Use of Measured Aerosol Optical Depth and Precipitable Water to Model Clear Sky Irradiance

— Predicted clear sky irradiance depends on atmospheric composition as well as solar position and extra-terrestrial irradiance. The effects on clear sky irradiance of year to year variations in atmospheric composition were studied using measurements of aerosol optical depth (AOD) and precipitable water (P wat ) at seven locations in the United States. Three clear sky models were evaluated, including one that uses Linke turbidity (T L ). This model was evaluated using historical, static T L as well as updated values derived from real-time AOD and P wat measurements. The average annual error in predicted clear sky irradiance using static T L did not differ significantly from year to year. Annual average error in predicted GHI was less than 5% for all models with no significant difference between models. The model with static T L had the lowest DNI errors, and the Bird model had the smallest GHI error but the largest DNI error. On average DNI and GHI were under-predicted.


I. INTRODUCTION
Predicting clear sky irradiance is important for estimating energy generation by solar power systems. Clear sky models predict the direct normal (DNI), diffuse horizontal (DHI) and global horizontal (GHI) components of irradiance on a cloudless day. Since the concentration of aerosol and water vapor in the atmosphere can affect all three of these irradiance components, they can also influence power production. We analyzed the effects of aerosol optical depth (AOD) and precipitable water (Pwat) on irradiance predictions from three clear sky models by comparing them with irradiance measurements at seven US locations. This paper is a report on our analysis.

II. METHODS
This section describes the differences between the clear sky models and the sources of atmospheric composition and irradiance measurements used in our analysis.

A. Clear Sky Models
Several numerical models are available for prediction of clear sky irradiance. Ineichen recently published a study of seven clear sky models [1], evaluating them using atmospheric data from the Monitoring Atmospheric Composition and Climate (MACC) project of the Copernicus Atmospheric Monitoring Service (CAMS). This data is provided by the European Center for Medium-Range Weather Forecasts (ECMWF). Ineichen concluded that the Simplified Solis model [2] demonstrated the smallest long term variance from measurements at twenty two irradiance stations mostly in Europe over an 8 year period. The National Renewable Energy Laboratory (NREL) performed a similar study [3] with irradiance and atmospheric data from the National Oceanic and Atmospheric Administration (NOAA) Earth System Research Laboratory (ESRL) Surface Radiation Network (SURFRAD) and found the Bird model [4]- [7] to be a better fit. We analyzed these models as well as the Ineichen-Perez model, popular due to its long-established implementation in PVsyst and in the PVLIB MATLAB and Python modeling libraries [8]- [10].
We compared the accuracies of Bird, Simplified Solis, and Ineichen-Perez models using PVLIB-Python. The Bird and Simplified Solis models take inputs of Pwat and broadband AOD measurements directly, but the Ineichen-Perez model [11], [12] uses Linke turbidity (TL) [13] as a parameter to represent both components of the atmosphere. PVLIB-Python provides a gridded static set of monthly TL values from 2003, obtained from the SoDa Pro website. We re-calculated the TL values from AOD and Pwat measurements using the method described in the next section and compared irradiance predictions from both the static and re-calculated TL values to demonstrate year to year variability.

B. Measurements of Atmospheric Composition
We used measurements of AOD and Pwat from the CAMS MACC project provided by ECMWF. This data is derived from an atmospheric model that assimilates satellite data from MODIS and is calibrated with independent ground measurements from AERONET [14]. Aerosol data at several wavelengths and total column water vapor are available over the entire globe at 0.75° increments every 3 hours from 2003 to 2012.
In our analysis, we calculated TL from broadband AOD and Pwat using Eq. (1) in which AM is airmass, calculated using the NREL solar position algorithm (SPA) form PVLIB, and δtotal.is the total atmospheric attenuation, derived in Eq. (2).
The method developed by Kasten [17], [18] is explained in detail by Ineichen and Perez [12], [19]. The contributions from pure Rayleigh scattering, δRayleigh, through a hypothetical "clean dry atmosphere" are combined with water absorption, δwater, and the broadband AOD to get the total atmospheric attenuation, δtotal, in Eq. (2).
There are several options for determining the broadband AOD, τaerosol. Molineaux [20] proposed using a single AOD measurement at 700 nm which is used in the Simplified Solis model. For the Bird model, Bird and Hulstrom [21] suggested two AOD measurements at 380 nm and 500 nm correlated by the expression in Eq. (3) where τ is AOD and λ is wavelength.
To calculate AOD at 380 nm, 500 nm and 700 nm, we obtained AOD at 550 nm and 1240 nm from the ECMWF MACC data. Then, assuming AOD is related to wavelength by the Angstrom turbidity model [15], [16], we calculated the Angstrom exponent, α, from AOD at the two wavelengths, and used α to obtain AOD at the desired wavelengths. This is demonstrated in Eq. (4).

