Calculation of Long-Wave Radiation

ISFF has been primarily using Epply pyrgeometers to measure long-wave (infrared) radiation. These radiometers measure the response of a thermopile within the radiometer dome (Rpile), which responds to the difference in radiation from the field of view minus the equivalent black-body radiation of the sensor housing (measured by Tcase). Thus, to first order the output of this sensor should be

Rlw = Rpile + SB * Tcase^4

where SB is the Stefan-Boltzmann constant, 5.67e-08 W/m^2/degK^4.

However, since the transmissivity of the radiometer's dome is not exactly 1 in the infrared, the sensor is slightly sensitive to the dome's temperature (Tdome). Also, the emissivity of the dome is not exactly 1 in the visible, so the sensor also is slightly sensitive to incoming short-wave radiation (Rsw). Thus, to second order, the output of this sensor should be

Rlw = Rpile + SB * ( Tcase^4 + B * ( Tcase^4 - Tdome^4 ) ) + f * Rsw

where B and f are sensor-specific values determined by shading tests performed in clear-sky conditions. In Colorado, we generally are able to achieve a change in Rsw of 600-800 W/m^2 to determine the change in Rlw (and thus f). B is initially determined in the laboratory by measuring the response to changing Tdome and Tcase, but we found it necessary to adjust these values to obtain a "square-wave" response during the shading tests. Values of B for our sensors range from 1.8-3.0 and of f from 0.5-1.9%.

Obviously, Rsw is either "in" or "out" corresponding to whether Rlw is "in" or "out".

We note that standard Epply pyrgeometers have one Tdome sensor (a thermistor attached to the inside of the dome), but several studies have shown that temperature gradients across the dome can result in significant errors. All of ISFF's Epply pyrgeometers have 3 thermistors to measure Tdome (at least since 1998), though we wire them in series and record only the average of all 3. (This is slightly in error, since the (non-linear) calibrations of the 3 thermistors could differ.)

Additionally, we note that we are in the process of implementing a procedure developed by Epply and NREL to perform laboratory calibrations of our pyrgeometers that check a large range of Rpile, Tdome, and Tcase and thus should provide a better determination of B.

Finally, we note that we are changing to the use of Kipp and Zonen pyrgeometers (CG4), which have a shallower dome that is in close thermal contact with the case. Since Tdome-Tcase is significantly smaller for these sensors, a correction using B is not needed.