Toward a global ocean data assimilation system based on ensemble optimum interpolation: altimetry data assimilation experiment

A global ocean data assimilation system based on the ensemble optimum interpolation (EnOI) has been under development as the Chinese contribution to the Global Ocean Data Assimilation Experiment. The system uses a global ocean general circulation model, which is eddy permitting, developed by the Institute of Atmospheric Physics of the Chinese Academy of Sciences. In this paper, the implementation of the system is described in detail. We describe the sampling strategy to generate the stationary ensembles for EnOI. In addition, technical methods are introduced to deal with the requirement of massive memory space to hold the stationary ensembles of the global ocean. The system can assimilate observations such as satellite altimetry, sea surface temperature (SST), in situ temperature and salinity from Argo, XBT, Tropical Atmosphere Ocean (TAO), and other sources in a straightforward way. As a first step, an assimilation experiment from 1997 to 2001 is carried out by assimilating the sea level anomaly (SLA) data from TOPEX/Poseidon. We evaluate the performance of the system by comparing the results with various types of observations. We find that SLA assimilation shows very positive impact on the modeled fields. The SST and sea surface height fields are clearly improved in terms of both the standard deviation and the root mean square difference. In addition, the assimilation produces some improvements in regions where mesoscale processes cannot be resolved with the horizontal resolution of this model. Comparisons with TAO profiles in the Pacific show that the temperature and salinity fields have been improved to varying degrees in the upper ocean. The biases with respect to the independent TAO profiles are reduced with a maximum magnitude of about 0.25°C and 0.1 psu for the time-averaged temperature and salinity. The improvements on temperature and salinity also lead to positive impact on the subsurface currents. The equatorial under current is enhanced in the Pacific although it is still underestimated after the assimilation.     

Towards a data assimilation system for morphodynamic modeling: bathymetric data assimilation for wave property estimation

Data assimilation is mainly concerned with the proper management of uncertainties. The main objective of the present work is to implement and analyze a data assimilation technique capable of assimilating bathymetric data into a coupled flow, wave, and morphodynamic model. For the case presented here, wave significant height, wave direction of incidence, and wave peak period are being optimized based on bathymetric data taken from a twin experiment. An adjoint-free variational scheme is used. In this approach, a linear reduced order model (ROM) is constructed as an approximation of the full model. The ROM is an autoregressive model of order 1 (AR1) that preserves the parametrization. Since the ROM is linear, the construction of its adjoint is straightforward, making the implementation of 4D variational data assimilation effortless. The scheme is able to update the morphodynamic model satisfactorily despite the fact that the model shows nonlinear behavior even for very small perturbations of all three parameters. The size and direction of the perturbations necessary for constructing the ROM have a significant impact on the performance of the technique.     

Correcting circulation biases in a lower-resolution global general circulation model with data assimilation

In this study, we aim at developing a new method of bias correction using data assimilation. This method is based on the stochastic forcing of a model to correct bias by directly adding an additional source term into the model equations. This method is presented and tested first with a twin experiment on a fully controlled Lorenz ’96 model. It is then applied to the lower-resolution global circulation NEMO-LIM2 model, with both a twin experiment and a real case experiment. Sea surface height observations are used to create a forcing to correct the poorly located and estimated currents. Validation is then performed throughout the use of other variables such as sea surface temperature and salinity. Results show that the method is able to consistently correct part of the model bias. The bias correction term is presented and is consistent with the limitations of the global circulation model causing bias on the oceanic currents.     

An explicit four-dimensional variational data assimilation method

A new data assimilation method called the explicit four-dimensional variational (4DVAR) method is proposed. In this method, the singular value decomposition (SVD) is used to construct the orthogonal basis vectors from a forecast ensemble in a 4D space. The basis vectors represent not only the spatial structure of the analysis variables but also the temporal evolution. After the analysis variables are ex-pressed by a truncated expansion of the basis vectors in the 4D space, the control variables in the cost function appear explicitly, so that the adjoint model, which is used to derive the gradient of cost func-tion with respect to the control variables, is no longer needed. The new technique significantly simpli-fies the data assimilation process. The advantage of the proposed method is demonstrated by several experiments using a shallow water numerical model and the results are compared with those of the conventional 4DVAR. It is shown that when the observation points are very dense, the conventional 4DVAR is better than the proposed method. However, when the observation points are sparse, the proposed method performs better. The sensitivity of the proposed method with respect to errors in the observations and the numerical model is lower than that of the conventional method.     

