Assessment of the effectiveness of POLYMODE data assimilation by a numerical barotropic model for synoptic motions

This paper considers the results of numerical experiments involving POLYMODE data assimilation by a barotropic model for synoptic ocean dynamics. The model's response the data assimilation for various space-time discretenesses of assimilation is studied. Results derived from the application of optimal interpolation algorithms and modified optimal filtration algorithms are compared. Qualitative similarity to the calculations carried out through the simulation modelling technique is noted. Optimal assimilation algorithms are determined, depending on the space-time discreteness used. An optimal sampling discreteness for the POLYMODE conditions is suggested.Translated by Vladimir A. Puchkin.     

Numerical experiments with data assimilation in the simplest dynamic-stochastic model for the ocean's synoptic variability closed at the level of the second moments

The results of numerical experiments with data assimilation in a non-linear model of the synoptic dynamics of the world's oceans are reported. The model's response to the data assimilation is studied at different values of the relative error in determining the initial fields and assimilation discreteness. The results of application of the algorithms of optimum filtration and optimum interpolation are compared. The advantages of the filtration algorithm employed are discussed only for the case of small errors in determining the initial fields and low assimilation discreteness. The possibility of deterioration of the prediction estimates in data assimilation with discreteness less than the typical time of variability of the average fields is noted.Translated by Mikhail M. Trufanov.     

现代海洋/大气资料同化方法的统一性及其应用进展

海洋／大气资料同化的理论基础是用数值模式作为动力学强迫对观测信息进行提炼，或者说，从包含观测误差(噪声)的空间分布不均匀的实测资料中依据动力系统自身的演化规律(动力学方程或模式)来确定海洋／大气系统状态的最优估计。本文对主要的现代海洋／大气资料同化方法，包括最优插值(()ptimal Interpolation，简称()Ⅰ)、变分方法(3—Dimensional Variational和4—Dimensional Variational，分别简称3DVAR和4DVAR)和滤波方法(Filtering)的原理、算法设计和实际应用进行系统地回顾，并对这些资料同化方法的优缺点进行分析和讨论。在滤波框架下，所有的现代资料同化方法都被统一了：()Ⅰ和3DVAR是不随时间变化的滤波器，4DVAR和卡曼滤波是线性滤波器，即非线性滤波的退化情形；而集合滤波能构建非线性的滤波器，因为集合在某种程度上体现了系统的非高斯信息。一个非线性滤波器的主要优点是能计算和应用随时间变化的各阶误差统计距，如误差协方差矩阵。将非线性滤波器计算的随时间变化的误差协方差矩阵引入到（）Ⅰ或4DVAR中，也许能实质性地改进这些传统方法。在实际应用中，方法的优劣可能取决于所选用的数值模式和可获得的计算资源，因此需针对不同的问题选取不同的资料同化方法。由于各种资料同化方法具有统一性，因此可建立测试系统来评价这些方法，从而对各种方法获得更深入的理解，改进现有的资料同化技术，并提高人们对海洋／大气环境的预测能力。     

同化技术在渤海溢油应急预报系统中的应用

溢油应急预报对溢油事故现场处理具有重要指导意义。国内外已开展大量溢油数值预报技术研究,但由于各类误差的引入(尤其风和流数值预报误差的引入)以及模型本身的不完善等各种原因导致溢油数值预报无法满足日益提高的溢油预报精度需求。随着现场观测技术和监测水平的提高,如何充分利用实时观测数据提高业务化溢油应急预报精度,并满足应急预报迅速快捷的要求,成为目前业务化溢油应急预报的首要问题。国家海洋环境预报中心于2008年实现了渤海溢油业务化预报系统的建立和业务化应用,本文针对当前渤海溢油业务化应急预报中存在的现实问题,利用已有渤海海上5个石油平台从2010年1月至2011年2月的风场观测数据,初步开展最优插值方法(optimal interpolation assimilation method,OI)同化技术在国家海洋环境预报中心渤海溢油应急预报系统风场订正的应用研究。本文采用交错订正方法,确定了OI同化技术中相关尺度因子的选取,从而实现在这5个观测站地理分布情况下,OI同化技术应用中参数的最优化,之后在理想实验和实际案例的应用中,该同化方法明显提高渤海溢油预报精度。本文为如何进一步利用同化方法迅速快捷地实现溢油应急预报精度的提高提供了一定研究基础。     

Optimization of the data assimilation algorithm in a model for synoptic dynamics of the velocity field

The results of numerical experiments involving data assimilation by a non-linear model for synoptic dynamics of the ocean are given. The results of application of simplified optimal filtration algorithms (with the correlation error function being parametrized for both linear and non-linear variants) and of the optimal interpolation are intercompared. The use of a non-linear equation to predict average values and a linear one to predict dispersion in the filtration algorithm is suggested as most appropriate for the cases, when anisotropy of the correlation function is to be included. In other cases, it is considered worth-while to apply optimal interpolation.Translated by V. Puchkin.     

