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.     

Comparative analysis between operational weather prediction models and QuikSCAT wind data near the Galician coast

Wind measurements from SeaWinds scatterometer on the NASA QuikSCAT satellite and wind forecasts from two different operational numerical models provided by MeteoGalicia were compared for a 4-year period (2002–2005) in Galician coast environment. Available wind data buoy measurements were also used to complement the analysis. A statistical analysis based on mean errors, root mean square errors and complex correlation was performed from spatial, temporal and directional points of view.In the spatial comparison no significant differences between models and satellite were observed and the error magnitudes of the models are compatible with typical QuikSCAT errors. The suitability of satellite wind estimations for data assimilation in these models must be further investigated. Negative bias of models with respect to the satellite was also confirmed with buoy data, in such a way that models overestimation is smaller than the satellite one. Big errors in wind direction appear in southeasterly and southwesterly winds for both satellite and models, contributing to high RMSE values when compared to buoy data. These errors were mainly attributed to the effect of insufficient spatial resolution near shore.     

Ocean wave spectrum estimation using measured vessel motions from an in-service container ship

This article is about the use of measured wave-induced vessel motions for estimation of ocean wave spectra by application of the wave buoy analogy. In the study, data from a larger, in-service container ship is considered. The estimation of wave spectra, equivalently sea state parameters, is based on measurements from, respectively, a gyro and two accelerometers leading to the simultaneous use of the pitching motion together with the horizontal and vertical accelerations in a position close to the forward perpendicular. The study of in-service data leads to contemplations about the vessel's advance speed, as the possible existence of sea current means that speed-over-ground (SOG) and speed-through-water (STW) will be different. The article discusses aspects related to advance speed in the context of the wave buoy analogy, and a smaller sensitivity study is conducted. Preceding to the sensitivity study, a comparison is made between sea state estimates by the wave buoy analogy and estimates obtained from a hindcast study. The article shows an acceptable agreement between the two sets of estimates. Following, the main conclusion from the sensitivity study on advance speed is that errors and uncertainties in the speed log have an effect on the estimates of the wave buoy analogy. In fact, the effect can be severe if reliable STW measurements are not available. In the final part, the article includes a few discussions about (non)stationary conditions in the context of the wave buoy analogy, and, although the effect on results is not necessarily detrimental, care must be shown when the wave buoy analogy is applied during in-service conditions.     

Prediction of wave parameters by using fuzzy inference system and the parametric models along the south coasts of the Black Sea

Forecasting of sea-state characteristics has a great importance in coastal and ocean engineering studies. Therefore, the purpose of this study was to investigate performances of Adaptive-Network-Based Fuzzy Inference System (ANFIS) and several parametric methods in the Black Sea. For this purpose, different fuzzy models with different input combinations were developed for two different wind data sources (TSMS and ECMWF) at two offshore buoy stations. It also aimed to apply several approaches to event-based data sets for wave predictions. Generally, in literature the tendency is to use time series data for wave predictions. In this kind of prediction approach, lagged time series data are taken as inputs and current or future variables are taken as output. In this study, event-based data for each independent storm were extracted from time series data. Simultaneous or concurrent data of wind speed, blowing duration, fetch length and wave characteristics were detected for each single storm. These event data were then used to set up models. The hindcast results were validated with significant wave height and mean wave period data recorded in Hopa and Sinop buoy stations. The performance of developed fuzzy models were also compared with that of four different parametric methods (Wilson, SPM, Jonswap, and CEM methods) applied for two wind data sources at both buoy stations. Finally, it was determined that in the prediction of both wave parameters (H _s and T _z) the ANFIS models (R = 0.66, squared correlation coefficient, and MAE = 0.37 m, mean absolute error, for the best model in prediction of H _s) were more accurate than the parametric methods (R = 0.63 and MAE = 0.75 m for the best model in prediction of H _s).     

