An atmospheric front is an imaginary surface that separates two distinct air masses and is commonly defined as the warm-air side of a frontal zone with high gradients of atmospheric temperature and humidity (Fig. 1, left). These fronts are a widely used conceptual model in meteorology, which are often encountered in the literature as two-dimensional (2D) front lines on surface analysis charts. This paper presents a method for computing three-dimensional (3D) atmospheric fronts as surfaces that is capable of extracting continuous and well-confined features suitable for 3D visual analysis, spatiotemporal tracking, and statistical analyses (Fig. 1, middle, right). Recently developed contour-based methods for 3D front extraction rely on computing the third derivative of a moist potential temperature field. Additionally, they require the field to be smoothed to obtain continuous large-scale structures. This paper demonstrates the feasibility of an alternative method to front extraction using ridge surface computation. The proposed method requires only the second derivative of the input field and produces accurate structures even from unsmoothed data. An application of the ridge-based method to a data set corresponding to Cyclone Friederike demonstrates its benefits and utility towards visual analysis of the full 3D structure of fronts.

We present a voxel-based rendering pipeline for large 3D line sets that employs GPU ray-casting to achieve scalable rendering including transparency and global illumination effects. Even for opaque lines we demonstrate superior rendering performance compared to GPU rasterization of lines, and when transparency is used we can interactively render amounts of lines that are infeasible to be rendered via rasterization. We propose a direction-preserving encoding of lines into a regular voxel grid, along with the quantization of directions using face-to-face connectivity in this grid. On the regular grid structure, parallel GPU ray-casting is used to determine visible fragments in correct visibility order. To enable interactive rendering of global illumination effects like low-frequency shadows and ambient occlusions, illumination simulation is performed during ray-casting on a level-of-detail (LoD) line representation that considers the number of lines and their lengths per voxel. In this way we can render effects which are very difficult to render via GPU rasterization. A detailed performance and quality evaluation compares our approach to rasterization-based rendering of lines.

Atmospheric fronts play a central role in meteorology, as the boundaries between different air masses and as fundamental features of extra-tropical cyclones. They appear in numerous conceptual model depictions of extra-tropical weather systems. Conceptually, fronts are three-dimensional surfaces in space possessing an innate structural complexity, yet in meteorology, both manual and objective identification and depiction have historically focused on the structure in two dimensions. In this work, we -a team of visualization scientists and meteorologists- propose a novel visualization approach to analyze the three-dimensional structure of atmospheric fronts and related physical and dynamical processes. We build upon existing approaches to objectively identify fronts as lines in two dimensions and extend these to obtain frontal surfaces in three dimensions, using the magnitude of temperature change along the gradient of a moist potential temperature field as the primary identifying factor. We introduce the use of normal curves in the temperature gradient field to visualize a frontal zone (i.e., the transitional zone between the air masses) and the distribution of atmospheric variables in such zones. To enable for the first time a statistical analysis of frontal zones, we present a new approach to obtain the volume enclosed by a zone, by classifying grid boxes that intersect with normal curves emanating from a selected front. We introduce our method by means of an idealized numerical simulation and demonstrate its use with two real-world cases using numerical weather prediction data.

Ensemble sensitivity analysis (ESA) has been established in the atmospheric sciences as a correlation-based approach to determine the sensitivity of a scalar forecast quantity computed by a numerical weather prediction model to changes in another model variable at a different model state. Its applications include determining the origin of forecast errors and placing targeted observations to improve future forecasts. We-a team of visualization scientists and meteorologists-present a visual analysis framework to improve upon current practice of ESA. We support the user in selecting regions to compute a meaningful target forecast quantity by embedding correlation-based grid-point clustering to obtain statistically coherent regions. The evolution of sensitivity features computed via ESA are then traced through time, by integrating a quantitative measure of feature matching into optical-flow-based feature assignment, and displayed by means of a swipe-path showing the geo-spatial evolution of the sensitivities. Visualization of the internal correlation structure of computed features guides the user towards those features robustly predicting a certain weather event. We demonstrate the use of our method by application to real-world 2D and 3D cases that occurred during the 2016 NAWDEX field campaign, showing the interactive generation of hypothesis chains to explore how atmospheric processes sensitive to each other are interrelated.

Jet-streams, their core lines and their role in atmospheric dynamics have been subject to considerable meteorological research since the first half of the twentieth century. Yet, until today no consistent automated feature detection approach has been proposed to identify jet-stream core lines from 3D wind fields. Such 3D core lines can facilitate meteorological analyses previously not possible. Although jet-stream cores can be manually analyzed by meteorologists in 2D as height ridges in the wind speed field, to the best of our knowledge no automated ridge detection approach has been applied to jet-stream core detection. In this work, we -a team of visualization scientists and meteorologists-propose a method that exploits directional information in the wind field to extract core lines in a robust and numerically less involved manner than traditional 3D ridge detection. For the first time, we apply the extracted 3D core lines to meteorological analysis, considering real-world case studies and demonstrating our method's benefits for weather forecasting and meteorological research.

In meteorology, cluster analysis is frequently used to determine representative trends in ensemble weather predictions in a selected spatio-temporal region, e.g., to reduce a set of ensemble members to simplify and improve their analysis. Identified clusters (i.e., groups of similar members), however, can be very sensitive to small changes of the selected region, so that clustering results can be misleading and bias subsequent analyses. In this article, we - a team of visualization scientists and meteorologists-deliver visual analytics solutions to analyze the sensitivity of clustering results with respect to changes of a selected region. We propose an interactive visual interface that enables simultaneous visualization of a) the variation in composition of identified clusters (i.e., their robustness), b) the variability in cluster membership for individual ensemble members, and c) the uncertainty in the spatial locations of identified trends. We demonstrate that our solution shows meteorologists how representative a clustering result is, and with respect to which changes in the selected region it becomes unstable. Furthermore, our solution helps to identify those ensemble members which stably belong to a given cluster and can thus be considered similar. In a real-world application case we show how our approach is used to analyze the clustering behavior of different regions in a forecast of "Tropical Cyclone Karl", guiding the user towards the cluster robustness information required for subsequent ensemble analysis.

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.

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.

Abstract For an ensemble of iso‐contours in multi‐dimensional scalar fields, we present new methods to a) visualize their dominant spatial patterns of variability, and b) to compute the conditional probability of the occurrence of a contour at one location given the occurrence at some other location. We first show how to derive a statistical model describing the contour variability, by representing the contours implicitly via signed distance functions and clustering similar functions in a reduced order space. We show that the spatial patterns of the ensemble can then be derived by analytically transforming the boundaries of a confidence interval computed from each cluster into the spatial domain. Furthermore, we introduce a mathematical basis for computing correlations between the occurrences of iso‐contours at different locations. We show that the computation of these correlations can be posed in the reduced order space as an integration problem over a region bounded by four hyper‐planes. To visualize the derived statistical properties we employ a variant of variability plots for streamlines, now including the color coding of probabilities of joint contour occurrences. We demonstrate the use of the proposed techniques for ensemble exploration in a number of 2D and 3D examples, using artificial and meteorological data sets.