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

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.