Advanced solar irradiance model and procedure for spectral solar heat gain calculation.

ABSTRACT

This paper proposes a validated and integrated calculation procedure for the prediction of solar spectra incident on vertical (or otherwise tilted) windows as a function of local climatic conditions in North America or, ultimately, any site in the world. This procedure is aimed at engineers with a modest background in meteorology, climatology, or atmospheric sciences and, therefore, tries to reconcile accuracy, flexibility, and ease of use. The procedure is backed by a thorough literature review and detailed performance assessment. The spectral radiation model (SMARTS) finally selected for its capabilities and performance (among other factors) is not based on any empirical relationship. It is capable of predicting spectral and broadband irradiance, as well as illuminance under cloudless skies at any location where the required inputs are available. The accuracy of the produced spectra is comparable to that from state-of-the-art rigorous atmospheric models or from the best instruments. Such accurate results can only be obtained if a precise description of the atmospheric conditions is input to the model.

A detailed methodology is described to obtain the basic atmospheric variables for any location in North America. It is anticipated that the current improvements in remote sensing from satellites will provide the means to extend the method to any site in the world. To illustrate the method, an example of application is provided for the various facades of the ASHRAE headquarters in Atlanta. Substantial improvements in the calculation of solar heat gains through spectrally selective fenestration and the resulting cooling loads in buildings are the ultimate benefits expected from the procedure.

INTRODUCTION

Recent decades have seen substantial changes and advances in glazing technologies. Considerable progress has been made on various issues such as improved solar and glare control, better visible transmittance, reduced heat loss, etc. Even more advanced technologies that should bring variable solar control and increased thermal resistance are actively being developed. All these technologies have at least one thing in common: they take advantage of the spectral selectivity of coatings, thin films, dyes, phase-change materials, etc. This spectral selectivity is purposely engineered to increase or decrease optical and/or thermal transmittance over specific spectral intervals. Consequently, these materials exhibit more or less spectral selectivity. This combines with the ever-changing solar spectrum to produce dynamically variable spectral energy distributions that ultimately enter a building and contribute to its thermal load.

It is essential to distinguish between standard calculations of the glazing's optical properties--where a single standard spectrum is used (Rubin et al. 1998; Mitchell et al. 2001) so that the performance of different glazings can be compared and rated relative to some common, but ideal, reference atmospheric conditions--and realistic calculations, corresponding to either "typical/average" or peak cooling load cases. To be realistic, these calculations must be based on different sets of spectra, themselves different from the standard spectrum just mentioned. The effect on the solar heat gain coefficient (SHGC) of changes in the incident spectrum is known to be significant under various conditions (McCluney 1993, 1996; Platzer 1995).

The conventional calculation method that is still used to predict SHGC and, by extension, the cooling load of buildings does not consider this dynamic spectral effect. This, in turn, produces errors in the resulting cooling load and may lead to the choice of non-optimal glazing from the standpoint of energy conservation or cost/performance ratio. It may also lead to errors in selecting or sizing the most energy-efficient HVAC system.

It now appears essential to give HVAC engineers the appropriate tools to perform these difficult calculations with both ease and accuracy. Although sophisticated tools now exist to predict the spectral and total transmittance of almost any kind of glazing (e.g., the WINDOW computer program [Mitchell et al. 2001]), there is no ASHRAE-sanctioned equivalent tool to predict the incident solar spectrum on fenestration. The objective of this research is to provide this essential front-end tool to advanced optical calculations for design purposes-hence, under clear skies.

SPECTRAL SOLAR IRRADIANCE: MEASUREMENT VS. MODELING

Recent years have seen significant progress in calculation methods for window optics as well as in radiometry, solar radiative transfer, and atmospheric processes modeling. There are now excellent laboratory or field spectroradiometers that can record the solar spectrum with great accuracy. However, their high cost makes them inaccessible to most users, and their operation, maintenance, and frequent calibration needs are costly as well as resource demanding in terms of highly skilled personnel and laboratory equipment. Spectral measurements are still considered the irreplaceable, ultimate reference in a variety of applications. They may also provide the only way to obtain accurate spectra under rapidly changing cloudy conditions. As a general rule, nevertheless, radiation models have some definitive advantages over measurements: low cost, progressive learning curve, speed of execution, and almost infinite possibilities to improve the model, to rapidly build large data sets, or to simulate any type of realistic or ideal conditions, etc. All these reasons justify the recourse to an appropriate model to address the problem at hand.

Existing Solar Radiation Models

In the history of ASHRAE thus far, the prediction of solar radiation incident on walls, windows, or solar energy systems involved broadband irradiance only. Prediction of spectral irradiance requires a much higher level of sophistication in modeling. Nevertheless, the findings obtained in this project have direct implication in the way broadband irradiance is predicted. This is the subject of a separate section below. Spectral radiation models can be classified into two main and very different categories: atmospheric models and engineering models. The first category consists of models that are rigorous in their description of atmospheric processes. Consequently, they are considered to provide the most accurate and detailed predictions of spectral irradiance. In particular, models such as MODTRAN (Berk et al. 1999), libRadtran (Mayer and Kylling 2005), and SBDART (Ricchiazzi et al. 1998) are reference models in atmospheric sciences. However, these models also have important drawbacks: (1) their irradiance predictions are limited to the horizontal plane, which automatically make them ineligible for the applications envisioned here, where vertical planes are the rule; (2) they are very complicated to use and require specialized inputs, making them out of reach to HVAC engineers; (3) they are not all in the public domain (MODTRAN in particular is very expensive); (4) they are not user-friendly and sometimes even need special computer skills to be run on a typical personal computer; (5) their execution time may be considerable; and (6) their outputs are not always what is really needed by engineers, nor in an easily understandable and manipulable form. In other words, these models are not suited at all for rapid prediction of numerous spectral distributions under varied climatic conditions in the building environment.

The second model category includes heavily parameterized models of various capabilities that have been proposed since the 1970s. Compared to atmospheric models, engineering models are much simpler in the description of the atmosphere, resolution of the equations of radiation transfer, and inputs needed and, consequently, offer extremely fast execution on personal computers. They are also less reliable and accurate than atmospheric models. The main difficulty when dealing with these models is to select one that has all the desired capabilities while offering maximum accuracy. The desired capabilities include:

* Separate calculation of direct, diffuse, reflected, and global irradiance incident on horizontal and tilted surfaces. (This is important because sun-facing windows receive mostly direct radiation, whereas windows facing away from the sun receive mostly diffuse radiation, whose spectrum is very different.)

* Sufficient resolution within the spectral range of significant optical transmission by glazings (i.e., at least 0.3-2.5 [micro]m).

* Use of available input data describing the main atmospheric variables.

* Validated applicability.

An in-depth survey of the literature has been conducted, and many publications have been found and carefully examined. Unfortunately, nearly all the models described there had to be eliminated during preselection because either they were "incomplete" (by not predicting global radiation on tilted planes) or their algorithms were not completely described or had problems that could not be resolved. Only three "complete" models, for which the computer code was available and in the public domain, survived the preselection process. These are:

* The Bird model (Bird 1984; Bird and Riordan 1986), better known as the SPCTRAL2 code, available from http://rredc.nrel.gov/solar/models/spectral/.

