Climate Change

Climate Change will have a significant effect upon global populations.

Severe weather events and rising sea levels

Disease and population displacement

Unprecedent melting of glaciers and the polar ice caps.

Climate Change

Dramatic increase in atmospheric concentrations of carbon dioxide (CO$_{2}$) over the past century.
Atmospheric carbon dioxide traps heat leading to a Greenhouse Effect.
The Greenhouse Effect¹ disrupts global weather patterns resulting in:

More frequent and severe weather events leading to natural disasters and population displacement.

Greenhouse effect

Problem Statement

Problem

Do changes in global atmospheric carbon dioxide levels correlate with variations in Australian environmental conditions?

Method

Statistical analyses were performed on changes in various environmental parameters (i.e. Australian maximum annual ambient temperatures and sea surface temperatures) and then compared to the known increase in carbon dioxide and sea levels over the past 100 years.

Data

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Atmospheric carbon dioxide

Atmospheric Carbon Dioxide data² was collected at the Mauna Loa Observatory by the UC Scripps CO$_{2}$ program and was downloaded from the Kaggle website (https://www.kaggle.com/ucsandiego/carbon-dioxide).
The dataset contains monthly CO$_{2}$ concentrations in parts per million (ppm) measured on the 08A calibration scale and collected at 24:00 hours on the 15^th of each month.
The data were treated to remove noise and seasonal variations.

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Australian annual maximum ambient temperature anomalies

Annual maximum ambient temperatures³ were downloaded from the Australian Government Bureau of Meterology website (http://www.bom.gov.au/).
Temperatures were provided for each of the six Australian states and the Northern Territory.
Temperatures are presented as anomalies or departures from the 1961-1990 average temperatures (the international standard period for the calculation of climate averages).

Data Cont.

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Australian sea surface temperatures

Changes in sea surface temperatures⁴ recorded at a number of regions around Australia were downloaded from the Australian Government Bureau of Meterology website (http://www.bom.gov.au/).
Temperature changes were calculated based on an average annual sea surface temperature (1961-1990) of 22.3^oC (the international standard period for the calculation of climate averages).

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Global mean sea levels

Global mean sea level (GMSL) data⁵ was downloaded from the CSIRO Oceans and Atmosphere website (http://www.cmar.csiro.au/sealevel/index.html).
Changes in global averaged sea level since 1993 were estimated from satellite altimeter measurements and data from 1880 were determined by combining in situ sea level data from coastal tide gauges and the spatial patterns of variability obtained from satellite altimeter data.
Data were calculated using a baseline of 1880 sea levels.

Historical Rate of Change in CO$_{2}$ and Various Environmental Parameters

par(mfrow=c(2,2), mai=c(1, 1, 0.5, 1))
plot(CO2_levels ~ Date, data = CO2, xlab="Year", ylab = "CO2 conc (ppm)", col="blue", pch=16, cex=0.8, main="Carbon Dioxide Levels")
plot(GMSL ~ Year, data = sea_level, ylab = "sqrt(GMSL) (mm)", col="blue", pch=16, cex=0.8, main="Sea Levels")
plot(Temp_Change ~ Year, data = water, ylab = "Sea Surface Temp Anomaly (C)", col="blue", pch=16, cex=0.8, main="Sea Temp Anomalies")
plot(Temp_Change ~ Year, data = air, ylab = "Max Temp Anomaly (C)", col="blue", pch=16, cex=0.8, main="Max Ambient Temp Anomalies")

Data Distribution

par(mfrow=c(1,2))
plotNormalHistogram(water$Temp, col="antiquewhite2", main="Max Ambient Temperatures", linecol="blue2", xlab="")
plotNormalHistogram(air$Temp, col="antiquewhite2", main="Sea Surface Temperatures", linecol="blue2", xlab="")

- Histograms of Maximum Ambient and Sea Surface Temperatures overlaid with a normal curve.

Hypothesis Testing

Overall Regression Model

The overall regression model $y = \alpha + \beta x + \epsilon$ was tested (F-test) using the hypothesis:

$H_0:$ The data does not fit the linear regression model.

$H_A:$ The data fits the linear regression model.

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Intercept

Statistical significance for the intercept ($\epsilon$) was tested (t-test) using the hypothesis:

Null Hypothesis - The intercept is equal to 0.

