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

Table of Contents

5.0 Sources of Solar Radiation and Meteorological Data

Part 2: How to Data Base was Produced

6.0 Model Estimates of Solar Radiation

Under partly cloudy skies, because of the random and unknown location of the clouds, no model can accurately estimate the solar radiation incident on the earth's surface at any given time and location. Hence, the model used to estimate solar radiation when measured data were not available was designed specifically to reproduce the statistical and stochastic characteristics of multi year solar radiation data sets. This resulted in the sacrifice of accuracy for specific hours. Modeled values for individual hours (under partly cloudy skies), therefore, may differ greatly from measured values, had they been made.

It was anticipated that a multi year data base will most often be used to create design- and typical-year subsets; to establish normals, means, and extremes; and to select or evaluate sites for large solar energy systems. Given these uses, it is important that simulated data sets accurately represent the following statistical and stochastic characteristics of measured data.


Stochastic A block diagram of the meteorological-statistical (METSTAT) solar radiation model developed for the NSRDB is shown in Figure 6-1. Several features of the model were critical to meeting data base objectives. Hourly calculations using hourly total and opaque cloud cover, hourly precipitable water vapor, daily aerosol optical depth, and daily albedo input data automatically produced representative diurnal and seasonal patterns, daily autocorrelations, and persistence. Placing the statistical algorithms between the input data and the deterministic algorithms led to proper cross-correlations between the direct normal, diffuse horizontal, and global horizontal components.

The deterministic algorithms were designed to meet the objective of creating data sets with accurate monthly means. The statistical algorithms randomly varied input parameters (cloud cover and aerosol optical depth) such that monthly data sets exhibit representative statistical characteristics. Daily rather than hourly variations of aerosol optical depth were applied to retain the smooth diurnal patterns that are observed under cloudless skies.

Volume 2 of the data base documentation contains a full description of the development of the model. The mathematical details of the algorithms will also be found there, along with detailed evaluations of the model performance.

6.1 Direct Normal Algorithms

6.1.1 Cloudless Sky Transmittance

The cloudless sky direct normal transmittance algorithms are essentially those given by Bird and Hulstrom (1981) and Iqbal (1983) (Parameterization Model C). The only exceptions are the algorithm for water vapor absorption and the algorithm for the combined effect of aerosol absorption and scattering, which were somewhat modified. All of these algorithms are broadband (solar spectrum) parameterizations and include:

6.1.2 Cloud Transmittance

The parametric cloud transmittance algorithms were developed using subsets of data assembled from NWS-SOLRAD network stations for the years from 1977 through 1980. The variables for data in the subsets were fixed within narrow ranges and came from across the United States for all months. This reduced the probability of developing algorithms that would exhibit regional or seasonal biases. The cloud effect algorithms included:

The total direct normal transmittance (TN) is then given by


6.2 Diffuse Horizontal Algorithms

6.2.1 Atmospheric Scattering

The deterministic algorithms that estimate the diffusion of radiation by the atmosphere are:

6.2.2 Scattering by Clouds

The deterministic algorithms that estimate the scattering of solar radiation by clouds are:

6.2.3 Multiple Surface-to-Atmosphere/Cloud Reflections

Some of the solar radiation incident on the earth's surface is scattered back toward the atmosphere. Some of this backscattered radiation is in turn scattered back to the surface by the atmosphere and/or clouds, and the process repeats itself. This multiple scattering process serves to increase the total diffuse radiation incident upon the surface. The intensity of these multiple surface-to-atmosphere/cloud reflections is a function of the albedo (solar spectrum reflectance) of the surface and the atmosphere and clouds.

This process is of greatest significance when there is snow on the ground under partly cloudy skies. The model algorithm calculates daily values of surface albedo from snow depth, a terrain factor, and the number of days since the last snow storm. These algorithms are based in part on the work of Baker, Skaggs, and Ruschy (1991) and Baker, Ruschy, and Wall (1990), who studied the reduction of albedo with time (days since last snowfall) and the effects of vegetative ground cover and snow depth.

