Climate Change

Apr 5, 2019

There have been many studies documenting that the average global temperature has been increasing over the last century. The consequences of a continued rise in global temperature will be dire. Rising sea levels and an increased frequency of extreme weather events will affect billions of people.

In this analysis, I’ll attempt to study the relationship between average global temperature and several other factors.

The file climate_change.csv contains climate data from May 1983 to December 2008. The available variables include:

Year: the observation year.
Month: the observation month.
Temp: the difference in degrees Celsius between the average global temperature in that period and a reference value. This data comes from the Climatic Research Unit at the University of East Anglia.
CO2, N2O, CH4, CFC.11, CFC.12: atmospheric concentrations of carbon dioxide (CO2), nitrous oxide (N2O), methane (CH4), trichlorofluoromethane (CCl3F; commonly referred to as CFC-11) and dichlorodifluoromethane (CCl2F2; commonly referred to as CFC-12), respectively. This data comes from the ESRL/NOAA Global Monitoring Division.
- CO2, N2O and CH4 are expressed in ppmv (parts per million by volume – i.e., 397 ppmv of CO2 means that CO2 constitutes 397 millionths of the total volume of the atmosphere)
- CFC.11 and CFC.12 are expressed in ppbv (parts per billion by volume).
Aerosols: the mean stratospheric aerosol optical depth at 550 nm. This variable is linked to volcanoes, as volcanic eruptions result in new particles being added to the atmosphere, which affect how much of the sun’s energy is reflected back into space. This data is from the Godard Institute for Space Studies at NASA.
TSI: the total solar irradiance (TSI) in W/m2 (the rate at which the sun’s energy is deposited per unit area). Due to sunspots and other solar phenomena, the amount of energy that is given off by the sun varies substantially with time. This data is from the SOLARIS-HEPPA project website.
MEI: multivariate El Nino Southern Oscillation index (MEI), a measure of the strength of the El Nino/La Nina-Southern Oscillation (a weather effect in the Pacific Ocean that affects global temperatures). This data comes from the ESRL/NOAA Physical Sciences Division.

We are interested in how changes in these variables affect future temperatures, as well as how well these variables explain temperature changes so far. To do this, first read the dataset climate_change.csv.

climate <- read.csv("climate_change.csv")
str(climate)

'data.frame':   308 obs. of  11 variables:
 $ Year    : int  1983 1983 1983 1983 1983 1983 1983 1983 1984 1984 ...
 $ Month   : int  5 6 7 8 9 10 11 12 1 2 ...
 $ MEI     : num  2.556 2.167 1.741 1.13 0.428 ...
 $ CO2     : num  346 346 344 342 340 ...
 $ CH4     : num  1639 1634 1633 1631 1648 ...
 $ N2O     : num  304 304 304 304 304 ...
 $ CFC.11  : num  191 192 193 194 194 ...
 $ CFC.12  : num  350 352 354 356 357 ...
 $ TSI     : num  1366 1366 1366 1366 1366 ...
 $ Aerosols: num  0.0863 0.0794 0.0731 0.0673 0.0619 0.0569 0.0524 0.0486 0.0451 0.0416 ...
 $ Temp    : num  0.109 0.118 0.137 0.176 0.149 0.093 0.232 0.078 0.089 0.013 ...

summary(climate)

      Year          Month             MEI               CO2       
 Min.   :1983   Min.   : 1.000   Min.   :-1.6350   Min.   :340.2  
 1st Qu.:1989   1st Qu.: 4.000   1st Qu.:-0.3987   1st Qu.:353.0  
 Median :1996   Median : 7.000   Median : 0.2375   Median :361.7  
 Mean   :1996   Mean   : 6.552   Mean   : 0.2756   Mean   :363.2  
 3rd Qu.:2002   3rd Qu.:10.000   3rd Qu.: 0.8305   3rd Qu.:373.5  
 Max.   :2008   Max.   :12.000   Max.   : 3.0010   Max.   :388.5  
      CH4            N2O            CFC.11          CFC.12     
 Min.   :1630   Min.   :303.7   Min.   :191.3   Min.   :350.1  
 1st Qu.:1722   1st Qu.:308.1   1st Qu.:246.3   1st Qu.:472.4  
 Median :1764   Median :311.5   Median :258.3   Median :528.4  
 Mean   :1750   Mean   :312.4   Mean   :252.0   Mean   :497.5  
 3rd Qu.:1787   3rd Qu.:317.0   3rd Qu.:267.0   3rd Qu.:540.5  
 Max.   :1814   Max.   :322.2   Max.   :271.5   Max.   :543.8  
      TSI          Aerosols            Temp        
 Min.   :1365   Min.   :0.00160   Min.   :-0.2820  
 1st Qu.:1366   1st Qu.:0.00280   1st Qu.: 0.1217  
 Median :1366   Median :0.00575   Median : 0.2480  
 Mean   :1366   Mean   :0.01666   Mean   : 0.2568  
 3rd Qu.:1366   3rd Qu.:0.01260   3rd Qu.: 0.4073  
 Max.   :1367   Max.   :0.14940   Max.   : 0.7390

