scholarly journals Combined State-Parameter Estimation with the LETKF for Convective-Scale Weather Forecasting

2020 ◽  
Vol 148 (4) ◽  
pp. 1607-1628 ◽  
Author(s):  
Y. Ruckstuhl ◽  
T. Janjić
Keyword(s):  
Parameter Estimation ◽  
Gaussian Noise ◽  
Roughness Length ◽  
Surface Wind ◽  
Model Error ◽  
Surface Fluxes ◽  
Model Parameters ◽  
State Variables ◽  
Augmented State ◽  
The Impact

Abstract We investigate the feasibility of addressing model error by perturbing and estimating uncertain static model parameters using the localized ensemble transform Kalman filter. In particular we use the augmented state approach, where parameters are updated by observations via their correlation with observed state variables. This online approach offers a flexible, yet consistent way to better fit model variables affected by the chosen parameters to observations, while ensuring feasible model states. We show in a nearly operational convection-permitting configuration that the prediction of clouds and precipitation with the COSMO-DE model is improved if the two-dimensional roughness length parameter is estimated with the augmented state approach. Here, the targeted model error is the roughness length itself and the surface fluxes, which influence the initiation of convection. At analysis time, Gaussian noise with a specified correlation matrix is added to the roughness length to regulate the parameter spread. In the northern part of the COSMO-DE domain, where the terrain is mostly flat and assimilated surface wind measurements are dense, estimating the roughness length led to improved forecasts of up to 6 h of clouds and precipitation. In the southern part of the domain, the parameter estimation was detrimental unless the correlation length scale of the Gaussian noise that is added to the roughness length is increased. The impact of the parameter estimation was found to be larger when synoptic forcing is weak and the model output is more sensitive to the roughness length.

Combined state-parameter estimation with the LETKF for convective-scale weather forecasting

2020 ◽  
Author(s):  
Yvonne Ruckstuhl ◽  
Tijana Janjic
Keyword(s):  
Parameter Estimation ◽  
Gaussian Noise ◽  
Roughness Length ◽  
Surface Wind ◽  
Model Error ◽  
Surface Fluxes ◽  
Model Parameters ◽  
State Variables ◽  
Augmented State ◽  
The Impact

<p>We investigate the feasibility of addressing model error by perturbing and  estimating uncertain static model parameters using the localized ensemble transform Kalman filter. In particular we use the augmented state approach, where parameters are updated by observations via their correlation with observed state variables. This online approach offers a flexible, yet consistent way to better fit model variables affected by the chosen parameters to observations, while ensuring feasible model states. We show in a nearly-operational convection-permitting configuration that the prediction of clouds and precipitation with the COSMO-DE model is improved if the two dimensional roughness length parameter is estimated with the augmented state approach. Here, the targeted model error is the roughness length itself and the surface fluxes, which influence the initiation of convection. At analysis time, Gaussian noise with a specified correlation matrix is added to the roughness length to regulate the parameter spread. In the northern part of the COSMO-DE domain, where the terrain is mostly flat and assimilated surface wind measurements are dense, estimating the roughness length led to improved forecasts of up to six hours of clouds and precipitation. In the southern part of the domain, the parameter estimation was detrimental unless the correlation length scale of the Gaussian noise that is added to the roughness length is increased. The impact of the parameter estimation was found to be larger when synoptic forcing is weak and the model output is more sensitive to the roughness length.</p>

Filtering Nonlinear Turbulent Dynamical Systems through Conditional Gaussian Statistics

2016 ◽  
Vol 144 (12) ◽  
pp. 4885-4917 ◽  
Author(s):  
Nan Chen ◽  
Andrew J. Majda
Keyword(s):  
Compressible Flows ◽  
Model Error ◽  
Model Parameters ◽  
Test Model ◽  
State Variables ◽  
Model Errors ◽  
Skeleton Model ◽  
Highly Nonlinear ◽  
Unobserved Variables ◽  
Augmented State

