An application of the A-4DEnVar to coupled parameter optimization

In variational methods, coupled parameter optimization (CPO) often needs a long minimization time window (MTW) to fully incorporate observational information, but the optimal MTW somehow depends on the model nonlinearity. The analytical four-dimensional ensemble-variational (A-4DEnVar) considers model nonlinearity well and avoids adjoint model. It can theoretically be applied to CPO. To verify the feasibility and the ability of the A-4DEnVar in CPO, “twin” experiments based on A-4DEnVar CPO are conducted for the first time with the comparison of four-dimensional variational (4D-Var). Two algorithms use the same background error covariance matrix and optimization algorithm to control variates. The experiments are based on a simple coupled ocean-atmosphere model, in which the atmospheric part is the highly nonlinear Lorenz-63 model, and the oceanic part is a slab ocean model. The results show that both A-4DEnVar and 4D-Var can effectively reduce the error of state variables through CPO. Besides, two methods produce almost the same results in most cases when the MTW is less than 560 time steps. The results are similar when the MTW is larger than 560 time steps and less than 880 time steps. The largest MTW of 4D-Var and A-4DEnVar are 1 200 time steps. Moreover, A-4DEnVar is not sensitive to ensemble size when the MTW is less than 720 time steps. A-4DEnVar obtains satisfactory results in the case of highly nonlinear model and long MTW, suggesting that it has the potential to be widely applied to realistic CPO.     

A 4D-variational approach applied to an eddy-permitting North Atlantic configuration: Synthetic and real data assimilation of altimeter observations

The increasing number of oceanic observations calls for the use of synthetic methods to provide consistent analyses of the oceanic variability that will support a better understanding of the underlying mechanisms. In this study, a 1/3° eddy-permitting model of the North Atlantic (from 20°S to 70°N) is combined with a 4D-variational method to estimate the oceanic state from altimeter observations. This resolution allows a better extraction of the physical content of altimeter data since the model spatial scales are more consistent with the data than coarser assimilation exercises because of a lower error in model representativity. Several strategies for the assimilation window are tested through twin experiments carried out under the following conditions: different window lengths and either a quasi-static (also known as progressive) variational assimilation with progressive extension of the window, or a simpler direct method without prior assimilation. From our set of experiments, the most efficient strategy is the use of both a simple direct assimilation method and a 90-day window. The assimilation of synthetic altimeter data constrains the model-temperature, -salinity and -velocity fields mainly over the first 1300 m where the error is the largest. Improvements occur not only in quiescent regions, but also in more energetic meso-scale regimes. Despite the existence of model- and surface forcing-errors as well as large errors in the first guess, the assimilation of real altimeter data proves to be consistent with our twin experiments. Indeed, the analyses show a better detachment of the Gulf Stream, weaker regional biases and more accurate positions for meso-scale structures. Independent hydrographic data (Argo floats and CTD cruises) and transports estimates along the OVIDE 2002 cruise show an improvement of the analysed oceanic state with respect to the assimilation-free case though water mass properties are still incorrectly represented. After assimilation, the North Atlantic heat transport in the model is in good agreement with independent estimates based on hydrographic data.     

EnKF和SIR-PF在贝叶斯滤波框架下的比较和结合

贝叶斯估计理论为非线性、非高斯系统的数据同化提供了一个统一的框架。在本文中,我们利用著名的洛伦茨吸引子(Lorenz'63)模式对两种基于贝叶斯滤波理论的数据同化方法——集合卡尔曼滤波器(EnKF)和重取样粒子滤波器(SIR-PF)——进行了较为全面的比较。比较的结果揭示了两种方法的优缺点:即当集合成员数目较多时,SIR-PF的同化效果优于EnKF;反之,则EnKF的表现较好。进一步地,我们使用统计方法分析了两者表现的差异和原因。最近提出的一种集合卡尔曼粒子滤波器(EnKPF)通过使用一个可控的参数整合EnKF和SIR-PF的分析格式,可以结合两者的优点。本文在充分比较两种方法的前提下,重新阐释并改进了原有的EnKPF算法,使之适用于非线性的观测算子。通过使用相同的洛伦茨模式实验,我们揭示了EnKPF实质上提供了关于EnKF和SIR-PF的连续插值,使得后两者可以视为其特殊情况。并且,在集合成员数目有限的前提下,EnKPF可以在一定程度上避免滤波退化的发生,取得优于EnKF和SIR-PF的同化效果。     

