Switching between space and time: Spatio-temporal analysis with
cubble

H. Sherry Zhang

Monash University, Australia

2023 May 02

Hi!

• A final year PhD student in the Department of Econometrics and Business Statistics

• My research centers on exploring multivariate spatio-temporal data with data wrangling and visualisation tool.

• Find me on

  • Twitter: huizezhangsh,
  • GitHub: huizezhang-sherry, and
  • https://huizezhangsh.netlify.app/

• Thanks for the invitation to speak

• Today I will be talking about …

• First, a little bit about myself

• I’m Sherry Zhang, …

• …

• Here are the details to find me on Twitter, GitHub, and my website

Multivariate spatio-temporal data can be commonly found in the society: in finance and economics, stock prices and economic indicators are tracked over time; in logistics, supermarkets collect product level data to decide the optimal stock levels for different stores; in meteorology, weather stations record climate variables to monitor climate change and its impact on different sectors.

Spatio-temporal data are recorded with data-time and geographic location information. Multivariate means that multiple variables are recorded. This could include, for example, in weather station data, temperature, precipitation, wind speed and direction

However, all three aspects are ideally considered together to tackle contemporary problems, such as monitoring droughts which requires historical climate data to understand “normal” conditions for any spatial neighborhood, and the interplay of precipitation, temperature and other relevant variable(s), for example, ice melt for high altitude mountain region.

This research addresses the challenge of investigating multivariate spatio-temporal data, by providing new tools for organising, visualizing and explaining relationships.

This illustration here shows how the three research topics are related. The solutions are to provide easy ways to pivot between the three components, to allow focusing on multivariate or spatio-temporal analysis and new pipelines to construct indexes.

When fixing the time, the data are reduced to multivariate and can be analyzed using multivariate methods such as dimension reduction. The particular dimension reduction investigated in this thesis is called projection pursuit, which contains an optimization component. Diagnostic plots can be useful here to track the performance of these optimization algorithms.

When the data are collected at different locations in space, software from geoinformatics can be useful to analyze the spatial aspect of the data. However, existing spatial and temporal data analysis software are built upon different data formats. This creates frictions in the data analysis to constantly rearrange that data format to work with the software. We designed a spatio-temporal data structure to organise the data.

Multivariate spatio-temporal variables are often combined into a single index series for decision making. But index definition and construction are vastly different in different fields and different researchers making it difficult to understand how they might perform slight changes in the formula, or how competing indexes compare.

Spatio-temporal data

People can talk about a whole range of different things when they refer to their data as spatio-temporal!

The focus of today will be on vector data.

Here we have three different types: vector, raster, trajectory data (explain each)

vector data have time series measured at a collection of locations

raster data use gridded cells to represent a continuous space and each cell, or pixel, has variables measured at different time points. An example of raster data could be satellite images.

There is also trajectory data where points are moving in the space and time in the same time. This type of data can be found in ecology to track animal movements.

In my talk today, we will focus on vector data. But I want to start by giving you the big picture.

Example of vector data

Physical sensors that measure the temperature, rainfall, and wind speed & direction

Physical sensors are a common source of vector spatio-temporal data. Here is the picture of a fancy weather sensor.

On the right, the wind speed cup and the wind vane measure the wind speed and direction.

The rain gauge on the left has a standard diameter, based on which rainfall is measured in mm and the thermo sensor below it measures the temperature.

Instruments like this are placed across Australia to record climate data on a daily or sometimes half hourly basis.

Australian weather station data:

stations

# A tibble: 88 × 6
  id            lat  long  elev name              wmo_id
  <chr>       <dbl> <dbl> <dbl> <chr>              <dbl>
1 ASN00001006 -15.5  128.   3.8 wyndham aero       95214
2 ASN00002032 -17.0  128. 203   warmun             94213
3 ASN00003080 -17.6  124.  77.5 curtin aero        94204
4 ASN00005007 -22.2  114.   5   learmonth airport  94302
5 ASN00006044 -25.9  114.   9   denham             94402
# … with 83 more rows

ts

# A tibble: 32,208 × 5
  id          date        prcp  tmax  tmin
  <chr>       <date>     <dbl> <dbl> <dbl>
1 ASN00001006 2020-01-01   164  38.3  25.3
2 ASN00001006 2020-01-02     0  40.6  30.5
3 ASN00001006 2020-01-03    16  39.7  27.2
4 ASN00001006 2020-01-04     0  38.2  27.3
5 ASN00001006 2020-01-05     2  39.3  26.7
# … with 32,203 more rows

• Let’s put these in a data context.

