Wide-swath Altimeter Research Articles

Facilitating Inversion of the Error Covariance Models for the Wide-Swath Altimeters

Wide-swath satellite altimeter observations are contaminated by errors caused by the uncertainties in the geometry and orientation of the on-board interferometer. These errors are strongly correlated across the track, while also having similar error structures in the along-track direction. We describe a method for modifying the geometric component of the error covariance matrix which facilitates accuracy in the removal of the respective error modes from the signal and improves computational efficiency of the data assimilation schemes involving wide-swath altimeter observations. The method has been tested using the Surface Water and Ocean Topography simulator. We show substantial computer cost savings in the pseudo-inversion of the respective error covariance matrix. This efficiency improvement comes with a few per cent error in the approximation of the original covariance model simulating uncertainties in the geometry and orientation of the on-board interferometer.

Prospects for future satellite estimation of small-scale variability of ocean surface velocity and vorticity

Prospects for future satellite estimation of small-scale variability of ocean surface velocity and vorticity

Estimation of Rain Rate from Airborne Doppler W-Band Radar in CalWater-2

ABSTRACTThe NOAA W-band radar was deployed on a P-3 aircraft during a study of storm fronts off the U.S. West Coast in 2015 in the second CalWater (CalWater-2) field program. This paper presents an analysis of measured equivalent radar reflectivity factor Zem profiles to estimate the path-averaged precipitation rate and profiles of precipitation microphysics. Several approaches are explored using information derived from attenuation of Zem as a result of absorption and scattering by raindrops. The first approach uses the observed decrease of Zem with range below the aircraft to estimate column mean precipitation rates. A hybrid approach that combines Zem in light rain and attenuation in stronger rain performed best. The second approach estimates path-integrated attenuation (PIA) via the difference in measured and calculated normalized radar cross sections (NRCSm and NRCSc, respectively) retrieved from the ocean surface. The retrieved rain rates are compared to estimates from two other systems on the P-3: a Stepped Frequency Microwave Radiometer (SFMR) and a Wide-Swath Radar Altimeter (WSRA). The W-band radar gives reasonable values for rain rates in the range 0–10 mm h−1 with an uncertainty on the order of 1 mm h−1. Mean profiles of Zem, raindrop Doppler velocity, attenuation, and precipitation rate in bins of rain rate are also computed. A method for correcting measured profiles of Zem for attenuation to estimate profiles of nonattenuated profiles of Ze is examined. Good results are obtained by referencing the surface boundary condition to the NRCS values of PIA. Limitations of the methods are discussed.

Low-Mode Internal Tide Propagation in a Turbulent Eddy Field

AbstractUnderstanding and predicting how internal tides distort and lose coherence as they propagate through the ocean has been identified as a key issue for interpreting data from the upcoming wide-swath altimeter mission Surface Water and Ocean Topography (SWOT). This study addresses the issue through the analysis of numerical experiments where a low-mode internal tide propagates through a quasigeostrophic turbulent jet. Equations of motion linearized around the slower turbulent field are projected onto vertical modes and assumed to describe the dynamics of the low-mode internal tide propagation. Diagnostics of the terms responsible for the interaction between the wave and the slow circulation are computed from the numerical outputs. The large-scale change of stratification, on top of eddies and jet meanders, contributes significantly to these interaction terms, which is shown to be consistent with an independent scaling analysis. The sensitivity of interaction terms to a degradation of the slow field spatial and temporal resolution indicates that present-day observing systems (Argo network, altimetry) may lack the spatial resolution necessary to correctly predict internal tide evolution. The upcoming SWOT satellite mission may improve upon this situation. The number of vertical modes required to properly estimate interaction terms is discussed. These results advocate development of a simplified model based on solving a modest number of the linearized equations subject to a prescribed mesoscale field and internal tide sources.

Nonstationary Internal Tides Observed Using Dual-Satellite Altimetry

AbstractDual-satellite crossover data from the Jason-2 and Cryosat-2 altimeter missions are used in a novel approach to quantify stationary and nonstationary tides from time-lagged mean square sea surface height (SSH) differences, computed for lags from 1 to 1440 h (60 days). The approach is made feasible by removing independent estimates of the stationary tide and mesoscale SSH variance, which greatly reduces the sampling error of the SSH statistics. For the semidiurnal tidal band, the stationary tidal variance is approximately 0.73 cm2, and the nonstationary variance is about 0.33 cm2, or 30% of the total. The temporal correlation of the nonstationary tide is examined by complex demodulation and found to be oscillatory with first 0 crossing at 400 h (17 days). Because a significant fraction of the time-variable mesoscale signal is resolved at time scales of roughly 150 h by the present constellation of satellite altimeters, the results suggest that it may be feasible to predict the nonstationary tide from modulations of the resolved mesoscale, thus enhancing the efficacy of tidal corrections for planned wide-swath altimeters such as the Surface Water and Ocean Topography (SWOT) mission.

