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We investigate to what extent correlating the Fourier components at slightly shifted frequencies of the fluctuations of the electric field measured with a one-dimensional antenna array on board of a satellite flying over a plane, allows one to measure the two-dimensional brilliance temperature as function of position in the plane. We find that the achievable spatial resolution resulting from just two antennas is of the order of $h\chi$, with $\chi=c/(\Delta r \omega_0)$, both in the direction of flight of the satellite and in the direction perpendicular to it, where $\Delta r$ is the distance between the antennas, $\omega_0$ the central frequency, $h$ the height of the satellite over the plane, and $c$ the speed of light. Two antennas separated by a distance of about 100m on a satellite flying with a speed of a few km/s at a height of the order of 1000km and a central frequency of order GHz allow therefore the imaging of the brilliance temperature on the surface of Earth with a resolution of the order of one km. For a single point source, the relative radiometric resolution is of order $\sqrt{\chi}$, but for a uniform temperature field in a half plane left or right of the satellite track it is only of order $1/\chi^{3/2}$, indicating that two antennas do not suffice for a precise reconstruction of the temperature field. Several ideas are discussed how the radiometric resolution could be enhanced. In particular, having $N$ antennas all separated by at least a distance of the order of the wave-length, allows one to increase the signal-to-noise ratio by a factor of order $N$, but requires to average over $N^2$ temperature profiles obtained from as many pairs of antennas., Comment: 39 pages of latex in preprint format, 2 figures

The use of the Van Cittert--Zernike theorem for the formulation of the visibility function in satellite-based Earth observation with passive radiometers does not take into account the relative motion of the observer (the satellite antenna) with respect to sources of the electro-magnetic fields at the surface of the Earth. The motion of the observer leads on the one hand to a more complex signal due to a pixel-dependent Doppler shift that is neglected in the standard derivation of the Van Cittert--Zernike theorem, but on the other hand one may hope that it could be employed for a temporal aperture synthesis, where virtual baselines are created through the motion of the satellite. Here, we generalize the formulation of the aperture synthesis concept to the case of observers moving with respect to the sources, and to the correlation of fields measured at times that differ by the travel time of the observer along a virtual baseline. Our derivation is based on first principles, starting with the wave propagation in the Earth reference frame of electro-magnetic fields arising from incoherent current sources, and Lorentz transforming the fields into the reference frame of the satellite. Our detailed study leads to the remarkable conclusion that the delay time due to observer motion cancels exactly the Doppler effect. This justifies the neglect of the Doppler effect in existing imaging systems based on the standard Van Cittert--Zernike theorem., Comment: 13 pages in IOP MST format

Soil Moisture Active Passive (SMAP) mission and the Soil Moisture and Ocean Salinity (SMOS) missions provide brightness temperature and soil moisture estimates every 2-3 days. SMAP brightness temperature observations were compared with SMOS observations at 40o incidence angle. The brightness temperatures from the two missions are close to each other but SMAP observations show a warmer TB bias (about 0.64 K: V pol and 1.14 K: H pol) as compared to SMOS. SMAP and SMOS missions use different retrieval algorithms and ancillary datasets which result in further inconsistencies between their soil moisture products. The reprocessed constant-angle SMOS brightness temperatures (SMOS-SMAP) were used in the SMAP soil moisture retrieval algorithm to develop a consistent multi-satellite product. The integrated product has an increased global revisit frequency (1 day) and period of record that is unattainable by either one of the satellites alone. The SMOS-SMAP soil moisture retrievals compared with in situ observations show a retrieval accuracy of less than 0.04 m3/m3. Results from the development and validation of the integrated soil moisture product will be presented.

In this paper we review the use of satellite-based remote sensing in combination with in situ data to inform Earth surface modelling. This involves verification and optimization methods that can handle both random and systematic errors and result in effective model improvement for both surface monitoring and prediction applications. The reasons for diverse remote sensing data and products include (i) their complementary areal and temporal coverage, (ii) their diverse and covariant information content, and (iii) their ability to complement in situ observations, which are often sparse and only locally representative. To improve our understanding of the complex behavior of the Earth system at the surface and sub-surface, we need large volumes of data from high-resolution modelling and remote sensing, since the Earth surface exhibits a high degree of heterogeneity and discontinuities in space and time. The spatial and temporal variability of the biosphere, hydrosphere, cryosphere and anthroposphere calls for an increased use of Earth observation (EO) data attaining volumes previously considered prohibitive. We review data availability and discuss recent examples where satellite remote sensing is used to infer observable surface quantities directly or indirectly, with particular emphasis on key parameters necessary for weather and climate prediction. Coordinated high-resolution remote-sensing and modelling/assimilation capabilities for the Earth surface are required to support an international application-focused effort.

Soil Moisture Active Passive (SMAP) mission and the Soil Moisture and Ocean Salinity (SMOS) missions provide brightness temperature and soil moisture estimates every 2-3 days. SMAP brightness temperature observations were compared with SMOS observations at 40o incidence angle. The brightness temperatures from the two missions are not consistent. SMAP observations show a warmer TB bias (about 1.27 K: V pol and 0.62 K: H pol) as compared to SMOS. SMAP and SMOS missions use different retrieval algorithms and ancillary datasets which result in further inconsistencies between their soil moisture products. The reprocessed constant-angle SMOS brightness temperatures were used in the SMAP soil moisture retrieval algorithm to develop a consistent multi-satellite product. The integrated product has an increased global revisit frequency (1 day) and period of record that is unattainable by either one of the satellites alone. Results from the development and validation of the integrated soil moisture product will be presented.