Forecasting ocean wave energy: The ECMWF wave model and time series methods

Recently, the technology has been developed to make wave farms commercially viable. Since electricity is perishable, utilities will be interested in forecasting ocean wave energy. The horizons involved in short-term management of power grids range from as little as a few hours to as long as several days. In selecting a method, the forecaster has a choice between physics-based models and statistical techniques. A further idea is to combine both types of models. This paper analyzes the forecasting properties of a well-known physics-based model, the European Center for Medium-Range Weather Forecasts (ECMWF) Wave Model, and two statistical techniques, time-varying parameter regressions and neural networks. Thirteen data sets at locations in the Atlantic and Pacific Oceans and the Gulf of Mexico are tested. The quantities to be predicted are the significant wave height, the wave period, and the wave energy flux. In the initial tests, the ECMWF model and the statistical models are compared directly. The statistical models do better at short horizons, producing more accurate forecasts in the 1-5 h range. The ECMWF model is superior at longer horizons. The convergence point, at which the two methods achieve comparable degrees of accuracy, is in the area of 6 h. By implication, the physics-based model captures the underlying signals at lower frequencies, while the statistical models capture relationships over shorter intervals. Further tests are run in which the forecasts from the ECMWF model are used as inputs in regressions and neural networks. The combined models yield more accurate forecasts than either one individually.     

Temporal evolution of innovation and residual statistics in the ECMWF variational data assimilation systems

The temporal evolution of innovation and residual statistics of the ECMWF 3D‐ and 4D‐Var data assimilation systems have been studied. First, the observational method is applied on an hourly basis to the innovation sequences in order to partition the perceived forecast error covariance into contributions from observation and background errors. The 4D‐Var background turns out to be ignificantly more accurate than the background in the 3D‐Var. The estimated forecast error variance associated with the 4D‐Var background trajectory increases over the assimilation window. There is also a marked broadening of the horizontal error covariance length scale over the assimilation window. Second, the standard deviation of the residuals, i.e., the fit of observations to the analysis is studied on an hourly basis over the assimilation window. This fit should, in theory, reveal the effect of model error in a strong constraint variational problem. A weakly convex curve is found for this fit implying that the perfect model assumption of 4D‐Var may be violated with as short an assimilation window as six hours. For improving the optimality of variational data assimilation systems, a sequence of retunes are needed, until the specified and diagnosed error covariances agree.     

基于无结构网格有限体积法的风暴潮数值预报模式

基于无结构三角单元网格和有限体积法,建立了一个高精度高分辨率的风暴潮二维数值预报模式。该模式采用对岸线有较强拟合能力的无结构网格对求解区域进行离散,采用藤田公式和宫崎正卫风场模式模拟气压场和风场。由于台风暴潮在近岸地区受底部地形的影响,可能引起非线性较强的波动,从而产生陡度大的波面,因此模式中利用Roe的通量函数给出守恒方程的无粘性通量。针对复杂的海底地形,对模式专门进行了通量梯度项与源项的平衡。应用此模型模拟和预报珠江口地区的风暴潮增水,取得了较满意的结果。     

Forecasting ocean waves: Comparing a physics-based model with statistical models

The literature on ocean wave forecasting falls into two categories, physics-based models and statistical methods. Since these two approaches have evolved independently, it is of interest to determine which approach can predict more accurately, and over what time horizons. This paper runs a comparative analysis of a well-known physics-based model for simulating waves near shore, SWAN, and two statistical techniques, time-varying parameter regression and a frequency domain algorithm. Forecasts are run for the significant wave height, over horizons ranging from the current period (i.e., the analysis time) to 15 h. Seven data sets, four from the Pacific Ocean and three from the Gulf of Mexico, are used to evaluate the forecasts. The statistical models do extremely well at short horizons, producing more accurate forecasts in the 1–5 hour range. The SWAN model is superior at longer horizons. The crossover point, at which the forecast error from the two methods converges, is in the area of 6 h. Based on these results, the choice of statistical versus physics-based models will depend on the uses to which the forecasts will be put. Utilities operating wave farms, which need to forecast at very short horizons, may prefer statistical techniques. Navies or shipping companies interested in oceanic conditions over longer horizons will prefer physics-based models.     