Initial results from long-term measurements of atmospheric humidity and related parameters in the marine boundary layer at two locations in the Gulf of Mexico

Measurements of boundary layer moisture have been acquired from Rotronic MP-100 sensors deployed on two NDBC buoys in the northern Gulf of Mexico from June through November 1993. For one sensor, which was retrieved approximately 8 months after deployment, the post- and precalibrations agreed closely and fell well within WMO specifications for accuracy. The second sensor operated continuously from June 1993 to February 1997 (3.5 years). Buoy observations of relative humidity and supporting data were used to calculate specific humidity and the surface fluxes of latent and sensible heat. Specific humidities from the buoys were compared with observations of moisture obtained from nearby ship reports, and the correlations were generally high (0.7–0.9). Surface gravity wave spectra were also acquired. The time series of specific humidity and the other buoy parameters revealed three primary scales of variability, small (h), synoptic (days), and seasonal (months). The synoptic variability was clearly dominant and occurred primarily during September, October, and November. Most of the synoptic variability was due to frontal systems that dropped down into the Gulf of Mexico from the continental US followed by air masses which were cold and dry. Cross-correlation analyses of the buoy data indicated that: (1) the moisture field was highly coherent over distances of 800 km or more in the northern Gulf of Mexico; and (2) both specific humidity and air temperature served as tracers of the motion associated with propagating atmospheric disturbances. These correlation analyses also revealed that the prevailing weather systems generally entered the buoy domain from the South prior to September, but primarily from the North thereafter. Spectra of the various buoy parameters indicated strong diurnal and semidiurnal variability for barometric pressure and sea surface temperature (SST) and lesser variability for air temperature, wind speed and significant wave height. The surface fluxes of latent and sensible heat were dominated by the synoptic events which took place from September through November with the transfer of latent heat being primarily from the ocean to the atmosphere. Finally, an analysis of the surface wave observations from each buoy, which included calculations of wave age and estimates of surface roughness, indicate that major heat and moisture flux events coincide with periods of active wave growth, although the data were insufficient to identify any causal relationships.     

Filling up gaps in wave data with genetic programming

A given time series of significant wave heights invariably contains smaller or larger gaps or missing values due to a variety of reasons ranging from instrument failures to loss of recorders following human interference. In-filling of missing information is widely reported and well documented for variables like rainfall and river flow, but not for the wave height observations made by rider buoys. This paper attempts to tackle this problem through one of the latest soft computing tools, namely, genetic programming (GP). The missing information in hourly significant wave height observations at one of the data buoy stations maintained by the US National Data Buoy Center is filled up by developing GP models through spatial correlations. The gap lengths of different orders are artificially created and filled up by appropriate GP programs. The results are also compared with those derived using artificial neural networks (ANN). In general, it is found that the in-filling done by GP rivals that by ANN and many times becomes more satisfactory, especially when the gap lengths are smaller. Although the accuracy involved reduces as the amount of gap increases, the missing values for a long duration of a month or so can be filled up with a maximum average error up to 0.21 m in the high seas.     

Assessment of wind quality for oceanographic modelling in semi-enclosed basins

The quality of surface winds derived from four meteorological models is assessed in the semi-enclosed Adriatic Sea over a 2-month period: a global hydrostatic model ECMWF T511 (40 km resolution), a hydrostatic limited area model LAMBO (20 km), and two non-hydrostatic limited area models: LAMI (7 km) and COAMPS™ (4 km). These wind models are used to drive a 2 km resolution wave model (SWAN) of the Adriatic, and wind and wave results are compared with observations at the ISMAR oceanographic tower off Venice. Waves are also compared at buoy locations near Ancona and Ortona. Consistently with earlier studies, the ECMWF fields underestimate the wind magnitude and do not reproduce the known spatial structure of strong wind events. The results show that the higher-resolution, limited area models LAMI and COAMPS exhibit better amplitude response than the coarser ECMWF: there is a 3- to 4-fold reduction of the wind underestimation at the platform (from 36% to 8–11%). The wave response is also improved with LAMI and COAMPS: there is a 2-fold reduction in the underestimation of wave heights at the platform. These non-hydrostatic models also produce wind fields with more realistic small-scale, spatial structure during strong wind events. The temporal correlation between observed and modelled wind, however, is highest with the global ECMWF model due to the fact that large-scale features can be predicted deterministically, whereas small-scale features can only be predicted stochastically. Models with less small-scale structure have better correlation because they have less “noise.” This explanation is supported by increased correlation between modelled and observed waves, the waves representing a smoothing of the wind over fetch and duration. Although there is room for improvement, the high-resolution, non-hydrostatic models (LAMI and COAMPS) offer significant advantages for driving oceanographic simulations in semi-enclosed basins such as the Adriatic Sea.     