Airborne Rain-Rate Measurement with a Wide-Swath Radar Altimeter

Abstract The NOAA Wide-Swath Radar Altimeter (WSRA) uses 80 narrow beams spread over ±30° in the cross-track direction to generate raster lines of sea surface topography at a 10-Hz rate from which sea surface directional wave spectra are produced. A ±14° subset of the backscattered power data associated with the topography measurements is used to produce independent measurements of rain rate and sea surface mean square slope at 10-s intervals. Theoretical calculations of rain attenuation at the WSRA 16.15-GHz operating frequency using measured drop size distributions for both mostly convective and mostly stratiform rainfall demonstrate that the WSRA absorption technique for rain determination is relatively insensitive to both ambient temperature and the characteristics of the drop size distribution, in contrast to reflectivity techniques. The variation of the sea surface radar reflectivity in the vicinity of a hurricane is reviewed. Fluctuations in the sea surface scattering characteristics caused by changes in wind speed or the rain impinging on the surface cannot contaminate the rain measurement because they are calibrated out using the WSRA measurement of mean square slope. WSRA rain measurements from a NOAA WP-3D hurricane research aircraft off the North Carolina coast in Hurricane Irene on 26 August 2011 are compared with those from the stepped frequency microwave radiometer (SFMR) on the aircraft and the Next Generation Weather Radar (NEXRAD) National Mosaic and Multi-Sensor Quantitative Precipitation Estimation (QPE) system.

On Eddy Viscosity, Energy Cascades, and the Horizontal Resolution of Gridded Satellite Altimeter Products*

Abstract Motivated by the recent interest in ocean energetics, the widespread use of horizontal eddy viscosity in models, and the promise of high horizontal resolution data from the planned wide-swath satellite altimeter, this paper explores the impacts of horizontal eddy viscosity and horizontal grid resolution on geostrophic turbulence, with a particular focus on spectral kinetic energy fluxes Π(K) computed in the isotropic wavenumber (K) domain. The paper utilizes idealized two-layer quasigeostrophic (QG) models, realistic high-resolution ocean general circulation models, and present-generation gridded satellite altimeter data. Adding horizontal eddy viscosity to the QG model results in a forward cascade at smaller scales, in apparent agreement with results from present-generation altimetry. Eddy viscosity is taken to roughly represent coupling of mesoscale eddies to internal waves or to submesoscale eddies. Filtering the output of either the QG or realistic models before computing Π(K) also greatly increases the forward cascade. Such filtering mimics the smoothing inherent in the construction of present-generation gridded altimeter data. It is therefore difficult to say whether the forward cascades seen in present-generation altimeter data are due to real physics (represented here by eddy viscosity) or to insufficient horizontal resolution. The inverse cascade at larger scales remains in the models even after filtering, suggesting that its existence in the models and in altimeter data is robust. However, the magnitude of the inverse cascade is affected by filtering, suggesting that the wide-swath altimeter will allow a more accurate determination of the inverse cascade at larger scales as well as providing important constraints on smaller-scale dynamics.

Assimilation of virtual wide swath altimetry to improve Arctic river modeling

Global surface water variations are still difficult to monitor with current satellite measurements. The future Surface Water and Ocean Topography (SWOT) mission is designed to address this issue. Its main payload will be a wide swath altimeter which will provide maps of water surface elevations between 78°S and 78°N over a 120 km swath. This study aims to combine coupled hydrologic/hydraulic modeling of an Arctic river with virtual SWOT observations using a local ensemble Kalman smoother to characterize river water depth variations. We assumed that modeling errors are only due to uncertainties in atmospheric forcing fields (precipitation and air temperature) and different SWOT orbits were tested. First, we tested orbits that all have a three day repeat period but differ in terms of their spatial coverage of the study reach; these orbits correspond to the first three months of the mission, which will be dedicated to calibration and validation experiments. For these orbits, the mean spatial Root Mean Square Error (RMSE) in modeled channel water depth decreased by between 29% and 79% compared to the modeled RMSE with no assimilation, depending on the spatial coverage. The corresponding mean temporal RMSE decrease was between 54% and 91%. We then tested the nominal orbit with a twenty two day repeat period which will be used during the remaining lifetime of the mission. Unlike the three day repeat orbits, this orbit will observe all continental surfaces (except Antartica and the northern part of Greenland) during one repeat period. The assimilation of SWOT observations computed with this nominal orbit into the hydraulic model leads to a decrease of 59% and 66% in the mean spatial and temporal RMSE in modeled channel water depth, respectively. These results show the huge potential of the future SWOT mission for land surface hydrology, especially at high latitudes which will be very well sampled during one orbit repeat period. Still, further work is needed to reduce current modeling uncertainties and to better characterize SWOT measurement errors.

