National Solar Radiation Data Base User's Manual (1961-1990)

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6.0 Model Estimate of Solar Radiation

Part 2: How the Data Base was Produced

7.0 Synthetic Calibration (SYNCAL) Procedures

As early as the 1960s, Flowers and Helfert (1966) recognized the need and the feasibility of compensating for certain solar radiometer response characteristics (temperature and zenith angle) to achieve much improved accuracy in the measurement of solar radiation. Nevertheless, even to this day (September 1992) the procedures they recommended are not usually followed, and single calibration factors are used to process all data.

A general temperature correction of the pre-1976 global horizontal data was effected during the production of the SOLMET/ERSATZ data base (SOLMET, Vol. 2 1979). These temperature-corrected data, found in field 109 of the SOLMET data tapes, are the pre-1976 data used for the production of the NSRDB. Furthermore, the pyranometers used for post-1976 measurements were constructed with a temperature correction circuit. Therefore, the SYNCAL procedures described in this section were designed only to correct for the angular response characteristics of pyranometers.

If pyranometer sensor surfaces were always perfectly planar and level, and if the globes surrounding the sensors were always perfectly formed, there would be no azimuth angle differences in pyranometer responses. However, because such imperfections are not infrequent, SYNCAL was designed to correct for azimuth angle response characteristics as well as zenith angle.

It was not possible to use field or laboratory procedures to determine the angular response characteristics of the pyranometers used prior to 1976 because most of these instruments had been lost or broken during shipments. Furthermore, the cost of fully characterizing all of the pyranometers used from 1961 to 1990 would have been prohibitive. Therefore, a synthetic calibration and characterization procedure, using comparisions between modeled and measured global horizontal data, was devised.

Initially, it was planned to use the synthetic calibration procedure only for global horizontal data collected before 1976, when instrument calibrations were almost universally suspect. However, the procedure was also used for post-1976 data, as another check on data quality. Although infrequent, a few apparent calibration problems were found after 1976 that required the use of a calibration correction factor.

Because the optimum or minimum uncertainty for global horizontal data had been determined to be ± 5% (see Section 8.3.1), a general rule of thumb was adopted whereby apparent calibration errors less than this were ignored. This rule was invoked to avoid uncertain adjustments of measured data to achieve agreement with an imperfect model.

7.1 Developing the Calibration Correction Factors (CCFs)

The SYNCAL procedure used to derive calibration correction factors for global horizontal measurements involved several steps briefly described here.

The dates during which each pyranometer was in use at each station in the NWS-SOLRAD Network were determined from SOLMET, Vol. 2 (1979) and from handwritten station records obtained from NOAA's Solar Radiation Facility in Boulder, Colorado. For non-NOAA stations, it was initially assumed that the same pyranometer had been used during the entire period of record for the station. The following steps were then performed for each instrument that had been used at each station.

Total sky cover data were used to select those hours with no reported clouds. Because solar radiation data represent the integration of energy during the 60 minutes preceding the hour, only cloudless sky hours preceded by a cloudless sky hour were used to calculate calibration correction factors. Calculations also were limited to hours with zenith angles less than 80o at the midpoint of the hour. Both measurements and model estimates were considered to be too uncertain for larger zenith angles.

Using the hours selected from step 2, the ratio of modeled estimates to measured global horizontal radiation were used to obtain a calibration correction factor (CCF = Igmod/lgmeas). The hourly CCFs were then used to calculate daily average CCFs that were used to generate time series plots of the correction factors for each instrument.

The time series plots of CCFs for each instrument were visually examined to look for discontinuities, such as those shown in Figure 7-1. The station records for Fresno, California, indicated that an instrument change had occurred on February 5, 1963. These results, however, indicate that the instruments were actually changed on about October 22, 1962 (the CCFs in 1963 agree with those after October 22 in 1962). Many instances of unrecorded instrument or calibration factor changes were found. These "apparent" instrument change dates were then used to initiate new calculations, then step 3 was repeated.

Once serial plots free of significant discontinuities were obtained, a linear least squares fit to the daily average CCFs for each instrument was obtained (see Figure 7-2). The slope of the line fit to the data was used to determine the average daily rate of change of the pyranometer sensitivity during the entire period of its use at that station. The daily rate of change was used to remove the drift from all of the hourly CCFs.

The drift-corrected hourly CCFs for each instrument were binned, i.e., placed in 10o by 20o zenith angle-azimuth angle cells. The number (count), mean, and standard deviation of the CCFs in each 10o by 20o cell was calculated and used to form matrices such as those shown in Figure 7-3 for Santa Maria, California (corresponds to the data in Figure 7-2).

