(25): Estimation of Missing Diffuse Radiation

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(25): Estimation of Missing Diffuse Radiation

Post by support » Mon Mar 14, 2005 1:19 am -1100

I want to convert my radiation data by using the above method, but I have only measured data on global radiation, no diffuse radiation. On the other hand, I have data on the cloud cover. Are those of any use?

If necessary, you may estimate diffuse radiation as follows:

I_diff = I_glob - (1-b/8) * I_dir_normal * sin(gamma).

Here I_glob is the measured global radiation, b the cloud cover averaged over the measuring interval and expressed in eighths, gamma the solar altitude and I_dir_normal the direct normal radiation estimated for the measuring location and cloudless sky which can be determined as follows:

I_dir_normal = I0 * exp( -TL * dr0 * m * p/1013.25 ),

with
  • I0: extraterrestrial solar radiation, i.e. before attenuation through the atmosphere, for the J-th day of the year.
    I0 = 1367 * (1 + 0.03344 * cos(0.9856°*J - 2.72°)) W/m²
  • TL: Linke turbidity factor; describes the ratio of the vertical optical thickness of a turbid and moist atmosphere to the vertical optical thickness of the pure and dry atmosphere. You need to determine a representative value for the measurement location by comparing with measured radiation data on cloudless days. TL may vary strongly for different weather situations and seasons; you will only be able to allow for these variations in a very rough approximation, or you may have to ignore them altogether.
    For comparing calculated radiation values for different turbidity factors with measured global radiation data you may use the following empirical parameterisation for the global radiation from a cloudless sky:
    I_glob = 0.84 * I0 * sin(gamma) * exp( -0.027 * p/1013.25 * TL / sin(gamma) )
  • m: relative optical air mass for solar altitude gamma, describes the longer optical path through the atmosphere at oblique incidence, compared with vertical incidence:
    m = 1 / ( sin(gamma) + 0.50572*exp( -1.6364*ln(gamma+6.07995) ) );
  • dr0: vertical optical thickness of the pure and dry standard atmosphere.
    For gamma > 5° use the approximating formula dr0 = 1/(0.9 * m + 9.4),
    for gamma <= 5° interpolate dr0 in the following table:

    gamma dr0
    5 0.0548
    4 0.0519
    3 0.0491
    2 0.0463
    1 0.0435
    0 0.0408
    -1 0.0381
  • p/1013.25: pressure correction for reducing the optical thickness of the standard atmosphere with barometric pressure p0 = 1013.25 hPa at sea level to the current atmospheric pressure p.
More details can e.g. be found in:
VDI 3789 Umweltmeteorologie, Blatt 2: Wechselwirkungen zwischen Atmosphäre und Oberflächen; Berechnung der kurz- und der langwelligen Strahlung.