Calculating the phytochrome photoequilibrium
In the examples below we use the solar spectral data included in
package ‘photobiology’ as a data frame in object
sun.spct.
We can calculate the phytochrome photoequilibrium from spectral
irradiance data contained in a source_spct object as
follows.
## [1] 0.68341
We can also calcualte the red:far-red photon ratio, in this second
example, for the same spectrum as above
## R:FR[q:q]
## 1.266704
## attr(,"radiation.unit")
## [1] "q:q ratio"
which is equivalent to calculating it using package ‘photobiology’
directly
q_ratio(sun.spct, Red("Smith10"), Far_red("Smith10"))
## R:FR[q:q]
## 1.266704
## attr(,"radiation.unit")
## [1] "q:q ratio"
We can, and should whenever spectral data are available, calculate
the photoequilibrium as above, directly from these data. It is possible
to obtain and approximation in case of the solar spectrum and other
broad spectra, using the red:far-red photon ratio. The calculation,
however, is only strictly valid, for di-chromatic illumination with red
plus far-red light.
Pfr_Ptot_R_FR(R_FR(sun.spct))
## R:FR[q:q]
## 0.7051691
Here we calculated the R:FR ratio from spectral data, but in practice
one would use this function only when spectral data is not available as
when a R plus FR sensor is used. We can see that in such a case the
photoequilibrium calculated is only a rough approximation. For sunlight,
in the example above when using spectral data we obtained a value of
0.683 in contrast to 0.705 when using the R:FR photon ratio. For other
light sources differences can be much larger. Furthermore, here we used
the true R:FR ratio calculated from the spectrum, while broad-band
red:far-red sensors guive only an approximation, which is good for
sunlight, but which will be innacurate for artifical light, unless a
special calibration is done for each type of lamp.
In the case of monochromatic light we can still use the same
functions, as the defaults are such that we can use a single value as
the ‘w.length’ argument, to obtain the Pfr:P ratio. For monochromatic
light, irradiance is irrelevant for the photoequilibrium
(steady-state).
## [1] 0.869649
## [1] 0.01749967
## [1] 0.86964902 0.01749967
## [1] 0.3859998
We can also plot Pfr:Ptot as a function of wavelength (nm) of
monochromatic light. The default is to return a vector for short input
vectors, and a response_spct object otherwise, but this can
be changed through argument spct.out.
autoplot(Pfr_Ptot(300:770), unit.out = "photon",
w.band = Plant_bands(),
annotations = c("colour.guide", "labels", "boxes")) +
labs(y = "Phytochrome photoequilibrium, Pfr:Ptot ratio")
It is, of course, also possible to use base R plotting functions, or
as shown here functions from package ‘ggplot2’
ggplot(data = Pfr_Ptot(300:770), aes(w.length, s.q.response)) +
geom_line() +
labs(x = "Wavelength (nm)",
y = "Phytochrome photoequilibrium, Pfr:Ptot ratio")
In the case of dichromatic illumination with red (660 nm) and far-red
(730 nm) light, we can use a different function that takes the R:FR
photon ratio as argument.
These computations are valid only for true mixes of light at
these two wavelengths but not valid for broad spectra like sunlight and
especially inaccurate for plant growth lamps with peaks in their output
spectrum, such as most discharge lamps (sodium, mercury, multi-metal,
fluorescent tubes) and many LED lamps.
## [1] 0.6919699
## [1] 0.04747996
Pfr_Ptot_R_FR(c(1.15,0.01))
## [1] 0.69196990 0.04747996
It is also easy to plot Pfr:P ratio as a function of R:FR photon
ratio. However we have to remember that such values are exact only for
dichromatic light, and only a very rough approximation for wide-spectrum
light sources. For wide-spectrum light sources, the photoequilibrium
should, if possible, be calculated from spectral irradiance data.
ex6.data <- data.frame(r.fr=seq(0.01, 5.0, length.out=100), Pfr.p=numeric(100))
ex6.data$Pfr.p <- Pfr_Ptot_R_FR(ex6.data$r.fr)
ggplot(data=ex6.data, aes(r.fr, Pfr.p)) +
geom_line() +
labs(x ="R:FR photon ratio",
y = "Phytochrome photoequilibrium, Pfr:Ptot ratio")
Water vapour in air
The functions described in this section and the following one have
been migrated from package ‘photobiology’ (>= 0.12.0) to
‘photobiologyPlants’ (>= 0.6.0).