孟加拉湾海域背景流–中尺度涡–高频扰动之间的相互作用

基于一套涡分辨模式数据,本文利用一种新的泛函工具—多尺度子空间变换—将孟加拉湾（BOB）海域的环流系统分解到背景流（>96 d）、中尺度（24～96 d）和高频尺度（<24 d）3个子空间,并用正则传输理论探讨了3个尺度子空间之间内在的非线性相互作用。结果表明,BOB西北部边界和斯里兰卡岛东部是BOB海域多尺度相互作用最显著的区域,中部则较弱。前两个区域的背景流大多正压、斜压不稳定,动能和有效位能正则传输主要表现为正向级串;后者则以逆尺度动能级串为主。具体来说,在BOB西北部与斯里兰卡东部,中尺度涡动能（EKE）主要来源于正压能量路径（即背景流动能向EKE传输）,其次来源于斜压能量路径（即背景流有效位能向中尺度有效位能传输,并进一步转换为EKE）。通过这两个能量路径得到的EKE向更高频的扰动传输能量,起到了耗散中尺度涡的作用。不同于此二者,BOB中部海域的EKE和高频尺度动能主要通过斜压路径获得,随后通过逆尺度级串将动能返还给背景流。苏门答腊岛的西北部也是中尺度和高频尺度扰动较强的海域,正压能量路径和斜压能量路径均是该海域扰动能的来源,但以斜压能量路径为主。     

Heavy metal removal efficiencies in a river–marsh system estimated from patterns of metal accumulation in sediments

Estuaries have long been thought to be effective traps for river-borne contaminants; however, accurately predicting removal efficiencies remains problematic. In the Quinnipiac River, CT, marsh system, patterns of metal accumulation (Ag, Cd, Cu, Pb) in sediments were used to estimate heavy metal removal efficiencies. Linear and multivariate regression models were fit to sediment metal concentrations to estimate removal curves and surfaces, which avoided the large temporal variability commonly encountered when using direct water column measurements. Second order regressions normalized to the shortest distance to the river channel were found to have the best fit (r>0.67) with the lowest standard error (<32%). The heavy metal removal efficiencies estimated by comparing total metal accumulation in marsh sediments with riverine flux were Ag=21%, Cd=6%, Cu=14%, and Pb=17%, which are comparable to the maximum removal efficiency of riverine suspended particulate matter (28%).     

Mathematical Models for Combined Refraction-Diffraction of Waves on Non-Uniform Current and Depth

Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given.     

A Dynamical Statistical Model for Prediction of a Tropical Cyclone

A dynamical statistical method is applied for operational forecasting of the Bay of Bengal tropical cyclone “Nargis” of April–May 2008. The method consists of three forecast components, namely (a) analysis of Genesis Potential Parameter (GPP) and maximum potential intensity, (b) track prediction, and (c) 12 hourly intensity prediction for forecasts up to 72 hours. The results of the study showed that GPP could provide necessary predictive signal at early stages of development on the further intensification of the low pressure system into a tropical cyclone. The landfall forecast position errors by different operational numerical models (NWP) showed landfall position errors ranging from 10 km to 150 km and landfall time error ranges from 6 hours early to 6 hours delay. The dynamical statistical model is capable to provide 12 hourly nearly realistic intensity forecasts up to 60 hours of forecast.     

Role of the metric in forecast error growth: how chaotic is the weather?

