Noodles: a tool for visualization of numerical weather model ensemble uncertainty

EnConVis: A Unified Framework for Ensemble Contour Visualization

Ensemble simulation is a crucial method to handle potential uncertainty in modern simulation and has been widely applied in many disciplines. Many ensemble contour visualization methods have been introduced to facilitate ensemble data analysis. On the basis of deep exploration and summarization of existing techniques and domain requirements, we propose a unified framework of ensemble contour visualization, EnConVis (Ensemble Contour Visualization), which systematically combines state-of-the-art methods. We model ensemble contour visualization as a four-step pipeline consisting of four essential procedures: member filtering, point-wise modeling, uncertainty band extraction, and visual mapping. For each of the four essential procedures, we compare different methods they use, analyze their pros and cons, highlight research gaps, and attempt to fill them. Specifically, we add Kernel Density Estimation in the point-wise modeling procedure and multi-layer extraction in the uncertainty band extraction procedure. This step shows the ensemble data's details accurately and provides abstract levels. We also analyze existing methods from a global perspective. We investigate their mechanisms and compare their effects, on the basis of which, we offer selection guidelines for them. From the overall perspective of this framework, we find choices and combinations that have not been tried before, which can be well compensated by our method. Synthetic data and real-world data are leveraged to verify the efficacy of our method. Domain experts' feedback suggests that our approach helps them better understand ensemble data analysis.

Fuzzy Spreadsheet: Understanding and Exploring Uncertainties in Tabular Calculations

Spreadsheet-based tools provide a simple yet effective way of calculating values, which makes them the number-one choice for building and formalizing simple models for budget planning and many other applications. A cell in a spreadsheet holds one specific value and gives a discrete, overprecise view of the underlying model. Therefore, spreadsheets are of limited use when investigating the inherent uncertainties of such models and answering what-if questions. Existing extensions typically require a complex modeling process that cannot easily be embedded in a tabular layout. In Fuzzy Spreadsheet, a cell can hold and display a distribution of values. This integrated uncertainty-handling immediately conveys sensitivity and robustness information. The fuzzification of the cells enables calculations not only with precise values but also with distributions, and probabilities. We conservatively added and carefully crafted visuals to maintain the look and feel of a traditional spreadsheet while facilitating what-if analyses. Given a user-specified reference cell, Fuzzy Spreadsheet automatically extracts and visualizes contextually relevant information, such as impact, uncertainty, and degree of neighborhood, for the selected and related cells. To evaluate its usability and the perceived mental effort required, we conducted a user study. The results show that our approach outperforms traditional spreadsheets in terms of answer correctness, response time, and perceived mental effort in almost all tasks tested.

Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)

This article presents a computational framework for the Principal Geodesic Analysis of merge trees (MT-PGA), a novel adaptation of the celebrated Principal Component Analysis (PCA) framework (K. Pearson 1901) to the Wasserstein metric space of merge trees (Pont et al. 2022). We formulate MT-PGA computation as a constrained optimization problem, aiming at adjusting a basis of orthogonal geodesic axes, while minimizing a fitting energy. We introduce an efficient, iterative algorithm which exploits shared-memory parallelism, as well as an analytic expression of the fitting energy gradient, to ensure fast iterations. Our approach also trivially extends to extremum persistence diagrams. Extensive experiments on public ensembles demonstrate the efficiency of our approach - with MT-PGA computations in the orders of minutes for the largest examples. We show the utility of our contributions by extending to merge trees two typical PCA applications. First, we apply MT-PGA to data reduction and reliably compress merge trees by concisely representing them by their first coordinates in the MT-PGA basis. Second, we present a dimensionality reduction framework exploiting the first two directions of the MT-PGA basis to generate two-dimensional layouts of the ensemble. We augment these layouts with persistence correlation views, enabling global and local visual inspections of the feature variability in the ensemble. In both applications, quantitative experiments assess the relevance of our framework. Finally, we provide a C++ implementation that can be used to reproduce our results.

A Comparison of Spatiotemporal Visualizations for 3D Urban Analytics

Recent technological innovations have led to an increase in the availability of 3D urban data, such as shadow, noise, solar potential, and earthquake simulations. These spatiotemporal datasets create opportunities for new visualizations to engage experts from different domains to study the dynamic behavior of urban spaces in this under explored dimension. However, designing 3D spatiotemporal urban visualizations is challenging, as it requires visual strategies to support analysis of time-varying data referent to the city geometry. Although different visual strategies have been used in 3D urban visual analytics, the question of how effective these visual designs are at supporting spatiotemporal analysis on building surfaces remains open. To investigate this, in this paper we first contribute a series of analytical tasks elicited after interviews with practitioners from three urban domains. We also contribute a quantitative user study comparing the effectiveness of four representative visual designs used to visualize 3D spatiotemporal urban data: spatial juxtaposition, temporal juxtaposition, linked view, and embedded view. Participants performed a series of tasks that required them to identify extreme values on building surfaces over time. Tasks varied in granularity for both space and time dimensions. Our results demonstrate that participants were more accurate using plot-based visualizations (linked view, embedded view) but faster using color-coded visualizations (spatial juxtaposition, temporal juxtaposition). Our results also show that, with increasing task complexity, plot-based visualizations perform better in preserving efficiency (time, accuracy) compared to color-coded visualizations. Based on our findings, we present a set of takeaways with design recommendations for 3D spatiotemporal urban visualizations for researchers and practitioners. Lastly, we report on a series of interviews with four practitioners, and their feedback and suggestions for further work on the visualizations to support 3D spatiotemporal urban data analysis.

