Advances in extracting current profiles from X-band radar images with a focus on retrieving subsurface current

This paper addresses key problems regarding the focusing of synthetic aperture radar (SAR) images of ocean surface waves, explaining why applying a processor defocus will generally yield an enhanced image, why the same defocus applies to both image modulations brought about by the radar cross section and by the velocity bunching process, and why the effects apply to both single-look and multilook systems independently of look relocation. Two interpretations are given for the case when surface scatterers are stationary, but modulated in reflectivity (radar cross section) by a propagating wavefield. The first interpretation is what will be called a degrade-and-shift model. In it, a processor focusing adjustment degrades a point image. However, the overall image can be enhanced because an appropriate defocus results in a shifting of points in such a way that the image can most closely resemble the image of the time-invariant (or frozen) reflectivity. The second interpretation is a defocus-and-refocus model in which the image of a time-varying reflectivity is defocused and may be refocused to enhance the image. In justifying this defocus-and-refocus model, it is shown that the radar return from stationary scatterers of time-varying reflectivities is identical to that from physically moving scatterers of constant reflectivity. Thus, the two interpretations are not contradictory; they are, fundamentally, equivalent. The models support the use of a processor defocus corresponding to one half the wave phase velocity. Both qualitative and quantitative illustrations of the effects are given. Finally, it is shown that the same defocusing effect applies to image modulations brought about by the velocity bunching process. >

Present models explaining radar imaging of ocean surface waves have considered variations in radar cross section of the tilted or roughened surface and velocity bunching effects caused by the doppler shifts of moving scatterers. It is pointed out here that simple “layover” effects will cause an additional, significant modulation of the image brightness that increases the visibility of range‐traveling waves.

[1] We have collected time series data of short oceanic waves as a part of the International Polar Year (IPY) 2007–2008. Using a shipboard laser wave slope (LAWAS) system operating at 900 nm, we have obtained wave slopes measurements up to 60 rad m−1 wave number. We have compared our in situ wave slopes with collocated and concurrent high-resolution upwind Normalized Radar Cross Sections (NRCS) collected by QuikSCAT. The LAWAS measured wave slope spectra were consistent with local wind speeds and QuikSCAT measured NRCS. Our measured short wave mean slopes indicate their enhancement by long waves (0–1 rad m−1) at small values of long-wave slope. Concurrent with wave slope measurements, the strength of the reflected LAWAS light beam was analyzed in terms of the light attenuation coefficient at 900 nm. We have observed a correlation between surface elevation and light attenuation. The mechanism of wave modulated beam attenuation was found to be related to the instantaneous long wave skewness.

This paper investigates the radar imaging of ocean waves under two separate wind speed and sea state conditions using an X band real aperture radar (RAR). It is shown experimentally that for the case of higher sea state and wind speed (9.1 m/s), the RAR is capable of imaging the waves from all directions including the azimuth. The case for low sea state and wind speed (4.5 m/s), however, shows somewhat stronger imaging contrast in the range direction with reduced contrast for the azimuth‐traveling waves. The results of the aircraft observations are compared with numerical simulations of a RAR imaging model. Simulations show that cross tilt is a viable mechanism for enhancing the azimuthal modulations, but the results are sensitive to the level of upwind/cross‐wind anisotropy of the shortwave spectrum. Simulations also show that the variations in incidence angle create irregularities in the azimuthal angle distribution.

Abstract. The paper deals with the feasibility study of the sea state monitoring starting from X-band radar images. The exploitation of radar images allows to achieve a global vision of the sea state compared to the local vision given by the usual sensors as the buoys. The processing approach is based on the formulation of problem as an inverse one where starting from the electromagnetic field backscattered by the sea surface, the information about the sea state are retrieved. The reliability of the inversion procedure is shown by processing synthetic and experimental data where particular attention is focussed to the determination of the sea current and speed of the vessel.

