A Closed-Form Expression of Soil Temperature Sensing Depth at L-Band

L-band passive microwave remote sensing is one of the most effective methods to map the global soil moisture distribution, yet, at which soil depth satellites are measuring is still inconclusive. Recently, with the Lv's multilayer soil effective temperature scheme, such depth information can be revealed in the framework of the zeroth-order incoherent model when soil temperature varies linearly with soil optical depth. In this paper, we examine the relationships between soil temperature microwave sensing depth, penetration depth, and soil effective temperature, considering the nonlinear case. The soil temperature sensing depth often also named penetration depth is redefined as the depth where soil temperature equals the soil effective temperature. A method is developed to estimate soil temperature sensing depth from one pair of soil temperature and moisture measurement at an arbitrary depth, the soil surface temperature, and the deep soil temperature which is assumed to be constant in time. The method can be used to estimate the soil effective temperature and soil temperature sensing depth.