The Science and Mathematics of Earth’s Temperatures – Part 2

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The Science and Mathematics
of Earth’s Temperatures
Part 2


 

This article is Part 2, in a series of articles.

You can read Part 1 of this article, at:
https://agree-to-disagree.com/the-science-and-mathematics-of-earths-temperatures

To summarise Part 1:

I have recently downloaded actual absolute temperature data, for over 24,000 real locations on the Earth (it took me about 7 days to download it).

Not just average temperatures, but

  • yearly and monthly average temperatures
  • yearly and monthly average high temperatures
  • yearly and monthly average low temperatures
  • some yearly and monthly record high temperatures
  • some yearly and monthly record low temperatures

I have analysed this data, and developed 3 or 4 new types of graph, to show people the data.

I have written 4 articles based on this temperature data, so far.

https://agree-to-disagree.com/how-far-to-reverse-global-warming

https://agree-to-disagree.com/gw-temperature-distributions-1

https://agree-to-disagree.com/the-comb-of-death

https://agree-to-disagree.com/the-upside-down-comb-of-death

This article will be the 5th article to analyse this temperature data. However, this article will be quite different to the previous 4 articles. This article will use linear regressions, to develop a global temperature model of the Earth. This model will be used to predict:

  • the average temperature, of every country on Earth
  • the temperature of the coldest month, of every country on Earth
  • the temperature of the hottest month, of every country on Earth

The temperature model of the Earth will be based on 4 factors:

  • the average latitude of the country
  • the average longitude of the country
  • the average elevation of the country
  • the area of the country

I am sure that many people will expect my temperature model of the Earth to be very inaccurate.

Let me give you a quick summary of what I have achieved, using just these 4 factors. I have been able to explain:

  • over 94% of the variation in the average temperature, of every country on Earth
  • over 90% of the variation in the temperature of the coldest month, of every country on Earth
  • about 59% of the variation in the temperature of the hottest month, of every country on Earth

I consider these results to be quite astonishing. When I started, I would have been very happy to explain 60% to 80% of the variation in these temperatures.

Instead, I have achieved R-squared values of about 0.94, 0.90, and 0.59, between the model’s estimates of the temperatures, and the actual temperature data that I have downloaded.

In case you think that I am just talking about a few countries, let me state clearly, that I am talking about a total of 216 different countries. Big and small, narrow and wide, over all latitudes and longitudes, over all elevations, and of many different areas.

I have included all countries that I could get data for. For some strange reason, there is no data for Poland. I don’t know why. I had to rely on the website that I downloaded the temperature data from.

Because of the size of this project, I expect to write a series of articles, examining different aspects of the temperature model of the Earth.


In Part 2 of this article, I will show some graphs which prove how accurate my temperature model of the Earth is.

I will then reveal the secret of why my temperature model of the Earth is so accurate, but also very simple.

 

 

Graph Average

 

Graph Coldest

 

Graph Hottest

 

The previous graph shows that the temperature model of the Earth for the hottest month, is not as accurate as the average temperature, or the coldest month temperature.

Looking at the hottest month graph, it is fairly obvious why this is. There are quite a few countries which have a hottest temperature which is significantly hotter, than the estimated hottest temperature.

What would cause this? The following table shows these hotter countries.

 

Table Hottest Part 2

 

Can you see why my temperature model of the Earth, has not estimated the hottest month of these countries accurately?

The reason is, that these countries have an arid, or dry, climate (for at least part of the year).

My temperature model of the Earth, only looks at latitude, longitude, elevation, and area. You can’t expect it to accurately predict the temperature, when other factors are important.

One of the things that is surprising about my temperature model of the Earth, is that it can still accurately predict the average temperature, and the coldest month temperature, for these arid or dry countries.

This should teach us an important lesson. Different factors determine the average temperature, the coldest month temperature, and the hottest month temperature.

My temperature model of the Earth, provides a starting point, for estimating the temperatures of a country. Where the estimate is not accurate, then other factors must be found, to explain the inaccuracy of the estimate. Factors like an arid or dry climate, or the presence of the Gulf Stream, can explain why the estimate is not accurate.


What is the secret, that makes my temperature model of the Earth so accurate, but also very simple.

The reason is, that I have separated the temperature estimates from the actual latitude of a country, and based the temperature estimates on the “effective” latitude.

An example will help to explain this.

Canada has an average latitude of 50 N.


In the northern hemisphere summer, the sun reaches the Tropic of Cancer (23.5° north).

So Canada has an “effective” latitude of ( 50  –  23.5 ) = 26.5

The hottest month temperature is based on this “effective” latitude, of 26.5

Canada’s estimated hottest month temperature = +25.3 degrees Celsius.

Canada’s actual hottest month temperature = +23.5 degrees Celsius.

Actual hottest month minus estimated hottest month  = -1.8 degrees Celsius.


In the northern hemisphere winter, the sun reaches the Tropic Capricorn (23.5° south).

So Canada has an “effective” latitude of ( 50  +  23.5 ) = 73.5

The coldest month temperature is based on this “effective” latitude, of 73.5

Canada’s estimated coldest month temperature = -10.7 degrees Celsius.

Canada’s actual coldest month temperature = -15.0 degrees Celsius.

Actual coldest month minus estimated coldest month  = -4.3 degrees Celsius.


Canada’s average “effective” latitude, is 50 N. This is the same as its actual latitude. I will explain the reason for this, later.

The average temperature is based on this “effective” latitude, of 50.0

Canada’s estimated average temperature = +6.2 degrees Celsius.

Canada’s actual estimated temperature = +4.1 degrees Celsius.

Actual average temperature minus estimated average temperature  = -2.1 degrees Celsius.


 

The graph of the “effective” latitude, versus the actual latitude (for each of the 3 temperature measurement types [average, coldest month, and hottest month]), is simple.

It provides a clear explanation of why different countries have different temperatures.

 

Effective Latitude

 

Some interesting things to notice about this graph:

  • all latitudes north of the Arctic circle (66.5° north), and south of the Antarctic circle (66.5° south), have a coldest month “effective” latitude of 90 [ there is no sunlight at some time of the year ]
  • all latitudes between the Tropic of Cancer (23.5° north), and the Tropic of Capricorn (23.5° south), have a hottest month “effective” latitude of zero. [ the sun is directly overhead at some time of the year ]
  • all latitudes between the Arctic circle (66.5° north), and the Tropic of Cancer (23.5° north), have an average temperature “effective” latitude which is equal to the actual latitude
  • all latitudes between the Antarctic circle (66.5° south), and the Tropic of Capricorn (23.5° south), have an average temperature “effective” latitude which is equal to the actual latitude
  • latitudes between the Tropic of Cancer (23.5° north), and the Tropic of Capricorn (23.5° south), have a similar average temperature “effective” latitude (but it varies a bit as you get further from the equator)

Part 3 of this article, will examine how important the different factors are, in determining the temperatures. What is the relative importance of latitude, longitude, elevation, and area.

If anybody has any questions about my temperature model of the Earth, I will try to answer them.

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