Variability of the Solar Resource in the United States

The variability of the solar resource is an important consideration in the need to adequately characterize the variability with measurements and for predicting future solar power plant performance. This analysis disregards predictable variability, such as that caused by site latitude and time of day, and concentrates on less predictable behavior caused by climate. The solar variability is closely related to the variability of climate in time and space, because atmospheric forces and constituents have a strong impact on the amount of solar radiation absorbed, reflected, or otherwise prevented from reaching the Earth’s surface.

With knowledge of the likelihood of variability from year to year, users are provided some justification for selecting a particular period of time for measurements adequate to characterize the solar resource. Likewise, with knowledge of variability across distance, users can make some statement of the applicability of a measurement to a location some distance away. Knowledge of variability then becomes valuable when deciding how long to make measurements at a particular location and whether the character of the solar resource at that location can be extended to other nearby locations.

Gueymard and Wilcox (2011) have analyzed 8 years of data (1998–2005) from the NSRDB in the realms of temporal and spatial variability. The analysis summarized the values in each 10-km by 10-km cell in the SUNY satellite-derived data in the NSRDB and calculated monthly mean daily totals, annual mean daily totals, and mean daily total for the entire 8-year period. The values were analyzed by temporal and spatial variability.

Temporal variability. For each cell, the 8 annual values were used to calculate a COV. The 8- year mean irradiance <Ep> and each annual value Ei were used to derive the standard deviation of the data set. Because there are no missing values, the standard deviation simplifies to

σt = [ ( < Ep > –Ei )2 / 8 ]1/2 (6-2)

The temporal COV is

Ct = σt / < Ep> (6-3)

To understand the variability in a seasonal scope, the process was repeated on a monthly level— for example, the 8 Januarys, Februarys, etc. The results, expressed in percent, represent the variability in the solar resource year by year at the cell’s geographic location. The resulting COV for DNI for all cells plotted as a contour map of the United States is shown in Figure 6-11, which provides a quick visual measure of differences in interannual variability. The temporal COV for the 48 U.S. states ranges from a low of 0.49% in south-central Washington to a high of 15.8% in northwest Washington (which has an interesting contrast of climate within a single state).

Spatial variability. The 8-year daily total irradiation means for each 10-km by 10-km cell were compared to a matrix of surrounding cells to determine the variability of the solar resource within the matrix (see Figure 6-12).

Figure 6-12. A 3-by-3 grid layout with anchor cell in the center and 8 surrounding neighbor cells.

Image from NREL

Here, the standard deviations of the surrounding cells were calculated as

σs = [ Σ (Ep – Ei )2 / n ]1/2 (6-4) The spatial COV is

𝐶𝑡 =_<𝐸𝜎𝑡_𝑝> (6-5)

The same process was applied to the 8-year means on a monthly level—all Januarys, Februarys, etc.

Two matrix sizes were analyzed: a 3 by 3 (see Figure 6-12) and a 5 by 5. These represent areas of approximately 30 km by 30 km and 50 km by 50 km, respectively, and likewise roughly represent an area within 15 km and 25 km of a measurement site. The results for DNI, expressed in percent, are mapped in Figure 6-13, which provides a quick visual representation of how the solar resource varies throughout space. For DNI, the values range from 0.12% in central Missouri to approximately 11.5% along a corridor between Los Angeles and San Bernardino, California. Variability tends to be higher in coastal areas (particularly the California coast) and in mountainous areas. Greater variability occurs in the 5-by-5 matrix, which is to be expected because of the effects of terrain. Further, the general pattern of high and low variability remains the same between the two maps, indicating that in locations of significant variability, the

Figure 6-13. DNI spatial coefficient of variability for a (top) 3-by-3 cell matrix and (bottom) 5-by-5 cell matrix for the average DNI from 1998–2005. Image from NREL

The underlying data for these maps are available from NREL to provide users with the actual values for each 10-km by 10-km cell both in units of % COV and Wh/m2_{. Users should be} cautioned that the 8-year period may not be long enough to produce definitive variability values, and the uncertainty of this analysis has not been defined. NREL plans to update this data set by drawing from a longer period of record; however, the results here are very likely accurate enough to reveal the relative variability of the solar resource throughout the United States.

Using these variability statistics, users can better understand the extent of measurements required to best characterize the solar resource for a particular application. In areas with low interannual variability, a shorter measurement period may suffice. In areas with low spatial variability, a measurement station could possibly represent the solar resource at nearby locations, negating the need for additional measurements. An analyst can use this information to better build confidence in a data set as being sufficient for an analysis and can use these data to understand the

Similar analysis was carried out for the gridded TMY data set (1998–2009) (Habte et al. 2014). The spatial variability analysis was implemented by comparing a center pixel to neighboring pixels (Figure 6-14). A COV value was generated for each configuration shown in Figure 6-15.

Figure 6-14. The distribution of the pixels in each spatial variability analysis. The black center pixels were compared to each of the gray pixels. Images from NREL

Figure 6-15. Map showing spatial variability among neighboring pixels. Images from NREL

The higher variation in the DNI compared to the GHI was attributed to the opacity of sky and also aerosols (Gueymard and Wilcox 2011). The magnitude of variation (COV) in the DNI increased rapidly as the distance between the center pixel and the farthest pixel increased (Figure 6-15). The variation of DNI with adjacent pixels could provide system performance analysts with essential information about how the system energy output will be spatially variable in certain

The temporal variability was also analyzed using a standard deviation for the monthly gridded NSRDB (1998–2009) data. The purpose of this analysis was to understand the effectiveness of the TMY data in representing the long-term variations. Figure 6-16 shows the standard deviation distribution of the GHI and DNI data set for all pixels in the United States. The yellow box illustrates confidence interval coverage of 95%, and the red line is the mean point of the 95% confidence interval data.

Figure 6-16. Monthly standard deviation distributions in kWh/m2_{/day for the NSRDB gridded DNI}

and GHI data sets. Illustrations from NREL

As illustrated above, the standard deviations of the irradiance for each month provide useful information about the temporal variability of a typical data set. The annual temporal variations included in the typical data set do not depict the monthly variations; therefore, the user of the TMY data set must assess the importance of shorter term (monthly) compared to long-term (annual) temporal variability when applying the data to a specific system performance project.