基于Metropolis优化的叠前全局迭代地质统计学反演方法

叠前地质统计学反演将随机模拟与叠前反演相结合,不仅可以反演各种储层弹性参数,还提高了反演结果的分辨率.基于联合概率分布的直接序贯协模拟方法可以在原始数据域对数据进行模拟,不需要对数据进行高斯变换,拓展了地质统计学反演的应用范围;而联合概率分布的应用确保了反演参数之间相关性,提高了反演的精度.本文将基于联合概率分布的直接序贯协模拟方法与蒙特卡洛抽样算法相结合,参考全局随机反演策略,提出了基于蒙特卡洛优化算法的全局迭代地质统计学反演方法.为了提高反演的稳定性,我们修改了局部相关系数的计算公式,提出了一种新的基于目标函数的优化局部相关系数计算公式并应用到协模拟之中.模型测试及实际数据应用表明,该方法可以很好的应用于叠前反演之中.

     

基于波场传播方向的波动方程偏移有效去噪方法(英文)

本文研究分析了双程波波动方程偏移成像中广泛存在的三种主要噪声,特别是针对过去研究中没能很好解决的存在于高速盐丘悬垂边界附近的射线状噪声,提出了基于优化成像条件的有效去噪方法。射线状噪声主要来自于震源一侧波场的下行透射波分量和接收阵列一侧波场的上行散射波互相关成像。这一部分能量具有较强的互相关性,但并不携带真实的反射面信息。它广泛存在叠前偏移成像中,与信号在强度上同量级。多数情况下偏移成像中的相关噪声由方向性传播的波场能量产生。利用波场梯度得到的波场传播角度,可以分离出噪声对应的波场能量,并在成像条件中减去。采用这一方法可以有效地去除多种噪声,包括直达波噪声、散射波噪声和射线状噪声。该去噪方法不依赖波场外推算子,在需要时可以方便地运用到几乎所有的波动方程偏移中去。并且该去噪方法针对噪声的物理根源,对信号的损害很小。对去噪后的偏移成像结果额外地进行波数域滤波处理,可以进一步提高叠加图像的质量。这一去噪方法在超广角单程波偏移成像中取得良好效果,我们同时期待其在其他双程波波动方程偏移特别是逆时偏移(RTM)中的成功运用。     

An explicit four-dimensional variational data assimilation method based on the proper orthogonal decomposition: Theoretics and evaluation

The proper orthogonal decomposition (POD) method is used to construct a set of basis functions for spanning the ensemble of data in a certain least squares optimal sense. Compared with the singular value decomposition (SVD), the POD basis functions can capture more energy in the forecast ensemble space and can represent its spatial structure and temporal evolution more effectively. After the analysis variables are expressed by a truncated expansion of the POD basis vectors in the ensemble space, the control variables appear explicitly in the cost function, so that the adjoint model, which is used to derive the gradient of the cost function with respect to the control variables, is no longer needed. The application of this new technique significantly simplifies the data assimilation process. Several assimilation experiments show that this POD-based explicit four-dimensional variational data assimilation method performs much better than the usual ensemble Kalman filter method on both enhancing the assimilation precision and reducing the computation cost. It is also better than the SVD-based explicit four-dimensional assimilation method, especially when the forecast model is not perfect and the forecast error comes from both the noise of the initial filed and the uncertainty of the forecast model. Supported by the National Natural Science Foundation of China (Grant No. 40705035), National High Technology Research and Development Program of China (Grant No. 2007AA12Z144), Knowledge Innovation Project of Chinese Academy of Sciences (Grant Nos. KZCX2-YW-217 and KZCX2-YW-126-2), and National Basic Research Program of China (Grant No. 2005CB321704)     

The SEEK filter method for data assimilation in oceanography: a synthesis

This paper reviews the developments of the singular evolutive extended Kalman (SEEK) filter method used for data assimilation in oceanography, since the original paper by Pham et al. (J Mar Syst 16:3–4, 323–340 1998a). First, a short review is presented of the context of data assimilation in oceanography and of the variety of numerical ocean codes and configurations in which the SEEK filter has been implemented using different data sets for assimilation. Then, the paper provides an exposition of the different versions of the SEEK filter developed during the past 10 years and discusses their relative merits for scientific or operational implementations. A classification of the algorithmic variants is proposed, and several possible improvements of the generic methodology are mentioned in the perspective of new assimilation challenges.     

An estimation method for effective stress changes in a reservoir from 4D seismics data

Advances in seismics acquisition and processing and the widespread use of 4D seismics have made available reliable production‐induced subsurface deformation data in the form of overburden time‐shifts. Inversion of these data is now beginning to be used as an aid to the monitoring of a reservoir's effective stress. Past solutions to this inversion problem have relied upon analytic calculations for an unrealistically simplified subsurface, which can lead to uncertainties. To enhance the accuracy of this approach, a method based on transfer functions is proposed in which the function itself is calibrated using numerically generated overburden strain deformation calculated for a small select group of reference sources. This technique proves to be a good compromise between the faster but more accurate history match of the overburden strain using a geomechanical simulator and the slower, less accurate analytic method. Synthetic tests using a coupled geomechanical and fluid flow simulator for the South Arne field confirm the efficacy of the method. Application to measured time‐shifts from observed 4D seismics indicates compartmentalization in the Tor reservoir, more heterogeneity than is currently considered in the simulation model and moderate connectivity with the overlying Ekofisk formation.     

