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Open AccessTechnical Note

Technical Note on the Dynamic Changes in Kalman Gain when Updating Hydrodynamic Urban Drainage Models

1
Department of Environmental Engineering, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
2
DHI, DK-2970 Hørsholm, Denmark
3
WaterZerv, DK-2700 Brønshøj, Denmark
*
Author to whom correspondence should be addressed.
Geosciences 2018, 8(11), 416; https://doi.org/10.3390/geosciences8110416
Received: 15 October 2018 / Accepted: 7 November 2018 / Published: 13 November 2018
(This article belongs to the Special Issue Hydrology of Urban Catchments)
To prevent online models diverging from reality they need to be updated to current conditions using observations and data assimilation techniques. A way of doing this for distributed hydrodynamic urban drainage models is to use the Ensemble Kalman Filter (EnKF), but this requires running an ensemble of models online, which is computationally demanding. This can be circumvented by calculating the Kalman gain, which is the governing matrix of the updating, offline if the gain is approximately constant in time. Here, we show in a synthetic experiment that the Kalman gain can vary by several orders of magnitude in a non-uniform and time-dynamic manner during surcharge conditions caused by backwater when updating a hydrodynamic model of a simple sewer system with the EnKF. This implies that constant gain updating is not suitable for distributed hydrodynamic urban drainage models and that the full EnKF is in fact required. View Full-Text
Keywords: backwater; data assimilation; distributed urban drainage models; Ensemble Kalman Filter; Kalman gain; sewer surcharge backwater; data assimilation; distributed urban drainage models; Ensemble Kalman Filter; Kalman gain; sewer surcharge
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MDPI and ACS Style

Borup, M.; Madsen, H.; Grum, M.; Mikkelsen, P.S. Technical Note on the Dynamic Changes in Kalman Gain when Updating Hydrodynamic Urban Drainage Models. Geosciences 2018, 8, 416.

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