* The SMARTS model and code (Gueymard 1995, 2001), available from http://rredc.nrel.gov/solar/models/SMARTS/.

* The SUNSPEC code (McCluney and Gueymard 1993), available from www.fsec.ucf.edu/bldg/active/fenestration/software/sunspec1/sunspec.exe.

Unfortunately, SPCTRAL2 has not been updated since the early 1980s--and will never be, due to the passing of its original author. The SUNSPEC code is a user-friendly version of the original SMARTS model (Gueymard 1993a) and no update to the algorithm (that would differentiate it from SMARTS) is expected. This leaves SMARTS as the only current model (version 2.9.5 of the code has been released recently). Table 1 summarizes the main characteristics of the three preselected models.

Model Selection

Because of the economic importance of correctly predicting the cooling loads of buildings and, hence, their solar gain through fenestration, and because of the goal of developing a reference procedure here, a thorough exercise had to be devised to select the model with the best characteristics and validate its use. This elaborate assessment indeed constitutes an essential part of this research. A preliminary step was devoted to selecting the reference model from the pool of three candidates listed in Table 1. A few spectra measured at the National Renewable Energy Laboratory (NREL) in Golden, Colorado, at an altitude of 1829 m (6000 ft) were used for that purpose, along with the ancillary data needed as inputs to the models. These data are routinely measured at this site and available from http://www.nrel.gov/midc/srrl_bms/. The predictions of all three models were degraded (whenever possible) to match the bandwidth and wavelength step size of the instruments. Figures 1 and 2 are typical examples of this series of tests. In Figure 1, the irradiance spectrum measured on a 40[degrees] tilted plane facing south is compared to the spectra predicted by the three candidate models for typical midday winter conditions (i.e., under a very clear sky). An LI-1800 field spectroradiometer is used here, with a 6 nm bandwidth and 2 nm step size. This rugged single-monochromator instrument has a silicon detector with no thermal control and has been carefully characterized (Myers 1989). Its nominal 300-1100 nm spectral range must be reduced in practice to a usable range of about 35-1000 nm for model validation purposes to guarantee an overall [+ or -]5% uncertainty. Similar results for direct normal irradiance on a sunny autumn afternoon are presented in Figure 2. The instrument used here is a double-monochromator OL-750 laboratory-grade spectroradiometer capable of scanning the spectrum between 250 and 2400 nm, with both a bandwidth and wavelength step of 5 nm. The latter instrument's accuracy is more stable over the spectrum than that of the LI-1800 instrument, as discussed elsewhere (Gueymard et al. 2002). Figure 2 also compares the relative difference (in percent) between the measured spectrum, used here as the reference, and the predictions of each model (SMARTS, SPCTRAL2, and SUNSPEC) after proper smoothing to match the instrument's bandwidth (5 nm). Note that the latter process presents a difficulty in the case of SPCTRAL2 because of its excessively coarse resolution, introducing gaps in the resulting spectrum. The shaded area represents the uncertainty limits of the instrument ([+ or -]5%). There are spectral areas where this theoretical uncertainty might be larger because of instrumental limitations (e.g., the switchover between two different detectors around 1100 nm), the signal's weakness (e.g., below 310 nm, above 2300 nm, or in strong absorption bands), or sharp spectral changes that cannot be completely resolved (e.g., the strong oxygen band at 760 nm or around the 940 nm water vapor band). Interruptions in the graph are intentional (for legibility); they correspond to the strongest absorption bands where the signal is very low and the associated comparisons meaningless anyway. Compared to the OL-750 spectrum considered as the reference here, SMARTS clearly appears to perform best, with a relative difference better than [+ or -]5% over most of the spectrum, i.e., within the instrument's uncertainty limits. From the wealth of similar results now available, only summarized here for conciseness, it is concluded that SMARTS provides the best predictions of the three candidate models. This can be related to the fact that, compared to the two other models, SMARTS has the finest resolution, the most detailed algorithm, and has been updated many times since its preliminary version of 1993.

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Model Validation

The final validation exercise, aimed at evaluating the absolute accuracy of the SMARTS predictions, is broken up into a series of three subtasks:

1. Compare the predictions of SMARTS to benchmark spectra obtained with rigorous radiative transfer codes. This is done for a series of atmospheric conditions and solar geometries. The tools selected here for generating these benchmark spectra are the three atmospheric codes mentioned earlier: MODTRAN, libRadtran, and SBDART. MODTRAN generates spectral irradiance for spectral intervals measured in wavenumbers rather than wavelengths; therefore, all its outputs of irradiance per unit wavenumber had to be converted into irradiance per unit wavelength and degraded to the lower resolution of SMARTS. A postprocessor was specially developed for this, using an energy-conserving rectangular filter with a bandwidth equal to the resolution used by SMARTS: 0.5 nm in the ultraviolet (UV), 1 nm in the 400-1700 nm waveband, and 5 nm beyond 1705 nm. It is important to note that the rigorous codes used here as reference necessarily have extremely slow execution. For instance, libRadtran and MODTRAN execution times are 1060 and 3790 s, respectively, for a single case aimed at calculating both direct and diffuse irradiance over the whole shortwave spectrum, compared to about 0.13 s for SMARTS, for the same conditions and on the same personal computer.

2. Compare the SMARTS predictions to measured spectra obtained under realistic conditions with first-class spectroradiometers. Because there is no single detector able to measure radiation accurately over the whole spectral range under scrutiny here (0.3-2.5 [micro]m), the spectral limits of this part of the study are those of the instruments.

3. Compare the SMARTS predictions to experimental measurements on tilted and vertical planes. Whereas spectral measurements on a 40[degrees] plane facing south are routinely made at NREL, no reference measurements on vertical planes were known to exist when this project started. Fortunately, a handful of spectral measurements could be specifically performed for this project at NREL.

For the second and third steps, the testing procedure used here is generally called a "radiative closure experiment." If all inputs to a spectral radiation model are ideally known, the spectra it predicts should be identical to the spectra measured with an ideally perfect spectrometer. In the real world, not all inputs can be obtained locally at the exact time needed, the available inputs are somewhat uncertain, and the reference instrument is not perfect. The larger the number of input variables to be measured is (because they have an important role in the modeling), the more uncertain the results of the performance tests are. Moreover, the stringent requirements of the procedure limits its applicability to at most a handful of experimental sites in the world, where all these spectral and ancillary measurements can be acquired simultaneously. To obtain meaningful results, two parasitic sources of error need to be separated from the inherent model's error: measurement error and propagation error. In the present case, the latter is caused by imperfect description of the exact atmospheric conditions that prevailed during the measurement, causing inadvertent prediction error. This is why extreme care is taken here to use only the most accurate data describing the atmospheric conditions so that the intrinsic model error can be estimated. If high-quality input data are available to describe the main extinction processes and the spectrometer's uncertainty is known, a model will pass the test if its predictions are within the uncertainty limits of the reference instrument. In a model's normal use, it can be anticipated that less optimal input data are available, thereby increasing the prediction uncertainty. This is discussed further in a section below.

