Empirical Project 1 Solutions

These are not model answers. They are provided to help students, including those doing the project outside a formal class, to check their progress while working through the questions using the Excel, R, or Google Sheets walk-throughs. There are also brief notes for the more interpretive questions. Students taking courses using Doing Economics should follow the guidance of their instructors.


These solutions are based on data downloaded in January 2018. Your solutions may differ slightly if using more updated data.

Part 1.1 The behaviour of average surface temperature over time

  1. According to the source mentioned in the question:

‘Temperature anomalies indicate how much warmer or colder it is than normal for a particular place and time. For the GISS analysis, normal always means the average over the 30-year period 1951–1980 for that place and time of year. This base period is specific to GISS, not universal. But note that trends do not depend on the choice of the base period: If the absolute temperature at a specific location is two degrees higher than a year ago, so is the corresponding temperature anomaly, no matter what base period is selected, since the normal temperature used as base point is the same for both years.

Note that regional mean anomalies (in particular global anomalies) are not computed from the current absolute mean and the 1951–1980 mean for that region, but from station temperature anomalies. Finding absolute regional means encounters significant difficulties that create large uncertainties. This is why the GISS analysis deals with anomalies rather than absolute temperatures. For a more detailed discussion of that topic, see The elusive absolute surface air temperature.’

There are many valid ways to summarize this in your own words, for example:

Temperature anomaly measures, at any given place and time, the difference between observed temperature and the reference long-term average, or ‘normal’ temperature value. The long-term average is typically computed by averaging 30 or more years of data. The GISS analysis, for example, uses the average temperature from the period 1951–1980. A positive anomaly indicates that the observed temperature is warmer than the baseline long-term average temperature.

The use of anomalies, compared to other measures such as absolute temperature, allows for a more accurate representation of temperatures over larger areas. It provides a frame of reference that allows for more meaningful comparisons between locations.

The compilation of other indicators, such as absolute average temperatures, are difficult and controversial. The absolute average temperature data is more susceptible to uncertainties and inaccuracies. Temperature stations are unevenly distributed, in regions with very few stations, interpolation must be made over large areas. The temperature at a mountain top is lower than at the bottom. If a mountainous area is in general cooler than the baseline in a given month, the anomaly will show that temperatures for both locations (the top and bottom areas of a mountain) are below the reference value. If we use absolute temperature, however, the disparity between the measures at a mountain top and bottom would be quite large. Using anomalies also diminishes problems when stations are added, removed or missing.

  1. Solution figure 1.1 shows an example chart for January.

Solution figure 1.1 An example of a line chart with average temperature anomaly for January on the vertical axis and time (1880–2016) on the horizontal axis.

  1. Line charts for each season, using average temperature anomaly for that season on the vertical axis and time (1880–2016) on the horizontal axis, are shown in Solution figures 1.2–1.5.

Solution figure 1.2 A line chart showing average temperature anomaly for spring.

Solution figure 1.3 A line chart showing average temperature anomaly for summer.

Solution figure 1.4 A line chart showing average temperature anomaly for autumn.

Solution figure 1.5 A line chart showing average temperature anomaly for winter.

Solution figure 1.6 A line chart with annual average temperature anomaly on the vertical axis and time (1880–2016) on the horizontal axis.

  1. We are concerned about global temperature changes over time, so it is vital to look at the behaviour of the same variable over time. While averages of temperature taken over longer periods (one year or one decade) are more useful at revealing the overall trend of global warming, the averages taken over shorter periods (such as seasons) can give us more detailed information about the underlying mechanisms of global warming. Seasonal and monthly data can help us see the difference in patterns compared to what we observe in the annual data. For example, we could see if the rising annual average temperatures are due to temperatures rising only in a few months, or due to temperatures rising in all months.

Figure 1.4 Northern hemisphere temperatures over the long run (1000–2006).

Part 1.2 Variation in temperature over time

  1. Solution figures 1.7 and 1.8 show the variation in temperature over time for the periods 1951–1980 and 1981–2010 respectively.
Range of temperature anomaly (T) Frequency
−0.30 0
−0.25 2
−0.20 7
−0.15 6
−0.10 8
−0.05 12
0.00 7
0.05 14
0.10 12
0.15 11
0.20 8
0.25 3
0.30 0
0.35 0
0.40 0
0.45 0
0.50 0
0.55 0
0.60 0
0.65 0
0.70 0
0.75 0
0.80 0
0.85 0
0.90 0
0.95 0
1.00 0
1.05 0

Solution figure 1.7 A frequency table for 1951–1980.