Synthetic aperture radar images of ocean waves were obtained in conjunction with reference wave data near Marineland, Florida, December 14, 1975. Each of the various types of measurements were processed into a form that allowed direct comparisons with the others. Maxima of radar spectra occurred at the same frequencies as the maxima of reference wave height spectra. In a comparison of a radar spectrum with observed spectra of wave height, wave orbital velocity, and surface slope the high‐frequency portion of the radar spectrum lay near and between the wave height and the orbital velocity spectra but differed significantly from the surface slope spectrum. The radar‐derived mean directions and model‐fitted directional spreads of wave energy were close to the values from a directional wave buoy and indicated the accuracy of radar measurements of wave direction. However, a directional plot of a radar spectrum near shore at the frequency of the maximum showed a sharper peak than such a plot of a fitted spectrum derived from reference data. The high directional resolution of the radar, in addition to its making observations at different locations, allowed radar images to provide information about ocean waves not available from the other instruments. As a swell propagated across the continental shelf, it was scattered in direction, apparently by the irregularities of the bottom, and very little of its energy reached shore. The shorter sea waves had a narrow directional distribution when first observed offshore that may have been sharpened by interaction with the Gulf Stream. Radar images showed effects of bottom refraction on the sea waves as they moved into progressively shallower water.

The wind shear stress at the ocean surface drives momentum exchange across the air-sea interface regulating atmospheric and oceanic phenomena. Theoretically, the mean wind stress acts in a reference frame moving with the ocean surface; however, the relative motion between the air and ocean surface layers is conventionally neglected in bulk transfer formulae. Recent developments improving air-sea momentum flux quantification advocate for explicitly defining the air-sea relative wind, especially in the regime of low wind forcing, where surface currents may approach a significant fraction of the total wind speed. Yet, in practice, this new approach is typically applied using opportunistic definitions of the near-surface current. Here, we build on this recent work and propose a general framework for the bulk air-sea momentum flux that directly accounts for vertical current shear and surface waves in quantifying the stress at the interface. Our approach partitions the stress at the interface into viscous skin and (wave) form drag components, each applied to their relevant surface advections, which are quantified using the inertial motions within the sub-surface log layer and the modulation of waves by currents predicted by linear theory, respectively. The efficacy of this approach is demonstrated using an extensive oceanic dataset from the Coastal Endurance Array (Ocean Observatories Initiative) offshore of Newport, Oregon (2017–2023) that includes co-located measurements of direct covariance wind stress, directional wave spectra, and current profiles. As expected, our framework does not alter the overall dependence of momentum flux on mean wind forcing, and we found the largest impacts at relatively low wind speeds. Below 3 m s $$^{-1}$$ , accounting for sub-surface shear reduced form drag variation by 40–50% as compared to a current-agnostic approach; as compared to a shear-free current, i.e., slab ocean, a 35% reduction in form drag variation was found. At this wind forcing, neglecting the currents led to systematically overestimating the form stress by 20 to 50%—an effect that could not be captured by using the slab ocean approach. This framework builds on the existing understanding of wind-wave-current interaction, yielding a novel formulation that explicitly accounts for the role of current shear and surface waves in air-sea momentum flux. This work holds significant implications for air-sea coupled modeling in general conditions.

