Better state estimates by combining models and observations
Observations provide information about a physical system, but rarely cover the entire domain or all the quantities of interest. Numerical models describe how the system evolves, but are subject to uncertainty in initial conditions, forcing and model simplifications. Data assimilation combines these sources of information while accounting for uncertainty in both.
The result is an updated estimate of the system's state and its uncertainty, which can provide the starting point for a new forecast. Depending on the problem and method, data assimilation can also be used to estimate unknown model parameters.
How we can help
- Connect observations to simulators: Develop calculations that make model outputs comparable with measurements, and characterise relevant sources of uncertainty.
- Develop and adapt assimilation methods: Select and extend ensemble-based methods to suit the model dynamics, available observations and computational resources.
- Make use of sparse measurements: Investigate how observations at a limited number of locations can improve estimates of a larger spatial field.
- Make ensemble computations more efficient: Combine fast simulators, GPU computing and multilevel methods to explore more possible outcomes.
- Evaluate estimates and forecasts: Assess predictive skill, uncertainty estimates and sensitivity to observation coverage and assumptions about model and measurement errors.
Ensemble-based methods
An ensemble is a collection of model realisations representing different possible states and trajectories. Each realisation is advanced using the simulator. As observations become available, the ensemble is updated to reflect the new information.
We develop and compare methods including:
- Ensemble Kalman filters: Use statistical relationships within the ensemble to update the model state from differences between simulated and observed quantities.
- Multilevel methods: Combine coupled ensembles at different model resolutions to reduce the computational cost of estimating relevant statistics.
- Particle filters: Represent uncertainty using weighted model realisations and can accommodate distributions that are not well described by a Gaussian approximation. These methods require particular care in systems with many degrees of freedom.
The choice of method depends on the system's nonlinearity, the number of observations, the distribution of uncertainty and the cost of each simulation. We therefore consider the assimilation method and simulator together.
Working with sparse observations
A central focus of our research is data assimilation with spatially sparse observations. A measurement provides direct information at one location, while the aim may be to update currents, water levels or other quantities across an entire domain. How far that information should influence the model depends on both the physics and the statistical relationships within the ensemble.
Limited ensemble sizes can introduce spurious correlations and misleading updates. Insufficient ensemble spread can also lead to overconfidence in the model. We investigate how methods can be adapted to provide useful updates and realistic uncertainty estimates when observations are limited.
Fast simulators make more possible outcomes accessible
Ensemble-based data assimilation requires many simulations. Efficient numerical methods and effective use of computing hardware are therefore integral to our work. Through GPU Ocean, we have developed and used GPU-accelerated ensembles of simplified ocean models for data assimilation and uncertainty analysis.
This work is particularly connected to coastal circulation and storm surge modelling. Uncertainty in current fields also affects drift predictions, with applications in search and rescue and pollutant transport. Our contribution is the development of numerical methods and computational tools in collaboration with domain specialists and users.
Selected publications
- Comparison of Ensemble-Based Data Assimilation Methods for Sparse Oceanographic Data.
- Multi-Level Data Assimilation for Ocean Forecasting using the Shallow-Water Equations.
Work with us
Do you have a numerical model and observations that you would like to use more effectively together? Contact our Applied Computational Science research group to discuss method development, simulator coupling and the evaluation of data assimilation.