Posts for Tag: graphics

Visualizing The Growth of Atmospheric CO2 Concentration

Posted In: Environment
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The current CO2 concentration in the atmosphere is over 400 parts per million (ppm). This has grown about 46% since pre-industrial levels (~280 ppm) in the early 1800s. The growing concentration of CO2 is a big concern because it is the most prevalent greenhouse gas, which is increasing the temperature of the planet and leading to substantial changes in the Earth’s climate patterns.

This graph visualizes the growth in CO2 concentration in the atmosphere (mainly from CO2 emissions due to human activities, such as burning fossil fuels for energy production, deforestation and other industrial processes). The graph starts at 1980 when CO2 concentration in the atmosphere was around 340ppm. It has grown significantly since then.

One of the interesting aspects of CO2 concentration is that it is not identical all around the globe, as it takes awhile for the atmosphere to mix. The graph shows geographic differences in CO2 concentration as well as seasonal ups and downs, that underly an overall growing trend in annual average (mean) concentration.

Seasonal trends in CO2 concentration occur due to differences in the amount of plant growth across different months. Spring and summer plant growth in the northern hemisphere causes a significant amount of photosynthesis, and CO2 absorption, relative to the fall and winter. This plant growth causes a very large amount of CO2 to be absorbed by plants and a noticeable reduction in the amount of CO2 in the atmosphere. The southern hemisphere spring and summer (northern hemisphere fall and winter) aren’t as obvious because there is much less land in the southern hemisphere and the land that is there is close to the tropics and green all year round.

CO2 concentration can change by about 4-5 ppm due to the “breathing” of plants, which is pretty significant. The total weight of CO2 in the atmosphere is about 3 trillion tonnes of CO2, so 4-5 ppm is about 1% of this or 30 billion tons of CO2 removed by plant life each spring/summer.

Data and Tools:

Data comes from the US National Oceanic and Atmospheric Administration (NOAA). Data was downloaded using an automated python script and the graphs were made using javascript and the open-sourced Plot.ly javascript engine.

CO2 concentration graph

Assembling the World Country-By-Country

Posted In: Maps
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Watch the world assemble country-by-country based on a specific statistic



This map lets you watch as the world is built-up one country at a time. This can be done along the following statistical dimensions:

  • Country name
  • Population – from United Nations (2017)
  • GDP – from United Nations (2017)
  • GDP per capita
  • GDP per area
  • Land Area – from CIA factbook (2016)
  • Population density
  • Life expectancy – from World Health Organization (2015)
  • or a random order

These statistics can be sorted from small to large or vice versa to get a view of the globe and its constituent countries in a unique and interesting way. It’s a bit hypnotic to watch as the countries appear and add to the world one by one.

You can use this map to display all the countries that have higher life expectancy than the United States:
select “Life expectancy”, sort from “high to low” and use the scroll bar to move to the United States and you’ll get a picture like this:
Countries with higher life expectancy than US

or this map to display all the countries that have higher population density than the United States:
select “Population density, sort from “high to low” and use the scroll bar to move to the United States and you’ll get a picture like this:
Countries with higher population density than US

I hope you enjoy exploring the countries of the world through this data viz tool. And if you have ideas for other statistics to add, I will try to do so.

Data and tools: Data was downloaded primarily from Wikipedia: Life expectancy from World Health Organization (2015) | GDP from United Nations (2017) | Population from United Nations (2017) | Land Area from CIA factbook (2016)
The map was created with the help of the open source leaflet javascript mapping library

Estimating pi (π) using Monte Carlo Simulation

Posted In: Math
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This interactive simulation estimates the value of the fundamental constant, pi (π), by drawing lots of random points to estimate the relative areas of a square and an inscribed circle.

Pi, (π), is used in a number of math equations related to circles, including calculating the area, circumference, etc. and is widely used in geometry, trigonometry and physics.

This app estimates the value of pi by comparing the area of a square and an inscribed circle. The areas are calculated by randomly placing dots into the square and then counting how many of them are also inside the circle. If you do this enough times, you will get a rough ratio of the relative areas of the two shapes. These points are plotted on the graph (red if the fall inside the circle and blue if the fall outside).

