Lexcube: Interactive Visualization of Large Earth System Data Cubes

Many subsystems of Earth are constantly monitored in space and time and undergo continuous anthropogenic interventions. However, research into this transformation remains largely inaccessible to the public due to the complexity of the Big Data generated by models and Earth observation. To overcome this barrier, we present the Leipzig Explorer of Earth Data Cubes (lexcube.org), an interactive Earth data visualization that allows users to explore terabyte-scale datasets with minimal latency through space, time, variables, and model variants. With over 2800 users and 163,000 API requests since its public release in May 2022, lexcube.org is a novel interactive data cube visualization that embraces the concept of “data cubes,” enabling an equal treatment of space and time. We expect this development to be particularly relevant for the emerging exascale Digital Twins of Earth, as interactive visualizations in real-time could remove access barriers and help democratize Earth system sciences.

Many subsystems of Earth are constantly monitored in space and time and undergo continuous anthropogenic interventions.However, research into this transformation remains largely inaccessible to the public due to the complexity of the Big Data generated by models and Earth observation.To overcome this barrier, we present the Leipzig Explorer of Earth Data Cubes (lexcube.org),an interactive Earth data visualization that allows users to explore terabyte-scale datasets with minimal latency through space, time, variables, and model variants.With over 2800 users and 163,000 API requests since its public release in May 2022, lexcube.org is a novel interactive data cube visualization that embraces the concept of "data cubes," enabling an equal treatment of space and time.We expect this development to be particularly relevant for the emerging exascale Digital Twins of Earth, as interactive visualizations in real-time could remove access barriers and help democratize Earth system sciences.

W
ith the advances in monitoring the Earth system and its components in space and time, we now have contiguous spatiotemporal data streams available at the global scale.The Earth surface (i.e., vegetation on land, aquatic bodies, ice sheets) and other surfaces are constantly monitored and analyzed with satellite remote sensing. 1 With the development of new satellite missions, the spatial and temporal resolution of the available datasets continuously rises.Using advanced machine learning tools and model-data fusion, the global set of Earth observations (EOs) is increasingly used in tandem with in-situ observations on the ground to derive meaningful parameters of a wide range of biophysical land surface processes. 17Today, the emerging suite of data streams enables scientists to better quantify the effects of climate change, human land use change and intensification, and other types of secondary anthropogenic interventions on the world ecosystems. 20Such observations are crucial for evaluating models, which are used for forecasting impacts of climate change. 7Along these lines, the Global Climate Observing System (GCOS), an initiative by the World Meteorological Organization (WMO), the Intergovernmental Oceanographic Commission of the United Nations Educational, Scientific and Cultural Organization (IOC-UNESCO), the United Nations Environment Programme (UNEP), and the International Science Council (ISC), agreed on prioritizing the derivation of 54 "essential" climate variables.a Space agencies such as the European Space Agency (ESA), the U.S. American National Aeronautics and Space Administration (NASA), and others support these initiatives with their missions. 9Likewise essential biodiversity variables (EBVs) have been defined by the Group on Earth Observations (GEO), 18,20 and further initiatives of this kind are on their way.
The steady increase in spatiotemporal resolutions as well as in the multidimensionality of datasets inflate dataset sizes up to several terabytes and petabytes.This poses substantial challenges in data accessibility and processing for the wider public and even for Earth scientists.This is why much research is currently invested in making big Earth data analysis-ready and interoperable (e.g., via data cube concepts). 4,6,15ata cubes present an opportunity to advance Earth system science 16 by leveraging a simple data structure, which is enhanced using sets of standards and specifications in order to make data easily interoperable and accessible b (e.g., CF Conventions).c Currently, multiple regional as well as global data cubes solutions are being developed by following predefined standards (e.g., Open Data Cube).d,e However, such approaches are still primarily serving the needs of scientists with high data literacy.In contrast, visualizations are suited also for nonexperts to recognize patterns and trends in large amounts of data as well as to detect anomalies.
In order to facilitate research processes and easily gain insights from large data cubes, here we develop an approach for interactively visualizing data cubes generated from multivariate remote sensing data and climate model outputs.The idea is to develop a system that scales efficiently with terabytes of data.This is important today, where the climate modeling community is embracing the idea of building digital twins of the Earth. 3These are models that operate at very high resolution, and ideally also allow users to explore their own "if, then" scenarios and questions.Digital Twins are also planned for the forestry sector 5 and hydrology and will probably soon lead to another dimension of data availability.However, in order to exploit these data streams efficiently, allowing precise statements based on modeling outputs, or analyzing correlations over longer periods of time, we need to have powerful interactive visualization tools.