The valid (not missing) CCFs for each 10o zenith angle range were averaged to obtain a vector of correction factors (CCFvec), indicating the variation of the pyranometer sensitivity with zenith angle. A weighted (according to the cosine of the zenith angle) average of the drift-corrected hourly CCFs was also calculated to obtain a calibration correction factor for use under isotropic (overcast) skies (CCFiso). The CCFiso, slope (M) of the daily average CCFs, and the CCFvec were all displayed with the matrices of zenith-azimuth cell data as shown in Figure 7-3

The information shown in Figure 7-3 was developed for each pyranometer used at each of the 56 Primary stations in the NSRDB. This information was examined to select from several options for effecting calibration corrections. The vector and the matrices were examined to determine if sufficient data of adequate quality had been found to accurately define the pyranometer angular response characteristics. For the example, shown in Figure 7-3, the count of hourly CCFs in each cell and the standard deviation of the values in each cell indicate that the response characteristics were well defined by a large data sample. For many instruments this was not the case. Either the period of use was too short or the weather was too cloudy to form an adequate set of data. In these instances, the CCFiso was used to correct all data. For other instruments, the data set was adequate to define the zenith angle response (CCFvec) but not the azimuth angle response. In a few rare instances, the data were not adequate to define even the CCFiso, and no corrections were made.

Once the quality of the information had been determined, a decision was made regarding the need to perform a correction of the data. If the CCFs appeared to fall within or close to the optimum uncertainty established for global horizontal measurements (± 5%) no corrections were made. If the angular response characteristics were determined to be acceptable, but the needed corrections exceeded the ± 5% limit during any time that the instrument was in use, then the CCFiso, adjusted for the daily drift of the instrument response, was imposed. In Figure 7-3, we note a large zenith angle change (10% from 15o to 75o) but very little azimuth variation in response and a large (14.5%) drift (see Figure 7-2) during the three years of use. Therefore, the CCFvec, adjusted for daily drift was used to correct the data for these years. For some instruments, the matrix of correction factors (CCFmat) was selected.

7.2 Applying the Calibration Correction Factors

Some of the empty cells (-99.000) in the vectors and matrices were empty because the sun never occupies that region of the sky at that latitude. The cells for zenith angles from 80o to 90o were always empty because the algorithm excluded data in this range (step 2). Other cells might be empty just because no cloudless hours ever occurred when the sun was in that region. Therefore, in order to ensure the presence of a correction factor whenever needed, all of the cells in the vectors and matrices were filled through processes of extrapolation, interpolation, or weighted averaging of surrounding cells.

In order to simplify the computer application of the algorithm, an isotropic CCFiso, daily drift (M), and CCFmat were always employed. When no calibration correction was to be made, the CCFiso, M, and all of the cells in CCFmat were set to 1.0. When only the isotropic correction was to be made, all of the cells in CCFmat were set to the CCFiso value. When a zenith-angle correction was called for (with no azimuth angle correction), each column of the matrix, CCFmat, was filled with the corresponding CCFvec value. And, of course, when both zenith and azimuth angle corrections were to be made, the original CCFmat was employed.

Following the required modification (if any) of the CCFiso, M, and CCFmat correction factors, the calibration correction factor to be applied to each hourly datum (CCFapp) was determined from the equation


where Therefore, under skies free of opaque clouds (OPQ = 0), CCFapp was determined only by the values found in CCFmat, adjusted for daily drift. Under overcast skies (OPQ = 10), only the CCFiso value was applied. Under partly cloudy skies, a combination (weighted by opaque sky cover) of CCFmat, and CCFiso values, plus drift, determined CCFapp.

In the presence of translucent clouds (e.g., cirrus), the correction would be in error because the translucent clouds could affect both the direct beam and diffuse sky radiation. No attempt was made to account for this because the effects were relatively small and of uncertain magnitude. The corrections made under partly cloudy skies should also be considered as estimates, because of the random effects that can be attributed to the position of the clouds in the sky.

7.3 Summary Comments

The synthetic calibration (SYNCAL) procedure developed for the NSRDB represents an improvement over the SYI/CSN procedure used for the SOLMET/ERSATZ data base. The improved features of SYNCAL are summarized below:

More information on the development, validation, and application of synthetic calibration factors will be found in Volume 2 of the data base documentation.

8.0 Data Base Quality

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