Wave Data Assimilation Research Articles

Assimilation of Wave Data for Simulations of Typhoon Waves in the South China Sea

A sequential assimilation method is applied to improve the accuracy of wave simulations in the South China Sea. Typhoon Nesat was chosen to be used for the numerical experiment. The assimilation is based on Optimal Interpolation(OI) which can minimize the Root-Mean-Square error in the analysis. Using the method of OI, wave height and mean period data observed by three buoys have been assimilated into the third generation ocean wave model(SWAN). The results show that the assimilation can correct the difference between the wave model and observations, and the result of significant wave height is superior to that of mean period.

Wave data assimilation using a hybrid approach in the Persian Gulf

The main goal of this study is to develop an efficient approach for the assimilation of the hindcasted wave parameters in the Persian Gulf. Hence, the third generation SWAN model was employed for wave modeling forced by the 6-h ECMWF wind data with a resolution of 0.5°. In situ wave measurements at two stations were utilized to evaluate the assimilation approaches. It was found that since the model errors are not the same for wave height and period, adaptation of model parameter does not result in simultaneous and comprehensive improvement of them. Therefore, an approach based on the error prediction and updating of output variables was employed to modify wave height and period. In this approach, artificial neural networks (ANNs) were used to estimate the deviations between the simulated and measured wave parameters. The results showed that updating of output variables leads to significant improvement in a wide range of the predicted wave characteristics. It was revealed that the best input parameters for error prediction networks are mean wind speed, mean wind direction, wind duration, and the wave parameters. In addition, combination of the ANN estimated error with numerically modeled wave parameters leads to further improvement in the predicted wave parameters in contrast to direct estimation of the parameters by ANN.

A new methodology for using buoy measurements in sea wave data assimilation

One of the main drawbacks in modern sea wave data assimilation models is the limited temporal and spatial improvement obtained in the final forecasting products. This is mainly due to deviations coming either from the relevant atmospheric input or from the dynamics of the wave model, resulting to systematic errors of the forecasted fields of numerical wave models, when no observation is available for assimilation. A potential solution is presented in this work, based on a combination of advanced statistical techniques, data assimilation systems, and wave models. More precisely, Kalman filtering algorithms are implemented into the wave model WAM and the results are assimilated by an Optimum Interpolation Scheme, in order to extend the beneficial influence of the latter in time and space. The case studied concerns a 3-month period in an open sea area near the South-West coast of the USA (Pacific Ocean).

Non-linear wave data assimilation with an ANN-type wind-wave model and Ensemble Kalman Filter (EnKF)

Non-linear data assimilation for a wind-wave dynamical surrogate model in a reduced space is presented. A dynamic artificial neural network is used for surrogate modeling. It provides a fast emulation of a wind-wave model which is used for the evaluation of the system states during a small period of time. The system state consists of wave height and wave direction in the reduced space which is affected by the reduced space wind field. The projection from the full space to the reduced one is performed by a principal component analysis. Ensemble methods require the evaluation of dynamics for a large number of statistical ensembles, so coupling this surrogate (instead of a full model) with an Ensemble Kalman Filter (EnKF) leads to computational efficiency. Application of the procedure is demonstrated through 6 month hindcast study of wind waves over the Caspian Sea using the third-generation wave model and the analysis of the ECMWF wind field. The trained network is embedded into the stochastic environment. Then, the EnKF is used to find estimate of the system states. Experiments show that the proposed data assimilation technique can correct the prediction of the wind-waves requiring just a modest execution time.

Optimal interpolation of buoy data into a deterministic wind–wave model

Third-generation wave models have been evolved in 1980s with the state-of-the-art physics of wave generation. Using these models, the real time wave estimation is made possible but, in general, it is found to be underpredicted. This is mainly due to the smoothened wind vectors from the atmospheric model. An accurate prediction of wind is thus necessary to improve the wave prediction further. A better way of overcoming the discrepancies in the wind is by the way of wave data assimilation. In the present study, an operationally efficient yet a versatile assimilation model, optimal interpolation (OI), has been presented. The weighting matrix, so-called gain matrix, has been formulated according to the model physics by which the wind generates waves. The efficiency of the assimilative model using real time buoy observations at the Arabian Sea has been evaluated and described in this article. The root mean square error reduction of wave height is found to be of the order of 30–50% at the validation stations.

