Precise inland surface altimetry (PISA) with nadir specular echoes from Sentinel-3: Algorithm and performance assessment

Abstract In the recent years satellite radar altimetry has evolved from pulse-limited low resolution mode (LRM) to a synthetic aperture radar (SAR) high resolution mode. The SAR mode focusses and coherently sums all radar return echoes within the 2-s time window the target surface area is in the antenna beam. In principle the SAR processing improves along-track resolution. Land contamination has been a major concern for inland waters altimetry and SAR can reduce land interference. This paper shows that the physics of specular echoes from smooth inland waters leads to a very different approach which we call precise inland surface altimetry (PISA). PISA uses only echoes within the specular "flash" period, which is approximately the time the satellite nadir crosses over the water body. The processing is four orders of magnitude less than SAR. Land interference is negligible because specular water echoes are usually >50 dB greater than land. Sentinel-3 SRAL dataset on the salar de Uyuni (Bolivia) is used to evaluate PISA ranging precision. During inundation (wet months), echoes are at the theoretical maximum radar cross section (RCS), σ = 129 dBsm, and ranging precision is ~1 mm. In dry months the echoes are quasi-specular, with σ = 70–100 dBsm, and ranging precision is ~1 cm. The precision assessment is made with variate-differences, with pass-to-pass repeatability, and by comparison with GPS measurements. In addition to the salar de Uyuni analysis we gathered σ statistics on five millions Sentinel-3 SRAL Ku-band altimeter bursts (one burst = 64 contiguous echoes) from 52 passes of Sentinel-3A track 167 over South America. We illustrate specular and quasi-specular waters on lakes, a river, and a fjord. Ranging precision is similar to Uyuni, in the 1 mm-1 cm range. Water surface slopes of 1–3 cm/km are detected. We propose a simple rule-set to distinguish specular waveforms (σ >100 dBsm, sidelobes (with Hamming window) of −37 dB or lower) and quasi-specular (σ >70 dBsm, sidelobes lower than −20 dB), and non-specular (sidelobes> − 20 dB). PISA is appropriate to specular and quasi-specular echoes

Monads and Quantitative Equational Theories for Nondeterminism and Probability

The monad of convex sets of probability distributions is a well-known tool for modelling the combination of nondeterministic and probabilistic computational effects. In this work we lift this monad from the category of sets to the category of extended metric spaces, by means of the Hausdorff and Kantorovich metric liftings. Our main result is the presentation of this lifted monad in terms of the quantitative equational theory of convex semilattices, using the framework of quantitative algebras recently introduced by Mardare, Panangaden and Plotkin

Environmental bisimulations for probabilistic higher-order languages

Environmental bisimulations for probabilistic higher-order languages are studied. In contrastwith applicative bisimulations, environmental bisimulations are known to be more robust and do not require sophisticated techniques such as Howe's in the proofs of congruence. As representative calculi, call-by-name and call-by-value λ-calculus, and a (call-by-value) λ-calculus extended with references (i.e., a store) are considered. In each case, full abstraction results are derived for probabilistic environmental similarity and bisimilarity with respect to contextual preorder and contextual equivalence, respectively. Some possible enhancements of the (bi)simulations, as "up-to techniques," are also presented. Probabilities force a number of modifications to the definition of environmental bisimulations in nonprobabilistic languages. Some of thesemodifications are specific to probabilities, others may be seen as general refinements of environmental bisimulations, applicable also to non-probabilistic languages. Several examples are presented, to illustrate the modifications and the differences

A Comparison between Coastal Altimetry Data and Tidal Gauge Measurements in the Gulf of Genoa (NW Mediterranean Sea)

Satellite altimetry data from X-TRACK products were analyzed for an overall assessment of their capability to detect coastal sea level variability in the Ligurian Sea. Near-coastal altimetry data, collected from 2009 to 2016 along track n.044, were compared with simultaneous high frequency sampled data at the tidal station in Genoa (NW Mediterranean Sea). The two time series show a very good agreement: correlation between total sea level elevation from the altimeter and sea level variation from the tidal gauge is 0.92 and root mean square difference is 4.5 cm. Some relevant mismatches can be ascribed to the local high frequency coastal variability due to shelf and harbor oscillation detected at the tidal station, which might not be observed at the location of the altimetry points of measurement. The analysis evidences discrepancies (root mean square difference of 4.7 cm) between model results for open sea tides and harmonic analysis at the tidal station, mainly occurring at the annual and semiannual period. On the contrary, the important part of dynamic atmospheric correction due to the inverse barometer effect, well agrees with that computed at the tidal station

