scholarly journals Simultaneous Estimation of Microphysical Parameters and Atmospheric State with Simulated Radar Data and Ensemble Square Root Kalman Filter. Part I: Sensitivity Analysis and Parameter Identifiability

2008 ◽  
Vol 136 (5) ◽  
pp. 1630-1648 ◽  
Author(s):  
Mingjing Tong ◽  
Ming Xue
Keyword(s):  
Parameter Estimation ◽  
Estimation Procedure ◽  
Radar Data ◽  
Simultaneous Estimation ◽  
Square Root ◽  
Wind Fields ◽  
Fundamental Parameters ◽  
Multiple Parameters ◽  
Microphysical Parameters ◽  
True Values

Abstract The possibility of estimating fundamental parameters common in single-moment ice microphysics schemes using radar observations is investigated for a model-simulated supercell storm by examining parameter sensitivity and identifiability. These parameters include the intercept parameters for rain, snow, and hail/graupel, and the bulk densities of snow and hail/graupel. These parameters are closely involved in the definition of drop/particle size distributions of microphysical species but often assume highly uncertain specified values. The sensitivity of model forecast within data assimilation cycles to the parameter values, and the issue of solution uniqueness of the estimation problem, are examined. The ensemble square root filter (EnSRF) is employed for model state estimation. Sensitivity experiments show that the errors in the microphysical parameters have a larger impact on model microphysical fields than on wind fields; radar reflectivity observations are therefore preferred over those of radial velocity for microphysical parameter estimation. The model response time to errors in individual parameters are also investigated. The results suggest that radar data should be used at about 5-min intervals for parameter estimation. The response functions calculated from ensemble mean forecasts for all five individual parameters show concave shapes, with unique minima occurring at or very close to the true values; therefore, true values of these parameters can be retrieved at least in those cases where only one parameter contains error. The identifiability of multiple parameters together is evaluated from their correlations with forecast reflectivity. Significant levels of correlation are found that can be interpreted physically. As the number of uncertain parameters increases, both the level and the area coverage of significant correlations decrease, implying increased difficulties with multiple-parameter estimation. The details of the estimation procedure and the results of a complete set of estimation experiments are presented in Part II of this paper.

scholarly journals Simultaneous Estimation of Microphysical Parameters and Atmospheric State with Simulated Radar Data and Ensemble Square Root Kalman Filter. Part II: Parameter Estimation Experiments

2008 ◽  
Vol 136 (5) ◽  
pp. 1649-1668 ◽  
Author(s):  
Mingjing Tong ◽  
Ming Xue
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Radar Data ◽  
Filter Method ◽  
Simultaneous Estimation ◽  
Observation Data ◽  
Square Root ◽  
Model Errors ◽  
Microphysical Parameters

Abstract The ensemble Kalman filter method is applied to correct errors in five fundamental microphysical parameters that are closely involved in the definition of drop/particle size distributions of microphysical species in a commonly used single-moment ice microphysics scheme, for a model-simulated supercell storm, using radar data. The five parameters include the intercept parameters for rain, snow, and hail/graupel and the bulk densities of hail/graupel and snow. The ensemble square root Kalman filter (EnSRF) is employed for simultaneous state and parameter estimation. The five microphysical parameters are estimated individually or in different combinations starting from different initial guesses. A data selection procedure based on correlation information is introduced, which combined with variance inflation, effectively avoids the collapse of the spread of parameter ensemble, hence filter divergence. Parameter estimation results demonstrate, for the first time, that the ensemble-based method can be used to correct model errors in microphysical parameters through simultaneous state and parameter estimation, using radar reflectivity observations. When error exists in only one of the microphysical parameters, the parameter can be successfully estimated without exception. The estimation of multiple parameters is less reliable, mainly because the identifiability of the parameters becomes weaker and the problem might have no unique solution. The parameter estimation results are found to be very sensitive to the realization of the initial parameter ensemble, which is mainly related to the use of relatively small ensemble sizes. Increasing ensemble size generally improves the parameter estimation. The quality of parameter estimation also depends on the quality of observation data. It is also found that the results of state estimation are generally improved when simultaneous parameter estimation is performed, even when the estimated parameter values are not very accurate.

scholarly journals Comparison of different algorithms for simultaneous estimation of multiple parameters in kinetic metabolic models

2010 ◽  
Vol 7 (3) ◽  
Author(s):  
Syed Murtuza Baker ◽  
Kai Schallau ◽  
Björn H. Junker
Keyword(s):  
Parameter Estimation ◽  
Computational Models ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Simultaneous Estimation ◽  
Multiple Parameters ◽  
Reliable Parameter ◽  
Metabolic Models ◽  
Parameter Values

