Model-Based Spatial Data Fusion

Two spatial data sets are considered to be similar if they originate from the same stochastic process in terms of their spatial structure. Many tests have been developed over recent years to test the similarity of certain types of spatial data, such as spatial point patterns, geostatistical data and images. This research proposes a generic spatial similarity test able to handle various types of spatial data, for example images (modelled spatially), point patterns, marked point patterns, geostatistical data and lattice patterns. A simulation study is done in order to test the method for each spatial data set. After the simulation study, it was concluded that the proposed spatial similarity test is not sensitive to the user-defined resolution of the pixel image representation. From the simulation study, the proposed spatial similarity test performs well on lattice data, some of the unmarked point patterns and the marked point patterns with discrete marks. We illustrate this test on property prices in the City of Cape Town and the City of Johannesburg, South Africa.

Uncertainty quantification is a crucial step of cosmological mass-mapping that is often ignored. Suggested methods are typically only approximate or make strong assumptions of Gaussianity of the shear field. Probabilistic sampling methods, such as Markov chain Monte Carlo (MCMC), draw samples form a probability distribution, allowing for full and flexible uncertainty quantification, however these methods are notoriously slow and struggle in the high-dimensional parameter spaces of imaging problems. In this work we use, for the first time, a trans-dimensional MCMC sampler for mass-mapping, promoting sparsity in a wavelet basis. This sampler gradually grows the parameter space as required by the data, exploiting the extremely sparse nature of mass maps in wavelet space. The wavelet coefficients are arranged in a tree-like structure, which adds finer scale detail as the parameter space grows. We demonstrate the trans-dimensional sampler on galaxy cluster-scale images where the planar modelling approximation is valid. In high-resolution experiments, this method produces naturally parsimonious solutions, requiring less than 1% of the potential maximum number of wavelet coefficients and still producing a good fit to the observed data. In the presence of noisy data, trans-dimensional MCMC produces a better reconstruction of mass-maps than the standard smoothed Kaiser-Squires method, with the addition that uncertainties are fully quantified. This opens up the possibility for new mass maps and inferences about the nature of dark matter using the new high-resolution data from upcoming weak lensing surveys such as Euclid.

The role of soil organic carbon (SOC) is crucial not only for numerous soil functions and processes but also for addressing various environmental crises and challenges we face. Consequently, the demand for information on the spatiotemporal variability of SOC is increasing, posing new methodological challenges, such as the need for information on SOC and SOC changes with quantified uncertainty across a wide variety of spatial scales and temporal periods. Our objective was to present a methodology based on a combination of machine learning and space–time geostatistics to predict the spatiotemporal variability of SOC stock with quantified uncertainty at various spatial supports (i.e., point support, 1 × 1 km, 5 × 5 km, 10 × 10 km, 25 × 25 km, counties, and the entire country) for Hungary, between 1992 and 2016. The role of geostatistics is pivotal, as it accounts for the spatiotemporal correlation of the interpolation errors, which is essential for reliably quantifying the uncertainty associated with spatially aggregated SOC stock and SOC stock change predictions. Five times repeated 10-fold leave-location-out cross-validation was used to evaluate the point support predictions and uncertainty quantifications, yielding acceptable results for both SOC stock (ME = −0.897, RMSE = 19.358, MEC = 0.321, and G = 0.912) and SOC stock change (ME = 0.414, RMSE = 16.626, MEC = 0.160, and G = 0.952). We compiled a series of maps of SOC stock predictions between 1992 and 2016 for each support, along with the quantified uncertainty, which is unprecedented in Hungary. It was demonstrated that the larger the support, the smaller the prediction uncertainty, which facilitates the identification and delineation of larger areas with statistically significant SOC stock changes. Moreover, the methodology can overcome the limitations of recent approaches in the spatiotemporal modelling of SOC, allowing the prediction of SOC and SOC changes, with quantified uncertainty, for any year, time period, and spatial scale. This methodology is capable of meeting the current and anticipated demands for dynamic information on SOC at both national and international levels.

