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

Table of Contents

7.0 Synthetic Calibration (SYNCAL) Procedures

Part 2: How the Data Base was Produced

8.0 Data Base Quality

The quality of the solar radiation data in the NSRDB is indicated by two quality flags attached to each hourly value and each solar radiation statistic. The first of these flags, the source flag, identifies the source of the data and is described in Part 1- Section 3.0. The second flag, the uncertainty flag, provides a quantitative estimate (for the solar radiation elements) of the confidence you can have in the data. This section provides information on the methods employed to calculate uncertainties and should help you make good decisions regarding the use of the data.

8.1 Quality Assessment of Measured Solar Radiation Data

Because of the difficulties frequently encountered when measuring solar radiation and the resultant unknown quality of some solar radiation data (see Section 4.0), a major effort was undertaken to develop procedures and software for performing post-measurement quality assessment of these data. Such assessments were needed to ensure that the data selected for model development and other applications were of the highest quality available. The assessments also were needed to calculate the uncertainty of measured solar radiation data. A quality assessment software package (SERI QC) was developed to address these needs.

SERI QC is based on the establishment of boundaries or limits within which acceptable data are expected to lie. This is similar to previous quality assessment procedures that used extraterrestrial values for the upper limit and zero for the lower limit within which solar radiation data were expected to lie. SERI QC increased the sophistication of this approach by establishing much more restrictive boundaries specific to each station-month.

SERI QC operates in a unitless K-space, i.e., solar radiation normalized to extraterrestrial values. An example of the expected limits and boundaries established by SERI QC is given in Figure 8-1. The K-space variables that form the abscissa and ordinate in this figure are defined according to the expressions


(8-2)(8-3) where

Kn is the atmospheric transmission of the direct beam radiation from the solar disk, Kt is usually referred to as the clearness or cloudiness index, and Kd could be referred to as the effective diffuse transmittance. For the sake of simplicity, Kd, representing the diffuse component, is not displayed in Figure 8-1.

The hourly data values plotted in Figure 8-1 are the actual data collected by the NWS at Nashville, Tennessee, during April 1978 and April 1980 (no direct normal data were collected in April 1977 or 1979). The best quality data available from the NWS were collected during the four years from 1977 to 1980. Hence, data available from these four years were used to establish empirical limits and boundaries of acceptable data for NWS SOLRAD stations.

The heavy dashed lines represent the expected maximum global horizontal and direct normal values and the curved boundaries around the scatter plot of the data were empirically determined by these data. This was implemented by positioning a limited set of boundary shapes around the data. The position of the boundaries were adjusted in Kt increments of 0.025 such that up to 5% (approximately) of the data lay outside the boundaries. This criterion was based both on the assumption that some of the data were in error and a desire to limit the acceptance of erroneous data to small percentages.

The use of empirical boundaries established with data from 1977 to 1980 was justified by a number of factors including (1) the use of new instruments installed in 1977, which were well maintained during these four years; (2) the establishment of good calibration procedures maintained throughout this period; (3) the determination that boundary extremes could be reproduced using a solar radiation model; and (4) results that behaved according to expectations based on atmospheric processes and the climate characteristics at the stations involved (e.g., high diffuse values were observed during the winter with snow on the ground and scattered clouds).

Referring to Figure 8-1, Kt and Kn values of 1.0 are, by definition, global horizontal and direct normal extraterrestrial irradiance. Therefore, most previous quality control procedures would accept any data lying within the entire Kt-Kn space shown on this figure. When empirical maximum values for Kt and Kn are imposed, the area of acceptability is reduced to the area outlined by the heavy dashed lines. The maximum limits are based on the maximum values achieved by good quality data, as shown on the figure. Values approaching 0 are not found on these plots because data from times just after sunrise and just before sunset have been excluded from these plots. Zero values are observed, of course.

These maximum and minimum limits are employed when only one element of solar radiation has been measured. They significantly reduce the area of acceptability, provide a better assessment of data quality, and lead to the assignment of lower uncertainties.

When both global horizontal and direct normal measurements have been made, the area of acceptability can be further reduced to the region enclosed by the curved boundaries. This region encompasses about 95% of the data points and encloses less than 15% of the Kt-Kn space. When two component data fall within such boundaries, a further reduction in the assigned uncertainty can be made.

