Reduced Solar Constant

The Reduced Solar Constant Shortwave method implements the shortwave radiation algorithm described within TVA (1972) and Follum et al, (2015). The method estimates the amount of shortwave radiation at a specific location (grid cell or subbasin) by reducing the solar constant (1366 Watts / square meter) using several factors including distance from the earth to the sun, atmospheric scattering, and slope/aspect of the terrain. If the basin model is not georeferenced and/or doesn't have an associated terrain model, these calculations will proceed assuming the location is at the equator and at sea-level.

Basic Concept and Equations

The solar constant represents the extraterrestrial radiation, S₀ at the atmosphere's surface a mean distance from the sun and perpendicular to the direction of radiation. By the time rays have travelled down to the earth's surface, the magnitude of solar radiation from the top of the atmosphere has been reduced and attenuated by several factors included in the equation below from Follum et al, 2015:

$\begin{array}{l}SW=S_0K_rK_a_t_mK_cK_vK_sK_t\end{array}$

where:

$\begin{array}{l}SW\end{array}$ is the incident shortwave radiation at the land surface

$\begin{array}{l}K_r\end{array}$ is the adjustment for distance from the earth to the sun

$\begin{array}{l}K_a_t_m\end{array}$ is the reduction due to atmospheric scattering of radiation

$\begin{array}{l}K_c\end{array}$ is the reduction due to radiation absorption by clouds

$\begin{array}{l}K_v\end{array}$ is a vegetation transmission coefficient to account for canopy coverage

$\begin{array}{l}K_s\end{array}$ is the reduction due to slope of the terrain

and $\begin{array}{l}K_t\end{array}$ is topographic shading

The adjustment for the distance from the sun based on the day of the year is given by the equation below (TVA, 1972):

$\begin{array}{l}\displaystyle K_r={[1.0+0.017cos((\frac{2\pi}{365}(186-JD))]}^{-2}\end{array}$

where JD is the Julian Day of the year.

The atmospheric scattering adjustment accounts for the thickness of the atmosphere, aerosols and moisture in the air based on the land surface elevation is given by Allen et al, 2005:

$\begin{array}{l}\displaystyle K_a_t_m=0.75 + (2* 10^{-5})*Elev\end{array}$

Reduction due to cloud reflection and absorption is given by (TVA, 1972):

$\begin{array}{l}\displaystyle K_c = 1.0 -0.65N^2\end{array}$

where N is the fractional cloud cover.

If the solar radiation hits at a directly perpendicular angle K_s would be simplified as 1, as that is rarely the case, Duffie and Beckman (1991) developed a method to calculate the angle of incidence ( $\begin{array}{l}\phi\end{array}$ ) using the latitude, slope and azimuth angle of the grid cell, solar declination as calculated by Shuttleworth (1993) and sun hour angles:

$\begin{array}{l}\displaystyle cos(\phi)=sin(L)sin(\delta)cos(\beta)-cos(L)sin(\delta)sin(\beta)cos(Z_s)+cos(L)cos(\delta)cos(ℎ)cos(\beta)+sin(L)cos(\delta)cos(ℎ)sin(\beta)cos(Z_s)+cos(\delta)sin(ℎ)sin(\beta)sin(Z_s)\end{array}$

The reduction due to the land aspect is given by the cosine of $\begin{array}{l}\phi\end{array}$ :

$\begin{array}{l}\displaystyle K_s=cos(\phi})\end{array}$

Nearby topography can shade the land surface, resulting in a decrease in the solar radiation reaching that location. This reduction can be estimated using solar azimuth (Duffie and Beckman, 1980) and solar elevation angles along with topography geometry to determine if the direct line of solar radiation is blocked from reaching a given cell's surface. If the sun rays are blocked, $\begin{array}{l}K_t\end{array}$ is set to 0 for that hour and if it is not blocked, $\begin{array}{l}K_t\end{array}$ is set to 1.

In HEC-HMS, this equation does not take into account canopy reduction, cloud absorption or topographic shading, so $\begin{array}{l}K_v\end{array}$ , $\begin{array}{l}K_c\end{array}$ , and $\begin{array}{l}K_t\end{array}$ are taken as 1.

Required Parameters

The user must select the method for computing Solar Declination, Aspect Reduction, Earth Distance Reduction, and Atmospheric Absorption Reduction. The methods are pre-loaded into HEC-HMS and are selected from a dropdown list in the component editor.