Wave data assimilation using ensemble error covariances for operational wave forecast

Most of the present operational data assimilation techniques provide an improved estimate of the system state up to the current time level based on measurements. From a forecasting viewpoint, this corresponds to an updating of the initial conditions of a numerical model. The standard forecasting procedure is then to run the model into the future, driven by predicted boundary and forcing conditions. In the wind–wave modelling context, the impact of the initial wave conditions quickly disappears within 6–12 h. Thus, after a certain forecast horizon, the model predictions are no better than from an initially uncorrected model. This paper considers a novel approach to wave data assimilation and demonstrates that through the measurement forecast (made using so-called local models), the entire model domain can be corrected over extended forecast horizons (i.e., long after the updated initial conditions have lost their influence), thus offering significant improvements over the conventional methodology. The proposed data assimilation scheme can be executed in the post-processor and is operationally viable with the requirement of insignificant execution time. This scheme produces an efficiency of 30–60% in reducing root mean square error wave height over a forecast period up to 24 h. The application of this proposed data assimilation procedure is demonstrated through a real-world wave data assimilation case study in the South East Asian Seas. The distribution of error forecasts over the entire model domain was estimated using a steady gain matrix derived from the ensemble of spatial error covariances. The improvements in the prediction of wave characteristics are highlighted.

The Impact of Altimeter Sampling Patterns on Estimates of Background Errors in a Global Wave Model

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.

On the retrieval of significant wave heights from spaceborne Synthetic Aperture Radar (ERS-SAR) using the Max-Planck Institut (MPI) algorithm

Synthetic Aperture Radar (SAR) onboard satellites is the only source of directional wave spectra with continuous and global coverage. Millions of SAR Wave Mode (SWM) imagettes have been acquired since the launch in the early 1990's of the first European Remote Sensing Satellite ERS-1 and its successors ERS-2 and ENVISAT, which has opened up many possibilities specially for wave data assimilation purposes. The main aim of data assimilation is to improve the forecasting introducing available observations into the modeling procedures in order to minimize the differences between model estimates and measurements. However there are limitations in the retrieval of the directional spectrum from SAR images due to nonlinearities in the mapping mechanism. The Max-Planck Institut (MPI) scheme, the first proposed and most widely used algorithm to retrieve directional wave spectra from SAR images, is employed to compare significant wave heights retrieved from ERS-1 SAR against buoy measurements and against the WAM wave model. It is shown that for periods shorter than 12 seconds the WAM model performs better than the MPI, despite the fact that the model is used as first guess to the MPI method, that is the retrieval is deteriorating the first guess. For periods longer than 12 seconds, the part of the spectrum that is directly measured by SAR, the performance of the MPI scheme is at least as good as the WAM model.

Forecast Divergences of a Global Wave Model

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 (LSWH) 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 (LU10) has a similar distribution with a stronger latitudinal dependence. It is found that both LSWH and LU10 increase as the forecast period increases. The increase in LSWH is partly due to LU10 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.

The impact of inhomogenous background errors on a global wave data assimilation system

One of the main limitations in current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. In this work, models for the observational error variance, background error variance and background error correlations are developed based on the results of previous studies. These are tested in a global wave data assimilation system and the resulting wave forecasts are verified against independent observations from buoys. Forecasts of significant wave height show substantial improvement over the Australian Bureau of Meteorology's current operational wave forecasting system. However, forecasts of peak period are not similarly improved. The regional impacts of the new assimilation scheme are found to vary on a seasonal basis. Overall, it is shown that the inclusion of a latitudinally dependent background error, and improved specification of the background and observational error variances can reduce the root-mean-square error of 24-hour forecast Significant Wave Height by almost 10%.

Background errors in a global wave model determined from altimeter data

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 [1986]. This 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 paper, correlations of the differences between modeled SWH and bias‐corrected ERS‐2 data are calculated. The irregular sampling pattern of the altimeter is accounted for by adjusting the correlation length scales according to latitude and the calculated length scale. The results show that the length scale of the background errors varies significantly over the globe, with the largest scales at low latitudes and shortest scales at high latitudes. Very little seasonal or year‐to‐year variability in the correlation length scales is detected. Conversely, the magnitude of the background error variance is found to have considerable seasonal and year‐to‐year variability. By separating the altimeter ground tracks into ascending and descending tracks, it is possible to examine, to a limited extent, whether any anisotropy exists in the background errors.

Wave assimilation and numerical prediction

An adjoint variational method for wave data assimilation in the LAGFD-WAM wave model is proposed. The adjoint equation of the wavenumber energy spectrum balance equation is derived. And fortunately, its characteristic equations are the same as those in the LAGFD-WAM wave model. Simple experiments on the functional optimization and assimilation effectiveness during the prediction period indicated that the adjoint variational method is effective for wave assimilation and that the initial optimization of the wave model is important for the short-range wave prediction. All of this is under the assumption that the wind field is accurate, the method is the important first step for combined wind and wave data assimilation systems.