The three parts of Figure 8-1 show data, max-min limits, and boundaries for three different air mass or solar zenith angle ranges. Air mass is a unitless quantity that indicates the relative length of the path of the solar beam as it passes through the atmosphere. When the sun is directly overhead (zenith angle = 0o) the air mass is 1.0; at a zenith angle of 60o the air mass is 2.0; and when the sun is on the horizon (zenith angle = 90o) the air mass is 35.6. The air mass at 90o is not infinite because of the curvature of the earth.

SERI QC assigns limits and boundaries for three air mass ranges (low = 1.0 to 1.25; medium = 1.25 to 2.5; and high = 2.5 to 5.58). Changes in limits and boundary positions with smaller changes in air mass are not significant.

Finally, when all three of the solar radiation elements are available (global horizontal, direct normal, and diffuse horizontal) redundancy can be used to further reduce the uncertainty of the data. This is accomplished by calculating the global from the direct normal and diffuse, all in K-space,


and by comparing the calculated global (Ktc) with the measured global (Kt). This comparison provides a direct indication of the accuracy of all three measurements. It is possible, of course, that offsetting measurement errors could partially invalidate this comparison. Nevertheless, when hourly values of global horizontal, direct normal, and diffuse horizontal agree within a specified error limit, the lowest possible uncertainty for solar radiation data can be assigned.

In addition to determining if the solar radiation data fall within expected boundaries, SERI QC calculates the distance in K-space) by which data fall outside the boundaries. The flagging system used by SERI QC records these distances and indicates whether one-element, two-element or three-element data were involved and whether the data point was below or above expected boundaries. The SERI QC flags, therefore, permit the assignment of uncertainties that are dependent on the nature of the test performed (one, two, or three components) and-the distance by which the data point exceeds expected limits. A more detailed description of SERI QC can be found in the User's Manual for Quality Assessment of Solar Radiation Data (NREL 1993) .

8.2 Standard Methods for Calculating Uncertainties

The uncertainty flags assigned to NSRDB hourly values and statistics of solar radiation were derived using modifications of a standard method developed during the last 15 years by the standards and professional engineering communities. The objective of measurement uncertainty analysis is stated in the American Society of Mechanical Engineers (ASME) report (ASME 1985): " provide numerical estimates of an upper limit of precision error, bias error, and the combination of these into uncertainty." For the purposes of the NSRDB, uncertainty can be defined as the interval about the reported solar radiation value that is expected to encompass the true value, 95% of the time. For example, for all hours for which direct normal radiation is reported to be 1000 Wh/m2 with an uncertainty of 10%, the user can expect that the true direct normal radiation was between 900 and 1100 Wh/m2 95% of the time.

Each measurement process contains errors. Errors are the difference between a measured or reported value and the true value of the parameter in question. They are classified as: (1) systematic or bias (fixed offset) errors and (2) random (precision or repeatability) errors, which are assumed to follow the Gaussian (Normal) distribution. The calculation of uncertainties requires identification, classification (bias or random), and quantification of every significant source of error.

Quantification requires assignment of a numerical value to each of the identified and classified error sources. This step is usually based on empirical tests, measured data, instrument specifications, calibration results, etc. When data are not available, engineering judgment, experience, or previous knowledge must be used to estimate the magnitude of the error. The bias and random error magnitudes are then combined into total bias and random components of uncertainty, which are in turn used to compute the total uncertainty.

Random errors are the result of independent influences on the measurement process, which change with each measurement. They are recorded as an integral part of the data, varying with each individual measurement. Their magnitudes are estimated from the standard deviation(s) of repeated measurements. Because of their statistical nature, increasing the sample size (n) normally will result in a reduction in the magnitude of these errors.

Bias errors are those errors that are fixed and present for every measurement using specified procedures and instruments. For example, if an instrument has been miscalibrated, every measurement made with that instrument will exhibit the same error resulting from the miscalibration. The fact that calibration standards themselves contain bias errors that contribute to measurement errors is often overlooked.

Once all errors have been identified and quantified, they are combined to provide an estimate of uncertainty. The U95 method was used for combining solar radiation measurement errors. Using this method, the total bias error is determined by taking the square root of the sum of the squares (root-sum-square) of all bias errors. The root-sum-square (RSS) of all random error sources is used to obtain the total random error. The uncertainty of individual measurements or samples is determined from


where It is well known that measurement accuracy can be improved by averaging a series of measurements. Therefore, the random component of uncertainty is reduced when the final value is derived from more than one measurement or sample (Barry 1978). Thus, the uncertainty of the monthly mean of daily measurements is calculated as


This assumes that the uncertainty of each daily measurement is the same. For annual means, the random component of error is divided by the square root of 365.

