Create → RTS File for Qnet Longwave Flux

The input variables for modeling the net flux of longwave radiation are defined as follows:

Tair = air temperature [deg C]
RH = relative humidity [unitless] (in [0,1])
albedo = surface albedo [unitless] (in [0,1])
cloud fraction = fraction of sky covered by clouds [unitless] (in [0,1])
canopy fraction = fraction of sky covered by canopy [unitless] (in [0,1])
Tsurf = surface temperature [deg C]
emsurf = surface emissivity [unitless] (in [0,1])
eair = vapor pressure of air [mbar, not kPa]

For each variable, you may choose from the droplist of data types. For the "Scalar" data type, enter a numeric value with the units indicated in the dialog. For the other data types, enter a filename. Values in files must also use the indicated units.

Single grids and grid sequences are assumed to be stored as RTG and RTS files, respectively. Time series are assumed to be stored as text files, with one value per line. For a time series or grid sequence, the time between values must coincide with the timestep provided.

The timestep between frames in the new grid sequence (RTS file) should typically be about one hour and should match the timestep that will be used to model the Snowmelt or Evaporation processes. The number of frames in the RTS file will depend on the start and stop times, as well as the timestep. The start time, stop time and timestep should match those used to create the new shortwave radiation file with extension "*.Qn-SW".


Equations Used to Compute Longwave Radiation

QLW = (LWin - LWout) = net longwave radiation [W / m2]
LWin = emair * σ * (Tair + 273.15)4 = incoming longwave radiation
LWout = emsurf * σ * (Tsurf + 273.15)4   +
     (1 - emsurf) * LWin = outgoing longwave radiation
esat = 6.11 * exp[(17.3 * T) / (T + 237.3)] = saturation vapor pressure [mbar, not KPa]
eair = esat(Tair) * RH = vapor pressure of air [mbar]
emair = [(1 - F) * 1.72 * [eair / (Tair + 273.15)]1/7   *
     (1 + 0.22 * C2)] + F = emissivity of air [unitless]

Notes on the Equations

This routine creates a grid sequence (RTS file format) of net longwave radiation flux, QLW, that is used for the energy-balance methods of Snowmelt and Evaporation. The incoming and outgoing longwave radiation are computed using the Stefan-Boltzman law as follows:

LWin = emair * σ * (Tair + 273.15)4
LWout = emsurf * σ * (Tsurf + 273.15)4 + (1 - emsurf) * LWin

where emair is the emissivity of air, emsurf is the emissivity of the surface (e.g. snow), and σ = 5.67e-8 [W/(m2 K4)] is the Stefan-Boltzman constant. Tair and Tsurf are the temperatures of the air and the surface (e.g. snow) in degrees Celsius.

The emissivity of air can be computed from the relative humidity, RH, the air temperature, Tair, the fraction of sky covered by clouds, C, and the fraction of sky covered by the forest canopy, F. First, the vapor pressure (in millibars, not kPa) is computed using the Brutsaert (1975) method as:

esat = 6.11 * exp[(17.3 * T) / (T + 237.3)]        Brutsaert (1975)
eair = esat(Tair) * RH

[Note that the value 237.3 in Brutsaert's equation is not a misprint.] Then, emair is computed as:

emair = [(1 - F) * 1.72 * [eair / (Tair + 273.15)]1/7 * (1 + 0.22 * C2)] + F.

For additional information, see the help page for the shortwave radiation calculator.


References

Brutsaert, W. (1975) On a derivable formula for long-wave radiation from clear skies, Water Resources Research, 11, 742-744.

Dingman, S.L (2002) Physical Hydrology, 2nd ed., Prentice Hall, New Jersey. (see Chapter 7, pp. 285-299)