SummaryComputational models in systems biology are usually characterized by a lack of reliable parameter values. This is especially true for kinetic metabolic models. Experimental data can be used to estimate these missing parameters. Different optimization techniques have been explored to solve this challenging task but none has proved to be superior to the other. In this paper we review the problem of parameter estimation in kinetic models. We focus on the suitability of four commonly used optimization techniques of parameter estimation in biochemical pathways and make a comparison between those methods. The suitability of each technique is evaluated based on the ability of converging to a solution within a reasonable amount of time. As most local optimization methods fail to arrive at a satisfactory solution we only considered the global optimization techniques. A case study of the upper part of Glycolysis consisting 15 parameters is taken as the benchmark model for evaluating these methods.

scholarly journals Algorithm for Simultaneous Parameter Estimation of A Multiharmonic Signal

2012 ◽  
Vol 19 (4) ◽  
pp. 693-702 ◽  
Author(s):  
Predrag B. Petrović
Keyword(s):  
Parameter Estimation ◽  
Fundamental Frequency ◽  
Finite Impulse Response ◽  
Signal Reconstruction ◽  
Spectral Estimation ◽  
Estimation Procedure ◽  
Simultaneous Estimation ◽  
Harmonic Compensation ◽  
Estimation Algorithms ◽  
Estimation System

Abstract Estimating the fundamental frequency and harmonic parameters is basic for signal modelling in a power supply system. Differing from the existing parameter estimation algorithms either in power quality monitoring or in harmonic compensation, the proposed algorithm enables a simultaneous estimation of the fundamental frequency, the amplitudes and phases of harmonic waves. A pure sinusoid is obtained from an input multiharmonic input signal by finite-impulse-response (FIR) comb filters. Proposed algorithm is based on the use of partial derivatives of the processed signal and the weighted estimation procedure to estimate the fundamental frequency, the amplitude and the phase of a multi-sinusoidal signal. The proposed algorithm can be applied in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The simulation results verify the effectiveness of the proposed algorithm.

scholarly journals Simultaneous Estimation of Microphysical Parameters and the Atmospheric State Using Simulated Polarimetric Radar Data and an Ensemble Kalman Filter in the Presence of an Observation Operator Error

2010 ◽  
Vol 138 (2) ◽  
pp. 539-562 ◽  
Author(s):  
Youngsun Jung ◽  
Ming Xue ◽  
Guifu Zhang
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
State Estimation ◽  
Radar Data ◽  
The State ◽  
Polarimetric Radar ◽  
Observation Operator ◽  
Operator Error ◽  
Microphysical Parameters ◽  
Positive Impacts

Abstract The impacts of polarimetric radar data on the estimation of uncertain microphysical parameters are investigated through observing system simulation experiments when the effects of uncertain parameters on the observation operators are also considered. Five fundamental microphysical parameters (i.e., the intercept parameters of rain, snow, and hail and the bulk densities of snow and hail) are estimated individually or collectively using the ensemble square root Kalman filter. The differential reflectivity ZDR, specific differential phase KDP, and radar reflectivity at horizontal polarization ZH are used individually or in combinations for the parameter estimation while the radial velocity and ZH are used for the state estimation. In the process, the parameter values estimated in the previous analysis cycles are used in the forecast model and in observation operators in the ensuing assimilation cycle. Analyses are first performed that examine the sensitivity of various observations to the microphysical parameters with and without observation operator error. The results are used to help interpret the filter behaviors in parameter estimation. The experiments in which either a single or all five parameters contain initial errors reveal difficulties in estimating certain parameters using ZH alone when observation operator error is involved. Additional polarimetric measurements are found to be beneficial for both parameter and state estimation in general. It is found that the polarimetric data are more helpful when the parameter estimation is not very successful with ZH alone. Between ZDR and KDP, KDP is found to produce larger positive impacts on parameter estimation in general while ZDR is more useful in the estimation of the intercept parameter of hail. In the experiments that attempt to correct errors in all five parameters, the filter fails to correctly estimate the snow intercept parameter and the density with or without polarimetric data, seemingly due to the small sensitivity of the observations to these parameters and complications involving the observation operator error. When these two snow parameters are not corrected during the estimation process, the estimations of the other three parameters and of all of the state variables are significantly improved and the positive impacts of polarimetric data are larger than that of a five-parameter estimation. These results reveal the significant complexity of the estimation problem for a highly nonlinear system and the need for careful sensitivity analysis. The problem is potentially more challenging with real-data cases when unknown sources of model errors are inevitable.

