Name: Joan of Arc Multistructural Relational Extended Abstract √ Grade: Excellence Marker: N NS Fully N NS Fully N NS Fully posed a comparison investigative question √ selected and used appropriate displays √ identified features in the data and related this to the context finding an appropriate model and using the model to make a forecast communicated findings in a conclusion √ √ √ √ Purpose statement and Conclusion were near perfect. Marker’s Judgement EXCELLENCE √ Investigate time series data, with statistical insight involves integrating statistical and contextual knowledge throughout the statistical enquiry cycle, and may include reflecting about the process; considering other relevant variables; evaluating the adequacy of any models; or showing a deeper understanding of models. Plan/Purpose: Global warming (now more commonly referred to as Climate Change) is associated with the effects of Earth’s increasing surface temperature. More than ever before, governments are concerned with the consequences of human actions in industrial practices, deforestation which release “Greenhouse gases” into the atmosphere. According to http://www.niwa.co.nz/our-science/climate/information-and-resources/clivar/greenhouse , these greenhouse gases contribute to the absorption of infrared heat onto Earth, and warming the surface. (known as the Greenhouse effect) The Earth is incredibly sensitive to temperature change and the overall change of just one degree can be significant. On http://hyperphysics.phyastr.gsu.edu/hbase/thermo/grnhse.html there are claims that by increasing the temperature of the Earth’s surface “disastrous consequences” will occur in on nature, including melting ice, rising sea levels and natural disasters, such as flooding or drought. However, some people believe that global warming does not exist and there is not enough evidence to justify the imminent disasters that are to come if we do not change our unsustainable ways. I am going to investigate the patterns and trends of maximum temperatures over the past 20 years in Madrid (a Northern Hemisphere city) and Christchurch (a Southern Hemisphere city) and compare my findings to published scientific reports. I wish to find out whether the average temperatures in Christchurch and Madrid is increasing and could possibly confirm that global warming is taking place. Data: The data provided is maximum and minimum air temperatures of Madrid and Christchurch each month over 20 years, from 2000 to 2012. Long term trend: From 2000 to 2013, the raw data fluctuates approximately between 35°C to 6°C. The trend line starts at approximately 23°C and finishes at about 19°C. An interesting feature about this graph is that the trend line of Madrid’s temperature seems to be quite consistent, with little change in increasing or decreasing temperature. Residuals: There seems to be no obvious pattern in the residual plot. The largest residual is approximately 10°C, which is large (34%) when compared with the range of the data (356=29°C) A residual of this magnitude represents more than 10% of this range. (Any residual more than 10% of the overall range is considered to be significant) Seasonal effect: The seasonal patterns of maximum temperatures in Madrid become consistent as the years progress. (as seen by the red to blue graphs). Average seasonal highs (peaks) occur at July-August and seasonal lows (troughs) occur at January and December. This is typical to the Northern hemisphere seasonal temperatures as July and August correlates to the Summer season (high temperatures) in Madrid and January and December match the Winter season (low temperatures). A surprising feature is an outlier temperature in March 2001, where the maximum temperature significantly drops to 7.1°C. Component Contribution Maximum temperature in Min Max Range Approx % Madrid (°C) Contribution Raw data 6 35 29 Trend 20 23 3 10% Seasonal -11 12 23 79% Residual of greatest magnitude 10 10 34% The main source of maximum temperature in Madrid appears to be the seasonal effect, with 79% of the overall variation explained by the seasonal effect. Trend and residual components account for the remaining variability in the series. INZight has created the predictions of maximum temperatures in Madrid for the next 2 years (below) with their prediction (confidence) intervals. Month Year Predicted Lower Upper value value value Nov 2012 17.5835 12.07302 23.09397 Dec 2012 9.030564 3.406929 14.6542 Jan 2013 9.126722 3.38865 14.8648 Feb 2013 11.09462 5.240846 16.94838 Mar 2013 15.09022 9.119512 21.06092 Apr 2013 17.13634 11.04748 23.22519 May 2013 23.82193 17.61372 30.03014 Jun 2013 28.93076 22.60202 35.25951 Jul 2013 31.39579 24.94534 37.84623 Aug 2013 32.32305 25.74975 38.89634 Sep 2013 27.75876 21.06148 34.45604 Oct 2013 21.75519 14.93281 28.57758 Nov 2013 17.11839 9.27773 24.95905 Dec 2013 8.565455 0.611768 16.51914 Jan 2014 8.661613 0.593513 16.72971 Feb 2014 10.62951 2.445628 18.81338 Mar 2014 14.62511 6.324103 22.92611 Apr 2014 16.67123 8.251772 25.09069 May 2014 23.35682 14.8176 31.89604 Jun 2014 28.46565 19.80538 37.12593 Jul 2014 30.93068 22.14807 39.71328 Aug 2014 31.85794 22.95175 40.76413 Sep 2014 27.29366 18.26263 36.32467 Oct 2014 21.29009 12.13301 30.44716 The model forecasts that in August 2013, the maximum temperature in Madrid Is 32°C. At this time, the actual maximum temperature is likely to lie between 26°C and 39°C. A visual inspection of the model from 2000 to 2012 indicates that the predicted value is quite realistic, as it is similar in magnitude to previous ‘August’ values, but the prediction interval is too large to make a reliable prediction. Hence, the Holt-Winters model is unlikely to make inaccurate predictions because the prediction interval is reasonably large. In particular, the unrealistic prediction intervals suggest that the maximum temperatures of Madrid during December and January can be as low as 0.6°C (almost freezing, however these seem to match similar minimum temperatures in Madrid) and as high as 41°C in August, almost 5°C greater than previous maximum temperature values. The size of a prediction interval is significantly influenced by the magnitude of residuals . Given that the residuals were reasonably large, the prediction interval is reasonably reasonably large ( ±6.5°C) . Long Term Trend: From 1999 to 2012, the raw data fluctuates between 24°C to 10°C. The trend line also starts at approximately 17°C and finishes at approximately 18°C. An interesting feature about this graph is that the trend line of Christchurch’s maximum temperature seems to be quite consistent, with little change in increasing or decreasing temperature over time. Residuals: There seems to be no obvious pattern in the residual plot. The largest residual is approximately 3°C, which is large (20%) when compared with the range of the data (2510=15°C) A residual of this magnitude represents more than 10% of this range. (Any residual more than 10% of the overall range is considered to be significant) Seasonal effect: The seasonal patterns of maximum temperatures in Christchurch follow a reasonably consistent pattern throughout the years. Average seasonal highs (peaks) occur in December-January and seasonal lows (troughs) occur in July. This is typical to the Southern hemisphere seasonal temperatures as December and January correlate to the Summer season (high temperatures) in Christchurch and July matches the Winter season (low temperatures). Component Contribution Maximum temperature in Min Max Range Approx % Christchurch (°C) Contribution Raw data 10 25 15 Trend 17 18 1 6.7% Seasonal -6 5.5 11.5 77% Residual of greatest magnitude 3 3 20% The main source of maximum temperature in Christchurch appears to be the seasonal effect, with 77% of the overall variation explained by the seasonal effect. Trend and residual components account for the remaining variability in the series. INZight has created the predictions of maximum temperatures in Christchurch for the next 2 years (below) with their prediction (confidence) intervals. Month Year Predicted Lower Upper value value value Nov 2012 19.41257 16.47776 22.34738 Dec 2012 21.19953 18.26467 24.1344 Jan 2013 22.69312 19.75816 25.62808 Feb 2013 21.74365 18.80852 24.67878 Mar 2013 20.4681 17.53272 23.40348 Apr 2013 18.09247 15.15674 21.02821 May 2013 14.47908 11.54287 17.41529 Jun 2013 11.41821 8.481395 14.35502 Jul 2013 11.38537 8.447796 14.32295 Aug 2013 12.77413 9.835625 15.71263 Sep 2013 15.50103 12.56141 18.44065 Oct 2013 16.57802 13.63708 19.51897 Nov 2013 19.4622 16.3773 22.54709 