Benefits and Cautions in Data Assimilation Strategies: An Example of Modeling Groundwater Recharge

Assimilating recent observations improves model outcomes for real-time assessments of groundwater processes. This is demonstrated in estimating time-varying recharge to a shallow fractured-rock aquifer in response to precipitation. Results from estimating the time-varying water-table altitude (h) and recharge, and their error covariances, are compared for forecasting, filtering, and fixed-lag smoothing (FLS), which are implemented using the Kalman Filter as applied to a data-driven, mechanistic model of recharge. Forecasting uses past observations to predict future states and is the current paradigm in most groundwater modeling investigations; filtering assimilates observations up to the current time to estimate current states; and FLS estimates states following a time lag over which additional observations are collected. Results for forecasting yield a large error covariance relative to the magnitude of the expected recharge. With assimilating recent observations of h, filtering and FLS produce estimates of recharge that better represent time-varying observations of h and reduce uncertainty in comparison to forecasting. Although model outcomes from applying data assimilation through filtering or FLS reduce model uncertainty, they are not necessarily mass conservative, whereas forecasting outcomes are mass conservative. Mass conservative outcomes from forecasting are not necessarily more accurate, because process errors are inherent in any model. Improvements in estimating real-time groundwater conditions that better represent observations need to be weighed for the model application against outcomes with inherent process deficiencies. Results from data assimilation strategies discussed in this investigation are anticipated to be relevant to other groundwater processes models where system states are sensitive to system inputs.     

Variational Data Assimilation Technique in Mathematical Modeling of Ocean Dynamics

Problems of the variational data assimilation for the primitive equation ocean model constructed at the Institute of Numerical Mathematics, Russian Academy of Sciences are considered. The model has a flexible computational structure and consists of two parts: a forward prognostic model, and its adjoint analog. The numerical algorithm for the forward and adjoint models is constructed based on the method of multicomponent splitting. The method includes splitting with respect to physical processes and space coordinates. Numerical experiments are performed with the use of the Indian Ocean and the World Ocean as examples. These numerical examples support the theoretical conclusions and demonstrate the rationality of the approach using an ocean dynamics model with an observed data assimilation procedure.     

Full-Wave Seismic Data Assimilation: Theoretical Background and Recent Advances

The seismological inverse problem has much in common with the data assimilation problem found in meteorology and oceanography. Using the data assimilation methodology, I will formulate the seismological inverse problem for estimating seismic source and Earth structure parameters in the form of weak-constraint generalized inverse, in which the seismic wave equation and the associated initial and boundary conditions are allowed to contain errors. The resulting Euler?CLagrange equations are closely related to the adjoint method and the scattering-integral method, which have been successfully applied in full-3D, full-wave seismic tomography and earthquake source parameter inversions. I will review some recent applications of the full-wave methodology in seismic tomography and seismic source parameter inversions and discuss some challenging issues related to the computational implementation and the effective exploitation of seismic waveform data.     

Sorption of Iron on Surfaces: Modelling,Data Evaluation,and Measurement Uncertainty

Assessment of the likely outcome of engineered invention strategies in acid mine drainage often involves complex geochemical modelling activities. Geochemical modelling is based on chemical thermodynamic data. In addition sorption models, kinetical reaction rates and transport tools are included into the modelling codes because the interactions between solution components and surfaces, reaction time and transport are considered important features characterising the site‐specific situation. In the determination of both thermodynamic data and sorption coefficients, speciation calculations play an important role. By applying the probabilistic speciation code Ljungskile to some simplified acid mine drainage scenarios, the strong impact of chemical speciation on the complete measurement uncertainty budget of geochemical modelling predictions is shown. The complete measurement uncertainty budget in combination with other metrological concepts like traceability is an essential element of quality assurance for experimental data. The elements of quality assurance are provided by international agreements and normative documents on national and international levels. The following discussion will focus on some metrological issues of sorption data.     