• The stations data records 30 Australia weather stations, along with their longitude, latitude, elevation, and name

[breath]

• On the temporal side, we have precipitation, maximum and minimum temperature collected daily for each station in 2020.

What’s available for spatio-temporal data? - stars

What’s available at that time is a package called stars, it uses a dense array to structure spatio-temporal data. You can think of it as stacking snapshots of the space along the time axis.

This is great for satellite data, but it may not be the most obvious solution for analysts who prefer to operate on a 2D table format.

Hence, I designed a data structure called cubble to handle saptio-temporal vector data.

Cubble: a spatio-temporal vector data structure

• Today I will introduce a new data structure, called cubble, for vector spatio-temporal data

• in short, cubble is a nested object built on tibble that allow easy pivoting between spatial and temporal form.

• we will first talk about how the two forms look like and then how you cna pivot beween them for different tasks.

• In the nested form, spatial variables are in columns out and temporal variables are nested into a list column called ts

• In the long form, the time series data are shown in columns and each row is cross identified by the site and date in a long table

Cubble: a spatio-temporal vector data structure

Cubble is a nested object built on tibble that allow easy pivoting between spatial and temporal form.

• The pair face_temporal() and face_spatial() to switch the cubble between the two forms.

• With face_temporal(), the focus of the data is now on the temporal face of the spatio-temporal cube and this corresponds to switch the data to the long form.

• With face_spatial(), the long cubble is switched back to the nested form, the spatial face of the datacube.

Cast your data into a cubble

(weather <- as_cubble(
  list(spatial = stations, temporal = ts),
  key = id, index = date, coords = c(long, lat)
))

# cubble:   id [88]: nested form
# bbox:     [113.53, -43.49, 153.64, -10.58]
# temporal: date [date], prcp [dbl], tmax [dbl], tmin [dbl]
  id            lat  long  elev name              wmo_id ts                
  <chr>       <dbl> <dbl> <dbl> <chr>              <dbl> <list>            
1 ASN00001006 -15.5  128.   3.8 wyndham aero       95214 <tibble [366 × 4]>
2 ASN00002032 -17.0  128. 203   warmun             94213 <tibble [366 × 4]>
3 ASN00003080 -17.6  124.  77.5 curtin aero        94204 <tibble [366 × 4]>
4 ASN00005007 -22.2  114.   5   learmonth airport  94302 <tibble [366 × 4]>
5 ASN00006044 -25.9  114.   9   denham             94402 <tibble [366 × 4]>
# … with 83 more rows

• the spatial data (stations) can be an sf object and temporal data (ts) can be a tsibble object.

• To cast the two separate tables into a cubble, you can supply them in a named list.

• You also need to tell cubble some identifiers it looks for

• The key argument is the spatial identifier that connects the two tables.

• The index argument is the temporal identifier that prescribes the timestamp.

• The coords argument is to used to specify the coordinate

[breath]

• From the cubble header, you can read that the key is id, there are 30 stations and it is in the nested form.

• The third line here shows you the available temporal variables and their types.

• Also, if the spatial and temporal data is an sf or tsibble object, they will be indicated in the header as well.