Cycling the representer algorithm for variational data assimilation with a nonlinear reduced gravity ocean model

The representer method was used by [Ngodock, H.E., Jacobs, G.A., Chen, M., 2006. The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: a comparison study using a nonlinear reduced gravity ocean model. Ocean Modelling 12, 378–400] in a comparison study with the ensemble Kalman filter and smoother involving a 1.5 nonlinear reduced gravity idealized ocean model simulating the Loop Current (LC) and the Loop Current eddies (LCE) in the Gulf of Mexico. It was reported that the representer method was more accurate than its ensemble counterparts, yet it had difficulties fitting the data in the last month of the 4-month assimilation window when the data density was significantly decreased. The authors attributed this failure to increased advective nonlinearities in the presence of an eddy shedding causing the tangent linear model (TLM) to become inaccurate. In a separate study [Ngodock, H.E., Smith, S.R., Jacobs, G.A., 2007. Cycling the representer algorithm for variational data assimilation with the Lorenz attractor. Monthly Weather Review 135 (2), 373–386] applied the cycling representer algorithm to the Lorenz attractor and demonstrated that the cycling solution was able to accurately fit the data within each cycle and beyond the range of accuracy of the TLM, once adjustments were made in the early cycles, thus overcoming the difficulties of the non-cycling solution. The cycling algorithm is used here in assimilation experiments with the nonlinear reduced gravity model. It is shown that the cycling solution overcomes the difficulties encountered by the non-cycling solution due to a limited time range of accuracy of the TLM. Thus, for variational assimilation applications where the TLM accuracy is limited in time, the cycling representer becomes a very powerful and attractive alternative, given that its computational cost is significantly lower than that of the non-cycling algorithm.     

Cycling the representer algorithm for variational data assimilation with a nonlinear reduced gravity ocean model

The representer method was used by [Ngodock, H.E., Jacobs, G.A., Chen, M., 2006. The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: a comparison study using a nonlinear reduced gravity ocean model. Ocean Modelling 12, 378–400] in a comparison study with the ensemble Kalman filter and smoother involving a 1.5 nonlinear reduced gravity idealized ocean model simulating the Loop Current (LC) and the Loop Current eddies (LCE) in the Gulf of Mexico. It was reported that the representer method was more accurate than its ensemble counterparts, yet it had difficulties fitting the data in the last month of the 4-month assimilation window when the data density was significantly decreased. The authors attributed this failure to increased advective nonlinearities in the presence of an eddy shedding causing the tangent linear model (TLM) to become inaccurate. In a separate study [Ngodock, H.E., Smith, S.R., Jacobs, G.A., 2007. Cycling the representer algorithm for variational data assimilation with the Lorenz attractor. Monthly Weather Review 135 (2), 373–386] applied the cycling representer algorithm to the Lorenz attractor and demonstrated that the cycling solution was able to accurately fit the data within each cycle and beyond the range of accuracy of the TLM, once adjustments were made in the early cycles, thus overcoming the difficulties of the non-cycling solution. The cycling algorithm is used here in assimilation experiments with the nonlinear reduced gravity model. It is shown that the cycling solution overcomes the difficulties encountered by the non-cycling solution due to a limited time range of accuracy of the TLM. Thus, for variational assimilation applications where the TLM accuracy is limited in time, the cycling representer becomes a very powerful and attractive alternative, given that its computational cost is significantly lower than that of the non-cycling algorithm.     

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.     

Assimilation of surface currents into a regionalmodel over Qingdao coastal waters of China

Surface currents measured by high frequency （HF） radar arrays are assimilated into a regional ocean model over Qingdao coastal waters based on Kalman filter method. A series of numerical experiments are per- formed to evaluate the performance of the data assimilation schemes. In order to optimize the analysis pro- cedure in the traditional ensemble Kalman filter （ENKF）, a different analysis scheme called quasiensemble Kaman filter （QENKF） is proposed. The comparisons between the ENKF and the QENKF suggest that both them can improve the simulated error and the spatial structure. The estimations of the background error covariance （BEC） are also assessed by comparing three different methods： Monte Carlo method; Canadian quick covariance （CQC） method and data uncertainty engine （DUE） method. A significant reduction of the root-mean-square （RMS） errors between model results and the observations shows that the CQC method is able to better reproduce the error statistics for this coastal ocean model and the corresponding external forcing. In addition, the sensibility of the data assimilation system to the ensemble size is also analyzed by means of different scales of the ensemble size used in the experiments. It is found that given the balance of the computational cost and the forecasting accuracy, the ensemble size of 50 will be an appropriate choice in the Qingdao coastal waters.     