Probability Theory as Logic: Data Assimilation for Multiple Source Reconstruction

Probability theory as logic (or Bayesian probability theory) is a rational inferential methodology that provides a natural and logically consistent framework for source reconstruction. This methodology fully utilizes the information provided by a limited number of noisy concentration data obtained from a network of sensors and combines it in a consistent manner with the available prior knowledge (mathematical representation of relevant physical laws), hence providing a rigorous basis for the assimilation of this data into models of atmospheric dispersion for the purpose of contaminant source reconstruction. This paper addresses the application of this framework to the reconstruction of contaminant source distributions consisting of an unknown number of localized sources, using concentration measurements obtained from a sensor array. To this purpose, Bayesian probability theory is used to formulate the full joint posterior probability density function for the parameters of the unknown source distribution. A simulated annealing algorithm, applied in conjunction with a reversible-jump Markov chain Monte Carlo technique, is used to draw random samples of source distribution models from the posterior probability density function. The methodology is validated against a real (full-scale) atmospheric dispersion experiment involving a multiple point source release.     

Fundamental Control Functions and Error Analysis in Variational Data Assimilation

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The equation for the error of the optimal solution (analysis) is derived through the errors of the input data (background and observation errors). The numerical algorithm is developed to compute the sensitivity coefficients for the analysis error using the fundamental control functions. Application to the variational data assimilation problem for a model of ocean thermodynamics is considered.     

Overview of the EUROSAM project and a Decision Support System

The EUROpean SAlt marshes Modelling (EUROSAM) project is part of the Thematic Network European Land–Ocean Interaction Studies programme. The main aims of the EUROSAM project were to fill in some of the main gaps in the understanding of ecological processes, to integrate this knowledge into models to predict the likely response of salt marsh ecosystems to environmental changes, and to make the knowledge available to decision-makers. Research work and model development for the project were carried out by researchers in France, Portugal, the Netherlands, and England, and included studies on sediment dynamics and interactions with vegetation, plant population dynamics and genetics, models of organic matter production and cycling, studies of animal communities, food webs and organic matter fluxes, and development of hydrodynamic models at different scales: salt marsh, bay, and estuary.This paper describes the main aims and outputs of the EUROSAM project, and the incorporation of the findings and models into a prototype Decision Support System (DSS). The EUROSAM DSS is designed as a guide for the non-specialist to understand the important role and functioning of salt marshes, and for use as a management tool. Example scenarios were selected from the work within the project to illustrate the interactions between components of the salt marsh–mudflat ecosystem, and the potential impact of human activities and environmental change on the salt marsh system.     

集合资料同化中方差滤波技术研究及试验

本文基于YH4DVAR业务系统构建了集合资料同化试验平台,利用10个集合样本统计得到的流依赖背景误差能显著改进业务应用中背景误差方差的结构和大小.但是受样本数的限制,背景误差方差的集合估计值中引入了大量的随机取样噪声.为了降低噪声对估计值的影响,本文采用谱滤波方法,根据信号和噪声尺度的统计特征构造一个低通滤波器来滤除背景误差方差估计值中的大部分随机取样噪声.在2013年第九号台风"飞燕"的集合方差滤波试验中,10个样本的滤波结果优于30个样本的集合估计值.谱滤波方法的成功应用有效降低了集合资料同化系统对集合样本数的要求,将是集合资料同化系统未来业务化运行的一项不可或缺的关键技术.     

