Sequential Assimilation Methods Research Articles

A Flow‐Dependent Targeted Observation Method for Ensemble Kalman Filter Assimilation Systems

AbstractIn this study, we developed a flow‐dependent sequential assimilation‐based targeted observation method by minimizing the analysis error variance under the framework of the ensemble Kalman filter (EnKF). This approach considers the flow‐dependent variation in background error statistics when identifying optimal observational sites through the sequential assimilation method. Covariance localization is also introduced in this method, enabling computational efficiency and eliminating impacts from spurious observations. By quantifying the reduction in analysis error variances, the proposed method could estimate the potential improvements by each optimal observation while assimilated. With this method, we design an optimal observational array for sea level anomaly (SLA) prediction in the tropical Indian Ocean (TIO), which is implemented using a fully coupled climate model, the Community Earth System Model (CESM), in conjunction with a coupled assimilation system. The optimal observational array detected from this method was found to theoretically reduce the initial uncertainty by up to approximately 60% of the error variance. An observing system simulation experiment (OSSE) using the CESM and the coupled assimilation system, which was designed for validation purposes, confirms the theoretical reduction in the analysis error variance by the optimal observation array.

Data assimilation strategies for volcano geodesy

Ground deformation observed using near-real time geodetic methods, such as InSAR and GPS, can provide critical information about the evolution of a magma chamber prior to volcanic eruption. Rapid advancement in numerical modeling capabilities has resulted in a number of finite element models targeted at better understanding the connection between surface uplift associated with magma chamber pressurization and the potential for volcanic eruption. Robust model-data fusion techniques are necessary to take full advantage of the numerical models and the volcano monitoring observations currently available. In this study, we develop a 3D data assimilation framework using the Ensemble Kalman Filter (EnKF) approach in order to combine geodetic observations of surface deformation with geodynamic models to investigate volcanic unrest. The EnKF sequential assimilation method utilizes disparate data sets as they become available to update geodynamic models of magma reservoir evolution. While the EnKF has been widely applied in hydrologic and climate modeling, the adaptation for volcano monitoring is in its initial stages. As such, our investigation focuses on conducting a series of sensitivity tests to optimize the EnKF for volcano applications and on developing specific strategies for assimilation of geodetic data. Our numerical experiments illustrate that the EnKF is able to adapt well to the spatial limitations posed by GPS data and the temporal limitations of InSAR, and that specific strategies can be adopted to enhance EnKF performance to improve model forecasts. Specifically, our numerical experiments indicate that: (1) incorporating additional iterations of the EnKF analysis step is more efficient than increasing the number of ensemble members; (2) the accuracy of the EnKF results are not affected by initial parameter assumptions; (3) GPS observations near the center of uplift improve the quality of model forecasts; (4) occasionally shifting continuous GPS stations to provide variability in the locations of observations results in better model predictions than utilizing fixed locations when the number of available instruments is limited; (5) spotty InSAR data coverage on the flanks of a volcano due to topographic shadows and/or atmospheric interference does not adversely impact the effectiveness of EnKF if the available coverage is >50%; and (6) snow or glacial obstruction in the center of uplift can adversely impact EnKF forecasts. By utilizing these strategies, we conclude that the EnKF is an effective sequential model-data fusion technique for assimilating multiple geodetic observations to forecast volcanic activity at restless volcanoes.

Sequential Method with Incremental Analysis Update to Retrieve Leaf Area Index from Time Series MODIS Reflectance Data

High-quality leaf area index (LAI) products retrieved from satellite observations are urgently needed for crop growth monitoring and yield estimation, land-surface process simulation and global change studies. In recent years, sequential assimilation methods have been increasingly used to retrieve LAI from time series remote-sensing data. However, the inherent characteristics of these sequential assimilation methods result in temporal discontinuities in the retrieved LAI profiles. In this study, a sequential assimilation method with incremental analysis update (IAU) was developed to jointly update model states and parameters and to retrieve temporally continuous LAI profiles from time series Moderate Resolution Imaging Spectroradiometer (MODIS) reflectance data. Based on the existing multi-year Global Land Surface Satellite (GLASS) LAI product, a dynamic model was constructed to evolve LAI anomalies over time. The sequential assimilation method with an IAU technique takes advantage of the Kalman filter (KF) technique to update model parameters, uses the ensemble Kalman filter (EnKF) technique to update LAI anomalies recursively from time series MODIS reflectance data and then calculates the temporally continuous LAI values by combining the LAI climatology data. The method was tested over eight Committee on Earth Observing Satellites-Benchmark Land Multisite Analysis and Intercomparison of Products (CEOS-BELMANIP) sites with different vegetation types. The results indicate that the sequential method with IAU can precisely reconstruct the seasonal variation patterns of LAI and that the LAI profiles derived from the sequential method with IAU are smooth and continuous.

