Demonstrating parameter estimation with ensemble-based DA

Numerical weather prediction models are complex computer codes that estimate how the atmosphere will behave in the next few days. All weather forecasts evolve from an initial condition representing atmospheric properties in three spatial dimensions at a specific time. This initial state is determined by combining recent atmospheric observations with older forecasts. Both sources of information are uncertain. Thus, they are blended in a data assimilation procedure, which gives more weight to the least uncertain pieces of information. Weather models and data assimilation methods have steadily improved over the years. However, they are still affected by errors, which are larger in some areas than in others. This project aims to reduce forecast errors over mountains, where they tend to be larger. Weather models are based on a computational grid, that could be imagined as a pixelated version of the actual atmosphere. In the case of regional weather models, the three- dimensional pixels are about 1 km in the horizontal dimensions and about 100 m in the vertical. There are as many as 10 million of them. Weather models predict how winds, air temperature, air pressure, and humidity evolve in time in each pixel. There is a major complication in the process. Many meteorologically important processes occur naturally on spatial scales smaller than the pixel size; thus, they are invisible to weather models. Such processes include the absorption of solar and terrestrial radiation, the formation of clouds and precipitation, and atmospheric turbulence. Turbulence is chaotic air motion; over time, it tends to make atmospheric properties smoother. Meteorologists describe the impacts of atmospheric turbulence with mathematical relationships called parameterizations. These combine information from limited sets of historic field measurements with simplified theory. They may be astonishingly accurate in some weather conditions but perform poorly in others. Turbulence parameterizations are often imprecise over mountains, and we seek to improve them using the information contained in atmospheric observations. To do so, we exploit the same mathematical tools used in data assimilation but for a different purpose. Instead of using observations to estimate the state of the atmosphere, we use them to estimate the empirical parameters of turbulence parameterizations. In technical terms, this procedure is called ensemble-based parameter estimation and is a form of inverse modeling. We work toward the long-term goal of continuously adjusting parameterization schemes to current observations in actual weather forecasts. As a first step in that direction, we perform ensemble-based parameter estimation experiments with synthetic observations. These are drawn from a digital twin of the atmosphere, that is, a very-high-resolution numerical simulation that reproduces turbulent air motions very accurately.