8.3 Calculating the Uncertainty of Solar Radiation Data

The solar radiation data in the NSRDB were obtained from a variety of sources that can be placed in one of the following three categories:

The "true" solar radiation values to which assigned uncertainties are referenced are defined as follows: The standard methods for calculating uncertainty assume the use of a constantly controlled process whereby the instruments are maintained in the best working order possible. Measurements made in support of solar collector efficiency tests would likely meet this assumption. Although network operations for long-term monitoring of solar radiation may not satisfy this assumption (instruments are given only brief checks once each day), the calculation of uncertainties for solar radiation measurements began by assuming the maintenance of optimum conditions.

8.3.1 Optimum Uncertainties

The calculation of uncertainties for the many sources of solar radiation data acquired or estimated under a variety of circumstances was facilitated by defining "optimum" uncertainties for each of the sources. These "optimum" uncertainties are the uncertainties expected under optimum measurement or modeling conditions, using the instruments or models actually employed. For example, the optimum uncertainty for post-1976 measured global horizontal solar radiation is that uncertainty that would result if the instruments were properly calibrated and installed and used under the constant supervision of experts in the field of solar radiometry. Use of the term "optimum" in this context should not be interpreted in any other way.

Myers, Emery, and Stoffel (1989) and Wells (1992) identified the major sources of error associated with solar radiometers (pyranometers and pyrheliometers). The most significant measurement errors associated with the intrinsic characteristics of these instruments include:

All of these sources of error have been exhibited in varying degrees by the various instruments employed from 1961 to 1990. All of them can be categorized as random errors because their effects on individual hourly values will be a function of more or less randomly varying measurement and atmospheric conditions.

In addition to the intrinsic sources of error, the following factors contribute to errors in the calibration of the radiometers:

Calibration errors are bias errors because the effect of miscalibration is the same for all measurements.

Data acquisition and data processing errors were also addressed. These errors include many small random sources that affect both calibrations and individual measurements.

The results of the work of Myers, Emery, and Stoffel (1989) and Wells (1992) yielded the following optimum uncertainties for the measurement of the three major elements of solar radiation using thermopile pyranometers and pyrheliometers.

The reported uncertainties have been reduced to one significant figure because of the uncertainty associated with these calculations. This is not a reflection on the analytical procedures. Rather, it is a reflection on the lack of sufficient data on the characteristics of solar radiometers.

For application to the NSRDB, the concept of optimum uncertainties for reported values of solar radiation was extended to include each of the eight sources of solar radiation data, as indicated by the source flags. The meaning of the source flags is repeated here for easy reference.

The optimum uncertainties that were assigned to data in each of these source categories follow (G = global horizontal; N = direct normal; D = diffuse horizontal). The changes noted for one source versus another are based on the consensus of experts in the field and represent engineering judgments.

Flag A         G =   ± 5%       N =   ± 3%       D =   ± 7%

These uncertainties were established as described above.

Flag B         G =   ± 7%       N =   ± 3%       D =   ± 7%

If post-1976 global horizontal data need synthetic calibration corrections, this indicates significant calibration error and/or serious angular response problems. Because calibration corrections cannot completely mitigate such problems, the uncertainty of the global element has been increased by 2%.

Flag C         G =   ± 8%       N =   ± 5%       D =   ± 8%

Only pre-1976 global horizontal data have undergone a time shift from solar to local time and a synthetic calibration correction. The uncertainty of global data under optimum conditions was increased by an additional 1% to account for increased errors caused by the time shift.

Prior to 1976, the direct normal and diffuse elements were not measured. Hence, these elements will be model estimated when flag C is applied to the global element. The optimum uncertainties for modeled direct normal and diffuse horizontal elements, when accompanied by pre-1976 measured global horizontal values, were reduced by 1% from the optimum uncertainties of modeled data when all three elements are modeled (see below). This reduction in uncertainty results from the use of the METSTAT model in a procedure that limits the direct and diffuse values to those that result in agreement between measured and modeled global.

Flag D         G =   ± 5%       N =   ± 6%       D =   ± 6%

The uncertainty of hourly values for elements calculated from the other two elements will be calculated from the root-sum-square (RSS) of the uncertainty of the two measured elements. It was not possible to define optimum uncertainties for hourly data created in this way. Hence, the optimum uncertainties given for this source flag were only used for assigning uncertainties to monthly and annual statistics.