Visualizing Ensemble Predictions of Music Mood

Music mood classification has been a challenging problem in comparison with other music classification problems (e.g., genre, composer, or period). One solution for addressing this challenge is to use an ensemble of machine learning models. In this paper, we show that visualization techniques can effectively convey the popular prediction as well as uncertainty at different music sections along the temporal axis while enabling the analysis of individual ML models in conjunction with their application to different musical data. In addition to the traditional visual designs, such as stacked line graph, ThemeRiver, and pixel-based visualization, we introduce a new variant of ThemeRiver, called "dual-flux ThemeRiver", which allows viewers to observe and measure the most popular prediction more easily than stacked line graph and ThemeRiver. Together with pixel-based visualization, dual-flux ThemeRiver plots can also assist in model-development workflows, in addition to annotating music using ensemble model predictions.

Development and Evaluation of Two Approaches of Visual Sensitivity Analysis to Support Epidemiological Modeling

Computational modeling is a commonly used technology in many scientific disciplines and has played a noticeable role in combating the COVID-19 pandemic. Modeling scientists conduct sensitivity analysis frequently to observe and monitor the behavior of a model during its development and deployment. The traditional algorithmic ranking of sensitivity of different parameters usually does not provide modeling scientists with sufficient information to understand the interactions between different parameters and model outputs, while modeling scientists need to observe a large number of model runs in order to gain actionable information for parameter optimization. To address the above challenge, we developed and compared two visual analytics approaches, namely: algorithm-centric and visualization-assisted, and visualization-centric and algorithm-assisted. We evaluated the two approaches based on a structured analysis of different tasks in visual sensitivity analysis as well as the feedback of domain experts. While the work was carried out in the context of epidemiological modeling, the two approaches developed in this work are directly applicable to a variety of modeling processes featuring time series outputs, and can be extended to work with models with other types of outputs.

Visual Analysis and Detection of Contrails in Aircraft Engine Simulations

Contrails are condensation trails generated from emitted particles by aircraft engines, which perturb Earth's radiation budget. Simulation modeling is used to interpret the formation and development of contrails. These simulations are computationally intensive and rely on high-performance computing solutions, and the contrail structures are not well defined. We propose a visual computing system to assist in defining contrails and their characteristics, as well as in the analysis of parameters for computer-generated aircraft engine simulations. The back-end of our system leverages a contrail-formation criterion and clustering methods to detect contrails' shape and evolution and identify similar simulation runs. The front-end system helps analyze contrails and their parameters across multiple simulation runs. The evaluation with domain experts shows this approach successfully aids in contrail data investigation.

S4: Self-Supervised Learning of Spatiotemporal Similarity

We introduce an ML-driven approach that enables interactive example-based queries for similar behavior in ensembles of spatiotemporal scientific data. This addresses an important use case in the visual exploration of simulation and experimental data, where data is often large, unlabeled and has no meaningful similarity measures available. We exploit the fact that nearby locations often exhibit similar behavior and train a Siamese Neural Network in a self-supervised fashion, learning an expressive latent space for spatiotemporal behavior. This space can be used to find similar behavior with just a few user-provided examples. We evaluate this approach on several ensemble datasets and compare with multiple existing methods, showing both qualitative and quantitative results.

Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs-a series of ideas, approaches and methods taken from existing visualization research and practice-deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs-a series of ideas, approaches and methods taken from existing visualization research and practice-deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Visual Analysis of Multi-Parameter Distributions Across Ensembles of 3D Fields

For an ensemble of 3D multi-parameter fields, we present a visual analytics workflow to analyse whether and which parts of a selected multi-parameter distribution is present in all ensemble members. Supported by a parallel coordinate plot, a multi-parameter brush is applied to all ensemble members to select data points with similar multi-parameter distribution. By a combination of spatial sub-division and a covariance analysis of partitioned sub-sets of data points, a tight partition in multi-parameter space with reduced number of selected data points is obtained. To assess the representativeness of the selected multi-parameter distribution across the ensemble, we propose a novel extension of violin plots that can show multiple parameter distributions simultaneously. We investigate the visual design that effectively conveys (dis-)similarities in multi-parameter distributions, and demonstrate that users can quickly comprehend parameter-specific differences regarding distribution shape and representativeness from a side-by-side view of these plots. In a 3D spatial view, users can analyse and compare the spatial distribution of selected data points in different ensemble members via interval-based isosurface raycasting. In two real-world application cases we show how our approach is used to analyse the multi-parameter distributions across an ensemble of 3D fields.

A Comparative Study of Methods for the Visualization of Probability Distributions of Geographical Data

Probability distributions are omnipresent in data analysis. They are often used to model the natural uncertainty present in real phenomena or to describe the properties of a data set. Designing efficient visual metaphors to convey probability distributions is, however, a difficult problem. This fact is especially true for geographical data, where conveying the spatial context constrains the design space. While many different alternatives have been proposed to solve this problem, they focus on representing data variability. However, they are not designed to support spatial analytical tasks involving probability quantification. The present work aims to adapt recent non-spatial approaches to the geographical context, in order to support probability quantification tasks. We also present a user study that compares the efficiency of these approaches in terms of both accuracy and usability.