Measuring Storm Surge with an Airborne Wide-Swath Radar Altimeter

Abstract Over the years, hurricane track forecasts and storm surge models, as well the digital terrain and bathymetry data they depend on, have improved significantly. Strides have also been made in the knowledge of the detailed variation of the surface wind field driving the surge. The area of least improvement has been in obtaining data on the temporal/spatial evolution of the mound of water that the hurricane wind and waves push against the shore to evaluate the performance of the numerical models. Tide gauges in the vicinity of the landfall are frequently destroyed by the surge. Survey crews dispatched after the event provide no temporal information and only indirect indications of the maximum water level over land. The landfall of Hurricane Bonnie on 26 August 1998, with a surge less than 2 m, provided an excellent opportunity to demonstrate the potential benefits of direct airborne measurement of the temporal/spatial evolution of the water level over a large area. Despite a 160-m variation in aircraft altitude, an 11.5-m variation in the elevation of the mean sea surface relative to the ellipsoid over the flight track, and the tidal variation over the 5-h data acquisition interval, a survey-quality global positioning system (GPS) aircraft trajectory allowed the NASA scanning radar altimeter carried by a NOAA hurricane research aircraft to demonstrate that an airborne wide-swath radar altimeter could produce targeted measurements of storm surge that would provide an absolute standard for assessing the accuracy of numerical storm surge models.

Integrating Biogeochemistry and Ecology Into Ocean Data Assimilation Systems

Monitoring and predicting the biogeochemical state of the ocean and marine ecosystems is an important application of operational oceanography that needs to be expanded. The accurate depiction of the ocean's physical environment enabled by Global Ocean Data Assimilation Experiment (GODAE) systems, in both real-time and reanalysis modes, is already valuable for various for various applications, such as the fishing industry and fisheries management. However, most of these applications require accurate estimates of both physical and biogeochemical ocean conditions over a wide range of spatial and temporal scales. In this paper, we discuss recent developments that enable coupling new biogeochemical models and assimilation components with the existing GODAE systems, and we examine the potential of such systems in several areas of interest: phytoplankton biomass monitoring in the open ocean, ocean carbon cycle monitoring and assessment, marine ecosystem management at seasonal and longer time scales, and downscaling in coastal areas. A number of key requirements and research priorities are then identified for the future, GODAE systems will need to improve their representation of physical variables that are not yet considered essential, such as upper-ocean vertical fluxes that are critically important to biological activity. Further, the observing systems will need to be expanded in terms of in situ platforms (with intensified deployments of sensors for O-2 and chlorophyll, and inclusion of new sensors for nutrients, zooplankton, micronekton biomass, and others), satellite missions (e.g., hyperspectral instruments for ocean color, lidar systems for mixed-layer depths, and wide-swath altimeters for coastal sea level), and improved methods to assimilate these new measurements.

Contribution of a Wide-Swath Altimeter in a Shelf Seas Assimilation System: Impact of the Satellite Roll Errors

Abstract The authors investigate the potential qualitative improvement brought by wide-swath, interferometry-based ocean altimetry measurements with respect to classical nadir altimeters in a coastal/shelf data assimilation system. In addition, particular attention is paid to roll errors, which could significantly reduce the expected benefits of wide-swath altimetry. A barotropic, nonlinear free-surface model is set up over the European shelf as part of an ensemble Kalman filter. Experiments assimilating simulated data are performed over the North Sea to test the ability of altimeter configurations to reduce model errors due to the action of meteorological forcing in the presence of bathymetric uncertainties. A simplified wide-swath observation scheme is used, composed of nadir altimeter height plus a nadir-centered cross-track sea level slope measurement. The simplified wide-swath measurements are found to be able to constrain events unsampled by a single nadir altimeter owing to a wider domain of influence in the cross-track direction and the ability to detect cross-track gradients. Since the satellite-borne interferometer is highly sensitive to the platform behavior, especially satellite roll, experiments taking roll errors into account are then carried out. Whereas observational errors are considered independent in most data assimilation studies, the roll of the platform correlates those errors along the path of the satellite. Despite the large amplitude of the roll errors, the contribution of the wide-swath altimeter in coastal zones remains valuable as long as the roll frequency is known (within Gaussian error) and the assimilation scheme is designed to take observational error correlations into account.

