PermafrostTools: PermafrostTools

Description Usage Arguments Details Value Author(s) Examples

Computes an estimated thermal condictivity for snow based on snow density or on liquid water and ice content in the snow pack. Differing parameterizations are available. The result is an effective thermal conductivity as various processes (conduction, advection, diffusion, radiative transfer) are parameterised. In the ground, differing mixing model are applied to the proprtions and thermo-physical properties of ground constituents.

1 2	TermCond(mat, layers.sno = c(0), type.sno = "CALONNE", type.gnd = "COSENZA")

`mat`	Data frame with relevant ground properties. Needed: mat$ice (ice content, volumetric fraction) and mat$liq (liquid water content, volumetric fraction).
`layers.sno`	Index to identify snow layers within 'mat'.
`type.sno`	Character string indicating the type of parameterization to be used for snow; the standard is CALONNE. Available are: CALONNE: Calonne, N., Flin, F., Morin, S., Lesaffre, B., du Roscoat, S. R., & Geindreau, C. (2011). Numerical and experimental investigations of the effective thermal conductivity of snow. Geophysical Research Letters, 38(23), doi:10.1029/2011GL049234 "YEN": Yen, Y.-C. (1981). Review of thermal properties of snow, ice and sea ice (34 pages). Hanover, NH, USA. COSENZA: Cosenza, P., Guerin, R., & Tabbagh, A. (2003). Relationship between thermal conductivity and water content of soils using numerical modelling. European Journal of Soil Science, 54(3), 581–588. doi:10.1046/j.1365-2389.2003.00539.x STURM: Sturm, M., J. Holmgren, M. König, and K. Morris (1997), The thermal conductivity of seasonal snow, Journal of Glaciology, 43(143), 26–41. JORDAN: Jordan, R. E., Andreas, E. L., & Makshtas, A. P. (1999). Heat budget of snow-covered sea ice at North Pole 4. Journal of Geophysical Research, 104(C4), 7785. doi:10.1029/1999JC900011 WILLIAMS: Figure 4.11 in "The Frozen Earth: fundamentals of geocryology" by P. Williams and M. Smith, 1989.
`type.gnd`	Character string indicating the type of parameterization to be used for ground; the standard is "COSENZA". Available are: COSENZA: Cosenza, P., Guerin, R., & Tabbagh, A. (2003). Relationship between thermal conductivity and water content of soils using numerical modelling. European Journal of Soil Science, 54(3), 581–588. doi:10.1046/j.1365-2389.2003.00539.x GEOMETRIC: Geometric mean, intermediate mixed conductivity model, approximation of randomly oriented consituent elements. ARITHMETIC: Arithmetic mean, high mixed conductivity model, approximation of consituent elements layered parallel to temperature gradient. HARMONIC: Harmonic mean, low mixed conductivity model, approximation of consituent elements layered normal to temperature gradient.

Positive are to the right while left shifts are expressed as a negative number. All shifts are circular. Elements shifted off one end wrap around and are shifted onto the other end. This function mimicks the behaviour of SHIFT in IDL.

Returns the input data frame with the column kj updated in [W m-1 K-1] If this column does not exist in the input it is created.

Stephan Gruber <stephan.gruber@carleton.ca>

rho.i <-  917  # [kg m-3]
rho.l <- 1000  # [kg m-3]
mat   <- data.frame(ice = (0:600)/1000, 
                    liq = rep(0.0,601))
dens  <- mat$ice*rho.i + mat$liq*rho.l

mat <- TermCond(mat, type.sno = "CALONNE", layers.sno = 1:601)

plot(dens, mat$kj, type = "l", col = "black", main = 
     "Comparison of parameterization for snow thermal conductivity", 
     xlab = "Density [kg m-3]", ylab = "Thermal conductivity [W m-1 K-1]")

mat <- TermCond(mat , type.sno = "YEN", layers.sno = 1:601)
lines(dens, mat$kj, col = "red")

mat <- TermCond(mat , type.sno = "COSENZA", layers.sno = 1:601)
lines(dens, mat$kj, col = "blue")

mat <- TermCond(mat , type.sno = "STURM", layers.sno = 1:601)
lines(dens, mat$kj, col = "green")

mat <- TermCond(mat , type.sno = "WILLIAMS", layers.sno = 1:601)
lines(dens, mat$kj, col = "orange")

mat <- ermCond(mat , type.sno = "JORDAN", layers.sno = 1:601)
lines(dens, mat$kj, col = "darkorchid2")

legend("topleft", inset=.05, seg.len = 2, lty = 1, lwd =1,
  	   c("CALONNE","YEN","COSENZA", "STURM", "WILLIAMS", "JORDAN"), 
  	   col = c("black", "red", "blue", "green", "orange", "darkorchid2"))