RELATED WORK
There are a multitude of approaches for visualizing remote sensing and climate modeling data.The most common approach of scientific visualization in scientific workflows are open-source packages such as Matplotlib f (Python) and Makie.jlg (Julia).These are mature software solutions with a wide range of visualization types and capabilities for creating professional plots for use in publications.However, they are not designed to handle datasets that exceed the main memory (e.g., a dataset of hundreds of gigabytes).Once prompted with the visualization of larger datasets, the execution becomes much slower or even fails to complete.Also, these toolboxes are not per se leading to interactive graphics, but are extendable using the respective packages to include interactive elements.
In recent years, several other tools have been explicitly developed for visualizing and enabling user interactions with large, global datasets.Examples include xcube-viewer, h carbonplan-maps, i or the ESA interactive website "Climate from Space." j Such tools are well-equipped to deal with large amounts of spatiotemporal data and run in the web browser, allowing for an accessible and portable visualization once the server software has been set up.These visualizations usually opt for a spatial 2-D view on the world, with a UI slider allowing us to select a time step out of the dataset.However, this visualization approach disfavors the time dimension and does not allow us to recognize anomalies or trends happening through time.To compensate for this, some viewers offer to animate the spatial view through all available time steps.Still, a 2-D plot of the variable through time and latitude as in a Hovm€ oller diagram 10 can be more easily parsed by the human visual system and also be shared as an image, e.g., for the purpose of a publication.
Other solutions to convert animated trend visualizations to static images include overlaying frames ("traces"), or visualizing small multiples. 19However, overlaying data are not trivial when dealing with continuous numeric data recorded over a 2-D space such as in remote sensing.More exclusive and less common visualizations of remote sensing or climate modeling data are those in exhibitions and interactive installations (e.g., at museums or conferences).These vary in their interactivity and level of detail, but generally allow us to extract knowledge from the data in a very accessible way.However, due to their nature, they are exclusive in time and space and are usually restricted to few datasets.
Visualizations within a spatiotemporal 3-D coordinate system (i.e., space-time cube visualizations and derivatives) have found applications in various contexts before.In a review by Bach et al. 2 the authors compare several ways of applying different operations to the conceptual 3-D space-time cube to reduce it to a 2-D graphic.In the Lexcube visualization, a "filled" space-time cube is rendered with a projection camera, thereby following the authors' paradigms of "space and time cutting" and "3-D rendering" to generate a 2-D image from the 3-D dataset.Next to traditional geotemporal visualization, Li et al. 11 found that a 3-D space-time cube view can help visualize eye tracking data better than traditional 2-D gaze plots.In a similar vein, Filho et al. 8 found movement data to be well-suited for the 3-D space-time cube visualization and particularly improved on its usability with an immersive interface.While these authors and other works focus on the visualization of sparse data (e.g., lines within the 3-D space-time cube) the visualization of completely continuous remote sensing and modeling data requires different considerations due to the high density of the data.To visualize such "data cubes," two approaches have been previously introduced.The first approach involves data filtering ( e.g., discarding data voxels based on a threshold value or a spatial mask) and results in a volume visualization with some continuous objects and empty space in between.This idea has been first shown by Mahecha et al. in 2010, 14 masking out the oceans to allow a side view onto the continents and their temporal development.The alternative is visualizing the 3-D data as a "filled" space-time cube, which has been first seen in this domain context in a figure shared by Mahecha in 2017. 13Due to its easier understanding and simpler implementation, we opted for this approach with Lexcube.The spacetime cube visualization allows us to inspect the Hov-m€ oller diagrams, i.e., 2-D plots of the variables through time and latitude (or longitude, respectively), on the sides of the cube.This enables us to explore temporal patterns much more easily than traditional 2-D map-based visualization approaches.

