Your friend is getting married, and because they know you’re an expert on physical geography, they’d like you to choose between two possible places for the wedding planned for June 21. Based on the climate, where would you advise your friend to get married?
The two places under consideration are Vancouver Harbour, and Okanagan Centre, and it will probably be on June 21. The ceremony will be held outdoors early to mid-afternoon (the hottest time of day).
This lab uses a variety of statistical analyses to answer these questions. The techniques are all used by physical geographers in a range of different applications, not just in the planning of weddings.
After completion of this lab, you will be able to:
- Obtain historical Canadian climate data
- Calculate and interpret a mean
- Calculate the probability of extreme events
- Construct and interpret graphs showing climate change
First, we need to collect the data. This involves a bit of work.
We need data for 30 years to obtain a “climate normal”. Use the Environment Canada website.
The data for Vancouver Harbour are provided, but you’ll need to know how this was obtained because you’ll be collecting the same data for Okanagan Centre.
Search for Vancouver Harbour in the link above, and you will want daily data (not hourly data). We want 30 years of record (e.g. 1991-2020) for June 21. This is a “climate normal”. We will have to get the record for each year individually. For June 21, 2020, for example, you should have a maximum temperature of 20.7 ⁰C and zero precipitation.
Now complete the data for Okanagan Centre. The data for 2020 is already provided, but check to make sure that it is correct. Bear in mind that there may be some missing data; if it’s missing then insert a dash (-). If precipitation is marked “T” then that means that there was just a trace. Enter the “T” on the table, but count is as zero in the calculation of the mean. Note that there is no data available for 2019, there there is for all other years.
|Vancouver Harbour||Okanagan Centre|
|Year||Maximum Temperature (⁰C)||Total precipitation (mm)||Maximum temperature (⁰C)||Total precipitation (mm)|
- When you’ve finished the table, calculate the mean value for each variable at Okanagan Centre. Note that the mean can be calculated in Excel using the expression “=average(data)”, but you do not need to excel.
- What are these numbers telling you about the advisability of holding the wedding at Vancouver Harbour vs. Okanagan Centre?
You will want to make sure that it doesn’t rain and that it’s not ridiculously hot nor cold.
Based on the 30-year record it’s possible to calculate the probability of it being too hot or too cold. If we take the number of days that it rained over the 30-year normal period, and then calculate the percentage of times that it rained, then that is the probability of it raining on that day.
For example, suppose that it rained on that day 3 years out of 30, then 3/30 * 100 = 10%. If on the other hand you only had 27 years of record and it rained on 3 of them then the probability would be 3/27 * 100 = 11.1%
To do the calculations we will need to know how many years it rained. When doing the calculation do not include any years for which we don’t have a record. So if you only have, for example, 27 years of record then do the calculations based on 27 years of record, not 30 years of record.
We will also want to make sure that the temperatures aren’t too hot nor too cool. More specifically, we wouldn’t want temperatures over 30 ⁰C, nor under 20 ⁰C. To do the calculations we will need to know how many days out of the 30-year record the temperatures exceed 30 ⁰C or were below 20 ⁰C. Use these guidelines to determine the following.
- Calculate the probability of it raining on June 21 at Vancouver Harbour based on what has happened over the past 30 years.
- Calculate the probability of it raining on June 21 at Okanagan Centre based on what has happened over the past 30 years.
- What is the probability of temperatures exceeding 30 ⁰C on June 21 at Vancouver Harbour?
- What is the probability of temperatures being less than 20 ⁰C on June 21 at Vancouver Harbour?
- What is the probability of temperatures exceeding 30 ⁰C on June 21 at Okanagan Centre?
- What is the probability of temperatures being less than 20 ⁰C on June 21 at Okanagan Centre?
- Based on your responses to the above questions, what are your conclusions about where to hold the wedding?
When we calculate probabilities based on what has happened in the past, then we assume what statisticians call “stationarity”. This is an assumption that variations in measurements are due to random fluctuations, and are not associated with any systematic change. However, it’s possible that there is some underlying pattern of climate change. One simple way of examining that is to graph the data over time. Here we will use bar graphs for precipitation and line graphs for temperature.
Line graphs are generally used to show continuous data or something that is a property, e.g. temperature changes over time. Graphs have a horizontal axis (x-axis) and a vertical axis (y-axis). An easy way to remember this is “y to the sky”. Generally, the convention is that the x-axis is the independent variable and the y-axis is the dependent variable. In the case of our temperature graphs, the temperature (the dependent variable) depends on the month (the independent variable). The month doesn’t depend on the temperature.
Bar graphs present data as vertical or horizontal bars that are proportional in length to the value of something. They are used to show discrete or discontinuous data. For example, a bar graph is a good way to show the amount of precipitation that occurred over time. There will be one bar for each year, and the length of the 30 bars will be proportional to the amount of precipitation each year.
Drawing graphs is fairly easy by hand, but more professional looking graphs can easily be constructed using your laptop or other devices. One simple way is to use PowerPoint. Go to Insert > Chart > Bar or other types of graph. Alternatively, use your favourite search engine and look for an applet. We can also draw them in Excel, but it can be an involved process.
Checklist for graphs:
- Is the X-axis the independent variable?
- Are both axes labelled with units (e.g. ⁰C)?
- Does the graph have a title or figure caption?
- Do the size and scale makes sense – not cramped up, nor too much white space?
For this exercise, we will plot the June temperature and precipitation for Vancouver. Has it changed over the past 30 years? For your convenience, the data for Vancouver is listed below:
|June Precipitation||June average daily maximum Temperature|
- Draw a bar graph of June precipitation in Vancouver for the period 1991 – 2020.
- Draw a line graph of June mean daily maximum temperature in Vancouver for the period 1991- 2020.
- Are there any trends here? Your opinion will be a little subjective, but try to be as objective as possible. We know from data all over the world that climate change is real. Explain your results in that context.
- In the context of climate change, is the average for the past 30 years a good way to estimate the probability of what will happen next year? On the basis of climate trends we have identified, do you have any reason to adjust your thinking about the probability of rain or extreme temperatures in Vancouver?