The atmosphere is often cited as an archetypal example of a chaotic system, where prediction is limited by the model's sensitivity to initial conditions. Experiments have indeed shown that forecast errors, as measured in 500 hPa heights, can double in 1.5 d or less. Recent work, however, has shown that, when errors are measured in total energy, model error is the primary contributor to forecast inaccuracy. In this paper we attempt to reconcile these apparently conflicting sets of results by examining the role of the chosen metric. Using a simple medium-dimensional model for illustration, it is found that the metric has a strong effect, not just on apparent error growth, but on the perceived causes of error. If an insufficiently global metric is used, then it may appear that error is due to sensitivity to initial condition, when in fact it is caused by sensitivity to error in the other variables. If the goal is to diagnose the causes of error, a sufficiently global metric must be used. The simple model is used to predict the internal rate of growth of the ECMWF operational model, and preliminary results compared. It is found that both 500 hPa and total energy results are consistent with high model error and a relatively low internal rate of growth. Experiments are suggested to further verify the results for weather models.     

Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): Development and application for a baroclinic coastal upwelling system

We describe the development and preliminary application of the inverse Regional Ocean Modeling System (ROMS), a four dimensional variational (4DVAR) data assimilation system for high-resolution basin-wide and coastal oceanic flows. Inverse ROMS makes use of the recently developed perturbation tangent linear (TL), representer tangent linear (RP) and adjoint (AD) models to implement an indirect representer-based generalized inverse modeling system. This modeling framework is modular. The TL, RP and AD models are used as stand-alone sub-models within the Inverse Ocean Modeling (IOM) system described in [Chua, B.S., Bennett, A.F., 2001. An inverse ocean modeling system. Ocean Modell. 3, 137–165.]. The system allows the assimilation of a wide range of observation types and uses an iterative algorithm to solve nonlinear assimilation problems. The assimilation is performed either under the perfect model assumption (strong constraint) or by also allowing for errors in the model dynamics (weak constraints). For the weak constraint case the TL and RP models are modified to include additional forcing terms on the right hand side of the model equations. These terms are needed to account for errors in the model dynamics.Inverse ROMS is tested in a realistic 3D baroclinic upwelling system with complex bottom topography, characterized by strong mesoscale eddy variability. We assimilate synthetic data for upper ocean (0–450 m) temperatures and currents over a period of 10 days using both a high resolution and a spatially and temporally aliased sampling array. During the assimilation period the flow field undergoes substantial changes from the initial state. This allows the inverse solution to extract the dynamically active information from the synthetic observations and improve the trajectory of the model state beyond the assimilation window. Both the strong and weak constraint assimilation experiments show forecast skill greater than persistence and climatology during the 10–20 days after the last observation is assimilated.Further investigation in the functional form of the model error covariance and in the use of the representer tangent linear model may lead to improvement in the forecast skill.     

Learning from data for wind-wave forecasting

Along with existing numerical process models describing the wind-wave interaction, the relatively recent development in the area of machine learning make the so-called data-driven models more and more popular. This paper presents a number of data-driven models for wind-wave process at the Caspian Sea. The problem associated with these models is to forecast significant wave heights for several hours ahead using buoy measurements. Models are based on artificial neural network (ANN) and instance-based learning (IBL) .To capture the wind-wave relationship at measurement sites, these models use the existing past time data describing the phenomenon in question. Three feed-forward ANN models have been built for time horizon of 1, 3 and 6 h with different inputs. The relevant inputs are selected by analyzing the average mutual information (AMI). The inputs consist of priori knowledge of wind and significant wave height. The other six models are based on IBL method for the same forecast horizons. Weighted k-nearest neighbors (k-NN) and locally weighted regression (LWR) with Gaussian kernel were used. In IBL-based models, forecast is made directly by combining instances from the training data that are close (in the input space) to the new incoming input vector. These methods are applied to two sets of data at the Caspian Sea. Experiments show that the ANNs yield slightly better agreement with the measured data than IBL. ANNs can also predict extreme wave conditions better than the other existing methods.     