Research Aim
Here we present Lexcube, a new visualization platform that allows the interactive exploration of terabytescale remote sensing and climate modeling datasets.Lexcube visualizes data as space-time cubes, allowing users to inspect the six faces of the cube equally (see Figure 1).On the side faces of the cube, latitude by time and longitude by time diagrams are displayed, corresponding to Hovm€ oller diagrams.The time dimension is, therefore, treated as equal to the spatial dimensions.The Lexcube visualization is aimed to be highly portable, running in the web browser and possible to use even on mobile devices.The interaction with the visualization is targeted to be intuitive and close to mainstream geospatial applications such as Google Maps.Through this ease of use, the visualized datasets become much more accessible for high-level exploration, removing the need to download datasets and writing code.
This paper makes the following contributions:

INTERACTIVE VISUALIZATION IN APPLICATIONS
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recognize trends and anomalies in the time dimension more clearly than current state-ofthe-art 2-D map approaches.
› The visualization runs on many devices, including mobile devices such as tablets and smartphones.Since Lexcube requires relatively little network bandwidth and visualizes the current GPS position, it is possible to use it in the field and compare historic climate data from large datasets to the real-life situation on the go.

User Interaction
When presented with the Lexcube software, users see a 3-D cube on a black background with various UI elements at the edges and corners of the screen (see Figure 2).Users then have different options for interacting with the visualization.First, in the dataset menu, buttons and selection boxes allow users to choose the currently visualized dataset and parameter.It also allows users to change the current selection of the dataset using three two-ended sliders, one for each dimension.In the "expert mode" of Lexcube, it is possible to customize the color map gradient and the value range.Furthermore, it is possible to select a "display quality" that reduces visualization quality at the gain of reduced bandwidth and lower latency.Within the 3-D world, the user can interact in two ways.First, it is possible to change the perspective on the cube by dragging the cursor or touch input on the background, rotating the camera around the cube at a fixed distance.By using the mouse wheel or pinching two fingers, it is possible to change the distance of the camera to the cube.Second, interactions on the cube itself allow users to change the selection of the dataset in an intuitive way.It is possible to click and drag or touch and drag on any of the cube surfaces and the selection will move accordingly, if the bounds of the dataset are not yet reached.Furthermore, using the mouse wheel or pinching two fingers on any cube surface allows the user to zoom into or out of the current selection, "inside" or "outside" the current cube selection.In the 3-D world, dynamically moving axis labels gives a sense of orientation to the user and communicates the outer bounds of the dataset currently being visualized.
In the top right corner, the user interface offers four options.The first button allows us to activate geolocation tracking and displays a marker on the cube based on the current GPS device coordinates.The second button plays an animation through time, moving the cube through all of the available time span in around 15 seconds.The third button opens the dataset menu, which contains all remaining user interface options, i.e., changing dataset and parameter, changing the cube selection through sliders, adjusting the color map and its value range and other options.The last button opens Lexcube in full screen, if the client device supports it.

