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##### Description

This component has two functions. One is to distribute measured or estimated solar radiation values for a horizontal surface to the slope and aspect combination of each HRU. The second is to estimate missing solar radiation data.

Observed daily shortwave radiation (solrad) expressed in langleys per day (ly/d) can be input directly or estimated from daily air-temperature and precipitation data for watersheds where it is not available. solrad, measured on a horizontal surface, is adjusted to estimate swrad, the daily shortwave radiation received on the slope-aspect combination of each HRU. swrad is computed by:

$$swrad = (solrad * \frac {radpl\_potsw} {horad}) / radpl\_cossl$$

where

• $$radpl\_potsw$$ = the daily potential solar radiation for the slope and aspect of a radiation plane (ly),
• $$horad$$ = daily potential solar radiation for a horizontal surface (ly), and
• $$radpl\_cossl$$ = the cosine of the radiation plane slope

Tables consisting of daily estimates of the potential (clear sky) short-wave solar radiation for each radiation plane (radpl_potsw) are computed on the basis of hours between sunrise and sunset for each Julian day of the year in module Soltab.java. The potential short-wave solar radiation is also computed for each Julian day of the year for a horizontal plane at the centroid of the modeled basin (horad). Daily values of radpl_potsw and horad are calculated using a combination of methods described in Meeus (1999), Lee (1963), and Swift (1976).

For missing days or periods of record, solrad can be estimated using an air temperature / degree-day relationship described by Leaf and Brink (1973). This method was developed for a section of the Rocky Mountain Region of the United States. It appears most applicable to regions where predominantly clear skies prevail on days without precipitation. The method is shown graphically in the coaxial relation of . A daily maximum temperature is entered in the X-axis of part A and intersects the appropriate month curve. From this intersection point, one moves horizontally across the degree-day coefficient axis and intersects the curve in part B. From this point, the ratio of actual-to-potential radiation for a horizontal surface (solf) can be obtained.

Example of coaxial relationship for estimating shortwave solar radiation from maximum daily air temperature developed for northwestern Colorado.

An estimate of solrad is then computed by:

$$solrad=solf*horad$$

The ratio solf is developed for days without precipitation; thus, the computed solrad is for dry days. solrad for days with precipitation is computed by multiplying the dry day solrad times a precipitation correction factor ppt_adj. ppt_adj is determined based on the maximum air temperature (tmax) measured at the basin index temperature station (basin_tsta) on the day with precipitation and the current month. If tmax is greater than or equal to the monthly parameter tmax_index, then ppt_adj is computed by:

$$ppt_adj=(radadj\_slope*tdif)+radadj\_intcp$$

where

• $$tdif$$ = the difference between tmax and tmax_index

If tmax is less than tmax_index then ppt_adj is set equal to a user-defined constant radj_wppt for the period October through April or radj_sppt for the period May through September. The use of tmax_index is an attempt to distinguish between days where precipitation is convective in origin and days where precipitation is frontal in origin. Days with typically short convective storms may have more solar radiation than those days with frontal storms. The assumption is that for each month a maximum temperature threshold value can be used to distinguish between these storm types.

The input parameters required to use this procedure are the slope (dday_slope) and the y-intercept (dday_intcp) of the line that expresses the relationship between monthly maximum air temperature and a degree-day coefficient (dd). dd is computed by:

$$dd=(dday\_slope*tmax)+dday\_intcp$$

where

• $$tmax$$ = the observed daily maximum air temperature. The dd-solf relationship of add dday_temp link is assumed constant.

Monthly values of dday_slope and dday_intcp can be estimated from historic air- temperature and solar-radiation data. One method is to make monthly plots of tmax versus their daily degree-day coefficients, dd, for days without precipitation. The dd values for this plot are computed using and the daily solf ratios computed from historic data. A set of monthly lines then can be drawn through these points either visually or with linear- regression techniques. If there is a large difference in elevation between the climate station on the watershed and the station with radiation data, the air-temperature data associated with the radiation data should be adjusted to the elevation of the study-basin climate station.

A more rapid and coarse procedure is to establish two points for each monthly line using some average values. One point for each month is estimated using the average solf and average maximum temperature for days without precipitation. The second point is estimated using the maximum observed temperature for each month and a dd value of 15. Using this second procedure, curves shown in part A of were estimated for a region in northwest Colorado. Estimates of radj_wppt and radj_sppt are obtained from the radiation record. radj_wppt is the ratio of solf for days with precipitation to days without precipitation over the October through April period. radj_sppt is the ratio of solf for days with precipitation to days without precipitation over the May through September period.

##### References
• Leaf, C.F., and G.E. Brink, 1973, Hydrologic simulation model of Colorado subalpine forest: U.S. Department of Agriculture, Forest Service Research Paper RM-107, 23 p.
• Leavesley, G.H., R.W. Lichty, B.M. Troutman, and L.G. Saindon, 1983, Precipitation-runoff modeling system–user’s manual: U. S. Geological Survey Water Resources Investigations report 83-4238, 207 p.
• Lee, R., 1963, Evaluation of solar beam irradiation as a climatic parameter of mountain watersheds: Colorado State University Hydrology Papers, no. 2, 50 p.
• Meeus, J., 1999, Astronomical Algorithms: Richmond, Va., Willmann-Bell, Inc., 477 p.
• Swift, Lloyd W., Jr., 1976, Algorithm for solar radiation on mountain slopes: Water Resources Research, v. 12, no. 1, p. 108-112.