Data Visualization #14—Using python to create animated charts

In my previous post I noted that I would provide python code for the chart that is in the post. The chart was created using R statistical software, and the code for the python version can be found at the end of this post.

I find python a bit less intuitive than R but that’s most likely because I’ve been using R for a very long time and python for less long. There are reasons, I suppose, to favour one over the other, but for statistical analysis and data analysis I don’t necessarily see an advantage of one over the other. That being said, it is my sense that R does a better job of standardizing across various operating systems, which can be very helpful when you are a Linux user, as am I.

import numpy as np
import matplotlib.pyplot as plt
import networkx as nx
from matplotlib.animation import FuncAnimation 
plt.style.use('ggplot') # this is to make the plot look like an R ggplot

# a roulette array
roulette = np.append(np.array([0, 0]),np.arange(1, 37))
spins1000 = np.array(np.random.choice(roulette, size=(1000)))

# Define a cumulative mean function
def cum_mean(arr):
    cum_sum = np.cumsum(arr)
    return cum_sum / (np.arange(1, cum_sum.shape[0] + 1))     # as far as I can tell, matplotlib doesn't have a cumulative mean function; so I created one.


fig = plt.figure()
ax1 = fig.add_subplot(2, 1, 2)
ax2 = fig.add_subplot(2, 1, 1)
fig.tight_layout(pad=3.0)
fig.suptitle('Short-term Randomness versus Long-term Predictability', fontsize=14) 
ax2.set_xlabel('$n^th$ spin of roulette wheel')
ax2.set_ylabel('Value of $n^{th}$ spin')
ax2.set_xlim(0, 1000)
ax2.set_ylim(0, 37)

ax1.set_xlabel('$n^{th}$ spin of the roulette wheel')
ax1.set_ylabel('Cumulative mean of n spins')
ax1.set_xlim(0, 1000)
ax1.set_ylim(0, 37)

line, = ax1.plot([], [], lw=1.5)
scat, = ax2.plot([], [], 'o', markersize=2)

def init():
    line.set_data([], [])
    scat.set_data([], [])
    return line, scat,

def animate(i):
    x = np.linspace(0, 250, 250)
    y1 = cum_mean(spins1000)
    y2 = spins1000
    line.set_data(x[:i], y1[:i])
    scat.set_data(x[:i], y2[:i])
    return line, scat,

anim = FuncAnimation(fig, animate, init_func=init, frames=1000, interval=10, blit=True, save_count=1000)

plt.show()

anim.save('roullete_python.mp4') # saving as .mp4 because python creates massive gif files.

Data Visualization #13—Roulette and Temperature with R code

In the most recent post in my data visualization series I made an analogy between climate, weather and the spins of a roulette wheel that demonstrated that short-term randomness does not mean we can’t make accurate long-term predictions.

Towards the end of the post I appended an animation of 1000 random spins of a roulette wheel. In that post, I plotted the 1000 individual outcomes of these random spins of the roulette wheel. I chose to show only one outcome at a time as the animation cycled through all 1000 spins. In this post, I wanted to show you how to keep all of the outcomes from disappearing. Rather than having the value of each spin appear, and then disappear, I will change the code slightly to have every spin’s outcome stay on the plot, but faded so that the focus remains on the next spin value. Here’s what I mean.:

Created by Josip Dasović

Here is the R code for the image above:

## These are the packages needed to draw, and animate, the plots.
library(ggplot2)
library(gganimate)
library(dplyr)  # needed for cummean function

## Set up a data frame for the 1000 random spins of the roulette wheel

mywheel <-c(rep(0,2),1:36)  # a vector with the 38 wheel values
wheel.df<-data.frame("x"=1:1000,"y"=sample(mywheel,1000,rep=T))

## Plot, then animate the result of 1000 random spins of the wheel

## the code to plot
gg.roul.1000.point<- ggplot(wheel.df,aes(x, y, colour = "firebrick4")) + 
  geom_point(show.legend = FALSE, size=2) +
  theme_gray() + 
  labs(title = "1000 Random Spins of a Roulette Wheel", 
       x = expression("the"~n^th~"roll of the wheel"), 
       y = 'Value of a single spin') +
  theme(plot.title = element_text(hjust = 0.5, size = 14, color = "black")) +
  scale_y_continuous(expand = c(0, 0)) +
  transition_time(wheel.df$x) +
  shadow_mark(past = T, future=F, alpha=0.2)