Dec 2013 21.24916 18.16257 24.33576 Jan 2014 22.74275 19.65421 25.83128 Feb 2014 21.79328 18.70255 24.88401 Mar 2014 20.51773 17.42453 23.61094 Apr 2014 18.1421 15.04614 21.23807 May 2014 14.52871 11.42968 17.62774 Jun 2014 11.46784 8.365417 14.57026 Jul 2014 11.435 8.328855 14.54114 Aug 2014 12.82376 9.71354 15.93398 Sep 2014 15.55066 12.436 18.66532 Oct 2014 16.62765 13.50818 19.74713 The model forecasts that in July 2013, the maximum temperature in Christchurch is 11°C. At this time, the actual maximum temperature is likely to lie between 8.4°C and 14°C. A visual inspection of the model from 2000 to 2012 indicates that the predicted value is quite realistic, as it is similar in magnitude to previous ‘July’ values, but the prediction interval is too large to make a reliable prediction. Therefore, the Holt-Winters model is unlikely to make inaccurate predictions because the prediction interval is reasonably large. The size of a prediction interval is significantly influenced by the magnitude of residuals . Given that the residuals were reasonably large, the prediction interval is reasonably reasonably large ( ±3°C), though not as large as the residuals of Madrid’s maximum temperatures . “Compare and Contrast”: The trend line of the maximum temperatures of both Madrid and Christchurch do not seem to change significantly over the past 13 years. While the trend line of Madrid is between 19°C and 23°C, Christchurch’s maximum temperature is lower, between 17°C and 18°C. This reflects Spain’s continental/mediterranean climate (http://www.worldweatheronline.com/Madrid-weather-averages/Madrid/ES.aspx) which is typically warmer than New Zealand’s subtropical climate. (https://www.niwa.co.nz/education-and-training/schools/resources/climate/overview) At the end of 2012 (December), Madrid’s maximum temperature seems to be decreasing, while Christchurch’s temperature is increasing. This can be attributed by seasonality patterns, where it is becoming Winter in Madrid (in the Northern Hemisphere) and Summer in Christchurch (in the Southern hemisphere). It can also explain the contrasting peak and trough shown in July. Predictions vs Actual: In order to assess the model for prediction purposes the last three data values were removed, predictions found and then compared with the actual last three data values. This was repeated for both maximum temperatures in Madrid and Christchurch. Maximum temperatures in Madrid (°C) Month Year Actual Predicted Lower Upper value value value value Aug 2012 34.4 35.00499 29.57418 40.4358 Sep 2012 27.9 32.40783 26.93207 37.88359 Oct 2012 20.5 27.31714 21.79386 32.84042 Actual values and predictions are close for maximum temperatures in Madrid in August 2012 (0.6°C). However, the difference increases significantly in following months to as high as 6.8°C in October 2012), indicating the unreliability of this model for prediction purposes. Percentage differences between actual values and predictions are up to 33 %. It can also be seen that the actual maximum temperature of Madrid in October 2012 (20.5°C) does not fall within the 95% prediction (confidence) interval between 21.8°C to 32.8°C. Maximum temperatures in Christchurch (°C) Month Year Actual Predicted Lower Upper value value value value Aug 2012 12.7 12.7 9.732533 15.66233 Sep 2012 15.4 15.4 12.46889 18.39879 Oct 2012 16.9 16.3 13.37514 19.30523 Actual values and predictions are relatively closer for the maximum temperatures of Christchurch than Madrid, indicating the strength of this model for prediction purposes. Percentage differences between actual values and predictions are up to 3%. All actual values for maximum temperatures in Christchurch fall within the 95% prediction interval. I have created two new series- Madav (mean temperature in Madrid) and Chchav (mean temperature in Christchurch). These series reflect typical weather report data which provides the mean temperatures of the areas, rather than the maximum or minimum temperature (which fluctuate each year). Conclusion: (note: evidence for “Conclusion” can also be found throughout the report) The trend line of mean temperatures in both Madrid and Christchurch show no significant increase of decrease throughout the years. As shown by the maximum temperature seasonal trend series’, it is