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Data Assimilation in MIKE 1D

Data assimilation is a technique for combining measurements of the state of the system with the model dynamics in order to improve the knowledge of the system. The data assimilation module in MIKE 1D can be used for assimilation of water level and discharge measurements in the hydrodynamic model and for assimilation of concentration measurements in the advection-dispersion model.

Data assimilation weighs the confidence in the measurements and the confidence in the model prediction against each other and corrects the model states according to this. Two methods for data assimilation are implemented in MIKE 1D, their main difference being in how the above-mentioned measurement versus model weighting is obtained. The first method is based on a stationary gain function, which is specified by the user. The other method is based on the ensemble Kalman filter (EnKF). The implementation of the EnKF is experimental and is not available through the MIKE+ UI.

The stationary gain method (available as 'Updating with weighting function' in MIKE+) is a deterministic approach that does not explicitly address model uncertainties. Computationally it is only marginally more expensive than a simulation without assimilation, because it uses only a single simulation.

For the ensemble Kalman filter, the gain function is derived from statistics of an ensemble of slightly different simulations. The ensemble members are created by perturbing the boundaries and propagating the boundary uncer-tainty through the model. This formulation also allows for general uncertainty assessment, i.e. without assimilation of measurements.

Both methods use the same general filtering framework.

The data assimilation module can be used either in hindcasting mode for process studies and design purposes or as part of an operational forecasting system. In either case, the module provides an improved estimate of the state of the system which is consistent with the observed data. In an operational setting the data assimilation module is used for updating the state of the system prior to the time of forecast, and hence providing improved initial conditions for the forecast. After the time of forecast the model can be corrected using forecasts of model errors.

Application examples of the MIKE 11 data assimilation module can be found in Hartnack and Madsen 1, Madsen et al. 2 and Madsen and Skotner 3.

These example results are representative for results produced by the MIKE 1D data assimilation module.

The same principle has been used in both the MIKE 11 and the MIKE 1D data assimilation module.

They do, however, not use the same random number generator thus giving some differences in the results using the Ensemble Kalman filter especially when using a small number of ensembles.

  1. Hartnack, J.N., and Madsen, H.,2001, Data assimilation in river flow modelling, 4th DHI Software Conference, 6-8 June, 2001, Scanticon Conference Centre, Helsingør, Denmark ↩

  2. Madsen, H., Rosbjerg, D., Damgård, J., Hansen, F.S., 2003, Data assimilation in the MIKE 11 Flood Forecasting system using Kalman filtering, Water Resources Systems - Hydrological Risk, Management and Development (Proceedings of symposium HS02b held during IUGG2003 at Sapporo, July 2003). IAHS Publ. no. 281, 75-81. ↩

  3. Madsen, H., and Skotner, C., Adaptive state updating in real-time river flow forecasting - A combined filtering and error forecasting procedure, Journal of Hydrology, Volume 308, Issues 1-4, pp.302-312, 2005, ISSN 0022-1694, https://doi.org/10.1016/j.jhydrol.2004.10.030. ↩