GVN330 Climate Data Analysis
Assignment 3.1: Analysis of Paired data
Relationships between data-sets are of fundamental interest in climate data
analysis. These can be relationships between climate variables when studying
climatology, or relationships between climate variable and socio-economic or
environmental variables in applied climatology. Much research is currently
focused on the relationships between climate variables and one other dataset in
particular – time.
Reading
Wilks 3.5 – Exploratory Techniques for Paired data (Reading quiz 4)
A description of the formal definitions used in hypothesis testing you can find
easily, for example in the matlab documentation:
http://www.mathworks.se/help/stats/hypothesis-test-terminology.html
Many (most) people find this very confusing. If you are unsure what p-values and
statistical significant mean, the first few paragraphs from the following articles
may help you:
http://www.surveysystem.com/signif.htm
or:
http://www.statpac.com/surveys/statistical-significance.htm
Exercises:
Ass3.1 Create seasonal scatter plots showing the relationships between monthly
precipitation and the variables:

Maximum temperature

Minimum temperature

Diurnal temperature range (Tmax – Tmin)

Sea-level pressure
using the Saeve_daily.csv time-series. Summarize the relationships using
correlation statistics.
In this assignment you will look at the relationships between climate variables
and precipitation. The question you wish to answer is: which climate variable/s
are most closely related to precipitation? At the end of the assignment, you can
think about your results in the context of weather phenomena.
a) Load the data into Matlab.
You have calculated monthly max temp, min temp and precipitation in
Assignment1.7, so you can re-use your code, or if you saved the dave to a .mat
file, you can re-load it.
The monthly-average sea-level pressure data you can load from GUL
Documents/Assignment 3 documents/Saeve_psl.mat
Monthly average Diurnal Temperature Range you can calculate as Tmax – Tmin.
b) Create scatter plots.
You create scatter-plots in matlab using plot, and giving a symbol. eg
plot(x,y,'.');
For this assignment, I would like you to create one figure for each independent
variable: that is one figure showing the relationships between maximum
temperature and precipitation; one showing the relationships between
minimum temperature and precipitation, etc.
For each figure, use 4 axes (which you create using subplot) , one for each season.
For example, the first axis of the first plot could show a scatter plot of monthly
precipitation on the y-xaxis and monthly maximum temperature on the x-axis,
showing data for the winter months Dec, Jan, Feb.
Again, your code will be much simpler if you create a function to create the four
plots on the same figure!
CHECKPOINT: are you going to use a function? If so, compare the function
header (the line [output]=fun_name(inputs) and the comments at the top of the
file) with others. There are several ways to use a function to help here, so make a
note if you see other people with a different approach.
c) Create a table summarizing the correlation statistics.
Calculate the summary statistics for each plot:
- Spearman correlation coefficient
-Spearman p-value
- Statistical significance of the Spearman correlation (is the Spearman
correlation statistically-significant at the 95% confidence level?)
- The coefficient of determination, R2 (which is the Pearson correlation
coefficient squared)
Correlation coefficients and p-values are calculated using the function corr:
[CC, PV] = corr(x,y,'type','Spearman');
or
[CC, PV] = corr(x,y,'type',Pearson);
You decide how to arrange the results in your table!
Checkpoint – compare your table with other groups. Do you get the same
answers for statistical significance? Is your table lay-out easier/harder to follow?
There is much data to present!
Discussion: look at some of the relationships you have plotted and tabled.
- Why might the relationship between max temp and precipitation be the
opposite in summer and winter?
- Why might diurnal temperature range have a better relationship with
precipitation than either max or min temp alone in the non-winter seasons? Why
might it not be so useful in winter?
- Why is low sea-level pressure associated with precipitation?
We will discuss these in class, but think about them yourselves first please!