Synthetic aperture radar (SAR) is a coherent active microwave imaging method. In remote sensing it is used for mapping the scattering properties of the Earth's surface in the respective wavelength domain. Many physical and geometric parameters of the imaged scene contribute to the grey value of a SAR image pixel. Scene inversion suffers from this high ambiguity and requires SAR data taken at different wavelength, polarization, time, incidence angle, etc. Interferometric SAR (InSAR) exploits the phase differences of at least two complex-valued SAR images acquired from different orbit positions and/or at different times. The information derived from these interferometric data sets can be used to measure several geophysical quantities, such as topography, deformations (volcanoes, earthquakes, ice fields), glacier flows, ocean currents, vegetation properties, etc. This paper reviews the technology and the signal theoretical aspects of InSAR. Emphasis is given to mathematical imaging models and the statistical properties of the involved quantities. Coherence is shown to be a useful concept for system description and for interferogram quality assessment. As a key step in InSAR signal processing two-dimensional phase unwrapping is discussed in detail. Several interferometric configurations are described and illustrated by real-world examples. A compilation of past, current and future InSAR systems concludes the paper.

https://iopscience.iop.org/article/10.1088/0266-5611/14/4/001/pdf

Synthetic aperture radar interferometry

The air–sea fluxes of momentum, heat, freshwater and their components have been computed globally from 1948 at frequencies ranging from 6-hourly to monthly. All fluxes are computed over the 23 years from 1984 to 2006, but radiation prior to 1984 and precipitation before 1979 are given only as climatological mean annual cycles. The input data are based on NCEP reanalysis only for the near surface vector wind, temperature, specific humidity and density, and on a variety of satellite based radiation, sea surface temperature, sea-ice concentration and precipitation products. Some of these data are adjusted to agree in the mean with a variety of more reliable satellite and in situ measurements, that themselves are either too short a duration, or too regional in coverage. The major adjustments are a general increase in wind speed, decrease in humidity and reduction in tropical solar radiation. The climatological global mean air–sea heat and freshwater fluxes (1984–2006) then become 2 W/m2 and −0.1 mg/m2 per second, respectively, down from 30 W/m2 and 3.4 mg/m2 per second for the unaltered data. However, decadal means vary from 7.3 W/m2 (1977–1986) to −0.3 W/m2 (1997–2006). The spatial distributions of climatological fluxes display all the expected features. A comparison of zonally averaged wind stress components across ocean sub-basins reveals large differences between available products due both to winds and to the stress calculation. Regional comparisons of the heat and freshwater fluxes reveal an alarming range among alternatives; typically 40 W/m2 and 10 mg/m2 per second, respectively. The implied ocean heat transports are within the uncertainty of estimates from ocean observations in both the Atlantic and Indo-Pacific basins. They show about 2.4 PW of tropical heating, of which 80% is transported to the north, mostly in the Atlantic. There is similar good agreement in freshwater transport at many latitudes in both basins, but neither in the South Atlantic, nor at 35°N.

The global climatology of an interannually varying air–sea flux data set

The sections in this article are


1
Radiometers

2
Radar Scattering

3
Radar Scatterometers

4
Radar Altimeters

5
Ground-Penetrating Radars

6
Imaging Radars

7
Real-Aperture Radars

8
Synthetic-Aperture Radars

Microwave Remote Sensing

Review of several recent ocean surface wave models finds that while comprehensive in many regards, these spectral models do not satisfy certain additional, but fundamental, criteria. We propose that these criteria include the ability to properly describe diverse fetch conditions and to provide agreement with in situ observations of Cox and Munk [1954] and Jahne and Riemer [1990] and Hara et al. [1994] data in the high-wavenumber regime. Moreover, we find numerous analytically undesirable aspects such as discontinuities across wavenumber limits, nonphysical tuning or adjustment parameters, and noncentrosymmetric directional spreading functions. This paper describes a two-dimensional wavenumber spectrum valid over all wavenumbers and analytically amenable to usage in electromagnetic models. The two regime model is formulated based on the Joint North Sea Wave Project (JONSWAP) in the long-wave regime and on the work of Phillips [1985] and Kitaigorodskii [1973] at the high wavenumbers. The omnidirectional and wind-dependent spectrum is constructed to agree with past and recent observations including the criteria mentioned above. The key feature of this model is the similarity of description for the high- and low-wavenumber regimes; both forms are posed to stress that the air-sea interaction process of friction between wind and waves (i.e., generalized wave age, u/c) is occurring at all wavelengths simultaneously. This wave age parameterization is the unifying feature of the spectrum. The spectrum's directional spreading function is symmetric about the wind direction and has both wavenumber and wind speed dependence. A ratio method is described that enables comparison of this spreading function with previous noncentrosymmetric forms. Radar data are purposefully excluded from this spectral development. Finally, a test of the spectrum is made by deriving roughness length using the boundary layer model of Kitaigorodskii. Our inference of drag coefficient versus wind speed and wave age shows encouraging agreement with Humidity Exchange Over the Sea (HEXOS) campaign results.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JC00467

A unified directional spectrum for long and short wind-driven waves

1. Introduction 2. Observation techniques 3. Description of ocean waves 4. Statistics 5. Linear wave theory (oceanic waters) 6. Waves in oceanic waters 7. Linear wave theory (coastal waters) 8. Waves in coastal waters 9. The SWAN wave model Appendices References Index.