Abstract In this paper, a general conditional Gaussian framework for filtering complex turbulent systems is introduced. Despite the conditional Gaussianity, such systems are nevertheless highly nonlinear and are able to capture the non-Gaussian features of nature. The special structure of the filter allows closed analytical formulas for updating the posterior states and is thus computationally efficient. An information-theoretic framework is developed to assess the model error in the filter estimates. Three types of applications in filtering conditional Gaussian turbulent systems with model error are illustrated. First, dyad models are utilized to illustrate that ignoring the energy-conserving nonlinear interactions in designing filters leads to significant model errors in filtering turbulent signals from nature. Then a triad (noisy Lorenz 63) model is adopted to understand the model error due to noise inflation and underdispersion. It is also utilized as a test model to demonstrate the efficiency of a novel algorithm, which exploits the conditional Gaussian structure, to recover the time-dependent probability density functions associated with the unobserved variables. Furthermore, regarding model parameters as augmented state variables, the filtering framework is applied to the study of parameter estimation with detailed mathematical analysis. A new approach with judicious model error in the equations associated with the augmented state variables is proposed, which greatly enhances the efficiency in estimating model parameters. Other examples of this framework include recovering random compressible flows from noisy Lagrangian tracers, filtering the stochastic skeleton model of the Madden–Julian oscillation (MJO), and initialization of the unobserved variables in predicting the MJO/monsoon indices.

scholarly journals Constrained Parameter Estimation for a Mechanistic Kinetic Model of Cobalt–Hydrogen Electrochemical Competition during a Cobalt Removal Process

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 387
Author(s):  
Yiting Liang ◽  
Yuanhua Zhang ◽  
Yonggang Li
Keyword(s):  
Parameter Estimation ◽  
Kinetic Model ◽  
Model Parameters ◽  
Hydrogen Ions ◽  
Removal Process ◽  
Cobalt Removal ◽  
Estimation Scheme ◽  
Zinc Hydrometallurgy ◽  
The Impact ◽  
Parameter Estimation Scheme

A mechanistic kinetic model of cobalt–hydrogen electrochemical competition for the cobalt removal process in zinc hydrometallurgical was proposed. In addition, to overcome the parameter estimation difficulties arising from the model nonlinearities and the lack of information on the possible value ranges of parameters to be estimated, a constrained guided parameter estimation scheme was derived based on model equations and experimental data. The proposed model and the parameter estimation scheme have two advantages: (i) The model reflected for the first time the mechanism of the electrochemical competition between cobalt and hydrogen ions in the process of cobalt removal in zinc hydrometallurgy; (ii) The proposed constrained parameter estimation scheme did not depend on the information of the possible value ranges of parameters to be estimated; (iii) the constraint conditions provided in that scheme directly linked the experimental phenomenon metrics to the model parameters thereby providing deeper insights into the model parameters for model users. Numerical experiments showed that the proposed constrained parameter estimation algorithm significantly improved the estimation efficiency. Meanwhile, the proposed cobalt–hydrogen electrochemical competition model allowed for accurate simulation of the impact of hydrogen ions on cobalt removal rate as well as simulation of the trend of hydrogen ion concentration, which would be helpful for the actual cobalt removal process in zinc hydrometallurgy.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

scholarly journals Assessing the Impact of Changes in Land Surface Conditions on WRF Predictions in Arid Regions

2020 ◽  
Vol 21 (12) ◽  
pp. 2829-2853 ◽  
Author(s):  
Marouane Temimi ◽  
Ricardo Fonseca ◽  
Narendra Nelli ◽  
Michael Weston ◽  
Mohan Thota ◽  
...  
Keyword(s):  
Eddy Covariance ◽  
Soil Texture ◽  
Land Surface ◽  
Surface Wind ◽  
Surface Fluxes ◽  
Abu Dhabi ◽  
Horizontal Wind ◽  
Cold Bias ◽  
Near Surface ◽  
The Impact

