New solution to an old problem: improved parameter estimation of soil hydraulic functions

2020 ◽  
Author(s):  
Andreas Papritz ◽  
Peter Lehmann ◽  
Surya Gupta ◽  
Bonetti Sara ◽  
Dani Or
Keyword(s):  
New York ◽  
Parameter Estimation ◽  
Least Squares ◽  
Land Surface ◽  
Nonlinear Least Squares ◽  
Physical Review ◽  
Machine Learning Algorithms ◽  
Soil Water Retention ◽  
Estimated Parameters ◽  
Soil Hydraulic

<p>The representation of land surface properties in hydrologic and climatic models critically depends on soil hydraulic functions (SHF). Parameters of SHF are routinely identified from soil water retention (SWR) and hydraulic conductivity (HC) data by nonlinear least squares. This is a notoriously difficult task because typically only few measurements are available per sample or plot for estimating the many SHF parameters (up to seven for the van Genuchten-Mualem model). As a consequence, the estimated parameters are often highly uncertain and could yield unrealistic predictions of related physical quantities such as the characteristic length <em>L</em><sub>c</sub> for stage‑1 evaporation (Lehmann et al., 2008). We address these limitations by capitalizing on the conditional linearity of some of the SHF parameters. Conditional linear parameters, say <em><strong>μ</strong></em>, can be substituted in the least squares objective by an explicit estimate (Bates & Watts, 1988), leading to an objective that depends only on the remaining nonlinear parameters <em><strong>ν</strong></em><strong>.</strong> This step substantially reduces the dimensionality of the SHF estimation and improves the quality of estimated parameters. Additionally, instead of minimizing the least squares objective only with box constraints for <em><strong>ν</strong></em>, we minimize it by nonlinear programming algorithms that allow to physically constrain estimates of <em><strong>ν</strong></em> by <em>L</em><sub>c</sub>. We have implemented this estimation approach in an R software package capable of processing global SWR and HC data. Using ensemble machine learning algorithms, the novel parameter estimation results will be coupled with auxiliary covariates (vegetation, climate) to create improved global maps of SHF parameters.</p><p>References:</p><p>Bates, D. M. Watts, D. G. 1988. Nonlinear Regression Analysis and Its Applications. John Wiley & Sons, New York.</p><p>Lehmann, P., Assouline, S., Or, D. 2008. Characteristic lengths affecting evaporative drying of porous media. Physical Review E, 77, 056309, DOI 10.1103/PhysRevE.77.056309.</p>

scholarly journals Simultaneous estimation of land surface scheme states and parameters using the ensemble Kalman filter: identical twin experiments

2011 ◽  
Vol 15 (8) ◽  
pp. 2437-2457 ◽  
Author(s):  
S. Nie ◽  
J. Zhu ◽  
Y. Luo
Keyword(s):  
Parameter Estimation ◽  
Soil Moisture ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Land Surface ◽  
Estimation Method ◽  
State Parameter ◽  
Hydraulic Parameters ◽  
Constrained Estimation ◽  
Estimated Parameters

Abstract. The performance of the ensemble Kalman filter (EnKF) in soil moisture assimilation applications is investigated in the context of simultaneous state-parameter estimation in the presence of uncertainties from model parameters, soil moisture initial condition and atmospheric forcing. A physically based land surface model is used for this purpose. Using a series of identical twin experiments in two kinds of initial parameter distribution (IPD) scenarios, the narrow IPD (NIPD) scenario and the wide IPD (WIPD) scenario, model-generated near surface soil moisture observations are assimilated to estimate soil moisture state and three hydraulic parameters (the saturated hydraulic conductivity, the saturated soil moisture suction and a soil texture empirical parameter) in the model. The estimation of single imperfect parameter is successful with the ensemble mean value of all three estimated parameters converging to their true values respectively in both NIPD and WIPD scenarios. Increasing the number of imperfect parameters leads to a decline in the estimation performance. A wide initial distribution of estimated parameters can produce improved simultaneous multi-parameter estimation performances compared to that of the NIPD scenario. However, when the number of estimated parameters increased to three, not all parameters were estimated successfully for both NIPD and WIPD scenarios. By introducing constraints between estimated hydraulic parameters, the performance of the constrained three-parameter estimation was successful, even if temporally sparse observations were available for assimilation. The constrained estimation method can reduce RMSE much more in soil moisture forecasting compared to the non-constrained estimation method and traditional non-parameter-estimation assimilation method. The benefit of this method in estimating all imperfect parameters simultaneously can be fully demonstrated when the corresponding non-constrained estimation method displays a relatively poor parameter estimation performance. Because all these constraints between parameters were obtained in a statistical sense, this constrained state-parameter estimation scheme is likely suitable for other land surface models even with more imperfect parameters estimated in soil moisture assimilation applications.

