scholarly journals Probabilistic Inference Coupled with Possibilistic Reasoning for Robust Estimation of Hydrologic Parameters and Piecewise Characterization of Interactive Uncertainties

2016 ◽  
Vol 17 (4) ◽  
pp. 1243-1260 ◽  
Author(s):  
S. Wang ◽  
G. H. Huang ◽  
B. W. Baetz ◽  
W. Huang
Keyword(s):  
Expert Knowledge ◽  
Probability Distributions ◽  
Statistical Significance ◽  
Probabilistic Inference ◽  
Hydrologic Model ◽  
Factorial Analysis ◽  
Model Parameters ◽  
Xiangxi River ◽  
Parametric Interactions

Abstract This paper presents a factorial possibilistic–probabilistic inference (FPI) framework for estimation of hydrologic parameters and characterization of interactive uncertainties. FPI is capable of incorporating expert knowledge into the parameter adjustment procedure for enhancing the understanding of the nature of the calibration problem. As a component of the FPI framework, a Monte Carlo–based fractional fuzzy–factorial analysis (MFA) method is also proposed to identify the best parameter set and its underlying probability distributions in a fuzzy probability space. Factorial analysis of variance (ANOVA) coupled with its multivariate extensions are performed to explore potential interactions among model parameters and among hydrological metrics in a systematic manner. The proposed methodology is applied to the Xiangxi River watershed by using the conceptual hydrological model (HYMOD) to demonstrate its validity and applicability. Results reveal that MFA is capable of deriving probability density functions (PDFs) of hydrologic model parameters. Moreover, the sequential inferences derived from the F test and its multivariate approximations disclose the statistical significance of parametric interactions affecting individual and multiple hydrological metrics, respectively. The findings presented here indicate that parametric interactions are complex in a fuzzy stochastic environment, and the magnitude and direction of interaction effects vary in different regions of the parameter space as well as vary temporally because of the dynamic behavior of hydrologic systems.

Parametric Identification of Rotating Cavitation in a Three-Bladed Axial Inducer

2021 ◽  
Author(s):  
Antonio Costanzo ◽  
Dario Valentini ◽  
Giovanni Pace ◽  
Ruzbeh Hadavandi ◽  
Lucio Torre ◽  
...  
Keyword(s):  
High Performance ◽  
Statistical Significance ◽  
Likelihood Estimation ◽  
Parametric Identification ◽  
Flow Instabilities ◽  
Model Parameters ◽  
Promising Tool ◽  
Dual Sensor ◽  
Stationary Frame

Abstract The article illustrates the application of Bayesian estimation to the identification of flow instabilities, with special reference to rotating cavitation, in a three-bladed axial inducer using the unsteady pressure readings of a single transducer mounted on the casing just behind the leading edges of the impeller blades. The typical trapezoidal pressure distribution in the blade channels is parametrized and modulated in time and space for theoretically reproducing the expected pressure generated by known forms of cavitation instabilities (cavitation auto-oscillations, n-lobed rotating cavitation, higher-order surge/rotating cavitation modes). The Fourier spectra of the theoretical pressure so obtained in the rotating frame are transformed in the stationary frame, frequency broadened to better approximate the experimental results, and parametrically fitted by maximum likelihood estimation to the measured auto-correlation spectra. Each form of instability generates a characteristic distribution of sidebands in addition to its fundamental frequency. The identification makes use of this information for effective detection and characterization of multiple simultaneous flow instabilities with intensities spanning over about 20 dB down to about 4 dB signal-to-noise ratios. The same information also allows for effectively bypassing the aliasing limitations of traditional cross-correlation methods in the discrimination of multiple-lobed azimuthal instabilities from dual-sensor measurements on the same axial station of the machine. The method returns both the estimates of the model parameters and their standard deviations, providing the information needed for the assessment of the statistical significance of the results. The proposed approach represents therefore a promising tool for experimental research on flow instabilities in high-performance turbopumps.

scholarly journals Constraining subglacial processes from surface velocity observations using surrogate-based Bayesian inference

2021 ◽  
pp. 1-19
Author(s):  
Douglas Brinkerhoff ◽  
Andy Aschwanden ◽  
Mark Fahnestock
Keyword(s):  
Probability Distributions ◽  
Water Pressure ◽  
Model Development ◽  
Computational Cost ◽  
Hydrologic Model ◽  
Surface Velocity ◽  
Small Scale ◽  
Model Parameters ◽  
Stress Regime ◽  
Ice Dynamics

Abstract Basal motion is the primary mechanism for ice flux in Greenland, yet a widely applicable model for predicting it remains elusive. This is due to the difficulty in both observing small-scale bed properties and predicting a time-varying water pressure on which basal motion putatively depends. We take a Bayesian approach to these problems by coupling models of ice dynamics and subglacial hydrology and conditioning on observations of surface velocity in southwestern Greenland to infer the posterior probability distributions for eight spatially and temporally constant parameters governing the behavior of both the sliding law and hydrologic model. Because the model is computationally expensive, characterization of these distributions using classical Markov Chain Monte Carlo sampling is intractable. We skirt this issue by training a neural network as a surrogate that approximates the model at a sliver of the computational cost. We find that surface velocity observations establish strong constraints on model parameters relative to a prior distribution and also elucidate correlations, while the model explains 60% of observed variance. However, we also find that several distinct configurations of the hydrologic system and stress regime are consistent with observations, underscoring the need for continued data collection and model development.

scholarly journals Investigating the Dynamic Influence of Hydrological Model Parameters on Runoff Simulation Using Sequential Uncertainty Fitting-2-Based Multilevel-Factorial-Analysis Method

Water ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 1177 ◽  
Author(s):  
Shuai Zhou ◽  
Yimin Wang ◽  
Jianxia Chang ◽  
Aijun Guo ◽  
Ziyan Li
Keyword(s):  
Bulk Density ◽  
Hydrological Model ◽  
Latin Hypercube Sampling ◽  
Soil Bulk Density ◽  
Hydrologic Model ◽  
Factorial Analysis ◽  
Interactive Effects ◽  
Model Parameters ◽  
Analysis Method ◽  
Runoff Simulation

Hydrological model parameters are generally considered to be simplified representations that characterize hydrologic processes. Therefore, their influence on runoff simulations varies with climate and catchment conditions. To investigate the influence, a three-step framework is proposed, i.e., a Latin hypercube sampling (LHS-OAT) method multivariate regression model is used to conduct parametric sensitivity analysis; then, the multilevel-factorial-analysis method is used to quantitatively evaluate the individual and interactive effects of parameters on the hydrologic model output. Finally, analysis of the reasons for dynamic parameter changes is performed. Results suggest that the difference in parameter sensitivity for different periods is significant. The soil bulk density (SOL_BD) is significant at all times, and the parameter Soil Convention Service (SCS) runoff curve number (CN2) is the strongest during the flood period, and the other parameters are weaker in different periods. The interaction effects of CN2 and SOL_BD, as well as effective hydraulic channel conditions (CH_K2) and SOL_BD, are obvious, indicating that soil bulk density can impact the amount of loss generated by surface runoff and river recharge to groundwater. These findings help produce the best parameter inputs and improve the applicability of the model.

scholarly journals A hydro-climatological approach to predicting regional landslide probability using Landlab

2017 ◽  
Author(s):  
Ronda Strauch ◽  
Erkan Istanbulluoglu ◽  
Sai Siddhartha Nudurupati ◽  
Christina Bandaragoda ◽  
Nicole M. Gasparini ◽  
...  
Keyword(s):  
Soil Depth ◽  
Probability Distributions ◽  
Probability Model ◽  
Subsurface Flow ◽  
Grid Cell ◽  
Bimodal Distribution ◽  
Shallow Landslide ◽  
Hydrologic Model ◽  
Model Parameters ◽  
Infinite Slope Stability Model

Abstract. We develop a hydro-climatological approach to modeling of regional shallow landslide initiation that integrates spatial and temporal dimensions of parameter uncertainty to estimate an annual probability of landslide initiation. The physically-based model couples the infinite slope stability model with a steady-state subsurface flow representation and operates on a digital elevation model. Spatially distributed raster data for soil properties and a soil evolution model and vegetation classification from National Land Cover Data are used to derive parameters for probability distributions to represent input uncertainty. Hydrologic forcing to the model is through annual maximum recharge to subsurface flow obtained from a macroscale hydrologic model, routed on raster grid to develop subsurface flow. A Monte Carlo approach is used to generate model parameters at each grid cell and calculate probability of shallow landsliding. We demonstrate the model in a steep mountainous region in northern Washington, U.S.A., using 30-m grid resolution over 2,700 km2. The influence of soil depth on the probability of landslide initiation is investigated through comparisons among model output produced using three different soil depth scenarios reflecting uncertainty of soil depth and its potential long-term variability. We found elevation dependent patterns in probability of landslide initiation that showed the stabilizing effects of forests in low elevations, an increased landslide probability with forest decline at mid elevations (1,400 to 2,400 m), and soil limitation and steep topographic controls at high alpine elevations and post-glacial landscapes. These dominant controls manifest in a bimodal distribution of spatial annual landslide probability. Model testing with limited observations revealed similar model confidence for the three hazard maps, suggesting suitable use as relative hazard products. Validation of the model with observed landslides is hindered by the completeness and accuracy of the inventory, estimation of source areas, and unmapped landslides. The model is available as a component in Landlab, an open-source, Python-based landscape earth systems modeling environment, and is designed to be easily reproduced utilizing HydroShare cyberinfrastructure.

scholarly journals Non-Gaussian models of diffusion weighted imaging for detection and characterization of prostate cancer: a systematic review and meta-analysis

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
V. Brancato ◽  
C. Cavaliere ◽  
M. Salvatore ◽  
S. Monti
Keyword(s):  
Prostate Cancer ◽  
Systematic Review ◽  
Diffusion Weighted Imaging ◽  
Meta Analysis ◽  
Statistical Significance ◽  
Gaussian Model ◽  
Model Parameters ◽  
Diffusion Weighted ◽  
Non Gaussian

AbstractThe importance of Diffusion Weighted Imaging (DWI) in prostate cancer (PCa) diagnosis have been widely handled in literature. In the last decade, due to the mono-exponential model limitations, several studies investigated non-Gaussian DWI models and their utility in PCa diagnosis. Since their results were often inconsistent and conflicting, we performed a systematic review of studies from 2012 examining the most commonly used Non-Gaussian DWI models for PCa detection and characterization. A meta-analysis was conducted to assess the ability of each Non-Gaussian model to detect PCa lesions and distinguish between low and intermediate/high grade lesions. Weighted mean differences and 95% confidence intervals were calculated and the heterogeneity was estimated using the I2 statistic. 29 studies were selected for the systematic review, whose results showed inconsistence and an unclear idea about the actual usefulness and the added value of the Non-Gaussian model parameters. 12 studies were considered in the meta-analyses, which showed statistical significance for several non-Gaussian parameters for PCa detection, and to a lesser extent for PCa characterization. Our findings showed that Non-Gaussian model parameters may potentially play a role in the detection and characterization of PCa but further studies are required to identify a standardized DWI acquisition protocol for PCa diagnosis.

scholarly journals Unraveling the time-dependent relevance of input model uncertainties for a lumped hydrologic model of a pre-alpine karst system

2021 ◽  
Author(s):  
Daniel Bittner ◽  
Beatrice Richieri ◽  
Gabriele Chiogna
Keyword(s):  
Groundwater Recharge ◽  
Temporal Variations ◽  
Hydrologic Model ◽  
Time Dependent ◽  
Model Parameters ◽  
Lumped Parameter ◽  
Hydrodynamic Processes ◽  
Input Model ◽  
Karst Model ◽  
Input Uncertainties

AbstractUncertainties in hydrologic model outputs can arise for many reasons such as structural, parametric and input uncertainty. Identification of the sources of uncertainties and the quantification of their impacts on model results are important to appropriately reproduce hydrodynamic processes in karst aquifers and to support decision-making. The present study investigates the time-dependent relevance of model input uncertainties, defined as the conceptual uncertainties affecting the representation and parameterization of processes relevant for groundwater recharge, i.e. interception, evapotranspiration and snow dynamic, on the lumped karst model LuKARS. A total of nine different models are applied, three to compute interception (DVWK, Gash and Liu), three to compute evapotranspiration (Thornthwaite, Hamon and Oudin) and three to compute snow processes (Martinec, Girons Lopez and Magnusson). All the input model combinations are tested for the case study of the Kerschbaum spring in Austria. The model parameters are kept constant for all combinations. While parametric uncertainties computed for the same model in previous studies do not show pronounced temporal variations, the results of the present work show that input uncertainties are seasonally varying. Moreover, the input uncertainties of evapotranspiration and snowmelt are higher than the interception uncertainties. The results show that the importance of a specific process for groundwater recharge can be estimated from the respective input uncertainties. These findings have practical implications as they can guide researchers to obtain relevant field data to improve the representation of different processes in lumped parameter models and to support model calibration.

scholarly journals An FDA-Based Approach for Clustering Elicited Expert Knowledge

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 184-204
Author(s):  
Carlos Barrera-Causil ◽  
Juan Carlos Correa ◽  
Andrew Zamecnik ◽  
Francisco Torres-Avilés ◽  
Fernando Marmolejo-Ramos
Keyword(s):  
Functional Data ◽  
Expert Knowledge ◽  
Probability Distributions ◽  
Knowledge Elicitation ◽  
Parallel Analysis ◽  
Data Sets ◽  
Dimensional Problem ◽  
Prior Distributions ◽  
Infinite Dimensional ◽  
Finite Dimensional

Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile discrepant elicited prior distributions. This paper proposes the parallel analysis of clusters of prior distributions through a hierarchical method for clustering distributions and that can be readily extended to functional data. The proposed method consists of (i) transforming the infinite-dimensional problem into a finite-dimensional one, (ii) using the Hellinger distance to compute the distances between curves and thus (iii) obtaining a hierarchical clustering structure. In a simulation study the proposed method was compared to k-means and agglomerative nesting algorithms and the results showed that the proposed method outperformed those algorithms. Finally, the proposed method is illustrated through an EKE experiment and other functional data sets.

scholarly journals Industrial Plume Properties Retrieved by Optimal Estimation Using Combined Hyperspectral and Sentinel-2 Data

2021 ◽  
Vol 13 (10) ◽  
pp. 1865
Author(s):  
Gabriel Calassou ◽  
Pierre-Yves Foucher ◽  
Jean-François Léon
Keyword(s):  
Matched Filter ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Model Parameters ◽  
Surface Reflectance ◽  
Sequential Method ◽  
Modal Radius ◽  
Sentinel 2

Stack emissions from the industrial sector are a subject of concern for air quality. However, the characterization of the stack emission plume properties from in situ observations remains a challenging task. This paper focuses on the characterization of the aerosol properties of a steel plant stack plume through the use of hyperspectral (HS) airborne remote sensing imagery. We propose a new method, based on the combination of HS airborne acquisition and surface reflectance imagery derived from the Sentinel-2 Multi-Spectral Instrument (MSI). The proposed method detects the plume footprint and estimates the surface reflectance under the plume, the aerosol optical thickness (AOT), and the modal radius of the plume. Hyperspectral surface reflectances are estimated using the coupled non-negative matrix factorization (CNMF) method combining HS and MSI data. The CNMF reduces the error associated with estimating the surface reflectance below the plume, particularly for heterogeneous classes. The AOT and modal radius are retrieved using an optimal estimation method (OEM), based on the forward model and allowing for uncertainties in the observations and in the model parameters. The a priori state vector is provided by a sequential method using the root mean square error (RMSE) metric, which outperforms the previously used cluster tuned matched filter (CTMF). The OEM degrees of freedom are then analysed, in order to refine the mask plume and to enhance the quality of the retrieval. The retrieved mean radii of aerosol particles in the plume is 0.125 μμm, with an uncertainty of 0.05 μμm. These results are close to the ultra-fine mode (modal radius around 0.1 μμm) observed from in situ measurements within metallurgical plant plumes from previous studies. The retrieved AOT values vary between 0.07 (near the source point) and 0.01, with uncertainties of 0.005 for the darkest surfaces and above 0.010 for the brightest surfaces.

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