一个基于GPU并行加速的海啸数值模型

地震海啸通常发生在大洋板块向陆地板块俯冲的区域,距离震源最近的国家和地区往往在震后5～20 min之内就会遭受到海啸袭击。因此,及时的海啸预警和准确的海啸预报结果对于民众和决策者都至关重要。为了提升海啸预警效率,缩短海啸预报时间,本研究对COMCOT海啸数值模型进行了基于图形计算单元GPU的二次并行开发。将原模型中海啸传播计算模块通过CUDA＿C语言编写内核函数整体移植到GPU上并行加速,CPU负责模型其他代码的执行。为了减少CPU和GPU之间的数据通信,将吸收边界和变量更新函数一并改写。仅在需要输出的时间节点,GPU向CPU传递结果,其他时间步长,CPU和GPU之间只有指令和少量参数传输,基本可视为零耗时。基于GPU并行加速的COMCOT较串行版本效率提升超过67倍,加速性能显著优于基于CPU共享内存的OpenMP并行版本。交叉使用常水深和真实地形,采用均匀滑移海啸源和有限元海啸源对模型的计算结果进行了较为全面的分析检验,相对误差最大不超过1%,为大范围的越洋海啸实时计算提供了有力工具。     

A synthetic aperture radar sea surface distribution estimation by n-order Bézier curve and its application in ship detection

To dates,most ship detection approaches for single-pol synthetic aperture radar(SAR) imagery try to ensure a constant false-alarm rate(CFAR).A high performance ship detector relies on two key components:an accurate estimation to a sea surface distribution and a fine designed CFAR algorithm.First,a novel nonparametric sea surface distribution estimation method is developed based on n-order Bézier curve.To estimate the sea surface distribution using n-order Bézier curve,an explicit analytical solution is derived based on a least square optimization,and the optimal selection also is presented to two essential parameters,the order n of Bézier curve and the number m of sample points.Next,to validate the ship detection performance of the estimated sea surface distribution,the estimated sea surface distribution by n-order Bézier curve is combined with a cell averaging CFAR(CA-CFAR).To eliminate the possible interfering ship targets in background window,an improved automatic censoring method is applied.Comprehensive experiments prove that in terms of sea surface estimation performance,the proposed method is as good as a traditional nonparametric Parzen window kernel method,and in most cases,outperforms two widely used parametric methods,K and G0 models.In terms of computation speed,a major advantage of the proposed estimation method is the time consuming only depended on the number m of sample points while independent of imagery size,which makes it can achieve a significant speed improvement to the Parzen window kernel method,and in some cases,it is even faster than two parametric methods.In terms of ship detection performance,the experiments show that the ship detector which constructed by the proposed sea surface distribution model and the given CA-CFAR algorithm has wide adaptability to different SAR sensors,resolutions and sea surface homogeneities and obtains a leading performance on the test dataset.     

Sensitivity analysis of the climate of a chaotic system

This paper addresses some fundamental methodological issues concerning the sensitivity analysis of chaotic geophysical systems. We show, using the Lorenz system as an example, that a naïve approach to variational ("adjoint") sensitivity analysis is of limited utility. Applied to trajectories which are long relative to the predictability time scales of the system, cumulative error growth means that adjoint results diverge exponentially from the "macroscopic climate sensitivity"(that is, the sensitivity of time‐averaged properties of the system to finite‐amplitude perturbations). This problem occurs even for time‐averaged quantities and given infinite computing resources. Alternatively, applied to very short trajectories, the adjoint provides an incorrect estimate of the sensitivity, even if averaged over large numbers of initial conditions, because a finite time scale is required for the model climate to respond fully to certain perturbations. In the Lorenz (1963) system, an intermediate time scale is found on which an ensemble of adjoint gradients can give a reasonably accurate (O(10%)) estimate of the macroscopic climate sensitivity. While this ensemble‐adjoint approach is unlikely to be reliable for more complex systems, it may provide useful guidance in identifying important parameter‐combinations to be explored further through direct finite‐amplitude perturbations.     

