Average Temperature Fits

This notebook reproduces graphs from:

http://johncarlosbaez.wordpress.com/2014/05/29/warming-slowdown-2/



In [1]:

    
%pylab inline
import urllib2
import os
from IPython.display import Image
import numpy.ma as ma
from scipy.interpolate import UnivariateSpline









    



Populating the interactive namespace from numpy and matplotlib



In [2]:

    
url = "http://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries/Data/GLBTSSST.long.data"
filename = os.path.join("data", os.path.basename(url))
open(filename, "w").write(urllib2.urlopen(url).read())

Load the data (the last year will typically have missing values for the last few months):



In [3]:

    
D = genfromtxt(filename, skip_header=1, skip_footer=17, missing_values={None: "-999"}, usemask=True, dtype=int)
D









    Out[3]:





masked_array(data =
 [[1880 -34 -27 ..., -19 -17 -22]
 [1881 -13 -16 ..., -22 -26 -17]
 [1882 4 5 ..., -24 -24 -36]
 ..., 
 [2011 46 45 ..., 60 50 46]
 [2012 37 39 ..., 72 68 44]
 [2013 61 51 ..., -- -- --]],
             mask =
 [[False False False ..., False False False]
 [False False False ..., False False False]
 [False False False ..., False False False]
 ..., 
 [False False False ..., False False False]
 [False False False ..., False False False]
 [False False False ...,  True  True  True]],
       fill_value = 999999)

We average monthly temperature for each year (we have to divide by 100 to get the temperature is in C):



In [4]:

    
years = D[:, 0]
T = array(ma.average(D[:, 1:]/100., axis=1)) # Make sure 'average' ignores missing values

Calculate average temperature between the years 1950-1980 (including both ends):



In [5]:

    
Tavg = average(T[1950-years[0]:1980-years[0]+1])
Tavg









    Out[5]:





-0.0062365591397849467

Calculate temperature anomaly



In [6]:

    
Tanom = T - Tavg

Plot the data (first plot), compare to the original plot (second plot):



In [7]:

    
# Get the years and temperatures after 1950:
x = years[1950-years[0]:]
y = Tanom[1950-years[0]:]

figure(figsize=(10, 5))
bar(x, y, 0.4, lw=0)
xlim([1948, 2015])
xlabel("Year")
ylabel("Temperatuer anomaly in Degrees Celsius")
title("Mean Temperature Anomalies Relative to 1950-1980 baseline")
show()
Image(filename="data/UAH_LT_1979_thru_June_2013_v5.6.png")
show()
Image(url="http://math.ucr.edu/home/baez/ecological/galkowski/AnnualAnomaliesBarChart.png", width=620)









    












    Out[7]:

Let's calculate "two trendlines obtained by applying a smoothing spline, one smoothing more than another". It is not clear what spline parameters to use, so we chose cubic splines and smoothing parameters s=1 and s=0.4, that seem to reproduce the original graph at least qualitatively.



In [8]:

    
s = UnivariateSpline(x, y, k=3, s=1)
y_spline_1 = s(x)
s = UnivariateSpline(x, y, k=3, s=0.4)
y_spline_2 = s(x)

Plot the data (first plot), compare to the original plot (second plot):



In [9]:

    
figure(figsize=(10, 5))
bar(x, y, 0.4, lw=0)
plot(x, y_spline_1, "m-", lw=2)
plot(x, y_spline_2, "m--", lw=2)
xlim([1948, 2015])
xlabel("Year")
ylabel("Temperatuer anomaly in Degrees Celsius")
title("Mean Temperature Anomalies Relative to 1950-1980 baseline")
show()
Image(url="http://math.ucr.edu/home/baez/ecological/galkowski/TemplateForSyntheticModel_a.png", width=620)









    












    Out[9]: