Robot-Train Contour Maps

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Robot-Train Contour Maps


Robot-Train Logo

Welcome to Contour Map University (CMU). In this article, we will help people to acquire the knowledge and skills, that are needed to understand contour maps.

This is a practical course. It is full of colourful contour maps, and their corresponding line graphs. Pre-requisites for this course are:

  1. the ability to see shapes
  2. the ability to see colours
  3. a sense of humour

Contour maps were originally developed using English based “colours”. But they have now been translated into American based “colors”. American students should remember to divide all colours specified in this article by 3, to convert them into American based “colors”.

This course is suitable for almost anyone. Most high school students, and many primary school students, will be able to complete this course, with good grades. Some may even feel that the course was too easy.

Contour maps are not difficult. But many people find them confusing. They have a number of features which are counter-intuitive. This course will start by using simple examples, and will slowly build up to examples which are sophisticated and complex. If people are willing to make a little effort, then they should end up with a good “understanding” of contour maps.

Contour maps are colourful, triangular shaped, graphs. All of the example contour maps in this article, are based on train trips by Robot-Train (except for the last few). People may have come here expecting to learn about “global warming contour maps”. These are a similar type of contour map, which is based on a temperature series, like GISTEMP, or UAH. Global warming contour maps are more complex than Robot-Train contour maps. Once Robot-Train contour maps are understood, it is much easier to understand global warming contour maps. Robot-Train provides a precise, controllable environment, and it is easy to see the relationship between speed (the rate of change of distance), and a contour map. Global temperatures are not precise, or controllable, and they are very noisy (the signal is hard to see because of the “random” or “chaotic” temperature noise). This makes global warming contour maps an “advanced” course, which can be taken after this article.

A contour map uses colour, to display information about how fast something is changing. The “something”, can be any time-based data series. If you measure a “variable” (like distance, temperature, “how many”, height, weight, volume, density, etc), at different times, then you create a “time-based data series”. The time-based data series shows you how the “variable”, changed (or varied) over time.

What is the best way to study a time-based data series? One way is to plot an X-Y line graph, of the variable versus time. This is a good way to see what a variable does over time. It is important to realise, that a contour map does not make X-Y line graphs redundant. A contour map complements an X-Y line graph, and makes it easier to see some things. An X-Y line graph shows “absolute” values, a contour map shows “relative” values. You will get the best understanding of a time-based data series, by looking at both an X-Y line graph, AND a contour map.

Some people may have heard that contour maps are “too hard”, because they are based on “hundreds of thousands” of linear regressions. Do these people also believe that computers, and even calculators, are “too hard”, because they use technology that a “normal” person might not understand? Should we go back to using slide-rules, and paper-based calculations? In this article, all of the “calculations”, will be done for you. You can relax, and enjoy learning the important points. Unless you want to know the intimate details about how a contour map is made, you can leave those details to a computer program, or some other person.

Here is some information about Robot-Train. Robot-Train is a driverless train, which does not need to stop for rest or meal breaks. It can operate 24 hours per day, 365 days per year. Robot-Train has an engine at each end, and can travel just as fast “backwards”, as it can “forwards”. To make it easy for humans to understand, one end of Robot-train is called “the front”, and the other end is called “the back”. When travel is in the direction from “back” to “front”, Robot-Train is said to be “going forwards”, and the speeds are positive (+120 km/h). When travel is in the direction from “front” to “back”, Robot-Train is said to be “going backwards”, and the speeds are negative (-90 km/h). This system is similar to the one that is used for global warming contour maps, where an increasing temperature gives a positive warming rate, and a decreasing temperature gives a negative warming rate.

It is time to look at our first contour maps. Because contour maps use colour to display “rate of change” information, we need to define a suitable colour scheme. Robot-Train contour maps are concerned with “speed” (the rate of change of distance, over time). The company that owns Robot-Train is called Asimov. They have provided a document, which lists the ranges of Robot-Train’s speeds, that fall into various categories. We have taken that list, and added colours to represent each category. See the “legend”, below:

Robot-Train Legend

Each of the examples below, is based on a “Train Trip Plan”. The Train Trip Plan will be printed first, followed by the Robot-Train contour map, and the Robot-Train line graph. The contour map, and the line graph, were both created from the Train Trip Plan.

