These days, I'm no longer surprised when I hear about " unseasonably warm weather" on the news. However, there were many days in March when it felt particularly warm around Tokyo. The cherry blossoms in my neighborhood were blooming earlier than usual, so I felt like the seasons were changing so quickly.
This blog was influenced by a post by Xan , the developer of Graph Builder. The post is a graph that summarizes the flowering dates of cherry blossoms in Kyoto from 812 AD to the present. (The cherry blossom markers are beautiful, so please take a look.)
Kyoto cherry blossom peak bloom day since the year 812
https://public.jmp.com/packages/J_rDc8JMMdjJBJDf7fMbF
If you look at the smooth line drawn in this graph, you can see that from the latter half of the 19th century to the present, there has been a trend in which the blooming date of cherry blossoms has rapidly moved earlier.
The famous `` 400 °C rule'' states that the cherry blossom blooming date is determined by the day when the total daily average temperature in the area from February 1st reaches 400 °C. Therefore, it is thought that the early and late flowering is influenced by the temperature in February and March .
Therefore, I looked into the average temperature in Kyoto in February and March from 1970 to the present ( 2021 ).
The figure below shows the average temperature in February (orange) and the average temperature in March (red) for each year using a polygonal line and a smooth line (line that shows trends). (Data source: Japan Meteorological Agency)
The smooth line shows that the average temperature in February and March has been on the rise in recent years, but especially since 2010 , it has been rising rapidly in March , and the average temperature in March 2021 is 11.6 degrees Celsius. , the highest since 1970 .
So, how about using a control chart used in process control to investigate these annual changes in temperature? There are various types of control charts, but one of them, the EWMA control chart, can detect even small shifts (changes), so it may be possible to detect an upward trend in temperature as seen in the graph. With JMP 16 , EWMA has added various functions, so I can't think of anything else to do but give it a try. *
( * Similarly, there is a CUSUM control chart that detects small shifts .)
EWMAWhat is a control chart?
EWMA control chart stands for Exponentially Weighted Moving Average control chart. A normal X chart plots the value at that point in time, whereas in an EWMA chart, the value at that point also depends on past values. The more recent the degree of dependence, the greater the degree of dependence, and as you go back in time, the degree of dependence decreases exponentially.
When X i is the value at time i , the value Z i at time i on the EWMA control chart is calculated using the value Z i-1 one time before and the weight parameter λ ( lambda ) specified by the user. , is calculated using the following formula:
Z i = λ X i + (1- λ ) Z i-1
By default, the value of λ in JMP is 0.2 , but in this case, the EWMA control chart plots the values using 20% current information and the remaining 80% historical information.
Due to the nature of formulas, the amount of information (weight) used decreases exponentially as you go back into the past. The figure below shows the weight of past time points relative to the present time (point 0 ) when λ = 0.2 .
At the moment, the weight is 0.2 , but you can see that the weight decreases exponentially as you go back one point in time (-1) and two points in the past (-2) .
It is said that using EWMA control charts for process control makes it easier to detect small shifts (changes) in the process. From now on, I will draw an EWMA for the average temperature in Kyoto in February and March shown above.
JMP 16EWMA control chart for
JMP has always been able to draw EWMA control charts, but JMP 16 changes the interface and adds significantly better features. The main additional features are as follows.
- Along with the EWMA control chart, the X control chart and residual control chart are also displayed.
- Using the control panel in the report, you can change λ (lambda) and σ ( sigma ) and reflect them interactively on the control chart.
- The starting point of change can be detected.
EWMA control chart for average temperature in Kyoto ( February and March )
First, here is the EWMA control chart for February .
Three charts are drawn from top to bottom, and from top to bottom they are an EWMA control chart, an X control chart (a control chart using the temperature value itself), and a residual control chart.
A residual control chart is a plot of the residual calculated by subtracting the EWMA control chart value one point in time from the X control chart value at a certain point in time. For example, the residual for 2010 can be calculated by subtracting the 2019 EWMA value from the 2020 value.
The values entered in the "Settings panel" on the left are as follows.
Target value : Average value of the data. (EWMA control chart, green line on X control chart )
Sigma : Value indicating variation (σ). Estimated from data.
Lambda : weights explained above (default 0.2 )
The red line is the control limit line calculated at 3 σ (sigma).
If you look at the X control chart in the middle, you won't be able to find any similar trends at first glance. However, if you look at the EWMA control chart at the top, you can see a downward trend in the 70s and 80s , and an upward trend from 2018 onwards. However, the control limit line has not been exceeded in any of the years.
By the way, the blue dot plotted at the top right of the EWMA control chart is the predicted value for 2022 .
Next is the EWMA control chart for March . A clear trend can be seen.
The X chart is outside the upper control limit in 2021 . In the EWMA control chart, an upward trend can be seen in the 2010s , and in 2020 it moved out of the control limits.
The purple line drawn on the EWMA control chart indicates the starting point where the shift occurred. Although it could not be detected in the average temperature in February , it was able to detect small changes in the average temperature in March.
Although not shown here, a control chart showing a similar trend will be drawn for the average temperature in Tokyo. The trend toward the upper side of the EWMA control chart is proof that in recent years it has been warm even in March , and the cherry blossoms have been blooming early.
In JMP 16's EWMA control chart, when you change the target value, sigma, and Lambda settings from the "Settings panel" on the left, the control chart is immediately drawn with those settings. The figure below shows the March EWMA control chart when Lambda was changed to 0.1 . In other words, increasing the reliance on past data will result in this year ( 2021 ) falling outside the upper control limit.
Considering it as an environmental issue
For those who don't like the cold, it may be a blessing to get warmer quickly, but given the effects of global warming, we can't be too happy about it.
The `` Paris Agreement '' is well-known for current international environmental efforts, but there is also an earlier agreement, the `` Kyoto Protocol, '' established in Kyoto, which we talked about this time. The Kyoto Protocol was adopted in 1997 as a measure to combat global warming, but even now, more than 20 years later, it cannot be said that effective countermeasures have been taken.
President Biden took office in the United States and the country returned to the Paris Agreement in February of this year, but I feel that we are now at an important stage in our efforts to stop global warming.