no surprise to see the correlation of maximum (peak) and minimum (trough) temperatures correlating to the seasons of Summer and Winter, respectively in opposite hemispheres. (ie In July, Madrid has a peak temperature during Summer, while Christchurch has a minimum trough temperature reading in Winter) Because it is difficult to ascertain from the long-term trend graphs whether average temperatures could be rising or falling, I will assume that it is possible to construct the centred moving mean (CMM) of the average temperatures for Madrid and Christchurch with a linear graph to provide quantitative gradient values. Madrid Temperature Temperature (Degrees celsius) 30 y = 0.0103x + 13.999 25 20 15 10 5 2000M01 2000M06 2000M11 2001M04 2001M09 2002M02 2002M07 2002M12 2003M05 2003M10 2004M03 2004M08 2005M01 2005M06 2005M11 2006M04 2006M09 2007M02 2007M07 2007M12 2008M05 2008M10 2009M03 2009M08 2010M01 2010M06 2010M11 2011M04 2011M09 2012M02 2012M07 0 From this graph, it can be seen that every decade, the average temperature in Madrid is increasing by about 1.2°C (or increasing by 0.0103°C per month), or 12°C every 100 years. 20 Christchurch Temperature y = 0.0007x + 11.435 Temperature (Degrees celsius) 18 16 14 12 10 8 6 4 2 2000M01 2000M06 2000M11 2001M04 2001M09 2002M02 2002M07 2002M12 2003M05 2003M10 2004M03 2004M08 2005M01 2005M06 2005M11 2006M04 2006M09 2007M02 2007M07 2007M12 2008M05 2008M10 2009M03 2009M08 2010M01 2010M06 2010M11 2011M04 2011M09 2012M02 2012M07 0 Meanwhile, the average temperature in Christchurch is increasing by 0.084°C every decade (or increasing by 0.0007°C per month), or 0.84°C (almost 1°C ) every 100 years. Hence, the temperature difference of Madrid’s average temperature is significantly (about 14 times) greater than Christchurch over time. Given that Madrid and Christchurch are reliable cities to represent overall Northern and Southern temperatures (respectively), we could conclude that the Northern Hemisphere is in graver risk of significant temperature increase, while the long-term temperature increase in the Southern Hemisphere is relatively negligible, at about 1°C. Although one degree may be considered to be a negligible amount, the effects can be significant on the sensitive Earth. A report from http://climate.nasa.gov/effects explains that “small changes in temperature correspond to enormous changes in the environment.” For instance, at the end of the last ice age, “temperatures were only 5 to 9 degrees cooler than today” Another report on http://www.worldbank.org/en/news/press-release/2012/11/18/newreport-examines-risks-of-degree-hotter-world-by-end-of-century claims that a 4°C global temperature increase is grave news, fearing “the inundation of coastal cities; increasing risks for food production potentially leading to higher under and malnutrition rates; many dry regions becoming dryer, wet regions wetter; unprecedented heat waves in many regions, especially in the tropics; substantially exacerbated water scarcity in many regions; increased intensity of tropical cyclones; and irreversible loss of biodiversity, including coral reef systems.” However, it takes a decade for one degree increase, at least in Madrid. A 4°C increase would take about 30-40 years and even longer in Christchurch. The centred moving mean is only one way to analyse the series’ trends; a regular, consistent fluctuation of average temperatures in both cities over the past 20 years suggests to me that global warming is not a fast-growing issue in the Southern Hemisphere. Furthermore, in order to determine whether global warming is taking place, it would be worth considering the temperatures of other global areas, or whether Madrid and Christchurch would be representative cities in the Northern and Southern hemisphere, respectively. It would be worth considering other countries, especially those which emit significant amounts of Greenhouse gases. According to http://www.carbonplanet.com/country_emissions , United Arab Emirates produce the greatest amount of greenhouse gases per person (29.91 tonnes per person) in comparison to New Zealand’s 8.48 tonne per person production. Migrations Plant growth Animal behaviours Rapid change- significant differences Data over long time- tends to fluctuate (cause of residuals)