A Probability Density-Based Visual Analytics Approach to Forecast Bias Calibration

Biases inevitably occur in numerical weather prediction (NWP) due to an idealized numerical assumption for modeling chaotic atmospheric systems. Therefore, the rapid and accurate identification and calibration of biases is crucial for NWP in weather forecasting. Conventional approaches, such as various analog post-processing forecast methods, have been designed to aid in bias calibration. However, these approaches fail to consider the spatiotemporal correlations of forecast bias, which can considerably affect calibration efficacy. In this article, we propose a novel bias pattern extraction approach based on forecasting-observation probability density by merging historical forecasting and observation datasets. Given a spatiotemporal scope, our approach extracts and fuses bias patterns and automatically divides regions with similar bias patterns. Termed BicaVis, our spatiotemporal bias pattern visual analytics system is proposed to assist experts in drafting calibration curves on the basis of these bias patterns. To verify the effectiveness of our approach, we conduct two case studies with real-world reanalysis datasets. The feedback collected from domain experts confirms the efficacy of our approach.

Wasserstein Distances, Geodesics and Barycenters of Merge Trees

This paper presents a unified computational framework for the estimation of distances, geodesics and barycenters of merge trees. We extend recent work on the edit distance [104] and introduce a new metric, called the Wasserstein distance between merge trees, which is purposely designed to enable efficient computations of geodesics and barycenters. Specifically, our new distance is strictly equivalent to the $L$2-Wasserstein distance between extremum persistence diagrams, but it is restricted to a smaller solution space, namely, the space of rooted partial isomorphisms between branch decomposition trees. This enables a simple extension of existing optimization frameworks [110] for geodesics and barycenters from persistence diagrams to merge trees. We introduce a task-based algorithm which can be generically applied to distance, geodesic, barycenter or cluster computation. The task-based nature of our approach enables further accelerations with shared-memory parallelism. Extensive experiments on public ensembles and SciVis contest benchmarks demonstrate the efficiency of our approach - with barycenter computations in the orders of minutes for the largest examples - as well as its qualitative ability to generate representative barycenter merge trees, visually summarizing the features of interest found in the ensemble. We show the utility of our contributions with dedicated visualization applications: feature tracking, temporal reduction and ensemble clustering. We provide a lightweight C++ implementation that can be used to reproduce our results.

EPIsembleVis: A geo-visual analysis and comparison of the prediction ensembles of multiple COVID-19 models

We present EPIsembleVis, a web-based comparative visual analysis tool for evaluating the consistency of multiple COVID-19 prediction models. Our approach analyzes a collection of COVID-19 predictions from different epidemiological models as an ensemble and utilizes two metrics to quantify model performance. These metrics include (a) prediction uncertainty (represented as the dispersion of predictions in each ensemble) and (b) prediction error (calculated by comparing individual model predictions with the recorded data). Through an interactive visual interface, our approach provides a data-driven workflow for (a) selecting and constructing the COVID-19 model prediction ensemble based on the spatiotemporal overlap of available predictions of multiple epidemiological models, (b) quantifying the model performance using both the uncertainty of each model prediction ensemble, and the error of each ensemble member that represents individual model predictions, and (c) visualizing the spatiotemporal variability in the projection performance of individual models using a suite of novel ensemble visualization techniques, such as the data availability map, a spatiotemporal textured-tile calendar, multivariate rose chart, and time-series leaflet glyph. We demonstrate the capability of our ensemble visual interface through a case study that investigates the performance of weekly COVID-19 predictions, which are provided through the COVID-19 Forecast Hub UMass-Amherst Influenza Forecasting Center of Excellence [47] for the United States and United States Territories. The EPIsembleVis tool is implemented using open-source web technologies and adaptive system design, rendering it interoperable with Elasticsearch and Kibana for automatically ingesting COVID-19 predictions from online repositories, and it is generalizable for analyzing worldwide projections from more epidemiological models.

Uncertainty-Oriented Ensemble Data Visualization and Exploration using Variable Spatial Spreading

As an important method of handling potential uncertainties in numerical simulations, ensemble simulation has been widely applied in many disciplines. Visualization is a promising and powerful ensemble simulation analysis method. However, conventional visualization methods mainly aim at data simplification and highlighting important information based on domain expertise instead of providing a flexible data exploration and intervention mechanism. Trial-and-error procedures have to be repeatedly conducted by such approaches. To resolve this issue, we propose a new perspective of ensemble data analysis using the attribute variable dimension as the primary analysis dimension. Particularly, we propose a variable uncertainty calculation method based on variable spatial spreading. Based on this method, we design an interactive ensemble analysis framework that provides a flexible interactive exploration of the ensemble data. Particularly, the proposed spreading curve view, the region stability heat map view, and the temporal analysis view, together with the commonly used 2D map view, jointly support uncertainty distribution perception, region selection, and temporal analysis, as well as other analysis requirements. We verify our approach by analyzing a real-world ensemble simulation dataset. Feedback collected from domain experts confirms the efficacy of our framework.