System Overview
The Lexcube visualization platform allows for an interactive exploration of terabyte-scale datasets.This is achieved through numerous technical considerations.First, the visualization is built in a clientserver architecture in order to relieve the user of downloading the complete dataset and offload some computing load to a central server computer.When prompted for a visualization, the client requests the according data from the server, downloading only minimal data for each unique view on the data.The bandwidth is kept low by considering which data are visible to the user and by downsampling data that would have a higher resolution than the client can display.Fast random data access through precomputation and efficient organization of the data on the server-side allows for a low-latency interaction.The client itself is small in download size and implemented to be nonblocking, allowing for user input even while data are being downloaded and processed.Since the visualization is executed in the web browser, it is very portable and can be run even on mobile devices, such as tablets and smartphones.On touch-capable devices, the visualization can be controlled using common interaction gestures such as pinching two fingers for zooming and dragging anywhere on the visualized cube for moving the selection.Lexcube is designed to run at interactive frame rates even on low-end devices and in weak network scenarios through the option of choosing a desired visualization quality, analogous to video sharing websites offering different video resolutions, increasing or decreasing the visualization quality at the gain of reduced network bandwidth and decreased GPU load.

Tiling
Approach In order to be able to transmit only parts of the dataset in different resolutions, a typical tiling approach is implemented.Dividing the dataset into square tiles of a fixed size, it is possible to transmit only the data visible to the client.Furthermore, tiles can be generated and delivered at different level-of-detail, downsampling the data for clients with smaller display resolutions at powers of two.The space-time cube visualization comprises three distinct access patterns into the data, each corresponding to a pair of the three dimensions: longitude by latitude with indexing by time (front and back faces of the cube), longitude by time with indexing by latitude (top and bottom faces), and latitude by time with indexing by longitude (left and right faces).For each of these cases, tiles are generated from the source dataset, either in advance or on-demand during runtime.Since a generation of all tiles in these three index directions would correspond to a tripling of the dataset size, we instead implement a sparse 3-D grid.Instead of generating all possible tiles, we limit the generation to every Nth index in each direction, creating a sparse grid instead of a full 3-D volume.This sparsity factor can be tuned to linearly decrease the amount of total tiles, reduce the necessary generation time and required disk space.On the client side, any user input is aligned to the sparsity grid (i.e., rounded to the nearest Nth index value for each dimension).While low sparsity values are close to imperceptible, high sparsity values may negatively impact the user experience as it prevents users from making precise selections.Therefore, the sparsity factor has to be chosen as a compromise between generation time and disk space versus the quality of the user experience.As a balanced value, we chose a tile size of 256 Â 256 pixels and sparsity factors between 2 and 10, depending on the dataset resolution and available disk space.
Pregeneration Versus On-Demand-Generation It is possible to pregenerate all tiles, generate them only when a client requests them or a combination of both approaches.When generating tiles on-demand, the source dataset is accessed during run-time to construct the requested tiles.The resulting tiles may be stored on disk or in memory up to a certain limit.However, since the client may request tiles at a high levelof-detail (i.e., highly downscaled data from a large area in the source dataset) a tile request may force the server to read large parts of the source dataset.If the source dataset is indexed orthogonally to the request, this can result in decompressing gigabytes of data for a single visualization, negatively impacting the perceived latency and significantly increasing server load.
The advantage of pregenerating tiles is the low interaction latency, since the tiles only have to be read from the hard disk when requested.The disadvantage is the computing time and the disk space required for the initial generation of these tiles.However, with our approach to generating the tiles in 3-D space sparsely, the computing time and space required can be tuned linearly to be much lower.For our current main use case, the open-access scenario of lexcube.org with hundreds of users accessing a few preset data sets, pregenerating tiles allows for a low client latency with the few hours of pregeneration time being negligible and irrelevant to users.

Visualized Data Sets
For testing Lexcube, four datasets in increasing size and from different domains have been selected and

Technology Stack
The Lexcube software consists of a server and a client with various modules each (see Figure 3).The Lexcube server is implemented in Python using the FastAPI web server library and numerous scientific programming libraries.These include Numpy and OpenCV for efficient array operations and Xarray m for accessing the zarr and NetCDF datasets.By utilizing Xarray, Lexcube integrates into the existing open-source and standards ecosystem, e.g., extracting metadata from CF conventions.It is possible to visualize a wide range of existing datasets, with the only requirement being that the data are on a regular spatial grid.For lossless tile data compression, the Python library Numcodecs is used.It implements the Blosc meta compression algorithm with support for LZ4, Zstd, and more algorithms.For lossy compression, the specialized floating-point array compression algorithm zfp is used through its python library zfpy.The Lexcube client is developed using TypeScript.The space-time cube visualization is rendered with WebGL2 using Three.js.For decompressing the tile data sent by the server, a fork of numcodecs.js,which additionally implements zfp compression is used.
Numcodecs.jsmakes use of the WebAssembly technology, which allows us to execute transpiled C/C++ code at near-native performance in the web browser.This allows Lexcube to efficiently decompress tile data in the web browser at interactive performance, even on mobile devices.