Qualitative and Quantitative Description of Multibeam Echosounder Systematic Errors on Rocky Areas

This paper deals with the problem of systematic depth errors made in surveying dumped rocks with multibeam echosounder. These errors may induce dangers for navigation in very shallow water areas or huge costs for coastal engineering contractors who perform rock dumping operation and surveying. We analyze results from four different multibeam echosounder systems and compare those data to a reference digital terrain model of a dumped rocks area obtained from a 3D terrestrial laser scanner. The systematic depth errors are statistically described and analysed on local areas. Finally, we propose a look-up table linking the error amplitude with the rock size, resulting from our error analysis.     

Spatially and temporally varying adaptive covariance inflation for ensemble filters

Ensemble filters are used in many data assimilation applications in geophysics. Basic implementations of ensemble filters are trivial but are susceptible to errors from many sources. Model error, sampling error and fundamental inconsistencies between the filter assumptions and reality combine to produce assimilations that are suboptimal or suffer from filter divergence. Several auxiliary algorithms have been developed to help filters tolerate these errors. For instance, covariance inflation combats the tendency of ensembles to have insufficient variance by increasing the variance during the assimilation. The amount of inflation is usually determined by trial and error. It is possible, however, to design Bayesian algorithms that determine the inflation adaptively. A spatially and temporally varying adaptive inflation algorithm is described. A normally distributed inflation random variable is associated with each element of the model state vector. Adaptive inflation is demonstrated in two low-order model experiments. In the first, the dominant error source is small ensemble sampling error. In the second, the model error is dominant. The adaptive inflation assimilations have better mean and variance estimates than other inflation methods.     

基于VMD和WinLSP相结合的GNSS-R海平面高度估测模型

全球导航卫星系统反射（Global Navigation Satellite System-Reflectometry,GNSS-R）技术是一种新兴的监测海平面高度变化的技术。本文依据GNSS-R技术中的信噪比分析法的原理,通过分析其分离趋势项和提取振荡频率的过程,建立了新的估测模型以提高反演精度。针对传统模型存在的信号分离不佳的问题,本文提出使用变分模态分解（Variational Mode Decomposition,VMD）算法替换传统的最小二乘拟合法（Least Squares Fitting, LSF）进行趋势项分量的分离。在此基础上,本文引入基于凯塞窗函数改进的LSP(Lomb-Scargle Periodogram)频谱分析法（记为WinLSP）来减弱因频谱泄露带来的反演误差。在瑞典翁萨拉的GTGU站和美国阿拉斯加州的SC02站开展的海平面高度反演实验结果表明,本文建立的估测模型相比于传统模型具有更高的反演精度。基于VMD+WinLSP估测模型得到的GTGU站反演结果的均方根误差（RMSE）、相关系数和反演点数分别为4.70 cm、0.98和5 647。与传统的LSF+L...     

A general equation for performance analysis of multi-component propulsor with propeller

An integral panel method (IPM) that treats the different components of multi-component propulsors as a whole is presented for efficient propulsor performance analysis. The IPM requires consider only one blade of the propeller in the performance analysis, which significantly reduces the number of computation grid. The control equations of the IPM are derived in detail for podded propulsors, contra-rotating propellers and hybrid contra-rotating shaft pod propulsors, and based on these derivations, a general control equation for multi-component propulsors with propeller is derived. Comparison between numerical results and experimental data show that the IPM provides good accuracy for the performance analysis of multi-component propulsors with propeller. In addition, the error sources of IPM are discussed, and the reasonableness of these errors is evaluated.     

State-dependent Riccati equation-based robust dive plane control of AUV with control constraints

The paper treats the question of suboptimal dive plane control of autonomous underwater vehicles (AUVs) using the state-dependent Riccati equation (SDRE) technique. The SDRE method provides an effective mean of designing nonlinear control systems for minimum as well as nonminimum phase AUV models. It is assumed that the hydrodynamic parameters of the nonlinear vehicle model are imprecisely known, and in order to obtain a practical design, a hard constraint on control fin deflection is imposed. The problem of depth control is treated as a robust nonlinear output (depth) regulation problem with constant disturbance and reference exogenous signals. As such an internal model of first-order fed by the tracking error is constructed. A quadratic performance index is chosen for optimization and the algebraic Riccati equation is solved to obtain a suboptimal control law for the model with unconstrained input. For the design of model with fin angle constraints, a slack variable is introduced to transform the constrained control input problem into an unconstrained problem, and a suboptimal control law is designed for the augmented system using a modified performance index. Using the center manifold theorem, it is shown that in the closed-loop system, the system trajectories are regulated to a manifold (called output zeroing manifold) on which the depth tracking error is zero and the equilibrium state is asymptotically stable. Simulation results are presented which show that effective depth control is accomplished in spite of the uncertainties in the system parameters and control fin deflection constraints.     

