Data assimilation is a set of methods that enable the estimation of the state of a system based on observations and the underlying dynamical principles governing the system under observation (approximated by numerical modelling). A compromise is achieved between the two, based on the uncertainty and error characteristics of each.
A literature review identified key issues in applying data assimilation techniques as including: identifying the uncertainty to be focussed on, finding relevant timely observations, and estimating the error covariance structure - i.e. the extent to which an error observed at one site is representative of errors in nearby sites. To be effective, an application of data assimilation needs sufficient observations and error covariance to resolve the uncertainty of interest and determine the state of the system.
A survey of likely industrial uses found that available data in sediment dynamics problems was too sparse for data assimilation techniques to be useful. Similarly, in the downscaling wind modelling undertaken at coastal scale, the availability of observations is limited to single sites within a domain. With unknown error covariance, and wind field varying markedly over the coastal domain (Orr, 2005) it is thought unlikely that data assimilation will yield significant benefits. Hence, effort was focussed on waves and currents.
For currents, in collaboration with the Data Assimilation Research Centre at Reading University, HR Wallingford undertook an investigation into the use of data assimilation in prediction of storm surges in the North Sea. Initial work formed the MSc dissertation of Rowan Thainuruk (Thainuruk, 2013), and subsequently continued at HR Wallingford, with HR Wallingford’s results presented in a seminar at Reading University. We achieved the first use of the Particle Filter method (Van Leeuwen, 2009) with an unstructured mesh model (Figure 1), testing it with “perfect twin” experiments. Sensitivity to error covariance structure was investigated (Figure 2), with error covariance structure remaining a key uncertainty. Surge forecasts tested showed enhanced skill for the first 6 hours of the forecast.
| Figure 1: Unstructured mesh of flow model of the North Sea basin
|| Figure 2: Sensitivity of error in surge level to specification of error covariance.
For waves, the WaveSentry Bayesian approach (Harpham, 2016) was extended to include downscaling to nearshore, enabling the use of observations to add skill to nowcasting ensemble forecasts (e.g. as shown in Figure 3 that shows Met Office surge and offshore wave ensemble forecast for a site in the English Channel) and paving the way for probabilistic forecasting of coastal responses. High resolution local SWAN models trained Gaussian emulators which were then used in a meta-modelling approach to estimate nearshore wave transformation efficiently for all ensemble members. These systems allow for near-instantaneous re‑weighting of ensemble members, allowing observations to be used to add value to forecasts in the short time between waves being observed offshore and reaching the coast.
|Figure 3: Offshore ensemble wave forecast (Source: Met Office)|
|Authors||Doug Cresswell, Alan Cooper, Nigel Tozer, Michiel Knaapen|
|Keywords||Data assimilation, coastal modelling, particle filter, Bayesian method|
Harpham Q., N. Tozer, P. Cleverley, D. Wyncoll, D. Creswell. 2016. A Bayesian method for improving probabilistic wave forecasts by weighting ensemble members. Environmental Modelling & Software 84, 482-493.
Orr, A., Hunt, J. C. R., Capon, R., Sommeria, J., Cresswell, D. & Owinoh, A. 2005. Coriolis effects on wind jets and cloudiness along coasts. Weather.
Thainuruk, R. (2013) Using the Equivalent Weights Particle Filter to Predict Storm Surges for a Finite-element Model of the North Sea. Dissertation for MSc. Data Assimilation and Inverse Modelling in Geoscience, Department of Meteorology, University of Reading, 19th August 2013
Van Leeuwen, P.J. (2009). Particle Filtering in geosciences. Monthly Weather. Rev, 137 (12), 4089-4114.
To be effective, an application of data assimilation needs sufficient observations and error covariance to resolve the uncertainty of interest.