In this chapter, indexes of the Intra-Americas or Caribbean Low-Level Jet (IALLJ or CLLJ, respectively), Nino 3, Tropical North Atlantic (NATL), Atlantic Multidecadal Oscillation (AMO), and Outgoing Long Wave Radiation (OLR) are quantified for the period 1950–2007, to study their relationship with tropical cyclone (TC) frequency for summer–autumn of the Northern Hemisphere. A remarkable inverse relationship is found between both, the strength of the wind speed at 925 hPa and the vertical wind shear at low levels, and the monthly relative frequency of TCs for two selected areas in the Caribbean. The July peak in wind speed and low-level vertical wind shear are associated with a minimum in the monthly relative frequency of TCs. On the contrary, a decrease in the wind speed and vertical shears are associated with a maximum value of the relative frequency of TCs. Stronger (weaker) than normal IALLJ summer winds (July–August) during warm (cold) ENSO events imply a stronger (weaker) than normal vertical wind shear at low-levels in the Caribbean. This condition may inhibit (allow) deep convection, disfavoring (favoring) TC development during these months. Correlation values of the monthly mean CLLJ core winds and the monthly normalized values of NATL – Nino 3 index for 1950–2007 showed statistical significance greater than 99% during July–August. During El Nino years, low-level wind increases at the jet core strengthening the low level convergence near Central America at the jet exit and the low-level divergence in the central Caribbean at the jet entrance. The descending motion associated with the latter acts as an inhibiting factor for convection and TC development. TC activity in the Caribbean is not only sensitive to ENSO influences, but to the strength of the CLLJ vertical wind shear, to barotropic energy conversions induced by the lateral wind shear, to the intensity of the regional scale descending motion associated with the jet entrance, and to the SST cooling generated by the CLLJ at the sea surface. Climatology of a group of General Circulation Models used in the 2007 report of the IPCC were tested to study their ability to capture the low-level wind annual cycle over the Caribbean and the known CLLJ structure. Some models do not capture basic characteristics of the jet. A discussion of cyclone potential over the Caribbean, based on the relationships developed using the models climatology, is presented for the period 2010–2050. As a study case, the findings were contrasted with the observed 2008 climate over the IAS region. Rainy season for 2008 in Central America evolved in a way consistent with the presence of La Nina event and the meridional migration of the ITCZ. Wind anomalies associated with the IALLJ were larger (smaller) than normal during February (July) 2008, in agreement with earlier findings in regards to the relationship of the IALLJ and ENSO phases. The year of 2008 was very active for tropical storm formation in the Caribbean basin (10–22. 5∘N, 60–82. 5∘W). From 16 named storms observed in the Atlantic, 10 entered the Caribbean basin. Eight (five) Atlantic cyclones were hurricanes (strong hurricanes) and from the five hurricanes crossing the Caribbean basin, four were strong.

A new method to determine near‐surface vertical current shear from noncoherent marine X‐band radar (MR) data is introduced. A three‐dimensional fast Fourier transform is employed to obtain the wave number‐frequency spectrum of a MR image sequence. Near‐surface currents are estimated from the Doppler‐shifted surface gravity wave signal within the spectrum. They represent a weighted mean of the upper ocean flow. The longer the ocean waves on which the current estimates are based, the greater their effective depth. The novelty lies in the wave number‐dependent retrieval method, yielding ∼100 independent current estimates at effective depths from ∼2 to 8 m per ∼12 min measurement period. First, MR near‐surface vertical current shear measurements are presented using data collected from R/V Roger Revelle during the 2010 Impact of Typhoons on the Ocean in the Pacific experiment in the Philippine Sea. Shipboard acoustic Doppler current profiler (ADCP) and anemometer measurements as well as WAVEWATCH III (WW3) model results are used to demonstrate that results are in accord with physical expectations. The wind and wave‐driven Ekman flow is obtained by subtracting ADCP‐based background currents from the radar measurements. At ∼2 m, it is on average ∼1.6% of the wind speed and ∼38.9° to the right of the wind. With increasing effective depth, the speed factor decreases and the deflection angle increases. Based on WW3 results, the MR‐sensed Stokes drift speed is ∼50% of the Ekman flow at ∼2 m and ∼25% at ∼8 m. These findings are consistent with previous observations and Ekman theory.

Application research of wind profile radar in short-term heavy rainfall forecast of typhoon in Fujian Province