Sequential assimilation in the wind wave model for simulations of typhoon events around Taiwan Island

We investigate the effect of data assimilation in the Wind Wave Model (WWM, Hsu et al., 2005) for wind wave simulations of typhoon events using an Optimal Interpolation (OI) method in the coastal waters of Taiwan. The main point of the present study is that the assimilation is conducted for typhoon events with short-time periods around an island. Five real typhoon events were used for numerical assimilation experiments with different combinations of the key parameters: the correlation length, the ratio of the errors between the observation and the prediction, and the number of measuring stations. The retrieved wind velocity is obtained using the wave energy growth curve computed from the WWM. The wave energy dissipation function suggested by Makin and Kudryavtsev (1999) was adopted in the data assimilation. This study shows that assimilation can improve the initial performance of the wave model, but it becomes insignificant after about 12 h. In summary, the OI approach is shown to be a reliable assimilation scheme for the WWM applied to typhoon events in the coastal waters of Taiwan Island.     

Assimilation of historical SST data for long-term ENSO retrospective forecasts

In this study, the assimilation of historic SST (sea surface temperature) data was performed for long-term ENSO hindcasts. The emphasis was placed on the design of background error covariance (BEC) that dominates the transfer of SST information to the subsurface. Four different data-assimilation schemes, based on Optimal Interpolation (OI) algorithm, were proposed, and compared in terms of ENSO simulation and prediction skills for the period from 1876 to 2000.It was found that the data-assimilation scheme that has a three-dimensional BEC constructed from model simulations forced by observed wind stress can effectively correct the second-layer temperature in the SST assimilation and lead to the best ENSO prediction skill. Further analysis for the long-term hindcasts shows that the prediction skills have a striking decadal/interdecadal variability similar to that found in other models. These results provide a fundamental basis for the further study of ENSO predictability.     

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.     

基于地球系统模式的局地化粒子滤波器与集合卡尔曼滤波器同化实验

粒子滤波器(PF)是一种非常具有应用前景的非线性资料同化方法。但由于其算法本身存在的粒子退化问题,目前尚未被广泛地应用于大型地球物理模式。目前主流的集合同化系统仍然倾向于使用集合卡尔曼滤波器(EnKF)及其衍生方法。一种新近被提出的局地化粒子滤波器(LPF)在经典的粒子滤波器算法中引入局地化技术,可以使用较小的计算成本有效地避免退化问题,具有非常大的业务应用潜力。本文在全耦合的通用地球系统模式中开展了LPF和EnKF的同化实验,同化资料为模拟的卫星海表温度资料。着重考察了不同局地化参数对两种方法的不同影响,对比了局地化粒子滤波器与集合卡尔曼滤波器的同化效果差异。比较的结果表明,LPF的同化效果对于局地化参数的选择非常敏感,在使用最优局地化参数的条件下,LPF能达到与EnKF相当甚至优于后者的同化效果,并具有较大的改进空间。     

Data assimilation for a coastal area morphodynamic model: Morecambe Bay

This paper investigates the use of data assimilation in coastal area morphodynamic modelling using Morecambe Bay as a study site. A simple model of the bay has been enhanced with a data assimilation scheme to better predict large-scale changes in bathymetry observed in the bay over a 3-year period. The 2DH decoupled morphodynamic model developed for the work is described, as is the optimal interpolation scheme used to assimilate waterline observations into the model run. Each waterline was acquired from a SAR satellite image and is essentially a contour of the bathymetry at some level within the inter-tidal zone of the bay. For model parameters calibrated against validation observations, model performance is good, even without data assimilation. However the use of data assimilation successfully compensates for a particular failing of the model, and helps to keep the model bathymetry on track. It also improves the ability of the model to predict future bathymetry. Although the benefits of data assimilation are demonstrated using waterline observations, any observations of morphology could potentially be used. These results suggest that data assimilation should be considered for use in future coastal area morphodynamic models.     

