On the nudging terms at open boundaries in regional ocean models

For open boundary conditions (OBCs) in regional models, a nudging term added to radiative and/or advective conditions during the wave or flow propagation outward from the model domain of interest is widely used, to prevent the predicted boundary values from evolving to become quite different from the external data, especially for a long-term integration. However, nudging time scales are basically unknown, leading to many empirical selections. In this paper, a method for objectively estimating nudging time scales during outward propagation is proposed, by using internal model dynamics near the boundary. We tested this method and other several commonly used OBCs for cases of both an idealized model domain and a realistic configuration, and model results demonstrated that the proposed method improves the model solutions. Many similarities are found between the nudging and mixing time scales, in magnitude, spatial and temporal variations, since the nudging mainly replaces the effect of the mixing terms in this study. However, the mixing time scale is not an intrinsic property of the nudging term because in other studies the nudging term might replace terms other than the mixing terms and, thus, should reflect other characteristic time scales.     

潮流物理模型试验生潮控制时的复合模拟数据对接

根据几种不同情形探讨复合模拟中如何通过数值模拟为潮流物模试验提供开边界控制条件。对单边界物理模型,可由数模的调和常数得到物模边界控制所需的时间序列数据,实现单分潮、多分潮及大、中、小潮的模拟;对于历时较长的试验,可由数模得到长时间序列或周期性序列数据作为生潮的控制信号;对多边界模型,沿边界分为若干控制断面,由数模给出各断面的流量变化,对各断面分别进行流量控制;差时的复合模拟可使物理模型和数值模型互相提供边界条件或模型参数修正。     

A diagnostic stabilized finite-element ocean circulation model

A stabilized finite-element (FE) algorithm for the solution of oceanic large scale circulation equations and optimization of the solutions is presented. Pseudo-residual-free bubble function (RFBF) stabilization technique is utilized to enforce robustness of the numerics and override limitations imposed by the Babuška–Brezzi condition on the choice of functional spaces. The numerical scheme is formulated on an unstructured tetrahedral 3d grid in velocity–pressure variables defined as piecewise linear continuous functions. The model is equipped with a standard variational data assimilation scheme, capable to perform optimization of the solutions with respect to open lateral boundary conditions and external forcing imposed at the ocean surface. We demonstrate the model performance in applications to idealized and realistic basin-scale flows. Using the adjoint method, the code is tested against a synthetic climatological data set for the South Atlantic ocean which includes hydrology, fluxes at the ocean surface and satellite altimetry. The optimized solution proves to be consistent with all these data sets, fitting them within the error bars.The presented diagnostic tool retains the advantages of existing FE ocean circulation models and in addition (1) improves resolution of the bottom boundary layer due to employment of the 3d tetrahedral elements; (2) enforces numerical robustness through utilization of the RFBF stabilization, and (3) provides an opportunity to optimize the solutions by means of 3d variational data assimilation. Numerical efficiency of the code makes this a desirable tool for dynamically constrained analyses of large datasets.     

基于方向信息约束的遥感平台强跟踪定位算法

为了提高机载遥感平台在应对气流抖动和外界强干扰时的定位性能,在加速度自适应截断正态分布的基础上,通过Lagrange乘子法将速度方向信息约束到强跟踪滤波中,得到了基于方向信息约束的强跟踪定位算法。仿真表明:该算法通过在线控制使输出残差强制近似正交,充分利用了方向约束信息。与一般的强跟踪算法相比较,在提高定位精度的同时可及时响应空中机动,较好地解决了机载遥感平台在强机动干扰条件下的跟踪定位问题。     

一般曲线坐标系下波浪传播的数值模拟

在曲线坐标系下,建立了缓变水深水域波浪传播的数值模拟模型.模型适宜于复杂变化的边界形状,克服了各种代数坐标变换的局限性.在建立模型时,将原始的椭圆型缓坡方程的近似型式——依赖时间变化的抛物型方程,作为控制方程,既克服了一般抛物近似方法的缺点,又便利了方程的求解;从开边界条件、不同反射特性的固壁边界条件相统一的表达式出发,对边界条件进行处理;用ADI法数值求解控制方程.对模型的验证表明,数值解与物模实验值吻合良好,模型对于具有复杂边界的工程实际有较强的适应性.     