ML Workflow

Then, split the data into a training set, consisting of all the observations up to and including 2006, and a testing set consisting of the remaining years (hint: use subset). A training set refers to the data that will be used to build the model (this is the data we give to the lm() function), and a testing set refers to the data we will use to test our predictive ability.

climate_train <- subset(climate, Year <= 2006)
climate_test <- subset(climate, Year > 2006)
str(climate_train)

'data.frame':   284 obs. of  11 variables:
 $ Year    : int  1983 1983 1983 1983 1983 1983 1983 1983 1984 1984 ...
 $ Month   : int  5 6 7 8 9 10 11 12 1 2 ...
 $ MEI     : num  2.556 2.167 1.741 1.13 0.428 ...
 $ CO2     : num  346 346 344 342 340 ...
 $ CH4     : num  1639 1634 1633 1631 1648 ...
 $ N2O     : num  304 304 304 304 304 ...
 $ CFC.11  : num  191 192 193 194 194 ...
 $ CFC.12  : num  350 352 354 356 357 ...
 $ TSI     : num  1366 1366 1366 1366 1366 ...
 $ Aerosols: num  0.0863 0.0794 0.0731 0.0673 0.0619 0.0569 0.0524 0.0486 0.0451 0.0416 ...
 $ Temp    : num  0.109 0.118 0.137 0.176 0.149 0.093 0.232 0.078 0.089 0.013 ...

summary(climate_train)

      Year          Month             MEI               CO2       
 Min.   :1983   Min.   : 1.000   Min.   :-1.5860   Min.   :340.2  
 1st Qu.:1989   1st Qu.: 4.000   1st Qu.:-0.3230   1st Qu.:352.3  
 Median :1995   Median : 7.000   Median : 0.3085   Median :359.9  
 Mean   :1995   Mean   : 6.556   Mean   : 0.3419   Mean   :361.4  
 3rd Qu.:2001   3rd Qu.:10.000   3rd Qu.: 0.8980   3rd Qu.:370.6  
 Max.   :2006   Max.   :12.000   Max.   : 3.0010   Max.   :385.0  
      CH4            N2O            CFC.11          CFC.12     
 Min.   :1630   Min.   :303.7   Min.   :191.3   Min.   :350.1  
 1st Qu.:1716   1st Qu.:307.7   1st Qu.:249.6   1st Qu.:462.5  
 Median :1759   Median :310.8   Median :260.4   Median :522.1  
 Mean   :1746   Mean   :311.7   Mean   :252.5   Mean   :494.2  
 3rd Qu.:1782   3rd Qu.:316.1   3rd Qu.:267.4   3rd Qu.:541.0  
 Max.   :1808   Max.   :320.5   Max.   :271.5   Max.   :543.8  
      TSI          Aerosols            Temp        
 Min.   :1365   Min.   :0.00160   Min.   :-0.2820  
 1st Qu.:1366   1st Qu.:0.00270   1st Qu.: 0.1180  
 Median :1366   Median :0.00620   Median : 0.2325  
 Mean   :1366   Mean   :0.01772   Mean   : 0.2478  
 3rd Qu.:1366   3rd Qu.:0.01400   3rd Qu.: 0.4065  
 Max.   :1367   Max.   :0.14940   Max.   : 0.7390

str(climate_test)

'data.frame':   24 obs. of  11 variables:
 $ Year    : int  2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 ...
 $ Month   : int  1 2 3 4 5 6 7 8 9 10 ...
 $ MEI     : num  0.974 0.51 0.074 -0.049 0.183 ...
 $ CO2     : num  383 384 385 386 387 ...
 $ CH4     : num  1800 1803 1803 1802 1796 ...
 $ N2O     : num  321 321 321 321 320 ...
 $ CFC.11  : num  248 248 248 248 247 ...
 $ CFC.12  : num  539 539 539 539 538 ...
 $ TSI     : num  1366 1366 1366 1366 1366 ...
 $ Aerosols: num  0.0054 0.0051 0.0045 0.0045 0.0041 0.004 0.004 0.0041 0.0042 0.0041 ...
 $ Temp    : num  0.601 0.498 0.435 0.466 0.372 0.382 0.394 0.358 0.402 0.362 ...

