Numerical solution to the problem of variational assimilation of operational observational data on the ocean surface temperature

The problem of variational assimilation of satellite observational data on the ocean surface temperature is formulated and numerically investigated in order to reconstruct surface heat fluxes with the use of the global three-dimensional model of ocean hydrothermodynamics developed at the Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), and observational data close to the data actually observed in specified time intervals. The algorithms of the numerical solution to the problem are elaborated and substantiated, and the data assimilation block is developed and incorporated into the global three-dimensional model. Numerical experiments are carried out with the use of the Indian Ocean water area as an example. The data on the ocean surface temperature over the year 2000 are used as observational data. Numerical experiments confirm the theoretical conclusions obtained and demonstrate the expediency of combining the model with a block of assimilating operational observational data on the surface temperature.     

Observational data assimilation in the problem of Black Sea circulation and sensitivity analysis of its solution

The problem of the variational data assimilation of the sea-surface temperature for the model of the Black Sea dynamics has been formulated and numerically studied to reproduce surface heat fluxes. An analysis of sensitivity of the optimal solution to errors in observation data has been conducted. The results of numerical experiments have been presented.     

Simulating large-scale circulation in seas and oceans

The problem of simulating ocean general circulation is considered using an approach developed by G.I. Marchuk. Most attention is focused on problems associated with the application of multi-component-splitting and adjoint-equation methods and with the parameterization of turbulent-exchange processes. The statement of the problem, an algorithm of its solution, and the results of the four-dimensional temperature and salinity data assimilation in a model of World Ocean hydrodynamics are discussed. This algorithm yields qualitatively reliable results, and its main features are modularity, usability, and the possibility of using efficient implicit schemes.     

Reconstruction of eddies by assimilating satellite altimeter data into Princeton Ocean Model

An optimal interpolation assimilation model for satellite altimetry data is developed based on Princeton Ocean Model (POM), which is applied in a quasi-global domain, by the method of isotropic correlation between sea level anomaly (SLA) and sea temperature anomaly. The perfor- mance of this assimilation model is validated by the modeled results of SLA and the current patterns. Comparisons between modeling and satellite data show that both the magnitudes and distribution patterns of the simulated SLA are improved by assimilation. The most signiˉcant improvement is that meso-scale systems, e.g., eddies, are well reconstructed. The evolution of an eddy located in the northwest Paciˉc Ocean is traced by using the assimilation model. Model results show that during three months the eddy migrated southwestward for about 6 degrees before merging into the Kuroshio. The three dimensional structure of this eddy on 12 August 2001 is further analyzed. The strength of this warm, cyclonic eddy decreases with the increase of depth. The eddy shows di?erent horizontal patterns at di?erent layers, and the SLA and temperature ˉelds agree with each other well. This study suggests that this kind of data assimilation is economic and reliable for eddy reconstruction, and can be used as a promising technique in further studies of ocean eddies as well as other ˉne circulation structures.     

一维扩散方程整体观测资料下的初值变分同化反演

本文考虑一维扩散方程的反问题,利用变分同化方法通过观测资料来确定方程中的未知初值,通过分析观测误差对于初值误差的影响,证明变分同化初值收敛于原问题的真实参数,并得到了参数的收敛精度。同时将得到的初值代入预报模式中,得到预报解,并分析了预报解的收敛性和预报误差。     

集合同化方法在黄海海域海表面温度同化中的应用

The effects of sea surface temperature(SST) data assimilation in two regional ocean modeling systems were examined for the Yellow Sea(YS). The SST data from the Operational Sea Surface Temperature and Sea Ice Analysis(OSTIA) were assimilated. The National Marine Environmental Forecasting Center(NMEFC) modeling system uses the ensemble optimal interpolation method for ocean data assimilation and the Kunsan National University(KNU) modeling system uses the ensemble Kalman filter. Without data assimilation, the NMEFC modeling system was better in simulating the subsurface temperature while the KNU modeling system was better in simulating SST. The disparity between both modeling systems might be related to differences in calculating the surface heat flux, horizontal grid spacing, and atmospheric forcing data. The data assimilation reduced the root mean square error(RMSE) of the SST from 1.78°C(1.46°C) to 1.30°C(1.21°C) for the NMEFC(KNU) modeling system when the simulated temperature was compared to Optimum Interpolation Sea Surface Temperature(OISST) SST dataset. A comparison with the buoy SST data indicated a 41%(31%) decrease in the SST error for the NMEFC(KNU) modeling system by the data assimilation. In both data assimilative systems, the RMSE of the temperature was less than 1.5°C in the upper 20 m and approximately 3.1°C in the lower layer in October. In contrast, it was less than 1.0°C throughout the water column in February. This study suggests that assimilations of the observed temperature profiles are necessary in order to correct the lower layer temperature during the stratified season and an ocean modeling system with small grid spacing and optimal data assimilation method is preferable to ensure accurate predictions of the coastal ocean in the YS.     

