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Ali Tamizi and Ian R. Young

Abstract

The spatial structure of both the wind and wave fields within tropical cyclones is investigated using two large databases. The first of these was compiled from global overpasses of tropical cyclones by satellite altimeters. The second dataset consists of an extensive collection of North American buoy measurements during the passage of tropical cyclones (hurricanes). The combined datasets confirm the vortex structure of the tropical cyclone wind field with the strongest winds to the right (Northern Hemisphere) of the storm. The wave field largely mirrors the wind field but with greater right–left asymmetry that results from the extended fetch to the right of the translating tropical cyclone. The extensive in situ buoy database confirms previous studies indicating that the one-dimensional spectra are generally unimodal. The directional spectra are, however, directionally skewed, consisting of remotely generated waves radiating out from the center of the storm and locally generated wind sea. The one-dimensional wave spectra have many similarities to fetch-limited cases, although for a given peak frequency the spectra contain less energy than for a fetch-limited case. This result is consistent with the fact that much of the wave field is dominated by remotely generated waves.

Free access
Agustinus Ribal and Ian R. Young

Abstract

Global ocean wind speed observed from seven different scatterometers, namely, ERS-1, ERS-2, QuikSCAT, MetOp-A, OceanSat-2, MetOp-B, and Rapid Scatterometer (RapidScat) were calibrated against National Data Buoy Center (NDBC) data to form a consistent long-term database of wind speed and direction. Each scatterometer was calibrated independently against NDBC buoy data and then cross validation between scatterometers was performed. The total duration of all scatterometer data is approximately 27 years, from 1992 until 2018. For calibration purposes, only buoys that are greater than 50 km offshore were used. Moreover, only scatterometer data within 50 km of the buoy and for which the overpass occurred within 30 min of the buoy recording data were considered as a “matchup.” To carry out the calibration, reduced major axis (RMA) regression has been applied where the regression minimizes the size of the triangle formed by the vertical and horizontal offsets of the data point from the regression line and the line itself. Differences between scatterometer and buoy data as a function of time were investigated for long-term stability. In addition, cross validation between scatterometers and independent altimeters was also performed for consistency. The performance of the scatterometers at high wind speeds was examined against buoy and platform measurements using quantile–quantile (Q–Q) plots. Where necessary, corrections were applied to ensure scatterometer data agreed with the in situ wind speed for high wind speeds. The resulting combined dataset is believed to be unique, representing the first long-duration multimission scatterometer dataset consistently calibrated, validated and quality controlled.

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Alicia Takbash and Ian R. Young

Abstract

A novel approach to estimation of extreme value ocean significant wave height is investigated, in which data from adjacent regions are pooled to form a spatial ensemble. The equivalent duration of this ensemble region is the sum of the durations of the data pooled to form the ensemble. To create such a spatial ensemble, data from regions to be pooled must be independent and identically distributed. ERA-Interim reanalysis data are used to investigate the requirement of independent and identically distributed data on a global basis. As a result, typical spatial ensembles are defined for a number of regions of the world and the 100-yr return period significant wave height is calculated for these regions. It is shown that the method can result in a reduction in the confidence interval for such extreme value estimates of between 30% and 60%. The method is demonstrated both with ERA-Interim data and altimeter data.

Open access
Diana J. M. Greenslade and Ian R. Young

Abstract

One of the main limitations to current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. One method that may be used to determine background errors is the “NMC method.” This method examines the forecast divergence component of the background error growth by considering differences between forecasts of different ranges valid at the same time. In this paper, the NMC method is applied to global forecasts of significant wave height (SWH) and surface wind speed (U10).

It is found that the isotropic correlation length scale of the SWH forecast divergence (L SWH) has considerable geographical variability, with the longest scales just to the south of the equator in the eastern Pacific Ocean, and the shortest scales at high latitudes. The isotropic correlation length scale of the U10 forecast divergence (L U10) has a similar distribution with a stronger latitudinal dependence. It is found that both L SWH and L U10 increase as the forecast period increases. The increase in L SWH is partly due to L U10 also increasing. Another explanation is that errors in the analysis or the short-range SWH forecast propagate forward in time and disperse and their scale becomes larger. It is shown that the forecast divergence component of the background error is strongly anisotropic with the longest scales perpendicular to the likely direction of propagation of swell. In addition, in regions where the swell propagation is seasonal, the forecast divergence component of the background error shows a similar strong seasonal signal. It is suggested that the results of this study provide a lower bound to the description of the total background error in global wave models.

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Diana J. M. Greenslade and Ian R. Young

Abstract

One of the main limitations to current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. One method that may be used to determine background errors is the observational method of Hollingsworth and Lönnberg. The observational method considers correlations of the differences between observations and the background. For the case of significant wave height (SWH), potential observations come from satellite altimeters. In this work, the effect of the irregular sampling pattern of the satellite on estimates of background errors is examined. This is achieved by using anomalies from a 3-month mean as a proxy for model errors. A set of anomaly correlations is constructed from modeled wave fields. The isotropic length scales of the anomaly correlations are found to vary considerably over the globe. In addition, the anomaly correlations are found to be significantly anisotropic. The modeled wave fields are then sampled at simulated altimeter observation locations, and the anomaly correlations are recalculated from the simulated altimeter data. The results are compared to the original anomaly correlations. It is found that, in general, the simulated altimeter data can capture most of the geographic and seasonal variability in the isotropic anomaly correlation length scale. The best estimates of the isotropic length scales come from a method in which correlations are calculated between pairs of observations from prior and subsequent ground tracks, in addition to along-track pairs of observations. This method was found to underestimate the isotropic anomaly correlation length scale by approximately 10%. The simulated altimeter data were not so successful in producing realistic anisotropic correlation functions. This is because of the lack of information in the zonal direction in the simulated altimeter data. However, examination of correlations along ascending and descending ground tracks separately can provide some indication of the areas on the globe for which the anomaly correlations are more anisotropic than others.