/pdf/waves-in-oceanic-and-coastal-waters-6ofdu4icqi.pdf

Waves in Oceanic and Coastal Waters

The aerodynamic friction between air and sea is an important part of the momentum balance in the development of tropical cyclones. Measurements of the drag coefficient, relating the tangential stress ( frictional drag) between wind and water to the wind speed and air density, have yielded reliable information in wind speeds less than 20 m/s ( about 39 knots). In these moderate conditions it is generally accepted that the drag coefficient ( or equivalently, the aerodynamic roughness'') increases with the wind speed. Can one merely extrapolate this wind speed tendency to describe the aerodynamic roughness of the ocean in the extreme wind speeds that occur in hurricanes ( wind speeds greater than 30 m/s)? This paper attempts to answer this question, guided by laboratory extreme wind experiments, and concludes that the aerodynamic roughness approaches a limiting value in high winds. A fluid mechanical explanation of this phenomenon is given.

/pdf/on-the-limiting-aerodynamic-roughness-of-the-ocean-in-very-3wpslohza6.pdf

On the limiting aerodynamic roughness of the ocean in very strong winds

Recently published data taken in wind-wave tanks and on the ocean are shown to yield a growth rate, β, describing the transfer of energy and momentum directly from wind to surface waves, that is well described by the relation β = [(0.04±0.02)u*2ω cos θ]/c2 over a wide range of frequencies. Here u* is air friction velocity, ω is radian wave frequency, c is phase speed, and θ is the angle between wind and waves. Using this form and the requirement that the momentum flux from wind to waves not exceed the wind stress, we show that the total mean-square, upwind/downwind wave slope between the frequencies g/2πU10 and 20 Hz must be less than ρa/[ρω(0.04±0.02)], where ρa and ρω are air and water densities, g is gravitational acceleration, and U10 is wind speed at 10 m. Measurements of mean square slope both in wavetanks and on the ocean seem to show agreement with this limitation as long as the air-water interface is well defined. One implication of such a slope limitation is that mean slope spectral densities are limited to values which decrease as the peak frequency of a wind wave spectrum decreases. This may provide an explanation for the observation that mean-square, dominant wave slopes are typically smaller on the ocean than in wavetanks.

A relationship between wind stress and wave slope

This paper reviews basic synthetic aperture radar (SAR) theory of ocean wave imaging mechanisms, using both known work and recent experimental and theoretical results from the Marine Remote Sensing (MARSEN) Experiment. Several viewpoints that have contributed to the field are drawn together in a general analysis of the backscatter statistics of a moving sea surface. A common focus for different scattering models is provided by the mean image impulse response function, which is shown to be identical to the (spatially varying) frequency variance spectrum of the local complex reflectivity coefficient. From the analysis has emerged a more complete view of the SAR imaging phenomenon than has been previously available. A new, generalized imaging model is proposed.

Theory of synthetic aperture radar ocean imaging: A MARSEN view

The principle of conservation of action is applied to derive a spectral form for short, wind-generated waves on the ocean which is valid to second order in the slopes of longer surface waves. Using this form, composite surface theory is applied to microwave backscatter from the ocean surface in the Bragg regime to derive an expression for the normalized radar cross section of the sea, σ0, which is also valid to second order in long-wave slope. This expression is compared with previous data and empirical models of σ0 and is shown to account for the observed incidence angle, azimuth angle, wind speed, and polarization dependence. Comparisons are made at Ku and C band for incidence angles between 20° and 70°. The theory indicates the manner in which atmospheric stability, long-wave spectra, and sea surface temperature may influence σ0. Upwind-downwind asymmetry of σ0 is shown to occur because of the second-order interaction of short-wave modulation with the orbital velocities of long waves. Furthermore, the results suggest that the wind speed dependence of σ0 varies only slightly with microwave frequency, while the magnitude of σ0 increases somewhat with frequency until viscous or turbulent dissipation reduces short-wave growth rates and thus amplitudes. Implications for scatterometer algorithm development are discussed.

A two-scale model of short wind-generated waves and scatterometry

This report describes an experiment to make a completely non-contact open-channel discharge measurement. A van-mounted, pulsed doppler (10GHz) radar collected surface-velocity data across the 183-m wide Skagit River, Washington at a USGS streamgaging station using Bragg scattering from short waves produced by turbulent boils on the surface of the river. Surface velocities were converted to mean velocities for 25 sub-sections by assuming a normal open-channel velocity profile (surface velocity times 0.85). Channel cross-sectional area was measured using a 100 MHz ground-penetrating radar antenna suspended from a cableway car over the river. Seven acoustic doppler current profiler discharge measurements and a conventional current-meter discharge measurement were also made. Three non-contact discharge measurements completed in about a 1-hour period were within 1% of the gaging station rating curve discharge values. With further refinements, it is thought that open-channel flow can be measured reliably by non-contact methods.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999GL006087

William J. Plant

Papers

On the limiting aerodynamic roughness of the ocean in very strong winds

A relationship between wind stress and wave slope

Theory of synthetic aperture radar ocean imaging: A MARSEN view

A two-scale model of short wind-generated waves and scatterometry

measuring stream discharge by non‐contact methods: A Proof‐of‐Concept Experiment