A pretty good sponge: Dealing with open boundaries in limited-area ocean models

The problem of computing within a limited domain surrounded by open boundaries is discussed within the context of the shallow-water wave equations by comparing three different treatments, all of which surround the domain by absorbing zones intended to prevent reflections of outgoing waves. The first, which has attracted a lot of attention for use in electromagnetic and aeroacoustic applications, is intended to prevent all reflections. However, it has not yet been developed to handle the second important requirement of open boundaries, namely the ability to pass information about external conditions into the domain of interest. The other two treatments, which absorb differences from a specified external solution, allow information to pass through the open boundary in both directions. One, based on the flow relaxation scheme of [Martinsen, E.A., Engedahl, H., 1987. Implementation and testing of a lateral boundary scheme as an open-boundary condition in a barotropic ocean model. Coastal Eng. 11, 603–627] and termed here the “simple sponge,” relaxes all fields toward their external counterparts. The other, a simplification and generalization of the perfectly matched layer, referred to here as the “pretty good sponge,” avoids absorbing the component of momentum parallel to the open boundary. Comparisons for a case that is dominated by outgoing waves shows the pretty good sponge to perform essentially as well as the perfectly matched layer and better than the simple sponge. In comparisons for a geostrophically balanced eddy passing through open boundaries, the pretty good sponge out-performed the simple sponge when the only external information available was about the advecting flow, but when information about the nature of the eddy in the sponge zones was also available, the simple sponge performed better. For the case of an equatorial soliton passing through the boundary and no information provided about its nature outside the open domain, again the pretty good sponge performed better. Proving useful for situations governed by nonlinear equations forced by external conditions and being easy to implement, the pretty good sponge should be considered for use with existing limited-area ocean models.     

海洋表层温度对台风"蔷薇"路径和强度预测精度的影响

基于中尺度大气模式WRF(Weather Research and Forecasting Model),首先对2007年3次船舶辐射通量观测进行模拟,以检验WRF对长波和短波辐射通量的模拟能力,结果表明使用中国近海海洋环境数值预报系统环流模式POM(Princeton Ocean Model)模拟的高时空分辨率的海洋表层温度能够显著改进短波辐射通量的模拟,而对长波辐射通量模拟的改进不明显。然后,将业务化运行的中国近海海洋环境数值预报系统后报的逐时海洋表面温度(SST)作为WRF底边界条件,对2008年15号强台风"蔷薇"(Jangmi)过程进行了数值后报试验。结果表明,与使用NCEP/NCAR的SST试验后报的台风中心位置偏差相比,使用高时空分辨率的SST能够较为显著地改善"蔷薇"的路径模拟,台风中心位置模拟偏差减少11%,尤其在台风减弱阶段,台风中心位置模拟偏差减少37%。台风强度在台风发展的不同阶段对下垫面SST的变化敏感性不同。台风路径附近的海表面温度下降会导致海洋向大气输送的热量减少从而减弱台风强度。     

海洋表层温度对台风"蔷薇"路径和强度预测精度的影响

基于中尺度大气模式WRF(Weather Research and Forecasting Model),首先对2007年3次船舶辐射通量观测进行模拟,以检验WRF对长波和短波辐射通量的模拟能力,结果表明使用中国近海海洋环境数值预报系统环流模式POM(Princeton Ocean Model)模拟的高时空分辨率的海洋表层温度能够显著改进短波辐射通量的模拟,而对长波辐射通量模拟的改进不明显。然后,将业务化运行的中国近海海洋环境数值预报系统后报的逐时海洋表面温度(SST)作为WRF底边界条件,对2008年15号强台风"蔷薇"(Jangmi)过程进行了数值后报试验。结果表明,与使用NCEP/NCAR的SST试验后报的台风中心位置偏差相比,使用高时空分辨率的SST能够较为显著地改善"蔷薇"的路径模拟,台风中心位置模拟偏差减少11%,尤其在台风减弱阶段,台风中心位置模拟偏差减少37%。台风强度在台风发展的不同阶段对下垫面SST的变化敏感性不同。台风路径附近的海表面温度下降会导致海洋向大气输送的热量减少从而减弱台风强度。     