Tile Compression
In order to reduce network bandwidth and required server storage, compressing the generated tiles is essential.Lexcube implements both lossless and lossy compression, with lossy compression being selected by default.For lossless compression, the meta compressor Blosc using default settings (LZ4, compression level 5, byte shuffle filter) is used.For lossy compression, the specialized floating-point array compression library zfp 12 is used.
Since some parameters in the Earth System Data Cubes have been upsampled, i.e., contain repeated values in square blocks of N Â N in order to fit the higher resolution of the other parameters, it is possible to compress these parameters even further.After reducing upsampled data to its original size, zfp can compress the data more efficiently.However, downsampling needs to be negotiated with the current level-of-detail, since a parameter upsampled by factor 2 will appear regular at level-of-detail 1, where dimensions are halved.Therefore, usually only tiles of level-of-detail 0 benefit from the upsample detection.
In Table 2, compression ratios of a selection of parameters and the sum of all parameters of the Earth System Data Cube dataset are presented.While lossless compression reaches a compression ratio of 3.06 over all parameters, lossy compression using zfp performs significantly better with a ratio of

Client Rendering
On the client, Three.js is used to render a cube centered in the scene.In order to display the tile data on the cube, it needs to be stored in a texture.Lexcube utilizes the Three.jsDataTexture2DArray texture type, which in turn implements a 3-D texture with type float32 in WebGL2.For each side of the cube and each level-of-detail, one DataTexture2DArray with size 256 Ã 256 Ã tiles face,LoD is constructed, with tiles face,LoD being the total amount of tiles on that cube face and that level-of-detail LoD.Within the texture array, each index corresponds to one tile, ordered by their X and Y coordinates.Each texture is initially filled with a magic number known to the shader to signal that no data has yet been downloaded.Once a tile has been downloaded, it is inserted into the correct position of the texture array and the texture is uploaded to the GPU.The advantage of this approach is its simplicity in implementation.However, mipmapping is no longer easily achieved since adjacent tiles are located at different indices within the texture array.
The cube itself is rendered with a custom fragment shader.Inside the shader, the total size of the dataset and the currently visible selection is divided by each other to obtain the relative view within the full dataset.From this, it is possible to calculate which tile and the coordinates within the tile itself is displayed at the current fragment.Then, the floating-point data are read from the texture and colormapped according to the currently selected colormap value range and the 1D colormap texture.
The testing procedure has been programmed to benchmark six subsequent zoom operations with a 800 ms timeout between operations, downloading ca.50-100 tiles in total.The benchmark is repeated five times.The minimum, maximum, and average frames per second and the minimum, maximum, and average time from the user interaction until all visible tiles are downloaded and the first frame is rendered (= fullcycle interaction latency) are recorded.All timings use the performance.now()web browser API.