summary(climate_test)

      Year          Month            MEI               CO2       
 Min.   :2007   Min.   : 1.00   Min.   :-1.6350   Min.   :380.9  
 1st Qu.:2007   1st Qu.: 3.75   1st Qu.:-1.0437   1st Qu.:383.1  
 Median :2008   Median : 6.50   Median :-0.5305   Median :384.5  
 Mean   :2008   Mean   : 6.50   Mean   :-0.5098   Mean   :384.7  
 3rd Qu.:2008   3rd Qu.: 9.25   3rd Qu.:-0.0360   3rd Qu.:386.1  
 Max.   :2008   Max.   :12.00   Max.   : 0.9740   Max.   :388.5  
      CH4            N2O            CFC.11          CFC.12     
 Min.   :1772   Min.   :320.3   Min.   :244.1   Min.   :534.9  
 1st Qu.:1792   1st Qu.:320.6   1st Qu.:244.6   1st Qu.:535.1  
 Median :1798   Median :321.3   Median :246.2   Median :537.0  
 Mean   :1797   Mean   :321.1   Mean   :245.9   Mean   :536.7  
 3rd Qu.:1804   3rd Qu.:321.4   3rd Qu.:246.6   3rd Qu.:537.4  
 Max.   :1814   Max.   :322.2   Max.   :248.4   Max.   :539.2  
      TSI          Aerosols             Temp      
 Min.   :1366   Min.   :0.003100   Min.   :0.074  
 1st Qu.:1366   1st Qu.:0.003600   1st Qu.:0.307  
 Median :1366   Median :0.004100   Median :0.380  
 Mean   :1366   Mean   :0.004071   Mean   :0.363  
 3rd Qu.:1366   3rd Qu.:0.004500   3rd Qu.:0.414  
 Max.   :1366   Max.   :0.005400   Max.   :0.601

Next, build a linear regression model to predict the dependent variable Temp, using MEI, CO2, CH4, N2O, CFC.11, CFC.12, TSI, and Aerosols as independent variables (Year and Month should NOT be used in the model). Use the training set to build the model.

fit.climate <- 
  lm(Temp ~ MEI + CO2 + CH4 + N2O + CFC.11 + CFC.12 + TSI + Aerosols, 
     data = climate_train)

summary(fit.climate)


Call:
lm(formula = Temp ~ MEI + CO2 + CH4 + N2O + CFC.11 + CFC.12 + 
    TSI + Aerosols, data = climate_train)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.25888 -0.05913 -0.00082  0.05649  0.32433 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.246e+02  1.989e+01  -6.265 1.43e-09 ***
MEI          6.421e-02  6.470e-03   9.923  < 2e-16 ***
CO2          6.457e-03  2.285e-03   2.826  0.00505 ** 
CH4          1.240e-04  5.158e-04   0.240  0.81015    
N2O         -1.653e-02  8.565e-03  -1.930  0.05467 .  
CFC.11      -6.631e-03  1.626e-03  -4.078 5.96e-05 ***
CFC.12       3.808e-03  1.014e-03   3.757  0.00021 ***
TSI          9.314e-02  1.475e-02   6.313 1.10e-09 ***
Aerosols    -1.538e+00  2.133e-01  -7.210 5.41e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.09171 on 275 degrees of freedom
Multiple R-squared:  0.7509,    Adjusted R-squared:  0.7436 
F-statistic: 103.6 on 8 and 275 DF,  p-value: < 2.2e-16

The model R2 (the “Multiple R-squared” value) is 0.7509

Creating Our First Model

Which variables are significant in the model? We will consider a variable signficant only if the p-value is below 0.05. #### MEI, CO2, CFC.11, CFC.12, TSI, Aerosols

Understanding the Model

Current scientific opinion is that nitrous oxide and CFC-11 are greenhouse gases: gases that are able to trap heat from the sun and contribute to the heating of the Earth. However, the regression coefficients of both the N2O and CFC-11 variables are negative, indicating that increasing atmospheric concentrations of either of these two compounds is associated with lower global temperatures.