Optimal adjustment of the atmospheric forcing parameters of ocean models using sea surface temperature data assimilation

Abstract. In ocean general circulation models, near-surface atmospheric variables used to specify the atmospheric boundary condition remain one of the main sources of error. The objective of this research is to constrain the surface forcing function of an ocean model by sea surface temperature (SST) data assimilation. For that purpose, a set of corrections for ERAinterim (hereafter ERAi) reanalysis data is estimated for the period of 1989–2007, using a sequential assimilation method, with ensemble experiments to evaluate the impact of uncertain atmospheric forcing on the ocean state. The control vector of the assimilation method is extended to atmospheric variables to obtain monthly mean parameter corrections by assimilating monthly SST and sea surface salinity (SSS) climatological data in a low resolution global configuration of the NEMO model. In this context, the careful determination of the prior probability distribution of the parameters is an important matter. This paper demonstrates the importance of isolating the impact of forcing errors in the model to perform relevant ensemble experiments. The results obtained for every month of the period between 1989 and 2007 show that the estimated parameters produce the same kind of impact on the SST as the analysis itself. The objective is then to evaluate the long-term time series of the forcing parameters focusing on trends and mean error corrections of air–sea fluxes. Our corrections tend to equilibrate the net heat-flux balance at the global scale (highly positive in ERAi database), and to remove the potentially unrealistic negative trend (leading to ocean cooling) in the ERAi net heat flux over the whole time period. More specifically in the intertropical band, we reduce the warm bias of ERAi data by mostly modifying the latent heat flux by wind speed intensification. Consistently, when used to force the model, the corrected parameters lead to a better agreement between the mean SST produced by the model and mean SST observations over the period of 1989–2007 in the intertropical band.

Assimilation of Wave Data for Simulations of Typhoon Waves in the South China Sea

A sequential assimilation method is applied to improve the accuracy of wave simulations in the South China Sea. Typhoon Nesat was chosen to be used for the numerical experiment. The assimilation is based on Optimal Interpolation(OI) which can minimize the Root-Mean-Square error in the analysis. Using the method of OI, wave height and mean period data observed by three buoys have been assimilated into the third generation ocean wave model(SWAN). The results show that the assimilation can correct the difference between the wave model and observations, and the result of significant wave height is superior to that of mean period.

History matching of petroleum reservoir models by the Ensemble Kalman Filter and parameterization methods

The Ensemble Kalman Filter (EnKF) has been successfully applied in petroleum engineering during the past few years to constrain reservoir models to production or seismic data. This sequential assimilation method provides a set of updated static variables (porosity, permeability) and dynamic variables (pressure, saturation) at each assimilation time. However, several limitations can be pointed out. In particular, the method does not prevent petrophysical realizations from departing from prior information. In addition, petrophysical properties can reach extreme (non-physical) values. In this work, we propose to combine the EnKF with two parameterization methods designed to preserve second-order statistical properties: pilot points and gradual deformation. The aim is to prevent the departure of the constrained petrophysical property distributions from prior information. Over/under estimations should also be avoided. The two algorithms are applied to a synthetic case. Several parameter configurations are investigated in order to identify solutions improving the performance of the method.

Ensemble perturbation smoother for optimizing tidal boundary conditions by assimilation of High-Frequency radar surface currents – application to the German Bight

Abstract. High-Frequency (HF) radars measure the ocean surface currents at various spatial and temporal scales. These include tidal currents, wind-driven circulation, density-driven circulation and Stokes drift. Sequential assimilation methods updating the model state have been proven successful to correct the density-driven currents by assimilation of observations such as sea surface height, sea surface temperature and in-situ profiles. However, the situation is different for tides in coastal models since these are not generated within the domain, but are rather propagated inside the domain through the boundary conditions. For improving the modeled tidal variability it is therefore not sufficient to update the model state via data assimilation without updating the boundary conditions. The optimization of boundary conditions to match observations inside the domain is traditionally achieved through variational assimilation methods. In this work we present an ensemble smoother to improve the tidal boundary values so that the model represents more closely the observed currents. To create an ensemble of dynamically realistic boundary conditions, a cost function is formulated which is directly related to the probability of each boundary condition perturbation. This cost function ensures that the boundary condition perturbations are spatially smooth and that the structure of the perturbations satisfies approximately the harmonic linearized shallow water equations. Based on those perturbations an ensemble simulation is carried out using the full three-dimensional General Estuarine Ocean Model (GETM). Optimized boundary values are obtained by assimilating all observations using the covariances of the ensemble simulation.