Measuring the Effects of Scalar and Spherical Colormaps on Ensembles of DMRI Tubes

We report empirical study results on the color encoding of ensemble scalar and orientation to visualize diffusion magnetic resonance imaging (DMRI) tubes. The experiment tested six scalar colormaps for average fractional anisotropy (FA) tasks (grayscale, blackbody, diverging, isoluminant-rainbow, extended-blackbody, and coolwarm) and four three-dimensional (3D) spherical colormaps for tract tracing tasks (uniform gray, absolute, eigenmaps, and Boy's surface embedding). We found that extended-blackbody, coolwarm, and blackbody remain the best three approaches for identifying ensemble average in 3D. Isoluminant-rainbow colormap led to the same ensemble mean accuracy as other colormaps. However, more than 50 percent of the answers consistently had higher estimates of the ensemble average, independent of the mean values. The number of hues, not luminance, influences ensemble estimates of mean values. For ensemble orientation-tracing tasks, we found that both Boy's surface embedding (greatest spatial resolution and contrast) and absolute colormaps (lowest spatial resolution and contrast) led to more accurate answers than the eigenmaps scheme (medium resolution and contrast), acting as the uncanny-valley phenomenon of visualization design in terms of accuracy. Absolute colormap broadly used in brain science is a good default spherical colormap. We could conclude from our study that human visual processing of a chunk of colors differs from that of single colors.

eFESTA: Ensemble Feature Exploration with Surface Density Estimates

We propose surface density estimate (SDE) to model the spatial distribution of surface features-isosurfaces, ridge surfaces, and streamsurfaces-in 3D ensemble simulation data. The inputs of SDE computation are surface features represented as polygon meshes, and no field datasets are required (e.g., scalar fields or vector fields). The SDE is defined as the kernel density estimate of the infinite set of points on the input surfaces and is approximated by accumulating the surface densities of triangular patches. We also propose an algorithm to guide the selection of a proper kernel bandwidth for SDE computation. An ensemble Feature Exploration method based on Surface densiTy EstimAtes (eFESTA) is then proposed to extract and visualize the major trends of ensemble surface features. For an ensemble of surface features, each surface is first transformed into a density field based on its contribution to the SDE, and the resulting density fields are organized into a hierarchical representation based on the pairwise distances between them. The hierarchical representation is then used to guide visual exploration of the density fields as well as the underlying surface features. We demonstrate the application of our method using isosurface in ensemble scalar fields, Lagrangian coherent structures in uncertain unsteady flows, and streamsurfaces in ensemble fluid flows.

Scientific Visualization as a Microservice

In this paper, we propose using a decoupled architecture to create a microservice that can deliver scientific visualization remotely with efficiency, scalability, and superior availability, affordability and accessibility. Through our effort, we have created an open source platform, Tapestry, which can be deployed on Amazon AWS as a production use microservice. The applications we use to demonstrate the efficacy of the Tapestry microservice in this work are: (1) embedding interactive visualizations into lightweight web pages, (2) creating scientific visualization movies that are fully controllable by the viewers, (3) serving as a rendering engine for high-end displays such as power-walls, and (4) embedding data-intensive visualizations into augmented reality devices efficiently. In addition, we show results of an extensive performance study, and suggest how applications can make optimal use of microservices such as Tapestry.

A Structural Average of Labeled Merge Trees for Uncertainty Visualization

Physical phenomena in science and engineering are frequently modeled using scalar fields. In scalar field topology, graph-based topological descriptors such as merge trees, contour trees, and Reeb graphs are commonly used to characterize topological changes in the (sub)level sets of scalar fields. One of the biggest challenges and opportunities to advance topology-based visualization is to understand and incorporate uncertainty into such topological descriptors to effectively reason about their underlying data. In this paper, we study a structural average of a set of labeled merge trees and use it to encode uncertainty in data. Specifically, we compute a 1-center tree that minimizes its maximum distance to any other tree in the set under a well-defined metric called the interleaving distance. We provide heuristic strategies that compute structural averages of merge trees whose labels do not fully agree. We further provide an interactive visualization system that resembles a numerical calculator that takes as input a set of merge trees and outputs a tree as their structural average. We also highlight structural similarities between the input and the average and incorporate uncertainty information for visual exploration. We develop a novel measure of uncertainty, referred to as consistency, via a metric-space view of the input trees. Finally, we demonstrate an application of our framework through merge trees that arise from ensembles of scalar fields. Our work is the first to employ interleaving distances and consistency to study a global, mathematically rigorous, structural average of merge trees in the context of uncertainty visualization.

Visualization and Visual Analysis of Ensemble Data: A Survey

Over the last decade, ensemble visualization has witnessed a significant development due to the wide availability of ensemble data, and the increasing visualization needs from a variety of disciplines. From the data analysis point of view, it can be observed that many ensemble visualization works focus on the same facet of ensemble data, use similar data aggregation or uncertainty modeling methods. However, the lack of reflections on those essential commonalities and a systematic overview of those works prevents visualization researchers from effectively identifying new or unsolved problems and planning for further developments. In this paper, we take a holistic perspective and provide a survey of ensemble visualization. Specifically, we study ensemble visualization works in the recent decade, and categorize them from two perspectives: (1) their proposed visualization techniques; and (2) their involved analytic tasks. For the first perspective, we focus on elaborating how conventional visualization techniques (e.g., surface, volume visualization techniques) have been adapted to ensemble data; for the second perspective, we emphasize how analytic tasks (e.g., comparison, clustering) have been performed differently for ensemble data. From the study of ensemble visualization literature, we have also identified several research trends, as well as some future research opportunities.

