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Lecture 7
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Data Visualization

Jill P. Naiman

Spring 2020

Lecture 7

Warm-Up Activity

  1. What is the visualization trying to show?
  2. What are its methods?
  3. What are the strengths / weaknesses?

Seismic Sound Lab

In particular: Ground Motions for Hait and Tohoku

Weekly Viz Report

And the winner is...

notes: run the random number generator!

Office Hours this week

Tuesday 3:30pm-?, no office hours on Friday.



FYI: less internet availability during Spring Break

  • email, Slack, etc should all work if you have questions!

Homework over break

  1. Installations & trying some web interfaces out
  2. Extra Credit: Map viz

notes: there will be HW over break, but it will be installing things and trying out some web interfaces.

go to HW!

Where we are: Last week

notes: last week we started thinking a bit about making maps and their projections

Where we are: This week

notes: this week, we will talk more about maps & their projections and play with a few different mapping options in Python

Today's Main Topics

Part 1:

  • Evaluating Visualization Systems - Summary of HW Ideas
  • More on dashboards
  • Beginning map-dashboards with histogramming & bqplot

Part 2:

  • Maps - in more detail
    • Projections
    • Coordinate Systems
    • Infoviz/Choropleth maps
    • Plotting with CartoPy
    • Plotting with ipyleaflet
    • Plotting with geopandas
    • Geojson in general

notes: in more detail: last week we started with maps and how we can use bqplot to do a lot of mapping type stuff

This week we will play with a few different mapping and viz engines and deal with the JSON and geo-json format for storing data




Topic #1: Maps & their projections

Maps

Thinking about map projections is important for GIS data, and generic global info viz.

Let's start by thinking about the fact that...

Maps

Thinking about map projections is important for GIS data, and generic global info viz.

Let's start by thinking about the fact that...

The Earth is a sphere.

(Fun question: to what degree is it a sphere?)

Have you ever wrapped a piece of paper around a ball?

Projections

To map from one system to another, we must "project" from the original sphere to the flat object we are observing.

What are some things we could preserve during such a projection?

notes: One common conversion from sphere to plane is the squashed cylinder approach

This can be used to conserve straight lines (distances)

Projections

notes: There's always a weird way to do it too. Here we're exploding the sphere into lots of mostly planar pieces that we can just lie out side-by-side.

This may preserve shape well, but it will be hard to use to navigate!

Projections: Common Preservations

Typically, one or more of these will be preserved, or at least, the distortion will be minimized:

  • Area
  • Shape (Conformal)
  • Distance

Projections: Common Preservations

Typically, one or more of these will be preserved, or at least, the distortion will be minimized:

  • Area
  • Shape (Conformal)
  • Distance

There are other properties that can be preserved, as well. Typically, maps will be a "compromise" between preserving different properties.

What happens when we preserve one property over another?

Mercator is a "conformal" projection. What is wrong with this?

notes: conformal = shape preserving (at the expense of accurate size)

Projections: Distortions

We can characterize distortions in a projection by examining how a known shape appears on them. The Tissot Ellipse of Distortion is a method of showing this by drawing circles of a fixed radius and examining their elliptical distortion.

notes: so here for example, we see that the mercator projection has circles that stay circles, though they change in relative size depending on where they are on the map

What do you notice?

notes: Greenland and Antarctica are HUGE

notes: this projection is most accurate near the vertical center line

notes: Also known as "equirectangular", this is the favorite format of NASA because it's mathematically straightforward.

Note that the very top line of the image represents a single point on the globe.

notes: this is considered a good compromise between shape-preserving and angle preserving - but it's not perfect at either.

notes: this has even less distortion than mollweide, but the pointy ends don't feel very elegant and planet-like

notes: this is another nightmare scenario like Mercator that was initially created for navigation. Straight lines on this map are the shortest route, but area, shape, and size are distorted.

Discussion

What happens when we make a map that minimizes one region and maximizes another?

Discussion

<iframe width="1024" height="576" src="https://www.youtube.com/embed/vVX-PrBRtTY?rel=0" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

notes: after watching this, it's useful to know that the Peters projection is actually flawed as a teaching tool because of how much it distorts the shapes of countries near the poles.

Discussion

The True Size Of...

notes: Let's go see what Greenland actually looks like -- this was part of the intro, but I'll point it out again so you can really see it!