Other publications (Gueymard 2001, 2005, 2006; Gueymard et al. 2002; Myers et al. 2004) provide results and detailed discussions on this validation exercise, so only limited additional information is given here for conciseness. Figure 3 presents a typical result from the first step, where the global horizontal irradiances predicted by four models (SMARTS, MODTRAN, libRadtran, and SBDART) are compared for the same set of atmospheric conditions as those that were selected to develop a recent standard spectrum (Gueymard et al. 2002; ASTM 2003a). These conditions are typical of areas with very clear skies (low aerosol content). To remove all possible external sources of error in the comparison, the four models have been used with a common extraterrestrial spectrum (Gueymard 2004a), and the MODTRAN spectra have been downgraded to match the resolution of the other models using the postprocessor described earlier. The overall accuracy of SMARTS appears excellent, on the order of 1-2% compared to MODTRAN (chosen here as the reference because of its higher resolution), except in the strong absorption bands due to ozone, oxygen, and water vapor. Any discrepancies in these bands correspond to low irradiance. They are also mostly transient and, hence, disappear with moderate spectral smoothing. Interestingly, the performance of SMARTS is equivalent to or better than that of libRadtran and SBDART over the spectrum, and this remains true when other atmospheric conditions or solar positions are selected.

A typical result of the second step appears in Figure 4. It shows a direct normal spectrum predicted by SMARTS compared to that measured at NREL with a FieldSpec spectrometer. This portable instrument has a spectral range of 350-2400 nm and a bandwidth of 5 nm. There is good agreement between the two spectra beyond about 400 nm but not as good below, i.e., in the UV. This justifies more scrutiny to validate the model in the UV, in which band both the solar spectrum and glazing optical properties change rapidly with wavelength. Such a test appears in Figure 5, this time using a spectrum measured with a double-monochromator, laboratory-grade instrument (OL-750), which performs better in the UV than the FieldSpec. The OL-750's bandwidth (about 5 nm) is ten times cruder than the SMARTS resolution in that band. Because of the complex structure of both the extraterrestrial spectrum and the ozone absorption features in the UV, spectra of different resolution cannot be realistically compared directly. This is clearly demonstrated in Figure 5--the measured spectrum has considerably less structure than the raw predicted spectrum at 0.5 nm resolution. To reconcile the two spectra, the smoothing capability of SMARTS is used (as in all the other model-measurement comparisons discussed here) to mimic the instrument's characteristics, both by degrading the results to the instrument's resolution (assuming a Gaussian filter shape in this case) and by increasing the original step size (0.5 nm) to that of the instrument (5 nm). (This optional smoothing feature has no equivalent in other models and might prove essential to liberate the users from the burden of postprocessing the predicted spectra if they need to fit the output spectral files to the specific format of glazing transmittance data sets, for instance.)

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Figure 6 exemplifies the results obtained during the third step and presents a comparison between SMARTS and the measured spectra for vertical planes oriented south and west, at times in the morning when the former plane was receiving direct radiation but not the latter. The relative difference between the predicted and measured spectrum is here somewhat larger than in the previous cases. This is the consequence of a combination of adverse conditions, such as significant shading of the horizon, difficulties in estimating the groundreflected irradiance and anisotropic reflectance effects, or anisotropy of the aerosol optical characteristics. The westoriented surface, in particular, had significant natural and artificial obstructions on the horizon, which are responsible for the drop in measured irradiance below about 750 nm. Although the current version of the model is unable to evaluate the effects of horizon shading and obstacles, this could be a valuable improvement in future versions--should it be a requested feature.

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As a general conclusion of the experimental part of the general validation exercise, it can be stated that SMARTS can reproduce the intricacies of the solar spectrum and generally agrees with measurements to within the instrumental accuracy, inasmuch as all the most important input data can be accurately obtained independently. The results presented here confirm the previous findings that led ASTM and other institutions to use SMARTS to develop reference spectra. Some of them are already standardized (ASTM 2003a, 2003b).

Broadband Irradiance

Although the present contribution is aimed at spectral radiation and does not specifically cover the prediction of broadband irradiance, some important findings are presented here for further reference and to help stimulate future discussions or projects related to this issue. SMARTS is primarily a spectral model, but it automatically performs a series of numerical integrations over the spectrum to output the broadband irradiance corresponding to each component of interest (direct, diffuse, global on the horizontal or any tilted plane). The question that arises is whether these broadband irradiance predictions from SMARTS are comparable to the irradiance measured with regular broadband radiometers (pyrheliometers or pyranometers) or to those from the historical ASHRAE model (as described in the Handbook) or other models being developed in various ASHRAE research projects. Indeed, the Society is currently transitioning from a time when a single irradiance model was promoted in the Handbook to a situation where new solar radiation models are being proposed for various purposes. The multiplication of models performing similar tasks can be confusing. Two issues in particular need be critically addressed: (1) How will the different inputs required by these models be obtained and published--particularly if these models are intended to be applicable to a large number of worldwide sites? (2) Are the irradiances predicted by different models under identical ideal conditions within reasonable agreement?

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The former issue is largely beyond the scope of this paper, but elements of discussion (for the case of SMARTS at least) are provided in a section below. The latter issue can be addressed by submitting all potential models to a series of tests, where their predictions are compared to either reference predictions from rigorous atmospheric models (such as those discussed earlier) or to experimental irradiance data measured under carefully controlled conditions (i.e., with accurate measurements of the main models' input variables). This kind of performance assessment is described elsewhere (Gueymard 2003a, 2003b, 2007). Interestingly, a recent study (Michalsky et al. 2006) has provided a solid testing benchmark for which many input variables were obtained simultaneously with first-class instrumentation. This validation dataset has been assembled from the detailed measurements obtained during the aerosol intensive operational period that took place at the Southern Great Plains (SGP) site of the Atmospheric Radiation Measurement (ARM) program. The dataset consists of 30 individual cloudless-sky data points scattered among 13 days in the period 5-30 May 2003. Figure 7 compares the direct normal irradiance predicted by SMARTS and two flavors (1) of the historic ASHRAE radiation model to that of pyrheliometric measurements (obtained with either an absolute cavity radiometer or a first-class pyrheliometer). As could be expected from the discussion above and results presented elsewhere (Michalsky et al. 2006), the agreement between SMARTS and the measured data is excellent. In comparison, the ASHRAE model performs poorly, particularly under hazy conditions and low sun. (Conversely, other tests conducted using NREL's data showed that, under very clear conditions such as those prevalent at this high-altitude site, the predicted direct irradiance is significantly too low.) Similar conclusions are reached when comparing the diffuse horizontal irradiance predicted by the models under scrutiny and that measured with a state-of-the-art instrument--a ventilated pyranometer of a specific type, equipped with a tracking shade, in accord with the discussion in Michalsky et al. (2005) and references therein, shown in Figure 8. The ASHRAE model considers that diffuse irradiance is a fixed fraction of direct irradiance, causing an artificial limit at about 120 W/[m.sup.2] (38 Btu/h x [ft.sup.2]) and large underestimation during hazy periods. The results of this exercise confirm those from many previous studies that demonstrated the poor performance of the ASHRAE model under variable conditions (e.g., Galanis and Chatigny [1986] and Gueymard [1993b]). It is therefore recommended that the historical ASHRAE model be retired as soon as possible.

