Parameter estimation for peaky altimetric waveforms

Much attention has been recently devoted to the analysis of coastal altimetric waveforms. When approaching the coast, altimetric waveforms are sometimes corrupted by peaks caused by high reflective areas inside the illuminated land surfaces or by the modification of the sea state close to the shoreline. This paper introduces a new parametric model for these peaky altimetric waveforms. This model assumes that the received altimetric waveform is the sum of a Brown echo and an asymmetric Gaussian peak. The asymmetric Gaussian peak is parameterized by a location, an amplitude, a width, and an asymmetry coefficient. A maximum-likelihood estimator is studied to estimate the Brown plus peak model parameters. The Cramér–Rao lower bounds of the model parameters are then derived providing minimum variances for any unbiased estimator, i.e., a reference in terms of estimation error. The performance of the proposed model and the resulting estimation strategy are evaluated via many simulations conducted on synthetic and real data. Results obtained in this paper show that the proposed model can be used to retrack efficiently standard oceanic Brown echoes as well as coastal echoes corrupted by symmetric or asymmetric Gaussian peaks. Thus, the Brown with Gaussian peak model is useful for analyzing altimetric easurements closer to the coast

EUMETSAT Invitation To Tender 14/209556: JASON-CS SAR Mode Sea State Bias Study. Final report

This document represents the final report of a study funded by EUMETSAT about SAR mode Sea State Bias (SSB) for the Sentinel-6/Jason-CS mission. The study comprises a critical review of SSB estimation methods in conventional (low-resolution mode or LRM) altimetry, theoretical considerations about the effect of swell on SAR altimeter waveforms and empirical investigations with Cryosat-2 SAR mode data to detect swell effects in L1B and Level 2 Sea Surface Height (SSH). The report concludes by summarising the basis for the selection and derivation of the SAR altimeter sea state bias correction algorithm and the methods available to calibrate and validate SAR mode SSB corrections. Theoretical considerations based on simple SAR waveform modelling indicate that multipeaked waveforms could occur in the presence of swell, but that effects become clearly detectable only when swell height exceeds 4 meters, which is relatively rare. In the case of the Cryosat-2 data examined in this study, only 2% of samples satisfied this condition. Experimental investigations of Cryosat-2 SAR mode data in different swell conditions produce no consolidated evidence of swell effects. Although anomalous 20Hz waveforms are occasionally observed, no statistically detectable effect of swell is obtained in the overall results for average L1B waveform shapes and L2 1Hz SSH biases and precisions. However, it is stressed that analyses in this study were limited geographically by the availability of Cryosat-2 SAR mode acquisitions over the ocean that could be collocated with Envisat ASAR swell data. It is strongly advised that analyses should be repeated with a broader geographical scope, including data from the central Pacific and the Southern Ocean where high sea state and swell conditions are more prevalent. It is suggested that this could be achieved using Sentinel-3 SRTM and Sentinel-1 L2 swell products, should such data be available. Empirical SSB estimation methods offer the only viable way forward at present to estimate SAR mode SSB. Parametric, non-parametric and hybrid methods are all relevant, noting that hybrid methods may provide more robust estimates in those high sea state and swell conditions that are less densely populated and where effects will be more significant. The development of SAR mode SSB corrections should include additional dependence on sea state development, which would be consistent with the tendency in LRM towards three-parameters SSB models (e.g. Tran et al., 2010b; Pires et al., 2016). The challenges of calibrating and validating SAR mode SSB corrections are the same - i.e. no better, no worse - than for conventional altimetry. For SAR mode altimetry however, P-LRM offer a unique way of calibrating and validating SAR mode SSB against conventional altimetry by providing coincident range measurements that have been shown to be unbiased against conventional LRM. In the case of Sentinel-6/Jason-CS, interleaved SAR mode will deliver true LRM data that make it possible to tie the Jason-CS SAR mode mission to the long-term altimetric data record without the issues linked to the loss of precision seen for SAR burstmode P-LRM