## the code to animate
gg.roul.anim.point <- animate(gg.roul.1000.point, nframes=500, fps=25, width=500, height=280, renderer=gifski_renderer("gg_roulette_1000.gif"))  
 
## No plot and animate a line chart that depicts the cumulative mean from spin 1 to spin 1000.

gg.roul.1000.line <- ggplot(wheel.df, aes(x, y = cummean(y))) +
  geom_line(show.legend = FALSE, size=1, colour="firebrick4") +
  theme_gray() +
  ggtitle("Cumulative Mean of Roulette Wheel Spins is Stable over Time") +
  theme(plot.title = element_text(hjust = 0.5, size = 14, color = "black")) +
  labs(x = expression("the"~n^th~"roll of the wheel"), 
       y = 'Running (i.e., cumulative) Mean of all Rolls at Roll n') +
  scale_y_continuous(expand=c(0,0), limits=c(0,36)) +
  transition_reveal(wheel.df$x) +
  ease_aes('linear') 

gg.roul.anim.line <- animate(gg.roul.1000.line, nframes=500, fps=25, width=500, height=280, renderer=gifski_renderer("cummean_roulette_1000.gif"))  

## Now combine the plots into one figure, using the magick library

library(magick)

a_mgif <- image_read(gg.roul.anim.point)
b_mgif <- image_read(gg.roul.anim.line)

roul_gif <- image_append(c(a_mgif[1], b_mgif[1]),stack=TRUE)
for(i in 2:500){
  combined <- image_append(c(a_mgif[i], b_mgif[i]),stack=TRUE)
  roul_gif <- c(roul_gif, combined)
}

## Save the final file as a .gif file

image_write(roul_gif, "roulette_stacked_point_line_500.gif")

Stay tuned for a Python version of this chart.

Data Visualization # 12—Using Roulette to Deconstruct the ‘Climate is not the Weather’ response to climate “deniers”

If you are at all familiar with the politics and communication surrounding the global warming issue you’ll almost certainly have come across one of the most popular talking points among those who dismiss (“deny”) contemporary anthropogenic (human-caused) climate change (I’ll call them “climate deniers” henceforth). The claim goes something like this:

“If scientists can’t predict the weather a week from now, how in the world can climate scientists predict what the ‘weather’ [sic!] is going to be like 10, 20, or 50 years from now?”

Notably, the statement does possess a prima facie (i.e., “commonsensical”) claim to plausibility–most people would agree that it is easier (other things being equal) to make predictions about things are closer in time to the present than things that happen well into the future. We have a fairly good idea of the chances that the Vancouver Canucks will win at least half of their games for the remainder of the month of March 2021. We have much less knowledge of how likely the Canucks will be to win at least half their games in February 2022, February 2025, or February 2040.

Notwithstanding the preceding, the problem with this denialist argument is that it relies on a fundamental misunderstanding of the difference between climate and weather. Here is an extended excerpt from the US NOAA:

We hear about weather and climate all of the time. Most of us check the local weather forecast to plan our days. And climate change is certainly a “hot” topic in the news. There is, however, still a lot of confusion over the difference between the two.

Think about it this way: Climate is what you expect, weather is what you get.

Weather is what you see outside on any particular day. So, for example, it may be 75° degrees and sunny or it could be 20° degrees with heavy snow. That’s the weather.

Climate is the average of that weather. For example, you can expect snow in the Northeast [USA] in January or for it to be hot and humid in the Southeast [USA] in July. This is climate. The climate record also includes extreme values such as record high temperatures or record amounts of rainfall. If you’ve ever heard your local weather person say “today we hit a record high for this day,” she is talking about climate records.

So when we are talking about climate change, we are talking about changes in long-term averages of daily weather. In most places, weather can change from minute-to-minute, hour-to-hour, day-to-day, and season-to-season. Climate, however, is the average of weather over time and space.

The important message to take from this is that while the weather can be very unpredictable, even at time-horizons of only hours, or minutes, the climate (long-term averages of weather) is remarkably stable over time (assuming the absence of important exogenous events like major volcanic eruptions, for example).

Although weather forecasting has become more accurate over time with the advance of meteorological science, there is still a massive amount of randomness that affects weather models. The difference between a major snowstorm, or clear blue skies with sun, could literally be a slight difference in air pressure, or wind direction/speed, etc. But, once these daily, or hourly, deviations from the expected are averaged out over the course of a year, the global mean annual temperature is remarkably stable from year-to-year. And it is an unprecedentedly rapid increase in mean annual global temperatures over the last 250 years or so that is the source of climate scientists’ claims that the earth’s temperature is rising and, indeed, is currently higher than at any point since the beginning of human civilization some 10,000 years ago.