Although SMARTS is inherently capable of predicting accurate broadband irradiances in addition to spectral irradiances, the REST2 clear-sky broadband model (Gueymard 2004b, 2007) can be recommended if only broadband results are needed. It consists of a parameterization of SMARTS and therefore provides results of quasi-identical accuracy at a fraction of the complexity and computation time.

MODEL SENSITIVITY TO INPUT VARIABLES

It is clear from the previous sections that accurate spectra can be obtained only if a precise description of the atmospheric and environmental variables affecting the solar spectrum are used as inputs to the model. Table 2 provides a comprehensive list of variables that affect the solar spectrum, most of which are considered in SMARTS. For convenience and clarity, the inputs have been organized into three different categories: solar variables (describing the solar position and the extraterrestrial irradiance), atmospheric variables (describing the state of the atmosphere-ground system with respect to radiative effects), and site-specific variables (describing the immediate environment of the simulated receiver or glazing). Note that variables #20-22 have been added here for completeness because they are actually needed for proper simulation of any window in its real environment, but they are not considered in any existing spectral radiation model.

The approximate magnitude of each variable's effect is broken down for each component of irradiance (direct, diffuse, and global). On a vertical surface, the incident irradiance is mostly direct if in view of the sun and mostly diffuse if in the shade, so that the most influential input variables may be different in the two cases. The sun-surface geometry determines the sun's incidence angle, which is always a major variable. The most important atmospheric variables are generally the aerosol optical depth (characterized here by Angstrom's turbidity coefficient and wavelength exponent) and precipitable water (a measure of the total water vapor column). Relatively to very clear and dry conditions (typical of, e.g., high altitude or arctic sites), direct irradiance decreases if either turbidity or water vapor increases. However, the effect of turbidity is concentrated at wavelengths below about 900 nm, whereas the effect of water vapor is concentrated longward of 900 nm. These two effects thus produce opposite effects in terms of the spectrum's center of gravity. For diffuse irradiance, increasing water vapor also depletes the spectrum longward of 900 nm, but increasing turbidity has a two-tier effect--the irradiance increases first, but then decreases when a critical turbidity limit is reached. For more quantitative information, see Gueymard's (2005) introduction to using spectral ratios to characterize the relative effects of the sun's zenith angle, turbidity, and precipitable water on the direct spectrum.

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MODEL INPUTS: DATABASE PREPARATION

Another important part of this study is to prepare a database of all inputs necessary so that the selected model can be run easily and efficiently by nonexperts. This database can be described as a large table where, for each targeted city and for each season (summer or winter), an appropriate value of all necessary variables (listed in Table 2) is provided. As of this writing, the exact format in which this database will become available (e.g., for the ASHRAE Handbook--Fundamentals or other printed or electronic document) is not decided. Therefore, only a preliminary sample is provided here for reference. Even though this initial version of the database only includes data for a finite number of North American cities, it is emphasized that the methodology proposed here could be used in a subsequent project to develop a considerably larger, worldwide version of the database, as described in another section. The database will be designed to provide the user with assistance in intelligent selection of the needed input parameters.

The only parameters that are not included in the database (because entirely under the user's control) are date and time, ground albedo, and surface tilt and azimuth. At this point, no information can be provided regarding the corrections needed when the surface to simulate (e.g., a window) is partially shaded or does not "see" the whole sky dome due to nearby obstacles. In what follows, the methodology used to obtain the reference values for the other variables is described.

Variables Related to Aerosols and Water Vapor

As mentioned in previously, the most critical atmospheric variables affecting the spectrum under clear skies are aerosol turbidity and water vapor abundance (measured by precipitable water, PW). Turbidity is the most important variable of the two, is highly variable in both space and time, and the least frequently measured so that it is considered here as the pivotal variable, to be determined first. The best source of data is from tracking multiwavelength sunphotometers that measure direct radiation through a series of typically 5-7 narrowband filters, providing the quasi-monochromatic irradiance for as many wavelengths. These are adequately selected to derive the aerosol optical depth (AOD) in regions of the spectrum where gaseous absorption is low and, therefore, not a significant source of contamination. Using Angstrom's law relating the AOD at any wavelength, [[tau].sub.a[lambda]], to that at 1 [micro]m (usually referred to as Angstrom's turbidity coefficient, [beta]), it is possible to obtain [beta] and the Angstrom wavelength exponent, [alpha], by linearly fitting the data points (of AOD at different wavelengths) in log-log coordinates:

ln[[tau].sub.a[lambda]] = ln[beta] - [alpha] ln([lambda] / [[lambda].sub.0]) (1)

where [lambda] is wavelength, and [[lambda].sub.0] = 1 [micro]m or 1000 nm. For greater accuracy with SMARTS, this fit is done twice, for wavelengths shortward and longward of 500 nm, thus providing two values of [alpha], noted [[alpha].sub.1] and [[alpha].sub.2] in what follows.

Measurements of spectral AOD were quasi-inexistent only two decades ago. Since then, the need for such data in various applications (particularly climate change) has prompted the establishment of a few sunphotometric networks. For the application envisioned here, the densest and most comprehensive source of data is NASA's AERONET (Holben et al. 1998, 2001). Besides their automatic (2) monitoring of AOD on a 15-minute-interval basis, AERONET sites also report PW. This is an important asset because PW is the second most significant atmospheric variable under cloudless conditions. About 130 sites are part of the AERONET network in North America. However, many of these sites are not continuously operating, or have not accumulated enough data to allow any statistical analysis. Such analysis is necessary because of the seasonal and interannual variability of AOD. For instance, Figure 9 shows the mean monthly [beta] for an 11-year period at the GSFC site in Greenbelt, Maryland. The large variation (5x ratio, maximum to minimum) in the July value is particularly significant because it occurs during a critical period with regard to cooling loads and justifies more scrutiny. Furthermore, coincident measurements of dry-bulb or wet-bulb temperature are generally not available, so that defining "peak conditions" in the usual sense is difficult. The relatively limited measurement periods prevent a detailed month-by-month analysis. Considering the main emphasis of this project on peak conditions, a special statistical analysis has been devised. For each site, the daily data points were separated into two groups: summer (four months, June to September) and winter (four months, November to February). This seasonal arrangement is the result of numerous preliminary trial-and-error tests. Its purpose is to obtain good accuracy and representative peak conditions despite the lack of long data series at most sites. For each season, a frequency analysis of [beta] has been performed with the goal of determining the most frequent (peak) turbidity value during either season. Here again, extensive trial and error has been necessary to evaluate the optimal intervals (bins) to use for AOD. A good compromise was obtained with intervals of 0.01. The peak AOD is selected as the middle value for the bin (or adjacent bins) with the maximum frequency in the distribution, resulting in round numbers such as 0.035 (in the general case of one peak bin) or 0.040 (in the infrequent case of two adjacent peak bins). The nature of the AOD distribution is clearly not gaussian, but log-normal.

