EAS 535 Laboratory Exercise Solar Radiation
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1 EAS 535 Laboratory Exercise Solar Radiation Lab Objectives: Estimate the atmospheric optical depth and solar constant from a set of measurements of the total and diffuse solar radiation at the surface. Background: To a first approximation, ignoring the spectral characteristics of the atmosphere, the DIRECT solar radiation at the surface is related to the incoming radiation at the top of the atmosphere by the following expression. (1) where F dir is the directly transmitted radiation (Wm -2 ) F o is the solar constant (Wm -2 ) τ is the atmospheric optical depth (non-dimensional) µ o is the cosine of the solar zenith angle (non-dimensional) Taking natural logarithms of both sides of equation (1), we have (2) If we identify y and x then equation (2) is of the form y = mx+c (3) and the slope, which should be negative, will yield the optical depth, τ, whereas the intercept will yield ln (F o ) from which the solar constant can be calculated. Instruments to measure the directly transmitted solar radiation are called PYRHELIOMETERs. These are difficult to use and maintain. We will compute the direct radiation using a shaded PYRANOMETER which measures the TOTAL radiation. By shading the disk of the sun one measures the DIFFUSE radiation. The difference is the DIRECT radiation. General Instructions: 1
2 1. Read in the values of the time in decimal Julian date, the total radiation in Wm -2 and the diffuse radiation in Wm -2. The whole number of the date, 333, corresponds to November 29. The decimals correspond to the local standard (or clock) time such that midnight is.00, 6 a.m. is.25, noon is.50, etc. 2. From the column of Julian date create a column of local clock time by subtracting the date, 333, and converting decimal dates to hours. You will notice that the total and diffuse fluxes are negative at the beginning and end of the record corresponding to the periods before and after sunset. Estimate the instrument bias that should be removed from the two data sets so as to obtain essentially zero total and diffuse flux at night. The bias is different for the two fluxes. Subtract (or add) this bias from both columns of flux data. 3. Create a column of DIRECT FLUX = TOTAL FLUX DIFFUSE FLUX. You should now have a column of local standard (or clock) time and the bias corrected TOTAL, DIFFUSE and DIRECT fluxes. 4. Plot all three fluxes versus the local clock time. On a clear day such as this, the direct flux should reach a maximum value at LOCAL SOLAR NOON. Solar time = local time + solar correction Since Lafayette is not located at the longitude which defines Eastern Standard Time, the solar correction is not zero. By inspecting the column of DIRECT flux, estimate the SOLAR CORRECTION. Apply the solar correction to the column of local standard time to create a column of solar time. Replot the fluxes vs. solar time. You are now in a position to calculate the zenith angle needed in equation (1), which is a function of the day of the year, the geographic latitude, the solar declination and the hour angle. 5. Create a column with the hour angle which is calculated with: h = hour angle = 2π(solar time 12)/24 6. Use the following formulas to calculate the angle of declination of the sun. This is equal to the latitude at which the Sun is directly overhead at noon, so it varies from to 23.5º. 2
3 CAUTION: Trigonometric functions in EXCEL use RADIANS and not DEGREES so remember to convert. Calculate the declination angle, δ, for this date where jda = whole Julian date, i.e. 333 in this case (4) = , , , = 0.0, , , The solar zenith angle, θ o, is given by the equations: Φ sin δ + cos Ф cos δ cos h where Φ = latitude = 40º for Lafayette and h is the hour angle. Using these equations create a column of θ o in degrees and µ o = cos θ o. 3
4 θ o 90-Zenith angle (deg) Example of elevation angle (90 - zenith angle) variation as a function of day of the year for a site in Vancouver (lat = long=-123.1) 8. Choose a subset of the data for which the Sun is at least 5º above the horizon, i.e. θ o < 85º. Now plot y ln (F dir /µ o ) vs. x 1/µ o 4
5 9. Using the linear trend function of EXCEL, estimate the atmospheric optical depth, τ, and solar constant, F o. The value of F o is smaller than the actual value of approximately 1360 Wm -2. The primary reason for this discrepancy is that the atmosphere does not absorb and scatter radiation as a GREY body. Therefore, equation (1) is incorrect. It is strictly valid only for MONOCHROMATIC radiation. The discrepancy can further be attributed to errors in instrument calibration or to a dirty dome covering the sensor. 5
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