Climate change and its impact on ourenvironment: the statistical evidence

Sample project STAT301 project

Suhasini Subba Rao

Climate Change

Background: Climate Change

• Over the past thirty years there has been mounting evidence that theclimate is rapidly changing due to man-made emissions.

• Ice cores data is often used to estimate the composition of our atmospherein our ancient past.

• For thousand of years until the industrial revolution, the amount of CO2is the atmosphere has been relatively stable. However, from the startof the industrial revolution (200 years ago), when coal was used on amassive scale to power machines. The amount of CO2 realized into ouratmosphere has increased.

• In this project our focus is on the recent past. We study Earth’stemperatures from 1850s onwards, the amount of CO2 in our atmosphere

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from 1850s onwards and the size of the iceshelf in the Arctic from 1979onwards.

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Summary of project

• The data we study are the global temperature anomalies from 1850-2004and the yearly CO2 levels over the same period of time.

• We will also study the size of the Arctic ice-shelf from 1979 - 2016 (thisis measured using Satellite imaging). Data after 2016 is difficult to comeby due to changes in government policies for the EPA and NASA.

• We use the technique of linear regression to look for trends in thetemperature and determine if there is any statistical dependence betweentemperatures and CO2 levels.

• We use the independent sample t-test to analyze changes in the size ofArctic.

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The temperature and CO2 plots 1850-2004

• Above, on the left, we have plotted the yearly global temperatureanomalies against year (the average yearly temperature take overhundreds of weather stations). On the right we have plotted theyearly CO2 levels.

• Observe the rise in both the temperature and CO2 levels the past 150years.

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Regressing temperatures against year

• We fit the model Temp = −7.3 + 0.004× Y ear. Of course we can fit aline through anything, thus we analyze this slope.

To test if the positive slope is statistically significant we test H0 : Slope ≤0 against HA : Slope > 0.

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• The p-value is less than 0.01%, we reject the null. It strongly suggestingthat temperatures are increasing over the past 150 years. In other words,the increase cannot be explained by “random/statistical” variation.

• The 95% confidence interval for the slope is [0.0032, 0.0042]Celsius.

• Thus, on average, the temperature is increasing between[0.0032, 0.0042]Celsius a year.

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Explaining the rise

• Since CO2 gases traps heat in the atmosphere (very simply put) and theamount of CO2 in the atmosphere is increasing. It is widely believedthat the rise in temperatures is due to the increase in CO2.

• Thus we regress the CO2 on temperatures.

• Warning (advanced) In general, one needs to be cautious when applyingregression to random variables (with trend). It can lead to what is calledspurious correlation (in due to common trends). However, atmosphericphysics tells us that a rise in CO2 does lead to increases in temperatures.Thus, if we do observe a significant dependence, we can assume it is notspurious.

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The CO2 against temperatures

• For each year we observe a global temperature and a CO2 level. Usingthis we make a plot of the global temperatures against the CO2 levels.

• We fit a line (of best fit) between the CO2 and the temperatures isTemp = −0.35 + 0.079× CO2.

• If we test H0 : Slope ≤ 0 against HA : Slope > 0. The p-value is less

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than 0.01%, again we reject the null. The data strongly suggesting adependence between CO2 levels and temperature.

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Assessing the reliability of the statistical analysis

• As in all statistical analysis we need to assess the reliability of the p-values. For regression, this means the residuals should not deviate muchfrom normality (if the sample size is small, in our example it is large).

• We calculate the residuals in Statcrunch. The residuals look normal(from both QQplot and histogram). However, we need to be cautious asthe data is unlikely to be independent (this will mean the true formulafor the standard error is different).

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Impact of higher temperatures: Size of Arctic ice shelf• We plot the yearly size of the ice-

shelf against year from 1979 - 2016(measured using satellite imaging).

• Scientists believe there has beena dramatic decrease from the late1990s onwards. To check this,we partition the ice size data from1979-1997 and 1998-2016.

• To see if the change between the early years and the later years arestatistically significant, we apply an independent sample t-test for theyears 1979-1997 and 1998-2016 (there isn’t any matching).

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Size of arctic ice shelf

• We observe that the mean size of theiceshelf has dropped by 1.71. Scientistssay that increasing temperatures leadto a smaller iceshelf.

• Based on these observations, we test H0 : µearly − µlate ≤ 0 vs

HA : µearly − µlate > 0.

• The ice-shelf has dropped in size. This estimate, fits within what wethink should happen under the alternative hypothesis.

• The p-value is extremely small.

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• The small -p-value (less than 0.01%) this strongly suggests that the sizeof the ice-shelf has decreased in the past 20 years. A 95% confidenceinterval for the difference is [1.7± 2.04× 0.22] = [1.25, 2.14].

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Checking normality of sample mean

• The independent sample t-test depends on normality of the sample mean.

• To check this we uploaded the early and late data sets into statcrunch.

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• We used the sampling app to check the distribution of the sample mean.The distribution of the sample means are the green plots in the previousslide. The green histograms of the sample means look quite normal. Sothe normality assumption appears to be satisfied. Thus the p-values areprobably accurate (though we have to cautious as the data is dependentand we have assumed there is no relationship, which changes the standarderrors).

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Conclusions

• The data suggests that the global temperatures are increasing over time.

• One potential reason for the increase in termperatures is the rise in CO2levels, and our analysis supports this view.

• A further investigation of the size of the Arctic ice-shelf suggests asignificant decrease in its size. Possible due to the warming in Arcticoceans.

• Statistics Issues Whenever we apply statistical tools, we should alsoreflect on the assumptions we make. The fundamental assumption forall the methods described in this project is that the observations are notrelated (we call this dependent). However, as the observations are atime series, this is unlikely to hold, which an lead to incorrect conclusions

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(p-values etc). For complex data sets, more sophisticated tools need beto used.

• Conclusion Protect our planet, it is the only one with Pizza...

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Data sources

• It is important to disclose the source of data and to ensure the source isreliable.

• The data used in this project was provided by several national agencies:

• Temperature data: http://www.cru.uea.ac.uk/data

• CO2 data: https://www.esrl.noaa.gov/gmd/ccgg/trends/data.

html

• Ice Shelf data: https://www.epa.gov/climate-indicators/

climate-change-indicators-arctic-sea-ice

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