单纯形投影算子理论及在资料分析中的应用 Ⅰ.在方程模型资料预测中的应用

本文根据混沌系统奇怪吸引子在相空间中的伸缩和折叠的几何特征,建立了单纯形投影算子（simplexprojectionoperator）预测方法．该方法主要侧重考虑了被预测点的局部非线性特征及Lyapunov特征指数,避免了传统预测函数和方程的模拟问题,减少了模拟参量．对Lorenz方程和Logistic映射资料进行预测分析的结果表明,此方法简单易行,缩短了计算时间,在预测时问尺度及精度上具有较强的预测能力．     

The hydroacoustic method for the quantification of the gas flux from a submersed bubble plume

This article presents an inverse hydroacoustic method for the remote quantification of the total gas flux transported from an underwater bubble plume. The method includes the surveying of the bubble plume by a vertically looking echo sounder and the calculation of the flux using the spatial distribution of the ultrasound backscattering at a fixed depth. A simplified parameterization containing only a few parameters is introduced to describe the empirical bubble size distribution. The linear correlation between the backscattering cross section of the bubble stream and the vertical gas flux is found. The calculation procedure takes into account the occurrence of a gas hydrate film at the bubble’s surface. The influence of different parameters on the accuracy of the method is investigated. The resolution volume of the echo sounder corresponding to the fixed distance is considered as a two-dimensional spatial window. The method was applied to quantify the total convective methane flux at the Haakon-Mosby mud volcano (HMMV) depth 1280 m. The calculated values of the total flux near the bottom (100–400 t/year) are in good agreement with the independently estimated flux for the single bubble jet observed from the ROV (70 t/year). These calculations also show significant temporal variability of the flux at the HMMV. The total flux was found to vary by about a factor of 2–3 within time scales of days.     

High resolution downscaled ocean waves (DOW) reanalysis in coastal areas

Large-scale wave reanalysis databases (0.1°–1° spatial resolution) provide valuable information for wave climate research and ocean applications which require long-term time series (> 20 years) of hourly sea state parameters. However, coastal studies need a more detailed spatial resolution (50–500 m) including wave transformation processes in shallow waters. This specific problem, called downscaling, is usually solved applying a dynamical approach by means of numerical wave propagation models requiring a high computational time effort. Besides, the use of atmospheric reanalysis and wave generation and propagation numerical models introduce some uncertainties and errors that must be dealt with. In this work, we present a global framework to downscale wave reanalysis to coastal areas, taking into account the correction of open sea significant wave height (directional calibration) and drastically reducing the CPU time effort (about 1000 ×) by using a hybrid methodology which combines numerical models (dynamical downscaling) and mathematical tools (statistical downscaling). The spatial wave variability along the boundaries of the propagation domain and the simultaneous wind fields are taking into account in the numerical propagations to performance similarly to the dynamical downscaling approach. The principal component analysis is applied to the model forcings to reduce the data dimension simplifying the selection of a subset of numerical simulations and the definition of the wave transfer function which incorporates the dependency of the wave spatial variability and the non-uniform wind forcings. The methodology has been tested in a case study on the northern coast of Spain and validated using shallow water buoys, confirming a good reproduction of the hourly time series structure and the different statistical parameters.     

Climate-based Monte Carlo simulation of trivariate sea states

Accurate wave climate characterization, which is vital to understand wave-driven coastal processes and to design coastal and offshore structures, requires the availability of long term data series. Where existing data are sparse, synthetically generated time series offer a practical alternative. The main purpose of this paper is to propose a methodology to simulate multivariate hourly sea state time series that preserve the statistical characteristics of the existing empirical data. This methodology combines different techniques such as univariate ARMAs, autoregressive logistic regression and K-means clusterization algorithms, and is able to take into account different time and space scales. The proposed methodology can be broken down into three interrelated steps: i) simulation of sea level pressure fields, ii) simulation of daily mean sea conditions time series and iii) simulation of hourly sea state time series. Its effectiveness is demonstrated by synthetically generating multivariate hourly sea states from a specific location near the Spanish Coast. The direct comparison between simulated and empirical time series confirms the ability of the developed methodology to generate multivariate hourly time series of sea states. Finally, the potential of the proposed methodology to simulate multivariate time series at multiple locations and incorporate climate change issues is discussed.     