Spatio-temporal processes are ubiquitous and prevalent across disciplines. Understanding the mechanisms underlying processes and integrating this information into models is of great interest, as it can improve forecasting accuracy and align with scientific motivation. Examples of such models include Partial Differential Equation (PDE) Models or Physics-Informed Neural Network Models in the applied mathematics or deep learning community, respectively. However, these models often overlook uncertainty quantification despite its crucial role, considering that real-world processes necessarily involve inherent errors that physical laws cannot fully explain. Dynamic Spatio-Temporal Models (DSTMs) offer a flexible and effective approach by embedding physics laws within the Bayesian Hierarchical Model (BHM) framework and accounting for dependencies in space and time conditionally. This dissertation explores integrating physics laws while accounting for uncertainty within BHMs and neural network models for complex environmental processes. To start, a novel approach utilizing a level-set method and low-rank representation within a BHM is developed to model the evolution of wildfire boundaries in the presence of uncertainty in data and a lack of knowledge about the boundaries. Subsequently, a hybrid model that nests an echo state network within a level-set method to accommodate nonlinearity is developed. This model is computationally efficient and includes calibrated uncertainty quantification. Lastly, a new class of DSTMs, capable of accommodating both high and low extremes through a regime-switching scheme of stable distributions with varying tail indices, is presented. This last method is illustrated on fine particulate matter (PM2.5) observations emanating from wildfires in the prairie region of the US.

Tephra fallout hazard assessment is undertaken with probabilistic maps that rely on numerical models. Regarding maps production, the input parameters of the model (including atmospheric conditions), the physical approximations of the numerical simulations, and the probabilities of occurrence of different eruption types in specific time frames are among the most critical sources of uncertainty. We therefore present a tephra fallout hazard assessment study for two active volcanoes (Cotopaxi and Guagua Pichincha) in Ecuador. We utilize PLUME‐MoM/HYSPLIT models, and a procedure for uncertainty quantification where: (a) the uncertainty on eruptive source parameters and eruption type occurrence is quantified through expert elicitation; (b) we implement a new procedure for correlations between the different parameters, and (c) we use correction coefficients to take into account the uncertainty of the numerical model. Maps of exceedance probability given a deposit thickness threshold, and thickness maps given a probability of exceedance, are produced (a) for two eruptive scenarios (sub‐Plinian and Plinian) and (b) as a combination of these scenarios in case the next eruption will be sub‐Plinian or Plinian. These maps are described according to the uncertainty distribution of eruption type occurrence probabilities, considering their 5th percentile, mean, and 95th percentile values. We finally present hazard curves describing exceeding probabilities in 10 sensitive sites within the city of Quito. Additional information includes the areal extent and the population potentially affected by different isolines of tephra accumulation. This work indicates that full uncertainty quantification helps in providing more robust scientific information, improving the hazard assessment reliability.

In this paper, a generalized statistical tool is introduced to estimate key frames in a video sequence. The tool works based on the inter-relationship between different features of image frames in a video. The image feature vectors are plotted in feature space as points and a randomness measure is determined from the distribution of these points. The randomness measure of the feature vectors is defined with respect to simulated random point patterns and expressed as a probability value of a frame being a key frame. Since, depending on the video content more than one inter-relationship of features can be used to determine a single key frame, different probability values are derived to support a frame as a key frame. To integrate these probability values a combiner model is designed to uniquely decide the status of a key frame. The combiner model is based on the Dempster-Shafer theory of evidence. To demonstrate the idea, randomness measures, and consequently the probabilities of a frame to be a key frame, are obtained separately from spatial domain and frequency domain features. The combined probability value enhances the confidence in selecting a frame as a key frame. The result is tested on a number of standard video sequences and it outperforms the related approach