Alternate Hypothesis - The intercept is not equal to 0.

\[H_0: \alpha = 0 \]

\[H_A: \alpha \ne 0\]

Slope

Statistical significance for the slope ($\beta$) was tested (t-test) using the hypothesis:

Null Hypothesis - There was no relationship between x and y thus the slope is equal to 0.

Alternate Hypothesis - There was a relationship between x and y thus the slope is not equal to 0.

\[H_0: \beta = 0 \]

\[H_A: \beta \ne 0\]

Sea surface temperatures

Linear Regression Analysis

water_summary <- lm(Temp_Change ~ Year, data=water); water_summary %>% summary()

## 
## Call:
## lm(formula = Temp_Change ~ Year, data = water)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.46272 -0.11930 -0.01943  0.11359  0.43349 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.685e+01  9.216e-01  -18.29   <2e-16 ***
## Year         8.557e-03  4.706e-04   18.18   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1719 on 115 degrees of freedom
## Multiple R-squared:  0.7419, Adjusted R-squared:  0.7397 
## F-statistic: 330.6 on 1 and 115 DF,  p-value: < 2.2e-16

Confidence Interval

water_summary %>% confint()

##                     2.5 %        97.5 %
## (Intercept) -18.677271110 -15.026296754
## Year          0.007624816   0.009489183

Maximum ambient temperature anomalies

Linear Regression Analysis

air_summary <- lm(Temp_Change ~ Year, data=air); air_summary %>% summary()

## 
## Call:
## lm(formula = Temp_Change ~ Year, data = air)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8029 -0.2067 -0.0160  0.2398  0.7510 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -19.466859   2.102622  -9.258 2.83e-15 ***
## Year          0.009894   0.001071   9.238 3.14e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3422 on 105 degrees of freedom
## Multiple R-squared:  0.4483, Adjusted R-squared:  0.4431 
## F-statistic: 85.34 on 1 and 105 DF,  p-value: 3.142e-15

Confidence Interval

air_summary %>% confint()

##                     2.5 %       97.5 %
## (Intercept) -23.635969044 -15.29774870
## Year          0.007770027   0.01201719

Correlation Coefficient

Maximum ambient temperature anomalies

Correlation Coefficient

r <- cor(air$Temp_Change, air$Year, use = "complete.obs"); r

## [1] 0.6695863

Confidence Intervals

library(psychometric); CIr(r, n = 107, level = .95)

## [1] 0.5495962 0.7625095

.

Sea surface temperatures

Correlation Coefficient

r <- cor(water$Temp_Change, water$Year, use = "complete.obs"); r

## [1] 0.8613539

Confidence Intervals

CIr(r, n = 117, level = .95); detach("package:psychometric", unload=TRUE)

## [1] 0.8058227 0.9018672

Linear Regression Fit

par(mfrow=c(1,2))
plot(Temp_Change ~ Year, data = water, ylab = "Sea Surface Temp Anomaly (C)", xlim=c(1880, 2017), ylim=c(-0.7, 1), col="blue", pch=16, cex=0.7, main="Sea Surface Temp")
abline(water_summary, col="red", lwd=2)
plot(Temp_Change ~ Year, data = air, ylab = "Max Temp Anomaly (C)", xlim=c(1880, 2017), ylim=c(-1.3, 1.4), col="blue", pch=16, cex=0.7, main="Max Ambient Temp")
abline(air_summary, col="red", lwd=2)

Sea Surface Temperatures

Simple linear regression

Linearity assumed, normality of residuals OK, homoscedasticity OK, no influential cases
r = 0.86, r$^2$ = 0.74
Model ANOVA, F(1, 115) = 330.6, p < 0.001
a = -16.85, p < 0.001, 95% CI (-18.68, -15.03)
b = 0.009, p < 0.001, 95% CI (0.008, 0.009)

Decision

Overall Model: Reject H$_{o}$
Intercept: Reject H$_{o}$
Slope: Reject H$_{o}$
Sea Surface Temperature = -16.85 + 0.009 X Year

Conclusion:

There was a stastically significant positive linear relationship between Sea Surface Temperatures over time.

