Posts for Tag: earth

Visualizing the Variation in Sunlight by Latitude and Time of Year

Posted In: Science
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How does the Earth’s tilt affect sunlight and seasons by latitude?

This visualization looks at the variation in the amount of sunlight different latitudes receive over the different days of the year. The amount of sunlight can be classified in 3 different categories:

  • The number of hours of sunlight received each day
  • The average sunlight intensity (in watts per square meter)
  • The total amount of sunlight received across an entire latitude band (in gigawatt hours)

The default view is to see the number of hours of sunlight received by latitude on the current date, shown by the yellow bars. The sunlight hours range from 0 to 24 hours per day while most latitudes range from 9 to 15 hours.

If you hover over the yellow bars (or click on mobile), you will see the exact number of hours for that latitude band for that date.

Pressing the ‘Start Animation’ button, will change the angle of the sun relative to the Earth (as the earth rotates around the sun) and change the distribution of sunlight across the globe.  You can view this animation with the earth fixed and the sun angle changing (the default view) or with the sun location fixed and the earth’s tilt changing.

This visualization helps to show how the seasons come about. When the Northern Hemisphere is tilted towards the sun, the amount of sunlight it receives increases (hours of daylight, average sun intensity and total amount of sunlight received). As the hemisphere tilts away from the sun, the amount of sunlight it receives decreases. The amount of sunlight a region receives causes the seasons that we experience.

Interestingly, when you are at the equator, the amount of sunlight per day does not really vary too significantly over the course of the year, whereas if you are near the poles, the difference between summer and winter is very dramatic. When looking at total sunlight received, the poles generally have lower sunlight because even in their summer, there is much lower land area relative to the middle latitudes (close to the equator)

The second visualization shown here shows how the tilt of the Earth’s axis is changed over the course of the Earth’s revolution around the sun.  The Earth’s axis is tilted at 23.5 degrees relative to the plane of the Earth’s orbit around the sun. Like the last visualization, you can look at Earth the way we normally do (without the tilted axis) or from the perspective of the sun (with a tilted axis). This makes it a bit clearer why the tilt of the Earth’s axis can change from the north pole angled away to angled towards the sun.

 

Sources and Tools:

The equations for average daily solar insolation come from online lecture notes from University of Albany. The equations for number of hours of daylight comes from Wikipedia.   The visualizations are made using the javascript d3 data visualization library and the interface and animation are made using javascript.

 

daylight hours

What are the highest mountains on Earth? Measuring from sea level vs center of earth

Posted In: Geography
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The Highest Mountains On Earth Depend On How You Measure “High”

Mount Everest is famous for being the highest mountain on Earth. The peak is an incredible 8,848 meters (29,029 ft) above sea level. But that is only one way to measure the height of a mountain. Chimborazo, a mountain in Ecuador, holds the distinction for the mountain whose peak is the furthest from the center of the Earth. How is that possible? This is because the Earth is not a perfect sphere. Rather, due to the spinning of the Earth around it’s axis, the centrifugal force causes the equator to bulge out slightly. This flattened shape is called an oblate spheroid and makes the radius of the earth at the equator about 22 km (about 0.3%) larger than the radius to the poles. Mountains close to the equator will “start” further away from the center of the earth, than those at higher latitudes.

This graph plots over 800 of the highest mountains on Earth with their peak height above sea level on the x-axis and their peak distance from the center of the earth on the y-axis. Each point represents one mountain. The colors of the plots correspond to the latitude of the mountain. These mountains range from 3000 meters in height to 9000 meters in height. You can hover over a data point (or click on mobile) to get more information about the mountain. You can also switch from metric to imperial units with the button on the graph.

For a given mountain range at a certain latitude, you can see that as the mountain heights above sea level increases, so does their distance from the center of the Earth. Mountains in the southern hemisphere are colored in blue, those around the equator are green and yellow, and those in the northern hemisphere are red and orange. The mountains with the highest peaks above sea level are shown on the right side of the graph in red and orange (mostly in the Himalaya), with Mt Everest as the right most point on the graph (nearly 9000 meters tall).

Mountains with peaks the greatest distance from the center of the earth are found near the equator in light green/yellow and are found at the top of the graph. You’ll notice that a number of these mountains are higher than Mt Everest when looking at the distance from the center of the earth.

The Himalayas are the “highest” mountains on earth if you are measuring height from sea level, while the Andes are the “highest” if you measure from the center of the earth.

 

Calculating Distance from Earth’s Center to Mountain Peak

The distance from the center of the Earth is calculated from the following formula:
$$D_{mountain} = H_{mountain} + R_{lat}$$
where $D_{mountain}$ is the distance from center of earth to the top of the mountain, $H_{mountain}$ is the mountain height above sea-level and $R_{lat}$ is the radius of earth at the mountain’s latitude. The height is data that was downloaded from a list of mountain heights.

and the radius of the earth for a given latitude is calculated using the formula:
$$R_{lat}=\sqrt{a^2cos(lat)^2+b^2sin(lat)^2\over acos(lat)^2+bsin(lat)^2)}$$
where $a$ and $b$ are the equatorial and polar radii (6378.137 km and 6356.752 km respectively).
 

Earth Radius Calculator

Here is a calculator for determining the radius of Earth at a given latitude:

You can use this to calculate the distance from the center of the earth to sea level at your latitude.

 

Data and Tools:
Data on the heights of over 800 mountain peaks over 3000 meters in height was downloaded from Wikipedia. There ended up being alot of google searching and data cleaning to get it into suitable format for plotting. The calculations were made with javascript and plotted using plotly, the open source javascript graphing library.

Mountain Height Graph