Numerical computation of the electromagnetic bias in GNSS-R altimetry

In radar altimetry, the electromagnetic (EM) bias is originated by the smaller reflectivity of wave crests than troughs; thus, the average sea surface height is underestimated. Bias uncertainty is currently the largest factor in altimetry error budgets. The EM bias in a bistatic forward-scattering configuration at L-band, such as in Global Navigation Satellite Systems Reflectometry (GNSS-R) altimetry, remains one of the major sources of uncertainty in the altimetry error budget. In this paper, the EM bias is computed using numerical simulations. To do so, a time-dependent synthetic non-Gaussian sea surface is created using the Pierson-Moskowitz and Elfouhaily sea surface height spectra and spreading function. The sea surface is then discretized in facets andPeer ReviewedPostprint (author's final draft

Analysis of satellite altimeter signal characteristics and investigation of sea-truth data requirements

Results are presented of analysis of satellite signal characteristics as influenced by ocean surface roughness and an investigation of sea truth data requirements. The first subject treated is that of postflight waveform reconstruction for the Skylab S-193 radar altimeter. Sea state estimation accuracies are derived based on analytical and hybrid computer simulation techniques. An analysis of near-normal incidence, microwave backscattering from the ocean's surface is accomplished in order to obtain the minimum sea truth data necessary for good agreement between theoretical and experimental scattering results. Sea state bias is examined from the point of view of designing an experiment which will lead to a resolution of the problem. A discussion is given of some deficiencies which were found in the theory underlying the Stilwell technique for spectral measurements

Analytical Modeling and Performance Assessment of Micropulse Photon-counting Lidar System

The melting of polar ice sheets and evidence of global warming continue to remain prominent research interests among scientists. To better understand global volumetric change of ice sheets, NASA intends to launch Ice, Cloud and land Elevation Satellite-2 (ICESat-2) in 2017. ICESat-2 employs a high frequency photon-counting laser altimeter, which will provide significantly greater spatial sampling. However, the combined effects of sub-beam complex surfaces, as well as system effects on returning photon distribution have not been systematically studied. To better understand the effects of various system attributes and to help improve the theory behind lidar sensing of complex surfaces, an analytical model using a first principles 3-D Monte Carlo approach is developed to predict system performance. Based on the latest ICESat-2 design, this analytical model simulates photons which propagate from the laser transmitter to the scene, and reflected to the detector model. A radiometric model is also applied in the synthetic scene. Such an approach allows the study of surface elevation retrieval accuracy for landscapes, as well as surface reflectivities. It was found that ICESat-2 will have a higher precision on a smoother surface, and a surface with smaller diffuse albedo will on average result in smaller bias. Furthermore, an adaptive density-based algorithm is developed to detect the surface returns without any geometrical knowledge. This proposed approach is implemented using the aforementioned simulated data set, as well as airborne laser altimeter measurement. Qualitative and quantitative results are presented to show that smaller laser footprint, smoother surface, and lower noise rate will improve accuracy of ground height estimation. Meanwhile, reasonable detection accuracy can also be achieved in estimating both ground and canopy returns for data generated using Digital Imaging and Remote Sensing Image Generation (DIRSIG) model. This proposed approach was found to be generally applicable for surface and canopy finding from photon-counting laser altimeter data