长江口表层沉积物重矿物在不同粒级中的分布与研究意义

在粒度分析基础上,以0.5Φ为间距对长江口表层沉积物的不同粒级分样进行碎屑重矿物分析,并对各粒级重矿物特征与广粒级(1.5Φ～6Φ)进行相似度分析。结果表明,长江口沉积物粒度跨度大,从粗砂到泥(黏土)均有分布,粉砂含量高。样内不同粒级分样重矿物含量、种类和组合均有一定变化,样间表现出较一致的规律性。长江口出现碎屑重矿物30种左右,粗粒级分样中矿物种数为10余种,细粒级分样中重矿物种类增至20多种;3.5Φ～4.5Φ是重矿物种类多、矿物成分复杂的粒级区段。粗粒级(粒径大于3Φ)云母族富集,其重矿物组合为云母+角闪石,随粒级变细(粒径小于4Φ)云母急剧减少;闪石族分布粒级广泛,在3Φ～5Φ粒级含量相对较高;帘石族、稳定矿物尤其是金属矿物在粒径小于3.5Φ粒级逐渐增多。长江口重矿物整体组合为普通角闪石+绿帘石+褐铁矿,榍石为特征矿物。相似度分析表明,长江口沉积物样品中主要粒级与广粒级重矿物特征相近,能代表沉积物整体重矿物特征。长江口碎屑重矿物特征深受粒度分布的影响,其矿物种类、矿物组合和矿物指数及其所蕴含的水动力和物源意义都要结合粒度特征来综合分析。     

A Numerical Model for Typhoon Surges

-In this paper a simple and efficient implicit finite-difference scheme is used for depth-averagedtwo-dimensional storm surge model.This finite-difference scheme is simpler and more efficient than the wi-dely-used ADI scheme.Accuracy analysis and stability analysis indicate that the scheme has two-order ac-curacy and is unconditionally stable when the grid size is constant.The present analysis results show thatthe scheme is of higher numerical accuracy than that introduced by Maa(1990).After tested by ideal mod-els,a calculation example of a real typhoon surge is carried out,the results of the numerical simulation co-incide well with the observed data and the accuracy is sufficient for engineering applications.     

混沌系统的变结构同步控制

研究Lorenz混沌系统的同步控制问题,提出1种在多输入的情况下实现混沌同步的变结构控制算法.利用该算法设计的变结构同步控制律使得同步误差系统的运动在切换面上成为渐近稳定的滑动模态,从而较快的实现了混沌同步.通过对 Lorenz 混沌系统的理论分析和数值仿真,说明了该变结构同步控制策略的实用性和有效性.     

海底剖面声阻抗分布声遥测模拟实验研究

本文介绍一种声遥测海底平面层系声阻抗分布的模拟实验结果。实验在油漆厂冷却水池中进行,采用取样平均迭代的反演方法,对三介质层系的遥测结果与实测值较好地接近。     

Assimilation of temperature and salinity using isotropic and anisotropic recursive filters in Tropic Pacific

A data assimilation scheme used in the updated Ocean three-dimensional Variational Assimilation System (OVALS),OVALS2,is described.Based on a recursive filter (RF) to estimate the background error covariance (BEC) over a predetermined scale,this new analysis system can be implemented with anisotropic and isotropic BECs.Similarities and differences of these two BEC schemes are briefly discussed and their impacts on the model simulation are also investigated.An idealized experiment demonstrates the ability of the updated analysis system to construct different BECs.Furthermore,a set of three years experiments is implemented by assimilating expendable bathythermograph (XBT) and ARGO data into a Tropical Pacific circulation model.The TAO and WOA01 data are used to validate the assimilation results.The results show that the model simulations are substantially improved by OVALS2.The inter-comparison of isotropic and anisotropic BEC shows that the corresponding temperature and salinity produced by the anisotropic BEC are almost as good as those obtained by the isotropic one.Moreover,the result of anisotropic RF is slightly closer to WOA01 and TAO than that of isotropic RF in some special area (e.g.the cold tongue area in the Tropic Pacific).