Flag E to H         G =   ± 7%       N =   ± 6%       D =   ± 9%

These optimum uncertainties are for modeled data based on daily turbidity values derived from direct normal data collected at the site in question. These values are the result of the RSS of optimum values for flag A and an assigned 5% uncertainty for model estimates.

8.3.2 Calculating the Uncertainty of Modeled Values

The use of a statistical model to estimate a majority of the data in the data base presented special problems relative to the assignment of uncertainties. Because of the random statistical variations incorporated into the model estimates, individual hourly values under partly cloudy skies could be greatly different from actual measurements, had they been made. For instance, under partly cloudy skies it is possible for the sun to be completely occluded during an entire hour. It is also possible for the sun to shine brightly for an entire hour. Under these conditions, the uncertainty of individual hourly estimates, relative to the true solar radiation, would be very large.

However, it had never been intended that the model estimates would reproduce actual measured data. Rather, the METSTAT model was designed to simulate the statistical and stochastic characteristics of monthly and annual data sets. Given this objective, the assignment of uncertainties with reference to the true solar radiation for specific hours would not provide the user with useful information. It was decided, therefore, that the uncertainty of individual hourly values estimated by METSTAT should be interpreted to mean that 95% of the time the true mean of measured hourly values under fixed atmospheric conditions lies within the range established by the estimated mean plus or minus the uncertainty 95% of the time.

For example, if the average of 100 METSTAT estimates of global horizontal radiation at a specific time and place with fixed atmospheric conditions (e.g., total precipitable water = 2.2 cm, aerosol optical depth = 0.11, total sky cover = 5, and opaque sky cover = 2) equals 700 Wh/m2, with an uncertainty of 8%, then 95% of the time the true average global horizontal radiation that would result from several measurements under these conditions should lie between 644 Wh/m2 and 756 Wh/m2.

8.4 The Total Uncertainty of Measured Solar Radiation Data

The optimum uncertainties defined above were assigned to data from the respective sources whenever the optimum conditions pertaining to these sources existed. Under less than optimum conditions, the uncertainties were increased as described in the following sections.

8.4.1 Total Uncertainty of Post-1976 Data (Sources A and B)

The total uncertainty of post-1976 measured solar radiation data was calculated as the RSS of the optimum uncertainty and factors that increase the uncertainty


where All factors are expressed in percents.

Rtype increases the uncertainty of one- or two-element post-1976 data to account for the random errors of the quality assessment procedure. In other words, data falling within the expected max-min (one-element) or boundary (two-element) limits can be in error by a significant amount. The values of 3% and 6% are subjective estimates based on experience at NREL.

Rflg increases the uncertainty according to the magnitude by which SERI QC quality assessment limits and boundaries have been exceeded. This random error is given in percent of the extraterrestrial solar radiation.

Rstaq increases the uncertainty to account for random errors associated with the quality of station operations. The station quality index (Staqlty) is based on the percent of hourly data for a month that have a SERI QC flag greater than 29, thereby indicating missing data or values outside limits or boundaries by an amount greater than 7% of the extraterrestrial value. The 7% threshold is consistent with optimum uncertainties for measured and modeled global horizontal data.

Missing data are considered valid indicators of station quality for the following reasons:

From the above, it is apparent that uncertainties greater than 50% could have been assigned. However, all post-1976 measured data with flags greater than 41 were replaced with modeled values. In reality therefore, no uncertainties greater than 35% will be found in the NSRDB.

8.4.2 Total Uncertainty of Pre-1976 Data (Source C)

The total uncertainty of pre-1976 measured global horizontal data was always set equal to the optimum value (8%). Although the uncertainty of some of these data could exceed this value, there was no basis for making such a determination. Furthermore, all of these data were synthetically calibrated, and this value is consistent with that process and the accuracy of the METSTAT model for cloudless skies (used to determine calibration corrections).

8.4.3 Total Uncertainty of Calculated Data (Source D)

The total uncertainty of values calculated from the other two measured elements was determined from the RSS of the uncertainty of the two measured elements. For example, when the global horizontal element was calculated from measured direct normal and diffuse horizontal data, the uncertainty of the global (G) value was calculated from


where the total uncertainty of the direct normal (N) and diffuse horizontal (D) elements had previously been determined from the procedures described above. Similar RSS equations were used to estimate uncertainty when direct normal or diffuse horizontal values were calculated from the other two elements.

