Assimilation of lake water surface temperature observations using an extended Kalman filter

Abstract

A new extended Kalman filter (EKF)-based algorithm to assimilate lake water surface temperature (LWST) observations into the lake model/parameterisation scheme Freshwater Lake (FLake) has been developed. The data assimilation algorithm has been implemented into the stand-alone offline version of FLake. The mixed and non-mixed regimes in lakes are treated separately by the EKF algorithm. The timing of the ice period is indicated implicitly: no ice if water surface temperature is measured. Numerical experiments are performed using operational in-situ observations for 27 lakes and merged observations (in-situ plus satellite) for 4 lakes in Finland. Experiments are analysed, potential problems are discussed, and the role of early spring observations is studied. In general, results of experiments are promising: (1) the impact of observations (calculated as the normalised reduction of the LWST root mean square error comparing to the free model run) is more than 90% and (2) in cross-validation (when observations are partly assimilated, partly used for validation) the normalised reduction of the LWST error standard deviation is more than 65%. The new data assimilation algorithm will allow prognostic variables in the lake parameterisation scheme to be initialised in operational numerical weather prediction models and the effects of model errors to be corrected by using LWST observations.

• land surface data assimilation
• parameterisation of lakes
• extended Kalman filter

6. Acknowledgements

The author thanks Laura Rontu (Finnish Meteorological Institute) and Homa Kheyrollah Pour (University of Waterloo) for their help with preparing the data, Jean-François Mahfouf, Alina Barbu (Météo-France) and Kalle Eerola (Finnish Meteorological Institute) for useful discussions, Suleiman Mostamandi (Russian State Hydrometeorological University) for technical help and Emily Gleeson (Met Éireann) for the careful reading and suggestions for the language revision of the manuscript. Three anonymous reviewers made many useful comments. The work was partly supported by the European Space Agency (ESA-ESRIN) Contract No. 4000101296/10/I-LG (Support to Science Element, NorthHydrology Project).

Notes

¹The model horizontal resolution is 15 km, 60 levels in vertical.

²The following notation is used here: An analysis time is a moment in time when the analysis is performed to initialise the new forecast (increments are added to the background). A cycling period is a period between two analysis times. The (shortest) forecast length equals to the cycling period. Jacobians are calculated with the model runs for the full previous cycling period. Assimilation window is a time period around the analysis time, during which the available observations are picked to be assimilated.