Relief effects for passive microwave remote sensing

The signal of a microwave radiometer observing a land surface from space is composed of surface and atmospheric contributions, both of which depend on the relief. For proper interpretation of the data these effects should be quantified and, if necessary, taken into account. Relief effects are twofold: First, the path through the atmosphere between the surface and the sensor depends on the altitude of the emitting surface, thus leading to a height-dependent atmospheric influence. The effect can be taken into account by standard atmospheric radiative transfer models if the elevation of the surface and the atmospheric state are known. Second, and more relevant for the present discussion, is the variable topography of land surfaces, consisting of slopes, ridges and valleys, sometimes with characteristic alignments, and surfaces surrounded by elevated terrain. These surfaces can interact radiatively, not only with the atmosphere, but also with each other, leading to the tendency to enhance the effective emission. Under such circumstances, deviations occur from the standard hemispheric emission of a horizontal surface. The interactions not only depend on topography and emissivity, but also on the bistatic scattering behavior. Special attention will be paid to the radiation enhancement in a landscape of lambertian surfaces with elevated horizons. As an example, simulated data for southern Norway are shown. Introduction To assess potential error sources in algorithms based on passive microwave data, the quantification of all factors contributing to the measured microwave radiation is necessary. This paper deals with the effects of a terrain with variable height and with tilted surfaces on the measurement of microwave radiation by means of satellite-based radiometers. Although these effects can be quite significant for land remote sensing, so far they have not received proper attention. An example of relief effects are shown in an early image from Schaerer and Schanda (1974) at 3 mm wavelength where part of the radiation from the mountain is reflected by the lake of Thun (Figure 1). Furthermore the emission itself clearly deviates from a flat horizon. Also shown is a visible version of the same scene. Relief effects are twofold: First, the path between the radiation source at the surface and the sensor depends on the surface altitude, thus leading to a relief-dependent atmospheric contribution. This effect is the topic of Section 2, where the radiation from a horizontal surface with a flat horizon at a given altitude is described. Section 3 is devoted to a variable topography, consisting of valleys and ridges; characteristic effects on the passive microwave signal will be described and illustrated in Section 4. Flat horizon The classical geometry of remote sensing of the terrestrial surface is a pair of half spaces separated by a horizontal surface, leading to a flat horizon. In this situation there is no shadow of any kind. The relief effects are determined by the dependence of the emitted radiation on the altitude h of the surface. Blackbody radiation with a brightness temperature equal to the physical temperature T0 is produced in the lower half space, part of which is transmitted, and thus emitted (Te) into the upper half space where it is sensed by a radiometer (Figure 2). Radiation from the upper to the lower half space (Tsky) is much smaller than T0. The p-polarized emitted brightness temperature Te above a flat surface with reflectivity rp is given by Te= epT0 = (1-rp) T0 (1) The upwelling radiation Tup just above the surface is the sum of the radiation emitted by the lower half space and the radiation Tsky incident from the upper half space and being reflected at the surface towards the sensor: Tup = (1-rp)T0 +rp Tsky (2) The brightness temperature Tb at satellite level is the attenuated upwelling radiation plus the radiation emitted by the atmosphere in the direction toward the radiometer (atmospheric scattering and atmospheric temperature inhomogeneity being neglected for simplicity): Tb( ) = Tup t + Ta (1-t) (3) where t is the atmospheric transmissivity in the observation direction and Ta is the temperature of the atmosphere. The above equation applies to the polarization and direction corresponding to Tup. In case of an inhomogeneous atmosphere Ta has to be considered as an effective temperature Ta,up for upwelling radiation. For a plane-parallel atmosphere t is given by t(h, ) = exp(h/cos ) (4) where the zenith opacity h is the vertical path integral of the absorption coefficient (z) through the atmosphere, starting at the surface. The reflectivity rp at polarization p = h, v in (2) may be composed of a specular, polarized component rs,p and of a diffuse, unpolarized component rd: d p s p r r r , (5) The following discussion is concentrated on the derivation of expressions for Tup depending on properties of the relief. We will assume that we can approximate the total reflectivity rp by (5), where rs,p is a perfectly specular component and rd is a lambertian component, i.e. due to a perfectly rough surface. In Ulaby et al. (1981, Sec. 4-16.2), ) ( , p s r and rd are expressed by ) , ( p and 0 0 25 . 0 , respectively, where is the observation angle with respect to the surface normal, and p is the state of polarization (p = v, h). According to Ulaby et al. (1981), Tup can be written as s s s s sky sky p s p up d h T h T p r T e h T cos ) , , ( 4 ) , ( ) , ( ) ( ) , ( 0 0 , 0 , (6) where h is the height of the surface above sea level. The integral term in (6) is the diffusely scattered sky radiation, here to be called Td; as a result of Lambert scattering Td depends only on h. We assume that the incident sky radiation is unpolarized. For a plane-parallel atmosphere Tsky depends on s and h, thus the integral in (6) can be solved for s using s s s s d d d sin : 2 / 0 0 0 sin cos ) , ( 2 ) ( s s s s sky d d h T h T . (7) In case of an isothermal atmosphere at temperature Ta with a cosmic background Tc we have a c s sky T e e T h T s h s h ) 1 ( ) , ( cos / cos /