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Once the peak AOD is determined, the representative values of [alpha] and PW are then calculated as their mean for the peak bin(s). A sample of results thus obtained for summer conditions is reported in Table 3. This analysis makes the peak atmospheric conditions ([beta], PW, and [alpha]; i.e., the main variables determining the magnitude and shape of the solar spectrum) self-consistent. It cannot be guaranteed that these conditions are also coincident with the peak temperature and/or humidity, but such a perfect match would be impossible to obtain anyway, due to the lack of long-term sunphotometric data in particular.

As can be understood from Table 3, peak conditions vary widely from one location to another, even though some general climatic trends are obvious: (1) [beta] is normally the largest wherever large cities and sources of pollution exist (e.g., the Northeast, the Los Angeles basin, Mexico City); (2) Southeast locations have high PW due to their humid (nearly tropical) summer climate; conversely, southwestern or northern locations are dryer, with, therefore, much lower PW; and (3) [alpha] is normally higher in urban areas and lower in maritime areas, a consequence of the direct relationship between [alpha] and the aerosol size distribution. As could be expected also, [beta]'s peak values are generally lower for winter than for summer at nearly all sites. A direct consequence of the log-normal distribution is that [beta]'s mean value is often significantly larger than its most frequent value (i.e., the mode). Figure 10 shows an example of this frequency distribution for two extreme turbidity climates in summer, represented by Waskesiu, Canada, and Mexico City, Mexico.

A problem is that most AERONET sites are set up at the outskirts of large cities or even in rural or remote areas. An appropriate correction or extrapolation procedure would thus be needed in most cases whenever the simulation site is in a large city's downtown area. The difficulty is that there is no known method to deal with this distance effect. In any case, both gaseous and particulate pollution are likely to be far larger in city centers than in suburbs or rural areas. Gaseous pollution (particularly due to ozone and nitrogen dioxide) affects the shortwave solar spectrum through increased absorption in the UV and visible spectra. This can be dealt with in SMARTS by selecting the appropriate pollution index (variable #10 in Table 2) from a scale of 1 (no pollution) to 4 (extreme pollution). The main difficulty, however, is to estimate the effect of particulate pollution on turbidity. Irradiance measurements that have been carried out in some rapidly developing cities over long periods show a distinct decrease, suggesting (as could be expected) that a city's turbidity increases steadily as it grows. Consequently, the difference in [beta] between a downtown area and nearby rural areas is a function of the city's size and more generally of its pollution level. (A relatively small city might have large pollution-induced [beta] due to stronger-than-average industrial activity, for instance.) Finally, there are topographic and meteorological conditions that influence the dispersion of pollutants differently from one city to another or from one day to the other. All these factors make it impossible to propose a general, objective, and accurate way of correcting or extrapolating a rural [beta] value to obtain an inner-city [beta]. Nevertheless, an approximate method is developed in what follows. It is based on the availability of AOD retrievals from space-borne sensors. These retrievals are still significantly less accurate than ground-based sunphotometric measurements. (Actually, one of the main justifications of the AERONET project was to serve as ground truth for existing or forthcoming satellite data.) Even though the absolute accuracy of AOD satellite retrievals is far from perfect, it is assumed here that, over a relatively homogenous climatic area, the ratio between satellite- and ground-based [beta] is conserved. Data thus extrapolated are specially flagged as "secondary" data, as opposed to "primary" data for the ground-based values. Data from the multi-angle imaging spectroradiometer (MISR) instrument onboard the Terra satellite (launched Dec. 18, 1999) have been chosen here. The instrument has an intrinsic resolution of 275 m (902 ft), and details about it can be found elsewhere (http://www-misr.jpl.nasa.gov/). The Level 3 aerosol products used here can be obtained daily (available since March 2000) and are available on a 0.5 x 0.5[degrees] grid. Each pixel therefore represents an area of about 39 x 55 [km.sup.2] (24 x 35 [mi.sup.2]) at a latitude of 45[degrees]. Although the MISR instrument retrieves AOD at various wavelengths, the current version of the dataset only provides the AOD at 558 nm, [[tau].sub.558]. The corresponding [beta] coefficient can be evaluated through Angstrom's law, assuming an average [[alpha].sub.2] for the climatic area, resulting in [beta] = [[tau].sub.558][0.558.sup.[alpha]2]. After normalization of the peak [beta] ([[beta].sub.p]) by the seasonal average [beta] from MISR, [[beta].sub.m], the following equation can be used to estimate the [[beta].sub.p] at any secondary location from the ground-based values measured at n neighboring primary sites:

[FIGURE 10 OMITTED]

[[beta].sub.p]/[[beta].sub.m] = [[i = n].summation over (i = 1)](1/[D.sub.i])[([[beta].sub.p]/[beta].sub.m]).sub.i]/[[i = n].summation over (i = 1)](1/[D.sub.i]) (2)

where [D.sub.i] is the distance from neighboring site i to the new location. For practical reasons and because of the low density of primary sites, a maximum of three primary sites is used for each extrapolation. A similar technique is used to extrapolate PW, except that the NASA Water Vapor Project (NVAP, http://charm.larc.nasa.gov/GUIDE/dataset_documents/base_nvap_dataset.html) gridded dataset is used for normalization in this case. This assimilated dataset provides twice-daily values of PW for the same 0.5x0.5[degrees] grid as MISR (2000-2001) or on a cruder 1x1[degrees] grid for the period 1988-1999. A simplified method (still based on Equation 2 but without normalization) is used to extrapolate [alpha] because the current version of the MISR dataset does not provide the retrieved [alpha] values. This is not expected to entail significant error because the average [alpha] does not vary much over a given climatic area.

Other Variables

The total ozone abundance varies generally smoothly and little over space or time, and its effect on irradiance is second order (except in the UV, where it becomes firstorder), so that daily data either from a nearby ground station (of the international World Ozone and Ultraviolet Data Center network) or from space (e.g., with the total ozone mapping spectrometer [TOMS] instrument) can be efficiently used.

Finally, the minor atmospheric variables are given fixed "typical" values for each season. A summary of the site-specific variable inputs is provided in Table 4 for a few locations of very different population, environment, and climate, showing both primary and secondary sites. The last two columns provide typical values of two variables describing additional characteristics of the aerosol model to be used (rural, urban, or a mix of the two). These two variables (aerosol single-scattering albedo and asymmetry factor) only intervene in the calculation of diffuse radiation.

Other necessary inputs are not specified for each site because either (1) they can be permanently fixed to some default value for all cases (e.g., the C[O.sub.2] concentration or the extraterrestrial spectrum's source) or (2) they are completely under the user's control, depending on the simulation assumptions: sun position (or date, time, site coordinates and time zone), height above ground, facade geometry, ground albedo, and spectral results to print.

