Cinzia Zuffada

2‐cm GPS altimetry over Crater Lake

Dierences in electromagnetic path delay, be- tween direct Global Positioning System (GPS) signals and those reflected from the surface of Crater Lake, have led to lake surface height estimates with 2-cm precision in 1 sec- ond. This is the rst high-precision altimetric demonstra- tion with GPS from sucient altitude (480 m) to probe fundamental experimental errors, which bear on future air- and spaceborne passive GPS altimetry. It also serves as the rst demonstration of a new approach to altimetric remote sensing in the coastal region, an area that is poorly mea- sured by conventional radar altimetry. Time-series analy- sessuggest thattroposphericandthermalnoisefluctuations dominate the altimetric error in this experiment. Estimat- ing the dierential delay from several simultaneously visi- ble satellites may enable tropospheric error estimation and correction. Thermal noise on the reflected signal will be reduced with fully polarimetric observations and larger an- tenna apertures.

A novel approach to atmospheric profiling with a mountain‐based or airborne GPS receiver

The delay induced by the Earths atmosphere on the Global Positioning System (GPS) signal has been exploited in the last decade for atmospheric remote sensing. Ground-based GPS measurements are traditionally used to derive columnar water vapor content, while space-based GPS measurements, obtained by a receiver in a low-Earth orbit tracking GPS satellites occulting behind the Earths atmosphere, yield accurate, high-resolution profiles of refractivity, temperature, and water vapor. A GPS receiver on a mountain top or an airplane with a “downward looking” field of view toward the Earths limb is a novel concept presented here. We describe a generalized ray-tracing inversion scheme where spherical symmetry is assumed for the atmosphere, and the refractivity is modeled as piecewise exponential, with scale height changing from one atmospheric layer to the next. Additional refractivity data, derived from a model, might be introduced above the receiver as an a priori constraint, and are treated as properly weighted additional measurements. The exponential scale heights and a normalizing value of refractivity are retrieved by minimizing, in a least squares sense, the residuals between measured bending angles and refractivity and those calculated on the basis of the exponential model and ray-tracing. As a first validation step, we illustrate results comparing refractivity and temperature profiles obtained by this generalized ray-tracing scheme against those derived via the Abel inversion for the GPS/MET experiment. Additionally, we present results for a hypothetical situation where the receiver is located within the atmosphere at a height of 5 km. For the last case we investigate the accuracy of the retrieval both below and above the receiver at a set of locations in the atmosphere ranging from middle to tropical latitudes. The main objective is that of establishing whether the bending measurements have sufficient strength to allow for retrieval of refractivity below and possibly above the receiver location. Our findings suggest that accurate profiles of refractivity at heights ranging from the Earths surface to slighly above the receiver location can be derived by GPS data collected from within the atmosphere.

GEROS-ISS: GNSS REflectometry, Radio Occultation, and Scatterometry Onboard the International Space Station

GEROS-ISS stands for GNSS REflectometry, radio occultation, and scatterometry onboard the International Space Station (ISS). It is a scientific experiment, successfully proposed to the European Space Agency in 2011. The experiment as the name indicates will be conducted on the ISS. The main focus of GEROS-ISS is the dedicated use of signals from the currently available Global Navigation Satellite Systems (GNSS) in L-band for remote sensing of the Earth with a focus to study climate change. Prime mission objectives are the determination of the altimetric sea surface height of the oceans and of the ocean surface mean square slope, which is related to sea roughness and wind speed. These geophysical parameters are derived using reflected GNSS signals (GNSS reflectometry, GNSS-R). Secondary mission goals include atmosphere/ionosphere sounding using refracted GNSS signals (radio occultation, GNSS-RO) and remote sensing of land surfaces using GNSS-R. The GEROS-ISS mission objectives and its design, the current status, and ongoing activities are reviewed and selected scientific and technical results of the GEROS-ISS preparation phase are described.

Incoherent bistatic scattering from the sea surface at L-band

A bistatic electromagnetic wave scattering model for the sea surface is developed to examine its wind dependence property over a wide range of incident angles along the specular direction. This is done by combining an existing scattering model with a sea spectrum recently reported in the literature. In general, electromagnetic wave scattering from a rough surface is dependent on the Fourier transform of the nth power of its height correlation function which can be computed numerically from the surface spectrum. This transform relation indicates that scattering is sensitive not only to the surface spectrum but also to its convoluted properties. Generally, surface scattering is sensitive only to a portion of the surface correlation measured from the origin. The size of this portion is a function of three variables (the incident angle, the surface height standard deviation, and the exploring wavelength) and the rate of decay of the correlation function. The decay rate near the origin of the sea surface correlation is very small, so much so that at L-band this portion is too wide for a two-term approximation of the correlation function. This is true in spite of the fact that the sea surface has a very large rms height. Thus, a scattering model based on geometric optics is generally not applicable at L-band especially at large angles of incidence. An additional finding is that in specular scattering wind dependence is stronger at larger angles of incidence for incident angles between 0 and 70/spl deg/ over the wind speed range of 4 m/s-20 m/s.