Contributions to the determination of electromagnetic bias in Gnss-R altimetry

In this Ph. D. dissertation the electromagnetic bias in GNSS-R (Global Navigation Satellite Systems Reflectometry) altimetry has been studied. GNSS-R altimetry is a new type of system that uses navigation signals as signals of opportunity for Earth observation. The electromagnetic bias has been a topic of research for several decades in conventional radar altimetry, typically at C and Ku bands, and pointing in the nadir direction, but it is a new subject in altimetry GNSS-R. Previous studies on the electromagnetic bias have been first reviewed: the Weakly Non-Linear theory (WNL), the Modulation Transfer Function (MTF), and a combination of both models. After a brief study of both the WNL and the MTF, a combined method is selected, simulated and validated at Ku and C bands, and then extrapolated at L band, the band of the GNSS signals. Then, the EM bias is studied in the time domain and it is characterized using statistical descriptors. Finally, the impact of natural phenomena such as rain, waves and currents in the electromagnetic bias is calculated. In conclusion, this dissertation has demonstrated that the electromagnetic bias is not only a function of the wind speed (or waves), but also a function of both the incidence and azimuth angles. The study in the time domain has been shown that it exhibits a non-linear behavior. Moreover, heavy rains decrease the electromagnetic bias, as they damp the waves, while sea currents in the opposite direction of the wind speed increase the electromagnetic bias, because they increase the surface "roughness", while currents with the same direction of the wind, reduce itEn esta tesis doctoral se estudia el sesgo electromagnético en altimetría GNSS-R (Global Navigation Satellite Systems Reflectometry). La altimetría GNSS-R es un nuevo tipo de sistema que utiliza las señales de navegación como señales de oportunidad para la observación de la tierra. El sesgo electromagnético ha sido un tema de investigación durante varias décadas en altimetría radar convencional utilizando típicamente las bandas C y Ku, y apuntando en la dirección nadir, pero es un tema novedoso en altimetría GNSS-R. En primer lugar se revisan los estudios previos sobre el sesgo electromagnético: la Weakly Non-Linear theory (WNL), la Modulation Transfer Function (MTF), y modelos combinados de ambos. Después de un breve estudio tanto de la WNL como de la MTF, se selecciona un modelo combinado, se simula, y valida en las bandas C y Ku, y luego es extrapolado a la banda L, la banda de las señales de los GNSS. En segundo lugar, se estudia el sesgo electromagnético en el dominio del tiempo y es caracterizado utilizando descriptores estadísticos. Por último, se calcula el impacto de los fenómenos naturales como la lluvia, el oleaje y las corrientes en el sesgo electromagnético . En conclusión, esta tesis doctoral ha demostrado que el sesgo electromagnético no es sólo una función de la velocidad del viento (o del oleaje), sino que también es una función tanto del ángulo de incidencia, como del ángulo de acimut. El estudio en el dominio del tiempo ha demostrado que tiene un comportamiento no lineal. Por otra parte, las fuertes lluvias disminuyen el sesgo electromagnético, pues amortiguan las olas, mientras que las corrientes con dirección opuesta al viento aumentan el sesgo electromagnético, pues aumentan la "rugosidad" superficial, mientras que la corriente tiene la misma dirección de la velocidad del viento, lo reduce

A study of the capabilities of the geodetic satellite altimeter to measure ocean-surface characteristics Final engineering report

Signal processing techniques applicable to geodetic satellite altimeter progra

MARA (Multimode Airborne Radar Altimeter) system documentation. Volume 1: MARA system requirements document

The Multimode Airborne Radar Altimeter (MARA), a flexible airborne radar remote sensing facility developed by NASA's Goddard Space Flight Center, is discussed. This volume describes the scientific justification for the development of the instrument and the translation of these scientific requirements into instrument design goals. Values for key instrument parameters are derived to accommodate these goals, and simulations and analytical models are used to estimate the developed system's performance

An Improved Cryosat-2 Sea Ice Freeboard Retrieval Algorithm Through the Use of Waveform Fitting

We develop an empirical model capable of simulating the mean echo power cross product of CryoSat-2 SAR and SAR In mode waveforms over sea ice covered regions. The model simulations are used to show the importance of variations in the radar backscatter coefficient with incidence angle and surface roughness for the retrieval of surfaceelevation of both sea ice floes and leads. The numerical model is used to fit CryoSat-2 waveforms to enable retrieval of surface elevation through the use of look-up tables and a bounded trust region Newton least squares fitting approach. The use of a model to fit returns from sea ice regions offers advantages over currently used threshold retrackingmethods which are here shown to be sensitive to the combined effect of bandwidth limited range resolution and surface roughness variations. Laxon et al. (2013) have compared ice thickness results from CryoSat-2 and IceBridge, and found good agreement, however consistent assumptions about the snow depth and density of sea ice werenot used in the comparisons. To address this issue, we directly compare ice freeboard and thickness retrievals from the waveform fitting and threshold tracker methods of CryoSat-2 to Operation IceBridge data using a consistent set of parameterizations. For three IceBridge campaign periods from March 20112013, mean differences (CryoSat-2 IceBridge) of 0.144m and 1.351m are respectively found between the freeboard and thickness retrievals using a 50 sea ice floe threshold retracker, while mean differences of 0.019m and 0.182m are found when using the waveform fitting method. This suggests the waveform fitting technique is capable of better reconciling the seaice thickness data record from laser and radar altimetry data sets through the usage of consistent physical assumptions