Assessment of observational networks with the Representer Matrix Spectra method—application to a 3D coastal model of the Bay of Biscay

The development of coastal ocean modeling in the recent years has allowed an improved representation of the associated complex physics. Such models have become more realistic, to the point that they can now be used to design observation networks in coastal areas, with the idea that a “good” network is a network that controls model state error. To test this ability without performing data assimilation, we set up a technique called Representer Matrix Spectra (RMS) technique that combines the model state and observation error covariance matrices into a single scaled representer matrix. Examination of the spectrum and the eigenvectors of that matrix informs us on which model state error modes a network can detect and constrain amidst the observation error background. We applied our technique to a 3D coastal model in the Bay of Biscay, with a focus on mesoscale activity, and tested the performance of various altimetry networks and an in situ array deployment strategy. It appears that a single nadir altimeter is not efficient enough at capturing coastal mesoscale physics, while a wide swath altimeter would do a much better job. Testing various local in situ array configurations confirms that adding a current meter to a vertical temperature measurement array improves the detection of secondary variability modes, while shifting the array higher on the shelf break would obviously enhance the model constraint along the coast. The RMS technique is easily set up and used as a “black box,” but the utility of its results is maximized by previous knowledge of model state error physics. The technique provides both quantitative (eigenvalues) and qualitative (eigenvectors) tools to study and compare various network options. The qualitative approach is essential to discard possibly inconsistent modes.

Prospects for river discharge and depth estimation through assimilation of swath‐altimetry into a raster‐based hydrodynamics model

Surface water elevation profiles for a reach of the Ohio River were produced by the Jet Propulsion Laboratory Instrument Simulator to represent satellite measurements representative of those that would be observed by a wide swath altimeter being considered jointly by U.S. and European space agencies. The Ensemble Kalman filter with a river hydrodynamics model as its dynamical core was used to assimilate the water elevation synthetic observations, and to estimate river discharge. The filter was able to recover water depth and discharge, reducing the discharge RMSE from 23.2% to 10.0% over an 84‐day simulation period, relative to a simulation without assimilation. An autoregressive error model was instrumental in correcting boundary inflows, and increasing the persistence of error reductions between times of observations. The nominal 8‐day satellite overpass produced discharge relative errors of 10.0%, while 16‐day and 32‐day overpass frequencies resulted in errors of 12.1% and 16.9% respectively.

Sampling the mesoscale ocean surface currents with various satellite altimeter configurations

Ten-day composites of maximum cross-correlation (MCC) ocean surface current vectors from 1-km spatial resolution Advanced Very High Resolution Radiometer (AVHRR) 11-/spl mu/m thermal infrared images are used to simulate the ocean surface current retrieval capabilities of three satellite altimeter configurations over a large California coastal region. Ground track positions of the nadir sampling TOPEX/Poseidon (TP; now the Jason-1) satellite altimeters are used to compute the cross-track velocity components from the corresponding optimally interpolated MCC vectors for a ten-day period. Next, the Jason-1-only and the TP plus Jason-1 "tandem mission" sampling are simulated as well as the combination of all available satellite altimeters including European Remote Sensing Satellite 2 and Geosat Follow-On. Finally, we simulate surface current retrievals from the proposed Wide Swath Ocean Altimeter (WSOA), which will have both along- and cross-track velocity components over a spatial swath. Comparisons of vector current fields, their differences, and wavenumber spectra from optimally interpolated maps of the "simulated altimetry velocities" with the corresponding MCC field indicates that (1) the combined coverage from Jason-1 plus TP as well as the combination of all available satellite altimeters results in a better representation of the currents than that of Jason-1 alone and (2) the retrieved currents from the WSOA provide an even greater improvement over the tandem mapping and multiple satellites. It will be possible in the future to regularly map the mesoscale surface currents of the ocean with wide-swath ocean altimeters.