Which of the following is the simplest correct explanation for this contradiction? #### All of the gas concentration variables reflect human development - N2O and CFC.11 are correlated with other variables in the dataset.

Compute the correlations between all the variables in the training set.

cor(climate_train)

                Year         Month           MEI         CO2         CH4
Year      1.00000000 -0.0279419602 -0.0369876842  0.98274939  0.91565945
Month    -0.02794196  1.0000000000  0.0008846905 -0.10673246  0.01856866
MEI      -0.03698768  0.0008846905  1.0000000000 -0.04114717 -0.03341930
CO2       0.98274939 -0.1067324607 -0.0411471651  1.00000000  0.87727963
CH4       0.91565945  0.0185686624 -0.0334193014  0.87727963  1.00000000
N2O       0.99384523  0.0136315303 -0.0508197755  0.97671982  0.89983864
CFC.11    0.56910643 -0.0131112236  0.0690004387  0.51405975  0.77990402
CFC.12    0.89701166  0.0006751102  0.0082855443  0.85268963  0.96361625
TSI       0.17030201 -0.0346061935 -0.1544919227  0.17742893  0.24552844
Aerosols -0.34524670  0.0148895406  0.3402377871 -0.35615480 -0.26780919
Temp      0.78679714 -0.0998567411  0.1724707512  0.78852921  0.70325502
                 N2O      CFC.11        CFC.12         TSI    Aerosols
Year      0.99384523  0.56910643  0.8970116635  0.17030201 -0.34524670
Month     0.01363153 -0.01311122  0.0006751102 -0.03460619  0.01488954
MEI      -0.05081978  0.06900044  0.0082855443 -0.15449192  0.34023779
CO2       0.97671982  0.51405975  0.8526896272  0.17742893 -0.35615480
CH4       0.89983864  0.77990402  0.9636162478  0.24552844 -0.26780919
N2O       1.00000000  0.52247732  0.8679307757  0.19975668 -0.33705457
CFC.11    0.52247732  1.00000000  0.8689851828  0.27204596 -0.04392120
CFC.12    0.86793078  0.86898518  1.0000000000  0.25530281 -0.22513124
TSI       0.19975668  0.27204596  0.2553028138  1.00000000  0.05211651
Aerosols -0.33705457 -0.04392120 -0.2251312440  0.05211651  1.00000000
Temp      0.77863893  0.40771029  0.6875575483  0.24338269 -0.38491375
                Temp
Year      0.78679714
Month    -0.09985674
MEI       0.17247075
CO2       0.78852921
CH4       0.70325502
N2O       0.77863893
CFC.11    0.40771029
CFC.12    0.68755755
TSI       0.24338269
Aerosols -0.38491375
Temp      1.00000000

The following independent variables is N2O, highly correlated with (absolute correlation greater than 0.7)? #### CO2, CH4, CFC.12

The following independent variables is CFC.11, highly correlated with? #### CH4, CFC.12

Simplifying the Model

Given that the correlations are so high, let us focus on the N2O variable and build a model with only MEI, TSI, Aerosols and N2O as independent variables. Note, using the training set to build the model.

fit.climate.2 <- 
  lm(Temp ~ MEI + N2O + TSI + Aerosols, 
     data = climate_train)

summary(fit.climate.2)


Call:
lm(formula = Temp ~ MEI + N2O + TSI + Aerosols, data = climate_train)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.27916 -0.05975 -0.00595  0.05672  0.34195 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.162e+02  2.022e+01  -5.747 2.37e-08 ***
MEI          6.419e-02  6.652e-03   9.649  < 2e-16 ***
N2O          2.532e-02  1.311e-03  19.307  < 2e-16 ***
TSI          7.949e-02  1.487e-02   5.344 1.89e-07 ***
Aerosols    -1.702e+00  2.180e-01  -7.806 1.19e-13 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.09547 on 279 degrees of freedom
Multiple R-squared:  0.7261,    Adjusted R-squared:  0.7222 
F-statistic: 184.9 on 4 and 279 DF,  p-value: < 2.2e-16

The coefficient of N2O in this reduced model is 2.532e-02

(How does this compare to the coefficient in the previous model with all of the variables?) The model R2 is 0.7261

Automatically Building the Model

We have many variables in this analysis, and as we have seen above, dropping some from the model does not decrease model quality. R provides a function, step, that will automate the procedure of trying different combinations of variables to find a good compromise of model simplicity and R2.

This trade-off is formalized by the Akaike information criterion (AIC) - it can be informally thought of as the quality of the model with a penalty for the number of variables in the model.