Although the temperature at any point and place on earth in a typical year can vary from as high as the mid-50s degrees Celsius to as low as the -80s degrees Celsius (a range of some 130 degrees Celsius) the difference in the global mean annual temperature between 2018 and 2019 was only 0.14 degrees Celsius. That incorporates all of the polar vortexes, droughts, etc., over the course of a year. That is remarkably stable. And it’s not a surprise that global mean annual temperatures tend to be stable, given the nature of the earth’s energy system, and the concept of earth’s energy budget.

In the same way that earth’s mean annual temperatures tend to be very stable (accompanied by dramatic inter-temporal and inter-spatial variation), we can see that the collective result of many repeated spins of a roulette wheel is analogously stable (with similarly dramatic between-spin variation).

A roulette wheel has 38 numbered slots–36 of which are split evenly between red slots and black slots–numbered from 1 through 36–and (in North America) two green slots which are numbered 0, and 00. It is impossible to determine with any level of accuracy the precise number that will turn up on any given spin of the roulette wheel. But, we know that for a standard North American roulette wheel, over time the number of black slots that turn up will be equal to the number of red slots that turn up, with the green slots turning up about 1/9 as often as either red or black. Thus, while we have no way of knowing exactly what the next spin of the roulette wheel will be (which is a good thing for the casino’s owners), we can accurately predict the “mean outcome” of thousands of spins, and get quite close to the actual results (which is also a good thing for the casino owners and the reason that they continue to offer the game to their clients).

Below are two plots–the upper plot is an animated plot of each of 1000 simulated random spins of a roulette wheel. We can see that the value of each of the individual spins varies considerably–from a low of 0 to a high of 36. It is impossible to predict what the value of the next spin will be.

The lower plot, on the other hand is an animated plot, the line of which represents the cumulative (i.e. “running”) mean of 1000 random spins of a roulette wheel. We see that for the first few random rolls of the roulette wheel the cumulative mean is relatively unstable, but as the number of rolls increases the cumulative mean eventually settles down to a value that is very close to the ‘expected value’ (on a North Amercian roulette wheel) of 17.526. The expected value* is simply the sum of all of the individual values 0,0, 1 through 36 divided by the total number of slots, which is 38. Over time, as we spin and spin the roulette wheel, the values from spin-to-spin may be dramatically different. Over time, though, the mean value of these spins will converge on the expected value of 17.526. From the chart below, we see that this is the case.

Created by Josip Dasović

Completing the analogy to weather (and climate) prediction, on any given spin our ability to predict what the next spin of the roulette wheel will be is very low. [The analogy isn’t perfect because we are a bit more confident in our weather predictions given that the process is not completely random–it will be more likely to be cold and to snow in the winter, for example.] But, over time, we can predict with a high degree of accuracy that the mean of all spins will be very close to 17.526. So, our inability to predict short-term events accurately does not mean that we are not able to predict long-term events accurately. We can, and we do. In roulette, and for the climate as well.

TLDR: Just because a science can’t predict something short-term does not mean that it isn’t a science. Google quantum physics and randomness and you’ll understand what Einstein was referring to when he quipped that “God does not play dice.” Maybe she’s a roulette player instead?

  • Note: This is not the same as the expected dollar value of a bet given that casinos generate pay-off matrixes that are advantageous to themselves.

Nicholas Stern (of the Report) argues that climate agreement should not be legally binding

We used the last session of IS450 as a chance to hold a mock United Nations climate conference simulation. The participants brought forward many intriguing and instructive topics, and I applaud them for putting in the time and energy to make the simulation as successful as I, at least, judged it to be. At some point during the proceedings, there was majority agreement (finally!) on one small element of the overall framework resolution. Interestingly, though, immediately upon the successful passing of that small piece of the framework a couple of delegates put forward a motion to make the obligations legally binding. A heated discussion ensued debating the merits and disadvantages of such an approach.

In the current round of UNFCCC climate negotiations, behind held in Lima, Peru, Nicholas Stern (author of the well-known Stern Review Report on the Economics of Climate Change) has argued against making international climate treaty obligations legally binding. What is Lord Stern’s rationale for this?

“Some may fear that commitments that are not internationally legally-binding may lack credibility,” he said.