Up-To Techniques for Generalized Bisimulation Metrics

Bisimulation metrics allow us to compute distances between the behaviors of probabilistic systems. In this paper we present enhancements of the proof method based on bisimulation metrics, by extending the theory of up-to techniques to (pre)metrics on discrete probabilistic concurrent processes. Up-to techniques have proved to be a powerful proof method for showing that two systems are bisimilar, since they make it possible to build (and thereby check) smaller relations in bisimulation proofs. We define soundness conditions for up-to techniques on metrics, and study compatibility properties that allow us to safely compose up-to techniques with each other. As an example, we derive the soundness of the up-to-bisimilarity-metric-and-context technique. The study is carried out for a generalized version of the bisimulation metrics, in which the Kantorovich lifting is parametrized with respect to a distance function. The standard bisimulation metrics, as well as metrics aimed at capturing multiplicative properties such as differential privacy, are specific instances of this general definition

The Theory of Traces for Systems with Nondeterminism, Probability, and Termination

This paper studies trace-based equivalences for systems combining nondeterministic and probabilistic choices. We show how trace semantics for such processes can be recovered by instantiating a coalgebraic construction known as the generalised powerset construction. We characterise and compare the resulting semantics to known definitions of trace equivalences appearing in the literature. Most of our results are based on the exciting interplay between monads and their presentations via algebraic theories.Comment: This paper is an extended version of a LICS 2019 paper "The Theory of Traces for Systems with Nondeterminism and Probability". It contains all the proofs, additional explanations, material, and example

The theory of traces for systems with nondeterminism and probability

This paper studies trace-based equivalences for systems combining nondeterministic and probabilistic choices. We show how trace semantics for such processes can be recovered by instantiating a coalgebraic construction known as the generalised powerset construction. We characterise and compare the resulting semantics to known definitions of trace equivalences appearing in the literature. Most of our results are based on the exciting interplay between monads and their presentations via algebraic theories

Universal Quantitative Algebra for Fuzzy Relations and Generalised Metric Spaces

We present a generalisation of the theory of quantitative algebras of Mardare, Panangaden and Plotkin where (i) the carriers of quantitative algebras are not restricted to be metric spaces and can be arbitrary fuzzy relations or generalised metric spaces, and (ii) the interpretations of the algebraic operations are not required to be nonexpansive. Our main results include: a novel sound and complete proof system, the proof that free quantitative algebras always exist, the proof of strict monadicity of the induced Free-Forgetful adjunction, the result that all monads (on fuzzy relations) that lift finitary monads (on sets) admit a quantitative equational presentation.Comment: Appendix remove

Modeling Envisat RA-2 waveforms in the coastal zone: case-study of calm water contamination

Radar altimeters have so far had limited use in the coastal zone, the area with most societal impact. This is due to both lack of, or insufficient accuracy in the necessary corrections, and more complicated altimeter signals. This paper examines waveform data from the Envisat RA-2 as it passes regularly over Pianosa (a 10 km2 island in the NW Mediterranean). Forty-six repeat passes were analysed, with most showing a reduction in signal upon passing over the island, with weak early returns corresponding to the reflections from land. Intriguingly one third of cases showed an anomalously bright hyperbolic feature. This feature may be due to extremely calm waters in the Golfo della Botte (northern side of the island), but the cause of its intermittency is not clear. The modelling of waveforms in such a complex land/sea environment demonstrates the potential for sea surface height retrievals much closer to the coast than is achieved by routine processing. The long-term development of altimetric records in the coastal zone will not only improve the calibration of altimetric data with coastal tide gauges, but also greatly enhance the study of storm surges and other coastal phenomena

Tutti più smart? Il fenomeno del potenziamento cognitivo nella società contemporanea

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