Probabilistic Solar Forecasting in California Coastal Areas Using Post-Processed NWP

Patrick Mathiesen¹, JohnjoJohn Brown², and Jan Kleissl¹

¹Department of Mechanical and Aerospace Engineering

University of California, San Diego

La Jolla, CA

²Global Systems Division/Assimilation and Modeling Branch

Earth System and Research Laboratory

National Oceanic & Atmospheric Administration

Boulder, CO

Solar forecasting is essential to achieve high penetrations of solar PV technology.  For day-ahead solar forecasting, operational numerical weather prediction (NWP) models are most accurate.  However, previous studies have shown that NWP GHI output is generally positively biased.  Over many forecasts, this suggests that predicted cloud cover extent is too little and modeled clouds are optically too thin, significantly limiting NWP applicability for commonly cloudy regions.

For coastal California, summer marine layer fog and stratus conditions are very common, occurring for 50 or more days in May, June, and July of 2010.  While NWP models predict the synoptic conditions for which marine layer fog and stratus form correctly, modeled fog and stratus conditions over land are not extensive and generally evaporate very quickly.  As such, GHI prediction intervals (a forecast range of the likely minimum and maximum GHI based on historical NWP accuracy) for these regions are generally wide and impractical.  To improve upon this and compress the prediction interval, accurately predicted synoptic-scale conditions can be related to historical forecast accuracy.  Based on synoptic conditions, likely clear/cloudy days can be identified independent of NWP forecast GHI.  From this, regime dependent GHI prediction intervals can be established, shrinking for likely clear days and expanding for likely cloudy days.

We will first show that the North American Model (NAM) GHI biases are location and season dependent.  Specifically, the NAM under-predicts summer coastal fog and stratus conditions for southern California leading to an over-prediction of GHI (Fig. 1).  Though GHI forecast accuracy remains low, this study will demonstrate that the NAM correctly predicts the synoptic-scale conditions favorable for fog and stratus formation.  Assuming that synoptic-scale conditions are well predicted, we will relate the predicted direction of the 70 kPa geostrophic wind to GHI forecast accuracy.  Finally, prediction intervals, accurate for 80%-90% of forecasts, will be established for future forecasts based on the historical distribution of GHI biases.

Figure 1 compares the NAM against GOES Surface and Insolation (GSIP) GHI output for June 2010.

Fig. 1:  NAM bias error (W m^-2) for southern California in June 2010 compared to GSIP GHI data (squares are 12.5 km by 12.5 km).   Bias error is highest for regions approximately 20 km inland of coast (175 W m^-2), representing an under-prediction of summer coastal fog and stratus clouds over land.

Over oceanic grid points, NAM GHI bias is low.  Bias peaks at 175 W m^-2 for regions approximately 20 km inland.  This suggests that while the NAM predicts marine layer fog and stratus systems over the ocean accurately, cloud cover and extent over land is under predicted.  Further inland, as marine layer conditions become less prevalent, NAM GHI accuracy increases.

For summer, the presence of marine fog and stratus conditions is dependent on synoptic scale patterns.  Offshore geostrophic flow, often accompanied by deep subsidence, is generally associated with clear sky conditions for coastal regions.  Figure 2 relates the calculated 70 kPa geostrophic wind direction to NAM GHI RMSE.

Fig. 2:  NAM GHI RMSE (W m^-2) as a function of 70 kPa geostrophic wind direction and sun altitude.  Bins near the center of the plot are mid-day measurements while points near the edge correspond to low sun-altitude angles.  Easterly winds generally correspond to accurate NAM GHI forecasts (RMSE < 150 W m^-2) while westerly winds result in much higher RMSE (RMSE > 250 W m^-2).

Figure 2 shows that the NAM model predicts GHI with much greater accuracy when the synoptic-scale conditions predict off-shore flow.  This corresponds to clear days and the "Santa Ana" conditions.  For geostrophic conditions suggesting on-shore flow, NAM GHI accuracy significantly decreases and RMSE increases by over 100 W m^-2.  Figure 2 clearly demonstrates that GHI forecast accuracy can be related to synoptic-scale forecast conditions.  By establishing forecast accuracy as a function of geostrophic wind direction, 90% prediction intervals for future forecasts will be produced and finally validated.  This will provide effective minimum and maximum GHI predictions within which 90% of measurements will fall.