Influence of parameter estimation uncertainty in Kriging: Part 1 - Theoretical Development

Todini, E.

doi:10.5194/hess-5-215-2001

Cited by 38 publications

(26 citation statements)

References 24 publications

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“…The bias corrections computed using the proposed methodology (Eqn. (13) in Todini, 2001) for the three models mentioned above are given in Figs. 8a, 8b and 8c, while the increase in the standard deviation of the estimation error (obtained by means of Eqn.…”

Section: Analysis Of Parameter Estimation Uncertaintymentioning

confidence: 99%

“…8a, 8b and 8c, while the increase in the standard deviation of the estimation error (obtained by means of Eqn. (14) in Todini, 2001) is plotted in Figs. 9a, 9b and 9c.…”

Section: Analysis Of Parameter Estimation Uncertaintymentioning

confidence: 99%

“…As discussed by Todini (2001), the modified spherical model is used in this application instead of the more classical one of Eqn. (6) because it guarantees the continuity of the function, together with that of its first and second derivatives with respect to the parameters over the entire domain of existence, as it is required by Maximum Likelihood to be minimum variance (Kendall and Stuart, 1973).…”

Section: Parameter Estimationmentioning

confidence: 99%

“…The analysis of the effect of parameter estimation uncertainty on the estimated Kriging variables proposed in Part 1 (Todini, 2001) was applied to the mean annual precipitation of the Veneto region in Northern Italy.…”

Section: Introductionmentioning

confidence: 99%

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Influence of parameter estimation uncertainty in Kriging: Part 2 - Test and case study applications

Todini

Pellegrini

Mazzetti

2001

Hydrol. Earth Syst. Sci.

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The theoretical approach introduced in Part 1 is applied to a numerical example and to the case of yearly average precipitation estimation over the Veneto Region in Italy. The proposed methodology was used to assess the effects of parameter estimation uncertainty on Kriging estimates and on their estimated error variance. The Maximum Likelihood (ML) estimator proposed in Part 1, was applied to the zero mean deviations from yearly average precipitation over the Veneto Region in Italy, obtained after the elimination of a non-linear drift with elevation. Three different semi-variogram models were used, namely the exponential, the Gaussian and the modified spherical, and the relevant biases as well as the increases in variance have been assessed. A numerical example was also conducted to demonstrate how the procedure leads to unbiased estimates of the random functions. One hundred sets of 82 observations were generated by means of the exponential model on the basis of the parameter values identified for the Veneto Region rainfall problem and taken as characterising the true underlining process. The values of parameter and the consequent cross-validation errors, were estimated from each sample. The cross-validation errors were first computed in the classical way and then corrected with the procedure derived in Part 1. Both sets, original and corrected, were then tested, by means of the Likelihood ratio test, against the null hypothesis of deriving from a zero mean process with unknown covariance. The results of the experiment clearly show the effectiveness of the proposed approach.

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Section: Analysis Of Parameter Estimation Uncertaintymentioning

confidence: 99%

“…8a, 8b and 8c, while the increase in the standard deviation of the estimation error (obtained by means of Eqn. (14) in Todini, 2001) is plotted in Figs. 9a, 9b and 9c.…”

Section: Analysis Of Parameter Estimation Uncertaintymentioning

confidence: 99%

Section: Parameter Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Influence of parameter estimation uncertainty in Kriging: Part 2 - Test and case study applications

Todini

Pellegrini

Mazzetti

2001

Hydrol. Earth Syst. Sci.

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“…A Block Kriging technique, developed by Mazzetti and Todini (2004), was applied to interpolate the irregularly distributed surface observations. Within the framework of this approach, once the semi-variogram model has been defined (the Gaussian model in this case), the computation of the parameters of the Semi-variogram function is updated at each time step using a Maximum Likelihood estimator (Todini, 2001). On the other hand, the rainfall fields predicted by COSMO-LAMI were downscaled to each pixel of the hydrological model structure by assigning to the value of the nearest atmospheric model grid point.…”

Section: Topkapi Modelmentioning

confidence: 99%

A hydrometeorological model intercomparison as a tool to quantify the forecast uncertainty in a medium size basin

Amengual

Diomede

Marsigli

et al. 2008

Nat. Hazards Earth Syst. Sci.