Progressive Wasserstein Barycenters of Persistence Diagrams

This paper presents an efficient algorithm for the progressive approximation of Wasserstein barycenters of persistence diagrams, with applications to the visual analysis of ensemble data. Given a set of scalar fields, our approach enables the computation of a persistence diagram which is representative of the set, and which visually conveys the number, data ranges and saliences of the main features of interest found in the set. Such representative diagrams are obtained by computing explicitly the discrete Wasserstein barycenter of the set of persistence diagrams, a notoriously computationally intensive task. In particular, we revisit efficient algorithms for Wasserstein distance approximation [12,51] to extend previous work on barycenter estimation [94]. We present a new fast algorithm, which progressively approximates the barycenter by iteratively increasing the computation accuracy as well as the number of persistent features in the output diagram. Such a progressivity drastically improves convergence in practice and allows to design an interruptible algorithm, capable of respecting computation time constraints. This enables the approximation of Wasserstein barycenters within interactive times. We present an application to ensemble clustering where we revisit the k-means algorithm to exploit our barycenters and compute, within execution time constraints, meaningful clusters of ensemble data along with their barycenter diagram. Extensive experiments on synthetic and real-life data sets report that our algorithm converges to barycenters that are qualitatively meaningful with regard to the applications, and quantitatively comparable to previous techniques, while offering an order of magnitude speedup when run until convergence (without time constraint). Our algorithm can be trivially parallelized to provide additional speedups in practice on standard workstations. We provide a lightweight C++ implementation of our approach that can be used to reproduce our results.

Visual Analytics for the Representation, Exploration, and Analysis of High-Dimensional, Multi-faceted Medical Data

Medicine is among those research fields with a significant impact on humans and their health. Already for decades, medicine has established a tight coupling with the visualization domain, proving the importance of developing visualization techniques, designed exclusively for this research discipline. However, medical data is steadily increasing in complexity with the appearance of heterogeneous, multi-modal, multi-parametric, cohort or population, as well as uncertain data. To deal with this kind of complex data, the field of Visual Analytics has emerged. In this chapter, we discuss the many dimensions and facets of medical data. Based on this classification, we provide a general overview of state-of-the-art visualization systems and solutions dealing with high-dimensional, multi-faceted data. Our particular focus will be on multi-modal, multi-parametric data, on data from cohort or population studies and on uncertain data, especially with respect to Visual Analytics applications for the representation, exploration, and analysis of high-dimensional, multi-faceted medical data.

IVAN: An Interactive Herlofson’s Nomogram Visualizer for Local Weather Forecast

In 1947, N. Herlofson proposed a modification to the 1884 Heinrich Hertz’s Emagram with the goal of getting more precise hand-made weather forecasts providing larger angles between isotherms and adiabats. Since then, the Herlofson’s nomogram has been used every day to visualize the results of about 800 radiosonde balloons that, twice a day, are globally released, sounding the atmosphere and reading pressure, altitude, temperature, dew point, and wind velocity. Relevant weather forecasts use such pieces of information to predict fog, cloud height, rain, thunderstorms, etc. However, despite its diffusion, non-technical people (e.g., private gliding pilots) do not use the Herlofson’s nomogram because they often consider it hard to interpret and confusing. This paper copes with this problem presenting a visualization based environment that presents the Herlofson’s nomogram in an easier to interpret way, allowing the selection of the right level of detail and at the same time inspection of the sounding row data and the plotted diagram. Our visual environment was compared with the classic way of representing the Herlofson’s nomogram in a formal user study, demonstrating the higher efficacy and better comprehensibility of the proposed solution.

Visualization in Meteorology-A Survey of Techniques and Tools for Data Analysis Tasks

This article surveys the history and current state of the art of visualization in meteorology, focusing on visualization techniques and tools used for meteorological data analysis. We examine characteristics of meteorological data and analysis tasks, describe the development of computer graphics methods for visualization in meteorology from the 1960s to today, and visit the state of the art of visualization techniques and tools in operational weather forecasting and atmospheric research. We approach the topic from both the visualization and the meteorological side, showing visualization techniques commonly used in meteorological practice, and surveying recent studies in visualization research aimed at meteorological applications. Our overview covers visualization techniques from the fields of display design, 3D visualization, flow dynamics, feature-based visualization, comparative visualization and data fusion, uncertainty and ensemble visualization, interactive visual analysis, efficient rendering, and scalability and reproducibility. We discuss demands and challenges for visualization research targeting meteorological data analysis, highlighting aspects in demonstration of benefit, interactive visual analysis, seamless visualization, ensemble visualization, 3D visualization, and technical issues.

Persistence Atlas for Critical Point Variability in Ensembles

This paper presents a new approach for the visualization and analysis of the spatial variability of features of interest represented by critical points in ensemble data. Our framework, called Persistence Atlas, enables the visualization of the dominant spatial patterns of critical points, along with statistics regarding their occurrence in the ensemble. The persistence atlas represents in the geometrical domain each dominant pattern in the form of a confidence map for the appearance of critical points. As a by-product, our method also provides 2-dimensional layouts of the entire ensemble, highlighting the main trends at a global level. Our approach is based on the new notion of Persistence Map, a measure of the geometrical density in critical points which leverages the robustness to noise of topological persistence to better emphasize salient features. We show how to leverage spectral embedding to represent the ensemble members as points in a low-dimensional Euclidean space, where distances between points measure the dissimilarities between critical point layouts and where statistical tasks, such as clustering, can be easily carried out. Further, we show how the notion of mandatory critical point can be leveraged to evaluate for each cluster confidence regions for the appearance of critical points. Most of the steps of this framework can be trivially parallelized and we show how to efficiently implement them. Extensive experiments demonstrate the relevance of our approach. The accuracy of the confidence regions provided by the persistence atlas is quantitatively evaluated and compared to a baseline strategy using an off-the-shelf clustering approach. We illustrate the importance of the persistence atlas in a variety of real-life datasets, where clear trends in feature layouts are identified and analyzed. We provide a lightweight VTK-based C++ implementation of our approach that can be used for reproduction purposes.

