Gb.Su {bigleaf}

Boundary Layer Conductance according to Su et al. 2001

Description

A physically based formulation for the canopy boundary layer conductance to heat transfer according to Su et al. 2001.

Usage

Gb.Su(
  data,
  Tair = "Tair",
  pressure = "pressure",
  ustar = "ustar",
  wind = "wind",
  H = "H",
  zh,
  zr,
  d,
  z0m = NULL,
  Dl,
  fc = NULL,
  LAI = NULL,
  N = 2,
  Cd = 0.2,
  hs = 0.01,
  stab_formulation = c("Dyer_1970", "Businger_1971"),
  Sc = NULL,
  Sc_name = NULL,
  constants = bigleaf.constants()
)

Arguments

data

Data.frame or matrix containing all required variables

Tair

Air temperature (degC)

pressure

Atmospheric pressure (kPa)

ustar

Friction velocity (m s-1)

wind

Wind speed (m s-1)

H

Sensible heat flux (W m-2)

zh

Canopy height (m)

zr

Reference height (m)

d

Zero-plane displacement height (-), can be calculated using roughness.parameters

z0m

Roughness length for momentum (m). If not provided, calculated from roughness.parameters within wind.profile

Dl

Leaf characteristic dimension (m)

fc

Fractional vegetation cover [0-1] (if not provided, calculated from LAI)

LAI

One-sided leaf area index (-)

N

Number of leaf sides participating in heat exchange (defaults to 2)

Cd

Foliage drag coefficient (-)

hs

Roughness height of the soil (m)

stab_formulation

Stability correction function used (If stab_correction = TRUE). Either "Dyer_1970" or "Businger_1971".

Sc

Optional: Schmidt number of additional quantities to be calculated

Sc_name

Optional: Name of the additional quantities, has to be of same length than Sc_name

constants

Kelvin - conversion degree Celsius to Kelvin
pressure0 - reference atmospheric pressure at sea level (Pa)
Tair0 - reference air temperature (K)
Sc_CO2 - Schmidt number for CO2
Pr - Prandtl number (if Sc is provided)

Details

The formulation is based on the kB-1 model developed by Massman 1999. Su et al. 2001 derived the following approximation:

kB-1 = (k Cd fc^2) / (4Ct ustar/u(zh)) + kBs-1(1 - fc)^2

If fc (fractional vegetation cover) is missing, it is estimated from LAI:

fc = 1 - exp(-LAI/2)

The wind speed at the top of the canopy is calculated using function wind.profile.

Ct is the heat transfer coefficient of the leaf (Massman 1999):

Ct = Pr^-2/3 Reh^-1/2 N

where Pr is the Prandtl number (set to 0.71), and Reh is the Reynolds number for leaves:

Reh = Dl wind(zh) / v

kBs-1, the kB-1 value for bare soil surface, is calculated according to Su et al. 2001:

kBs^-1 = 2.46(Re)^0.25 - ln(7.4)

Gb (=1/Rb) for water vapor and heat are assumed to be equal in this package. Gb for other quantities x is calculated as (Hicks et al. 1987):

Gb_x = Gb / (Sc_x / Pr)^0.67

where Sc_x is the Schmidt number of quantity x, and Pr is the Prandtl number (0.71).

Value

A data.frame with the following columns:

Gb_h

Boundary layer conductance for heat transfer (m s-1)

Rb_h

Boundary layer resistance for heat transfer (s m-1)

kB_h

kB-1 parameter for heat transfer

Gb_Sc_name

Boundary layer conductance for Sc_name (m s-1). Only added if Sc_name and Sc_name are provided

Note

If the roughness length for momentum (z0m) is not provided as input, it is estimated from the function roughness.parameters within wind.profile. This function estimates a single z0m value for the entire time period! If a varying z0m value (e.g. across seasons or years) is required, z0m should be provided as input argument.

References

Su, Z., Schmugge, T., Kustas, W. & Massman, W., 2001: An evaluation of two models for estimation of the roughness height for heat transfer between the land surface and the atmosphere. Journal of Applied Meteorology 40, 1933-1951.

Massman, W., 1999: A model study of kB H- 1 for vegetated surfaces using 'localized near-field' Lagrangian theory. Journal of Hydrology 223, 27-43.

Hicks, B.B., Baldocchi, D.D., Meyers, T.P., Hosker, J.R., Matt, D.R., 1987: A preliminary multiple resistance routine for deriving dry deposition velocities from measured quantities. Water, Air, and Soil Pollution 36, 311-330.

See Also

Gb.Thom, Gb.Choudhury, aerodynamic.conductance

Examples

# Canopy boundary layer resistance (and kB-1 parameter) for a set of meteorological conditions,
# a leaf characteristic dimension of 1cm, and an LAI of 5
df <- data.frame(Tair=25,pressure=100,wind=c(3,4,5),ustar=c(0.5,0.6,0.65),H=c(200,230,250)) 
Gb.Su(data=df,zh=25,zr=40,d=17.5,Dl=0.01,LAI=5)

# the same meteorological conditions, but larger leaves
Gb.Su(data=df,zh=25,zr=40,d=17.5,Dl=0.1,LAI=5)

# same conditions, large leaves, and sparse canopy cover (LAI = 1.5)
Gb.Su(data=df,zh=25,zr=40,d=17.5,Dl=0.1,LAI=1.5)