cal_netLongwaveRadiation {simET}

Calculating net longwave radiation Rnl

Description

Calculating net longwave radiation Rnl

Usage

cal_netLongwaveRadiation(TKmax, TKmin, ea, Rs, Rso)

Arguments

TKmax

maximum absolute temperature during the 24-hour period [K].

TKmin

minimum absolute temperature during the 24-hour period [K].

ea

actual vapour pressure [kPa].

Rs

measured or calculated solar radiation [MJ m-2 day-1]. From cal_solarRadiation().

Rso

calculated clear-sky radiation [MJ m-2 day-1]. From cal_skySolarRadiation_withas_bs() or cal_skySolarRadiation_withas_elevation().

Value

A vector for net outgoing longwave radiation [MJ m-2 day-1]

Note

The rate of longwave energy emission is proportional to the absolute temperature of the surface raised to the fourth power. This relation is expressed quantitatively by the Stefan-Boltzmann law. The net energy flux leaving the earth's surface is, however, less than that emitted and given by the Stefan-Boltzmann law due to the absorption and downward radiation from the sky. Water vapour, clouds, carbon dioxide and dust are absorbers and emitters of longwave radiation. Their concentrations should be known when assessing the net outgoing flux. As humidity and cloudiness play an important role, the Stefan-Boltzmann law is corrected by these two factors when estimating the net outgoing flux of longwave radiation. It is thereby assumed that the concentrations of the other absorbers are constant. An average of the maximum air temperature to the fourth power and the minimum air temperature to the fourth power is commonly used in the Stefan-Boltzmann equation for 24-hour time steps. The term (0.34-0.14*sqrt(ea)) expresses the correction for air humidity, and will be smaller if the humidity increases. The effect of cloudiness is expressed by (1.35 Rs/Rso - 0.35). The term becomes smaller if the cloudiness increases and hence Rs decreases. The smaller the correction terms, the smaller the net outgoing flux of longwave radiation. Note that the Rs/Rso term in Equation 39 must be limited so that Rs/Rso <= 1.0. Where measurements of incoming and outgoing short and longwave radiation during bright sunny and overcast hours are available, calibration of the coefficients in Equation 39 can be carried out.

References

Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. FAO Irrigation and drainage paper No. 56. Rome: Food and Agriculture Organization of the United Nations, 1998.