In the absence of snow cover, monthly values of surface albedo were estimated from satellite images, a general knowledge of ground cover, and the reflectance of cover types. Atmospheric albedo was based on aerosol effects, and the albedo of clouds was determined from the product of cloud cover and assigned reflectances for opaque and translucent clouds. More details on this algorithm will be found in Volume 2 of the data base documentation.

6.2.4 Precipitation Switch

The final factor affecting diffuse radiation is precipitation. The occurrence of rain is usually, although not always, accompanied by a darkening of the sky. Therefore, the precipitation switch reduces diffuse radiation when rain or hail has been recorded and when opaque sky cover exceeds 7 tenths.

A study of diffuse data yielded no evidence that precipitation in the form of snow significantly affected the diffuse radiation incident upon a horizontal surface. Hence, the precipitation switch does not respond to snowfall events.

6.3 Statistical Algorithms

6.3.1 Cloudless Sky Algorithms

Under cloudless skies, it was assumed that the hour-to-hour variations of solar radiation would depend primarily on the solar zenith angle. Hourly variations of water vapor and aerosol optical depth do occur, but the hourly changes are usually small. This results in the smooth diurnal variations of solar radiation that are commonly observed under clear skies.

The hourly variations of water vapor were obtained from linear interpolations between the twice daily radiosonde soundings or from hourly observations of surface vapor pressure. Therefore, it was not necessary to apply a statistical algorithm to water vapor.

From Valko (1980), it was noted that daily variations of aerosol optical depth exhibit a lognormal distribution around the monthly mean. This was verified from our calculations used to determine monthly means. Therefore, a lognormal distribution function was used to effect random variations of aerosol optical depth on a daily basis.

6.3.2 Random Effects of Cloud Cover

The random effects of cloud position, type, and size dominate the random variation of the direct normal component of solar radiation. The standard deviation of direct normal radiation for research data subsets with 4, 6, and 8 tenths opaque cloud cover was found to be two to four times greater than the standard deviation under cloudless or overcast skies. The position of the clouds with respect to the sun and the observer is probably the controlling factor. Therefore, these combined effects will be referred to as cloud position effects.

The cumulative frequency distributions (cfd's) of direct normal radiation for low aerosol optical depth and low water vapor conditions were used to derive the cfd's representing the random effect of opaque cloud position and are shown in Figure 6-2. A random number generator with a uniform distribution from 0 to 1 was used with tables of the cfd's to obtain values of effective opaque sky cover. This nonparametric method transforms uniformly distributed random numbers into random numbers having the distribution represented by the cfd (Yevjevich 1972, p. 249). These values were used to calculate opaque sky cover transmittance.

From Figure 6-2, it is noted that the cfd's for 0 and 10 tenths observed opaque sky cover allow for actual sky covers between 0 to 0.5 tenths and 9.5 to 10 tenths, respectively. Therefore, as the cfd's indicate, under reported cloudless skies, there is a small but finite probability that the sun will be occluded by a small cloud for a small part of the hour.

Likewise, under reported overcast skies, there is a small probability that the sun will shine through a small break in the clouds for a short time.

However, there are conditions under which the sky will be truly clear or overcast for several hours or days at a time. Under these conditions, the probability of a stray cloud or a break in the clouds becomes very small. Therefore, whenever unbroken sequences of cloudless or overcast hours occurred, the range of values from the random number generator were restricted. For instance, for the second cloudless or overcast hour, the random number generator was restricted to values from 0 to 0.9 or 0.1 to 1.0, respectively. For 3 sequential hours the values were restricted to 0 to 0.8 and 0.2 to 1.0, etc., until for sequences of clear or overcast hours of 10 or more, the values were restricted to 0 to 0.1 and 0.9 to 10.0, respectively. This essentially eliminates the skewed portions of the cfd. This procedure ensured the generation of a smooth diurnal solar radiation pattern for truly cloudless and overcast days.

7.0 Synthetic Calibration (SYNCAL) Procedures

Table of Contents

Return to RReDC Homepage ( )