Discussion

Why is Europe at the center of all the maps we've looked at?

Discussion

notes: there is nothing specifically wrong with putting a pole at the center of the map

Discussion

notes: also see here that now the equator is very distorted

Discussion

notes: or why bother having a spherical or rectangular shape at all?

Discussion

notes: look how here there is very little distortion of size or shape

Maps: Coordinate Systems

Once we have our system of transformation, we need to have a method of representing positions.

Three common baseline methods:

  • Spherical coordinates
  • Latitude and Longitude
  • Degrees, minutes, seconds

Take care with:

  • Zero points
  • North/South, East/West
  • Ranges



Topic #2: Formatting for shape data

JSON & GeoJSON

notes: json is meant to be a way to store data that is "query" based - i.e. it lends itself to searches well

for this reason, it shows up in web development a lot

GeoJSON

notes: geojson is just a special json formatting for geographical data

it will specify the "shape" of the data file but also things like its default coordinate reference system which tells you something about the "center" and "stretch" of whatever it lists in its coordinates

GeoJSON

GeoJSON is:

  • data format for encoding geographic data structures
  • uses "geometries", "features" and "collections of features"
  • seven Geometry types/objects
    1. Point
    2. LineString
    3. Polygon
    4. MultiPoint
    5. MultiLineString
    6. MultiPolygon
    7. GeometryCollection
drawing

notes: cite: https://image.slidesharecdn.com/geojson-170417122110/95/geojson-1-638.jpg?cb=1492431924

We will see a lot of Polygons & MultiPolygons.

GeoJSON

Tips for dealing with GeoJSON:

  • use .keys() and progressively drill down to data of interest
  • look for location of properties and features

We will get practice at this during programming.

notes: often our issue will be linking the information stored in JSON file formats with that of whatever plotting routine we are using

we'll get some practice with this in the coding portion of class




Topic #3: Data & Viz Engines

Access to geometry files

  1. Cartopy
  2. ipyleaflet
  3. GeoPandas

Intro to cartopy

CartoPy is a toolkit that builds on matplotlib to create fast, easy map representations.

We will be relying on three key concepts:

  • Axes projections (similar to our polar projections)
  • Coordinate representations
  • Shapes

Using these, we will be able to build out many visualizations.

CartoPy: Projections

We start out by constructing an axes in CartoPy that uses a given projection:

import cartopy
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.add_subplot(111, projection=cartopy.crs.Mollweide())
ax.coastlines()

CartoPy: Coordinate Reference Systems

Transforming from a spherical reference system to a flat reference system is the job of the projection; transforming from one discretization of a sphere to another is the job of the coordinate system.

We can utilize Coordinate Reference Systems to describe the input coordinate system and the rasterization system are described.

For example, there are several different ways to draw "straight" lines. We can do both PlateCarree and Geodetic.

c_lat, c_lon = 40.1164, -88.2434
a_lat, a_lon = -18.8792, 47.5079
fig = plt.figure()
ax = fig.add_subplot(111, projection = cartopy.crs.PlateCarree())
ax.gridlines()
ax.coastlines()
ax.set_global()
ax.plot([c_lon, a_lon], [c_lat, a_lat], transform = cartopy.crs.PlateCarree())
ax.plot([c_lon, a_lon], [c_lat, a_lat], transform = cartopy.crs.Geodetic())

notes: the blue line is Plate Carree, which maintains a straight line on the lat-lon grid

the orange line is Geodetic, which maintains a straight line around the curvature of the Earth

notes: now even the blue line has some curvature because we are picking a best-of-both-worlds Mollweide projection that doesn't perfectly preserve angle or area.

ipyleaflet

Leaflet is another mechanism of plotting, displaying and interacting with maps.

We will very briefly play with this in Python - could be of use for those that were having issues with cartopy.

Geopandas

notes: the calls for geopandas is going to look very similar to pandas calls!

Geopandas

gdf = geopandas.read_file('mapfile.geojson')
gdf.head()
gdf.plot()

Geopandas

gdf = geopandas.read_file('mapfile.geojson')
gdf.head()
gdf.plot()

Map information sources:

Other Map Viz

  • Google Maps & Earth
  • WorldWide Telescope
  • CesiumJS
  • bqplot
  • Vega & friends

To Python!