Because the irradiance incident on vertical (as well as tilted) surfaces depends partly on the reflectance of the ground or of adjacent buildings, the spectral characteristics of this reflectance must be taken into account. This introduces a difficulty because the environment of one facade may be different from the next, especially in urban areas. The reflected irradiance is usually only a fraction of the total irradiance incident on a glazing. Determining the exact reflectance spectrum of each reflecting surface viewed by each particular window would be of an inextricable complexity. Therefore, in the case of the design conditions under scrutiny here, the user might elect to consider no reflecting obstacle (such as another building) and only a few generic ground types, such as lawn grass, asphalt, or concrete, for which the SMARTS albedo library offers spectral reflectance files.

EXAMPLE OF APPLICATION

The spectral method presented here is versatile and has already been used for solar energy applications. A recent publication (Myers and Gueymard 2004) illustrates the use of SMARTS in such a case, but most of the information it contains is applicable to buildings also. Furthermore, it is stressed that in addition to irradiance (spectral or broadband), the SMARTS model can also be used to predict illuminance, an important resource variable in daylighting applications, which is usually estimated by simpler empirical models of lower accuracy.

For this example, it is assumed that, during the forthcoming renovation phase of the ASHRAE headquarters building, highly spectrally selective fenestration will replace the existing one. The designer wants to analyze the spectral SHGC during a peak cooling load period and investigate whether different glazing characteristics would be justified, depending on wall orientation.

The building is located at a latitude of 33.834[degrees] and a longitude of -84.329[degrees]. Its elevation is about 300 m (984 ft) above sea level. It has a rectangular floor plan, whose main axis is rotated 28[degrees] counterclockwise from the east-west direction. The immediate surrounding of the building is a parking lot, whose albedo is simulated using spectral data for old asphalt, from the albedo library in SMARTS. Aerial photography reveals that, within a radius of at least 5 km (3.1 mi), the building as seen from above is within a suburban area where ground cover is constituted of two main elements: green vegetation and man-made constructions (roads and roofs). To simplify the simulation, it is estimated that the ground cover is 60% green vegetation and 40% asphalt, but the results are not very sensitive to the exact fraction of the two. Using the summer conditions in Table 3 and assuming that the peak cooling load occurs on August 21 at 16:00 Local Standard Time (Rock 2005), SMARTS can be used to obtain the spectral and broadband global irradiance on the roof and each facade, as well as their illuminance, for that specific moment. The directly illuminated facades are those facing NW and SW because the sun's incidence angle on the wall is <90[degrees], as shown in Table 5. This table also summarizes the broadband results (global irradiance and illuminance) for each surface. The predicted spectra for all the walls are compared in Figure 11, demonstrating the large difference in spectrum between the sunlit surfaces and the shaded ones.

FUTURE DEVELOPMENTS

This project's initial goal was to provide users with the necessary data to obtain spectra at a hundred sites in North America, focusing on the USA. During the course of this research, it appeared obvious that many potential users would soon request data for more sites in North America and for many sites in all parts of the world, so possibilities of generalization of the method have been investigated.

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

For the USA, it is certainly desirable to offer data for large cities (e.g., those with a population of at least 300,000) and, if possible, for all TMY2 sites (see http://rredc.nrel.gov/solar/old_data/nsrdb/tmy2/), as shown in Figure 12. The extrapolation method described above can be used effectively in this goal.

Although the AERONET network has been expanding rapidly since its inception, its current growth rate is relatively slow because of budgetary reasons in particular. It is therefore unlikely that its density over continents outside North America will be enough to allow effective extrapolation. Conversely, rapid progress is being made in the remote sensing of spectral AOD from space. Spectrometers with finer spectral and spatial resolution are regularly launched, and retrieval algorithms are improved continuously. It is therefore anticipated that, a few years from now, the absolute accuracy of remote-sensed AOD will become high enough that normalization with ground-based data, as used here, will become unnecessary. Although a single satellite sensor (MISR) is considered here, its data could be advantageously supplemented by that from other similar advanced sensors such as the moderate resolution imagine spectroradiometer (MODIS) or the spinning enhanced visible and infrared imager (SEVIRI). The envisioned final product would consist in a space-continuous information system based on gridded data derived essentially from satellite observations and covering the whole world.

SUMMARY AND DISCUSSION

The outcome of this research project is to propose a validated and integrated calculation procedure for the prediction of solar spectra incident on vertical (or otherwise tilted) windows as a function of local climatic conditions in North America. This procedure is aimed at engineers with modest background in meteorology, climatology, or atmospheric sciences and, therefore, attempts to reconcile accuracy, flexibility, and ease of use.

The proposed procedure is backed by thorough literature review and detailed performance assessment. The accuracy of the produced spectra is comparable to that from state-of-the-art rigorous atmospheric models or the best instruments. The procedure is not empirical, so its use can be extended to any other continent. It is, therefore, of general applicability but, at this stage, the needed atmospheric and climatic input data are only provided for a number of North American sites. These datasets are obtained directly from first-class ground-based instrumentation or indirectly from state-of-the-art remotesensing methods. The climatic dataset and the spectral radiation model are made as easy to use as possible, so that nonexperts can rapidly obtain spectral or broadband irradiance predictions for either summer or winter peak conditions.

With this general computerized procedure and the tabulated climatic input linked to a project's specific geometry and environment, HVAC engineers will be able to obtain reference spectra and combine them with the spectral optical characteristics of any type of glazing, particularly those that are spectrally selective. These custom reference spectra, being tuned to the particular conditions of each location and each project, effectively remove the current uncertainties associated with the use of a unique spectrum for all possible glazings and all locations--or of no spectrum at all. Therefore, the whole methodology provides an advanced, more accurate way of predicting the solar heat gain coefficient and fenestration cooling loads or of selecting the most energy-efficient glazing for a particular building (or even for each facade separately) at a specific site.

Besides its ability to generate any spectrum (as well as broadband irradiance, illuminance, or other specialized outputs) pertaining to local conditions, the proposed method is also able to emulate the current international procedures that are based on the reference spectra that have been recently standardized--because its atmospheric conditions are well documented. This capability should prove useful when comparing standard and realistic SHGC calculations for any particular glazing.

ACKNOWLEDGMENTS

Daryl Myers was highly instrumental by providing experimental information and by conducting spectral measurements at NREL specifically for this project. His help is deeply appreciated. Some data were obtained from the Atmospheric Radiation Measurement (ARM) program sponsored by the US Department of Energy. The AERONET staff and participants are thanked for their successful effort in establishing and maintaining the North American sites, whose data were advantageously used in this investigation. The author also wants to thank all members of the TC 4.5 Project Monitoring Committee for their encouragement and appreciation.

REFERENCES

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ASTM. 2003b. ASTM Standard G177-03, Standard Tables for Reference Solar Ultraviolet Spectral Distributions: Hemispherical on 37[degrees] Tilted Surface. Philadelphia: American Society for Testing and Materials.