Water vapour partial pressure in air depends on temperature and on
whether air is in equilibrium with liquid water or ice.Not considered
here, solutes in water and surface interactions also affect the
equilibrium. The examples below use the default equation for the
computation of saturated water vapour pressure. The default is Tetens’
equation from 1930. Currently supported methods are
"tetens", modified "magnus",
"wexler" and "goff.gratch".
water_vp_sat(20) # temperature in C, partial pressure in Pa
## [1] 2338.023
water_vp_sat(20) * 1e-3 # temperature in C, partial pressure in kPa
## [1] 2.338023
vp_sat.df <- data.frame(temperature = -20:100,
vp.sat = c(water_vp_sat(-20:-1, over.ice = TRUE),
water_vp_sat(0:100)) * 1e-3)
ggplot(vp_sat.df, aes(temperature, vp.sat)) +
geom_line() +
labs(x = "Temperature (C)", y = "Water valour pressure at saturation (kPa)")
Conversion of water vapour pressure to relative humidity and vice
versa is based on the curve shown in the figure above.
water_vp2RH(1000, 25) # Pa and C -> RH%
## [1] 31.57191
water_vp2mvc(1000, 25) # Pa and C -> mass per volume g m-3
## [1] 7.264556
The reverse conversion functions are water_RH2vp(),
water_mvc2vp().
If we know the actual vapour pressure we can compute at which
temperature this pressure would the saturating (RH = 100%), or dew
point.
## [1] 6.973856
If the vapour pressure is very low, instead of dew point we have to
compute the freezing point.
## [1] -2.40697
Function water_vp_sat_slope() can be used to compute the
slope of the curve in the figure above as a function of air temperature,
and function psychrometric_constant() to compute the
psychrometric constant as a function of air temperature.
Reference evapotranspiration
Evapotranspiration is the combined water fluxes between a vegetation
canopy and the atmosphere, It is the sum of transpiration (water that
evaporates inside leaves and flows through stomata) and evaporation
(water that evaporated from the soil and other surfaces, including from
the wet outer surfaces of plants and their leaves). Measured
evapotranspiration is described as actual evapotranspiration
(\(\mathrm{ET}\)), the maximum rate of
evapotranspiration of short vegetation canopy is called reference
evapotranspiration (\(\mathrm{ET}_\mathrm{ref}\)), also described
as potential evapotranspiration (\(\mathrm{PET}\))). Potential
evapotranspiration can be measured on irrigated vegetation, but can also
be estimated from meteorological conditions. Supported methods are the
current FAO recommended and some earlier ones still in use.
Instantaneous \(\mathrm{ET}_\mathrm{ref}\) expressed in
\(mm\ h^{-1}\) can be obtained with
ET_ref().
ET_ref(temperature = 20, # C
water.vp = water_RH2vp(relative.humidity = 70, # RH%
temperature = 20), # C -> Pa
wind.speed = 0, # m s-1
net.irradiance = 100) # W m-2
## [1] 0.172792
Daily \(\mathrm{ET}_\mathrm{ref}\)
expressed in \(mm\ d^{-1}\) can be
obtained with ET_ref_day()
ET_ref_day(temperature = 20, # C daily mean
water.vp = 1636.616, # Pa daily mean
wind.speed = 5, # m s-1 daily mean
net.radiation = 15e6) # 15 MJ / d / m2 daily total !
## [1] 7.199597
As many of other factions in the package, these functions are
vectorized.
ET_ref(temperature = 20, # C
water.vp = water_RH2vp(relative.humidity = (1:9) * 10, # RH%
temperature = 20), # C -> Pa
wind.speed = 5, # m s-1
net.irradiance = 10) # W m-2
## [1] 0.01733964 0.01733277 0.01732590 0.01731904 0.01731217 0.01730530 0.01729843
## [8] 0.01729157 0.01728470
Potential evapotranspiration is in most situation proportional to the
available radiant energy.
ET_ref_irrad.df <-
data.frame(irrad = (1:40) * 10,
ET.ref = ET_ref(temperature = 20, # C
water.vp = water_RH2vp(relative.humidity = 70, # RH%
temperature = 20), # C -> Pa
wind.speed = 5, # m s-1
net.irradiance = (1:40) * 10) # W m-2
)
ggplot(ET_ref_irrad.df, aes(irrad, ET.ref)) +
geom_line() +
labs(x = expression("Global radiation "*(W~m^{-2})),
y = expression("Reference evapotranspiration "*(mm~h^{-1})))
Function net_irradiance() simplifies the computation of
net irradiance, needed as input for the computation of reference
evapotranspiration.