The step function has one argument - the name of the initial model. It returns a simplified model. Using the step function in R to derive a new model, with the full model as the initial model (HINT: If your initial full model was called “climateLM”, you could create a new model with the step function by typing step(climateLM). Be sure to save your new model to a variable name so that you can look at the summary. For more information about the step function, type? step in your R console.)

fit.climate.step <- step(fit.climate)

Start:  AIC=-1348.16
Temp ~ MEI + CO2 + CH4 + N2O + CFC.11 + CFC.12 + TSI + Aerosols

           Df Sum of Sq    RSS     AIC
- CH4       1   0.00049 2.3135 -1350.1
<none>                  2.3130 -1348.2
- N2O       1   0.03132 2.3443 -1346.3
- CO2       1   0.06719 2.3802 -1342.0
- CFC.12    1   0.11874 2.4318 -1335.9
- CFC.11    1   0.13986 2.4529 -1333.5
- TSI       1   0.33516 2.6482 -1311.7
- Aerosols  1   0.43727 2.7503 -1301.0
- MEI       1   0.82823 3.1412 -1263.2

Step:  AIC=-1350.1
Temp ~ MEI + CO2 + N2O + CFC.11 + CFC.12 + TSI + Aerosols

           Df Sum of Sq    RSS     AIC
<none>                  2.3135 -1350.1
- N2O       1   0.03133 2.3448 -1348.3
- CO2       1   0.06672 2.3802 -1344.0
- CFC.12    1   0.13023 2.4437 -1336.5
- CFC.11    1   0.13938 2.4529 -1335.5
- TSI       1   0.33500 2.6485 -1313.7
- Aerosols  1   0.43987 2.7534 -1302.7
- MEI       1   0.83118 3.1447 -1264.9

summary(fit.climate.step)


Call:
lm(formula = Temp ~ MEI + CO2 + N2O + CFC.11 + CFC.12 + TSI + 
    Aerosols, data = climate_train)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.25770 -0.05994 -0.00104  0.05588  0.32203 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.245e+02  1.985e+01  -6.273 1.37e-09 ***
MEI          6.407e-02  6.434e-03   9.958  < 2e-16 ***
CO2          6.402e-03  2.269e-03   2.821 0.005129 ** 
N2O         -1.602e-02  8.287e-03  -1.933 0.054234 .  
CFC.11      -6.609e-03  1.621e-03  -4.078 5.95e-05 ***
CFC.12       3.868e-03  9.812e-04   3.942 0.000103 ***
TSI          9.312e-02  1.473e-02   6.322 1.04e-09 ***
Aerosols    -1.540e+00  2.126e-01  -7.244 4.36e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.09155 on 276 degrees of freedom
Multiple R-squared:  0.7508,    Adjusted R-squared:  0.7445 
F-statistic: 118.8 on 7 and 276 DF,  p-value: < 2.2e-16

R2 value of the model produced by the step function is 0.7508

Which of the following variable(s) were eliminated from the full model by the step function? #### It is interesting to note that the step function does not address the collinearity of the variables, except that adding highly correlated variables will not improve the R2 significantly. The consequence of this is that the step function will not necessarily produce a very interpretable model - just a model that has balanced quality and simplicity for a particular weighting of quality and simplicity (AIC).

Testing on Unseen Data

We have developed an understanding of how well we can fit a linear regression to the training data, but does the model quality hold when applied to unseen data?

Using the model produced from the step function, calculate temperature predictions for the testing dataset, using the predict function.

TempPredictions <- predict(fit.climate.step, newdata = climate_test)

climate.SSE = sum((TempPredictions - climate_test$Temp)^2)
climate.SST = sum((climate_test$Temp - mean(climate_train$Temp))^2)
1 - climate.SSE/climate.SST

[1] 0.6286051

Testing set R2 is 0.6286

R Data Analytics

Rihad Variawa

Data Scientist

I am the Sr. Data Scientist at Malastare AI and head of global Fintech Research, responsible for overall vision and strategy, investment priorities and offering development. Working in the financial services industry, helping clients adopt new technologies that can transform the way they transact and engage with their customers. I am passionate about data science, super inquisitive and challenge seeker; looking at everything through a lens of numbers and problem-solver at the core. From understanding a business problem to collecting and visualizing data, until the stage of prototyping, fine-tuning and deploying models to real-world applications, I find the fulfillment of tackling challenges to solve complex problems using data.