We consider the setting of a multi-way contingency table with ordinal classifications. The contribution of this paper is to propose a joint probability model for the uncensored variables that is apart from the imposed categorization. Specifically, for an m-way table, we assume that the cell counts arise as a binned point pattern over a bounded set in m-dimensional Euclidean space where the point pattern is a realization of a non-homogeneous Poisson process. The intensity which drives the point pattern is itself viewed as a realization of a log Gaussian process over the set. With such an approach we achieve full inference regarding the underlying joint distribution, in particular, inference for familiar associations between the ordinal variables in the absence of interval censoring. Additionally, inference can be provided for any newly created cells where such creation is achieved through redefinition of the ordinal classifications. That is, rather than ad hoc reallocation, we achieve a fully model-based reallocation enabling quantification of uncertainty. For a contingency table with nominal classifications as well, our approach creates an intensity for the ordinal variables for each level of the nominal variables. The methodology is detailed within a hierarchical framework, showing associated computation and convenient dimension reduction techniques to facilitate model fitting. We illustrate with both simulated data and a real census dataset.

This paper provides a review of the need, challenges and recent research aimed at quantifying anthropogenic CO2 emissions for urban areas at spatial scales below the whole city, and sub-annual temporal scales. With whole-city CO2 emissions budget research as a starting point, suburban efforts must first clearly identify the accounting framework, sectoral boundaries, chemical form, spatial domain and the space/time resolution desired. The only efforts, to date, have performed analysis in a few North American cities utilizing a combination of true “bottom-up” and space/time downscaling techniques. Numerous challenges are faced when estimating CO2 emissions at these scales, including data availability, data idiosyncrasy and uncertainty quantification. Though cities in high-income countries are in possession of the needed data, data availability may pose far greater difficulties in other parts of the world. Because much of the data that is available does not possess uncertainty estimates, quantification of CO2 emissions uncertainty similarly remains a large challenge. Suggested solutions include sensitivity testing of key inputs and parameters, fully propagated through estimation systems. To overcome data availability challenges, the exploration of high-resolution remote-sensing data offers insight into urban activity.

The applications of cone penetration technology (CPT) in geotechnical and geo-environmental engineering are increasing due to recent advances in electronics and sensors that can be installed on the cone. However, interpretation of CPT data is a complex process and most existing methods are either empirical or semi-empirical. In order to fully utilize the capability of CPT, issues of local feature identification, uncertainty quantification, and scale effects on the interpretation of collected data have to be addressed properly. In this paper, wavelet transform and wavelet variance are used to characterize the essential scales of CPT data, and wavelet transform modulus maxima and phases are used to detect instantaneous frequency change. The scale effects of site stratigraphy determination using CPT data are demonstrated. The results indicate that this wavelet-based approach can provide a promising tool to reduce uncertainties in CPT data interpretation.

Die casting is a type of metal casting in which a liquid metal is solidified in a reusable die. In such a complex process, measuring and controlling the process parameters are difficult. Conventional deterministic simulations are insufficient to completely estimate the effect of stochastic variation in the process parameters on product quality. In this research, a framework to simulate the effect of stochastic variation together with verification, validation, and uncertainty quantification (UQ) is proposed. This framework includes high-speed numerical simulations of solidification, microstructure, and mechanical properties prediction models along with experimental inputs for calibration and validation. Both experimental data and stochastic variation in process parameters with numerical modeling are employed, thus enhancing the utility of traditional numerical simulations used in die casting to have a better prediction of product quality. Although the framework is being developed and applied to die casting, it can be generalized to any manufacturing process or other engineering problems as well.

