Non-Probabilistic Uncertainty in Subsurface Hydrology and Its Applications: an Overview

Ozbek, M. M.; Pinder, George F.

doi:10.1007/s11267-005-9011-4

Cited by 7 publications

(4 citation statements)

References 54 publications

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“…The test problem considered for assessing the uncertainty analysis addresses transport of chemical species with constant source concentration in a saturated aquifer [16][17][18]…”

Section: Case Studymentioning

confidence: 99%

Development of possibilistic statistics and its application to quantify uncertainty of subsurface solute transport model

Pal

Datta

2019

Sādhanā

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Imprecise information on any system is addressed by possibility theory wherein the system is modeled as a fuzzy set. Alpha level representation of a fuzzy set in the form of an interval defines the possibility theory. Uncertainty of any model in this context is quantified as mean value ± standard deviation of a possibilistic (imprecise) parameter. This paper presents the possibilistic statistical techniques to estimate the mean and standard deviation of a possibilistic parameter of subsurface solute transport model. The solute transport model parameters, such as groundwater velocity, solute dispersion coefficient, etc., are sparse and imprecise in nature. Such parameters are characterized by the possibility distribution. In this paper, analytical expression of solute transport model is used to estimate the mean value and standard deviation of possibilistic spatial and temporal concentration of solute.

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“…The test problem considered for assessing the uncertainty analysis addresses transport of chemical species with constant source concentration in a saturated aquifer [16][17][18]…”

Section: Case Studymentioning

confidence: 99%

Development of possibilistic statistics and its application to quantify uncertainty of subsurface solute transport model

Pal

Datta

2019

Sādhanā

View full text Add to dashboard Cite

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“…In general, in many cases where uncertainty in model parameters is important, a Bayesian analysis is preferred over a simple deterministic analysis (Vicens et al, 1975). It should be noted, however, that uncertainty in datadriven modelling techniques is not purely random or probabilistic in nature (Dubois and Prade, 1997;Ozbek and Pinder, 2006), as is implied by adopting a Bayesian framework. An alternative to the probability based representation of uncertainty is through the use of fuzzy set theory, particularly in relation to possibility theory and fuzzy numbers.…”

Section: Uncertainty Analysis Using Bayesian and Fuzzy Number Frameworkmentioning

confidence: 99%

Comparing A Bayesian and Fuzzy Number Approach to Uncertainty Quantification in Short-Term Dissolved Oxygen Prediction

Khan¹,

Valeo²

2017

J ENVIRON INFORM

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A new autoregressive-type, updating fuzzy linear regression method is proposed to predict daily dissolved oxygen (DO) concentration in a highly urbanized riverine environment. Results of this model are compared to results from an updating Bayesian regression model. Both methods use lagged daily DO (at four different lags) as the independent variable. Uncertainty in the models is represented by a fuzzy number based approach in the first case, and by a Bayesian framework in the second. Real-time data from the Bow River in Calgary, Canada is used to calibrate the models sequentially to mimic a real-time updating model. Four different performance metrics were used to measure the performance of each model. Lastly, the input data resolution is reduced to measure the impact on model performance. Results show that the physical system can be adequately characterized using only one year of data. Both approaches can capture the general trend of daily DO, but the fuzzy number based method can better capture the changes in observed variability. The metrics for both models are comparable, with the one-day lag case categorized as "very good"; however, the performance reduces at higher lags. The fuzzy number method captures more low DO events than the Bayesian approach, with a much lower mean squared error. A possibility to probability transformation is used to highlight the risk of low DO days for the fuzzy case. Lastly, reducing the input data resolution from 96 to 6 points per day has a minimal impact on model performance, suggesting the limited efficacy or utility in increasing sampling rates.

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“…Data-driven modelling have intrinsic uncertainties associated with it that are not random or probabilistic in nature, thus, making it well suited for the use of fuzzy number theory (Dubois and Prade, 1997;Ozbek and Pinder, 2006). Fuzzy numbers use fuzzy sets (Zadeh, 1965) and possibility theory to describe uncertain or imprecise quantities, measurements or observations (Huang et al, 2010;Zhang and Achari, 2010;Khan and Valeo, 2015).…”

Section: Introductionmentioning

confidence: 99%

Short-Term Peak Flow Rate Prediction and Flood Risk Assessment Using Fuzzy Linear Regression

Khan¹,

Valeo²

2016

J ENVIRON INFORM

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ABSTRACT.A fuzzy linear regression (FLR) method is proposed that uses real-time data to accurately predict daily peak flow rate for the Bow and Elbow Rivers in southern Alberta. FLR model performance was compared to a non-fuzzy, error-in-variables model (EIV). Mean daily flow rate, with a delay of one, two, three or seven days was used as the independent variable. In implementing the FLR, a unique hybrid modelling approach was devised that treated peak flow rate as probabilistic and mean daily flow rate as possibilistic. Three gauge errors, 5%, 10% and 20%, were tested and compared to quantify uncertainty in observed flow rate. The research proposed a new method of computing the exceedance probability of peak flow rate using fuzzy numbers. NSE, PBIAS and RSR and a proposed rating system were used to evaluate and compare the methods. Two different calibration schemes were used, including a quasi-real time system. The tests demonstrated that FLR with a one day lag was a very good predictor of peak flow rate and outperformed EIV for two stations on the Bow River. A test dataset from the floods of June 2013 in Calgary was used for risk assessment. The FLR results demonstrated higher flexibility and sensitivity to the flood as it approached Calgary. The fuzzy method was able to capture the peak flow rate for the majority of the high flow rate days, while the EIV model was unable to predict this data within the 95% confidence interval.

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Non-Probabilistic Uncertainty in Subsurface Hydrology and Its Applications: an Overview

Cited by 7 publications

References 54 publications

Development of possibilistic statistics and its application to quantify uncertainty of subsurface solute transport model

Development of possibilistic statistics and its application to quantify uncertainty of subsurface solute transport model

Comparing A Bayesian and Fuzzy Number Approach to Uncertainty Quantification in Short-Term Dissolved Oxygen Prediction

Short-Term Peak Flow Rate Prediction and Flood Risk Assessment Using Fuzzy Linear Regression

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