Wave spectrum estimation conditioned on machine learning-based output using the wave buoy analogy

In this work, a hybrid approach for wave spectrum estimation is proposed. Fundamentally, the approach is based on the wave buoy analogy, processing ship response measurements, via a framework combining machine learning and a physics-based method dependent on available transfer functions. Specifically, a non-parametric (Bayesian) estimate is obtained of the directional wave spectrum conditioned on integral wave parameters established by a convolutional neural network. The developed method is assessed in a case study considering about two years of data obtained from an in-service container ship. The method produces good results, significantly improved when compared to the initial estimate made without constraints.     

阵列振荡浮子式波能转换装置试验

本文介绍了一种阵列振荡浮子式简易波能转换装置,试验证明了该波能转换装置在没有进行二次转换的情况下,不仅保证了波能采集系统的性能稳定性而且提高了能量转换效率,为振荡浮子式波能转换装置的工程应用提供了有益的参考。     

Improving assimilation of SeaWiFS data by the application of bias correction with a local SEIK filter

Ocean-biogeochemical models show typically significant errors in the representation of chlorophyll concentrations. The model state can be improved by the assimilation of satellite chlorophyll data with algorithms based on the Kalman filter. However, these algorithms do usually not account for the possibility that the model prediction contains systematic errors in the form of model bias. Accounting explicitly for model biases can improve the assimilation performance. To study the effect of bias estimation on the estimation of surface chlorophyll concentrations, chlorophyll data from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) are assimilated on a daily basis into the NASA Ocean Biogeochemical Model (NOBM). The assimilation is performed by the ensemble-based SEIK filter combined with an online bias correction scheme. The SEIK filter is simplified here by the use of a static error covariance matrix. The performance of the filter algorithm is assessed by comparison with independent in situ data over the 7-year period 1998–2004. The bias correction results in significant improvements of the surface chlorophyll concentrations compared to the assimilation without bias estimation. With bias estimation, the daily surface chlorophyll estimates from the assimilation show about 3.3% lower error than SeaWiFS data. In contrast, the error in the global surface chlorophyll estimate without bias estimation is 10.9% larger than the error of SeaWiFS data.     

Forecast verification of a 3D model of the Mediterranean Sea. The use of discrete wavelet transforms and EOFs in the skill assessment of spatial forecasts

The quality assessment of a nested model system of the Mediterranean Sea is realised. The model has two zooms in the Provençal Basin and in the Ligurian Sea, realised with a two-way nesting approach. The experiment lasts for nine weeks, and at each week sea surface temperature (SST) and sea level anomaly are assimilated. The quality assessment of the surface temperature is done in a spatio-temporal approach, to take into account the high complexity of the SST distribution. We focus on the multi-scale nature of oceanic processes using two powerful tools for spatio-temporal analysis, wavelets and Empirical Orthogonal Functions (EOFs). We apply two-dimensional wavelets to decompose the high-resolution model and observed SST into different spatial scales. The Ligurian Sea model results are compared to observations at each of those spatial scales, with special attention on how the assimilation affects the model behaviour. We also use EOFs to assess the similarities between the Mediterranean Sea model and the observed SST. The results show that the assimilation mainly affects the model large-scale features, whereas the small scales show little or no improvement and sometimes, even a decrease in their skill. The multiresolution analysis reveals the connection between large- and small-scale errors, and how the choice of the maximum correlation length of the assimilation scheme affects the distribution of the model error among the different spatial scales.     

Error correction of a predictive ocean wave model using local model approximation

Constructing models from time series with nontrivial dynamics is a difficult problem. The classical approach is to build a model from first principles and use it to forecast on the basis of the initial conditions. Unfortunately, this is not always possible. For example, in fluid dynamics, a perfect model in the form of the Navier–Stokes equations exists, but initial conditions and accurate forcing terms are difficult to obtain. In other cases, a good model may not exist. In either case, alternative approaches should be examined. This paper describes an alternative approach of combining observations and numerical model results in order to produce an accurate forecast. The approach is based on application of a method inspired by chaos theory for building nonlinear models from data called Local Models. Embedding theorem based on the time lagged embedded vectors is the basis for the local model. This technique is used for analysis and updating of numerical model output variables to forecast and correct the errors created by numerical model. The local model approximation is a powerful tool in the forecasting of chaotic time series and has been employed for wave prediction in a forecasting horizon from a few hours to 24 h. The efficacy of the local model as an error correction tool (by combining the model predictions with the observations) compared with the predictions of linear auto regressive models has been brought up. In the present study, the parameters driving the local model are optimized using evolutionary algorithms.     

海洋潜标系统布放动力学分析

布放是浮标系统投入使用前的一个关键的作业过程。研究海洋潜标系统布放过程中的水动力特性,对安全顺利地实现布放有重要的意义。考虑海洋潜标系统各部分的水动力作用和系留索的弹性变形,通过时域模拟海洋潜标系统在500m水深海域的采用浮标先行投放法的布放过程,计算了海洋潜标系统布放过程中的动态响应,并分析了波高、作业船速度和系留索弯曲刚度对布放的影响。得到的结果表明：锚位会滞后于锚投放点;系留索曲率和有效张力的最值都出现在缆索与锚的连接段;锚触底时缆索瞬时张力达到峰值;系留索的弯曲刚度是影响布放的重要因素,随着弯曲刚度增大,锚位明显前移,系留索的有效张力峰值和曲率都会降低;波高和作业船速度的改变对于浮标系统布放的动态响应的影响幅度很小。     

测波浮标与ADCP的现场对比试验研究

波浪测量对于海洋研究具有极其重要的意义.当前运用最广泛的海洋波浪测量装备有"波浪骑士"和声学多普勒流速剖面仪(ADCP).本文针对这2种测量装置,开展对比测试试验,对所测得的有义波高、平均跨零周期和谱峰波向等测试数据进行对比,分析验证2种测量装备的特点、适用性和准确度.     

Sea state estimation based on vessel motion responses: Improved smoothness and robustness using Bézier surface and L1 optimization

Floating structures oscillate in waves, where these wave-induced motions may be critical for various marine operations. An important consideration is thereby given to the sea states at the planning and operating stages for an offshore project. The most important information extracted from a sea state is the directional wave spectrum, indicating wave direction, significant wave height, and wave spectrum peak period. Among several available methods of measuring and estimating the directional wave spectrum, the wave buoy analogy technique based on vessel motion responses is an in situ and almost real-time solution without extra costs of devices. If the forms of the wave spectra are not predefined in the estimation, the method is called a nonparametric approach. Its most remarkable advantage is the flexible form, but the smoothness should be regulated. After the discrete Fourier transform has been applied to the measured vessel motions, smoothing is necessary. However, this process results in disturbed vessel cross-spectra and a lowpass characteristic of the windowing function. This paper presents a nonparametric approach for directional wave spectrum estimation based on vessel motion responses. It introduces novel smoothness constraints using Bézier surface and includes a more robust estimate using L1 optimization. Both techniques are applied to the wave buoy analogy for the first time. Numerical simulations are conducted to verify the proposed algorithm.     

Prediction of seasonal maximum wave height for unevenly spaced time series by Black Widow Optimization algorithm