AbstractA thorough evaluation of the Weather Research and Forecasting (WRF) Model is conducted over the United Arab Emirates, for the period September 2017–August 2018. Two simulations are performed: one with the default model settings (control run), and another one (experiment) with an improved representation of soil texture and land use land cover (LULC). The model predictions are evaluated against observations at 35 weather stations, radiosonde profiles at the coastal Abu Dhabi International Airport, and surface fluxes from eddy-covariance measurements at the inland city of Al Ain. It is found that WRF’s cold temperature bias, also present in the forcing data and seen almost exclusively at night, is reduced when the surface and soil properties are updated, by as much as 3.5 K. This arises from the expansion of the urban areas, and the replacement of loamy regions with sand, which has a higher thermal inertia. However, the model continues to overestimate the strength of the near-surface wind at all stations and seasons, typically by 0.5–1.5 m s−1. It is concluded that the albedo of barren/sparsely vegetated regions in WRF (0.380) is higher than that inferred from eddy-covariance observations (0.340), which can also explain the referred cold bias. At the Abu Dhabi site, even though soil texture and LULC are not changed, there is a small but positive effect on the predicted vertical profiles of temperature, humidity, and horizontal wind speed, mostly between 950 and 750 hPa, possibly because of differences in vertical mixing.

Parameter Estimation of Nonlinear Biomedical Systems Using Extended Kalman Filter Algorithm

2017 ◽  
pp. 76-99 ◽  
Author(s):  
Kamalanand Krishnamurthy
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Computational Models ◽  
Three Dimensional ◽  
Model Parameters ◽  
State Variables ◽  
Three Dimensional Model ◽  
Biomedical Systems ◽  
Estimation Of Model Parameters

Parameter estimation is a central issue in mathematical modelling of biomedical systems and for the development of patient specific models. The technique of estimating parameters helps in obtaining diagnostic information from computational models of biological systems. However, in most of the biomedical systems, the estimation of model parameters is a challenging task due to the nonlinearity of mathematical models. In this chapter, the method of estimation of nonlinear model parameters from measurements of state variables, using the extended Kalman filter, is extensively explained using an example of the three-dimensional model of the HIV/AIDS system.

Data Assimilation for a Coupled Ocean–Atmosphere Model. Part II: Parameter Estimation

2008 ◽  
Vol 136 (12) ◽  
pp. 5062-5076 ◽  
Author(s):  
Dmitri Kondrashov ◽  
Chaojiao Sun ◽  
Michael Ghil
Keyword(s):  
Parameter Estimation ◽  
State Estimation ◽  
Tropical Pacific ◽  
The State ◽  
Vector Model ◽  
Model Parameters ◽  
Ocean Atmosphere ◽  
Augmented State ◽  
Parameter Values ◽  
The Tropical Pacific

Abstract The parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upper-ocean model and a diagnostic atmospheric model. Model errors arise from the uncertainty in atmospheric wind stress. First, the state and parameters are estimated in an identical-twin framework, based on incomplete and inaccurate observations of the model state. Two parameters are estimated by including them into an augmented state vector. Model-generated oceanic datasets are assimilated to produce a time-continuous, dynamically consistent description of the model’s El Niño–Southern Oscillation (ENSO). State estimation without correcting erroneous parameter values still permits recovering the true state to a certain extent, depending on the quality and accuracy of the observations and the size of the discrepancy in the parameters. Estimating both state and parameter values simultaneously, though, produces much better results. Next, real sea surface temperatures observations from the tropical Pacific are assimilated for a 30-yr period (1975–2004). Estimating both the state and parameters by the EKF method helps to track the observations better, even when the ICM is not capable of simulating all the details of the observed state. Furthermore, unobserved ocean variables, such as zonal currents, are improved when model parameters are estimated. A key advantage of using this augmented-state approach is that the incremental cost of applying the EKF to joint state and parameter estimation is small relative to the cost of state estimation alone. A similar approach generalizes various reduced-state approximations of the EKF and could improve simulations and forecasts using large, realistic models.

scholarly journals Sensitivity-Based Parameter Calibration and Model Validation Under Model Error

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Na Qiu ◽  
Chanyoung Park ◽  
Yunkai Gao ◽  
Jianguang Fang ◽  
Guangyong Sun ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Calibration Method ◽  
Model Error ◽  
Model Parameters ◽  
Observation Data ◽  
Parameter Calibration ◽  
Bayesian Calibration ◽  
Modeling Errors ◽  
Model Discrepancy ◽  
Better Than