scholarly journals Quantifying soil hydraulic properties and their uncertainties by modified GLUE method

2017 ◽  
Vol 31 (3) ◽  
pp. 433-445
Author(s):  
Yifan Yan ◽  
Jianli Liu ◽  
Jiabao Zhang ◽  
Xiaopeng Li ◽  
Yongchao Zhao
Keyword(s):  
Confidence Interval ◽  
Least Squares ◽  
Water Content ◽  
Soil Water ◽  
Nonlinear Least Squares ◽  
Uncertainty Estimation ◽  
Model Parameters ◽  
Retention Curve ◽  
Least Squares Algorithm ◽  
Soil Hydraulic

AbstractNonlinear least squares algorithm is commonly used to fit the evaporation experiment data and to obtain the ‘optimal’ soil hydraulic model parameters. But the major defects of nonlinear least squares algorithm include non-uniqueness of the solution to inverse problems and its inability to quantify uncertainties associated with the simulation model. In this study, it is clarified by applying retention curve and a modified generalised likelihood uncertainty estimation method to model calibration. Results show that nonlinear least squares gives good fits to soil water retention curve and unsaturated water conductivity based on data observed by Wind method. And meanwhile, the application of generalised likelihood uncertainty estimation clearly demonstrates that a much wider range of parameters can fit the observations well. Using the ‘optimal’ solution to predict soil water content and conductivity is very risky. Whereas, 95% confidence interval generated by generalised likelihood uncertainty estimation quantifies well the uncertainty of the observed data. With a decrease of water content, the maximum of nash and sutcliffe value generated by generalised likelihood uncertainty estimation performs better and better than the counterpart of nonlinear least squares. 95% confidence interval quantifies well the uncertainties and provides preliminary sensitivities of parameters.

Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains

2009 ◽  
Author(s):  
James R. McCusker ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Time Scale ◽  
Prediction Error ◽  
Nonlinear Least Squares ◽  
Integrated Approach ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Single Model ◽  
Iterative Estimation

A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.

scholarly journals Parameter identification for symbolic regression using nonlinear least squares

2019 ◽  
Vol 21 (3) ◽  
pp. 471-501 ◽  
Author(s):  
Michael Kommenda ◽  
Bogdan Burlacu ◽  
Gabriel Kronberger ◽  
Michael Affenzeller
Keyword(s):  
Genetic Programming ◽  
Local Search ◽  
Parameter Identification ◽  
Least Squares ◽  
Automatic Differentiation ◽  
Nonlinear Least Squares ◽  
Symbolic Regression ◽  
Machine Learning Algorithms ◽  
Benchmark Problems ◽  
Marquardt Algorithm

AbstractIn this paper we analyze the effects of using nonlinear least squares for parameter identification of symbolic regression models and integrate it as local search mechanism in tree-based genetic programming. We employ the Levenberg–Marquardt algorithm for parameter optimization and calculate gradients via automatic differentiation. We provide examples where the parameter identification succeeds and fails and highlight its computational overhead. Using an extensive suite of symbolic regression benchmark problems we demonstrate the increased performance when incorporating nonlinear least squares within genetic programming. Our results are compared with recently published results obtained by several genetic programming variants and state of the art machine learning algorithms. Genetic programming with nonlinear least squares performs among the best on the defined benchmark suite and the local search can be easily integrated in different genetic programming algorithms as long as only differentiable functions are used within the models.

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