Analyzing uncertainty in spatial data is a vital task in many domains, as for example with climate and weather simulation ensembles. Although many methods support the analysis of uncertain 2D data, such as uncertain isocontours or overlaying of statistical information on plots of the actual data, it is still a challenge to get a more detailed overview of 2D data together with its statistical properties. We present cumulative height fields, a visualization method for 2D scalar field ensembles using the marginal empirical distribution function and show preliminary results using volume rendering and slicing for the Max Planck Institute Grand Ensemble.

In an era of quickly growing data set sizes, information reduction methods such as extracting or highlighting characteristic features become more and more important for data analysis. For single scalar fields, topological methods can fill this role by extracting and relating critical points. While such methods are regularly employed to study single scalar fields, it is less well studied how they can be extended to uncertain data, as produced, e.g., by ensemble simulations. Motivated by our previous work on visualization in climate research, we study new methods to characterize critical points in ensembles of 2D scalar fields. Previous work on this topic either assumed or required specific distributions, did not account for uncertainty introduced by approximating the underlying latent distributions by a finite number of fields, or did not allow to answer all our domain experts' questions. In this work, we use Bayesian inference to estimate the probability of critical points, either of the original ensemble or its bootstrapped mean. This does not make any assumptions on the underlying distribution and allows to estimate the sensitivity of the results to finite-sample approximations of the underlying distribution. We use color mapping to depict these probabilities and the stability of their estimation. The resulting images can, e.g., be used to estimate how precise the critical points of the mean-field are. We apply our method to synthetic data to validate its theoretical properties and compare it with other methods in this regard. We also apply our method to the data from our previous work, where it provides a more accurate answer to the domain experts' research questions.

A driving factor of the winter weather in Western Europe is the North Atlantic Oscillation (NAO), manifested by fluctuations in the difference of sea level pressure between the Icelandic Low and the Azores High. Different methods have been developed that describe the strength of this oscillation, but they rely on certain assumptions, e.g., fixed positions of these two pressure systems. It is possible that climate change affects the mean location of both the Low and the High and thus the validity of these descriptive methods. This study is the first to visually analyze large ensemble climate change simulations (the MPI Grand Ensemble) to robustly assess shifts of the drivers of the NAO phenomenon using the uncertain northern hemispheric surface pressure fields. For this, we use a sliding window approach and compute empirical orthogonal functions (EOFs) for each window and ensemble member, then compare the uncertainty of local extrema in the results as well as their temporal evolution across different CO2scenarios. We find systematic northeastward shifts in the location of the pressure systems that correlate with the simulated warming. Applying visualization techniques for this analysis was not straightforward; we reflect and give some lessons learned for the field of visualization.

To assess the reliability of weather forecasts and climate simulations, common practice is to generate large ensembles of numerical simulations. Analyzing such data is challenging and requires pattern and feature detection. For single time-dependent scalar fields, empirical orthogonal functions (EOFs) are a proven means to identify the main variation. In this paper, we present an extension of that concept to time-dependent ensemble data. We applied our methods to two ensemble data sets from climate research in order to investigate the North Atlantic Oscillation (NAO) and East Atlantic (EA) pattern.

Abstract Colormapping is one of the simplest and most widely used data visualization methods within and outside the visualization community. Uniformity, order, discriminative power, and smoothness of continuous colormaps are the most important criteria for evaluating and potentially improving colormaps. We present a local and a global automatic optimization algorithm in Euclidean color spaces for each of these design rules in this work. As a foundation for our optimization algorithms, we used the CCC‐Tool colormap specification (CMS); each algorithm has been implemented in this tool. In addition to synthetic examples that demonstrate each method's effect, we show the outcome of some of the methods applied to a typhoon simulation.

Many computer science disciplines (e.g., combinatorial optimization, natural language processing, and information retrieval) use standard or established test suites for evaluating algorithms. In visualization, similar approaches have been adopted in some areas (e.g., volume visualization), while user testimonies and empirical studies have been the dominant means of evaluation in most other areas, such as designing colormaps. In this paper, we propose to establish a test suite for evaluating the design of colormaps. With such a suite, the users can observe the effects when different continuous colormaps are applied to planar scalar fields that may exhibit various characteristic features, such as jumps, local extrema, ridge or valley lines, different distributions of scalar values, different gradients, different signal frequencies, different levels of noise, and so on. The suite also includes an expansible collection of real-world data sets including the most popular data for colormap testing in the visualization literature. The test suite has been integrated into a web-based application for creating continuous colormaps (https://ccctool.com/), facilitating close inter-operation between design and evaluation processes. This new facility complements traditional evaluation methods such as user testimonies and empirical studies.

Continuous colormaps are integral parts of many visualization techniques, such as heat-maps, surface plots, and flow visualization. Despite that the critiques of rainbow colormaps have been around and well-acknowledged for three decades, rainbow colormaps are still widely used today. One reason behind the resilience of rainbow colormaps is the lack of tools for users to create a continuous colormap that encodes semantics specific to the application concerned. In this paper, we present a web-based software system, CCC-Tool (short for Charting Continuous Colormaps) under the URL https://ccctool.com, for creating, editing, and analyzing such application-specific colormaps. We introduce the notion of "colormap specification (CMS)" that maintains the essential semantics required for defining a color mapping scheme. We provide users with a set of advanced utilities for constructing CMS's with various levels of complexity, examining their quality attributes using different plots, and exporting them to external application software. We present two case studies, demonstrating that the CCC-Tool can help domain scientists as well as visualization experts in designing semantically-rich colormaps.

