Generalization of the Van Cittert--Zernike theorem: observers moving with respect to sources

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 forma

Contribution of satellite observations to continental hydrology

Depuis plusieurs décennies, un nombre croissant de satellites observe la variabilité spatio-temporelle de plusieurs compartiments des eaux continentales (eaux libres, manteau neigeux, humidité du sol...). Ces observations ont permis de mieux comprendre les échanges d'eau au sein des bassins fluviaux et le couplage avec l'atmosphère et les océans. Elles ont aussi contribué à améliorer les prévisions d'inondation, la prévention de risques naturels et le suivi de l'évolution géomorphologique des zones en eau. Les futures missions spatiales, en améliorant la précision et la récurrence des mesures, deviendront un outil incontournable pour gérer les ressources en eau.Over the last decades, an increasing number of satellite missions has helped to observe the spatial and temporal variabilities of continental waters (surface water, surface snow, soil moisture, etc.). These observations helped to better understand water fluxes within river basins and their coupling with the atmosphere and oceans. They also contributed to improve flood forecasting, prevent natural hazards and track geomorphological changes in water bodies. Future satellite missions, with improved measurement accuracy and temporal sampling, will become essential tools for water resources management

Optical fibre coupling devices

This thesis deals with optical coupling systems and is divided in two parts. The first one is concerned with directional coupling between two graded index fibres made by a diffusion process. The theory and physics of ion exchange is studied, providing a theoretical description of the refractive index change. A mathematical method of solving the concentration dependent diffusion equation is given. Theoretical index distributions are thus obtained for circular waveguides. To compare theory with experiment, a device directly measuring the index profile of a circular fibre is described. The theory of propagation in round graded index fibres, is reviewed and a simplified coupling coefficient derived in order to determine the coupling efficiency. The coupling arrangement is described and the results discussed. It is shown that efficient tapping of power can be done with the high order modes, and eventually, at a much lower efficiency with the low order ones. The second part describes a theoretical study of optical contradirectional coupling between a single mode sandwich ribbon fibre and a thin film planar waveguide, longitudinal phase matching being achieved by means of a periodic corrugation, which is typically a grating etched into the film. Film-fibre couplers were tested and achieved an estimated efficiency of only due to the poor quality of the gratings. With several improvements in the set-up and specimens, an efficiency of over 60 is quite feasible. The application of the method for linking integrated optical devices is considered as well as a possible demultiplexer. The study presented provides the ground work for future development of integrated optical devices links and an active device

До питання про співвідношення праворозуміння та правової думки

У статті проаналізовано структуру праворозуміння, дано визначення поняття правова думка та вказано, що праворозуміння, як осмислення правової дійсності є складовою частиною правової думки.В статье проанализировано структуру правопонимания, дано определение понятия правовая мысль иопределено, что правопонимание как осмысление правовой действительности является составляющей правовой мысли.In the article are analyzed the structure of legal understanding, given the definition of legal thought and determined that the legal comprehension as a legal interpretation of reality is a part of legal thought

L-MEB: A simple model at L-band for the continental areas - Application to the simulation of a half-degree resolution and global scale data set.

L-band (1-2 GHz) microwave radiometry is the most relevant remote sensing technique to monitor soil moisture over land surfaces at the global scale. A synthetic multi-angular brightness temperature data set over land surfaces was simulated at 1.4 GHz, at a half-degree resolution and at the global scale (Pellarin et al., 2003a). This data set was built in order to develop and validate methods to retrieve soil moisture for near-future 1.4 GHz space missions. Brightness temperatures were computed using a simple model (L-MEB, L-band Microwave Emission of the Biosphere) based on radiative transfer equations. The L-MEB model is the result of an extensive review of the current knowledge of the microwave emission of various land covers (herbaceous and woody vegetation, frozen and unfrozen bare soil, snow, etc.) at L-Band considering that the model should be simple enough to be compatible with the simulation of a half-degree resolution and global scale data set. This model was parameterized for simulating L-band observations (in the 1-2 GHz range) but the model equations remain valid in a low frequency range (about 1 to 10 GHz) and thus including the L-, C- and X-bands. The soil and vegetation characteristics needed to initialize the L-MEB model were derived from existing land cover maps. Continuous simulations from a land-surface scheme for 1987 and 1988 provided time series of the main variables driving the L-MEB model: soil temperature at the surface and at depth, surface soil moisture, proportion of frozen surface soil moisture, and snow cover characteristics (depth, density, grain size, liquid water content). The different components of the emission model are described in the following sections. These sections present the general formulation of TB for a composite pixel and the microwave emission modules for soil, vegetation-covered surfaces, open water, snow-covered surfaces and atmospheric effects