Benchmark Results
The results are displayed in Table 3.It can be observed that even an older device such as the Tablet from 2015 rendering at 5 MP resolution (2732Â1842), Lexcube runs at an interactive 40.1 frames per second.On the other two, more recent devices, Lexcube also achieves interactive frame rates of 47.5 and 54.2 frames per second.For the full-cycle interaction latency, the Desktop performs the best with an average of 299 ms between finishing the user interaction and displaying the rendered frame after all tiles have been downloaded.The other two devices perform worse with 435.4 and 773.3 ms of total latency, which can still be considered a fast system response for a network-based interaction.Since the system does not block inputs while tiles are downloaded and decompressed, even cases of higher latencies for single interactions do not impact frame rates and allow the user to still interact with the system.In an additional benchmark, the capability of Lexcube to work under poor network conditions has been tested.Instead of the previously used 250 MBit/s network (¼ 31.25 MB/s download speed), the Desktop client has been benchmarked on a 500 KBit/s network (¼ 62 KB/s download speed) with 500 ms added latency.The results are displayed in Table 4.It can be observed that the interaction latency rises to ca. 16 seconds at the default display quality.As a measure to decrease latency in such a situation, the display quality can be adjusted.With display qualities of 25% and 50%, the latency decreases linearly to ca. 8 and ca. 12 seconds, respectively.
In total, we can conclude that Lexcube is capable of delivering high frame rates even on older mobile devices, allowing users to interactively explore the datasets.Lexcube is also able to operate under poor network conditions, though with much higher latencies.

USE CASES
The Lexcube visualization platform allows new user groups to consume and interact with large remote sensing datasets.In the following, three proven use cases for Lexcube are presented.

Use Case 2: Access Big Earth Data While in the Field
As part of an excursion to Hainich National Park, Germany, on 24 August 2022, we tested the visualization while in the field.Using the 3G mobile network in the area, it was possible to access the visualization with few seconds of latency for each data download.With the geolocation tracking, we could identify our current position during the excursion on the cube (see Figure 4).Having access to these large datasets while in the field on mobile devices allows us to see detailed historic data and temporal trends, all in context of the current device position and observations in the real world.Additionally, the lead investigators of the Digital Forest project involved in Hainich National Park have decided to showcase Lexcube in the final project exhibition, taking place in 2024/2025 in the National Park Centre, which sees few thousands of visitors yearly.The exhibition will feature an interactive touch screen monitor with the Lexcube software, allowing visitors to explore the various data cubes focused on the Hainich region from the project.This use case demonstrates how Lexcube significantly enhances the accessibility of large EO datasets, allowing for exploration of historic global and local datasets at the current device geolocation.It supports the field work of scientists and aids in their understanding of the underlying dynamic processes relevant to their specific research domains.

Use Case 3: Scientific Analysis-Finding Anomalies
The Lexcube visualization platform allows us to meet multiple scientific use cases.The most basic use case is the visual check of expectations and assumptions about the underlying dataset.For instance, the 3-D space-time cube will quickly reveal if all assumptions about a computation result are correct when visualized.This includes processing errors, anomalies introduced by the technical process and other discrepancies between the mental model of the dataset and the presented visualization.Going further, it is possible to do a high-level analysis of the visualized dataset.For example, it is possible to quickly understand the completeness of the dataset, which may be impaired by cloud cover, over both spatial and temporal extent.Furthermore, when animating the dataset through time, any errors or instabilities of the underlying georeferencing become obvious.Looking into the domain data, it is possible to verify existing high-level hypotheses Available: htt_ ps://twitter.com/i_nitze/status/1560589316585181185 with the visualization.These include the seasonality of many naturally occurring parameters, identifying extreme events or global trends, such as global greening.
Additionally, it is possible to generate hypotheses (e.g., on extreme event occurrences that were not picked by classical event detection methods).In that case, and others, the human visual pattern recognition may still outperform machine-based methods.This can also be leveraged to identify data inconsistencies invisible to algorithms and help uncover errors that were not spotted by previous quality assurance (QA) measures.Furthermore, it is possible to spot land-use changes that were not detected by time-series break-point detection methods.Combining human intuition and the visual pattern recognition, it is possible to exploit the interactive visualization to gain new scientific hypotheses.
As a prototype for future components in Lexcube that allow for deeper scientific analysis, we implemented an anomaly analysis mode.It allows us to compare one selected year in the dataset to all other years and visualizes their relative values (see Figure 5).This enables us to gain insight over how the years in the dataset compare both on a broader level (e.g., if the temperature in one year was generally higher than adjacent years), and on a more detailed level (e.g., finding out that the winter of one year was particularly cold, relative to adjacent years).Expert users who tested the anomaly analysis mode found the insights to be taken from seeing two cubes at once, one displaying absolute values while one cube shows a relative measure, valuable.They also expressed their wish for more analytic tools such as time-series plotting and data reduction through kernels.At the time of writing, the anomaly mode is not yet publicly available on lexcube.org.

DISCUSSION
The idea of Lexcube was conceptualized from the needs of users.They have expressed that it is not possible to visualize data as six-sided data cubes with existing software packages.According to them, visualization using data cubes would help explore spatiotemporal 3-D data and understand dynamics through time much better than current 2-D map-based approaches.Furthermore, since the source data such as the Earth System Data Cube contains hundreds of gigabytes of compressed data, the users were looking for a well-performing solution that could access these amounts of data interactively or at least in a reasonable amount of time.Additionally, we identified the need for an intuitive solution since the target user base is very diverse and not necessarily experts on computer science or using complex graphical user interfaces.Lexcube has been designed to be intuitive in the following ways: › Ease-of-entry: When starting the application, users are presented with a first visualization without any further input.
› Direct controls: For manipulating the visualization, we follow design principles of 2-D mapping applications translated to the concept of a 3-D data cube.On the cube, dragging the cursor or the finger across moves the underlying selection similar to a 2-D map.For rotating and moving the cube itself, we use orbit controls which can be generally quickly understood.As a small help in learning these controls, a very brief (20 seconds) tutorial screencast is shown when visiting the web page for the first time, visualizing the user controls in action.
› Interactivity: Through the very low response time and constantly high frames-per-second (see the "Benchmarking" section), users experience very low friction in the interaction.For novice users, this allows them to explore the data without having to mind the large source data set and possible resulting limitations when programming the data access oneself.For expert users, the interactivity enables them to explore the data and generate data cube visualizations very efficiently.

INTERACTIVE VISUALIZATION IN APPLICATIONS
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› Interoperability: By integrating with existing open-source technology and standards, Lexcube can visualize a wide range of existing Earth science data sets.Furthermore, the Numpy backend allows even 3-D data from completely different domains such as astrophysics and seismology to be visualized with their own three dimensions.
The described intuitiveness and filling a proven user need has led to Lexcube receiving great qualitative feedback from users.Additionally, promoting the tool via social media and conferences helped Lexcube become relatively popular in this niche community in a short amount of time.We think the described aspects can be useful to other visualization approaches and techniques to successfully find widerspread adoption "in the wild."

CONCLUSION AND OUTLOOK
To conclude, with the Lexcube software we make the following contributions: › The proven ability to run Lexcube on mobile devices while in the field and tracking the current GPS position increases the accessibility of the visualized datasets significantly.Furthermore, new user groups with less or no scientific background are now able to access terabytescale datasets from their smartphones.
For the future, several key improvements of Lexcube are planned.The aspect of visual analytics and scientific analysis within the cube visualization has been explored with the prototypical anomaly analysis mode in the "Use Case 3: Scientific Analysis-Finding Anomalies" section.Going into this direction, adding standard analytical tools such as plotted time-series for selected points will increase the scientific potential of Lexcube.Furthermore, an option to compare different time spans or parameters through visualizing multiple cubes at once would allow for an easier comparison between these different cube selections, see Figure 6.In addition, we are aiming at a tighter integration of the Lexcube visualization into existing and common scientific workflows, especially Jupyter notebooks.Building a portable Lexcube package that allows us to visualize any 3-D array from common scientific computing libraries such as Pandas, Xarray, Dask or Numpy would enable highly accessible, interactive visualizations for any kind of data.Implementing a lazy computation paradigm and on-demand tile generation capabilities, this approach could work even for much larger datasets than tested in this work.Finally, we are looking to extend the visualization currently limited to the surfaces of the space-time cube with a volume rendering of the insides of the current cube selection.The values of the rendered 3-D volume could then be discarded based on a threshold value to visualize space-time clouds of extreme values (e.g., for temperature or soil moisture) and discover extreme events in high-resolution climate models and remote sensing data.