Refined seaward boundary conditions for modelling shallow water waves in semi-enclosed water bodies

Based on the theory of characteristics, this research elaborates on the numerical treatment of two types of seaward boundary conditions for modelling long-wave dynamics in truncated estuarine and coastal domains. These seaward boundary conditions are devised for the solution of the fully non-linear shallow water equations in the time domain. The first type is the clamped boundary, at which the water level variation is given and the velocity is computed along the characteristic line going out of the domain. The second type is the non-reflecting boundary, where the incident wave information is introduced and the reflected waves from inside the computational domain are allowed to escape at the same time. The essence of its numerical implementation is to distinguish the inward and outward characteristics and to disconnect the incoming characteristic relation from the actual flow inside the domain. Compared with previous techniques, the present method includes extra terms in the derivation to account for the effects of the uneven bed, bottom friction and shape of the characteristic lines. A shock-capturing finite difference method is used to solve the shallow water equations in the deviatoric format, but the seaward boundary algorithms constructed herein are generic and applicable to other solvers. The necessity of these refinements is highlighted by simulating the tidal oscillation in the Persian/Arabian Gulf, periodic wave runup on the coastline and the wave resonance in a narrow harbour. It is found that neglecting the bed slope at the boundary may result in biased mean water levels in the prediction.     

Recent improvements to the physical model of the Bohai Sea,the Yellow Sea and the East China Sea Operational Oceano-graphy Forecasting System

In order to satisfy the increasing demand for the marine forecasting capacity, the Bohai Sea, the Yellow Sea and the East China Sea Operational Oceanography Forecasting System (BYEOFS) has been upgraded and improved to Version 2.0. Based on the Regional Ocean Modeling System (ROMS), a series of comparative experiments were conducted during the improvement process, including correcting topography, changing sea surface atmospheric forcing mode, adjusting open boundary conditions, and considering atmospheric pressure correction. (1) After the topography correction, the volume transport and meridional velocity maximum of Yellow Sea Warm Current increase obviously and the unreasonable bending of its axis around 36.1°N, 123.5°E disappears. (2) After the change of sea surface forcing mode, an effective negative feedback mechanism is formed between predicted sea surface temperature (SST) by the ocean model and sea surface radiation fluxes fields. The simulation errors of SST decreased significantly, and the annual average of root-mean-square error (RMSE) decreased by about 18％. (3) The change of the eastern lateral boundary condition of baroclinic velocity from mixed Radiation-Nudging to Clamped makes the unreasonable westward current in Tsushima Strait disappear. (4) The adding of mean sea level pressure correction option which forms the mean sea level gradient from the Bohai Sea and the Yellow Sea to the western Pacific in winter and autumn is helpful to increasing the fluctuation of SLA and outflow of the Yellow Sea when the cold high air pressure system controls the Yellow Sea area.     

Assessment of open boundary conditions on the elliptic formulation of the mild-slope equation

The performance of open boundaries in a finite differences scheme of the elliptic mild-slope equation is assessed. The wave propagation results show that lowest order parabolic radiation boundary conditions, unlike sponge layers combined with first order radiation boundary conditions, are an efficient alternative to first order radiation boundary conditions in order to improve the accuracy of the numerical solution of the problem.     

