Internal utility functions for the calculation of biophysical variables.

## Usage

```
biophysics_radiationDiurnalPattern(t, daylength)
biophysics_temperatureDiurnalPattern(
t,
tmin,
tmax,
tminPrev,
tmaxPrev,
tminNext,
daylength
)
biophysics_leafTemperature(absRad, airTemperature, u, E, leafWidth = 1)
biophysics_leafTemperature2(
SWRabs,
LWRnet,
airTemperature,
u,
E,
leafWidth = 1
)
biophysics_leafVapourPressure(leafTemp, leafPsi)
biophysics_irradianceToPhotonFlux(I, lambda = 546.6507)
biophysics_waterDynamicViscosity(temp)
```

## Arguments

- t
Time of the day (in seconds).

- daylength
Day length (in seconds).

- tmin, tmax
Minimum and maximum daily temperature (ºC).

- tminPrev, tmaxPrev, tminNext
Maximum and minimum daily temperatures of the previous and following day (ºC).

- absRad
Absorbed long- and short-wave radiation (in W·m-2).

- airTemperature
Air temperature (in ºC).

- u
Wind speed above the leaf boundary layer (in m/s).

- E
Transpiration flow (in mmol H20·m-2·s-1) per one sided leaf area basis.

- leafWidth
Leaf width (in cm).

- SWRabs
Absorbed short-wave radiation (in W·m-2).

- LWRnet
Net long-wave radiation balance (in W·m-2).

- leafTemp
Leaf temperature (ºC).

- leafPsi
Leaf water potential (MPa).

- I
Irradiance (in W*m-2).

- lambda
Wavelength (in nm).

- temp
Temperature (ºC).

## Value

Values returned for each function are:

`biophysics_leafTemperature`

and`biophysics_leafTemperature2`

: leaf temperature (in ºC)`biophysics_leafVapourPressure`

: leaf vapour pressure (in kPa)`biophysics_radiationDiurnalPattern`

: the proportion of daily radiation corresponding to the input time in seconds after sunrise.`biophysics_temperatureDiurnalPattern`

: diurnal pattern of temperature.`biophysics_waterDynamicViscosity`

: Water dynamic viscosity relative to 20ºC.

## Details

Functions `biophysics_leafTemperature`

and `biophysics_leafTemperature2`

calculate leaf temperature according to energy balance equation given in Campbell and Norman (1988).

Function `biophysics_radiationDiurnalPattern`

follows the equations given in Liu and Jordan (1960).

Function `biophysics_temperatureDiurnalPattern`

determines diurnal temperature pattern assuming a sinusoidal pattern with T = Tmin at sunrise and T = (Tmin+Tmax)/2 at sunset and a linear change in temperature between sunset and Tmin of the day after (McMurtrie et al. 1990).

Function `biophysics_waterDynamicViscosity`

calculates water dynamic viscosity following the Vogel (1921) equation.

## References

Campbell, G. S., and J. M. Norman. 1998. An introduction to environmental biophysics: 2nd edition. (eqns. 14.1 & 14.3)

B. Y. H. Liu and R. C. Jordan, “The interrelationship and characteristic distribution of direct, diffuse and total solar radiation,” Solar Energy, vol. 4, no. 3, pp. 1–19, 1960.

McMurtrie, R. E., D. A. Rook, and F. M. Kelliher. 1990. Modelling the yield of Pinus radiata on a site limited by water and nitrogen. Forest Ecology and Management 30:381–413.

H. Vogel, "Das Temperaturabhangigkeitsgesetz der Viskositat von Flussigkeiten", Physikalische Zeitschrift, vol. 22, pp. 645–646, 1921.