In calibrating model parameters, it is important to include the model discrepancy term in order to capture missing physics in simulation, which can result from numerical, measurement, and modeling errors. Ignoring the discrepancy may lead to biased calibration parameters and predictions, even with an increasing number of observations. In this paper, a simple yet efficient calibration method is proposed based on sensitivity information when the simulation model has a model error and/or numerical error but only a small number of observations are available. The sensitivity-based calibration method captures the trend of observation data by matching the slope of simulation predictions and observations at different designs and then utilizing a constant value to compensate for the model discrepancy. The sensitivity-based calibration is compared with the conventional least squares calibration method and Bayesian calibration method in terms of parameter estimation and model prediction accuracies. A cantilever beam example, as well as a honeycomb tube crush example, is used to illustrate the calibration process of these three methods. It turned out that the sensitivity-based method has a similar performance with the Bayesian calibration method and performs much better than the conventional method in parameter estimation and prediction accuracy.

COUPLED ANALYSIS OF DAMAGE IN MULTIPHASE MEDIA

2012 ◽  
Vol 04 (02) ◽  
pp. 1250008
Author(s):  
MARZIYEH FATHALIKHANI ◽  
BEHROUZ GATMIRI
Keyword(s):  
Damage Model ◽  
Coupled Analysis ◽  
Model Parameters ◽  
State Variables ◽  
Damage Development ◽  
Water Conductivity ◽  
Internal Length ◽  
Finite Element Program ◽  
Independent State ◽  
The Impact

In this paper, the theoretical framework of a coupled thermo-hydro-mechanical damage model dedicated to non-isothermal unsaturated porous media is presented. The damage variable is a second-order tensor, and the model has been formulated in independent state variables. The approach combines thermodynamic and micromechanical theories. The behavior laws have been derived from a postulated expression of Helmholtz free energy. The damaged rigidities have been computed by applying the Principle of Equivalent Elastic Energy (PEEE). Internal length parameters have been introduced in the expressions of liquid water conductivity, to account for cracking effects on fluid flows. Damage has been assumed to have an isotropic influence on air and heat flows, through the inelastic component of volumetric strains. The damage model has been implemented in θ-Stock Finite Element program. Some numerical studies are conducted to the impact of the thermal and mechanical loading on the evaluation of response of the unsaturated bentonite, and investigation of model parameters effect on damage development.

scholarly journals Impact of Geographic-Dependent Parameter Optimization on Climate Estimation and Prediction: Simulation with an Intermediate Coupled Model

2012 ◽  
Vol 140 (12) ◽  
pp. 3956-3971 ◽  
Author(s):  
Xinrong Wu ◽  
Shaoqing Zhang ◽  
Zhengyu Liu ◽  
Anthony Rosati ◽  
Thomas L. Delworth ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Surface Temperature ◽  
Parameter Optimization ◽  
General Circulation ◽  
Coupled Model ◽  
Model Parameters ◽  
Estimation And Prediction ◽  
Dependent Parameter ◽  
The Impact ◽  
Mean Square Errors

Abstract Because of the geographic dependence of model sensitivities and observing systems, allowing optimized parameter values to vary geographically may significantly enhance the signal in parameter estimation. Using an intermediate atmosphere–ocean–land coupled model, the impact of geographic dependence of model sensitivities on parameter optimization is explored within a twin-experiment framework. The coupled model consists of a 1-layer global barotropic atmosphere model, a 1.5-layer baroclinic ocean including a slab mixed layer with simulated upwelling by a streamfunction equation, and a simple land model. The assimilation model is biased by erroneously setting the values of all model parameters. The four most sensitive parameters identified by sensitivity studies are used to perform traditional single-value parameter estimation and new geographic-dependent parameter optimization. Results show that the new parameter optimization significantly improves the quality of state estimates compared to the traditional scheme, with reductions of root-mean-square errors as 41%, 23%, 62%, and 59% for the atmospheric streamfunction, the oceanic streamfunction, sea surface temperature, and land surface temperature, respectively. Consistently, the new parameter optimization greatly improves the model predictability as a result of the improvement of initial conditions and the enhancement of observational signals in optimized parameters. These results suggest that the proposed geographic-dependent parameter optimization scheme may provide a new perspective when a coupled general circulation model is used for climate estimation and prediction.

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