Shading

The shade covering a model segment is calculated by determining how far a shadow reaches across the surface. This is a function of the solar altitude, solar azimuth, segment orientation, tree height, channel width and the distance of the vegetation from the edge of the water. Data used in calculating the shading along the Lower Bull Run River were obtained from stream survey work conducted by Beak Consultants Inc., 1998.

The CE-QUAL-W2 subroutine ‘HEAT_EXCHANGE’ calculates solar declination Decl (radians), solar hour angle Hour (radians), and solar altitude A0 (degrees). The solar altitude A0 is the angle of the sun above the horizon, Figure 63. These variables are calculated in the following section of code:

******* Solar radiation

DATA EQT /-0.13, -0.23, -0.16, -0.02, 0.06, 0.00, -0.09,

. -0.08, 0.06, 0.22, 0.25, 0.10/

LONG0 = 15.0*INT(LONG/15.0)

Decl = 0.409280*COS(0.017214*(172.0-JDAYG))

X = (JDAY-JDAYG)*24.0

Hour = 0.261799*(X-(LONG-LONG0)*0.066667+EQT(M)-12.0)

SINAL = SIN(LAT*.017453)*SIN(D)+COS(LAT*.017453)*COS(D)*COS(H)

A0 = 57.2985*ASIN(SINAL)

where

LONG – longitude of the water body (degrees)

LAT – latitude of the water body (degrees)

X – day fraction (hours)

LONG0 – standard meridian of the time zone (degrees)

M – month number

EQT – monthly adjustment factor

‘0.261799’ – hours per radians

JDAYG – julian day (integer value)

JDAY – julian day (floating point value)

‘0.066667’ – hours per degree

‘0.017453’ – radians per degree

’57.2985’ – degrees per radian

SINAL – sine of the solar altitude A0

Azimuth AZ is the direction of the sun with respect to a north-south axis, Figure 64. Lee (1978) gives the following equation for azimuth.

Tree shadow length S_T is calculated using the tree height T and sun altitude A0, Figure 63.

The length of the shadow cast over the water S_W is determined with

E is the distance between the tree and the edge of water and phi0 is the segment orientation, Figure 64 and Figure 65. Finally, shadow length perpendicular S_N to the edge of the water is

and substituting for S_W

and S_T

A shading reduction factor was applied in cases when a model segment had potential shading along only part of its length or the vegetation density was low. For instance, if shade-producing vegetation exists along only half the length of a segment, a shade reduction factor of 0.5 was used. If this same shading was due to vegetation with only 80% density then the shading reduction factor would then be 40% (0.50x0.80) for the segment. In the case of the Lower Bull Run River shade reduction factors were set to 1.0 times a vegetation density estimated by Beak Consultants (1998) to indicate there was shading vegetation along all segments of the model grid but with less than 100% vegetation density.

The fraction which short wave solar radiation is reduced, , is the shadow length perpendicular to the edge of the water S_N multiplied by the shading reduction factor F and divided by the segment width .

Bank with Sun

The bank that has the sun behind it depends upon the angle of the segment phi0 and the solar azimuth, AZ. The convention used for defining left or right bank is dependent on the model segment numbering. If looking in the direction of increasing segment numbers, the ‘left bank’ is on the left and the ‘right bank’ is to the right. Table 39 summarizes the criteria used in selecting the bank with the sun behind it. The criteria were modified from Chen (1996) because the segment orientation angle is determined differently using CE-QUAL-W2. AZ is the solar azimuth and phi0 the orientation of the segment.
 
 

Bank with Sun
Right	or
Left		or

Seasonal Shading

The shading algorithm could be used to consider seasonal shading due to loss of foliage in the fall and regrowth in the spring. For the Lower Bull Run River seasonal shading was not considered because the predominant shading mechanisms are topography and coniferous trees.
 
 

Topographic Shading

The lower Bull Run River is characterized by steep terrain and a narrow channel indicating that shading due to local topography will considerably influence the amount of solar radiation reaching the water suraface. Figure 66 illustrates the influence of topographic shading on the water surface of a stream. In order to characterize the influence of topographic shading detailed topographic survey data of the river channel from the Water Bureau and USGS Digital Elevation map was used to slice 18 arrays around the center point of eah grid segement in the lower river model, Figure ###. Each array consisted of spatial and elevation data out to a distance of 100 m from the segment center point. From each array the maximum inclination angle was determined which dictates the topographic shading. The end result was for each segment of the model 18 maximum inclination angles were determined along with their orientation relative to the center point of the segment. The inclination angles were then used in the shading algorithm to determine if vegetative or topographic shading was dominating at a specific time during the day. If the sun’s inclination angle was below the the topographic inclination angle then topographic shading dominated and the solar radiation was reduced by 90%. The shading algorithm also determined the cloasest two inclination angles in the direction of the incoming solar radiation and used them to linearly interpolate an inclination angle for the specifica direction of the incoming solar radiation. If vegetative shading dominated then the vegetation density characterized through the shade reduction factor was then used to reduce the incoming solar radiation hitting the water surface.

Plots were made of the amount of shading along the Lower Bull Run River at different times of the day, for four different times of the year. Figure 67, Figure 68, Figure 69, and Figure 70 show the shading throughout the day on the winter solstice, vernal equinox, summer solstice and autumnal equinox respectively. A value of 0.0 is equivalent to 100% shading. A value of 1.0 is equivalent to no shade.

Figure 71 compares the percentage of shading along the Lower Bull Run River using the CE-QUAL-W2 model and two previous models. The models were all run for the same day, September 25, 1998 so the incoming solar radiation was consistent. Two sets of results were estimated using the shading algorithm developed for CE-QUAL-W2. The first used a shade reduction factor of 1.0 for all segments and the second represents the impact of the vegetation density as estimated by Beak Consultants (1998).