Integration of SMAP and SMOS Observations

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

Integrated SMAP and SMOS Soil Moisture Observations

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

SMOS L1C and L2 Validation in Australia

Extensive airborne field campaigns (Australian Airborne Cal/val Experiments for SMOS - AACES) were undertaken during the 2010 summer and winter seasons of the southern hemisphere. The purpose of those campaigns was the validation of the Level 1c (brightness temperature) and Level 2 (soil moisture) products of the ESA-led Soil Moisture and Ocean Salinity (SMOS) mission. As SMOS is the first satellite to globally map L-band (1.4GHz) emissions from the Earth?s surface, and the first 2-dimensional interferometric microwave radiometer used for Earth observation, large scale and long-term validation campaigns have been conducted world-wide, of which AACES is the most extensive. AACES combined large scale medium-resolution airborne L-band and spectral observations, along with high-resolution in-situ measurements of soil moisture across a 50,000km2 area of the Murrumbidgee River catchment, located in south-eastern Australia. This paper presents a qualitative assessment of the SMOS brightness temperature and soil moisture products

Toward vicarious calibration of microwave remote-sensing satellites in arid environments

The Soil Moisture and Ocean Salinity (SMOS) satellite marks the commencement of dedicated global surface soil moisture missions, and the first mission to make passive microwave observations at L-band. On-orbit calibration is an essential part of the instrument calibration strategy, but on-board beam-filling targets are not practical for such large apertures. Therefore, areas to serve as vicarious calibration targets need to be identified. Such sites can only be identified through field experiments including both in situ and airborne measurements. For this purpose, two field experiments were performed in central Australia. Three areas are studied as follows: 1) Lake Eyre, a typically dry salt lake; 2) Wirrangula Hill, with sparse vegetation and a dense cover of surface rock; and 3) Simpson Desert, characterized by dry sand dunes. Of those sites, only Wirrangula Hill and the Simpson Desert are found to be potentially suitable targets, as they have a spatial variation in brightness temperatures of <4 K under normal conditions. However, some limitations are observed for the Simpson Desert, where a bias of 15 K in vertical and 20 K in horizontal polarization exists between model predictions and observations, suggesting a lack of understanding of the underlying physics in this environment. Subsequent comparison with model predictions indicates a SMOS bias of 5 K in vertical and 11 K in horizontal polarization, and an unbiased root mean square difference of 10 K in both polarizations for Wirrangula Hill. Most importantly, the SMOS observations show that the brightness temperature evolution is dominated by regular seasonal patterns and that precipitation events have only little impact

SMOS/SMAP Synergy for SMAP Level 2 Soil Moisture Algorithm Evaluation

Soil Moisture Active Passive (SMAP) satellite has been proposed to provide global measurements of soil moisture and land freeze/thaw state at 10 km and 3 km resolutions, respectively. SMAP would also provide a radiometer-only soil moisture product at 40-km spatial resolution. This product and the supporting brightness temperature observations are common to both SMAP and European Space Agency's Soil Moisture and Ocean Salinity (SMOS) mission. As a result, there are opportunities for synergies between the two missions. These include exploiting the data for calibration and validation and establishing longer term L-band brightness temperature and derived soil moisture products. In this investigation we will be using SMOS brightness temperature, ancillary data, and soil moisture products to develop and evaluate a candidate SMAP L2 passive soil moisture retrieval algorithm. This work will begin with evaluations based on the SMOS product grids and ancillary data sets and transition to those that will be used by SMAP. An important step in this analysis is reprocessing the multiple incidence angle observations provided by SMOS to a global brightness temperature product that simulates the constant 40 degree incidence angle observations that SMAP will provide. The reprocessed brightness temperature data provide a basis for evaluating different SMAP algorithm alternatives. Several algorithms are being considered for the SMAP radiometer-only soil moisture retrieval. In this first phase, we utilized only the Single Channel Algorithm (SCA), which is based on the radiative transfer equation and uses the channel that is most sensitive to soil moisture (H-pol). Brightness temperature is corrected sequentially for the effects of temperature, vegetation, roughness (dynamic ancillary data sets) and soil texture (static ancillary data set). European Centre for Medium-Range Weather Forecasts (ECMWF) estimates of soil temperature for the top layer (as provided as part of the SMOS ancillary data) were used to correct for surface temperature effects and to derive microwave emissivity. ECMWF data were also used for precipitation forecasts, presence of snow, and frozen ground. Vegetation options are described below. One year of soil moisture observations from a set of four watersheds in the U.S. were used to evaluate four different retrieval methodologies: (1) SMOS soil moisture estimates (version 400), (2) SeA soil moisture estimates using the SMOS/SMAP data with SMOS estimated vegetation optical depth, which is part of the SMOS level 2 product, (3) SeA soil moisture estimates using the SMOS/SMAP data and the MODIS-based vegetation climatology data, and (4) SeA soil moisture estimates using the SMOS/SMAP data and actual MODIS observations. The use of SMOS real-world global microwave observations and the analyses described here will help in the development and selection of different land surface parameters and ancillary observations needed for the SMAP soil moisture algorithms. These investigations will greatly improve the quality and reliability of this SMAP product at launch