“That, in my view, is a serious mistake. The sanctions available under the Kyoto Protocol, for example, were notionally legally-binding but were simply not credible and failed to guarantee domestic implementation of commitments.”

In Lima, negotiators are trying to hammer out the format that mitigation efforts should take. By the end of March next year countries have to declare their hands, but they have yet to formalize what will be included in these commitments and what will not.

Lord Stern believes that grounding the process in the laws and promises that countries undertake by themselves is a better model for a deal than a top-down process like Kyoto.

“It will be enforceable and deliverable through the arrangements and laws in the countries themselves.

“That way you will get stronger ambition as countries won’t be tempted to be hesitant about some type of international sanction.”

What do you think about Lord Stern argument? Would you support voluntary obligations over mandatory ones?

Here is an interview with Lord Stern from earlier this week in Lima, wherein he speaks on the link between economic growth, development, and better climate responsibility?

 

UN Secretary-General Ban Ki-Moon Interviewed on Canadian Television

Host Peter Mansbridge, of the Canadian Broadcasting Coroporation’s (CBC) evening news program, The National, interviewed United Nations Secretary-General Ban Ki-Moon earlier this week on issues related to climate change and the Alberta oil sands. (I’ll have more next week about the anti-pipeline protests on Burnaby Mountain (in the vicinity of SFU) next week.)

Here are some excerpts:

Ban Ki-Moon: I know the domestic politics in Canada and Australia…but this is a global issue.

Peter Mansbridge: But the Canadian argument has always been, if everybody’s not in, we’re not in. [This obviously refers to the Kyoto Protocol’s division of countries into those that are required to make cuts (so-called Annex I countries) and those (mostly ‘developing’ countries) that do not.]

Ban Ki-Moon: China and [the] United States have taken such a bold initiative, Germany has been a leading country now, and [in] the European Union, twenty-eight countries have shown solidarity and unity. Therefore, it is only natural that Canada as one of the G-7 countries should take a leadership role.

The Secretary-General also spoke about the Alberta oil sands, which have been in the news lately in our part of the world as the result of protests aimed at Kinder Morgan over its plans to increase (three-fold) the flow of tar sands oil (bitumen) through an existing pipeline that runs through Burnaby Mountain to waiting oil tankers in Vancouver’s Burrard Inlet, to almost one million barrels per day.

Peter Mansbridge: Should Canadians, or the Canadian government, look beyond the oil sands to make its decisions about climate change?

Ban Ki-Moon: Energy is a very important, this is a cross-cutting issue. There are ways to make transformative changes from a fossil fuel-based economy to a climate-resilient economy by investing wisely in renewable energy resources.

Peter Manbridge: So back away from…

Ban Ki-Moon: Yes, Canada is an advanced economic country…you have many technological innovations, so with the technological innovation and financial capacity, you have many ways to make some transformative changes.

This is the key; the political and societal will has to be created and sustained to force our leaders to make the requisite changes, which will move our country towards an economy that is climate-resilient. An economically-sustainable future and economic well-being are not mutually exclusive. Indeed, there is every reason to believe that not not only are they not mutually exclusive, but that that each is necessary for the other. If we don’t start moving away from our “extractivist economic structure”, we in Canada face the prospect of a future with tremendous ecological and environmental degradation coupled with economic despair, when our leaders finally realize that rather than using our current wealth to innovate away from the extraction and toward energy innovation, we have squandered our wealth on fining ever cheaper ways to dig up crap that the world no longer wants to buy.

“Polluted and poor”–how’s that for a political campaign slogan?

Vancouver Archipelago–what will happen when Greenland and Antartic Ice Sheets melt

This blog is back from an end-of-semester-induced slumber with some important posts. Here is post, the first:

Here’s an intriguing map, posted on the spatialities.com web site.  It shows what Vancouver would look like with an expected 80-meter sea-level rise, which is what the United States Geological Survey predicts would happen were the Antarctic and Greenland ice sheets to melt completely (remember that these are land-based ice sheets).

Most of the current global land ice mass is located in the Antarctic and Greenland ice sheets (table 1). Complete melting of these ice sheets could lead to a sea-level rise of about 80 meters, whereas melting of all other glaciers could lead to a sea-level rise of only one-half meter.

Don’t go and sell your Fairview condo just yet, however, as this scenario is not projected to complete for between 1,000 and 10,000 years. Of course, this is a process that develops incrementally (though not linearly) over time and the city would be deeply affected adversely with only a fraction of that projected rise in sea levels.

