Worldwide impact of aerosol’s time scale on the predicted long-term concentrating solar power potential

Concentrating solar technologies, which are fuelled by the direct normal component of solar irradiance (DNI), are among the most promising solar technologies. Currently, the state-of the-art methods for DNI evaluation use datasets of aerosol optical depth (AOD) with only coarse (typically monthly) temporal resolution. Using daily AOD data from both site-specific observations at ground stations as well as gridded model estimates, a methodology is developed to evaluate how the calculated long-term DNI resource is affected by using AOD data averaged over periods from 1 to 30 days. It is demonstrated here that the use of monthly representations of AOD leads to systematic underestimations of the predicted long-term DNI up to 10% in some areas with high solar resource, which may result in detrimental consequences for the bankability of concentrating solar power projects. Recommendations for the use of either daily or monthly AOD data are provided on a geographical basis.

The frequency distributions of AOD shown at different time scales in this figure are computed using a moving average process with an averaging window of varying size, from daily to monthly, in progressive 1-day steps. This process is repeated for all available AOD observations at 214 sites of the Aerosol Robotic Network (AERONET). This worldwide network offers highquality AOD observations 48 that are widely considered the ultimate reference to validate other sources of AOD data. Overall, the AOD mean value (red curves in Figs. S1c and S1d) remains approximately constant over time scales from daily to monthly. The standard deviation (blue curves in Figs. S1c and S1d), however, decays monotonically. At monthly scales for some sites, this decay even reaches 60% of the standard deviation at daily scale Both the long-term mean and standard deviation values of the Ångström's aerosol turbidity coefficient from the MERRAero dataset (see Methods section) agree reasonably well with the long-term values evaluated at 214 AERONET sites worldwide. The major disagreements appear over the Amazon rainforest region.
In the regions with higher standard deviations (Fig. S2b), the change in long-term DNI with AOD's temporal scale is greater. These regions also coincide with those with greater mean aerosol turbidity coefficient (compare with Fig. S2a). Figure S3: Long-term annual DNI for the world. (a) Estimate from NASA's Surface meteorology and Solar Energy (SSE) database (see comments below). (b) Calculated long-term DNI bias that would affect the resource data in (a) if monthly rather than daily aerosol optical depth data were used to produce (a). (Maps are generated with the Matplotlib version 1.5.1 and Basemap version 1.0.8 Python libraries [URL: http://matplotlib.org/ and http://matplotlib.org/basemap/]).

Supplementary
The SSE dataset accounts for the direct effect of aerosols from a monthly climatology obtained from six years of results from the MATCH aerosol transport model. The monthly mode of their AOD predictions is actually used instead of the monthly mean to mitigate the bias issue that is in turn quantified globally in this study 56 . Further details are available at https://eosweb.larc.nasa.gov/sse/documents/SSE6Methodology.pdf. Note that SSE is probably not the most accurate DNI dataset, considering its coarse spatial resolution (1x1°) and other factors. However, it is in the public domain and its entire methodology is known, contrarily to other newer and more specialized-but commercial-datasets. Thus, SSE is a good target dataset for the present research purposes. We would like to acknowledge these data were obtained from the NASA Langley Research Center Atmospheric Science Data Center Surface meteorological and Solar Energy (SSE) web portal supported by the NASA LaRC POWER Project.
Supplementary Table S1 (and companion discussion): Inventory of the Aerosol Robotic Network (AERONET) test sites used in this study and ancillary information. Further information on the AERONET dataset and the data used here is provided in the Methods section.
The information provided in the columns is as follows: Station is the AERONET station name, Latit. is the latitude in degrees north, Longit. is the longitude in degrees east. The columns E[α i ] and E[τ i ] are the long-term mean Ångström's exponent and Ångström's turbidity parameter (i.e., AOD at 1 μm) obtained from instantaneous observations, respectively. The Ångström's turbidity parameter is calculated from multi-spectral instantaneous AOD observations between 440 and 870 nm using the Ångström's empirical formula τ = βλ -α , where β is the Ångström's turbidity parameter, α is the Ångström's exponent, and τ is an observed AOD at a wavelength λ (in microns) between 440 and 870 nm. Both, E[α i ] and E[τ i ] describe the aerosol climatology of each test site.
From the time series of instantaneous observations of β at every site, the departures, ε β , from each daily mean are accumulated over the entire record period and used to compute the longterm standard deviation of β at sub-daily scale (column SD[τ i,d  In contrast to this approach, which accounts for the sub-daily variations of AOD, the long-term mean DNI can be estimated with REST2 from the distribution of daily β observations. This approach neglects the sub-daily variations of AOD. The differences between this latter value and the former one are shown in the column Δ[DNI d ] for each station. At 203 out of the 214 test stations, the difference is less than 2%, which roughly corresponds to a mean deviation of about 7 W m -2 . This deviation is smaller than expected deviations in many DNI solar radiation models or even in some ground observations. Hence, as assumed in this study, a daily representation of AOD appears sufficient and commensurate with the current requirements and state-of-the-art in solar energy applications. The column E[τ d ] shows the long-term mean Ångström turbidity parameter obtained from the observed daily means. Note the very small deviation with respect to the long-term mean value obtained from instantaneous observations (i.e., E[τ i ]), as it is already shown for two AERONET stations in Supplementary Fig. S1c-d.
From the time series of daily mean β, the departures from each monthly mean are accumulated over the entire record period at every station and used to compute the long-term standard deviation of daily β at sub-monthly scale (column SD [τ d,m ]) as for the sub-daily case described above. This parameter accounts for the sub-monthly variability of daily β. Note this is a similar procedure as the one followed to compute SD [τ i,d ]. The comparison of SD [τ d,m ] and SD [τ i,d ] shows that the sub-daily variability of AOD is much lower, in average, than the daily variability at sub-monthly scale. (At many sites the daily variability is up to two orders of magnitude larger than the sub-daily variability). This result is aligned with one of the major assumptions made in this study, in virtue of which the AOD variability at sub-daily scale is neglected with respect to the variability at synoptic scales.
As for sub-daily scale, but at monthly scale, the columns E[DNI m ] and Δ[DNI m ] compare the calculation of the long-term mean DNI considering the day-by-day variation of β and approximating this value as simply the calculated DNI from the monthly distribution of β observations. In this case, as expected consistently with the results presented in this study, the differences at assuming a monthly β with respect to the more correct day-by-day calculation are much larger, being greater or equal than 3% at 24 of the test sites (highlighted in bold). Typically, these sites are characterized by high mean β and low mean α (i.e., coarse particles, such as desert dust).
Note that an important difference of this latter result with respect to the more comprehensive evaluation carried out using the Monte-Carlo analysis is that here a fixed optical air mass of 1.5 (i.e., fixed solar position) is assumed, which is not necessary in the stochastic framework. Note The rationale behind is that the latter is a calculation based on monthly periods while the former is based on a much longer multi-year period (indeed, the entire record period in each site).