杭州湾三维悬浮泥沙输运模型初始场的伴随法反演研究

在悬沙输运的数值模拟中,初始场的准确给定至关重要。目前诸多确定初始场的方案均存在一定的缺陷,初始场的准确性有待进一步提高。本文基于一个三维悬沙输运伴随同化模型,通过孪生实验和实际实验,对模型初始场进行了伴随法反演研究。在孪生实验中,首先验证了初始场的相对重要性;其次,探讨了初始场的反演结果对优化算法、初始猜测值、卫星遥感数据数量、同化时间窗口宽度和背景流场误差的敏感性;最后,比较了伴随法和插值法重构初始场的能力。孪生实验结果表明:最速下降法对初始场的优化反演效果要优于三种共轭梯度法和有限记忆BFGS法;初始场的反演效果对初始猜测值、卫星遥感数据数量和背景流场误差不敏感,而对同化窗口宽度较为敏感;与插值法相比,伴随法是重构模型初始场更有效的手段。实际实验中,在杭州湾海域同化典型的小潮时期和大潮时期的GOCI卫星遥感资料所得表层悬沙浓度数据,优化反演了初始场。实际实验结果表明:数据同化后,得到了更符合实际的最优初始场,表明伴随法是实现初始场优化反演的有效手段。该研究对进一步改进悬沙输运模型的初始化方案具有一定的参考价值,也对其他数值模型的初始化方案具有一定的借鉴价值。     

The impact of mean dynamic topography on a sea-level anomaly assimilation in the South China Sea based on an eddy-resolving model

The sea-level anomaly (SLA) from a satellite altimeter has a high accuracy and can be used to improve ocean state estimation by assimilation techniques. However, the lack of an accurate mean dynamic topography (MDT) is still a bothersome issue in an ocean data assimilation. The previous studies showed that the errors in MDT have significant impacts on assimilation results, especially on the time-mean components of ocean states and on the time variant parts of states via nonlinear ocean dynamics. The temporal-spatial differences of three MDTs and their impacts on the SLA analysis are focused on in the South China Sea (SCS). The theoretical analysis shows that even for linear models, the errors in MDT have impacts on the SLA analysis using a sequential data assimilation scheme. Assimilation experiments, based on EnOI scheme and HYCOM, with three MDTs from July 2003 to June 2004 also show that the SLA assimilation is very sensitive to the choice of different MDTs in the SCS with obvious differences between the experimental results and observations in the centre of the SCS and in the vicinity of the Philippine Islands. A new MDT for assimilation of SLA data in the SCS was proposed. The results from the assimilation experiment with this new MDT show a marked reduction (increase) in the RMSEs (correlation coefficient) between the experimental and observed SLA. Furthermore, the subsurface temperature field is also improved with this new MDT in the SCS.     

Generation of high resolution sea surface temperature using multi-satellite data for operational oceanography

In the present article, we introduce a high resolution sea surface temperature(SST) product generated daily by Korea Institute of Ocean Science and Technology(KIOST). The SST product is comprised of four sets of data including eight-hour and daily average SST data of 1 km resolution, and is based on the four infrared(IR) satellite SST data acquired by advanced very high resolution radiometer(AVHRR), Moderate Resolution Imaging Spectroradiometer(MODIS), Multifunctional Transport Satellites-2(MTSAT-2) Imager and Meteorological Imager(MI), two microwave radiometer SSTs acquired by Advanced Microwave Scanning Radiometer 2(AMSR2), and Wind SAT with in-situ temperature data. These input satellite and in-situ SST data are merged by using the optimal interpolation(OI) algorithm. The root-mean-square-errors(RMSEs) of satellite and in-situ data are used as a weighting value in the OI algorithm. As a pilot product, four SST data sets were generated daily from January to December 2013. In the comparison between the SSTs measured by moored buoys and the daily mean KIOST SSTs, the estimated RMSE was 0.71°C and the bias value was –0.08°C. The largest RMSE and bias were 0.86 and –0.26°C respectively, observed at a buoy site in the boundary region of warm and cold waters with increased physical variability in the Sea of Japan/East Sea. Other site near the coasts shows a lower RMSE value of 0.60°C than those at the open waters. To investigate the spatial distributions of SST, the Group for High Resolution Sea Surface Temperature(GHRSST) product was used in the comparison of temperature gradients, and it was shown that the KIOST SST product represents well the water mass structures around the Korean Peninsula. The KIOST SST product generated from both satellite and buoy data is expected to make substantial contribution to the Korea Operational Oceanographic System(KOOS) as an input parameter for data assimilation.     

A new approach for the determination of the drag coefficient from the upper ocean response to a tropical cyclone: a feasibility study

We seek to determine if a small number of measurements of upper ocean temperature and currents can be used to make estimates of the drag coefficient that have a smaller range of uncertainty than previously found. We adopt a numerical approach using forward models of the ocean’s response to a tropical cyclone, whereby the probability density function of drag coefficient values as a function of wind speed that results from adding realistic levels of noise to the simulated ocean response variables is sought. Allowing the drag coefficient two parameters of freedom, namely the values at 35 and at 45 m/s, we found that the uncertainty in the optimal value is about 20% for levels of instrument noise up to 1 K for a misfit function based on temperature, or 1.0 m/s for a misfit function based on 15 m velocity components. This is within tolerable limits considering the spread of measurement-based drag coefficient estimates. The results are robust for several different instrument arrays; the noise levels do not decrease by much for arrays with more than 40 sensors when the sensor positions are random. Our results suggest that for an ideal case, having a small number of sensors (20–40) in a data assimilation problem would provide sufficient accuracy in the estimated drag coefficient.     

