A Methodology to Improve the Predictability of Downward Shortwave Radiation: Preliminary Evidence from NOAA’s Surface Radiation Observatory at Penn State

A necessary condition for the successful integration of renewable energy technologies such as PV solar into the power grid is a high level of predictability in the downward shortwave (Global) radiation at the earth’s surface that solar energy technologies use as an input. The highly respected ERA5 reanalysis system produced by the Copernicus Climate Change Service at the European Centre for Medium-Range Weather Forecasts (ECMWF), which combines incomplete historical observations into estimates using data assimilation methods, is well positioned to produce these predictions. Unfortunately, the ERA5 predictions are not accurate. One example of this is provided by the predictive outcomes at NOAA’s surface radiation station at The Pennsylvania State University (PSU). A comparison of the ERA5 hourly values with the observed hourly values at PSU from January 1, 1999, through December 31, 2019, indicates that the predicted values are not accurate (Figure 1). In quantitative terms, the weighted mean percentage error (WMAPE) is about 38.9%. This grim result does not appear to be an outlier. For example, the WMAPE associated with ERA5 downward solar radiation values at NOAA’s Goodwin Creek (GWN, Mississippi) surface radiation station from January 1, 1999, through December 31, 2019, is about 38.8%. At NOAA’s Desert Rock (DRA, Nevada) and Fort Peck (FPK, Montana ) surface radiation stations, the WMAPEs are about 30.54% and 35.7%, respectively. At the Payerne (PAY) surface radiation station in Switzerland, the WMAPE is about 38.7%. At Japan’s Tateno (TAT) station, the WMAPE is approximately equal to 37.9 %. These are obviously nontrivial measures of predictive inaccuracy.

With the goal of improving predictability, the analysis begins by making two observations. First, incoming shortwave radiation over a typical day has a definitive pattern. Namely, the value equals zero before dawn and rises over the day until a maximum value is achieved. At this point, surface radiation declines until it again attains the value of zero. This pattern has statistical implications. Specifically, over many days, the value in hour t will be correlated with the value in t-24 and in other lagged hours. For example, the value at noon will be correlated with the values corresponding to noon from the previous days, while the value at hour 17 will be correlated with the values at hour 17 from previous days. Consistent with this view, the correlations in the downward radiation values at PSU have a distinct pattern (Figure 2). This pattern in the autocorrelations is also evident at other locations. Given that the past values of surface radiation are known at hour t, this pattern can be modeled to improve the accuracy of the downward radiation predictions at hour t.

The second observation is that while the contemporaneous correlations in downward shortwave radiation between locations can be very low (e.g., the correlation between the outcome at PSU and PAY in Switzerland is about 0.05), there are statistically significant relationships in the outcomes across locations that can be utilized to improve predictability. This is explored using the Vector Autoregressive Regression (VAR) method coupled with the notion of Granger Causality, a test based on whether the lagged values of some variable X are useful in predicting the current value of some variable Y. Because of its focus on the lagged values, the methodology does not contest the truism that the correlation between two contemporaneous variables does not imply causation. Using a pair-wise VAR modeling approach (e.g., PSU and FPK) coupled with a corresponding Granger test, the downward shortwave radiation outcomes at PSU exhibit two-way Granger Causality with each outcome at nine other locations worldwide. For example, there is two-way Granger Causality between the downward shortwave radiation values at PSU and FPK, even though the contemporaneous correlation is low.

With the above observations in mind, a comprehensive VAR model is estimated using hourly data from 10 observatories from across the world over the period January 1, 1999, through December 31, 2014. The locations include Kwajalein in the North Pacific, American Samoa, Boulder, Colorado, Mauna Loa in Hawaii, and the observatories discussed above (e.g., FPK). The analysis accommodated 76 hourly lags. Out-of-sample predictions of hourly downward shortwave radiation at PSU were calculated based on the estimated parameters. The results indicate that the predictions of downward shortwave radiation at PSU are more accurate when the lagged hourly outcomes at the nine other locations are factored into the predictions. Specifically, using a persistence forecast as a benchmark, the VAR results have a skill score equal to 0.46. The associated WMAPE is about 24.6%, considerably lower than that corresponding to the ERA5 values but still unacceptably high. The view here is that the results are encouraging because they suggest a clear pathway for further modeling improvements through the use of an ARCH/ARMAX ( autoregressive conditional heteroskedasticity/ autoregressive(AR)–moving-average(MA) model with exogenous inputs ) specification in which the ARCH component models the autoregressive nature of the volatility in downward shortwave radiation, the ARMA component models the more “ordinary” autoregressive process using AR and MA terms, and “X” incorporates exogenous inputs such as the ERA5 values. In short, this research has the potential to significantly improve the predictability of downward shortwave radiation, a prerequisite for the successful integration of solar energy technologies such as PV solar into the power grid.