In this work we introduce the Voronoi fundamental zone octonion (VFZO) interpolation framework for grain boundary (GB) structure-property models and surrogates. The VFZO framework offers an advantage over other five degree-of-freedom (5DOF) based property interpolation methods because it is constructed as a point set in a Riemannian manifold. This means that directly computed Euclidean distances approximate the original octonion distance with significantly reduced computation runtime (∼7 CPU minutes vs. 153 CPU days for a 50000×50000 pairwise-distance matrix). This increased efficiency facilitates lower interpolation error through the use of significantly more input data. We demonstrate grain boundary energy (GBE) interpolation results for a non-smooth validation function and simulated bi-crystal datasets for Fe and Ni using four interpolation methods: barycentric interpolation, Gaussian process regression (GPR) or Kriging, inverse-distance weighting (IDW), and nearest neighbor (NN)interpolation. These are evaluated for 50000 random input GBs and 10000 random prediction GBs. The best performance was achieved with GPR, which resulted in a reduction of the root mean square error(RMSE) by 83.0% relative to RMSE of a constant, average model. Likewise, interpolation on a large, noisy, molecular statics (MS) Fe simulation dataset improves performance by 34.4 % compared to 21.2 %in prior work. Interpolation on a small, low-noise MS Ni simulation dataset is similar to interpolation results for the original octonion metric (57.6 % vs. 56.4 %). A vectorized, parallelized, MATLAB interpolation function (interp5DOF.m) and related routines are available in our VFZO repository (github.com/sgbaird-5dof/interp) which can be applied to any of the 32 crystallographic point groups1. The VFZO framework offers advantages for computing distances between GBs, estimating property values for arbitrary GBs, and modeling surrogates of computationally expensive 5DOF functions and simulations.

The scarcity of housing has led more and more developers to turn to the conversion of former industrial areas into residential areas. Brownfield redevelopment involves the cleanup of contaminated soil to eliminate any health or environmental risk. The quantification of the amount of pollutant in soil is essential to carry out an efficient remediation. It involves sampling and analyzing the soil to determine the concentration of pollutant at a finite number of locations. It is therefore necessary to assess the pollutant amount at unknown locations to estimate the pollution for the whole site. The existing methods used by the depollution actors often lead to underestimation or overestimation of the contamination possibly creating environmental, economic and legal issues. This study aims to compare different methods to assess the mass of pollutant using data from a site contaminated with chlorinated solvents. The methods comprise currently used methods (Mean 1, Mean 2), simple interpolation methods (Thiessen Polygons, Natural Neighbor, Inverse Distance Weighting) and a method based on a complete geostatistical approach (Conditional Simulations). They are compared to determine the variability of the results obtained with a specific set of data depending on the chosen method. The deterministic methods, although easy to apply, will often underestimate the mass of pollutants contained in soil whereas the geostatistical approach can give a more realistic result, but is complex to implement.

In this work we introduce the Voronoi fundamental zone octonion (VFZO) interpolation framework for grain boundary (GB) structure-property models and surrogates. The VFZO framework offers an advantage over other five degree-of-freedom (5DOF) based property interpolation methods because it is constructed as a point set in a Riemannian manifold. This means that directly computed Euclidean distances approximate the original octonion distance with significantly reduced computation runtime (∼7 CPU minutes vs. 153 CPU days for a 50000×50000 pairwise-distance matrix). This increased efficiency facilitates lower interpolation error through the use of significantly more input data. We demonstrate grain boundary energy (GBE) interpolation results for a non-smooth validation function and simulated bi-crystal datasets for Fe and Ni using four interpolation methods: barycentric interpolation, Gaussian process regression (GPR) or Kriging, inverse-distance weighting (IDW), and nearest neighbor (NN)interpolation. These are evaluated for 50000 random input GBs and 10000 random prediction GBs. The best performance was achieved with GPR, which resulted in a reduction of the root mean square error(RMSE) by 83.0% relative to RMSE of a constant, average model. Likewise, interpolation on a large, noisy, molecular statics (MS) Fe simulation dataset improves performance by 34.4 % compared to 21.2 %in prior work. Interpolation on a small, low-noise MS Ni simulation dataset is similar to interpolation results for the original octonion metric (57.6 % vs. 56.4 %). A vectorized, parallelized, MATLAB interpolation function (interp5DOF.m) and related routines are available in our VFZO repository (github.com/sgbaird-5dof/interp) which can be applied to any of the 32 crystallographic point groups1. The VFZO framework offers advantages for computing distances between GBs, estimating property values for arbitrary GBs, and modeling surrogates of computationally expensive 5DOF functions and simulations.

Windstorms result in significant damage and economic loss and are a major recurring threat in many countries. Estimating surface-level wind speeds resulting from windstorms is a complicated problem, but geostatistical spatial interpolation methods present a potential solution. Maximum sustained and peak gust weather station data from two historic windstorms in Europe were analyzed to predict surface-level wind speed surfaces across a large and topographically varied landscape. Disjunctively sampled maximum sustained wind speeds were adjusted to represent equivalent continuously sampled 10-minute wind speeds and missing peak gust station data were estimated by applying a gust factor to the recorded maximum sustained wind speeds. Wind surfaces were estimated based on anisotropic and isotropic kriging interpolation methodologies. The study found that anisotropic kriging is well-suited for interpolating wind speeds in meso- and macro-scale areas because it accounts for wind direction and trends in wind speeds across a large, heterogeneous surface, and resulted in interpolation surface improvement in most models evaluated. Statistical testing of interpolation error for stations stratified by geographic classification revealed that stations in coastal and/or mountainous locations had significantly higher prediction errors when compared with stations in non-coastal/non-mountainous locations. These results may assist in mitigating losses to structures due to excessive wind events.