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Abstract. In the framework of AMPHORE, an INTERREG III B EU project devoted to the hydrometeorological modeling study of heavy precipitation episodes resulting in flood events and the improvement of the operational hydrometeorological forecasts for the prediction and prevention of flood risks in the Western Mediterranean area, a hydrometeorological model intercomparison has been carried out, in order to estimate the uncertainties associated with the discharge predictions. The analysis is performed for an intense precipitation event selected as a case study within the project, which affected northern Italy and caused a flood event in the upper Reno river basin, a medium size catchment in the EmiliaRomagna Region.Two different hydrological models have been implemented over the basin: HEC-HMS and TOPKAPI which are driven in two ways. Firstly, stream-flow simulations obtained by using precipitation observations as input data are evaluated, in order to be aware of the performance of the two hydrological models. Secondly, the rainfall-runoff models have been forced with rainfall forecast fields provided by mesoscale atmospheric model simulations in order to evaluate the reliability of the discharge forecasts resulting by the one-way coupling. The quantitative precipitation forecasts (QPFs) are provided by the numerical mesoscale models COSMO and MM5.Furthermore, different configurations of COSMO and MM5 have been adopted, trying to improve the description of the phenomena determining the precipitation amounts. In particular, the impacts of using different initial and boundary conditions, different mesoscale models and of increasing the horizontal model resolutions are investigated. The accuracy of QPFs is assessed in a threefold procedure. First, theseCorrespondence to: A. Amengual (arnau.amengual@uib.es) are checked against the observed spatial rainfall accumulations over northern Italy. Second, the spatial and temporal simulated distributions are also examined over the catchment of interest. And finally, the discharge simulations resulting from the one-way coupling with HEC-HMS and TOPKAPI are evaluated against the rain-gauge driven simulated flows, thus employing the hydrological models as a validation tool.The different scenarios of the simulated river flows -provided by an independent implementation of the two hydrological models each one forced with both COSMO and MM5 -enable a quantification of the uncertainties of the precipitation outputs, and therefore, of the discharge simulations.Results permit to highlight some hydrological and meteorological modeling factors which could help to enhance the hydrometeorological modeling of such hazardous events. Main conclusions are: (1) deficiencies in precipitation forecasts have a major impact on flood forecasts; (2) large-scale shift errors in precipitation patterns are not improved by only enhancing the mesoscale model resolution; and (3) weak differences in flood forecasting performance are found by using either a distributed continuous or a semi-distributed eventbas...

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Multi‐objective optimization of injection molding parameters, based on the Gkriging‐NSGA‐vague method

Fan

Huang

et al. 2019

J of Applied Polymer Sci

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Plastic production quality, manufacturing cost, and molding efficiency are three important indices for a new product development. In addition to injection molding process parameters (IMPP), runner system also has an important role in the injection molding process. In this study, the plastic production quality, manufacturing costs, and molding efficiency are considered as the optimized objectives. The design parameters include runner diameters and IMPP. The improved Kriging surrogate model (Gkriging), nondominated sorting genetic algorithm (NSGA-II), and multicriteria fuzzy decision-making approach (vague sets) are combined, and the Gkriging-NSGA-vague scheme is proposed to optimize the runner diameters and the IMPP. Firstly, the Gkriging model is established to map the correlation between design parameters and optimized objectives. Based on the Gkriging model, the NSGA-II is combined with predictive models to obtain the Pareto-optimal solutions. Then, the optimal Pareto-optimal solution is obtained by the vague approach. A multicavity mold with two different plastic parts is utilized as the design case. The optimization results indicate that the Gkriging-NSGAvague method is a powerful method for solving the multi-objective optimization problems.

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Influence of parameter estimation uncertainty in Kriging: Part 1 - Theoretical Development

Cited by 38 publications

References 24 publications

Influence of parameter estimation uncertainty in Kriging: Part 2 - Test and case study applications

Influence of parameter estimation uncertainty in Kriging: Part 2 - Test and case study applications

A hydrometeorological model intercomparison as a tool to quantify the forecast uncertainty in a medium size basin

Multi‐objective optimization of injection molding parameters, based on the Gkriging‐NSGA‐vague method

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