Stefan Boltzmann Longwave

The Stefan Boltzmann Longwave Method implements the longwave radiation algorithm described within TVA (1972) and Follum et al. (2015). The method estimates the amount of longwave radiation at a specific location (grid cell or subbasin) using the air temperature and relative humidity. As such, this method requires the use of a valid temperature and relative humidity method.

Downwelling longwave radiation at the top of the canopy and includes longwave radiation from air and clouds is estimated with:

$\begin{array}{l}\displaystyle LW_{toc}=\sigma\epsilon_a\cdot T_a^4\cdot(1+.17N^2)\end{array}$

where

$\begin{array}{l}\sigma\end{array}$ is the Stefan-Boltzmann constant

$\begin{array}{l}\epsilon_a\end{array}$ is air emissivity

N is fractional cloud clover

Within HEC-HMS, air emissivity in kPa is taken from Bras (1990) given by the equation:

$\begin{array}{l}\displaystyle (0.740 + 0.0049 * (RH/ 100.0 * (e^o * 100)))/100\end{array}$

where

RH is the relative humidity in percent and

$\begin{array}{l}e^o\end{array}$ is the saturation vapor pressure

The saturation pressure is taken from either Smith (1993) or FAO (1998).

Smith (1993) defines saturation vapor pressure, $\begin{array}{l}e^o\end{array}$ , in millibars as:

$\begin{array}{l}\displaystyle e^o=2.7489*10^8*e^{-4278.63/(T+242.792)}\end{array}$

where

T is the air temperature in Celsius

The FAO estimate for $\begin{array}{l}e^o\end{array}$ in kPa is given by equation 11 of FAO (1998):

$\begin{array}{l}\displaystyle e^o = 0.6108e[\frac{17.27T}{T+237.3}]\end{array}$

where T is the air temperature in Celsius.

Required Parameters

The user must select a temperature and relative humidity method to be used with this longwave radiation method in the Meteorologic Manager. Additionally, the user must choose the Atmospheric Emissivity Method, of which there is only one as of v4.12, Bras 1990 and the Saturation Vapor Pressure method.