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Alicia Takbash, Ian R. Young, and Øyvind Breivik

Abstract

The application of extreme-value analysis to long-duration (30 year) global altimeter and radiometer datasets is considered. In contrast to previous extreme-value analyses of satellite data, the dataset is sufficiently long to enable a peaks over threshold analysis to be undertaken. When applied to altimeter data for wind speed and significant wave height, this analysis produces values consistent with buoy validation data and previous numerical model reanalysis datasets. The spatial distributions produced are also consistent with the model reanalysis data. However, the altimeter data shows much greater finescale structure for wind speed, which is consistent with known tropical cyclone activity. The greater data density provided by radiometer measurements offers the potential to address altimeter undersampling. However, issues associated with the radiometer’s inability to measure wind speed in heavy rain events appears to create an unacceptable “fair weather” bias at extreme wind speeds. This renders the radiometer data of wind speed largely unusable for the investigation of wind speed extremes. The study also clearly demonstrates the limitations of the initial distribution method for extreme-value analysis, which is heavily biased by mean conditions.

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Alberto Meucci, Ian R. Young, and Øyvind Breivik

Abstract

The present work develops an innovative approach to wind speed and significant wave height extreme value analysis. The approach is based on global atmosphere–wave model ensembles, the members of which are propagated in time from the best estimate of the initial state, with slight perturbations to the initial conditions, to estimate the uncertainties connected to model representations of reality. The low correlation of individual ensemble member forecasts at advanced lead times guarantees their independence and allows us to perform inference statistics. The advantage of ensemble probabilistic forecasts is that it is possible to synthesize an equivalent dataset of duration far longer than the simulation period. This allows the use of direct inference statistics to obtain extreme value estimates. A short time series of six years (from 2010 to 2016) of ensemble forecasts is selected to avoid major changes to the model physics and resolution and thus ensure stationarity. This time series is used to undertake extreme value analysis. The study estimates global wind speed and wave height return periods by selecting peaks from ensemble forecasts from +216- to +240-h lead time from the operational ensemble forecast dataset of the European Centre for Medium-Range Weather Forecasts (ECMWF). The results are compared with extreme value analyses performed on a commonly used reanalysis dataset, ERA-Interim, and buoy data. The comparison with traditional methods demonstrates the potential of this novel approach for statistical analysis of significant wave height and wind speed ocean extremes at the global scale.

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Agustinus Ribal, Ali Tamizi, and Ian R. Young

Abstract

Four scatterometers, namely, MetOp-A, MetOp-B, ERS-2, and OceanSat-2 were recalibrated against combined National Data Buoy Center (NDBC) data and aircraft Stepped Frequency Microwave Radiometer (SFMR) data from hurricanes. As a result, continuous calibration relations over the wind speed range from 0 to 45 m s−1 were developed. The calibration process uses matchup criteria of 50 km and 30 min for the buoy data. However, due to the strong spatiotemporal wind speed gradients in hurricanes, a method that considers both scatterometer and SFMR data in a storm-centered translating frame of reference is adopted. The results show that although the scatterometer radar cross section is degraded at high wind speeds, it is still possible to recover wind speed data using the recalibration process. Data validation between the scatterometers shows that the calibration relations produce consistent results across all scatterometers and reduce the bias and root-mean-square error compared to previous calibrations. In addition, the results extend the useful range of scatterometer measurements to as high as 45 m s−1.

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Ian R. Young and Alexander V. Babanin

Abstract

This paper considers an experimental attempt to estimate the spectral distribution of the dissipation due to breaking of dominant waves. A field wave record with an approximately 50% dominant-breaking rate was analyzed. Segments of the record, comprising sequences of breaking waves, were used to obtain the “breaking spectrum,” and segments of nonbreaking waves were used to obtain the “nonbreaking spectrum.” The clear visible difference between the two spectra was attributed to the dissipation due to breaking. This assumption was supported by independent measurements of total dissipation of kinetic energy in the water column at the measurement location. It is shown that the dominant breaking causes energy dissipation throughout the entire spectrum at scales smaller than the spectral peak waves. The dissipation rate at each frequency is linear in terms of the wave spectral density at that frequency, with a correction for the directional spectral width. A formulation for the spectral dissipation function able to accommodate this effect is suggested. Directional spectra of the breaking and nonbreaking waves are also considered. It is shown that directional dissipation rates at oblique angles are higher than the dissipation in the main wave propagation direction.

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Cesar B. Rocha, William R. Young, and Ian Grooms

Abstract

This study investigates the representation of solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes, with particular attention to the incorporation of active surface buoyancy dynamics. This study extends two existing Galerkin approaches (A and B) and develops a new Galerkin approximation (C). Approximation A, due to Flierl, represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith, represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the boundaries are isopycnal surfaces. The authors discuss the advantages and limitations of approximations A, B, and C in terms of mathematical rigor and conservation laws and illustrate their relative efficiency by solving linear stability problems with nonzero surface buoyancy. With moderate number of modes, B and C have superior accuracy than A at high wavenumbers. Because B lacks the conservation of energy, this study recommends approximation C for constructing solutions to the surface active QG equations using the Galerkin series with standard vertical modes.

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