Abstract
Abstract Two approaches are proposed to introduce the surface energy storage into the cost function in a variational method for improving the estimates of surface turbulent heat fluxes. In the first approach, each of the energy storage terms is directly calculated based on available observations, and in the second approach, the total energy storage is fitted by the piecewise linear regression function. The heat flux estimates are validated with the eddy correlation (EC) measurements at two carefully selected stations with different land covers and weather conditions in northwestern China and east of the Tibetan Plateau, respectively. In contrast to the variational method without considering the energy storage in the cost function, two new approaches have improved the heat flux estimates, with the first approach being slightly better, especially around midday and/or under strong unstable conditions. It is also reasonable that the calculated/fitted energy storage with the measurements in the previous time period can be transferred for the heat flux estimates in the later time period. Furthermore, the heat flux estimates with both approaches are less sensitive to the errors in the profiles of temperature, humidity, and wind, as well as energy storage, so they may be more reliable.
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