Active open boundary forcing using dual relaxation time-scales in downscaled ocean models

Regional models actively forced with data from larger scale models at their open boundaries often contain motion at different time-scales (e.g. tidal and low frequency). These motions are not always individually well specified in the forcing data, and one may require a more active boundary forcing while the other exert less influence on the model interior. If a single relaxation time-scale is used to relax toward these data in the boundary equation, then this may be difficult. The method of fractional steps is used to introduce dual relaxation time-scales in an open boundary local flux adjustment scheme. This allows tidal and low frequency oscillations to be relaxed independently, resulting in a better overall solution than if a single relaxation parameter is optimized for tidal (short relaxation) or low frequency (long relaxation) boundary forcing. The dual method is compared to the single relaxation method for an idealized test case where a tidal signal is superimposed on a steady state low frequency solution, and a real application where the low frequency boundary forcing component is derived from a global circulation model for a region extending over the whole Great Barrier Reef, and a tidal signal subsequently superimposed.     

Optimal control of salinity boundary condition in a tidal model using a variational inverse method

A variational inverse data assimilation scheme is developed to estimate the salinity boundary conditions in a three-dimensional tidal hydrodynamic and salinity transport model. In this paper, the maximum incoming salinity value and the recovery time from the outflow salinity to the maximum incoming salinity at model open boundaries are treated as poorly known model control variables, and estimated using a variational inverse data assimilation scheme. The variational inverse model is tested in an idealized estuary using identical twin experiments, in which observed data are generated from the same model. Model tests with different initial guesses of the model control variables are conducted to evaluate the capability of the inverse model. A penalty technique is used to eliminate oscillations in the solution during the minimization process. The effects of preconditioning and penalty terms on the convergence rate are investigated. Model results demonstrate that the variational inverse model can be used to efficiently determine the optimal salinity open boundary conditions and improve the model state when there are no observed data available to specify the proper salinity open boundary conditions in a tidal model.     

Improvement on open boundaries on a time dependent numerical model of wave propagation in the nearshore region

An improvement on the simulation of outgoing waves on a time dependent numerical model for water wave propagation in the nearshore region is presented. The governing equations consist of a system of first order partial differential equations (PDEs), the equation of continuity and the equation of motion. A comparative study of first order radiation boundary conditions (BCs) and first order radiation BCs combined with sponge layers is presented for cases where outgoing waves leave the numerical domain of calculation through the open boundary. A reduction of spurious reflections from the numerical open boundaries can be obtained with an irrelevant increase in terms of computational cost.     

低雷诺数下圆柱强迫振动特性光滑粒子流体动力学模拟

基于光滑粒子流体动力学(SPH)方法,开发了能够准确描述水流作用下圆柱强迫振动特性的数学模型。通过引入适合于无网格粒子法的开边界算法,来模拟出入流边界条件,建立了具有造流功能的SPH数值水槽。圆柱及计算域的上下边界均采用修正的动力边界条件进行模拟。借助于粒子位移矫正和压力修正算法,避免了圆柱周围流体粒子压力大幅震荡以及结构下游区域出现空腔等非物理性现象。使用典型的圆柱绕流数据,验证了所建SPH模型的计算性能,研究了固定圆柱在低雷诺数情况下的尾涡脱落模式和升阻力变化规律。明确了低雷诺数下强迫振动圆柱在频率锁定以及非锁定区间内的升力变化规律,量化了升力与外界激励频率之间的关系。     

Large deformation three-dimensional static analysis of deep water marine risers

The problem of static three-dimensional, nonlinear, large deformation response of a marine riser is formulated within small strain theory and solved numerically. This type of analysis is necessary, for the new generation of drilling and production risers. The mathematical model takes properly into account the effects of internal and external pressure and the complete nonlinear boundary conditions, without linearizing the follower forces. The extensibility or inextensibility condition is used as the constitutive relation in the tangential direction. Torsion and bending are coupled. The external load and the boundary conditions are deformation dependent. A solution method is developed based on an incremental finite element algorithm, which involves a prediction-correction scheme. In the correction phase deformation dependent quantities are updated. The extensibility or inextensibility condition is used to reduce the degrees of freedom of the system. The numerical results of the developed computer code compare very well with available semi-analytical and numerical solutions. Three numerical applications are used to demonstrate the importance of large deformation, nonlinear and three-dimensional analyses.     