Spectral wave data assimilation for the prediction of waves in the North Sea

Spectral observations from pitch-and-roll buoys have been assimilated in a North Sea wave model, in order to study their impact on the wave analysis and forecast. The assimilation is based on Optimal Interpolation (OI) of a limited number of characteristic spectral parameters. In a case study, the propagation of the corrections through the model domain is followed, and it is clarified for which wave conditions the data assimilation has the largest influence on the forecast: this is especially the case for swell waves with long travel times between the assimilation site and the location where validation is carried out. A 1-year test has been carried out in which an analysis and subsequent forecast were produced four times a day. From a statistical analysis of the results a modest but systematic improvement of the 12-h forecast is found. When only swell cases are selected, the impact is more pronounced. It is argued that for shelf seas like the North Sea, more progress is to be expected from extension of the `conventional' observations network (buoys and wave radars) than from satellite measurements.

Annual validation of significant wave heights of ERS‐1 synthetic aperture radar wave mode spectra using TOPEX/Poseidon and ERS‐1 altimeter data

Significant wave heights retrieved globally during 1994 from low bit rate imagette spectra of the synthetic aperture radar (SAR) operating in the intermittent wave mode (SWM) onboard the first European Remote Sensing (ERS‐1) satellite (Hsswm) are validated using independent, buoy‐validated satellite altimeter data from TOPEX/Poseidon (Hstop) and ERS‐1 (Hsers). Hsswm is retrieved using the extended inversion algorithm of the fully nonlinear wave‐to‐SAR spectral integral transform [Hasselmann et al., 1996]. The statistical comparison shows that globally retrieved Hsswm agree remarkably well with collocated data of both altimeters. Histograms of global Hsswm are well approximated by the universal lognormal distribution function. A small but systematic underestimation of Hsswm with respect to both altimeters by 0.1 m is noticed. This bias is small compared to the uncorrelated root‐mean‐square (rms) deviation of 0.5 m. The underestimation originates from underestimations of the high sea states dominated by wind sea. The entire range of swell waves of Hsswm, however, corresponds very closely to Hstop. Thus the high accuracy of SWM‐retrieved swell wave heights substantiates their suitability for model validation and for operational wave data assimilation. To achieve also reliable estimates of the high sea states, the combined analysis of wave and wind data from both modeling and observation is the most promising approach.

Wave data assimilation with the Kalman filter

A new data assimilation method for ocean waves is presented, based on an efficient low-rank approximation to the Kalman filter. Both the extended Kalman filter and a truncated second-order filter are implemented. In order to explicitly estimate past wind corrections based on current wave measurements, the filter is extended to a fixed-lag Kalman smoother for the wind fields. The filter is tested in a number of synthetic experiments with simple geometries. Propagation experiments with errors in the boundary condition showed that the KF was able to accurately propagate forecast errors, resulting in spatially varying error correlations, which would be impossible to model with time-independent assimilation methods like OI. An explicit comparison with an OI assimilation scheme showed that the KF also is superior in estimating the sea state at some distance from the observations. In experiments with errors in the driving wind, the modeled error estimates were also in agreement with the actual forecast errors. The bias in the state estimate, which is introduced through the nonlinear dependence of the waves on the driving wind field, was largely removed by the second-order filter, even without actually assimilating data. Assimilation of wave observations resulted in an improved wave analysis and in correction of past wind fields. The accuracy of this wind correction depends strongly on the actual place and time of wave generation, which is correctly modeled by the error estimate supplied by the Kalman filter. In summary, the KF approach is shown to be a reliable assimilation scheme in these simple experiments, and has the advantage over other assimilation methods that it supplies explicit dynamical error estimates.

An optimal interpolation scheme for the assimilation of spectral wave data

An optimal interpolation scheme for assimilating two‐dimensional wave spectra is presented which is based on a decomposition of the spectrum into principal wave systems. Each wave system is represented by three characteristic parameters: significant wave height, mean propagation direction, and mean frequency. The spectrum is thereby reduced to a manageable number of parameters. From the correction of the wind‐sea system a correction of the local wind is derived. A 2‐month test of the system using wave spectra retrieved from ERS 1 synthetic aperture radar wave mode data in the Atlantic yielded consistent corrections of winds and waves. However, the corrected wind data alone, although valuable in identifying wind errors in critical high wind speed regions, are too sparsely distributed in space and time to be used in isolation and need to be combined with other data in an atmospheric data assimilation scheme. This emphasizes the need for the development of combined wind and wave data assimilation schemes for the optimal use of satellite wind and wave data.