Natural biological suppression of soil-borne diseases is a function of the activity and composition of soil microbial communities. Soil microbe and phytopathogen interactions can occur prior to crop sowing and/or in the rhizosphere, subsequently influencing both plant growth and productivity. Research on suppressive microbial communities has concentrated on bacteria although fungi can also influence soil-borne disease. Fungi were analyzed in co-located soils ‘suppressive’ or ‘non-suppressive’ for disease caused by Rhizoctonia solani AG 8 at two sites in South Australia using 454 pyrosequencing targeting the fungal 28S LSU rRNA gene. DNA was extracted from a minimum of 125 g of soil per replicate to reduce the micro-scale community variability, and from soil samples taken at sowing and from the rhizosphere at 7 weeks to cover the peak Rhizoctonia infection period. A total of ∼994,000 reads were classified into 917 genera covering 54% of the RDP Fungal Classifier database, a high diversity for an alkaline, low organic matter soil. Statistical analyses and community ordinations revealed significant differences in fungal community composition between suppressive and non-suppressive soil and between soil type/location. The majority of differences associated with suppressive soils were attributed to less than 40 genera including a number of endophytic species with plant pathogen suppression potentials and mycoparasites such as Xylaria spp. Non-suppressive soils were dominated by Alternaria, Gibberella and Penicillum. Pyrosequencing generated a detailed description of fungal community structure and identified candidate taxa that may influence pathogen-plant interactions in stable disease suppression.

We propose to develop advanced simulation codes, based upon an extreme parallelism, first principles kinetic approach, to address the challenges associated with the edge region of magnetically confined plasmas. This work is relevant to both existing magnetic fusion facilities and essential for next-generation burning plasma experiments, such as ITER where success is critically dependent upon H-mode operation achieving an edge pedestal of sufficient height for good core plasma performance without producing deleterious large scale edge localized instabilities. The plasma edge presents a well-known set of multi-physics, multi-scale problems involving complex 3D magnetic geometry. Perhaps the greatest computational challenge is the lack of scale separation – temporal scales for drift waves, Alfven waves, ELM dynamics for example have strong overlap. Similar overlap occurs on the spatial scales for the ion poloidal gyro-radius, drift wave and pedestal width. The traditional approach of separating fusion problems into weakly interacting spatial or temporal domains clearly breaks down in the edge. A full kinetic model (full-f model) must be solved to understand and predict the edge physics including non-equilibrium thermodynamic issues arising from the magnetic topology (the open field lines producing a spatially sensitive velocity hole), plasma wall interactions, neutral and atomic physics. The plan here is to model these phenomena within a comprehensive first principles set of equations without the need for the insurmountable multiple-codes coupling issues by building on the XGC1 code developed under the SciDAC Proto-FSP Center for Plasma Edge Simulation (CPES). This proposal includes the critical participants in the XGC1 development. We propose enhancing the capability of XGC1 by including all the important turbulence physics contained in kinetic ion and electron electromagnetic dynamics, by extending the PIC technology to incorporate several positive features found in the Eulerian grid technology, combining the coarse grained XGC0 code into it with a multiscale projective time integration technique to be developed in the project for experimental time scale simulation of the edge multi-physics, and by implementing modern computational technologies to move forward with the extreme scale heterogeneous hardware/software platform development. Ultra-fast edge localized instabilities, involving compressional Alven modes, will be studied using a proper MHD or two-fluid codes employing kinetic closure information from XGC. The proposed research integrates the most important physical processes on overlapping temporal and spatial scales, to study (i) transitions and thresholds for enhanced confinement regimes, (ii) the predictive understanding of the edge pedestal formation, structure and dynamics, (iii) the effect of the edge plasma on the core confinement, (iv) the physics of Edge Localized Modes and their suppression or mitigation via external control techniques, and (v) the heat load on the material wall. Our approach will implement physical models that are valid in their relevant collisionality regimes for current experiments and future burning plasma devices. Comparisons with experimental data will be made at multiple levels including characterization of turbulence dynamics, flux-gradient responses in the energy, particle and momentum channels, and observations of global phenomena such as L-H transitions, momentum generation, ELM dynamics, ELM-free regimes and the tokamak density limit. The proposal team has established strong connections, through joint membership, with other organizations that will be critical for success. These include FASTMath, SUPER and QUEST Institutes respectively for meshing tools and solvers; code performance tuning and uncertainty quantification as well as a proposed Data Management and Visualization Institute.. We will also be teaming with ongoing fusion SciDAC’s: CSWPI for RF-edge plasmas interactions; CEMM for the M3D MHD simulations and with PEPSC for incorporation of energetic particle physics. Finally, the team includes representatives from each of the major U.S. experimental facilities who will coordinate the validation program and the development of synthetic diagnostics.

