The angle between the line from an observer on the earth to the sun and a vertical line extending upward from the observer is called the zenith angle, θz (Figure 1:1-1). Solar noon occurs when this angle is at its minimum value for the day.
For a given geographical position, the relationship between the sun and a horizontal surface on the earth's surface is:
cosθz=sinδsinϕ+cosδcosϕcosωt 1:1.1.3
where δ is the solar declination in radians, ϕ is the geographic latitude in radians, ω is the angular velocity of the earth's rotation (0.2618 rad or 15˚ ), and t is the solar hour. equals zero at solar noon, is a positive value in the morning, and is a negative value in the evening. The combined term is referred to as the hour angle.
Sunrise, , and sunset, , occur at equal times before and after solar noon. These times can be determined by rearranging the above equation as:
1:1.1.4
and
1:1.1.5
Total daylength, is calculated:
1:1.1.6
At latitudes above or below , the absolute value of [ ] can exceed 1 and the above equation cannot be used. When this happens, there is either no sunrise (winter) or no sunset (summer) and must be assigned a value of 0 or 24 hours, respectively.
To determine the minimum daylength that will occur during the year, equation 1:1.1.6 is solved with the solar declination set to (-0.4102 radians) for the northern hemisphere or (0.4102 radians) for the southern hemisphere.
The only SWAT+ input variable used in the calculations reviewed in Section 1:1.1 is given in Table 1:1-1.
Table 1:1-1: SWAT+ input variables that are used in earth-sun relationship calculations.
Definition
Source Name
Input Name
Input file
Latitude of the weather generator station (degrees).
lat
latitude