Towards improved objective analysis of lake surface water temperature in a NWP model: preliminary assessment of statistical properties

Abstract

Information about the statistical structure of the lake surface water temperature (LSWT) field is needed for assimilation of lake observations into Numerical Weather Prediction (NWP) models, to describe the lake surface state at each grid-point containing lakes. In this study, we obtain the autocorrelation function for LSWT from two types of observations, in situ and satellite-based. We use summer time measurements during 2010–2014 over selected Fennoscandian lakes and Northern European domain. The estimated autocorrelations decrease exponentially (from 0.99 to 0.73 for in situ and from 0.97 to 0.61 for satellite observations), when the distance between observations increases from zero to one thousand kilometres .A large difference in lake depth leads to a decrease of the correlation. Typical error standard deviation of LSWT observations was found to be 0.9 $ ^{\,\circ } $C for in situ observations and 1.2$ ^{\,\circ } $C for satellite observations. The exponential approximation for the LSWT autocorrelation functions is proposed, which depends on both the distance and the difference in lake depth. These results are directly applicable for the LSWT objective analysis in NWP. New autocorrelation functions, which allow interpolation of observations within and between lakes, were used in numerical experiments with the High-Resolution Limited Area Model (HIRLAM). In this preliminary assessment, we suggest adaptation of the presently used functions by increasing the influence radius and taking into account the lake depth difference. Generalization of the results to cover the melting and freezing seasons, their assessment for different geographical areas as well as their application to other prognostic lake variables within NWP are foreseen.

Keywords

• Lake surface water temperature
• NWP
• objective analysis
• optimal interpolation
• autocorrelation function