scholarly journals Parameter and State Estimation of One-Dimensional Infiltration Processes: A Simultaneous Approach

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 134 ◽  
Author(s):  
Song Bo ◽  
Soumya R. Sahoo ◽  
Xunyuan Yin ◽  
Jinfeng Liu ◽  
Sirish L. Shah
Keyword(s):  
Kalman Filter ◽  
Vadose Zone ◽  
Ensemble Kalman Filter ◽  
Water Movement ◽  
Richards Equation ◽  
Residual Soil ◽  
Simultaneous Approach ◽  
One Dimensional ◽  
Gravitational Forces ◽  
Infiltration Processes

The Richards equation plays an important role in the study of agro-hydrological systems. It models the water movement in soil in the vadose zone, which is driven by capillary and gravitational forces. Its states (capillary potential) and parameters (hydraulic conductivity, saturated and residual soil moistures and van Genuchten-Mualem parameters) are essential for the accuracy of mathematical modeling, yet difficult to obtain experimentally. In this work, an estimation approach is developed to estimate the parameters and states of Richards equation simultaneously. In the proposed approach, parameter identifiability and sensitivity analysis are used to determine the most important parameters for estimation purpose. Three common estimation schemes (extended Kalman filter, ensemble Kalman filter and moving horizon estimation) are investigated. The estimation performance is compared and analyzed based on extensive simulations.

scholarly journals Parameters Estimation and Prediction of Water Movement and Solute Transport in Layered, Variably Saturated Soils Using the Ensemble Kalman Filter

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1520
Author(s):  
Zheng Jiang ◽  
Quanzhong Huang ◽  
Gendong Li ◽  
Guangyong Li
Keyword(s):  
Kalman Filter ◽  
Solute Transport ◽  
Ensemble Kalman Filter ◽  
Water Movement ◽  
Parameters Estimation ◽  
Saturated Soils ◽  
Hydrological Models ◽  
State Variables ◽  
Ensemble Size ◽  
Highly Nonlinear

The parameters of water movement and solute transport models are essential for the accurate simulation of soil moisture and salinity, particularly for layered soils in field conditions. Parameter estimation can be achieved using the inverse modeling method. However, this type of method cannot fully consider the uncertainties of measurements, boundary conditions, and parameters, resulting in inaccurate estimations of parameters and predictions of state variables. The ensemble Kalman filter (EnKF) is well-suited to data assimilation and parameter prediction in Situations with large numbers of variables and uncertainties. Thus, in this study, the EnKF was used to estimate the parameters of water movement and solute transport in layered, variably saturated soils. Our results indicate that when used in conjunction with the HYDRUS-1D software (University of California Riverside, California, CA, USA) the EnKF effectively estimates parameters and predicts state variables for layered, variably saturated soils. The assimilation of factors such as the initial perturbation and ensemble size significantly affected in the simulated results. A proposed ensemble size range of 50–100 was used when applying the EnKF to the highly nonlinear hydrological models of the present study. Although the simulation results for moisture did not exhibit substantial improvement with the assimilation, the simulation of the salinity was significantly improved through the assimilation of the salinity and relative solutetransport parameters. Reducing the uncertainties in measured data can improve the goodness-of-fit in the application of the EnKF method. Sparse field condition observation data also benefited from the accurate measurement of state variables in the case of EnKF assimilation. However, the application of the EnKF algorithm for layered, variably saturated soils with hydrological models requires further study, because it is a challenging and highly nonlinear problem.

scholarly journals A Decentralized Framework for Parameter and State Estimation of Infiltration Processes

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 681
Author(s):  
Song Bo ◽  
Jinfeng Liu
Keyword(s):  
Parameter Estimation ◽  
State Estimation ◽  
Vadose Zone ◽  
Three Dimensional ◽  
Water Dynamics ◽  
Richards Equation ◽  
Soil Water Dynamics ◽  
Decentralized Estimation ◽  
Gravitational Forces ◽  
Estimation Scheme

The Richards’ equation is widely used in the modeling soil water dynamics driven by the capillary and gravitational forces in the vadose zone. Its state and parameter estimation based on field soil moisture measurements is important and challenging for field applications of the Richards’ equation. In this work, we consider simultaneous state and parameter estimation of systems described by the three dimensional Richards’ equation with multiple types of soil. Based on a study on the interaction between subsystems, we propose to use decentralized estimation schemes to reduce the complexity of the estimation problem. Guidelines for subsystem decomposition are discussed and a decentralized estimation scheme developed in the framework of moving horizon state estimation is proposed. Extensive simulation results are presented to show the performance of the proposed decentralized approach.