THE REALIZATION OF THE ITERATIVE METHOD OF THE LEAST SQUARES FOR THE ESTIMATION OF STATIC OBJECT PARAMETERS IN MATLAB ENVIRONMENT

2017 ◽  
pp. 28-36
Author(s):  
Galina Vasil’evna Troshina ◽  
Alexander Aleksandrovich Voevoda
Keyword(s):  
Parameter Estimation ◽  
Iterative Method ◽  
Least Squares ◽  
Input Signal ◽  
Layer Structure ◽  
Estimation Procedure ◽  
Parameter Estimation Procedure ◽  
Noise Simulation ◽  
Static Object ◽  
Object Parameters

It was suggested to use the system model working in real time for an iterative method of the parameter estimation. It gives the chance to select a suitable input signal, and also to carry out the setup of the object parameters. The object modeling for a case when the system isn't affected by the measurement noises, and also for a case when an object is under the gaussian noise was executed in the MatLab environment. The superposition of two meanders with different periods and single amplitude is used as an input signal. The model represents the three-layer structure in the MatLab environment. On the most upper layer there are units corresponding to the simulation of an input signal, directly the object, the unit of the noise simulation and the unit for the parameter estimation. The second and the third layers correspond to the simulation of the iterative method of the least squares. The diagrams of the input and the output signals in the absence of noise and in the presence of noise are shown. The results of parameter estimation of a static object are given. According to the results of modeling, the algorithm works well even in the presence of significant measurement noise. To verify the correctness of the work of an algorithm the auxiliary computations have been performed and the diagrams of the gain behavior amount which is used in the parameter estimation procedure have been constructed. The entry conditions which are necessary for the work of an iterative method of the least squares are specified. The understanding of this algorithm functioning principles is a basis for its subsequent use for the parameter estimation of the multi-channel dynamic objects.

scholarly journals Simulation of X-Band Rainfall Observations from S-Band Radar Data

2006 ◽  
Vol 23 (9) ◽  
pp. 1195-1205 ◽  
Author(s):  
V. Chandrasekar ◽  
S. Lim ◽  
E. Gorgucci
Keyword(s):  
Doppler Radar ◽  
Theoretical Models ◽  
Radar Data ◽  
Shape Distribution ◽  
Microphysical Properties ◽  
Rain Medium ◽  
Microphysical Parameters ◽  
X Band ◽  
State Water ◽  
The Impact

Abstract To design X-band radar systems as well as evaluate algorithm development, it is useful to have simultaneous X-band observation with and without the impact of path attenuation. One way to develop that dataset is through theoretical models. This paper presents a methodology to generate realistic range profiles of radar variables at attenuating frequencies, such as X band, for rain medium. Fundamental microphysical properties of precipitation, namely, size and shape distribution information, are used to generate realistic profiles of X band starting with S-band observation. Conditioning the simulation from S band maintains the natural distribution of rainfall microphysical parameters. Data from the Colorado State University’s University of Chicago–Illinois State Water Survey (CHILL) radar and the National Center for Atmospheric Research S-band dual-polarization Doppler radar (S-POL) are used to simulate X-band radar variables. Three procedures to simulate the radar variables and sample applications are presented.

scholarly journals Retrieval of three-dimensional wind fields from Doppler radar data using an efficient two-step approach

2010 ◽  
Vol 3 (5) ◽  
pp. 4459-4495 ◽  
Author(s):  
C. López Carrillo ◽  
D. J. Raymond
Keyword(s):  
Variational Approach ◽  
Continuity Equation ◽  
Doppler Radar ◽  
Three Dimensional ◽  
Relevant Information ◽  
Radar Data ◽  
Wind Fields ◽  
Wind Retrieval ◽  
Complex Sampling ◽  
Doppler Radar Data

Abstract. In this work, we describe an efficient approach for wind retrieval from dual Doppler radar data. The approach produces a gridded field that not only satisfies the observations, but also satisfies the anelastic mass continuity equation. The method is based on the so-called three-dimensional variational approach to the retrieval of wind fields from radar data. The novelty consists in separating the task into steps that reduce the amount of data processed by the global minimization algorithm, while keeping the most relevant information from the radar observations. The method is flexible enough to incorporate observations from several radars, accommodate complex sampling geometries, and readily include dropsonde or sounding observations in the analysis. We demonstrate the usefulness of our method by analyzing a real case with data collected during the TPARC/TCS-08 field campaign.

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