Berk, A., G.P. Anderson, P.K. Acharya, L.S. Bernstein, J.H. Chetwynd, M.W. Matthew, E.P. Shettle, and S.M. Adler-Golden. 1999. MODTRAN4 User's Manual. Air Force Research Lab., Hanscom AFB, MA.

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Bird, R.E., and C. Riordan. 1986. Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes at the Earth's surface for cloudless atmospheres. J. Clim. Appl. Meteor 25:87-97.

Galanis, N., and R. Chatigny. 1986. A critical review of the ASHRAE solar radiation model. ASHRAE Transactions 92(1A):410-19.

Gueymard, C. 1993a. Development and performance assessment of a clear sky spectral radiation model. Proc. Solar '93 Conference, American Solar Energy Society, Washington, DC, pp. 433-38.

Gueymard, C. 1993b. Critical analysis and performance assessment of clear sky irradiance models using theoretical and measured data. Solar Energy 51:121-38.

Gueymard, C. 1995. SMARTS2, Simple model of the atmospheric radiative transfer of sunshine: Algorithms and performance assessment. Rep. FSEC-PF-270-95, Florida Solar Energy Center, Cocoa, FL.

Gueymard, C. 2001. Parameterized transmittance model for direct beam and circumsolar spectral irradiance. Solar Energy 71:325-46.

Gueymard, C. 2003a. Direct solar transmittance and irradiance predictions with broadband models. Part I: Detailed theoretical performance assessment. Solar Energy 74:355-79. Corrigendum, Solar Energy 76:513 (2004).

Gueymard, C. 2003b. Direct solar transmittance and irradiance predictions with broadband models. Part II: Validation with high-quality measurements. Solar Energy 74:381-95. Corrigendum, Solar Energy 76:515 (2004).

Gueymard, C. 2004a. The sun's total and spectral irradiance for solar energy applications and solar radiation models. Solar Energy 76:423-52.

Gueymard, C. 2004b. High performance model for clear-sky irradiance and illuminance. Proc. Solar 2004 Conf., American Solar Energy Society, Portland, OR.

Gueymard, C. 2005. Interdisciplinary applications of a versatile spectral solar irradiance model: A review. Energy 30:1551-76.

Gueymard, C. 2006. Prediction and validation of cloudless shortwave irradiance spectra for horizontal, tilted, or tracking receivers. Proc. Solar 2006 Conf., American Solar Energy Society, Denver, CO. To be published in Solar Energy.

Gueymard, C. 2007. REST2: High performance solar radiation model for cloudless-sky irradiance, illuminance and photosynthetically active radiation--Validation with a benchmark dataset. Solar Energy (forthcoming).

Gueymard, C., D. Myers, and K. Emery. 2002. Proposed reference irradiance spectra for solar energy systems testing. Solar Energy 73:443-67.

Holben, B.N., T.F. Eck, I. Slutsker, D. Tanre, J.P. Buis, Setzer, E. Vermote, J.A. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and S. Smirnov. 1998. AERONET--A federated instrument network and data archive for aerosol characterization. Remote Sens. Environ. 66:1-16.

Holben, B.N., D. Tanre, A. Smirnov, T.F. Eck, I Slutsker, N. Abuhassan, W.W. Newcomb, J. Schafer, B. Chatenet, F. Lavenu, Y.J. Kaufman, J. Vande Castle, A. Setzer, Markham, D. Clark, R. Frouin, R. Halthore, A. Karnieli, N.T. O'Neill, C. Pietras, R.T. Pinker, K. Voss, and G. Zibordi. 2001. An emerging ground-based aerosol climatology: Aerosol optical depth from AERONET. J. Geophys. Res., D106:12067-97.

Mayer, B., and A. Kylling. 2005. The libRadtran software package for radiative transfer calculations--Description and examples of use. Atmos. Chem. Phys. 5:1855-77.

McCluney, R. 1993. Sensitivity of optical properties and solar gain of spectrally selective glazing systems to changes in solar spectrum. Proc. Solar '93 Conf., American Solar Energy Society, Washington, DC.

McCluney, R. 1996. Sensitivity of fenestration solar gain to source spectrum and angle of incidence. ASHRAE Transactions 102(2):112-22.

McCluney, R., and C. Gueymard. 1993. SUNSPEC 1.0 Operating Manual. Florida Solar Energy Center, Rep. FSEC-SW-3-93.

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Myers, D.R. 1989. Estimates of uncertainty for measured spectra in the SERI spectral solar radiation data base. Solar Energy 43:347-53.

Myers, D.R., and C. Gueymard. 2004. Description and availability of the SMARTS spectral model for photovoltaic applications. Proc. 49th SPIE Annual Meeting, Denver, CO.

Myers, D.R., K. Emery, and C. Gueymard. 2004. Revising and validating spectral irradiance reference standards for photovoltaic performance evaluation. Trans. ASME, J. Solar Engng. 126:567-74.

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Rock, B.A. 2005. A user-friendly model and coefficients for slab-on-grade load and energy calculations. ASHRAE Transactions 111(2):122-36.

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Christian A. Gueymard, PhD

Member ASHRAE

Christian A. Gueymard is president of Solar Consulting Services, Colebrook, NH.

(1.) The coefficients of the model have changed recently, between the 2001 and 2005 editions of ASHRAE Handbook-Fundamentals. This undocumented change presumably results from an attempt to improve the model. It is apparent from the results presented here and the existing literature that the source of the problem is not in the coefficients' value but in the extreme simplicity and empiricism of the algorithm. Although, technically, there exist both an "old" and a "new" ASHRAE model, their performance is so similar that they are collectively referred to as "the ASHRAE model" in what follows.

(2.) Measurements are made automatically at regular intervals under all weather conditions. Cloudy periods are screened a posteriori with a sophisticated algorithm, so that AOD and PW data released as "Level 2" are assumed to represent cloudless periods only. Greenbelt, MD, for 1993 to 2003.

Table 1. Main Characteristics of the Candidate Spectral Radiation Models

            Latest   Year of        Spectral   Number of    Resolution,*
Model/Code  Version  Latest Update  Range, nm  Wavelengths  nm

SMARTS      2.9.5    2006           280-4000   2002          0.5-5
SPCTRAL2    2.0      1984           305-4000    122          5-100
SUNSPEC     1.0      1993           290-4000    545          2-50

*Depending on waveband.

Table 2. Necessary Inputs for Ideal Simulation and the Magnitude of
Their Effect on Predicted Irradiance

                                                 Irradiance
                                                 affected
Variable #  Description                          Direct  Diffuse  Global

            Solar variables
1           Zenith angle (1)                     ...     ...      ...
2           Azimuth angle (1)                    ...     ..       ..
3           Incidence angle (2)                  ...     ..       ..
4           Extraterrestrial spectrum            ..      ..       ..