A new methodology for using buoy measurements in sea wave data assimilation

One of the main drawbacks in modern sea wave data assimilation models is the limited temporal and spatial improvement obtained in the final forecasting products. This is mainly due to deviations coming either from the relevant atmospheric input or from the dynamics of the wave model, resulting to systematic errors of the forecasted fields of numerical wave models, when no observation is available for assimilation. A potential solution is presented in this work, based on a combination of advanced statistical techniques, data assimilation systems, and wave models. More precisely, Kalman filtering algorithms are implemented into the wave model WAM and the results are assimilated by an Optimum Interpolation Scheme, in order to extend the beneficial influence of the latter in time and space. The case studied concerns a 3-month period in an open sea area near the South-West coast of the USA (Pacific Ocean).     

Surface wave tomography method based on data from distant earthquakes

The standard method of surface wave tomography assumes the use of data on surface wave velocities measured on paths wholly located inside the region being investigated and oriented in different directions. If the data on group velocities obtained in the regional network of stations are used for this purpose, then the earthquake sources also should be situated within the limits of this region. If the region is small, then this requirement restricts the range of periods of surface waves and, correspondingly, the depth of research. The use of data from distant earthquakes enlarges the range of periods. However, it does not enable one to use the usual tomography method because of an inappropriate configuration of the system of paths: outside of the region in which the stations are located, the paths do not intersect, but, at the same time, the paths from a particular earthquake source toward the different stations of networks are very close over a large distance, and the mean correction to the velocity in the path sections outside of the network of stations can be accepted as identical. This assumption forms the basis of the proposed modification of the method of surface wave tomography, in which group velocities measured at stations of the local network from distant earthquakes are used. The lateral variations in the velocity are determined within the limits of the network, and the mean corrections to the velocity are determined on the paths from different earthquake sources in the sections outside of the network. As earlier, the condition of smoothness is imposed on the distribution of velocity variations, and the condition of smallness of the sum of their squares is imposed on the values of the corrections to the velocity. Testing of this method based on model examples and on real data obtained in the network of stations in Tibet showed its advantage over the standard tomography method.     

Unified global and regional wave model on a multi-resolution grid

Models for ocean surface wave forecasting in weather centres comprise global and regional systems in order to efficiently meet service demands. Regional models cannot run alone and have to use large area or global models to provide boundary wave spectra. The modern two-way nesting technique is to run the two models together with the regional model domain covered by both resolutions. An alternative method is to use a single multi-resolution grid that fits irregular coastlines and provides refined resolutions in selected regions. This paper presents a multi-resolution model based on a spherical multiple-cell (SMC) grid, which is designed to relax the CFL restriction of Eulerian advection time step at high latitudes by merging the conventional latitude-longitude grid cells. The implementation of the SMC grid in WAVEWATCH III is described, and a multi-resolution (6, 12 and 25 km) global SMC configuration is compared with a suite of nested grid ocean surface wave models, including 35-km global, 8-km European and 4-km UK regional models. Verification against buoy and platform wave observations indicates that the unified model is better than the 35-km global and very close in performance to the two regional models.     

A fuzzy logic based dynamic wave model inversion algorithm for canal regulation

A fuzzy logic based centralized control algorithm for irrigation canals is presented. Purpose of the algorithm is to control downstream discharge and water level of pools in the canal, by adjusting discharge release from the upstream end and gates settings. The algorithm is based on the dynamic wave model (Saint‐Venant equations) inversion in space, wherein the momentum equation is replaced by a fuzzy rule based model, while retaining the continuity equation in its complete form. The fuzzy rule based model is developed on fuzzification of a new mathematical model for wave velocity, the derivational details of which are given. The advantages of the fuzzy control algorithm, over other conventional control algorithms, are described. It is transparent and intuitive, and no linearizations of the governing equations are involved. Tuning of the algorithm and method of computation are explained. It is shown that the tuning is easy and the computations are straightforward. The algorithm provides stable, realistic and robust outputs. The disadvantage of the algorithm is reduced precision in its outputs due to the approximation inherent in the fuzzy logic. Feed back control logic is adopted to eliminate error caused by the system disturbances as well as error caused by the reduced precision in the outputs. The algorithm is tested by applying it to water level control problem in a fictitious canal with a single pool and also in a real canal with a series of pools. It is found that results obtained from the algorithm are comparable to those obtained from conventional control algorithms. Copyright © 2009 John Wiley & Sons, Ltd.     