Enhanced Ocean Scatterometry

During the third intensive observational period of the Surface Wave Dynamics Experiment (SWADE), an aircraft-based experiment was conducted on 5 March 1991 by deploying slow-fall airborne expendable current profilers (AXCPs) and airborne expendable bathythermographs (AXBTs) during a scanning radar altimeter (SRA) flight on the NASA NP-3A research aircraft. As the Gulf Stream (GS) moved into the SWADE domain in late February, maximum upper-layer currents of 1.98 m/s were observed in the core of the baroclinic jet where the vertical current shears were O(10(exp -2)/s). The SRA concurrently measured the sea surface topography, which was transformed into two-dimensional directional wave spectra at 5-6-km intervals along the flight tracks. The wave spectra indicated a local wave field with wavelengths of 40-60 m propagating southward between 120 deg and 180 deg, and a northward-moving swell field from 300 deg to 70 deg associated with significant wave heights of 2-4 m. As the AXCP descended through the upper ocean, the profiler sensed orbital velocity amplitudes of 0.2-0.5 m/s due to low-frequency surface waves. These orbital velocities were isolated by fitting the observed current profiles to the three-layer model based on a monochromatic surface wave, including the steady and current shear terms within each layer. The depth-integrated differences between the observed and modeled velocity profiles were typically less than 3 cm/s. For 17 of the 21 AXCP drop sites, the rms orbital velocity amplitudes, estimated by integrating the wave spectra over direction and frequency, were correlated at a level of 0.61 with those derived from the current profiles. The direction of wave propagation inferred from the AXCP-derived orbital velocities was in the same direction observed by the SRA. These mean wave directions were highly correlated (0.87) and differed only by about 5 deg.

Directional wave spectra and integrated wave parameters can be derived from X-band radar sea surface images. A vessel on the sea surface has a significant influence on wave parameter inversions that can be seen as intensive backscatter speckles in X-band wave monitoring radar sea surface images. A novel algorithm to eliminate the interference of vessels in ocean wave height inversions from X-band wave monitoring radar is proposed. This algorithm is based on the characteristics of the interference. The principal components (PCs) of a sea surface image sequence are extracted using empirical orthogonal function (EOF) analysis. The standard deviation of the PCs is then used to identify vessel interference within the image sequence. To mitigate the interference, a suppression method based on a frequency domain geometric model is applied. The algorithm framework has been applied to OSMAR-X, a wave monitoring system developed by Wuhan University, based on nautical X-band radar. Several sea surface images captured on vessels by OSMAR-X are processed using the method proposed in this paper. Inversion schemes are validated by comparisons with data from in situ wave buoys. The root-mean-square error between the significant wave heights (SWH) retrieved from original interference radar images and those measured by the buoy is reduced by 0.25 m. The determinations of surface gravity wave parameters, in particular SWH, confirm the applicability of the proposed method.

A Navier-Stokes solver in OpenFOAM® is combined with the Volume of Fluid (VOF) surface capturing method to investigate the wave interaction with depth-varying currents in intermediate and shallow waters. A special attention is paid to the separate effect of vertical current shear on near resonant triad wave interactions. It was found that in the presence of following vertical current shear, the wave exhibits a sharper crest and flatter trough, and the opposite is true in the presence of opposing vertical current shear. Our model results indicate that the wave steepness at which the current shear starts to affect the crest elevation is greater in deeper water than in shallower water. We found that adding vertical current shear to the uniform current further enhances the relative harmonic wave energy and the extent of triad interaction in the following current while weakens them in the opposing current. As a result, following and opposing current shear may cause wave to break at a lower and higher sea state respectively. Due to the increased wave nonlinearity in the presence of a following current shear, a linear superposition of the individual wave and current velocities is no longer adequate to represent the total horizontal velocity close to the free surface.

A new method for retrieving wind direction from X-band marine radar images is presented in this letter. The new algorithm investigates radar backscatter in the wavenumber domain and obtains wind direction from the wavenumber spectrum. Different from previous algorithms that detect rain-contaminated images and discard them, the new algorithm could be applied to both rain-contaminated and rain-free images. For rain-contaminated images collected under low wind speeds (i.e., less than 8 m/s), wind directions were retrieved based on spectral components with wavenumbers of [0.01, 0.2]. For rain-contaminated images obtained under high wind speeds and rain-free images, wind directions were retrieved from the spectrum with values at zero wavenumber. The algorithm has been tested using X-band radar images and shipborne anemometer data collected on the east coast of Canada. Comparison with the anemometer data shows that the root-mean-square error of wind directions retrieved from rain-contaminated images collected under low wind speeds is reduced by 25.1°.