            Atmospheric variables
5           Angstrom turbidity coefficient       ...     ...      ..
6           Angstrom wavelength exponent, two    ..      ..       ..
              wavebands
7           Precipitable water                   ...     ...      ...
8           Ozone column (3)                     .       .        .
9           Site pressure (4)                    .       .        .
10          Pollution level                      ..      ..       ..
11          Spectral ground reflectance, zonal   -       .        .
              average (5)
12          Aerosols' single-scattering albedo   -       .        .
              (broadband value)
13          Aerosols' asymmetry factor           -       .        .
              (broadband value)
14          Air temperature                      .       .        .
15          Season                               .       .        .
16          Carbon dioxide concentration         .       .        .

            Site-specific variables
17          Spectral foreground reflectance (6)  -       ..       ..
18          Surface tilt (7)                     ...     ..       ...
19          Surface azimuth (7)                  ...     ..       ...
20          Immediate sky shading (same          [..]    [..]     [..]
              building)
21          Background sky shading (other        [..]    [..]     [..]
              buildings ...)
22          Obstacles reflectance                -       [..]     [..]

Key:
... Major effect
.. Average effect
. Minor effect
- No effect
[]Effect currently not modeled
1 Calculated internally from date, local standard time, and geographic
coordinates of surface.
2 Calculated internally from tilt and azimuth of both sun and surface.
3 Major effect below 350 nm, moderate effect 500-700 nm, negligible
effect elsewhere.
4 If unknown, can be internally estimated from site's elevation and
latitude.
5 Average ground reflectance over an area about 5-10 km (3-6 mi) around
site.
6 Ground reflectance in the immediate foreground, within 100 m (300 ft)
of the surface.
7 Used to calculate incidence angle, see variable #3.

Table 3. Atmospheric Coefficients for Peak Summer Conditions, Obtained
from Analysis of Sunphotometric Data at a Sample of Sites in North
America

                                                                 [beta]
Site             State  Lat.    Long.     Elev. (m)  Elev. (ft)  Peak

Barrow           AK     71.312  -156.665     0          0        0.025
Bondville        IL     40.053   -88.372   212        696        0.035
Brookhaven       NY     40.870   -72.889    33        108        0.035
BSRN Boulder     CO     40.045  -105.006  1604       5262        0.045
Columbia SC      SC     34.023   -81.036   104        341        0.060
Flagstaff (MFR)  AZ     35.220  -111.630  2173       7129        0.025
Fresno           CA     36.782  -119.773     0          0        0.035
Halifax          NS     44.638   -63.594    65        213        0.035
La Jolla         CA     32.870  -117.250     0          0        0.045
Lanai            HI     20.735  -156.922    20         66        0.030
Los Alamos       NM     35.874  -106.326  2350       7710        0.015
Madison          WI     43.070   -89.410   326       1070        0.025
Mexico City      MX     19.334   -99.182  2268       7441        0.085
Monterey         CA     36.593  -121.855    50        164        0.035
Norfolk          VA     36.848   -76.259    20         66        0.045
Philadelphia     PA     40.036   -75.005    20         66        0.050
Stennis          MS     30.368   -89.617    20         66        0.085
Tucson           AZ     32.233  -110.953   779       2556        0.045
Walker Branch    TN     35.958   -84.288   365       1198        0.025

                                  Summer                    Start  End
Site             PW (cm)  [[alpha].sub.1]  [[alpha].sub.2]  MM/YY  MM/YY

Barrow           1.34     1.47             1.00             06/99  09/06
Bondville        1.85     1.62             1.36             06/96  06/06
Brookhaven       1.91     1.64             1.81             06/98  09/04
BSRN Boulder     1.40     1.66             1.35             06/01  08/06
Columbia SC      3.02     1.69             1.74             06/02  06/04
Flagstaff (MFR)  1.76     1.47             0.81             07/93  09/95
Fresno           1.63     1.33             1.73             06/02  09/04
Halifax          1.71     1.58             1.24             06/02  09/05
La Jolla         1.56     1.48             0.82             06/01  09/04
Lanai            3.15     0.63             0.95             08/96  09/03
Los Alamos       0.93     1.95             1.44             06/05  09/05
Madison          3.20     2.62             2.04             06/95  09/96
Mexico City      1.44     1.32             1.61             06/99  09/05
Monterey         1.76     1.60             1.27             06/02  09/03
Norfolk          2.73     1.55             1.71             06/02  09/02
Philadelphia     2.05     1.76             1.53             06/01  09/01
Stennis          4.00     1.57             1.54             06/00  09/03
Tucson           2.17     1.56             1.03             06/99  09/00
Walker Branch    1.70     1.83             2.09             06/00  09/05

Table 4. Necessary Main Inputs (and Their Proper Units) to Be Used with
the SMARTS Model for Summer Conditions at a Sample of Primary (P) or
Secondary (S) Sites*

                  Type of                                    Elevation,
Site       State  Site     Environment  Latitude  Longitude  km

Atlanta    GA     S        City         33.75      -84.38    0.315
Barrow     AK     P        Rural        71.31     -156.67    0
Bondville  IL     P        Rural        40.05      -88.37    0.212
Boulder    CO     P        Suburb       40.05     -105.01    1.604
Halifax    NS     P        Suburb       44.64      -63.59    0.065
Miami      FL     S        City         25.78      -80.18    0.005
Mexico     MX     P        City         19.33      -99.18    2.268
  City

Site       Time Zone  [beta]  [[alpha].sub.1]  [[alpha].sub.2]  PW, cm

Atlanta    -5         0.041   1.73             1.87             4.00
Barrow     -9         0.025   1.47             1.00             1.34
Bondville  -6         0.035   1.62             1.36             1.85
Boulder    -7         0.045   1.66             1.35             1.40
Halifax    -4         0.035   1.58             1.24             1.71
Miami      -5         0.045   1.59             1.24             4.50
Mexico     -6         0.085   1.32             1.61             1.44
  City

           Ozone,  Pollution              Single-Scattering
Site       atm-cm  index      Atmosphere  Albedo             Asymmetry

Atlanta    0.301   3          STS         0.85               0.60
Barrow     0.301   1          AS          0.95               0.65
Bondville  0.307   1          MLS         0.95               0.65
Boulder    0.294   2          MLS         0.90               0.62
Halifax    0.323   2          MLS         0.90               0.62
Miami      0.293   2          STS         0.90               0.62
Mexico     0.291   4          STS         0.75               0.60
  City

* The first four columns indicate non-input, additional information.
Please refer to the SMARTS User's Manual for additional details.

Table 5. Calculated Broadband Irradiance and Illuminance for the ASHRAE
Headquarters Building in Atlanta, GA, and Peak Cooling Load Conditions

               Wall Azimuth from                   Irradiance
Building Part  North              Incidence Angle  (W/[m.sup.2])

NE wall         62[degrees]       138.2[degrees]    66.9
SE wall        152[degrees]       101.1[degrees]    69.4
SW wall        242[degrees]        41.8[degrees]   669.6
NW wall        332[degrees]        78.9[degrees]   225.2
Roof           -                   50.3[degrees]   586.1

               Irradiance            Illuminance (klux)
Building Part  (Btu/h x [ft.sup.2])

NE wall         21.2                  8.5
SE wall         22.0                  9.0
SW wall        212.3                 78.4
NW wall         71.4                 27.1
Roof           185.8                 68.8