Maximum Ambient Temperature Anomalies

Simple linear regression

Linearity assumed, normality of residuals OK, homoscedasticity OK, no influential cases
r = 0.67, r$^2$ = 0.45
Model ANOVA, F(1, 105) = 85.34, p < 0.001
a = -19.47 , p < 0.001, 95% CI (-23.64, -15.30)
b = 0.010, p < 0.001, 95% CI (0.008, 0.012)

Decision

Overall Model: Reject H$_{o}$
Intercept: Reject H$_{o}$
Slope: Reject H$_{o}$
Ambient Temperature Anomaly = -19.47 + 0.010 X Year

Conclusion:

There was a stastically significant positive linear relationship between Sea Surface Temperature Anomalies over time.

Testing Assumptions

Annual maxmium ambient temperature anomalies

par(mfrow=c(2,2)); plot(air_summary, col="blue", pch=16, lwd=2, cex=0.8)

The residual vs fitted and square root or the standardized residuals plots indicate that this is a linear relationship and the data are homoscedastic.

The residuals vs leverage plot indicates no data points are outliers having a disproportionate influence on the fit of the regression model.

The qq-plot shows that the data fit a normal distribution.

Testing Assumptions Cont.

Sea surface temperatures

par(mfrow=c(2,2)); plot(water_summary, col="blue", pch=16, lwd=2, cex=0.8)

The residual vs fitted and square root or the standardized residuals plots indicate that this is a linear relationship and the data are homoscedastic.

The residuals vs leverage plot indicates no data points are outliers having a disproportionate influence on the fit of the regression model.

The qq-plot shows that the data fit a normal distribution.

Discussion

Other studies have demonstrated an increase in atmospheric CO$_{2}$ levels over the past 70 years.²

Atmospheric samples in ice cores show disproportionate increase in CO$_{2}$ since the Industrial Revolution^2,6.

Increased atmospheric CO$_{2}$ levels have been proposed to lead to higher ambient temperatures.
We have shown a significant linear increase in Australian ambient maximum temperatures (~0.01$^o$C/year) and sea surface temperatures (~0.009$^o$C/year) over the past century.
Anticipated that increases in ambient temperatures will lead to further maleting of the poar ice caps contributing to rises in sea levels¹.

Studies have shown that sea levels have steadily risen of the past century.⁵

By 2300 sea levels are predicted to increase to < 1m if CO$_{2}$ levels are stabilized to < 500 ppm or could reach ~3m if levels rise above 700 ppm.

.

$CO_{2} levels$ Sea Level rise

References

https://climate.nasa.gov/causes/
Keeling, Charles D., Stephen C. Piper, Timothy P. Whorf, and Ralph F. Keeling Evolution of natural and anthropogenic fluxes of atmospheric CO$_{2}$ from 1957 to 2003. Tellus B. 63 (2011): 1-22.
Australian Bureau of Meterology
Huang, B., V.F. Banzon, E. Freeman, J. Lawrimore, W. Liu, T.C. Peterson, T.M. Smith, P.W. Thorne, S.D. Woodruff, and H.-M. Zhang, 2015: Extended Reconstructed Sea Surface Temperature version 4 (ERSST.v4): Part I. Upgrades and intercomparisons. Journal of Climate 28:3, 911-930
Church, J. A. and N.J. White (2011), Sea-level rise from the late 19th to the early 21st Century. Surveys in Geophysics, 32, 585-602
Barnola J. M., Raynaud D., Korotkevich Y. S. and Lorius C. (1987) Vostok ice core provides 160,000-year record of atmospheric CO$_{2}$. Nature, 329, 408-414

Climate Change in Austalia

Historical changes in carbon dioxide and environmental factors

RPubs link information

Climate Change

Climate Change will have a significant effect upon global populations.

Climate Change

Greenhouse effect

Problem Statement

Problem

Method

Data

Atmospheric carbon dioxide

Australian annual maximum ambient temperature anomalies

Data Cont.

Australian sea surface temperatures

Global mean sea levels

Historical Rate of Change in CO\(_{2}\) and Various Environmental Parameters

Data Distribution

Hypothesis Testing

Overall Regression Model

Intercept

Slope

Sea surface temperatures

Maximum ambient temperature anomalies

Correlation Coefficient

Maximum ambient temperature anomalies

Sea surface temperatures

Linear Regression Fit

Sea Surface Temperatures

Simple linear regression

Decision

Conclusion:

Maximum Ambient Temperature Anomalies

Simple linear regression

Decision

Conclusion:

Testing Assumptions

Annual maxmium ambient temperature anomalies

Testing Assumptions Cont.

Sea surface temperatures

Discussion

References