Numerical modeling of ocean hydrodynamics with variational assimilation of observational data

Models and methods of the numerical modeling of ocean hydrodynamics dating back to the pioneering works of A.S. Sarkisyan are considered, with emphasis on the formulation of problems and algorithms of mathematical modeling and the four-dimensional variational assimilation of observational data. An algorithm is proposed for studying the sensitivity of the optimal solution to observational data errors in a seasurface temperature assimilation problem in order to retrieve heat fluxes on the surface. An example of a solution of the optimal problem of the World Ocean hydrodynamics with the assimilation of climatic temperature and salinity observations is offered.     

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

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

基于ROMS模式利用集合最优插值同化沿轨海表面高度异常数据的研究

The ensemble optimal interpolation （EnOI） is applied to the regional ocean modeling system （ROMS） with the ability to assimilate the along-track sea level anomaly （TSLA）. This system is tested with an eddy-resolving system of the South China Sea （SCS）. Background errors are derived from a running seasonal ensemble to account for the seasonal variability within the SCS. A fifth-order localization function with a 250 km localization radius is chosen to reduce the negative effects of sampling errors. The data assimilation system is tested from January 2004 to December 2006. The results show that the root mean square deviation （RMSD） of the sea level anomaly decreased from 10.57 to 6.70 cm, which represents a 36.6% reduction of error. The data assimilation reduces error for temperature within the upper 800 m and for salinity within the upper 200 m, although error degrades slightly at deeper depths. Surface currents are in better agreement with trajectories of surface drifters after data assimilation. The variance of sea level improves significantly in terms of both the amplitude and position of the strong and weak variance regions after assimilating TSLA. Results with AGE error （AGE） perform better than no AGE error （NoAGE） when considering the improvements of the temperature and the salinity. Furthermore, reasons for the extremely strong variability in the northern SCS in high resolution models are investigated. The results demonstrate that the strong variability of sea level in the high resolution model is caused by an extremely strong Kuroshio intrusion. Therefore, it is demonstrated that it is necessary to assimilate the TSLA in order to better simulate the SCS with high resolution models.     

Evolution equation for the error correlation function of vorticity prediction used by a barotropic synoptic motion model to assimilate data

An exact equation is derived for the error correlation function of model processes, governed by a barotropic vortex balance equation in a linear approximation. This equation can be effectively applied to assimilate data with small spatial-temporal discreteness when the assumption on error correlation function's stationarity (homogeneity, isotropicity) proves to be incorrect and leads to unsatisfactory results.Translated by Vladimir A. Puchkin.     

Coupling a two-way nested primitive equation model and a statistical SST predictor of the Ligurian Sea via data assimilation

A primitive equation model and a statistical predictor are coupled by data assimilation in order to combine the strength of both approaches. In this work, the system of two-way nested models centred in the Ligurian Sea and the satellite-based ocean forecasting (SOFT) system predicting the sea surface temperature (SST) are used. The data assimilation scheme is a simplified reduced order Kalman filter based on a constant error space. The assimilation of predicted SST improves the forecast of the hydrodynamic model compared to the forecast obtained by assimilating past SST observations used by the statistical predictor. This study shows that the SST of the SOFT predictor can be used to correct atmospheric heat fluxes. Traditionally this is done by relaxing the model SST towards the climatological SST. Therefore, the assimilation of SOFT SST and climatological SST are also compared.     

The Adriatic Sea M2 and K1 tides by 3D model and data assimilation

In the present work we explore the impact of assimilating local tide-gauge and altimetric data on the quality of predicting the major Adriatic tides (M₂ and K₁). To that end we compute optimal tidal open boundary conditions for a 3D high-resolution finite-element model by using an incremental assimilation formalism. The essence of the method is the use of two dynamical models where the solution in the complex 3D high-resolution model is sought via assimilation of prediction errors into the simpler 2D model with explicit inverse. In the central numerical experiment, harmonic constants from 12 tide gauges are assimilated and the results are analysed at 31 locations, hence 19 independent ones. The data assimilation contributes to the reduction of maximum amplitude error from 5.6 to 0.5 cm for M₂ and from 3.9 to 0.1 cm for K₁. The assimilation procedure is repeated by assimilating suitably processed Topex/Poseidon altimeter data, again validating the outcome at 31 tide gauge locations. The result was very similar to the gauge-data assimilation outcome. The model output is also validated with the current data, not used in the assimilation. At two locations and at three depths the model was able to reproduce the major and the minor semi-axes of tidal ellipses, as well as their orientations very well.