C. Measurements of Clear Sky Irradiance
To evaluate the clear sky irradiance models and the measurement sources of AOD and Pwat, predictions of DNI, DHI and GHI were compared to SURFRAD measurements of irradiance, ambient temperature, relative humidity and pressure at either 1-minute or 3-minute intervals. The SURFRAD stations listed in Table I were used for the years from 2003 to 2012. Down-sampled measurements at 3-minute intervals were filtered for clear sky conditions using PVLIB-Python with a 30-minute window and clear sky calculated using Simplified Solis. Measurements below a GHI threshold of 200 W/m 2 were also removed.
Mean bias error (MBE) was calculated between the filtered measured data and the predictions using the formula in Eq. (5) in which N is the number of measurements. Relative error was obtained by dividing the calculated MBE by the average of the measurements. The analysis was done in a Python notebook that can be accessed from an online repository at https://github.com/mikofski/pvsc44-clearsky-aod.      In Fig. 5 and 6, different clear sky models are compared to measured data at Bondville, IL on July 16 th , 2006.    5), for each clear sky model. The box bounds the the 2 nd and 3 rd quartiles, the whiskers show the 5% and 95% confidence bounds, the dashed red line is the mean, the solid black line is the median, and the flyers are values that fall outside of the confidence bounds. Fig. 7 and 8 show comparisons between clear sky models by year in different colors. Fig. 7 shows that there are no significant long term trends in DNI errors and no significant differences between models. The Ineichen-Perez model with static TL shows no trend from year to year while the models using ECMWF MACC data show an increasing negative error with time. The Bird model had the largest mean yearly error. Fig. 8 shows that there are no significant long term trends in GHI errors and no significant differences between models. The Ineichen-Perez model with static TL shows no trend from year to year while the models using ECMWF MACC data show an increasing negative error with time. The Simplified Solis model had the largest mean yearly error.
From the year to year comparison, there does not appear to be significant difference between the use of static and realtime atmospheric data in clear sky predictions. The increasing yearly mean bias observed in DNI and GHI year to year box plots for models using real-time AOD and Pwat may be an artifact of the measured atmospheric data. For GHI the increase in relative mean bias error is less than 5%.   There are no significant differences in DNI errors by month or by model. The Bird model has the largest mean monthly errors. There is a seasonal bias in GHI errors for all models, including the Ineichen-Perez model with static TL, so the seasonal bias cannot be an artifact of the AOD and Pwat measurements unless it arises from a common instrument error. The seasonal bias under-predicts GHI in summer, with a delta between the summer and winter mean error of less than 5%. Fig. 9. Comparison of DNI errors at all stations by months (colors) shows no statistical differences by month or model. Fig. 10. Comparison of GHI errors at all stations by months (colors) show a seasonal bias, with a delta between summer and winter mean error of less than 5%. Fig. 11 and 12 show regional variations in error between clear sky models by stations in different colors. The average monthly errors are grouped by station for all months and years. Fig. 8

IV. CONCLUSIONS
A study of variations in clear sky irradiance due to AOD and Pwat has shown that for the seven stations and the ten-year period examined in this study there is no significant improvement in model accuracy when using real-time AOD and Pwat measurements. There is a seasonal bias in the GHI error that does not appear to be caused by the real-time AOD and Pwat measurements because it also appears in the errors from model using static TL. The average monthly errors in GHI were not significantly different between models and were all less than 5%. The Ineichen-Perez model with static TL had the lowest errors for DNI, but were not significantly different than the Simplified Solis model. The Bird model had significantly larger errors for DNI, but had the lowest GHI median error.