Applied Mathematics GIDP
American Meteorological Society Annual Meeting
Satellite images provide a basis for estimating global horizontal irradiance over areas on the scale of a city or larger. In this work, we aim to improve satellite derived estimates by combining them with ground sensor data and an advection model in a Bayesian framework to produce both improved estimates and forecasts. We use a data assimilation technique known as the Local Ensemble Transform Kalman Filter (LETKF). The LETKF is a square root filter in which calculations are performed in the space spanned by ensemble members, a lower dimensional subspace of the state space. This allows for a reduction in computational complexity because the number of ensemble members (around 50) is significantly lower than the dimension of the state space (hundreds of thousands). Within this framework, we utilize satellite images taken from the GOES-15 geostationary satellite (available every 15-30 minutes) as well as ground data taken from irradiance sensors and rooftop solar arrays (available every 5 minutes). We use an advection model, driven by wind forecasts from a numerical weather model, which stimulates cloud motion. This model is then used to span the time between measurements as well as to create forecasts. We present preliminary results showing the effectiveness of this method to produce irradiance estimates, forecasts, and uncertainty projections are affected by the localization and inflation in the LETKF, cloud motion uncertainty, and random cloud structure perturbations. Benefits and drawbacks of the present framework as well as future improvements are also discussed.
Abstract for Lay Audience
As the consequences of global warming come into focus, the need for our society to reduce our carbon emissions becomes more immediate. Though the promise of renewable energy is bright due to its low societal externalities and rapidly dropping costs, one major barrier to the wide adoption of both wind and solar power production is the variability inherent in the technologies. Grid management will be forced to evolve from the current state in which the energy supply, from coal or natural gas, can be controlled to meet demand to one in which large portions of the energy supply are made up of renewables which are primarily controlled by the weather.
If this hurdle is not overcome our power grid could become unstable, forcing us to rely more on controllable, but polluting, energy sources such as coal and natural gas. Since we are unable to control how bright the sun shines or how hard the wind blows, we must be able to forecast it. This is the focus of my present work: make renewable energy forecastable so that it can be a viable source of reliable energy.
Our approach to improving irradiance forecasts is to combine different sources of information in a novel mathematical framework. The sources of information are: numerical weather models, satellite images, power output of rooftop solar panels, and irradiance sensors distributed over the area of a city (in this case Tucson, AZ). We use a Bayesian data assimilation framework to combine these sources of information in an optimal way and to assess the uncertainty of our irradiance forecasts. In this framework, we assimilate new measurements into our current state estimate by carefully taking into consideration the relative confidence we have in both the new measurement and our current state estimate. This means that the more confident we are in a piece of information the more it will affect our new state estimate. The process of repeating this procedure over time with an evolving state estimate is commonly referred to as data assimilation.
Existing irradiance forecasting techniques do not make use of all the data sources we consider. For example, we combine satellite images, which cover the entire globe, but provide uncertain irradiance estimates, with ground sensors, which sparsely cover the Tucson area, but are very accurate. Satellite-derived irradiance estimates are inherently uncertain due to the nature of satellite measurements. The satellite measures the amount of light reflected from the top of the cloud, but we need to know the amount of light transmitted through the cloud. Modeling the amount of light transmitted through the cloud is error-prone due to both measurement uncertainty and modeling assumptions. Our approach allows us to improve the spatially expansive satellite estimate with the more accurate but spatially sparse ground sensor measurements which measure directly the light transmitted through clouds.
This work focuses on using the LETKF to combine satellite images, ground sensors, a numerical weather model, and an advection model to create irradiance forecasts. This will allow us to create forecasts from the irradiance fields produced by combining satellite images and ground sensors using cloud motion fields derived from a numerical weather model. This framework gives us the ability to not only improve the irradiance field by assimilating new satellite and ground sensor observations, but also the cloud motion field. Satellite images can also be used to create “observations” of the cloud motion field by using sparse optical flow on successive satellite images. These “observations” can then be assimilated into the cloud motion field leading to further improvements. Successful completion of this research will allow for the creation of irradiance estimates over large areas, the size of a city, which will be accurate over time scales, minutes to hours, important to grid management in the presence of renewable energy.