Assimilating Amounts of Precipitation Using a New Four-Dimensional Variational Method

Observations of accumulated precipitation are extremely valuable for effectively improving rainfall analysis and forecast. It is, however, difficult to use such observations directly through sequential assimilation methods, such as three–dimensional variational data assimilation or an Ensemble Kalman Filter. In this study, the authors illustrate a new approach that makes effective use of precipitation data to improve rainfall forecast. The new method directly obtains an optimal solution in a reduced space by fitting observations with historical time series generated by the model; it also avoids the implementation of tangent linear model and its adjoint. A lot of historical samples are produced as the ensemble of precipitation observations with the fully nonlinear forecast model. The results show that the new approach is capable of extracting information from precipitation observations to improve the analysis and forecast. This method provides comparable performance with the standard fourdimensional variational data assimilation at a much lower computational cost.

Incremental Analysis Update Implementation into a Sequential Ocean Data Assimilation System

Abstract This study deals with the enhancement of a sequential assimilation method applied to an ocean general circulation model (OGCM). A major drawback of sequential assimilation methods is the time discontinuity of the solution resulting from intermittent corrections of the model state. The data analysis step can induce shocks in the model restart phase, causing spurious high-frequency oscillations and data rejection. A method called Incremental Analysis Update (IAU) is now recognized to efficiently tackle these problems. In the present work, an IAU-type method is implemented into an intermittent data assimilation system using a low-rank Kalman filter [Singular Evolutive Extended Kalman (SEEK)] in the case of an OGCM with a 1/3° North Atlantic grid. A 1-yr (1993) experiment has been conducted for different setups in order to evaluate the impact of the IAU scheme. Results from all of the different tests are compared with a specific interest in high-frequency output behaviors and solution consistency. The improvements brought up by the IAU implementation, such as the disappearance of spurious high-frequency oscillations and the time continuity of the solution, are shown. An overall assessment of the impact of this new approach on the assimilated runs is discussed. Advantages and drawbacks of the IAU method are pointed out.

A singular evolutive extended Kalman filter for data assimilation in oceanography

In this work, we propose a modified form of the extended Kalman filter (KF) for assimilating oceanic data into numerical models. Its development consists essentially of approximating the error covariance matrix by a singular low rank matrix, which amounts in practice to making no correction in those directions for which the error is the most attenuated by the system. This not only reduces the implementation cost but may also improve the filter stability as well. These `directions of correction' evolve with time according to the model evolution, which constitutes the most original feature of this filter and distinguishes it from other sequential assimilation methods based on the projection onto a fixed basis of functions. A method for initializing the filter based on the empirical orthogonal functions (EOF) is also described. An example of assimilation based on the quasi-geostrophic (QG) model for a square ocean domain with a certain wind stress forcing pattern is given. Although this is only a simple test case designed to assess the feasibility of the method, the results are very encouraging.

Variational assimilation of simulated acoustic tomography data and point observations: A comparative study

A simple advection‐diffusion model is used to generate synthetic acoustic tomography data and local temperature observations which are then assimilated by a numerical model. The data are assimilated using the following two methods: a variational adjoint method and a sequential assimilation technique formulated as a minimization problem. The “success” of the analyses are gauged by comparing them to the true fields and, in the adjoint assimilation experiments, by also performing analysis of error and resolution. Results show that with the same number of acoustic rays and point observations the initial temperature field is well reproduced whether acoustic data or local temperature data are used. Model and observation errors are introduced in the main assimilation experiments by adding random noise to the velocities of the model that generates the data but not into the assimilation model (model error). On top of that, extra random noise is added directly to the “observations” (observation error). The results are compared to experiments where only one source of error is introduced and to “identical twin” experiments in which there are neither model nor observation errors and therefore model and data are perfectly compatible. The effect of model error is to produce analyses whose error grows with time even in the presence of diffusion which tends to reduce such errors, whereas observation errors produce analyses similar to the identical twin experiments. The detrimental effect of model (and observation) errors can be reduced by weighting properly the background or a priori information which is used to regularize the analyses. It is found that the analyses from sequential assimilation methods are more sensitive to this weight. Adjoint‐variational assimilation is used to determine other model parameters (in this case, one of the advective velocities of the model) as a method to correct model deficiencies from data.