Switch between the two forms

long form

(weather_long <- weather %>% 
  face_temporal())

# cubble:  date, id [88]: long form
# bbox:    [113.53, -43.49, 153.64, -10.58]
# spatial: lat [dbl], long [dbl], elev [dbl],
#   name [chr], wmo_id [dbl]
  id          date        prcp  tmax  tmin
  <chr>       <date>     <dbl> <dbl> <dbl>
1 ASN00001006 2020-01-01   164  38.3  25.3
2 ASN00001006 2020-01-02     0  40.6  30.5
3 ASN00001006 2020-01-03    16  39.7  27.2
4 ASN00001006 2020-01-04     0  38.2  27.3
5 ASN00001006 2020-01-05     2  39.3  26.7
# … with 32,203 more rows

back to the nested form:

(weather_back <- weather_long %>% 
   face_spatial())

# cubble:   id [88]: nested form
# bbox:     [113.53, -43.49, 153.64, -10.58]
# temporal: date [date], prcp [dbl], tmax [dbl],
#   tmin [dbl]
  id         lat  long  elev name  wmo_id ts      
  <chr>    <dbl> <dbl> <dbl> <chr>  <dbl> <list>  
1 ASN0000… -15.5  128.   3.8 wynd…  95214 <tibble>
2 ASN0000… -17.0  128. 203   warm…  94213 <tibble>
3 ASN0000… -17.6  124.  77.5 curt…  94204 <tibble>
4 ASN0000… -22.2  114.   5   lear…  94302 <tibble>
5 ASN0000… -25.9  114.   9   denh…  94402 <tibble>
# … with 83 more rows

identical(weather_back, weather)

[1] TRUE

• Here is what a cubble look like when being switched between the long and the nested form.

  • With the weather object we just created, we turn it into the long form with the function face_temporal()

• Notice that the third line in the header now changes to see the available spatial variables

[breath]

• On the right, weather_long is switched back the nested form with the function face_spatial()

• As you can see from the last line of code, face_temporal() and face_spatial() are the exact inverse.

• Hence weather_back and weather are identical

Access variables in the other form

Reference temporal variables with $

weather %>% 
  mutate(avg_tmax = mean(ts$tmax, na.rm = TRUE))

# cubble:   id [88]: nested form
# bbox:     [113.53, -43.49, 153.64, -10.58]
# temporal: date [date], prcp [dbl], tmax [dbl], tmin [dbl]
  id            lat  long  elev name              wmo_id ts                 avg_tmax
  <chr>       <dbl> <dbl> <dbl> <chr>              <dbl> <list>                <dbl>
1 ASN00001006 -15.5  128.   3.8 wyndham aero       95214 <tibble [366 × 4]>     36.7
2 ASN00002032 -17.0  128. 203   warmun             94213 <tibble [366 × 4]>     35.8
3 ASN00003080 -17.6  124.  77.5 curtin aero        94204 <tibble [366 × 4]>     35.9
4 ASN00005007 -22.2  114.   5   learmonth airport  94302 <tibble [366 × 4]>     33.2
5 ASN00006044 -25.9  114.   9   denham             94402 <tibble [366 × 4]>     27.1
# … with 83 more rows

Move spatial variables into the long form

weather_long %>% unfold(long, lat)

# cubble:  date, id [88]: long form
# bbox:    [113.53, -43.49, 153.64, -10.58]
# spatial: lat [dbl], long [dbl], elev [dbl], name [chr], wmo_id [dbl]
  id          date        prcp  tmax  tmin  long   lat
  <chr>       <date>     <dbl> <dbl> <dbl> <dbl> <dbl>
1 ASN00001006 2020-01-01   164  38.3  25.3  128. -15.5
2 ASN00001006 2020-01-02     0  40.6  30.5  128. -15.5
3 ASN00001006 2020-01-03    16  39.7  27.2  128. -15.5
4 ASN00001006 2020-01-04     0  38.2  27.3  128. -15.5
5 ASN00001006 2020-01-05     2  39.3  26.7  128. -15.5
# … with 32,203 more rows

• Sometimes, you may need to access variables from the other form for your analysis.

• For example, we may want to calculate some per station summary of the time series data.

• We can refer to the temporal variables from the nested form with the $ sign.

• Here I’m calculating the average maximum temperature across the whole year for each station and I need to get access to tmax from the list-column ts.

• In the long form, you need the cubble verb unfold() to move the spatial variables into the long form.

• Here I move the two coordinate columns into the long form and later we will see how it can help us to create a glyph map.