Open boundaries in short wave simulations — A new approach

A new way of implementing radiation boundary conditions in finite difference schemes is reported. Instead of prescribing the incident field at the model boundary, waves are generated inside the model boundary. All outgoing waves are absorbed at open boundaries using so-called “sponge” layers.     

The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems: Part II - Performance and application to the California Current System

The Regional Ocean Modeling System (ROMS) 4-dimensional variational (4D-Var) data assimilation systems have been systematically applied to the mesoscale circulation environment of the California Current to demonstrate the performance and practical utility of the various components of ROMS 4D-Var. In particular, we present a comparison of three approaches to 4D-Var, namely: the primal formulation of the incremental strong constraint approach; the dual formulation “physical-space statistical analysis system”; and the dual formulation indirect representer approach. In agreement with theoretical considerations all three approaches converge to the same ocean circulation estimate when using the same observations and prior information. However, the rate of convergence of the dual formulation was found to be inferior to that of the primal formulation. Other aspects of the 4D-Var performance that relate to the use of multiple outer-loops, preconditioning, and the weak constraint are also explored. A systematic evaluation of the impact of the various components of the 4D-Var control vector (i.e. the initial conditions, surface forcing and open boundary conditions) is also presented. It is shown that correcting for uncertainties in the model initial conditions exerts the largest influence on the ability of the model to fit the available observations. Various important diagnostics of 4D-Var are also examined, including estimates of the posterior error, the information content of the observation array, and innovation-based consistency checks on the prior error assumptions. Using these diagnostic tools, we find that more than 90% of the observations assimilated into the model provide redundant information. This is a symptom of the large percentage of satellite data that are used and to some extent the nature of the data processing employed. This is the second in a series of three papers describing the ROMS 4D-Var systems.     

Modeling the water circulation in the North Atlantic in the scope of the CORE-II experiment

A numerical experiment on the reproduction of the variability in the state of North Atlantic water in 1948–2007 with a spatial resolution of 0.25° has been performed using the global ocean model developed at Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), and the Shirshov Institute of Oceanology (IO RAS) (the INM–IO model). The data on the state of the atmosphere, radiation fluxes, and bulk formulas of the CORE-II protocol are used as boundary conditions. Five successive 60-year calculation cycles have been performed in order to obtain the quasi-equilibrium state of a model ocean. For the last 20 years, the main elements of large-scale ocean circulation have been analyzed and compared with the WOA09 atlas data and the results of other models.     

An analytical model with three sub-regions for m2 tide in the yellow sea and the East China Sea

In this study an analytical tide model of uniform width with three sub-regions is presented. The three-subregions model takes into account step-like variations in depths in the direction of the channel as a way to examine the M₂ tide of the East China Sea (ECS) as well as the Yellow Sea (YS). A modified Proudman radiation condition has been applied at the northern open head, while the sea surface elevation is specified at the southern open boundary. It is seen that, due to the presence of an abrupt change in depth, co-amplitude lines of the M₂ tide are splitted to the east and west near the end of the ECS shelf region. Variations in depths, bottom friction and the open head boundary conditions all contribute to the determination of formation of amphidromes as well as overall patterns of M₂ tidal distribution. It is seen that increasing water depth and bottom friction in the ECS shelf results in the westward shift of the southern amphidrome. There is however no hint at all of the well-known degenerated tidal pattern being formed. It is inferred that a lateral variation of water depth has to be somehow incorporated to represent the tidal patterns in ECS in a realistic manner. Regarding the radiation factor introduced by Fang et al. (1991), use of a value larger than one, possibly with a phase shift, appears to be a proper way of incorporating the reflected waves from the northern Yellow Sea (NYS). Key words - analytical model, M₂ tide, Kelvin wave, Yellow Sea, East China Sea