# Contents

## Idea

Create some plots related to the Carbon cycle and do some simple time analysis in both time and frequency domain using Sage and its built in support for time series.

## Details

### Diagrams

The classic Keeling curve, plotted up to January 2011 in Sage with default aspect ratio for Sage List_plot:

Here is a plot of the whole series but showing season corrected values (also using the default aspect ratio):

I think it can be better with setting it default aspect ratio to one, so we’ll try that as well and add some major grid lines:

Trend - season corrected also with SAGE aspect ratio one:

Here is one with the code below showing the interpolated date moving average over six months and also axis labels:

Let us look at some typical properties of time series, the Hurst exponent and autocorrelation to detect degree of randomness and tendence. The Hurst exponent is 0.23 and it indicates that the CO2 time series has a tendency to decrease between values will probably be followed by an increase.

Here is a draft plot of the FFT of the time series:

### Draft Code

Trying to see if the TimeSeries in Sage, can be used better instead, by eg using moving averages. The code below reflects the plotting with aspect ratio equal to one and also using Timeseries for months larger than two. I am just checking that it could also be used for one

# based on http://wiki.sagemath.org/interact/web made by Marshall Hampton CC 3.0
import urllib2 as U
import time

current_year = time.localtime().tm_year
datalines = []
for a_line in co2data:
if a_line.find('Creation:') != -1:
cdate = a_line
if a_line[0] != '#':
temp = a_line.replace('\n','').split(' ')
temp = [float(q) for q in temp if q != '']
datalines.append(temp)
@interact
def azimco2viewer(month = [1,2,6,12,24],trend= True):
if trend:
co2_data = [q[5] for q in datalines]
else:
co2_data = [q[4] for q in datalines]
yr_data = [q[2] for q in datalines]
if month>2:
co2ts = finance.TimeSeries(co2_data)
co2ts = co2ts.simple_moving_average(month)
co2_data = co2ts.list()
lp = list_plot(zip(yr_data,co2_data), plotjoined=True, rgbcolor=(1,0,0))
lp.axes_labels(['$year$','$CO_2ppm$'])
lp.show(axes = True, figsize = [5,7], aspect_ratio=1.0,gridlines=True)