Turgor Loss Point

The function TurgorLossPoint fits the data using the Gauss-Newton algorithm of nls() to a combined exponential and linear model. The exponential and linear parts are extracted and RWD at turgor loss point is localized at their point of minimum distance. The result is outputted as a list and a plot:

pv <- RelativeWaterDeficit(pressure_volume_data)
TurgorLossPoint(pv)

Osmotic Potential

The function OsmoticPot allows the calculation of water potential at turgor loss point, osmotic potential at full saturation and apoplastic fraction.

First, RWD at turgor loss point is derived by the function TurgorLossPoint. The osmotic potential is then derived by fitting a linear regression line with the Gauss-Newton algorithm of nls() to the water potential data following the turgor loss point. The y- and x-axis intercept of the regression line gives the osmotic potential at full hydration (op.full.sat) and the apoplastic fraction (apo.fract), respectively. Water potential at turgor loss point equals the value of the osmotic potential fit at the relative water deficit at turgor loss point:

pv <- RelativeWaterDeficit(pressure_volume_data)
OsmoticPot(pv)

Modulus of Elasticity

Modulus of elasticity can be determined by the function ModElasticity. Relative water deficit at turgor loss point and osmotic potential are first calculated via the functions ‘TurgorLossPoint’ and ‘OsmoticPot’.

Pressure potential is derived by subtracting osmotic potential from water potential. The part of the pressure potential prior the turgor loss point is then fitted linearly and the modulus of elasticity (M.Elasticity) equals the slope of the fitted line:

ModElasticity(pv)

Driving force for transpiration

Vapor pressure deficit is calculated by the humidity and temperature during the experiment which need to be allocated to the weight loss measurements fist. The function WeatherAllocation calculates averages within a measurement period by approximate integration and normalization of the weather as a function of time:

library(pvldcurve)
data <- WeatherAllocation(leaf_drying_data, weather_data)

Mole fraction vapor pressure deficit can be calculated individually by the use of the function VaporPressureDeficit as:

data <- VaporPressureDeficit(data)

\(VPD =(1 - RH / 100) * (VPsat / AP)\)

whereas \(RH\) = relative humidity \((percentage)\), \(AP\) = atmospheric pressure \((kPA)\), \(VPsat\) = saturation vapor pressure \((kPA)\), whereas:

\(VPsat = 0.61121 * exp ((18.678 - T * 234.5^{-1}) (T * 257.14 + T))\)

or:

data <- SaturationVaporPressure(data)

where \(T\) = air temperature \((degree Celsius)\). Atmospheric pressure at the experimental site can be specified as an argument. It is by default 101.325 \(kPA\).

Transpiration

Transpiration \((mmol s^{-1} m^{-2})\) is calculated by the function Transpiration as:

data <- Transpiration(data, 
                      fresh.weight = "fresh.weight")

\(T = \Delta FM * 1000 (\Delta t * 60 * LA * 2 /10000 * 18.01528)^{-1}\)

whereas \(T\) = transpiration, \(\Delta FM\) = reduction of fresh weight \((g)\), \(\Delta t\) = time unit \((min)\), \(LA\) = single-sided leaf area \((cm^2)\) \(\Delta FM\) can be calculated by WeightDifference and \(\Delta t\) by TimeInterval:

data:wd <- WeightDifference(data)
data_ti <- TimeInterval(data)

Conductance

The function Conductance calculates mole-based conductance \((mmol s^{-1} m^{-2})\) as:

\(g = Tp / VPD\)

It doesn’t require the prior transformation of data but works with the raw data :

data <- Conductance(data,  
                    fresh.weight = "fresh.weight")

Concentration based conductance \((mm s^{-1})\) is derived from mole-based conductance as:

\(g(conc) = g * R * (T + 273.15) / AP / 1000\)

where \(R\) = gas constant.

data <- Conductance(data,  
                    fresh.weight = "fresh.weight",
                    driving.force = "conc")

Stomatal Closure

The point of stomatal closure is reached when the leaf drying curve settles irreversibly to linear water loss. First, calculate RWD based on the interval between two measurements and time since start \((min)\) of the experiment:

data <- RWDInterval(leaf_drying_data, 
                    fresh.weight = "fresh.weight")
data <- TimeSinceStart(data)

To find the point of stomatal closure, the conductances by time since start curves are fitted using the Gauss-Newton algorithm of nls() to a combined exponential and linear model. The exponential and linear parts are extracted and time since start at stomatal closure is localized at the point where the slope of the exponential part of the fit is higher than a threshold value.

The threshold value is calculated by the use of the parameter b of the exponential part of the fit \((a * exp(b * x))\): \(-(b^2 * sens)\). The sensitivity argument (\(sens\)) is 60 by default and can be specified individually using the argument ‘threshold’.

RWD at stomatal closure is then calculated by linear regression of RWD and time since start.

Before using this function, check the raw data for an initial plateau. If the exponential decline does not onset directly, fitting might not succeed. In the inherent dataset, plateauing data points are marked in a separate column.

data <- WeatherAllocation(leaf_drying_data, weather_data) 
data <- TimeSinceStart(data)
data <- RWDInterval(data, 
                    fresh.weight = "fresh.weight")
data <- data[data$fw.plateau != "yes",] 
data <- Conductance(data, 
                    fresh.weight = "fresh.weight")

StomatalClosure(data)

Removing noises in the fresh weight values is recommend prior using StomatalClosure(). The function FittedFW will do so via fitting of the fresh weight values to a combined exponential and linear model using the port algorithm of nls():

data <- WeatherAllocation(leaf_drying_data, weather_data) 
data <- TimeSinceStart(data)
data <- data[data$fw.plateau != "yes",] 
data <- FittedFW(data)

Thereby, calculation of stomatal closure is improved:

data <- WeatherAllocation(leaf_drying_data, weather_data) 
data <- TimeSinceStart(data)
data <- data[data$fw.plateau != "yes",] 
data <- FittedFW(data, graph = FALSE)
data <- RWDInterval(data, 
                    fresh.weight = "fitted.fw")
data <- Conductance(data, 
                    fresh.weight = "fitted.fw")

StomatalClosure(data)

Minimum conductance

Minimum conductance is calculated with the function Gmin by the leaf drying curve in three ways. First, The coordinates of stomatal closure are determined via the function StomatalClosure(). Then, conductance data including and following stomatal closure is extracted and the average is taken (mean.gmin). A linear regression is applied to the data including gmin at stomatal closure, which is determined by the function StomatalClosure(), and the y axis intercept (gmin.full.sat) and the coordinate at the RWD point of stomatal closure (lin.gmin) are calculated from the function.

data <- WeatherAllocation(leaf_drying_data, weather_data) 
data <- TimeSinceStart(data)
data <- data[data$fw.plateau != "yes",] 
data <- FittedFW(data, graph = FALSE)
data <- RWDInterval(data, fresh.weight = "fitted.fw")
data <- Conductance(data, fresh.weight = "fitted.fw")

Gmin(data)