Introduction
Spatiotemporal data is located in space and time which may be conceptualised and actualised as a 3D/4D space defined by geographical and a temporal coordinate systems that is often called the ‘spacetime cube’. Maps are other visualisations are ‘views’ onto data within the cube impemented through a number of graphic processes (Bach et al. 2017).
While all data has a temporal aspect as it was collected and collated at sometime, but to me there is a diffence between a dataset that contains temporal information and one that is truely ‘temporal’, and that this applies to visualisations and well as data. As an example, consider a thematic map of English Civil War battle sites and dated battle sites on a topographic map. The Civil War map is a ‘temporal map’ as its primary purpose is to communicate spatiotemporal information, whereas the topographic map is a general purpose map. This is not a hard distinction, bu instead a dimension along which to data and visualisations may be evaluated.
Temporal data and visualisations are employed in a very wide variety of contexts, but may be condisered in respect of four general use needs. They are used to show,
- The age of things in a landscape
- Past and future landscapes
- Motion and change
- Scaling relationships
A range of graphic approaches may be employed to address the first three needs, including lablels, temporal symbolisation, figure partitioning and swiping, small multiples, animation, and 3D space-time volumes. Strommel diagrams show space-time scaling relationships. Neither use needs or graphic approaches are exclusive, with visualisations meeting one or more needs through the application several graphic processes and techniques. The Civil War map shows both a past landcape of war and the age of a specific thing (‘battles’) in the landscape. Here, space-time visualisations are structured by use rather than by graphic form and with examples of graphic approaches have been employed to meet these needs. Before this, however, conceptual relationships between the spacetime cube and visualisations of data within it will be considered.
The space-time data cube
Spatiotemporal data may be conceptialised as exiting within a spacetime data cube, and visualisations transformations of that data through cutting, flattening, juxtaposing, and 3D rendering (Bach et al. 2017). A modified form of Bach et al.’s classification is outlined here.
Cutting
Cutting or ‘slicing’ divides the space time cube along one or more dimension into ‘slices’. Slices along the time axis are ‘time slices’, while slices parallel to the axis are ‘spatial slices’ and cutting along multiple axis are ‘spatiotemporal’. Here slices fill the cube, but this is not a requirement.
Flattening
Flattening collapses data within a space-time cube or slice along one of its axes, for example merging all time slices into a single 2D image. It is analagous to a long exposure photograph.
2D perspective views ‘flatten’ 3D space-time data spaces from a viewpoint, but perspective distorts the mapping between location and shape in the data and their corresponding marks on the page.
I include 3D perspective as a type of flattening, and seperate the flattening of cube dimensions from the subsequent symbolisation of data within the flattened slices. Bach et al. ‘colour flattening’ is a time flattening followed by temporal symbolisation.
Juxtaposition
Visualising multiple flattened slices requires each to be juxtapositioned in relation to the others. Flattened slices may be juxtaposed in space as small multiples or as a two-slice ‘swipe’ or difference map, or as an animation or time slider application (a controlled animation).
Temporal symbolisation
Flattening collapses a cube or slice to a plane within which data is symbolised. Symbols that do not indicate time are ‘aspatial symbols’, wheras those that communicate time are ‘temporal symbols’. Time may be symbolised using graphic dimension (e.g. colour or size) or labels.
Time rings sized by age and coloured by value are provide a compact way of showing change through time at point loactions.
Space-time visualisation
Cutting, flattening, juxtapostion, 3D rendering, and symbolisation actions are combined to create spatiotemporal visualisations that show, the age of things in a landscape, a past or future landscape, change, or a space-time scale relationship.
The age of things in a landscape
A ‘palimplest’ is a manuscript on which later writing has been superimposed on earlier writing, reducing the legability of both texts, but mostly the older; however to may also be used more generally to describe any pattern that is the composite product of the effects of multiple over-writting events. Landscapes are palimpests of pattern created at different times with different circumstances. The English landscape is a rich tapestry created over millennia of geological time followed by the ‘time of man’.
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If I go up on the North Downs not far from where I live, I can walk the same route as my prehistoric ancestors along the Hog’s Back Ridge path, and although this may be wishful thinking as I am probably far more Anglo-Saxon than Celtic, nevertheless we are both natives of this land. The Ridge is made of Cretaceous chalk deposited in warm shallow seas near the equator inhabited by all manner of life including ammonites and Mosasaurus folded by ripples generated as Africa collided with Europe to form the Alps. From here I can look down on ancient woodland, Roman roads, Normon chruches, Medieval field systems, a canal constructed in the Industrial Revolution now used for recreation, and post-war urban sprawl. Every landscape has such stories to tell. Landscape character and geological maps are examples of palimpest maps that use temporal symbology and labels to show how landscapes are time-structured by past human activity and earth history.
As mentioned in the introduction my interest in time began young with the challenge of picturing past environments and how they changed over tens and hundreds of milllions of year. Many years later I was fortunate to recieve funding to applying GIS in evolutionary science that morphed into an intererst in how to model and visualise evolutionary pattern in space and time, This is a complex task as taxa have geographical presence in space and time space connected through their shared evolutionary ancestry which is often represented as a tree.
The movement and evolution of life on earth across geological time scales and past human action has created the palimpest of biodiversity we experience today. The discipline of historical biogeography aims to discover and explain pattern in the distibution of life on earth and its evolutionary relationships. The geophylogenetic approach to visualisation ‘spatialises’ evolutionary trees by geo-locating tip nodes at the centroid of extent species ranges and then applying a spatial averaging algorithun up the tree to locate internal nodes to create a spatiotemporal tree (refs). The Brown Bear geophylogeny is a simple example of a geophylogeny displayed as a 3D space-time rendering.