Why do you need a glyph map?

Here is a typical plot you may have seen when someone tries to visualise their spatio-temporal data. The x and y axes are the coordinates, here I simplify it with only two points, but in reality you may see a collection of points in space or a raster image. Each facet here shows the space in different timestamp and the values are mapped into color.

The problem of this type of visualisation is that it becomes difficult to comprehend the temporal structure of the data since you have to compare points at the same location across panels to digest the pattern.

Why do you need a glyph map?

Instead the temporal pattern is much easier to observe if shown in a time series plot.

What a glyph map do is to put the time series glyph in the place of the location, so you can see the temporal trend in the space.

Glyph map transformation

DATA %>%
  ggplot() +
  geom_glyph(
    aes(x_major = X_MAJOR, x_minor = X_MINOR,
        y_major = Y_MAJOR, y_minor = Y_MINOR)) +
  ...

• I have a short illustration to show you how the transformation works

• Here (1) shows a single station on the map with its long and lat coordinate and (2) is its associated time series.

• Here you know the range of your x and y axis and you can use linear algebra to transform them into a different scale.

• In step (3), the time series in still the same but its scale has been transformed to a width of 1 and heights of 0.3 and the center in this scale is where the original point lays.

• Once we have the time series in the transformed axes, they can be placed onto the map as in (4)

• To make a glyph map, you can use the geom_glyph function from the cubble package.

• It requires a pair of major and a pair of minor variable as required aesthetics

• The major variable are the spatial coordinates, long and lat here and the minor variable are the temporal coordinates, date and tmax here.

Aggregated temp. by month

cb <- as_cubble(
  list(spatial = stations, temporal = ts),
  key = id, index = date, 
  coords = c(long, lat)
)

cb_glyph <- cb %>%
  face_temporal() %>%
  mutate(month = lubridate::month(date)) %>%
  group_by(month) %>% 
  summarise(tmax = mean(tmax, na.rm = TRUE)) %>%
  unfold(long, lat)

cb_glyph %>% 
  ggplot(aes(x_major = long, 
             x_minor = month,
             y_major = lat, 
             y_minor = tmax)) +
  geom_sf(data = oz_simp, fill = "grey90",
          color = "white", inherit.aes = FALSE) +
  geom_glyph_box(width = 1.3, height = 0.5) + 
  geom_glyph(width = 1.3, height = 0.5) + 
  ggthemes::theme_map()

Now with German stations

• This is a full example of using glyph map to explore Australian weather pattern.

• The code has three blocks.

• In the first block we first create a cubble object form the stations and ts data.

• The second block involves wrangling the data using the nested and long form.

• Sampling 20 stations is a spatial operations, so it is performed in the nested form.

• Then we need to do a summary of average maximum temperature by month. It is a temporal operation, so the cubble is then switched to the long form with face_temporal().

• The glyph map requires both the spatial and temporal axes variables as aesthetics, so we move the column long and lat with unfold() into the long form.

• The last chunk shows the ggplot2 code to make the glyph map with geom_glyph()

[breath]

• On the map, you can see that the temperature curve in the north and south (the Tasmania Island) are relative constant throughout the year.

• Those inland stations, for example in the eastern Australia, have a much visible variation in the year, as compared to the coastline ones.

• And remember Australia is in the southern hemisphere, so winter is in the June, July, and August and the temperature is in the U-shape.

Acknowledgements

• The slides are made with Quarto, available at

https://sherryzhang-germany2023.netlify.app

• All the materials used to prepare the slides are available at

https://github.com/huizezhang-sherry/germany2023

Reference

• cubble: https://huizezhang-sherry.github.io/cubble/

• Wickham, H., Hofmann, H., Wickham, C., & Cook, D. (2012). Glyph‐maps for visually exploring temporal patterns in climate data and models. Environmetrics, 23(5), 382-393: https://vita.had.co.nz/papers/glyph-maps.pdf

• This wraps up my talk today.

• Cubble has already made its way to CRAN

• There will be a version update on cubble in the next two weeks, so stay tuned!

• Thanks for listening