8.4.4 Total Uncertainty of Modeled Data (Sources E-H)

The general or optimum uncertainties of METSTAT estimates of solar radiation were based on the optimum uncertainties of the measured data used during the development of the model and evaluations of the model performance under cloudless skies. These optimum modeled data uncertainties were increased according to the following algorithms.


(8-10) (8-11) (8-12) (8-13) (8-14) where

8.5 Calculating the Uncertainty of Monthly and Annual Statistics

When calculating the uncertainty of monthly and annual statistics, all random errors are decreased by the reciprocal of the square root of the sample size (n) (Barry 1978). Bias errors are not reduced, however, except in those instances for which biases become random. When calculating the uncertainty of 30-year statistics, it was assumed that all of the biases could be randomized, except for the modeling bias associated with errors in the estimate of aerosol optical depth.

After considerable evaluation and much discussion, it was decided that the uncertainties assigned to monthly and annual means should not be less than the optimum uncertainties assigned to the hourly values for each of the data sources (see Section 8.3.1), plus the effect of the modeling bias error attributed to errors in aerosol optical depth estimates. This determination was based on the following considerations:

Therefore, the total uncertainty of the monthly mean for each element was calculated as


where and the other parameters are as defined previously. The first term in equation (8-15) was not allowed to become less than Uopt.

For annual and 30-year monthly and annual means, the first term in equation (8-15) was always smaller than Uopt. Therefore, the total uncertainty of these statistics were calculated as


The uncertainties calculated for monthly and annual means of daily totals were also assigned to the distributions of hourly means and the cumulative frequency distributions of hourly values. Although this does not constitute a rigorous analysis of the uncertainty of these statistics, it is consistent with the state of the art of solar radiation measurements; i.e., the information available will not support a more rigorous analysis.

The user should recognize that the uncertainties assigned to the monthly and annual statistics are probably conservative for those stations that were well operated and for which a large quantity of good quality data had been collected. This is consistent with the philosophy of uncertainty analyses, which prefers to err on the high side, not the low.

8.6 Using the Solar Radiation Quality Flags

The source and uncertainty flags assigned to the solar radiation data can be used for a number of purposes. For example, the flags could be used to aid in the selection of station-months to form typical- and design-year data subsets. Individual users can use the quality flags to set their own limits of acceptability for whatever application they have in mind. For example, the user may want to only use those data containing at least one measured component and may also want to set some maximum uncertainty limit as a data screen. Regardless of the specifics of the application, users can use these flags to set confidence limits for their designs or performance evaluations.

8.7 The Uncertainty of Meteorological Data

Information was not readily available for the calculation of the uncertainty of meteorological data. The subjective uncertainty statements made in Table 3-9 should be considered in the light of the following information.

All surface airways hourly observational data were subjected to some form of quality control. During the earlier years, this was almost entirely a manual effort. As more sophisticated techniques of processing were introduced, the quality control procedures became more automated. Observations are checked for conformance to established observing and coding practices, for internal consistency, for serial, or for time-oriented consistency, and against defined limits for each meteorological element.

Snow depths are measured at several locations near the NWS facility and are averaged to obtain the reported depth. In the absence of wind, these data should be of reasonably good quality. At windy sites, where drifting of the snow occurs, the uncertainty of the reported value may be greater than under calm conditions. However, since the snow depth data were used only to establish an estimate of surface albedo, no further analysis of the quality of this data was undertaken.

The quality of precipitable water data obtained from surface measurements and adjacent sites was assessed by comparing these estimates with radiosonde data for several years of data. These analyses showed that the standard error between the estimated values and the radiosonde values was always less than 1 cm, and at most locations and for most seasons the standard error was found to be less than 0.5 cm. The impact of these errors on the model estimates of solar radiation were incorporated into the calculation of uncertainties for the solar radiation data.

All aerosol optical depth values used in the NSRDB were calculated according to the procedures outlined in Section 6.2.3. Since very few accurate measurements of aerosol optical depth exist, calculated values were used throughout. These estimates of aerosol optical depth are no better than the quality of the direct normal radiation data that were used in their calculation. For times and locations for which direct normal data were not available, uncertainties from 10% to 50% were assigned to the estimates of aerosol optical depth.

The quality flags for meteorological elements are available only in the TD-3282 format. They were not incorporated into the NSRDB synoptic format.

9.0 The Production Process

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