黄、渤海冷空气海浪场的集合预报试验

利用欧洲集合天气预报系统51个预报风场驱动SWAN海浪模式,对黄、渤海2013年12月-2014年2月期间受冷空气影响的海浪场进行数值模拟试验,并利用浮标观测资料对海浪集合预报结果进行初步检验分析,结果显示:从逐时平均偏差结果可知,24h预报时效内集合平均与控制预报性能相近,48~72h预报时效内,集合平均明显优于控制预报,但均比实况偏小;集合分位值(75、90百分位值和极端值)明显优于集合平均,且预报时效越长,优势越明显,集合预报极端值与实况相当或略偏大;从逐24h平均偏差结果可知,集合分位值(75、90百分位值和极端值)比集合平均和控制预报更接近实况。总的分析表明:集合分位值(75、90百分位值和极端值)对受冷空气影响的海浪场具有较强的分辨能力,可以提高对海浪场的预报水平,且有较好的应用潜力。     

Methodology for estimation of river discharge and application of the Zhujiang River Estuary(ZRE)

The ZRE is a very complicated estuary with multi-river inlets. The total sum of river discharge in the upstream(away from the tidal influence region) of the Zhujiang River can be easily measured. However, when the total river discharges into the estuary from eight inlets, it is a very difficult task to obtain a continuous river discharge flux data from each branch of the Zhujiang River. However, the different ratios of river discharges between the river branches can significantly affect the estuarine circulation feature and baroclinic process. Moreover, the accuracy of numerical forecast for the estuarine circulation is very much dependent on the accuracy of the time history of the river discharge flux for each branch. Therefore, it is important to estimate river discharge from each branch in order to improve the accuracy of the model forecast for the circulation of the ZRE. The development of a new estimation method of the river discharges is focused on based on the system identification theory, numerical modeling and the time history data from the CODAR observed sea surface current. The new approach has been appfied to estimating the time history (hourly) of river discharge from each branch in the upstream of the ZRE.     

基于机器学习的内孤立波波要素关系研究

内孤立波在海洋中的传播会携带能量和动量,不同振幅的内孤立波对海洋中的能量交换及海上工程等影响也不同,因此,研究内孤立波振幅与半波宽度、水深、分层条件、密度等水文特征参量之间的关系显得尤为重要.以往在研究中建立内孤立波振幅与它们之间的关系时,会受到不同理论有效适用范围的限制.本文借助实验室的水槽方法,设计了不同的水深、分...     

Oceanic response to atmospheric forcing derived from different climatic data sets. Intercomparison study for the Black Sea

Available climatic and atmospheric analysis data have been used to prepare forcing functions for the Black Sea numerical model, based on the Bryan-Semtner-Cox Modular Ocean Model and including parameterizations for the atmosphere-ocean exchange, inflow through the strait of Bosphorus and the Mediterranean plume. Atmospheric data from different sources are compared and the drawbacks of some of them illustrated. A new wind stress data set, based on ship observations, is prepared. Compared to the existing wind stress estimates, the present ones use additional data and more accurate parameterization of the boundary layer physics. The intercomparison between forcing data sets is focused on the heat flux and freshwater flux at the sea surface.The model simulates adequately vertical stratification, seasonal variability and horizontal patterns. Five data sets for heat flux, freshwater flux and wind stress are used in different combinations to study the model response. The large differences between the simulations, forced by different wind stress and identical thermohaline forcing, justify the computation of the new wind stress. Though the forcing data used are perhaps close to the best available at the moment for the Black Sea, the model simulations range in large intervals and some of them are very poor. The model responses to forcing functions of different origin give rough estimates on the possible errors in present-day simulations. Some inconsistencies give clear indications that further verifications, improvements of the forcing functions, and intercomparisons between the responses simulated by the ocean circulation models are needed.     

运用混合回归模型预报赤潮

通过先行建立每个影响因子的非线性回归模型,然后作总体线性回归,首次给出了用混合回归模型预报赤潮的方法。这样就改进了现有的用多元线性回归模型进行赤潮预报的方法,提高了赤潮预报的准确性。