Range of temperature anomaly (T) Frequency
−0.30 0
−0.25 0
−0.20 0
−0.15 0
−0.10 1
−0.05 3
0.00 2
0.05 7
0.10 1
0.15 5
0.20 3
0.25 4
0.30 7
0.35 7
0.40 4
0.45 6
0.50 8
0.55 4
0.60 4
0.65 5
0.70 7
0.75 4
0.80 6
0.85 2
0.90 0
0.95 0
1.00 0
1.05 0

Solution figure 1.8 A frequency table for 1981–2010.

Solution figure 1.9 A column chart for 1951–1980.

Solution figure 1.10 A column chart for 1981–2010.

  1. In the period 1951–1980, the value corresponding to the 3rd decile is −0.1, and the value corresponding to the 7th decile is 0.11. Temperature anomalies below −0.1 are therefore considered ‘cold’, and temperature anomalies above 0.11 are considered ‘hot’.
  1. In the period 1981–2010, 2.2% of temperatures would be considered ‘cold’ (compared to 30% in 1951–1980), and 84.4% of temperatures would be considered ‘hot’ (compared to 30% in 1951–1980). The increase in the percentage of ‘hot’ weather and decrease in the percentage of ‘cold’ weather suggests that we are experiencing hotter weather more frequently in 1981–2010.
1921–1950 1951–1980 1981–2010
DJF −0.06 −0.0007 0.52
MAM −0.06 0.0007 0.50
JJA −0.05 0.0007 0.41
SON 0.07 0.0003 0.43
DJF 0.06 0.05 0.07
MAM 0.03 0.03 0.07
JJA 0.02 0.01 0.06
SON 0.02 0.03 0.10

Solution figure 1.11 Mean and variance per season for periods 1921–1950, 1951–1980, and 1981–2010.

The temperature anomalies in DJF have a larger variance than those in JJA. The variance in DJF is about three times larger than that in JJA, particularly until 1980. For the period 1981–2010, the JJA temperature anomalies start becoming more variable.

  1. The column charts in Question 2(a) (Solution figures 1.9 and 1.10) and the table in Question 5(a) (Solution figure 1.11) suggest that temperatures are becoming more variable over time. However, (as stated in the article), many scientists argue that the increasing spread is merely a reflection of the fact that some regions of the world are warming faster than others. The government should look at temperature variability in their particular region to see if there is a similar pattern to that of the northern hemisphere in general, before deciding how much to spend on mitigating the effects of extreme weather events.

Part 1.3 Carbon emissions and the environment

  1. The location of the observatory at the summit of Mauna Loa means the data is representative of the globe. This is because the observatory is surrounded by miles of bare lava, eliminating the influence of CO2 absorbed or emitted locally by plants, soils, and human activities. Data collected at the observatory is selected to minimize the effects of anomalies and other shocks. The measurements are also calibrated rigorously and frequently, and compared to others taken at laboratories using different methods. Systematic and persistent biases are less than 0.2 ppm (parts per million), indicating that the measurements are highly accurate.
  1. Both measures are constructed based on monthly mean CO2 mole fraction. The mole fraction of CO2, expressed as parts per million (ppm), is the number of molecules of CO2 in every one million molecules of dried air (water vapor removed). The trend mean mole fraction for each month is determined by removing the seasonal cycles. Trend values are linearly interpolated for missing values. The interpolated value is the sum of the average seasonal cycle value and the trend value.

The data shows that the levels of CO2 are typically higher when recorded in spring and summer as plants absorb and consume more CO2 in these months than in autumn and winter. During autumn and winter, plants decrease photosynthesis and become net producers of CO2. Many scientists argue that climate change has led to higher rates of photosynthesis during growth seasons and higher rates of exhalation in autumn and winter. Climate change can therefore increase the seasonality of CO2 levels.

  1. The graph in Solution figure 1.12 suggests a positive relationship between CO2 and time.

Solution figure 1.12 Trend and interpolated monthly mean CO2 (mole fraction).

Solution figure 1.13 Scatterplot CO2 vs temperature (June).

  1. The months chosen to produce Solution figures 1.14 and 1.15 are January and December. The correlation coefficient for January is 0.82, and the correlation coefficient for December is 0.81, both indicating a strong positive linear correlation.

Solution figure 1.14 A scatterplot showing CO2 levels and temperature anomaly for January.

Solution figure 1.15 A scatterplot showing CO2 levels and temperature anomaly for December.