For those who may doubt that the world’s glaciers are melting, here is video of the largest glacier ‘calving’ event ever caught on film. The end of the clip demonstrates the extent of change in the rate of melting and glacial retreat over the last century. Just watch!

‘Game-changing’ news regarding climate change?

You may also have awoken this morning to reports of  a potentially ‘game-changing’ deal between the United States and China, which pledges to reduce greenhouse gas (GHG) emissions. [Note: the US media likes to use the sports-derived phrase ‘game-changing’ to refer to significant events.]  This is certainly a significant development in the politics of climate change. Indeed, the two countries are the world’s largest emitters of GHGs and until today the two have been engaged in a game of what Paul Harris has called “you go first!” From the looks of it, they have both chosen to ‘go first’.

According to news reports, here are some of the details:

[President] Obama is setting a new target for the U.S., agreeing to cut greenhouse gas emissions to 26 to 28 percent below 2005 levels by 2025. The current U.S. target is to reach a level of 17 percent below 2005 emissions by 2020…

[President] Xi committed China to begin reducing its carbon dioxide emissions, which have risen steadily, by about 2030, with the intention of trying to reach the goal sooner, according to a statement released by the White House.

China, the world’s largest greenhouse-gas emitter, also agreed to increase its non-fossil fuel share of energy production to about 20 percent by 2030, according to the White House.

Is the negotiated agreement ideal? Not nearly. China will still be increasing its total GHG emissions until about 2030. Despite this, however, the deal has been met with some praise from environmental groups for the symbolic significance of the deal, which makes the potential for getting a positive deal agreed in Paris next year more likely.

Jake Schmidt, director of international programs for the Natural Resources Defense Council, a Washington-based environmental group, said no other countries can have as big an impact on the climate debate as the U.S. and China.

“They shape how the market invests,” he said. “They’ve also been two of the most difficult players in the history of the climate negotiations so the fact that they are coming out and saying they are going to take deep commitments will be a powerful signal to the rest of the world.”

Of course, not everyone is happy. Soon-to-be US Senate Majority Leader, Mitch McConnell (R-KY) is outraged:

mcconelll climate change

US Midterm Election Results and Climate Change

Election results in the United States are mostly final and the Republican Party has had a big night, capturing control of the US Senate, which combined with a Republican-controlled House of Representative means that President Barack Obama will face a united (in party name, at least) Republican Congress upon the opening of the new Congressional session–the 114th–which meets for the first time in early January of next year.

The New York Times has a handy graphic, summarizing the disconcerting results (from the perspective of climate change politics) of exit polls earlier today. This seems to be disheartening news to those who wish to see the United States government become more proactive in the are of climate politics and climate change. As you can see, while six in 10 voters said that climate change is a problem, fully 83\% of the partisans of the majority party in Congress believe the same.

us_midterm_elections_exit_polls_climatechange

Canadian Minister Aglukkaq’s Opening Statement at the 19th COP in Warsaw

In a couple of weeks time, we will be finishing up the course with a UN simulation. Each of the participants will be required to give a 1-minute (maximum!) opening presentation to the conference. Here is the opening statement of Honourable Leona Aglukkaq, Minister of the Environment, Minister of the Canadian Northern Economic Development Agency and Minister for the Arctic Council, to the 19th Conference of the Parties (COP19) to the United Nations Framework Convention on Climate Change (UNFCCC) held in Warsaw, Poland in 2013. Your opening statements should follow a similar structure (but not length!).

Domestic Politics and Climate Change

Last week we discussed the role of domestic politics–institutions, electoral systems, partisanship, etc.,–on national political leaders’ attitudes towards and policies on climate change. We noted that the Canadian federal governments stance toward mitigation and adaptation changed dramatically upon the ascension of the Conservatives to power in 2006 (a minority government). The majority government that Harper was able to win in 2011 signalled the death knell for Canada’s involvement in the Kyoto process as Harper’s government reneged on Canada’s obligations quickly thereafter.

The United States, meanwhile, enters the final week of the biennial “midterm elections”, with most candidates (and the public) focused on issues other than climate change. When climate change is mentioned, however, the candidates responses are not reassuring. Have a look at this video for an impressive compilation of candidates’ responses to whether they believe in the existence of anthropogenic climate change. Incidentally, for a comprehensive debunking of Representative Steve Pearce’s claim that 31,000 scientists signed a petition claiming that there was no global warming, click here.