Variational data assimilation for parameter estimation: application to a simple morphodynamic model

Data assimilation is a sophisticated mathematical technique for combining observational data with model predictions to produce state and parameter estimates that most accurately approximate the current and future states of the true system. The technique is commonly used in atmospheric and oceanic modelling, combining empirical observations with model predictions to produce more accurate and well-calibrated forecasts. Here, we consider a novel application within a coastal environment and describe how the method can also be used to deliver improved estimates of uncertain morphodynamic model parameters. This is achieved using a technique known as state augmentation. Earlier applications of state augmentation have typically employed the 4D-Var, Kalman filter or ensemble Kalman filter assimilation schemes. Our new method is based on a computationally inexpensive 3D-Var scheme, where the specification of the error covariance matrices is crucial for success. A simple 1D model of bed-form propagation is used to demonstrate the method. The scheme is capable of recovering near-perfect parameter values and, therefore, improves the capability of our model to predict future bathymetry. Such positive results suggest the potential for application to more complex morphodynamic models.     

An equivalent layer magnetization model for Australia based on Magsat data

An equivalent layer magnetization model for Australia and adjacent oceanic areas is presented. The model is obtained by linear inversion of Magsat anomaly data measured in the altitude range 325–550 km. The anomaly data set has been isolated from the raw data set by use of models of the core field and very long wavelength external fields, and is internally consistent. Certain major structural features of the Australian continent are geographically associated with magnetization anomalies. A first-order difference is seen between the Tasman Zone and the Precambrian cratonic areas: magnetization anomalies are much more subdued in the former, possibly reflecting a shallowing of the Curie isotherm within the crust. A profile of the vertical integral of magnetization is presented for a crustal section extending from the Gawler Block to the southeast coast. It is shown that the magnetization variations are probably due partly, but not wholly, to depth to Curie isotherm variations; gross magnetization variations among at least three distinct crustal units must be involved.     

基于集合卡尔曼滤波的湖泊富营养化模型Delft3D-BLOOM数据同化

富营养化模型是进行湖泊水环境质量预测和管理的重要工具,然而模型客观存在的误差一直是应用者关心的重要问题.数据同化作为连接观测数据与数值模型的重要方法,可以有效提高模型的准确性.集合卡尔曼滤波(En KF)是众多数据同化算法中应用最为广泛的一种,可进行非线性系统的数据同化,并能有效降低数据同化的计算量.本研究以太湖作为具体实例,选择Delft3D-BLOOM作为富营养化模型,在数值实验确定En KF集合数为100、观测误差方差为1%、模拟误差方差为10%的基础上分别进行模型状态变量同化以及状态变量与关键参数同步同化.结果显示,仅同化状态变量时,模型预测精度有所增加;同时同化状态变量和关键参数时,可显著提升模型在湖泊水环境质量预测中的精度.该研究为应用集合卡尔曼滤波以提高复杂的湖库富营养化模型模拟精度提供了有效的方法.     

Inverse model method for estimating assimilation by aquatic invertebrates

Physiological data indicate that a 3-compartment model appropriately represents ingestion, assimilation, and accumulation of somatic and reproductive tissue by an aquatic invertebrate predator. A secondary production model calibrated to growth and respiration data is used to constrain the model equations. Inverse solution methods are used to estimate rate constants for digestion and for net accrual of tissue by growing animals at different temperatures. Predicted time to 50% maximum digestion matches well with the empirical rate of digestion of prey enzymes in the predator gut. Model-derived digestion rates are consistent with the assimilation rate constant obtained by independent radiotracer methods, and with experimental detection time for prey enzymes. The model approach permits parameter estimation within a complex system of equations so that results can be compared with experimental data.     

Using data assimilation method to calibrate a heterogeneous conductivity field conditioning on transient flow test data

A data assimilation method is developed to calibrate a heterogeneous hydraulic conductivity field conditioning on transient pumping test data. The ensemble Kalman filter (EnKF) approach is used to update model parameters such as hydraulic conductivity and model variables such as hydraulic head using available data. A synthetical two-dimensional flow case is used to assess the capability of the EnKF method to calibrate a heterogeneous conductivity field by assimilating transient flow data from observation wells under different hydraulic boundary conditions. The study results indicate that the EnKF method will significantly improve the estimation of the hydraulic conductivity field by assimilating continuous hydraulic head measurements and the hydraulic boundary condition will significantly affect the simulation results. For our cases, after a few data assimilation steps, the assimilated conductivity field with four Neumann boundaries matches the real field well while the assimilated conductivity field with mixed Dirichlet and Neumann boundaries does not. We found in our cases that the ensemble size should be 300 or larger for the numerical simulation. The number and the locations of the observation wells will significantly affect the hydraulic conductivity field calibration.