A Train Trip Plan consists of a number of steps. For example:

  1. drive at 160 km/h for 6 hours
  2. drive at -80 km/h for 4 hours

All Train Trips Plans in this article are 10 hours long.

Have a look at each example, and try to see how the Robot-Train contour map, and Robot-Train line graph, match the Train Trip plan. Also, try to see how the contour map, and line graph, correspond to each other. It is possible to create a contour map from a line graph, and it is also possible to create a line graph from a contour map. Can you work out how this is done?


Train Trip Plan A

  1. drive at +160 km/h for 10 hours

Graph 1 and 2


Train Trip Plan B

  1. drive at +100 km/h for 10 hours

Graph 3 and 4


Train Trip Plan C

  1. drive at zero km/h for 10 hours

Graph 5 and 6


Train Trip Plan D

  1. drive at -100 km/h for 10 hours

Graph 7 and 8


Train Trip Plan E

  1. drive at -160 km/h for 10 hours

Graph 9 and 10.png


Train Trip Plan F

  1. drive at +160 km/h for 5 hours
  2. drive at -160 km/h for 5 hours

The 5 “constant speed” Train Trips above, showed how the colour on a Robot-Train contour map depends on the speed that Robot-Train travelled at. When he travelled at a constant speed, then all time intervals, of every length, show the same colour.

Now things are going to get more “colourful”. It is important to realise that the speeds that Robot-Train travels at, can be seen by the colour just above the X-axis. If you look just above 4 on the X-axis, then the colour shows the speed that Robot-Train was travelling at, when the elapsed time was 4 hours.

So where does the spectrum of colours come from, that are higher than the X-axis (see the next contour map). They come from a “sort of” averaging, that occurs for time intervals above the X-axis.

For example, look at the point on the following graph, at X=6 and Y=7. The length of the time interval is 7 hours, and the middle of the time interval was 6 hours. So the time interval went from 6 – (7 / 2) = 2.5
to 6 + (7 / 2) = 9.5

So the interval when from 2.5 to 9.5

From 0 to 5, Robot-Train was going +160 km/h

From 5 to 10. Robot-Train was going -160 km/h

So for the interval from 2.5 to 9.5, Robot-Train was travelling at +160 km/h from 2.5 to 5 (which is 2.5 hours), and he was travelling at -160 km/h from 5 to 9.5 (which is 4.5 hours).

2.5 hours at +160 km/h  +  4.5 hours at -160 km/h  =  -320 km in 7 hours

-320 km in 7 hours  =  about -45 km/h

Look up -45 km/h on the legend, and the colour is light-green.

So the point on the graph, at X=6 and Y=7, is coloured light green.

Repeat that procedure for every point (or time interval) on the contour map, and you have created a contour map.

[People who check if the point on the graph, at X=6 and Y=7, is coloured light green, will find that it is NOT light-green. It is actually “medium-green”.

So why did I calculate it incorrectly?

Remember that I said that it was “sort of” an average. It is actually calculated using a linear regression. So if you use “simple averaging”, like I did, you will get near the right result, but you will not always be exactly right. Light-green is close to medium-green.]

Train Trip Plan F  (repeated from above)

  1. drive at +160 km/h for 5 hours
  2. drive at -160 km/h for 5 hours

Graph 11 and 12


Train Trip Plan G

  1. drive at +160 km/h for 5 hours
  2. drive at -80 km/h for 5 hours

Graph 13 and 14


Train Trip Plan H

  1. drive at -80 km/h for 5 hours
  2. drive at +160 km/h for 5 hours

Graph 15 and 16


Train Trip Plan I

  1. drive at +40 km/h for 2 hours
  2. drive at +80 km/h for 2 hours
  3. drive at +100 km/h for 2 hours
  4. drive at +120 km/h for 2 hours
  5. drive at +140 km/h for 2 hours

Graph 17 and 18


Train Trip Plan J

  1. drive at -140 km/h for 2 hours
  2. drive at -120 km/h for 2 hours
  3. drive at -100 km/h for 2 hours
  4. drive at -80 km/h for 2 hours
  5. drive at -40 km/h for 2 hours

Graph 19 and 20


Train Trip Plan K

  1. drive at +40 km/h for 1.25 hours
  2. drive at +80 km/h for 1.25 hours
  3. drive at +120 km/h for 1.25 hours
  4. drive at +160 km/h for 1.25 hours
  5. drive at +160 km/h for 1.25 hours
  6. drive at +120 km/h for 1.25 hours
  7. drive at +80 km/h for 1.25 hours
  8. drive at +40 km/h for 1.25 hours

Graph 21 and 22


Train Trip Plan L  –  (a Robot-Train “slowdown”)

  1. drive at +100 km/h for 6 hours
  2. drive at +40 km/h for 2 hours
  3. drive at +100 km/h for 2 hours

I planned this Robot-Train Trip, to see if I could “model” a slowdown.