An Interactive Framework for Visualization of Weather Forecast Ensembles

Numerical Weather Prediction (NWP) ensembles are commonly used to assess the uncertainty and confidence in weather forecasts. Spaghetti plots are conventional tools for meteorologists to directly examine the uncertainty exhibited by ensembles, where they simultaneously visualize isocontours of all ensemble members. To avoid visual clutter in practical usages, one needs to select a small number of informative isovalues for visual analysis. Moreover, due to the complex topology and variation of ensemble isocontours, it is often a challenging task to interpret the spaghetti plot for even a single isovalue in large ensembles. In this paper, we propose an interactive framework for uncertainty visualization of weather forecast ensembles that significantly improves and expands the utility of spaghetti plots in ensemble analysis. Complementary to state-of-the-art methods, our approach provides a complete framework for visual exploration of ensemble isocontours, including isovalue selection, interactive isocontour variability exploration, and interactive sub-region selection and re-analysis. Our framework is built upon the high-density clustering paradigm, where the mode structure of the density function is represented as a hierarchy of nested subsets of the data. We generalize the high-density clustering for isocontours and propose a bandwidth selection method for estimating the density function of ensemble isocontours. We present novel visualizations based on high-density clustering results, called the mode plot and the simplified spaghetti plot. The proposed mode plot visually encodes the structure provided by the high-density clustering result and summarizes the distribution of ensemble isocontours. It also enables the selection of subsets of interesting isocontours, which are interactively highlighted in a linked spaghetti plot for providing spatial context. To provide an interpretable overview of the positional variability of isocontours, our system allows for selection of informative isovalues from the simplified spaghetti plot. Due to the spatial variability of ensemble isocontours, the system allows for interactive selection and focus on sub-regions for local uncertainty and clustering re-analysis. We examine a number of ensemble datasets to establish the utility of our approach and discuss its advantages over state-of-the-art visual analysis tools for ensemble data.

EnsembleLens: Ensemble-based Visual Exploration of Anomaly Detection Algorithms with Multidimensional Data

The results of anomaly detection are sensitive to the choice of detection algorithms as they are specialized for different properties of data, especially for multidimensional data. Thus, it is vital to select the algorithm appropriately. To systematically select the algorithms, ensemble analysis techniques have been developed to support the assembly and comparison of heterogeneous algorithms. However, challenges remain due to the absence of the ground truth, interpretation, or evaluation of these anomaly detectors. In this paper, we present a visual analytics system named EnsembleLens that evaluates anomaly detection algorithms based on the ensemble analysis process. The system visualizes the ensemble processes and results by a set of novel visual designs and multiple coordinated contextual views to meet the requirements of correlation analysis, assessment and reasoning of anomaly detection algorithms. We also introduce an interactive analysis workflow that dynamically produces contextualized and interpretable data summaries that allow further refinements of exploration results based on user feedback. We demonstrate the effectiveness of EnsembleLens through a quantitative evaluation, three case studies with real-world data and interviews with two domain experts.

Visualizing Uncertain Tropical Cyclone Predictions using Representative Samples from Ensembles of Forecast Tracks

A common approach to sampling the space of a prediction is the generation of an ensemble of potential outcomes, where the ensemble's distribution reveals the statistical structure of the prediction space. For example, the US National Hurricane Center generates multiple day predictions for a storm's path, size, and wind speed, and then uses a Monte Carlo approach to sample this prediction into a large ensemble of potential storm outcomes. Various forms of summary visualizations are generated from such an ensemble, often using spatial spread to indicate its statistical characteristics. However, studies have shown that changes in the size of such summary glyphs, representing changes in the uncertainty of the prediction, are frequently confounded with other attributes of the phenomenon, such as its size or strength. In addition, simulation ensembles typically encode multivariate information, which can be difficult or confusing to include in a summary display. This problem can be overcome by directly displaying the ensemble as a set of annotated trajectories, however this solution will not be effective if ensembles are densely overdrawn or structurally disorganized. We propose to overcome these difficulties by selectively sampling the original ensemble, constructing a smaller representative and spatially well organized ensemble. This can be drawn directly as a set of paths that implicitly reveals the underlying spatial uncertainty distribution of the prediction. Since this approach does not use a visual channel to encode uncertainty, additional information can more easily be encoded in the display without leading to visual confusion. To demonstrate our argument, we describe the development of a visualization for ensembles of tropical cyclone forecast tracks, explaining how their spatial and temporal predictions, as well as other crucial storm characteristics such as size and intensity, can be clearly revealed. We verify the effectiveness of this visualization approach through a cognitive study exploring how storm damage estimates are affected by the density of tracks drawn, and by the presence or absence of annotating information on storm size and intensity.