An improved algorithm for the retrieval of ocean wave spectra from synthetic aperture radar image spectra

An earlier algorithm for retrieving two‐dimensional wave spectra from synthetic aperture radar (SAR) image spectra is improved by using a modified cost function and introducing an additional iteration loop in which the first‐guess input spectrum is systematically updated. For this purpose a spectral partitioning scheme is applied in which the spectrum is decomposed into a finite number of distinct wave systems. At each iteration step, the individual wave systems of the partitioned nth‐guess wave spectrum are adjusted to agree in mean energy, frequency, and direction with the corresponding mean values of the associated wave systems of the SAR‐inverted wave spectrum. The algorithm retrieves smooth wave spectra, avoiding the discontinuities which tended to arise in the previous algorithm in the transition region near the azimuthal wavenumber cutoff of the SAR image spectrum. The azimuthal cutoff of the SAR spectrum is also reproduced more accurately. The greatest improvement of the new retrieval algorithm is obtained when the discrepancies between the initial first‐guess wave spectrum and the observed SAR spectrum are large. In this case the additional updating loop for the input spectrum enables the retrieved spectrum to adjust such that the simulated SAR spectrum matches more closely the observed SAR spectrum. The overall correlation of a large set of simulated SAR spectra with the measured SAR spectra is found to be significantly higher than with the previous algorithm, indicating that the algorithm not only overcomes isolated shortcomings of the earlier algorithm but also yields retrieved wave spectra which are generally more consistent with the input SAR data. An additional practical advantage of the new algorithm is that it returns spectral partioning parameters which can be used in SAR wave data assimilation schemes.

Assimilation of wave data into the wave model WAM using an impulse response function method

A new method for the assimilation of wave data into a third‐generation wave model is presented. Deviations between observed and modeled wave spectra are used to derive corrections of the wind field which drives the wave model. The wave field can then be subsequently corrected by a new integration of the wave model with the improved wind field. A basic difficulty of such dynamically consistent wave data assimilations schemes which correct both wind and wave data is the nonsynchronous and nonlocal nature of the wind field corrections: errors observed in the wave spectrum at a given measurement time and location can be produced by errors in the wind field at much earlier times and far distant locations. Formally, these problems can be rigorously resolved by the adjoint modeling method. However, in practice, the adjoint technique requires an order of magnitude more computer time than the integration of the wave model itself. Here an alternative method is developed. The linearized wave model equation which relates small wind to wave spectrum changes is inverted. The central assumption of the inversion is that the wind impact functions representing the impulse response (Green's) function of the wave evolution can be approximated by a δ‐function. Physically, this implies that the wind field perturbations responsible for observed perturbations in the wave spectrum can be regarded as strongly localized in space and time for any given component of the spectrum. To obtain stable estimates, the corrections for different wave components are averaged over wavenumber clusters representing different wave systems. For cases in which the linear approximation is inadequate, the method can be applied iteratively. Tests of the concept and application of the method for a number of synthetic wind field cases are encouraging.

Wave data assimilation in the WAM wave model

Abstract Using the adjoint technique, wave height data have been assimilated into the third generation ocean wave model WAM, which runs operationally at ECMWF. WAM describes the evolution of a two-dimensional wave spectrum and it is driven by surface winds. WAM considers three source functions: wind input, dissipation by white capping and non-linear wave-wave interactions between the different components of the spectrum. The wind input term is taken from the theory of Janssen (1991). According to this theory, the drag coefficient depends not only on the wind speed but also on the wave spectrum through the wave stress. Up to now, a one-gridpoint version of the adjoint of the WAM has been constructed and tested. The assimilation scheme optimizes the driving wind sequence. The potential benefit of the scheme is investigated by performing some idealized experiments.

Variational Wave Data Assimilation in a Third-Generation Wave Model

Abstract The adjoint of the wave model WAM, which runs operationally performing global wave forecast at the European Centre for Medium-Range Weather Forecasts, has been constructed. In this model, the nonlinear interactions are described by the discrete interaction approximation of Hasselmann et al., and the wind input and the dissipation are consistent with the theory of Janssen. The drag coefficient depends not only on the wind speed, but also on the wave-induced stress, reflecting in this way the dependence of winds on waves. The adjoint scheme constitutes a new (the first variational) method to assimilate arbitrary wave data into the WAM. Up to now, this had been done using an optimal interpolation technique (sequential method), and only for wave heights. The new assimilation scheme has been tested with a one-gridpoint version of the WAM. Assimilating only wave data-significant wave height and mean wave direction—is sufficient to reconstruct all wind fields, significant wave height, and two-dimensiona...