The next graph after this one, is a real Slowdown Map, based on the real GISTEMP Global Land and Ocean temperature series (1970 to 2018). After you look at this contour map (the Robot-Train slowdown), and the next graph (the real GISTEMP slowdown), have a look at the graph after that. It presents the Robot-Train slowdown, and the real GISTEMP slowdown, side by side. This makes comparing them easy.

Graph 23 and 24


Global Warming Contour Map  –  (a real “slowdown”)

This is a “real” global warming contour map, based on the GISTEMP Global Land and Ocean temperature series (1970 to 2018).

To make it easy to see the slowdown, this global warming contour map uses only 2 colours:

  • yellow for any date range that has a warming rate which is less than or equal to +1.0 degrees Celsius per century
  • dark-orange for any date range that has a warming rate which is greater than +1.0 degrees Celsius per century

On a “real” global warming contour map, there is temperature “noise” (random and chaotic temperature changes). This noise makes it difficult to accurately “read” warming rates, when the Y-axis value is between 0 and 5. The Y-axis shows the “Length of Date Range”, so warming rates for date ranges of length 5 years or less, are difficult to read accurately. This should be remembered, when comparing a Robot-Train contour map, to a “real” global warming contour map. All Robot-Train contour maps in this article, have no noise.

Graph 25 and 26


Compare a Robot-Train “slowdown”, to a real “slowdown”.

The Robot-Train contour map shows just 1 slowdown. The real global warming contour map shows multiple slowdowns.

The Robot-Train slowdown, goes from 6 to 8 on the X-axis. The real recent slowdown, goes from about 2005 to 2010 on the X-axis.

Graph 23 and 25


Train Trip Plan M  –  (a Robot-Train “special trip”)

  1. drive at -89 km/h for 2.25 hours
  2. drive at +129 km/h for 2.25 hours
  3. drive at -11 km/h for 2.25 hours
  4. drive at +129 km/h for 3.25 hours

I planned this Robot-Train Trip, to see if I could duplicate the global warming contour map for the GISTEMP Global Land and Ocean temperature series (1880 to 2018), using just 4 simple steps.

This GISTEMP temperature series that I used, contains 829 temperature readings. The “warming rate” can be different, between each pair of readings. So there are possibly 828 different real “warming rates”. I am trying to “model” GISTEMP, using just 4 “warming rates”. So don’t expect an exact match.

The next graph is my simple 4 step “model” of GISTEMP. The next graph after that, is the real GISTEMP temperature series. The next graph after that, shows the simple 4 step “model”, side by side, with the real GISTEMP temperature series. This makes comparing them easier.

Graph 27 and 28


Global Warming Contour Map  –  (this is a real GISTEMP temperature series)

This is a “real” global warming contour map, based on the GISTEMP Global Land and Ocean temperature series (1880 to 2018).

Remember, that on a “real” global warming contour map, there is temperature “noise” (random and chaotic temperature changes). This noise makes it difficult to accurately “read” warming rates, when the Y-axis value is between 0 and 5. The Y-axis shows the “Length of Date Range”, so warming rates for date ranges of length 5 years or less, are difficult to read accurately. This should be remembered, when comparing a Robot-Train contour map, to a “real” global warming contour map. All Robot-Train contour maps in this article, have no noise.

Graph 29 and 30 new


Compare a simple 4 step Robot-Train Trip, to the real GISTEMP temperature series (1880 to 2018).

The simple 4 step Robot-Train Trip, was designed to try and “model” the real GISTEMP temperature series.

The real global warming contour map is displaying GISTEMP Global Land and Ocean temperature series, from 1880 to 2018.

This GISTEMP temperature series that I used, contains 829 temperature readings. The “warming rate” can be different, between each pair of readings. So there are possibly 828 different real “warming rates”. I am trying to “model” GISTEMP, using just 4 “warming rates”. So don’t expect an exact match.

Graph 27 and 29