Temperature sensors and m_{x} and other parameters are the current calibration values for the sensor from equations 9‑14a, and 9‑14b. After calculating S_{xnew}, 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 (Z_{flowx} 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 (Z_{x} from equations 9‑17a and 9‑17b) and current values for the voltage reading on the flow sensor (V_{flowx}) with the pump/blower OFF.
The calibration routine averages 10 seconds of data for V_{flowx} and then resets the zero:
9‑38a
9‑38b
After calculating Z_{flowx}, 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 P_{freq} is the current pulse frequency (2 to 750,000 Hz), P_{width} is the pulse width (667 ns) and Q_{peakx} 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 (DAC_{x}) and a parameter relating DAC setting to light intensity (Q_{calx}). The peak intensity of each LED is calculated from these coefficients:
9‑41a
9‑41b
A given configuration provides a steady-state modulation frequency Mod_{rate} 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 P_{width} is 667E-9 seconds
The total amount of light incident on the leaf from the LEDs is then calculated from
9‑43
Freq_{set} will be either the steady-state modulation frequency Mod_{rate} if not during a flash, Freq_{flash} 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. PAR_{flr} 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.
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 v_{F} is read from the ADC and Z_{flr} 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
where φPSII comes from the flash as shown above, Q_{amb} 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.
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 H_{2}O mole fraction | H2O_r | mmol mol^{−1} | 9‑25 |
Sample H_{2}O mole fraction | H2O_s | mmol mol^{−1} | 9‑26 |
Leaf H_{2}O mole fraction | H2O_leaf | mmol mol^{−1} | 9‑27 |
Leaf Area | leaf_area | cm^{2} | NA |
Fluorometry group
The fluorometry group includes variables in Table 9‑3.
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 |