Information Guided Exploration of Scalar Values and Isocontours in Ensemble Datasets

Uncertainty of scalar values in an ensemble dataset is often represented by the collection of their corresponding isocontours. Various techniques such as contour-boxplot, contour variability plot, glyphs and probabilistic marching-cubes have been proposed to analyze and visualize ensemble isocontours. All these techniques assume that a scalar value of interest is already known to the user. Not much work has been done in guiding users to select the scalar values for such uncertainty analysis. Moreover, analyzing and visualizing a large collection of ensemble isocontours for a selected scalar value has its own challenges. Interpreting the visualizations of such large collections of isocontours is also a difficult task. In this work, we propose a new information-theoretic approach towards addressing these issues. Using specific information measures that estimate the predictability and surprise of specific scalar values, we evaluate the overall uncertainty associated with all the scalar values in an ensemble system. This helps the scientist to understand the effects of uncertainty on different data features. To understand in finer details the contribution of individual members towards the uncertainty of the ensemble isocontours of a selected scalar value, we propose a conditional entropy based algorithm to quantify the individual contributions. This can help simplify analysis and visualization for systems with more members by identifying the members contributing the most towards overall uncertainty. We demonstrate the efficacy of our method by applying it on real-world datasets from material sciences, weather forecasting and ocean simulation experiments.

A Statistical Direct Volume Rendering Framework for Visualization of Uncertain Data

With uncertainty present in almost all modalities of data acquisition, reduction, transformation, and representation, there is a growing demand for mathematical analysis of uncertainty propagation in data processing pipelines. In this paper, we present a statistical framework for quantification of uncertainty and its propagation in the main stages of the visualization pipeline. We propose a novel generalization of Irwin-Hall distributions from the statistical viewpoint of splines and box-splines, that enables interpolation of random variables. Moreover, we introduce a probabilistic transfer function classification model that allows for incorporating probability density functions into the volume rendering integral. Our statistical framework allows for incorporating distributions from various sources of uncertainty which makes it suitable in a wide range of visualization applications. We demonstrate effectiveness of our approach in visualization of ensemble data, visualizing large datasets at reduced scale, iso-surface extraction, and visualization of noisy data.

Effects of ensemble and summary displays on interpretations of geospatial uncertainty data

Ensemble and summary displays are two widely used methods to represent visual-spatial uncertainty; however, there is disagreement about which is the most effective technique to communicate uncertainty to the general public. Visualization scientists create ensemble displays by plotting multiple data points on the same Cartesian coordinate plane. Despite their use in scientific practice, it is more common in public presentations to use visualizations of summary displays, which scientists create by plotting statistical parameters of the ensemble members. While prior work has demonstrated that viewers make different decisions when viewing summary and ensemble displays, it is unclear what components of the displays lead to diverging judgments. This study aims to compare the salience of visual features – or visual elements that attract bottom-up attention – as one possible source of diverging judgments made with ensemble and summary displays in the context of hurricane track forecasts. We report that salient visual features of both ensemble and summary displays influence participant judgment. Specifically, we find that salient features of summary displays of geospatial uncertainty can be misunderstood as displaying size information. Further, salient features of ensemble displays evoke judgments that are indicative of accurate interpretations of the underlying probability distribution of the ensemble data. However, when participants use ensemble displays to make point-based judgments, they may overweight individual ensemble members in their decision-making process. We propose that ensemble displays are a promising alternative to summary displays in a geospatial context but that decisions about visualization methods should be informed by the viewer’s task.

Visualizing High-Dimensional Data: Advances in the Past Decade

Massive simulations and arrays of sensing devices, in combination with increasing computing resources, have generated large, complex, high-dimensional datasets used to study phenomena across numerous fields of study. Visualization plays an important role in exploring such datasets. We provide a comprehensive survey of advances in high-dimensional data visualization that focuses on the past decade. We aim at providing guidance for data practitioners to navigate through a modular view of the recent advances, inspiring the creation of new visualizations along the enriched visualization pipeline, and identifying future opportunities for visualization research.

PRODIGEN: visualizing the probability landscape of stochastic gene regulatory networks in state and time space

Background

Visualizing the complex probability landscape of stochastic gene regulatory networks can further biologists’ understanding of phenotypic behavior associated with specific genes.

Results

We present PRODIGEN (PRObability DIstribution of GEne Networks), a web-based visual analysis tool for the systematic exploration of probability distributions over simulation time and state space in such networks. PRODIGEN was designed in collaboration with bioinformaticians who research stochastic gene networks. The analysis tool combines in a novel way existing, expanded, and new visual encodings to capture the time-varying characteristics of probability distributions: spaghetti plots over one dimensional projection, heatmaps of distributions over 2D projections, enhanced with overlaid time curves to display temporal changes, and novel individual glyphs of state information corresponding to particular peaks.

Conclusions

We demonstrate the effectiveness of the tool through two case studies on the computed probabilistic landscape of a gene regulatory network and of a toggle-switch network. Domain expert feedback indicates that our visual approach can help biologists: 1) visualize probabilities of stable states, 2) explore the temporal probability distributions, and 3) discover small peaks in the probability landscape that have potential relation to specific diseases.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1447-1) contains supplementary material, which is available to authorized users.

Generalized box-plot for root growth ensembles

Background

In the field of root biology there has been a remarkable progress in root phenotyping, which is the efficient acquisition and quantitative description of root morphology. What is currently missing are means to efficiently explore, exchange and present the massive amount of acquired, and often time dependent root phenotypes.

Results

In this work, we present visual summaries of root ensembles by aggregating root images with identical genetic characteristics. We use the generalized box plot concept with a new formulation of data depth. In addition to spatial distributions, we created a visual representation to encode temporal distributions associated with the development of root individuals.

Conclusions

The new formulation of data depth allows for much faster implementation close to interactive frame rates. This allows us to present the statistics from bootstrapping that characterize the root sample set quality. As a positive side effect of the new data-depth formulation we are able to define the geometric median for the curve ensemble, which was well received by the domain experts.

Multi-Resolution Climate Ensemble Parameter Analysis with Nested Parallel Coordinates Plots

Due to the uncertain nature of weather prediction, climate simulations are usually performed multiple times with different spatial resolutions. The outputs of simulations are multi-resolution spatial temporal ensembles. Each simulation run uses a unique set of values for multiple convective parameters. Distinct parameter settings from different simulation runs in different resolutions constitute a multi-resolution high-dimensional parameter space. Understanding the correlation between the different convective parameters, and establishing a connection between the parameter settings and the ensemble outputs are crucial to domain scientists. The multi-resolution high-dimensional parameter space, however, presents a unique challenge to the existing correlation visualization techniques. We present Nested Parallel Coordinates Plot (NPCP), a new type of parallel coordinates plots that enables visualization of intra-resolution and inter-resolution parameter correlations. With flexible user control, NPCP integrates superimposition, juxtaposition and explicit encodings in a single view for comparative data visualization and analysis. We develop an integrated visual analytics system to help domain scientists understand the connection between multi-resolution convective parameters and the large spatial temporal ensembles. Our system presents intricate climate ensembles with a comprehensive overview and on-demand geographic details. We demonstrate NPCP, along with the climate ensemble visualization system, based on real-world use-cases from our collaborators in computational and predictive science.

Decal-Maps: Real-Time Layering of Decals on Surfaces for Multivariate Visualization

We introduce the use of decals for multivariate visualization design. Decals are visual representations that are used for communication; for example, a pattern, a text, a glyph, or a symbol, transferred from a 2D-image to a surface upon contact. By creating what we define as decal-maps, we can design a set of images or patterns that represent one or more data attributes. We place decals on the surface considering the data pertaining to the locations we choose. We propose a (texture mapping) local parametrization that allows placing decals on arbitrary surfaces interactively, even when dealing with a high number of decals. Moreover, we extend the concept of layering to allow the co-visualization of an increased number of attributes on arbitrary surfaces. By combining decal-maps, color-maps and a layered visualization, we aim to facilitate and encourage the creative process of designing multivariate visualizations. Finally, we demonstrate the general applicability of our technique by providing examples of its use in a variety of contexts.

Multi-Granular Trend Detection for Time-Series Analysis

Time series (such as stock prices) and ensembles (such as model runs for weather forecasts) are two important types of one-dimensional time-varying data. Such data is readily available in large quantities but visual analysis of the raw data quickly becomes infeasible, even for moderately sized data sets. Trend detection is an effective way to simplify time-varying data and to summarize salient information for visual display and interactive analysis. We propose a geometric model for trend-detection in one-dimensional time-varying data, inspired by topological grouping structures for moving objects in two- or higher-dimensional space. Our model gives provable guarantees on the trends detected and uses three natural parameters: granularity, support-size, and duration. These parameters can be changed on-demand. Our system also supports a variety of selection brushes and a time-sweep to facilitate refined searches and interactive visualization of (sub-)trends. We explore different visual styles and interactions through which trends, their persistence, and evolution can be explored.

A Visual Analytics Approach for Categorical Joint Distribution Reconstruction from Marginal Projections

Oftentimes multivariate data are not available as sets of equally multivariate tuples, but only as sets of projections into subspaces spanned by subsets of these attributes. For example, one may find data with five attributes stored in six tables of two attributes each, instead of a single table of five attributes. This prohibits the visualization of these data with standard high-dimensional methods, such as parallel coordinates or MDS, and there is hence the need to reconstruct the full multivariate (joint) distribution from these marginal ones. Most of the existing methods designed for this purpose use an iterative procedure to estimate the joint distribution. With insufficient marginal distributions and domain knowledge, they lead to results whose joint errors can be large. Moreover, enforcing smoothness for regularizations in the joint space is not applicable if the attributes are not numerical but categorical. We propose a visual analytics approach that integrates both anecdotal data and human experts to iteratively narrow down a large set of plausible solutions. The solution space is populated using a Monte Carlo procedure which uniformly samples the solution space. A level-of-detail high dimensional visualization system helps the user understand the patterns and the uncertainties. Constraints that narrow the solution space can then be added by the user interactively during the iterative exploration, and eventually a subset of solutions with narrow uncertainty intervals emerges.

Time-Hierarchical Clustering and Visualization of Weather Forecast Ensembles

We propose a new approach for analyzing the temporal growth of the uncertainty in ensembles of weather forecasts which are started from perturbed but similar initial conditions. As an alternative to traditional approaches in meteorology, which use juxtaposition and animation of spaghetti plots of iso-contours, we make use of contour clustering and provide means to encode forecast dynamics and spread in one single visualization. Based on a given ensemble clustering in a specified time window, we merge clusters in time-reversed order to indicate when and where forecast trajectories start to diverge. We present and compare different visualizations of the resulting time-hierarchical grouping, including space-time surfaces built by connecting cluster representatives over time, and stacked contour variability plots. We demonstrate the effectiveness of our visual encodings with forecast examples of the European Centre for Medium-Range Weather Forecasts, which convey the evolution of specific features in the data as well as the temporally increasing spatial variability.

Visualization of Time-Varying Weather Ensembles across Multiple Resolutions

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.