When I first wrote the software to build spatial trees most evolutionary trees were quite small, but this has changed over the last 15 years with the publication of ‘supertrees’ of several thousand species and large species range map databases. The Mammal Geophlyogeny Dashboard time is a prototype exploration platform to a geophylogeny of nearly 4000 extant mammal in which node age is scaled to the elevation axis of a virtual globe. Node and branch data including diversification date are provided in pop-ups. The tree can be filtered by taxonomy, age and bearing, and contexturalised against a palaeocontinental reconstruction and other data.
The entire geophylogeny is a ‘hairball’ within which spatial and temporal pattern lies which must be discovered and presented. Statistical maps of node and branch attributes are one approach that may be applied to extract general pattern, for example mapping median node age by colour shows how nodes separating clades on different continents tend to be old, as well as older clusters within some continents, noticably Australia. Querying the tree allows the isolation of specific local pattern from the tree, for example, nodes with sister clades with Amazonian and Atlantic Forest distributions sized by their age shows how node age varies, but also parallelism in connecting branches. The mammal geophylogeny is large with visualisations aided at showing pattern within it although some contextural information is provided in the web app. To understand and communicate the underlying drives of change required pattern to be placed in the context of earth history change.
Many years ago I agreed to look into historical biogeographical pattern in the Goodidae family of Mexican freshwater fish but did not realise quite what a labyrinth I was to decend into, and remain. The Goodidae are believed to have migrated from the southern United States to Cental Mexico in the Late Miocene, where they dispersed and evolved as the rivers and lakes they lived in reconfigured as the Trans-Mexican Volcanic Belt mountain chain rose beneath them. Understanding this complex historical and geographical problem requires linking disperate and partial, geological, geomorphological, and biological data together, to infer past change in drainage network connectivity and basin extent, and how that drove movement and diversification.
The challenge is to find and show conguence in location, direction, and time of geographic breaks in the distribution of Goodeide sister clades that may be the conseqence of a change in the river network splitting an ancestral population. Synthesis of palaeo-reconstructions with modern high-resolution digital data allows this.
This is one attempt at a synthesis of Goodeide historical biographical pattern and inferred watershed change. Potential vicariant event (PVE) orientation lines (black) connect disjunct and partially overlapping sister clade ranges. Modern watersheds are medium thickness grey lines. Past watersheds are brown and mostly dated to geological periods that are often broad and non-standard. PVE direction is inferred from spatial and temporal conguence to a watershed change event. A recent within species migration is also shown dated to an eruption (purple). Directed PVEs that are not linked to watershed change are linked to the waxing and waning of palaeolake systems. It would be good to add the lakes as well as adding the geological period to PVE labels and modifying the legend to include absolute values.
Past and future landscapes
Past landscapes may be accessed through historical maps, documents, memory, and scientific reconstruction. Past and future landscapes are designed/reconstructed and/or simulated. Visualisations of other times are flattened time slices of the data cube, or in the case of virtual and augmented reality a 4D-spacetime cube.
Virtual reality immerses you in a past or future place, while augmented reality allow places to be seen in situ
Change
The third general use of temporal maps is to show change through motion, as velocity, in distance, and across landscapes.
Motion
While ‘time and place’ maps emphasise the Motion Features may have more than one spatial and temporal location to explicitly show change in a single graphic. Change may be visualised discrete snapshots or a continious trace. In the map of the world’s economic center of gravity, change is represented as both descreate dated points and continious spatiotemporal arrows.
The map the world’s economic centre shows a single moving point, other datasets are larger with more complex pattern better shown as an animation.
A moving point traces a timeline through a rendered space-time cube.
Velocity
Velocity maps show how fast something is moving. Temporal colouring does not show the direction of movement of Antacrtic ice-sheets but it can be inferred from the context.
Vector arrows may show both direction and velocity.
Distance
Distance and time are linked through veocity. Isochrones (lines of equal time) trace the time that it takes to get to or from a place, for example, London.
Continious time shading is an alternative to using isolines and discrete time colour classes.
(Fig 1 in Rudolfson et al. 2020).
Landscape change
Change requires motion but may also be visualised as a juxtapositon of states.
Temporal partitioning patitions a space into sections in which information about different times are displayed. The partitioning of Ordnance Survey map design though time and the time slice photograph are static example, while and swipe apps are interactive partitons.
Difference maps show distance in value (velocity) between two times. It is flattening with maths!
Difference maps are an example of ‘small multiples’ that juxtapose time-slices on space, but the viewer must mentally render change between slices. A single time cut creates a map of a past landscape. Temporal cuts may also be juxtaposed in time as an animation that shows states and their transitions, but not the series as a while.
An animation is a stack of time-slices that are displayed sequentially to create an illusion of continious movement and change. Time slices in an an animation may be of equal time, for example annual, or variable intervening time periods or duration that do not linearly scale to ‘play’ time iunless ‘padded’ in some way. The Surbiton Urbanisation 1837 to 2024 has eight equally-spaced time slices. so jumps rather than flows.
Glyph maps cut data into spatial slices that is flattened its two spatial dimensions and plotted as small multiple time series
Space-time scaling
Gallileo’s equation of motion suggests that, on average, processes in a smaller physical system will be faster than those in larger systems. Stommel diagrams, named after Henry Stommel, plot the spatial and temporal scale of features and processes against axes of spatial and temporal scale. Many systems show spatial scaling, however, care should be taken as system boundaries are many be natural or cuturally determined, and likely fuzzy.
