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.     

A reduced-dynamics variational approach for the assimilation of altimeter data into eddy-resolving ocean models

A new method of assimilating sea surface height (SSH) data into ocean models is introduced and tested. Many features observable by satellite altimetry are approximated by the first baroclinic mode over much of the ocean, especially in the lower (but non-equatorial) and mid latitude regions. Based on this dynamical trait, a reduced-dynamics adjoint technique is developed and implemented with a three-dimensional model using vertical normal mode decomposition. To reduce the complexity of the variational data assimilation problem, the adjoint equations are based on a one-active-layer reduced-gravity model, which approximates the first baroclinic mode, as opposed to the full three-dimensional model equations. The reduced dimensionality of the adjoint model leads to lower computational cost than a traditional variational data assimilation algorithm. The technique is applicable to regions of the ocean where the SSH variability is dominated by the first baroclinic mode. The adjustment of the first baroclinic mode model fields dynamically transfers the SSH information to the deep ocean layers. The technique is developed in a modular fashion that can be readily implemented with many three-dimensional ocean models. For this study, the method is tested with the Navy Coastal Ocean Model (NCOM) configured to simulate the Gulf of Mexico.     

海洋环流模式中卫星遥感资料同化的应用进展

物理海洋研究长久以来一直受到观测资料不足的制约,然而这一状况随着现代观测技术的迅猛发展得到了很大的改善。卫星遥感技术的发展提供了覆盖全球的、连续、实时的卫星观测数据,这是其他任何资料都无法比拟的。这些数据大部分难以直接运用来改善气候预测或数值模拟分析,然而资料同化技术的出现和发展改善了这一情况。     

气候模式中海洋数据同化对热带降水偏差的影响

本文采用海洋卫星观测海表温度(SST)和海面高度异常(SLA)数据,对国家海洋局第一海洋研究所地球系统模式FIO-ESM(First Institute of Oceanography Earth System Model version 1.0)中海洋模式分量进行了集合调整卡尔曼滤波(EAKF)同化,对比分析了大气环流、湿度和云量对海洋数据同化的响应,探讨了海洋同化对热带降水模拟偏差的影响。结果表明:海洋数据同化能有效改善海表温度和上层海洋热含量的模拟,30°S~30°N纬度带内年平均SST的绝均差降低60%。同化后大气模式模拟的赤道两侧信风得到明显改善,上升气流在赤道以北热带地区增强而在赤道以南热带地区减弱,热带降水模拟的动力结构更为合理,水汽和云量分布也更切合实际。热带年平均降水的空间分布和强度在同化后均得到改善,赤道以南的纬向年平均降水峰值显著降低,降水偏差明显减小,同化后30°S~30°N纬度带内年平均降水绝均差降低35%。     

海洋温盐度资料多变量同化研究进展

早期海洋资料同化仅考虑温度的调整而忽略盐度的变化,这往往会带来虚假信息,可能导致密度场被严重恶化,同化后的结果甚至比没有同化任何观测资料时还要差。为了解决这个问题,海洋资料同化中的一些温、盐度多变量调整方案便被提出来了。本文对广泛应用于多变量分析的资料同化方法及不同温、盐度多变量调整方案进行了系统的回顾,对它们的优缺点进行了分析与讨论,并指出了不同调整方案的适用条件及应用现状,最后对Argo资料在海洋资料同化中的重要性及今后的研究重点进行了探讨。     

Analysis of the response of a non-linear data assimilation algorithm in a one-dimensional model of the upper ocean

A one-dimensional (1D) integral dynamico-stochastic model of the upper ocean with a non-linear assimilation algorithm is considered. The accuracy of computing the characteristics of the upper layer depends essentially on the values of the empirical coefficients. A numerical experiment was carried out which verified the efficiency of the model's adaptive mechanism operation when different values of the empirical coefficients and their variances were preset. Recommendations on assigment of the model's initial parameters are derived.Translated by Mikhail M. Trufanov.     

ARGO data assimilation into the ocean dynamics model with high spatial resolution using Ensemble Optimal Interpolation (EnOI)

The article proposes parallel implementation of the Ensemble Optimal Interpolation (EnOI) data assimilation (DA) method in eddy-resolving World Ocean circulation model. The results of DA experiments in North Atlantic with ARGO drifters are compared with the multivariate optimal interpolation (MVOI) DA scheme. The sensitivity of the model error, i.e., the difference between the model and observations depending on the number of ensemble elements, is also assessed and presented. The effectiveness of this method over the MVOI scheme is confirmed. The model outputs with and without assimilation are also compared with independent sea surface temperature data from ARMOR 3d.     

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.     

An adjoint method for the assimilation of statistical characteristics into eddy-resolving ocean models

The study investigates perspectives of the parameter estimation problem with the adjoint method in eddy-resolving models. Sensitivity to initial conditions resulting from the chaotic nature of this type of model limits the direct application of the adjoint method by predictability. Prolonging the period of assimilation is accompanied by the appearance of an increasing number of secondary minima of the cost function that prevents the convergence of this method. In the framework of the Lorenz model it is shown that averaged quantities are suitable for describing invariant properties, and that secondary minima are for this type of data transformed into stochastic deviations. An adjoint method suitable for the assimilation of statistical characteristics of data and applicable on time scales beyond the predictability limit is presented. The approach assumes a greater predictability for averaged quantities. The adjoint to a prognostic model for statistical moments is employed for calculating cost function gradients that ignore the fine structure resulting from secondary minima. Coarse resolution versions of eddy-resolving models are used for this purpose. Identical twin experiments are performed with a quasigeostrophic model to evaluate the performance and limitations of this approach in improving models by estimating parameters. The wind stress curl is estimated from a simulated mean stream function. A very simple parameterization scheme for the assimilation of second-order moments is shown to permit the estimation of gradients that perform efficiently in minimizing cost functions.     

