Definition of component effective emissivity for heterogeneous and non-isothermal surfaces and its approximate calculation

Abstract

Measurement of land surface temperature faces many problems. For example, each pixel over land surface is likely to be heterogeneous and non-isothermal with both vegetation canopy and background soil, and the three-dimensional structure of canopy often makes the canopy radiation angular dependent. It is difficult to define an overall land surface temperature and emissivity at pixel scale for heterogeneous and non-isothermal surfaces. After recalling several definitions of effective emissivities, component effective emissivity is defined in this paper under the conditions of local thermal equilibrium and a constant material emissivity for surface temperature variation in the normal Earth environment. Component effective emissivities make it possible to retrieve the component temperature based on multi-directional measurements. The sum of component effective emissivities is equal to the overall effective emissivity, which can be used to inverse pixel-averaged effective temperature. Taking the continuous plant/soil system as an example, the Monte Carlo method is used to simulate the effective emissivities, and an analytical expression equation (AEE) of the effective emissivities including direct-line emission and single scattering contribution is developed. Monte Carlo simulated results show that the sum of direct-line emission and single scattering effective emissivity is close to overall effective emissivity when soil and leaf are set to 0.94 and 0.98 respectively. Then component and overall effective emissivities calculated by Monte Carlo method and AEE are compared, and their differences are analysed for different soil and leaf emissivities. It is shown that when soil and leaf emissivities are set respectively to 0.94 and 0.98, the differences are less than 0.006 within a 50° view zenith angle. When soil or leaf emissivity is set to 0.9, the difference reaches 0.025 or 0.016, which is large enough to introduce a 1 K error in land surface temperature inversion when this effective emissivity is used. The paper finally proposes that the linear relationship of difference with soil and leaf emissivity can be used to compensate the errors.