On 2015-07-09 07:40, Jonno wrote:
> I was thinking of doing that or having 2 surface plots but I think it
> would be visually quite confusing.
> I was trying to think of an example since I'm sure someone has come up
> with a nice way to display this kind of data.
> Imagine if the data was average temperature (a) and average rainfall (b)
> for a region in the world (lat/long = x,y). The goal is to display the
> data such that it's obvious where the locations are that have closest to
> the ideal temp/rain combination.
> How would you go about that?
It's not an easy thing to visualize in general. You might want to look
at approaches to visualizing complex functions (i.e., functions whose
input and output are both complex variables). These essentially map
pairs (a, b) to pairs (x, y) as in your situation, and mathematicians
have come up with various ways to visualize them. Some are described at
https://www.pacifict.com/ComplexFunctions.html and the wikipedia article
at https://en.wikipedia.org/wiki/Complex_analysis has some links in the
references to web pages for graphing such functions.
If the data are measured at (or can be reasonably reduced to) discrete
points (as temp/rainfall are likely to be), another possibility is a
scatterplot using, say, the color and size of the markers as indicators
of the two variables (e.g., red/blue for hot/cold temp, larger/smaller
circles for higher/lower rainfall).
In some cases, like your example with temperature and rainfall, you may
instead be able to combine the two output dimensions into a single one
that somehow captures the overall "distance" from the ideal point. That
is, for a given point, if your goal is to show how close it is to the
ideal *combination* of temp and rain, you may not need to display how
close it is on each dimension separately, but just how close it is to
the ideal overall. Exactly how to compute this would vary based on the
data (e.g., standardizing the values and taking the euclidean distance
from the ideal).
Your temp/rainfall example caught my eye because a few years ago I did
a blog post on a similar topic, considering temperature and humidity
(http://iq.brenbarn.net/2011/11/18/good-days-mate/). There I decided to
graph just a single variable, namely the number of days on which either
temperature *or* humidity is outside a "comfortable" range. Obviously
this approach may not make sense for every situation. But what I mean
is that, in some cases, you can use domain-specific knowledge about what
the dimensions mean to combine them into one dimension that approximates
what it is you're trying to illustrate with the graph.
--
Brendan Barnwell
"Do not follow where the path may lead. Go, instead, where there is no
path, and leave a trail."
--author unknown
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