Also shown on the graph is the value of our estimate of pi as the simulation progresses, from a few points to many thousands, to millions of points. We can see that when we have only a few points, the value may not be very accurate but as the number of points increases the value of our estimate gets closer to the true value. Running the simulation will add and plot 1 million points. After the first 100 points are added, the rate at which points are added increases. You’ll notice this as the speed at which dots fills up the square increases and because the plot is shown with a logarithmic x-axis.

Here is the math:
Length of side of square: $2 \times r$
radius of circle: $r$
Area of square: $A_{square} = 4r^2$
Area of circle: $A_{circle} = \pi r^2$

The ratio of areas is $A_{circle}/A_{square} = \pi r^2 / 4r^2 = \pi / 4$
Solving for pi: $\pi = 4 \times A_{circle}/A_{square} \approx 4 \times N_{dots_{circle}}/N_{dots_{square}}$
So pi is estimated as 4 times the ratio of dots in the circle vs square

Tools:
This was programmed in javascript, canvas and plotted using the open source plotly javascript plotting library.
estimating pi using monte carlo

Current Bay Area Air Quality

Posted In: Environment | Health
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Fires are once again raging in California and air quality in one of the most populated metropolitan areas in the country (the San Francisco Bay Area) is quite poor. This map show current air quality in the Bay Area. For more information see the EPA’s Air Quality website.

AQI colors

EPA has assigned a specific color to each AQI category to make it easier for people to understand quickly whether air pollution is reaching unhealthy levels in their communities. For example, the color orange means that conditions are "unhealthy for sensitive groups," while red means that conditions may be "unhealthy for everyone," and so on.

Air Quality Index
Levels of Health Concern
Numerical
Value
Meaning
Good 0 to 50 Air quality is considered satisfactory, and air pollution poses little or no risk.
Moderate 51 to 100 Air quality is acceptable; however, for some pollutants there may be a moderate health concern for a very small number of people who are unusually sensitive to air pollution.
Unhealthy for Sensitive Groups 101 to 150 Members of sensitive groups may experience health effects. The general public is not likely to be affected.
Unhealthy 151 to 200 Everyone may begin to experience health effects; members of sensitive groups may experience more serious health effects.
Very Unhealthy 201 to 300 Health alert: everyone may experience more serious health effects.
Hazardous 301 to 500 Health warnings of emergency conditions. The entire population is more likely to be affected.

For more information and additional maps see the EPA’s Air Quality website.

Should You Invest (Or Wait) When The Stock Market Is At An All-Time-High?

Posted In: Financial Independence | Money
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The stock market has been on a bull run (hitting numerous all time highs) for the last 8+ years and it’s not clear when it will end. Whenever there’s been an extended bull run, one question that comes to mind “Should I invest in the market now, or wait until a pullback?” The question comes about because of fear and loss aversion: fear that the market will drop right after they invest and the observation that people want to avoid losses more than they value gains. However, historically, the correct answer, at least over the last 69 years, has been to invest and not to try to time the market.

This was also demonstrated in the Market Timing Game; that people are pretty bad at predicting the direction of the markets and given the upward trend of the market, it’s simpler and more likely than not, better to just stay invested in the market. The corollary to this is that when you have additional money to invest (e.g. from regular savings from your paycheck or a one-time event like the sale of a house), it makes sense to invest the money and not worry about whether the market is at a high or low point. Some graphs that look at the distribution of returns when the market is at an all time high (ATH) can help answer this question of whether you expect to see worse returns than investing at other times.
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Shall We Play A (Market Timing) Game?

Posted In: Financial Independence | Money
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The Market Timing Game simulation is premised on the idea that buying-and-holding index investing and index funds are a no-brainer investment strategy and market timing (i.e. trying to predict market direction and trading accordingly) is a less than optimal strategy. The saying goes “Time in the market not timing the market”. In this simulation, you are given a 3-year market period from sometime in history (between 1950 and 2018) or you can run in Monte Carlo mode (which picks randomly from daily returns in this period) and you start fully invested in the market and can trade out of (and into) the market if you feel like the market will fall (or rise). The goal is to see if you can beat the market index returns.
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