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Faculty of Engineering and Built Enviroment School of Civil and Enviromental Engineering 0105772w imasengo@yahoo.com / The problem of missing data, insufficient length of hydrological data series and poor quality is common in developing countries. This problem is much more prevalent in developing countries than it is in developed countries. This situation can severely affect the outcome of the water systems managers’ decisions (e.g. reliability of the design, establishment of operating policies for water supply, etc). Thus, numerous data interpolation (infilling) techniques have evolved in hydrology to deal with the missing data. The current study presents merely a methodology by combining different approaches and coping with missing (limited) hydrological data using the theories of entropy, artificial neural networks (ANN) and expectation-maximization (EM) techniques. This methodology is simply formulated into a model named ENANNEX model. This study does not use any physical characteristics of the catchment areas but deals only with the limited information (e.g. streamflow or rainfall) at the target gauge and its similar nearby base gauge(s). The entropy concept was confirmed to be a versatile tool. This concept was firstly used for quantifying information content of hydrological variables (e.g. rainfall or streamflow). The same concept (through directional information transfer index, i.e. DIT) was used in the selection of base/subject gauge. Finally, the DIT notion was also extended to the evaluation of the hydrological data infilling technique performance (i.e. ANN and EM techniques). The methodology was applied to annual total rainfall; annual mean flow series, annual maximum flows and 6-month flow series (means) of selected catchments in the drainage region D “Orange” of South Africa. These data regimes can be regarded as useful for design-oriented studies, flood studies, water balance studies, etc. The results from the case studies showed that DIT is as good index for data infilling technique selection as other criteria, e.g. statistical and graphical. However, the DIT has the feature of being non-dimensionally informational index. The data interpolation iii techniques viz. ANNs and EM (existing methods applied and not yet applied in hydrology) and their new features have been also presented. This study showed that the standard techniques (e.g. Backpropagation-BP and EM) as well as their respective variants could be selected in the missing hydrological data estimation process. However, the capability for the different data interpolation techniques of maintaining the statistical characteristics (e.g. mean, variance) of the target gauge was not neglected. From this study, the relationship between the accuracy of the estimated series (by applying a data infilling technique) and the gap duration was then investigated through the DIT notion. It was shown that a decay (power or exponential) function could better describe that relationship. In other words, the amount of uncertainty removed from the target station in a station-pair, via a given technique, could be known for a given gap duration. It was noticed that the performance of the different techniques depends on the gap duration at the target gauge, the station-pair involved in the missing data estimation and the type of the data regime. This study showed also that it was possible, through entropy approach, to assess (preliminarily) model performance for simulating runoff data at a site where absolutely no record exist: a case study was conducted at Bedford site (in South Africa). Two simulation models, viz. RAFLER and WRSM2000 models, were then assessed in this respect. Both models were found suitable for simulating flows at Bedford.

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Interpolation is essential in digital image processing, especially magnification. Many different approaches to interpolation specific to magnification have been developed in an effort to overcome the shortcomings of bilinear and bicubic interpolation. One of these approaches, Constraint-Based Interpolation, produces an image that is free of jaggies and has less blurring than bilinear or bicubic interpolation. Although Constraint-Based Interpolation produces a visually pleasing image, there are user-chosen parameters that make the algorithm difficult to use. In this thesis we propose a method for automatic selection of those parameters and an extension of Constraint-Based Interpolation to other forms of image manipulation, such as skew, rotation, warp, or any other invertable image transformation. By extending Constaint-Based Interpolation the same improvements observed in magnification could be observed in these other image transformations.

Inorganic contaminants, including potentially toxic metals (PTMs), originating from un-reclaimed abandoned mine areas may accumulate in soils and present significant distress to environmental and public health. The ability to generate realistic spatial distribution models of such contamination is important for risk assessment and remedial planning of sites where this has oc-curred. This study evaluated the prediction accuracy of optimized ordinary kriging compared to spatial regression-informed cokriging for PTMs (Zn, Mn, Cu, Pb, and Cd) in soils near abandoned mines in Bumpus Cove, Tennessee, USA. Cokriging variables and neighborhood sizes were system-atically selected from prior statistical analyses based on the association with PTM transport and soil physico-chemical properties (soil texture, moisture content, bulk density, pH, cation exchange capacity (CEC), and total organic carbon (TOC)). A log transform was applied to fit the frequency histograms to a normal distribution. Superior models were chosen based on six diagnostics (ME, RMS, MES, RMSS, ASE, and ASE-RMS), which produced mixed results. Cokriging models were preferred for Mn, Zn, Cu, and Cd, whereas ordinary kriging yielded better model results for Pb. This study determined that the preliminary process of developing spatial regression models, thus enabling the selection of contributing soil properties, can improve the interpolation accuracy of PTMs in abandoned mine sites.