Demonstrating soil moisture remote sensing with observations from the UK TechDemoSat-1 satellite mission

The ability of spaceborne Global Navigation Satellite System (GNSS) bistatic radar receivers to sense changes in soil moisture is investigated using observations from the low Earth orbiting UK TechDemoSat-1 satellite (TDS-1). Previous studies using receivers on aircraft or towers have shown that ground-reflected GNSS signals are sensitive to changes in soil moisture, though the ability to sense this variable from space has yet to be quantified. Data from TDS-1 show a 7 dB sensitivity of reflected signals to temporal changes in soil moisture. If the effects of surface roughness and vegetation on the reflected signals can be quantified, spaceborne GNSS bistatic radar receivers could provide soil moisture on relatively small spatial and temporal scales.

Synthesis of novel all-dielectric grating filters using genetic algorithms

The feasibility of novel all-dielectric waveguide grating filters is demonstrated, using a genetic algorithm (GA) to solve for material dielectric constants and geometric boundaries separating homogeneous regions of the periodic cell. In particular, the GAs show that simple geometries (not previously reported) utilizing a small number of layers and/or gratings can be found to yield bandpass or stop-band filters with user defined linewidth. The evaluation of the fitness of a candidate design entails the solution of an integral equation for the electric field in the cell using the method of moments (MoM). Our implementation is made efficient by using only very few design frequency points and accurately approximating a given filter transfer function by a quotient of polynomials as a function of frequency. Additionally, the problem impedance matrices are conveniently represented as the product of a material independent matrix and a vector of dielectric constants, thus allowing us to fill the matrices only once. Our code has been parallelized for the Cray T3D to take advantage of the intrinsic parallelization efficiencies offered by the GAs. Solutions are illustrated for a very narrow-band single-grating transmission filter and a relatively broad-band double grating reflection filter. Additionally, a solution for a five homogeneous layers Fabry-Perot filter is also presented.

Modeling three-dimensional scatterers using a coupled finite element-integral equation formulation

Finite-element modeling has proven useful for accurately simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength. To practically compute a solution to exterior problems, the domain must be truncated at some finite surface where the Sommerfeld radiation condition is enforced, either approximately or exactly. This paper outlines a method that couples three-dimensional finite-element solutions interior to a bounding surface with an efficient integral equation solution that exactly enforces the Sommerfeld radiation condition. The general formulation and the main features of the discretized problem are first briefly outlined. Results for far and near fields are presented for geometries where an analytic solution exists and compared with exact solutions to establish the accuracy of the model. Results are also presented for objects that do not allow an analytic solution, and are compared with other calculations and/or measurements.

First Spaceborne Observation of Sea Surface Height Using GPS‐Reflectometry

An analysis of spaceborne Global Positioning System reflectometry (GPS-R) data from the TechDemoSat-1 (TDS-1) satellite is carried out to image the ocean sea surface height (SSH). An SSH estimation algorithm is applied to GPS-R delay waveforms over two regions in the South Atlantic and the North Pacific. Estimates made from TDS-1 overpasses during a 6 month period are aggregated to produce SSH maps of the two regions. The maps generally agree with the global DTU10 mean sea surface height. The GPS-R instrument is designed to make bistatic measurements of radar cross section for ocean wind observations, and its altimetric performance is not optimized. The differences observed between measured and DTU10 SSH can be attributed to limitations with the GPS-R instrument and the lack of precision orbit determination by the TDS-1 platform. These results represent the first observations of SSH by a spaceborne GPS-R instrument.

Polarization properties of the GPS signal scattered off a wind-driven ocean

A Global Positioning System (GPS) transmitter-receiver pair form a bistatic radar for ocean remote sensing when the receiving platform carries a downlooking antenna capable of collecting the GPS signal scattered off the ocean surface. The aggregate GPS signal scattered by the ocean and received in a general bistatic configuration has been calculated for representative geometries and a variety of wind speeds and directions, using the integral equation method (IEM) combined with a realistic ocean correlation function (spectrum). The role of polarization of the reflected signal is investigated and its dependence on wind speed and direction is analyzed to assess its suitability as a detector of the wind vector. The complexity of the scattering calculations is handled by an efficient integration scheme based on combining Gaussian quadrature with a local interpolation of the surface correlation function. Additionally, since a large number of scattering contributions are required the code has been parallelized for efficiency. Some relevant features of the parallelization scheme are outlined.

Coherence time and statistical properties of the GPS signal scattered off the ocean surface and their impact on the accuracy of remote sensing of sea surface topography and winds

A GPS transmitter-receiver pair forms a bistatic radar for ocean remote sensing when the receiving platform carries a down-looking antenna capable of collecting the GPS signal scattered off the ocean surface. The average received power versus time is derived as a function of viewing geometry, system parameters and ocean state. This waveform is crucial for the derivation of the sea surface topography (from its leading edge) or wind speed and direction (from its trailing edge). In predicting the accuracy of either measurement it is important to understand how accurately the average power can be determined in practical situations. This starts with the determination of the coherence time of the scattering, over which the received signal can be integrated for optimal signal to noise ratio. Additionally, the real signal is affected by self-noise which introduces variability from one sample to another. This work examines the coherence properties of the modeled received power as a function of sea state and scattering geometry. In particular the coherence time variability between leading and trailing edges is addressed, and its impact on the accuracy of either sea surface topography or wind speed and direction measurements is addressed. In particular, having determined the integration time necessary to produce independent samples, the incoherent summation time required for a given measurement accuracy is derived. Furthermore, the lag-to-lag correlation is addressed, leading to a covariance analysis formulation for the formal error in height retrieval.