Abstract Scientific visualization deals with increasingly complex data consisting of multiple fields. Typical disciplines generating multivariate data are fluid dynamics, structural mechanics, geology, bioengineering, and climate research. Quite often, scientists are interested in the relation between some of these variables. A popular visualization technique for a single scalar field is the extraction and rendering of isosurfaces. With this technique, the domain can be split into two parts, i.e. a volume with higher values and one with lower values than the selected isovalue. Fiber surfaces generalize this concept to two or three scalar variables up to now. This article extends the notion further to potentially any finite number of scalar fields. We generalize the fiber surface extraction algorithm of Raith et al. [RBN∗19] from 3 to d dimensions and demonstrate the technique using two examples from geology and climate research. The first application concerns a generic model of a nuclear waste repository and the second one an atmospheric simulation over central Europe. Both require complex simulations which involve multiple physical processes. In both cases, the new extended fiber surfaces helps us finding regions of interest like the nuclear waste repository or the power supply of a storm due to their characteristic properties.

Abstract In order to gain probabilistic results, ensemble simulation techniques are increasingly applied in the weather and climate sciences (as well as in various other scientific disciplines). In many cases, however, only mean results or other abstracted quantities such as percentiles are used for further analyses and dissemination of the data. In this work, we aim at a more detailed visualization of the temporal development of the whole ensemble that takes the variability of all single members into account. We propose a visual analytics tool that allows an effective analysis process based on a hierarchical clustering of the time‐dependent scalar fields. The system includes a flow chart that shows the ensemble members' cluster affiliation over time, reflecting the whole cluster hierarchy. The latter one can be dynamically explored using a visualization derived from a dendrogram. As an aid in linking the different views, we have developed an adaptive coloring scheme that takes into account cluster similarity and the containment relationships. Finally, standard visualizations of the involved field data (cluster means, ground truth data, etc.) are also incorporated. We include results of our work on real‐world datasets to showcase the utility of our approach.

Ensemble simulations are used in climate research to account for natural variability. For medium-term decadal predictions, each simulation run is initialized with real observations from a different day resulting in a set of possible climatic futures. Understanding the variability and the predictive power in this wealth of data is still a challenging task. In this paper, we introduce a visual analytics system to explore variability within ensembles of decadal climate predictions. We propose a new interactive visualization technique (clustering timeline) based on the Sankey diagram, which conveys a concise summary of data similarity and its changes over time. We augment the system with two additional visualizations, filled contour maps and heatmaps, to provide analysts with additional information relating the new diagram to raw data and automatic clustering results. The usefulness of the technique is demonstrated by case studies and user interviews.

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.

Performance attributes such as energy use or natural ventilation are becoming rapidly more important in the design of modern buildings. As a basis for the improvement of existing visualization techniques in this application domain, we provide a detailed tasks and requirements analysis using feedback from an architect. State-of-the-art visualization strategies used for building performance simulation results are then evaluated by comparing them to the quality aspects derived before. This assessment specifically reveals shortcomings with respect to the applied techniques for visualizing spatiotemporal data. Therefore, we discuss the potential of utilizing other visualization techniques to meet the identified prerequisites and reveal future directions based on these findings.

Due to its nonlinear nature, the climate system shows quite high natural variability on different time scales, including multiyear oscillations such as the El Niño Southern Oscillation phenomenon. Beside a shift of the mean states and of extreme values of climate variables, climate change may also change the frequency or the spatial patterns of these natural climate variations. Wavelet analysis is a well established tool to investigate variability in the frequency domain. However, due to the size and complexity of the analysis results, only few time series are commonly analyzed concurrently. In this paper we will explore different techniques to visually assist the user in the analysis of variability and variability changes to allow for a holistic analysis of a global climate model data set consisting of several variables and extending over 250 years. Our new framework and data from the IPCC AR4 simulations with the coupled climate model ECHAM5/MPI-OM are used to explore the temporal evolution of El Niño due to climate change.

Abstract Current unsteady multi‐field simulation data‐sets consist of millions of data‐points. To efficiently reduce this enormous amount of information, local statistical complexity was recently introduced as a method that identifies distinctive structures using concepts from information theory. Due to high computational costs this method was so far limited to 2D data. In this paper we propose a new strategy for the computation that is substantially faster and allows for a more precise analysis. The bottleneck of the original method is the division of spatio‐temporal configurations in the field (light‐cones) into different classes of behavior. The new algorithm uses a density‐driven Voronoi tessellation for this task that more accurately captures the distribution of configurations in the sparsely sampled high‐dimensional space. The efficient computation is achieved using structures and algorithms from graph theory. The ability of the method to detect distinctive regions in 3D is illustrated using flow and weather simulations.

The visualization and exploration of multivariate data is still a challenging task. Methods either try to visualize all variables simultaneously at each position using glyph-based approaches or use linked views for the interaction between attribute space and physical domain such as brushing of scatterplots. Most visualizations of the attribute space are either difficult to understand or suffer from visual clutter. We propose a transformation of the high-dimensional data in attribute space to 2D that results in a point cloud, called attribute cloud, such that points with similar multivariate attributes are located close to each other. The transformation is based on ideas from multivariate density estimation and manifold learning. The resulting attribute cloud is an easy to understand visualization of multivariate data in two dimensions. We explain several techniques to incorporate additional information into the attribute cloud, that help the user get a better understanding of multivariate data. Using different examples from fluid dynamics and climate simulation, we show how brushing can be used to explore the attribute cloud and find interesting structures in physical space.