# 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

#### Over time

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 auto-correlation to detect degree of randomness and tendencies. The Hurst exponent is 0.23 and it indicates that the $CO_2$ time series has a tendency to decrease between values will probably be followed by an increase. We can conclude that the time series from Mauna Loa is not a random walk as well, due to the fact that random walk processes always has a Hurst exponent of 0.5.

#### Frequency Domain

Here is a draft plot of the FFT of the time series - i intend to show next how you can achieve smoothing by using hamming windows which by using Sage and the inluded libraries Scipy/Numpy which have support for that. One can also use R, but I am not very proficient in R, so I leave that to others!

Question. What are those narrow peaks you see after the series has gone on for a short while?

### Part of the draft Code

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
# Staffan Liljegren removed regression code - which you can see at the above URL - and
# added the Time series features. TBD enable the fft and smoothing as part of the viewer

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(ma_month = [1,2,6,12,24],trend= True, fft= False):
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 ma_month>2:
co2ts = finance.TimeSeries(co2_data)
co2ts = co2ts.simple_moving_average(ma_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 = [7,7], aspect_ratio=1.0,gridlines=True)