Semi-Lagrangian methods for a finite element coastal ocean model

Coastal ocean hydrodynamic models are subject to a number of stability constraints. The most important of these are the Courant–Friedrichs–Levy (CFL) constraint on gravity waves, a Courant (Cr) number constraint on advection, and a time step constraint on the vertical component of viscous stresses. The model described here removes these constraints using a semi-implicit approximation in time and a semi-Lagrangian approximation for advection. The accuracy and efficiency of semi-Lagrangian methods depends crucially on the methods used to calculate trajectories and interpolate at the foot of the trajectory. The focus of this paper is on evaluation of several new and old semi-Langrangian methods. In particular, we compare 3 methods to calculate trajectories (Runge–Kutta (RK2), analytical integration (AN), power-series expansion (PS)) and 3 methods to interpolate (local linear (LL), global linear (GL), global quadratic (GQ)) on unstructured grids. The AN and PS methods are both efficient and accurate, and the latter can be expanded in a straightforward manner to treat time-dependent velocity. The GQ interpolation method provides a major step in introducing efficient and accurate semi-Lagrangian methods to unstructured grids.     

资料同化技术的发展及其在海洋科学中的应用

同顾了资料同化技术,特别是基于最优控制和统计估计这两大理论基础发展起来的几种资料同化方法的研究进展,以及这些方法在海洋科学研究中的应用现状.可以看到,由于海洋观测资料(如地转海洋学实时观测阵(Array for Real-time Geostrophic Oceanography,Argo)、热带大气海洋阵列(Trop...     

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.     

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.     

Sequential updating assimilation of simulated Geosat altimeter data from mesoscale features into a two-layer quasi-geostrophic model

A sequential updating method for assimilating Geosat altimeter data into an eddyresolving, quasi-geostrophic model is examined using simulated data of mesoscale features taken from a control run solution. The upper-layer streamfunction in the model is updated by the altimeter data on satellite tracks (at 110 km intervals) at times of observations (with 17-day cycles). To evaluate data suitability, the correlation between the data and the assimilation solution just before update is compared with the correlation between the two data with a 1-cycle separation: i.e., predictability is compared with persistence. The assimilation method is tested on mesoscale features such as linear Rossby waves, unstable mesoscale meanders in a jet and dipole eddies over realistic deep ocean topography. The assimilation method is successful for reconstructing the mesoscale features that evolve gradually or extend over more than one track. Assimilation is degraded by quick evolution of smaller scale features; i.e the unstable meanders that have short wavelengths and are not well captured by the altimeter with the low cross-track resolution, and the mesoscale features, whose lower layer component receives effects of bottom topography in the data but is underestimated due to inefficient downward transfer of the surface data in the assimilation.     

Kuroshio extension variability explored through assimilation of TOPEX/POSEIDON altimeter data into a quasi-geostrophic model

Mesoscale features in the eastward extension of the Kuroshio were investigated using assimilation of TOPEX/POSEIDON (T/P) data into a three-layer quasi-geostrophic model. The T/P data exhibited an elongated state of the southern recirculation gyre in 1993–95 and 1997, between whose two periods the gyre had a contracted state in 1995–96. A few stationary eddies were located in the southern gyre during the contracted state. The baroclinic instability, which was indicated by the phase shift from the uppermost-to the lowest-layer anomalies toward the downstream side, was evident near the Kuroshio Extension (KE) path. Since the instability never appeared in the artificial model without bottom topography, the topographic barrier for the eastward flow in the lowest layer was a necessary condition for the instability. The instability synchronized with the transition in the western region of the KE axis from the elongated to the contracted states. This evolution was interpreted as if the baroclinic instability played some part in the KE states and was a trigger for the transition from the elongated to the contracted states.     

An ocean data assimilation system and reanalysis of the World Ocean hydrophysical fields

A new version of the ocean data assimilation system (ODAS) developed at the Hydrometcentre of Russia is presented. The assimilation is performed following the sequential scheme analysis–forecast–analysis. The main components of the ODAS are procedures for operational observation data processing, a variational analysis scheme, and an ocean general circulation model used to estimate the first guess fields involved in the analysis. In situ observations of temperature and salinity in the upper 1400-m ocean layer obtained from various observational platforms are used as input data. In the new ODAS version, the horizontal resolution of the assimilating model and of the output products is increased, the previous 2D-Var analysis scheme is replaced by a more general 3D-Var scheme, and a more flexible incremental analysis updating procedure is introduced to correct the model calculations. A reanalysis of the main World Ocean hydrophysical fields over the 2005–2015 period has been performed using the updated ODAS. The reanalysis results are compared with data from independent sources.     

Monitoring of the large-scale dynamics of the ocean based on the assimilation of satellite data

An examle of satellite monitoring of the large-scale dynamics of the eastern sector of the tropical Atlantic Ocean in April 1990 is considered. As the satellite-derived data, a series of averaged 5-day maps of the remote data on the upper ocean temperature field obtained from satellites of the NOAA series was used. The profundity of the effect of the satellite data is estimated. Recommendations are provided. for selecting the regions most appropriate for rapid analysis of the circulation using satellite data.Translated by Mikhail M. Trufanov.