Uncertainty quantification in climate ensembles is an important topic for the domain scientists, especially for decision making in the real-world scenarios. With powerful computers, simulations now produce time-varying and multi-resolution ensemble data sets. It is of extreme importance to understand the model sensitivity given the input parameters such that more computation power can be allocated to the parameters with higher influence on the output. Also, when ensemble data is produced at different resolutions, understanding the accuracy of different resolutions helps the total time required to produce a desired quality solution with improved storage and computation cost. In this work, we propose to tackle these non-trivial problems on the Weather Research and Forecasting (WRF) model output. We employ a moment independent sensitivity measure to quantify and analyze parameter sensitivity across spatial regions and time domain. A comparison of clustering structures across three resolutions enables the users to investigate the sensitivity variation over the spatial regions of the five input parameters. The temporal trend in the sensitivity values is explored via an MDS view linked with a line chart for interactive brushing. The spatial and temporal views are connected to provide a full exploration system for complete spatio-temporal sensitivity analysis. To analyze the accuracy across varying resolutions, we formulate a Bayesian approach to identify which regions are better predicted at which resolutions compared to the observed precipitation. This information is aggregated over the time domain and finally encoded in an output image through a custom color map that guides the domain experts towards an adaptive grid implementation given a cost model. Users can select and further analyze the spatial and temporal error patterns for multi-resolution accuracy analysis via brushing and linking on the produced image. In this work, we collaborate with a domain expert whose feedback shows the effectiveness of our proposed exploration work-flow.

With the rapid advancement of spatial multi-omics technologies, the simultaneous analysis of molecular profiles and spatial locations has provided unprecedented insights into cellular heterogeneity and tissue microenvironments. However, data sparsity and the diversity of data distributions hinder the effective integration and analysis of spatial multi-omics data. In this study, we propose a novel ensemble learning framework based on dual-graph regularized anchor concept factorization, named SMODEL, for detecting spatial domains from spatial multi-omics data. SMODEL employs an element-wise weighted ensemble strategy to integrate multiple base clustering results, and leverages anchor concept factorization and dual-graph regularization to learn robust spatial consensus representations. We evaluated the performance of SMODEL on both real and simulated spatial multi-omics datasets, encompassing various technologies, tissue types, and species. Experimental results demonstrate that SMODEL not only outperforms existing methods in spatial domain identification but also effectively captures tissue structure, thereby enhancing the understanding of cellular heterogeneity.

The global trend of ever increasing volumes of digital data is also evident in spatial and spatiotemporal datasets, as it is estimated that approximately 80 percent of all databases have a spatial component. Furthermore the spatial community is witnessing a diversification in data availability, with complementary datasets available from diverse providers. Thus, government agencies using spatial information are now faced with the challenge of using heterogeneous spatial and spatiotemporal datasets. Consequently, there is an ever-increasing need for reliable and highly automated spatial data integration. The integration may be spatial, whereby two or more datasets depicting complementary information for the same area are brought together to extend their coverage or to aggregate their content; or temporal, whereby two or more similar datasets conveying the same thematic information at different time instances are brought together to analyze the evolution of their content. In this chapter we present some of the dominant approaches for these two types of information integration for geospatial applications, both at the spatial and the spatiotemporal domain. We also present some of the recently developed approaches to spatial and spatiotemporal queries, and discuss their role in spatiotemporal pattern detection and analysis.