Quantification of Exhumation from Sonic Velocity Data, Cooper Basin, Australia, and Implications for Hydrocarbon Exploration

Exhumation (defined as rock uplift minus surface uplift) in the Cooper Basin of South Australia and Queensland has been quantified using the compaction methodology. The sonic log, which is strongly controlled by the amount of porosity, is an appropriate indicator of compaction, and hence is used for quantifying exhumation from compaction. The traditional way of estimating exhumation based on the degree of overcompaction of a single shale unit has been modified and five units ranging in age from Permian to Triassic have been analysed. The results reveal that exhumation increases eastwards from the South Australia into the Queensland sector of the basin. The results show that exhumation in Late Triassic – Early Jurassic times, after the Cooper Basin deposition, seems to be 200–400 m higher than exhumation in Late Cretaceous – Tertiary times, after the Eromanga Basin deposition. This study has major implications for hydrocarbon exploration. Maturation of source rocks will be greater for any given geothermal history if exhumation is incorporated in maturation modelling. Exhumation values can also be used to improve porosity predictions of reservoir units in undrilled targets.     

A Genetic Algorithm Variational Approach to Data Assimilation and Application to Volcanic Emissions

Variational data assimilation methods optimize the match between an observed and a predicted field. These methods normally require information on error variances of both the analysis and the observations, which are sometimes difficult to obtain for transport and dispersion problems. Here, the variational problem is set up as a minimization problem that directly minimizes the root mean squared error of the difference between the observations and the prediction. In the context of atmospheric transport and dispersion, the solution of this optimization problem requires a robust technique. A genetic algorithm (GA) is used here for that solution, forming the GA-Variational (GA-Var) technique. The philosophy and formulation of the technique is described here. An advantage of the technique includes that it does not require observation or analysis error covariances nor information about any variables that are not directly assimilated. It can be employed in the context of either a forward assimilation problem or used to retrieve unknown source or meteorological information by solving the inverse problem. The details of the method are reviewed. As an example application, GA-Var is demonstrated for predicting the plume from a volcanic eruption. First the technique is employed to retrieve the unknown emission rate and the steering winds of the volcanic plume. Then that information is assimilated into a forward prediction of its transport and dispersion. Concentration data are derived from satellite data to determine the observed ash concentrations. A case study is made of the March 2009 eruption of Mount Redoubt in Alaska. The GA-Var technique is able to determine a wind speed and direction that matches the observations well and a reasonable emission rate.     

Some Physical and Computational Issues in Land Surface Data Assimilation of Satellite Skin Temperatures

Skin temperatures that reflect the radiating temperature of a surface observed by infrared radiometers are one of the most widely available products from polar orbiting and geostationary satellites and the most commonly used satellite data in land surface assimilation. Past work has indicated that a simple land surface scheme with a few key parameters constrained by observations such as skin temperatures may be preferable to complex land use schemes with many unknown parameters. However, a true radiating skin temperature is sometimes not a prognostic variable in weather forecast models. Additionally, recent research has shown that skin temperatures cannot be directly used in surface similarity forms for inferring fluxes. This paper examines issues encountered in using satellite derived skin temperatures to improve surface flux specifications in weather forecast and air quality models. Attention is given to iterations necessary when attempting to nudge the surface energy budget equation to a desired state. Finally, the issue of mathematical operator splitting is examined in which the surface energy budget calculations are split with the atmospheric vertical diffusion calculations. However, the high level of connectivity between the surface and first atmospheric level means that the operator splitting leads to high frequency oscillations. These oscillations may hinder the assimilation of skin temperature derived moisture fluxes.     

PEST and AEM Modeling for Data Acquisition Planning

A well-planned field data collection program should be designed to (1) collect a sufficient set of data of the right types at the right locations, and (2) collect a parsimonious set of data to avoid unnecessary costs. Combining PEST and a simple analytic element method (AEM) groundwater flow model for the site of interest provides a relatively simple, low-cost method of developing such a program. AEM models are well suited to this approach because they are quick to develop yet hydraulically accurate, reducing impacts on project budgets at early data collection planning stages; and quick to run, solving rapidly for the many iterations that PEST requires to generate good parameter estimates. This article shows two examples of this method: one for a steady state watershed model, and one for a transient pumping test project to demonstrate that PEST coupled with a simple AEM model that sketches out the key features of a site conceptual model can be an efficient tool in planning key parts of a hydrogeologic site investigation.