›
FIGURE 1.A user with the Lexcube application on her smartphone, visualizing a dataset of the protected area "Auwald forest," Leipzig, Germany, while walking through it.The spatiotemporal data visualization shows longitude by latitude on the cube front face, and latitude/longitude by time on the side faces.This data cube view enables visual comprehension of temporal patterns and trends.Here, the kNDVI spectral index (Kernel Normalized Difference Vegetation Index) based on satellite imagery from a commercial data provider is on display.

FIGURE 2 .
FIGURE 2. Default view of the Lexcube visualization on lexcube.org.

FIGURE 3 .
FIGURE 3. System overview of the Lexcube client-server architecture.Tiles are pregenerated once and saved in the server-side tile storage.The dataset definitions and tiles are accessed by the client through a REST API and a Websocket connection, respectively.On the client-side, the tiles are saved in the local tile cache, the data textures, where they can be accessed from the cube WebGL shader, visualizing the downloaded data according to the current color map.
As a first use case, we are hosting a publicly accessible instance of the Lexcube visualization software at lexcube.org.Since the launch of lexcube.org in May 2022 during the ESA Living Planet Symposium until the writing of this article in March 2023, 2829 unique users have accessed the lexcube.orgvisualization, generating 163,031 API requests.Due to the interest by ESA staff, Lexcube was spontaneously featured on a panel on data visualization and online with a blog post on the ESA EO4Society website.n The offering of lexcube.org also found very positive response on social media, gathering 21,000 video views, 774 likes, and 205 retweets on Twitter over three tweets and 273 likes and 22 shares on

FIGURE 4 .
FIGURE 4. Lexcube visualization with activated geolocation tracking on a mobile device during our excursion to Hainich National Park, Germany.The white dot in the lower left corner displays the current GPS position.The displayed dataset shows the kNDVI spectral index based on Sentinel-2 data of the national park.

FIGURE 5 .
FIGURE 5. Lexcube visualization with activated anomaly comparison.The right cube shows a comparison between the three displayed years.The middle year, 2019, has been selected by the user cursor, is colored in plain white, and serves as a reference.The years before and afterward are colored according to their relative values, showcasing potential anomalies to the user.

›
The Lexcube software allows us to interactively explore and visualize terabyte-scale crossdomain remote sensing datasets.It works on datasets of different standard formats such as zarr and NetCDF based on a client-server software architecture.With the 3-D space-time cube visualization, temporal anomalies and trends are more clearly visible than in current 2-D map approaches.

FIGURE 6 .
FIGURE 6.Multiple screenshots stitched together with photo manipulation software to showcase a prototypical visualization of multiple cubes at once.Displayed are 72 parameters of the Earth System Data Cube dataset.

TABLE 1 .
Table of datasets successfully visualized with Lexcube.At the time of writing, the global daily spectral indices dataset is not yet publicly available at lexcube.org.The EAC4 CAMS dataset is in NetCDF format, the other three datasets are in zarr format.
successfully visualized, see Table1.The size of the datasets ranges from few gigabytes to few terabytes, While one dataset, the EAC4 CAMS global reanalysis, is stored in the NetCDF format, k the other three datasets are stored in the zarr format.l

TABLE 2 .
Results of using different compression techniques on parameters in the Earth System Data Cube dataset with a tile sparsity of 10.Lossless compression is done using Blosc with default settings (LZ4, level 5, byte shuffle).Lossy compression is done using zfp with the tolerance parameter set to 0.1% of the global value range.Compression sizes are rounded to one decimal place, and ratios to two decimal places.The uncompressed size of each parameter varies due to different basetypes (float32, float64) and varying dataset time periods.
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TABLE 3 .
Results of benchmarks on different devices.For FPS values, 30 to 81 samples have been recorded depending on device performance.For full-cycle interaction latency, 30 samples have been recorded.All values are rounded to one decimal place.