A more accurate scheme for calculating Earth's skin temperature

The theoretical framework of the vertical discretization of a ground column for calculating Earth’s skin temperature is presented. The suggested discretization is derived from the evenly heat-content discretization with the optimal effective thickness for layer-temperature simulation. For the same level number, the suggested discretization is more accurate in skin temperature as well as surface ground heat flux simulations than those used in some state-of-the-art models. A proposed scheme (“op(3,2,0)”) can reduce the normalized root–mean–square error (or RMSE/STD ratio) of the calculated surface ground heat flux of a cropland site significantly to 2% (or 0.9 W m−2), from 11% (or 5 W m−2) by a 5-layer scheme used in ECMWF, from 19% (or 8 W m−2) by a 5-layer scheme used in ECHAM, and from 74% (or 32 W m−2) by a single-layer scheme used in the UCLA GCM. Better accuracy can be achieved by including more layers to the vertical discretization. Similar improvements are expected for other locations with different land types since the numerical error is inherited into the models for all the land types. The proposed scheme can be easily implemented into state-of-the-art climate models for the temperature simulation of snow, ice and soil.