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A Revised Force–Restore Model for Land Surface Modeling

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  • 1 School of Meteorology, and Center for Analysis and Prediction of Storms, The University of Oklahoma, Norman, Oklahoma
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Abstract

To clarify the definition of the equation for the temperature toward which the soil skin temperature is restored, the prediction equations in the commonly used force–restore model for soil temperature are rederived from the heat conduction equation. The derivation led to a deep-layer temperature, commonly denoted T2, that is defined as the soil temperature at depth πd plus a transient term, where d is the e-folding damping depth of soil temperature diurnal oscillations. The corresponding prediction equation for T2 has the same form as the commonly used one except for an additional term involving the lapse rate of the “seasonal mean” soil temperature and the damping depth d. A term involving the same also appears in the skin temperature prediction equation, which also includes a transient term. In the literature, T2 was initially defined as the short-term (over several days) mean of the skin temperature, but in practice it is often used as the deep-layer temperature. Such inconsistent use can lead to drift in T2 prediction over a several-day period, as is documented in this paper. When T2 is properly defined and initialized, large drift in T2 prediction is avoided and the surface temperature prediction is usually improved. This is confirmed by four sets of experiments, each for a period during each season of 2000, that are initialized using and verified against measurements of the Oklahoma Atmospheric Surface-Layer Instrumentation System (OASIS) project.

Corresponding author address: Dr. Ming Xue, School of Meteorology, University of Oklahoma, 100 East Boyd, Norman, OK 73019. mxue@ou.edu

Abstract

To clarify the definition of the equation for the temperature toward which the soil skin temperature is restored, the prediction equations in the commonly used force–restore model for soil temperature are rederived from the heat conduction equation. The derivation led to a deep-layer temperature, commonly denoted T2, that is defined as the soil temperature at depth πd plus a transient term, where d is the e-folding damping depth of soil temperature diurnal oscillations. The corresponding prediction equation for T2 has the same form as the commonly used one except for an additional term involving the lapse rate of the “seasonal mean” soil temperature and the damping depth d. A term involving the same also appears in the skin temperature prediction equation, which also includes a transient term. In the literature, T2 was initially defined as the short-term (over several days) mean of the skin temperature, but in practice it is often used as the deep-layer temperature. Such inconsistent use can lead to drift in T2 prediction over a several-day period, as is documented in this paper. When T2 is properly defined and initialized, large drift in T2 prediction is avoided and the surface temperature prediction is usually improved. This is confirmed by four sets of experiments, each for a period during each season of 2000, that are initialized using and verified against measurements of the Oklahoma Atmospheric Surface-Layer Instrumentation System (OASIS) project.

Corresponding author address: Dr. Ming Xue, School of Meteorology, University of Oklahoma, 100 East Boyd, Norman, OK 73019. mxue@ou.edu

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