Problems of variational assimilation of observational data for ocean general circulation models and methods for their solution

Problems of the variational assimilation of satellite observational data on the temperature and level of the ocean surface, as well as data on the temperature and salinity of the ocean from the ARGO system of buoys, are formulated with the use of the global three-dimensional model of ocean thermodynamics developed at the Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS). Algorithms for numerical solutions of the problems are developed and substantiated, and data assimilation blocks are developed and incorporated into the global three-dimensional model. Numerical experiments are performed with the use of the Indian Ocean or the entire World Ocean as examples. These numerical experiments support the theoretical conclusions and demonstrate that the use of a model with an assimilation block of operational observational data is expedient.     

集合最优平滑同化方法的研究与应用

海洋状态场的历史变化过程对其分布状态有重要影响。在观测资料稀疏的情况下,合理利用历史观测资料能够为海洋数据同化提供大量有效信息。然而在目前的顺序资料同化过程中,往往只同化当前时刻的观测数据,没有考虑到历史观测资料对当前状态的约束。四维变分虽然可以体现变量在时间维度的演变过程,但引入伴随方程会增加计算代价。本文基于集合最优平滑同化算法（Ensemble Optimal Smoothing,EnOS）探讨了一种在数据同化中加入历史观测资料的简易可行方案,其能够根据历史观测数据估计当前状态,并进行单点同化实验和区域同化实验来验证该方案的有效性。实验结果表明,将历史观测资料引入到同化过程中可以把控时间演变趋势,减小分析数据与真实值之间的偏差,更有效地消除数值模式误差,提高同化质量。     

A theoretical study of the multigrid three-dimensional variational data assimilation scheme using a simple bilinear interpolation algorithm

In order to solve the so-called "bull-eye" problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational(3DVAR) data assimilation scheme,a smoothing term,equivalent to a penalty term,is introduced into the cost function to serve as a means of troubleshooting.A theoretical analysis is first performed to figure out what on earth results in the issue of "bull-eye",and then the meaning of such smoothing term is elucidated and the uniqueness of solution of the multigrid 3DVAR with the smoothing term added is discussed through the theoretical deduction for one-dimensional(1D) case,and two idealized data assimilation experiments(one-and two-dimensional(2D) cases).By exploring the relationship between the smoothing term and the recursive filter theoretically and practically,it is revealed why satisfied analysis results can be achieved by using such proposed solution for the issue of the multigrid 3DVAR.     

Assimilation of hydrological observation data for calculating currents in seas and oceans

This paper considers the main steps in improving the methods for calculating the ocean (sea) dynamics on the basis of observational data on sea-water temperature and salinity. The results of diagnostic and adaptation calculations for the near-equatorial area of the West Atlantic in the area of the Lomonosov countercurrent formation are presented. We consider the problem of the complex use of measurements of temperature, salinity, and current velocity in the POLYMODE polygons with their assimilation into the model using a Kalman filter. The results of calculations of the coordinated fields with the mechanism of geostrophic adaptation and using asynchronous measurements obtained by the Razrezy program are given. We discuss further modifications of the assimilation algorithms for hydrological observation data in models of sea dynamics and the principles of adaptation of hydrophysical fields that made it possible to reconstruct the climate fields of the Black Sea and to reproduce the basin dynamics for 23 years.     

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。     

The impact of ocean data assimilation on seasonal predictions based on the National Climate Center climate system model

An ensemble optimal interpolation (EnOI) data assimilation method is applied in the BCC_CSM1.1 to investigate the impact of ocean data assimilations on seasonal forecasts in an idealized twin experiment framework. Pseudo-observations of sea surface temperature (SST), sea surface height (SSH), sea surface salinity (SSS), temperature and salinity (T/S) profiles were first generated in a free model run. Then, a series of sensitivity tests initialized with predefined bias were conducted for a one-year period; this involved a free run (CTR) and seven assimilation runs. These tests allowed us to check the analysis field accuracy against the “truth”. As expected, data assimilation improved all investigated quantities; the joint assimilation of all variables gave more improved results than assimilating them separately. One-year predictions initialized from the seven runs and CTR were then conducted and compared. The forecasts initialized from joint assimilation of surface data produced comparable SST root mean square errors to that from assimilation of T/S profiles, but the assimilation of T/S profiles is crucial to reduce subsurface deficiencies. The ocean surface currents in the tropics were better predicted when initial conditions produced by assimilating T/S profiles, while surface data assimilation became more important at higher latitudes, particularly near the western boundary currents. The predictions of ocean heat content and mixed layer depth are significantly improved initialized from the joint assimilation of all the variables. Finally, a central Pacific El Ni?o was well predicted from the joint assimilation of surface data, indicating the importance of joint assimilation of SST, SSH, and SSS for ENSO predictions.     

