Physical Analytics - Renewable Energy, Weather and Climate Forecasting

Description: Accurate forecasts of the atmospheric state have been a particularly challenging problem yet have enormous social and economic benefits. Among many important applications of atmospheric forecasts, the need for the forecast of variable solar and wind energy generation is becoming pressing with increasing penetration of solar and wind energy to the total energy mix. Forecasts of enhanced accuracy are highly desired for reliable grid operation at reduced cost and a more efficient electricity market. Recently, we showed that significant accuracy improvements can be achieved if we combine the individual model forecasts using a machine-learning based approach which takes into account appropriately additional state parameters beyond these need to be explicitly forecasted.

The multi-model blending method can be understood from Figure 1, which hypothesizes the accuracy of various forecasting approaches for different time horizons. The long-term average consists of using a constant climatological value or climate model forecasts. The model approach corresponds to the use of numerical weather prediction models, which rarely achieve good accuracy at short time horizon due to the period they require to achieve numerical stability. A Lagrangian approach provides good accuracy for a few hours ahead via, for example, advecting the most recent upwind observations in space and time to estimate when clouds might reach a forecasting site. Finally, the Eulerian approach uses the persistence of the last observation, which shows highest accuracy at very short forecasting horizons.


Figure 1: Depiction of forecast accuracy of various approaches and models as a function of forecast time horizon.

An key feature - situation-dependent blending - endows this approach high forecast accuracy perfomance and distinguishes it from conventional multi-model ensemble methods. This can be understood by the following equation yielding an optimal forecast (Cblend)  for a given parameter (wind, irradiance etc), which can be represented as a linear combination of models (or expert systems),

with τ as the forecast horizon, x the location and spatial extent of the forecast, and s the weather situation defined by a set of environmental parameters E (including forecasted ones). Cm are the forecasts associated with each model and  wm the respective machine-learned weightings. wm is a function of forecast horizon, location, and weather situation s. The index m corresponds to each different model, including Eulerian, Lagrangian, model, and climatological inputs.

Figure 2 provides an architectural view of the technology as we applied it to renewable energy forecasting. A “big” data bus provides atmospheric information (such as temperature, wind, cloud properties etc) from various forecasting models. For solar, a radiative transfer model converts these atmospheric information into irradiance. The different forecasts are blended and then converted to power using an irradiance to power (for solar) or a wind to power (for wind) model. A machine learning module provides the blending (weight) coefficients. Initially the system is trained on historical data but as new measurements become available it constantly improves. The training starts with analyzing how the errors of the individual forecast models depend on a large set of atmospheric state parameters using functional analysis of variance. From the analysis, a reduced set of state parameters (E) which has significant impact on the models’ forecast errors is selected. Then, the parameters E, the forecasted and the measured values of the parameter of interest are fed into a machine-learning module to derive the situation-dependent weight coefficients. 


Figure 2: Architectural view of situation-dependent, machine learning based multi-model blending.

The situation-dependent model blending method has been successfully applied to a number of forecasting problems, including solar power, wind power, precipitation, and particulate matter pollution etc. in various geographical areas and for hour-, day-, and month-ahead forecasting time horizons. In all cases, substantial accuracy improvements have been observed - typically over 30% improvement with respect to the best individual input models - demonstrating that it is a general framework for enhancing modeling of complex systems. Please refer to the presentations and publications below for  more information and forecasting results. You can also find below a demo website containing real-time blended forecasts of contiguous US wide solar irradiance.

Recent presentations: 

Recent publications:


Recent press:



         US Wide Solar Forecast

Key patents: