Assessing local and spatial uncertainty with HER method

2021 ◽  
Author(s):  
Stephanie Thiesen ◽  
Uwe Ehret
Keyword(s):  
Uncertainty Analysis ◽  
Spatial Configuration ◽  
Order Relation ◽  
Uncertainty Estimation ◽  
Indicator Kriging ◽  
Distribution Functions ◽  
Spatial Uncertainty ◽  
Cumulative Distribution ◽  
Trade Offs ◽  
Entropy Reduction

<p>Uncertainty analysis is a critical subject for many environmental studies. We have previously combined statistical learning and Information Theory in a geostatistical framework for overcoming parameterization with functions and uncertainty trade-offs present in many traditional interpolators (Thiesen et al. 2020). The so-called Histogram via entropy reduction (HER) relaxes normality assumptions, avoiding the risk of adding information not available in the data. The authors showed that, by construction, the method provides a proper framework for uncertainty estimation which accounts for both spatial configuration and data values, while allowing one to introduce or infer properties of the field through the aggregation method. In this study, we explore HER method in the light of uncertainty analysis. In general, uncertainty at any particular unsampled location (local uncertainty) is frequently assessed by nonlinear interpolators such as indicator and multi-gaussian kriging. HER has shown to be a unique approach for dealing with uncertainty estimation in a fine resolution without the need of modeling multiple indicator semivariograms, order-relation violations, interpolation/extrapolation of conditional cumulative distribution functions, or stronger hypotheses of data distribution. In this work, this nonparametric geostatistical framework is adapted to address local and spatial uncertainty in the context of risk mapping. We investigate HER for handling estimations of threshold-exceeding probabilities to map the risk of soil contamination by lead in the well-known dataset of the region of Swiss Jura. Finally, HER method is extended to assess spatial uncertainty (uncertainty when several locations are considered together) through sequential simulation. Its results are compared to indicator kriging and benchmark models available in the literature generated for this particular dataset.</p><p>Thiesen S, Vieira DM, Mälicke M, Loritz R, Wellmann JF, Ehret U (2020) Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics. Hydrol Earth Syst Sci 24:4523–4540. https://doi.org/https://doi.org/10.5194/hess-24-4523-2020</p>

scholarly journals Assessing local and spatial uncertainty with nonparametric geostatistics

2021 ◽  
Author(s):  
Stephanie Thiesen ◽  
Uwe Ehret
Keyword(s):  
Soil Contamination ◽  
Probability Distributions ◽  
Order Relation ◽  
Indicator Kriging ◽  
Spatial Uncertainty ◽  
Probability Aggregation ◽  
Entropy Reduction ◽  
Multiple Indicator ◽  
Indicator Variograms ◽  
Fine Resolution

Abstract Uncertainty quantification is an important topic for many environmental studies, such as identifying zones where potentially toxic materials exist in the soil. In this work, the nonparametric geostatistical framework of histogram via entropy reduction (HER) is adapted to address local and spatial uncertainty in the context of risk of soil contamination. HER works with empirical probability distributions, coupling information theory and probability aggregation methods to estimate conditional distributions, which gives it the flexibility to be tailored for different data and application purposes. To explore the method adaptation for handling estimations of threshold-exceeding probabilities, it is used to map the risk of soil contamination by lead in the well-known dataset of the region of Swiss Jura. Its results are compared to indicator kriging (IK) and to an ordinary kriging (OK) model available in literature. For the analyzed dataset, IK and HER achieved the best performance and exhibited comparable accuracy and precision of their predictions. When compared to IK, HER has shown to be a unique approach for dealing with uncertainty estimation in a fine resolution, without the need of modeling multiple indicator variograms, correcting order-relation violations, or defining interpolation/extrapolation of distribution. Finally, to avoid the well-known smoothing effect when using point estimations (this is the case with kriging, but also with HER) and to provide maps that reflect the spatial fluctuation of the revealed reality, we demonstrate how HER can be used in combination with sequential simulation to assess spatial uncertainty (uncertainty jointly over several locations).

scholarly journals Assessing local and spatial uncertainty with nonparametric geostatistics

2021 ◽  
Author(s):  
Stephanie Thiesen ◽  
Uwe Ehret
Keyword(s):  
Soil Contamination ◽  
Probability Distributions ◽  
Order Relation ◽  
Indicator Kriging ◽  
Spatial Uncertainty ◽  
Probability Aggregation ◽  
Entropy Reduction ◽  
Multiple Indicator ◽  
Indicator Variograms ◽  
Fine Resolution

AbstractUncertainty quantification is an important topic for many environmental studies, such as identifying zones where potentially toxic materials exist in the soil. In this work, the nonparametric geostatistical framework of histogram via entropy reduction (HER) is adapted to address local and spatial uncertainty in the context of risk of soil contamination. HER works with empirical probability distributions, coupling information theory and probability aggregation methods to estimate conditional distributions, which gives it the flexibility to be tailored for different data and application purposes. To explore how HER can be used for estimating threshold-exceeding probabilities, it is applied to map the risk of soil contamination by lead in the well-known dataset of the region of Swiss Jura. Its results are compared to indicator kriging (IK) and to an ordinary kriging (OK) model available in the literature. For the analyzed dataset, IK and HER predictions achieve the best performance and exhibit comparable accuracy and precision. Compared to IK, advantages of HER for uncertainty estimation in a fine resolution are that it does not require modeling of multiple indicator variograms, correcting order-relation violations, or defining interpolation/extrapolation of distributions. Finally, to avoid the well-known smoothing effect when using point estimations (as is the case with both kriging and HER), and to provide maps that reflect the spatial fluctuation of the observed reality, we demonstrate how HER can be used in combination with sequential simulation to assess spatial uncertainty (uncertainty jointly over several locations).

scholarly journals Spatial interpolation of rain-field dynamic time-space evolution based on radar rainfall data

2020 ◽  
Vol 51 (3) ◽  
pp. 521-540
Author(s):  
Peng Liu ◽  
Yeou-Koung Tung
Keyword(s):  
Temporal Distribution ◽  
Radar Data ◽  
Indicator Kriging ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Radar Rainfall ◽  
Time Space ◽  
Geostatistical Approach ◽  
Wide Range ◽  
Dynamic Time

Abstract Accurate and reliable measurement and prediction of the spatial and temporal distribution of rain field over a wide range of scales are important topics in hydrologic investigations. In this study, a geostatistical approach was adopted. To estimate the rainfall intensity over a study domain with the sample values and the spatial structure from the radar data, the cumulative distribution functions (CDFs) at all unsampled locations were estimated. Indicator kriging (IK) was used to estimate the exceedance probabilities for different preselected threshold levels, and a procedure was implemented for interpolating CDF values between the thresholds that were derived from the IK. Different probability distribution functions of the CDF were tested and their influences on the performance were also investigated. The performance measures and visual comparison between the observed rain field and the IK-based estimation suggested that the proposed method can provide good results of the estimation of indicator variables and is capable of producing a realistic image.

Estimation of Source Term Uncertainty in a Severe Accident With Correlated Variables

2014 ◽  
Author(s):  
Xiaoyu Zheng ◽  
Hiroto Itoh ◽  
Hitoshi Tamaki ◽  
Yu Maruyama
Keyword(s):  
Uncertainty Analysis ◽  
Nuclear Power ◽  
Source Term ◽  
Correlation Coefficients ◽  
Sampling Technique ◽  
Latin Hypercube Sampling ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Severe Accident ◽  
Source Terms

The quantitative evaluation of the fission product release to the environment during a severe accident is of great importance. In the present analysis, integral severe accident code MELCOR 1.8.5 has been applied to estimating uncertainty of source term for the accident at Unit 2 of the Fukushima Daiichi nuclear power plant (NPP) as an example and to discussing important models or parameters influential to the source term. Forty-two parameters associated with models for the transportation of radioactive materials were chosen and narrowed down to 18 through a set of screening analysis. These 18 parameters in addition to 9 parameters relevant to in-vessel melt progression obtained by the preceding uncertainty study were input to the subsequent sensitivity analysis by Morris method. This one-factor-at-a-time approach can preliminarily identify inputs which have important effects on an output, and 17 important parameters were selected from the total of 27 parameters through this approach. The selected parameters have been integrated into uncertainty analysis by means of Latin Hypercube Sampling technique and Iman-Conover method, taking into account correlation between parameters. Cumulative distribution functions of representative source terms were obtained through the present uncertainty analysis assuming the failure of suppression chamber. Correlation coefficients between the outputs and uncertain input parameters have been calculated to identify parameters of great influences on source terms, which include parameters related to models on core components failure, models of aerosol dynamic process and pool scrubbing.

scholarly journals A copula-based multivariate drought indicator to design and monitor nature-based solutions

2020 ◽  
Author(s):  
Sisay Debele ◽  
Jeetendra Sahani ◽  
Federico Porcù ◽  
Leonardo Aragão ◽  
Christos Spyrou ◽  
...  
Keyword(s):  
Uncertainty Analysis ◽  
Meteorological Data ◽  
Distribution Functions ◽  
Extreme Drought ◽  
Cumulative Distribution ◽  
Drought Risk ◽  
Statistical Tool ◽  
Horizon 2020 ◽  
Po Valley ◽  
Drought Indicators

<p><strong>Abstract </strong></p><p>Droughts are comprehensive and complex naturally occurring hazards in any climatic region around the world and often result in the loss of life and severe ecosystem damage. Drought monitoring is usually based on single-variables that may not represent the corresponding risk appropriately to its multiple causation and impact characteristics under current and future climate scenarios. In order to address this issue, the multidimensional copulas function, which is a flexible statistical tool, could be applied to develop multivariate drought indicators and solve the complicated and nonlinear associations. The aim of this paper is to develop reliable designing, monitoring and prediction indicators for the proper assessment and intervention of drought risk by nature-based solutions (NBS). Using a copula-based multivariate drought indicator (CMDI) that considers all possible variables related to meteorological, agricultural and hydrological droughts is essential for better drought risk assessment and intervention. The CMDI was developed by integrating univariate marginal cumulative distribution functions of meteorological (precipitation), agricultural (soil moisture) and hydrological (streamflow) variables into their joint cumulative distribution function. CMDI was then applied to the selected study catchment (Po Valley, Italy and Spercheios River, Greece) using hydro-meteorological data from gauging stations and ERA5 gridded data for the period 1979-2017.  The result of CMDI showed moderate, severe and extreme drought frequencies in the two selected catchments. The constructed CMDI captured more severe to extreme drought occurrence than the considered single drought indicators. This proved that the CMDI could appropriately represent the complex and interrelated natural variables. The uncertainty analysis based on Monte Carlo experiments confirmed that CMDI is a more robust and reliable approach for assessing, planning and designing a nature-based intervention for drought risk. The findings of this research can provide a reliable way to develop approaches that can be used for assessing and predicting non-linearly related variables or any risk that may occur simultaneously or cumulatively over time.   </p><p>Keywords: Drought risk; multidimensional copulas; multivariate indicators, uncertainty analysis; frequency   </p><p><strong>Acknowledgements</strong>: This work is carried out under the framework of OPERANDUM (OPEn-air laboRAtories for Nature baseD solUtions to Manage hydro-meteo risks) project, which is funded by the Horizon 2020 under the Grant Agreement No: 776848.</p>

scholarly journals Do galactic bars depend on environment?: an information theoretic analysis of Galaxy Zoo 2

2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee
Keyword(s):  
Spatial Distribution ◽  
Mutual Information ◽  
Local Density ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Host Galaxy ◽  
Data Sets ◽  
Data Set ◽  
Information Theoretic

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.

scholarly journals Composite Aerosol Optical Depth Mapping over Northeast Asia from GEO-LEO Satellite Observations

2021 ◽  
Vol 13 (6) ◽  
pp. 1096
Author(s):  
Soi Ahn ◽  
Sung-Rae Chung ◽  
Hyun-Jong Oh ◽  
Chu-Yong Chung
Keyword(s):  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Northeast Asia ◽  
Low Earth Orbit ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Radiometric Calibration ◽  
Climate Data ◽  
Error Statistics ◽  
Spatiotemporal Resolution

This study aimed to generate a near real time composite of aerosol optical depth (AOD) to improve predictive model ability and provide current conditions of aerosol spatial distribution and transportation across Northeast Asia. AOD, a proxy for aerosol loading, is estimated remotely by various spaceborne imaging sensors capturing visible and infrared spectra. Nevertheless, differences in satellite-based retrieval algorithms, spatiotemporal resolution, sampling, radiometric calibration, and cloud-screening procedures create significant variability among AOD products. Satellite products, however, can be complementary in terms of their accuracy and spatiotemporal comprehensiveness. Thus, composite AOD products were derived for Northeast Asia based on data from four sensors: Advanced Himawari Imager (AHI), Geostationary Ocean Color Imager (GOCI), Moderate Infrared Spectroradiometer (MODIS), and Visible Infrared Imaging Radiometer Suite (VIIRS). Cumulative distribution functions were employed to estimate error statistics using measurements from the Aerosol Robotic Network (AERONET). In order to apply the AERONET point-specific error, coefficients of each satellite were calculated using inverse distance weighting. Finally, the root mean square error (RMSE) for each satellite AOD product was calculated based on the inverse composite weighting (ICW). Hourly AOD composites were generated (00:00–09:00 UTC, 2017) using the regression equation derived from the comparison of the composite AOD error statistics to AERONET measurements, and the results showed that the correlation coefficient and RMSE values of composite were close to those of the low earth orbit satellite products (MODIS and VIIRS). The methodology and the resulting dataset derived here are relevant for the demonstrated successful merging of multi-sensor retrievals to produce long-term satellite-based climate data records.

Probabilistic finite element analysis in heat transfer to a nuclear fuel rod bumper support

2004 ◽  
Vol 218 (12) ◽  
pp. 1499-1505
Author(s):  
Rama Subba Reddy Gorla
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Nuclear Fuel ◽  
Cost Effective ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Element Analysis ◽  
Transfer Rates ◽  
Fuel Rod ◽  
Design Variables

Heat transfer from a nuclear fuel rod bumper support was computationally simulated by a finite element method and probabilistically evaluated in view of the several uncertainties in the performance parameters. Cumulative distribution functions and sensitivity factors were computed for overall heat transfer rates due to the thermodynamic random variables. These results can be used to identify quickly the most critical design variables in order to optimize the design and to make it cost effective. The analysis leads to the selection of the appropriate measurements to be used in heat transfer and to the identification of both the most critical measurements and the parameters.

scholarly journals Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Thabet Abdeljawad ◽  
Saima Rashid ◽  
Zakia Hammouch ◽  
İmdat İşcan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Fractional Derivatives ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Auxiliary Result ◽  
Fractal Sets ◽  
Different Types ◽  
Novel Applications ◽  
Class Of Functions ◽  
Harmonically Convex Functions

Abstract The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers are p-convex. The method we present is an alternative in showing the classical variants associated with generalized p-convex functions. Some parts of our results cover the classical convex functions and classical harmonically convex functions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.

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