数据同化在浅海温度同步性调查中的应用

建立了一个功能较为完善的四维同化系统,解决了温度调查资料中存在的同步性问题。为了检验同化方法和模式程序的正确性,以及讨论同步性误差的校正效果,从同化结果与锚系调查数据、同化结果与遥感数据、比对断面均方根误差和海表平均温度4个方面进行了探讨,结果表明:1)同化结果与锚系调查数据对比显示,改进参数的NMC方法(来自美国国家气象中心)能够适用于长江口外海域中的温度四维同化,同化温度结果与锚系调查数据在变化趋势上一致,在数值上最大差异不超过0.4℃;2)同化结果与遥感数据对比显示,同化结果能够将调查资料推演到完整的时空范围,并具有较好的变化趋势和精度;3)根据比对断面均方根误差分析,调查资料中两个比对断面温度间的均方差误差为3.8℃,而同化结果与实测数据的均方根误差低于0.6℃,说明同化方法有效地降低了调查资料中的同步性误差;4)海表平均温度分析显示,同化结果能够避免调查不同步引起的各种温度斑块,并且其温度分布和锋面结构能够更如实地反映实际情况。     

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 analysis of hydrophysical fields on the northwestern shelf of the Black Sea

A numerical experiment with assimilation of hydrological observational data from a survey in October 2007 on the northwestern shelf of the Black Sea was carried out using the hydrodynamic model with nonlinear equations of motion, equations of heat and salt advection, and data assimilation. The results of this calculation are compared with thermohydrodynamic fields obtained without taking into account temperature and salinity measurements. It is shown that allowance for the observation data leads to qualitative and quantitative differences in the structure of the hydrophysical fields. Mesoscale eddies and intense jet streams that agree with satellite observations were found in the field of currents and were investigated. These eddies are not resolved in low-resolution field experiments.     

4DVAR Data Assimilation with the Regional Ocean Modeling System (ROMS): Impact on the Water Mass Distributions in the Yellow Sea

In this study, we evaluate the performance of the recently developed incremental strong constraint 4-dimensional variational (4DVAR) data assimilation applied to the Yellow Sea (YS) using the Regional Ocean Modeling System (ROMS). Two assimilation experiments are compared: assimilating remote-sensed sea surface temperature (SST) and both the SST and in-situ profiles measured by shipboard CTD casts into a regional ocean modeling from January to December of 2011. By comparing the two assimilation experiments against a free-run without data assimilation, we investigate how the assimilation affects the hydrographic structures in the YS. Results indicate that the SST assimilation notably improves the model behavior at the surface when compared to the non-assimilative free-run. The SST assimilation also has an impact on the subsurface water structure in the eastern YS; however, the improvement is seasonally dependent, that is, the correction becomes more effective in winter than in summer. This is due to a strong stratification in summer that prevents the assimilation of SST from affecting the subsurface temperature. A significant improvement to the subsurface temperature is made when the in-situ profiles of temperature and salinity are assimilated, forming a tongue-shaped YS bottom cold water from the YS toward the southwestern seas of Jeju Island.     

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.     

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.     

背景误差协方差矩阵不同求逆方案在高度计资料同化试验中的应用比较

针对海表高度计资料的同化,考查了背景误差协方差矩阵的不同求逆方案对同化效果的影响。所使用的求逆方案包括避免求逆的经验正交函数方案(EOF/EOF_var)、递归滤波方案(RF/RF_var)以及采用初等变换法直接求逆的方案(Inv)。基于上述方案开展了热带太平洋地区2002年1-7月的TOPEX/Poseidon高度计资料同化试验,并利用SODA再分析资料和TAO观测资料评估了各方案对温度场的同化效果,主要得到如下结果:与SODA相比较,Inv方案对模式温度场改进甚微,其余四种方案在100~300 m深度之间对温度场改进较多,在其它深度范围内则改进较少;与TAO观测相比较,EOF_var、RF_var方案对模式温度场改进最多,EOF和RF方案次之,Inv方案则对温度场改进甚少。