Sealevel.info → AvgSLR → acceleration_primer

# How to recognize “acceleration” in a graph

Do you know how to recognize “acceleration” in a graph, at a glance?

It is very simple. In a nutshell:

**1.** **Concave-up.** If the graph (with “time” or “age” represented by the horizontal “x-axis,” and “position” or “level” represented by the vertical “y-axis”) “**curves upward**” then it represents positive **acceleration** (regardless of whether the overall trend is upward or downward). Here are three examples:

**2.** **Concave-down.** If the graph (with “time” represented by the “x-axis”) “**curves downward**” then it represents **deceleration,** a/k/a “negative acceleration,” (regardless of whether the overall trend is upward or downward). Here are three examples:

**3.** **Neither concave-up nor concave-down.** If the graph shows a **straight line**, then it is said to be “**linear**.” That means there is **no acceleration**, or “acceleration is zero.” Here are three examples:

If that is unclear, Google will find some videos which explain it:

https://www.google.com/search?q=what+does+acceleration+look+like+on+a+graph&tbm=vid

### Example

Now look, for example, at this 111-year record of sea-level at Honolulu, juxtaposed with carbon dioxide (CO_{2}):

*(Click on the graph for an interactive version, in which you can hover your mouse cursor over the traces to see the values.)*

The green trace is CO_{2}. Do you see that CO_{2} rise accelerated, quite dramatically, after WWII?

The blue trace is sea-level. Of course it is sloshing up and down a bit,
over periods of a decade or two, but do you see that there has
been __no__ sustained __acceleration__ in response to the rise in CO_{2} levels?
Although CO_{2} level has accelerated, sea-level rise has remained linear.

(That's what the sea-level measurement data shows __everywhere__, BTW.)