Dual state-parameter optimal estimation of one-dimensional open channel model using ensemble Kalman filter

2013 ◽  
Vol 25 (4) ◽  
pp. 564-571 ◽  
Author(s):  
Rui-xun Lai ◽  
Hong-wei Fang ◽  
Guo-jian He ◽  
Xin Yu ◽  
Ming Yang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Open Channel ◽  
Channel Model ◽  
State Parameter ◽  
Optimal Estimation ◽  
One Dimensional

One-Dimensional Soil Moisture Simulation Using Ensemble Kalman Filter

2012 ◽  
Vol 212-213 ◽  
pp. 177-180
Author(s):  
Xiao Lei Fu ◽  
Zhong Bo Yu ◽  
Yu Li ◽  
Hai Shen Lv ◽  
Di Liu ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Soil Layer ◽  
Model Parameters ◽  
Deep Soil ◽  
One Dimensional ◽  
Initial Soil Moisture ◽  
Initial Soil

Data assimilation is a method which integrates model and observation. In hydrology, ensemble Kalman filter (EnKF) as a sequential data assimilation method is often used to correct model parameters, thus improve the simulated accuracy. In this study, we conduct one numerical experiment to predict soil moisture using the one-dimensional soil moisture system based on ensemble Kalman filter and Simple Biosphere (SiB2) Model at Meilin study area, China. The simulated period is divided into two parts: 0-60h and 60-240h. The results show that EnKF is an efficient method in assimilating the soil moisture, especially in soil surface layer and deep soil layer; in addition, the efficiency of EnKF depends on the selection of initial soil moisture profile. With different initial soil moisture profiles, the performance of EnKF is different at the first few assimilated time, but with time grows, it can improve the simulated accuracy significantly.

Correction of pumping station parameters in a one-dimensional hydrodynamic model using the Ensemble Kalman filter

2019 ◽  
Vol 568 ◽  
pp. 108-118 ◽  
Author(s):  
Xiaohui Lei ◽  
Yu Tian ◽  
Zhao Zhang ◽  
Lingling Wang ◽  
Xiaohua Xiang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Hydrodynamic Model ◽  
Ensemble Kalman Filter ◽  
One Dimensional ◽  
Pumping Station

The Ensemble Kalman Filter for Continuous Updating of Reservoir Simulation Models

2005 ◽  
Vol 128 (1) ◽  
pp. 79-87 ◽  
Author(s):  
Yaqing Gu ◽  
Dean S. Oliver
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Water Saturation ◽  
State Variables ◽  
Time Step ◽  
Two Phase ◽  
One Dimensional ◽  
Reservoir State

This paper reports the use of ensemble Kalman filter (EnKF) for automatic history matching. EnKF is a Monte Carlo method, in which an ensemble of reservoir state variables are generated and kept up-to-date as data are assimilated sequentially. The uncertainty of reservoir state variables is estimated from the ensemble at any time step. Two synthetic problems are selected to investigate two primary concerns with the application of the EnKF. The first concern is whether it is possible to use a Kalman filter to make corrections to state variables in a problem for which the covariance matrix almost certainly provides a poor representation of the distribution of variables. It is tested with a one-dimensional, two-phase waterflood problem. The water saturation takes large values behind the flood front, and small values ahead of the front. The saturation distribution is bimodal and is not well modeled by the mean and variance. The second concern is the representation of the covariance via a relatively small ensemble of state vectors may be inadequate. It is tested by a two-dimensional, two-phase problem. The number of ensemble members is kept the same as for the one-dimensional problem. Hence the number of ensemble members used to create the covariance matrix is far less than the number of state variables. We conclude that EnKF can provide satisfactory history matching results while requiring less computation work than traditional history matching methods.

scholarly journals Comparison of data assimilation methods based on the classical, ensemble and local Kalman filter by the example of the advection equation and Lorenz system

2018 ◽  
pp. 507-515
Author(s):  
Д.А. Ростилов ◽  
М.Н. Кауркин ◽  
Р.А. Ибраев
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Lorenz System ◽  
Parallel Implementation ◽  
Advection Equation ◽  
Ensemble Kalman Filters ◽  
One Dimensional ◽  
The Mean ◽  
The Lorenz System

Статья посвящена сравнению трех методов усвоения данных наблюденй: фильтр Калмана (Kalman Filter, KF), ансамблевый фильтр Калмана (Ensemble Kalman Filter, EnKF) и локальный фильтр Калмана (Local Kalman Filter, LKF). Выполнены численные эксперименты по усвоению синтетических данных этими методами в двух разных моделях, описываемых системами дифференциальных уравнений. Первая описывается одномерным линейным уравнением адвекции, а вторая - системой Лоренца. Проведено сравнение средних ошибок и времени исполнения этих методов при различных размерах модели, которые согласуются с теоретическим оценками. Показано, что вычислительная сложность ансамблевого и локального фильтров Калмана растет линейно с увеличением размера модели, в то время как у первого метода эта сложность растет со скоростью куба. Рассмотрена эффективность одной из возможных параллельных реализаций локального фильтра Калмана. The paper is devoted to the comparison of three data assimilation methods: the Kalman Filter (Kalman Filter, KF), the ensemble Kalman Filter (EnKF), and the local Kalman Filter (LKF). A number of numerical experiments on data assimilation by these methods are performed on two different models described by systems of differential equations. The first one is a simple one-dimensional linear equation of advection and the second one is the Lorenz system. The mean errors and the execution time of these assimilation methods are compared for different model sizes. The numerical results are consistent with the theoretical estimates. It is shown that the computational complexity of local and ensemble Kalman filters grows linearly with the size of the model, whereas in the classical Kalman Filter this complexity increases according to the cubic law. The efficiency of parallel implementation of the local Kalman filter is considered.

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