The present study aimed to predict the maximum seasonal wave height by new integrative data driven methods. For this purpose, two data-driven techniques, that are, the Adaptive Neuro-Fuzzy Inference System (ANFIS) and the Support Vector Regression (SVR), were applied, and a BWO algorithm was used as an integrated method (ANFIS-BWO and SVR-BWO). In addition, the Particle Swarm Optimization (PSO) algorithm was used as a method integrated with SVR and ANFIS (SVR-PSO and ANFIS-PSO) to compare the performance of the newly developed methods (ANFIS-BWO and SVR-BWO). The wave data were collected in different seasons by a buoy station deployed in the southern Baltic Sea by the Institute of Hydro-Engineering of the Polish Academy of Sciences. Seasonal simulations were performed to investigate the effect of seasons on the maximum wave height. The wave data constituted an unevenly spaced time series. The maximum wave height was modeled using the maximum wave height period (T_max), the significant wave height (H_s), the significant wave period (T_s), and time steps (Δt). The results showed that the application of BWO and PSO algorithms increased the accuracy of ANFIS and SVR by about 18.45%. Moreover, the results show that PSO increased the accuracy of ANFIS and SVR by about 17.98% and 21.59%, respectively. The results of different runs indicated that the BWO is more stable to reach the global solution than PSO. The results also show that show that SVR-BWO is the most accurate model.     

Investigation of ship waves in a narrow channel

This paper presents a discussion of the characteristics of ship waves in a narrow channel restricted by vertical walls, based on observed data and the results computed by a 2-D model. In the numerical model, the propagation of waves generated by a moving ship is simulated by solving 2-D depth-integrated Boussinesq equations. To get the boundary conditions at the location of the ship, the slender-ship approximation is employed. A field observation was carried out at a straight length of navigation channel. The ships targeted in the observations are two kinds of waterbuses with lengths of 28 and 24 m. The relative depth Froude number for the river current, an appropriate parameter for assessing the influence of the current on ship wave characteristics in a navigation channel, ranged from 0.47 to 0.76. The observed maximum wave height varied between 0.13 and 1.26 m. The maximum wave height of the wave train is sharply increased when the relative depth Froude number exceeds 0.6. The results computed by the present model agree fairly well with the observed data.     

Application of a SEEK filter to a 1D biogeochemical model of the Ligurian Sea: Twin experiments and real in-situ data assimilation

The Singular Evolutive Extended Kalman (SEEK) filter has been implemented to assimilate in-situ data in a 1D coupled physical-ecosystem model of the Ligurian Sea. The biogeochemical model describes the partly decoupled nitrogen and carbon cycles of the pelagic food web. The GHER hydrodynamic model (1D version) is used to represent the physical forcings. The data assimilation scheme (SEEK filter) parameterizes the error statistics by means of a set of empirical orthogonal functions (EOFs). Twin experiments are first performed with the aim to choose the suitable experimental protocol (observation and estimation vectors, number of EOFs, frequency of the assimilation,…) and to assess the SEEK filter performances. This protocol is then applied to perform real data assimilation experiments using the DYFAMED data base. By assimilating phytoplankton observations, the method has allowed to improve not only the representation of the phytoplankton community, but also of other variables such as zooplankton and bacteria that evolve with model dynamics and that are not corrected by the data assimilation scheme. The validation of the assimilation method and the improvement of model results are studied by means of suitable error measurements.     

一种计算SES船尾波(Wash wave)的数值方法

本文提出了一种无限深水中表面效应船(Surface Effect Ship,SES)尾波(Wash wave)数值方法.SES的尾波被表达成分布在气垫上的压力在静水中航行产生的兴波波浪场.在线性势流假设下,该尾波可解析地表示为积分形式,而其被积函数带有奇性并高频振荡.文中提出了一个变换,使变换后对不同的航速,SES船形(气垫形状)和所要计算的波浪场位置尾波计算中的被积函数是单调变化,因而易于数值计算.积分中的奇性也予以去除.数值计算结果表明本文提出的数值方法具有较高的计算效率而且结果与已发表的结果吻合良好.文中给出了一些SES船尾波(Wash wave)的计算结果,并进一步分析了SES尾波(Wash wave)中的局部和非局部波浪场成分.文中还尝试使用本文方法预报常规高速双体船的尾波(Wash wave),结果发现预报与水池测量结果相当吻合.     

基于边界元方法的二维全非线性数值波浪水槽(英文)

The development of a two dimensional numerical wave tank (NWT) with a rocker or piston type wavemaker based on the high order boundary element method (BEM) and mixed Eulerian-Lagrangian (MEL) is examined. The cauchy principle value (CPV) integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the corner problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.