In news etc. ” I'm not so surprised these days when I hear "unseasonable warmth", but this year 3 There were many days when I felt that the moon around Tokyo was particularly warm. The cherry blossoms in my neighborhood were blooming earlier than usual, so I felt that the seasons were changing early.
This blog is the developer of Graph Builder Xan Inspired by Mr.'s post. The post is the year when the cherry blossoms in Kyoto bloom. 812 It is a graph summarized from the year to the present. (The cherry blossom marker is beautiful, so please have a look.)
Kyoto cherry blossom peak bloom day since the year 812
https://public.jmp.com/packages/J_rDc8JMMdjJBJDf7fMbF
Looking at the smooth lines drawn in this graph, 19 From the latter half of the century to the present, we can see that there is a trend in which the cherry blossoms bloom rapidly.
The flowering day of the cherry blossoms is in that area 2 Month 1 The total daily average temperature from day to day 400 "The day when it reaches ℃ is a guide. 400 The "law of ℃" is famous. Therefore, early and late flowering is 2,3 It is thought that the temperature of the moon has an effect.
Therefore, 1970 From year to present ( 2021 Until year) 2,3 I checked the average temperature of Kyoto in the month.
The figure below shows each year 2 Monthly average temperature (orange), 3 The average monthly temperature (red) is shown by a polygonal line and a smooth line (a line that shows the trend). (Data source: Japan Meteorological Agency)
From smooth lines, in recent years twenty three You can see that the average monthly temperature is on the rise, but especially 2010 After the year 3 The moon is rising sharply this year 2021 Year 3 The average monthly temperature is 11.6 ℃ and 1970 It has been the highest since the year.
Then these How about using a control chart used in process control to investigate changes in temperature from year to year? There are various types of control charts, one of which EWMA Since the control chart can detect even small shifts, it may be possible to detect the upward trend of temperature as seen in the graph. exactly, JMP 16 so EWMA Has various additional functions, so I can't think of anything other than trying it out. *
( * Similarly, as a control chart to detect small shifts CUSUM ( Cumulative sum ) There is a control chart. )
EWMA What is a control chart?
The EWMA chart is an abbreviation for Exponentially Weighted Moving Average chart. Normal X The control chart plots the values at that time, whereas the control chart plots the values at that time. EWMA In the control chart, the value at that time also depends on the past value. The more recent the degree of dependence, the greater the degree of dependence, and the more retroactive it is, the smaller the degree of dependence is exponentially.
X i To i When it is the value at the time EWMA Of the control chart i Value at the time Z i Is that 1 Value before time point Z i-1 And the user-specified weight parameter λ ( lambda ) Is used to calculate with the following formula.
Z i = λ X i + (1- λ ) Z i-1
By default in JMP, the value of λ is 0.2 But at this time EWMA In the control chart, 20% The current information, the rest 80% You are plotting the values using past information.
Due to the nature of the formula, the amount (weight) of information used decreases exponentially as we go back in time. The figure below is λ = 0.2 At the moment (0 Time point ) Shows the weight of the past point in time.
At the moment 0.2 There is a weight of 1 Before the point (-1) , 2 Before the point (-2) You can see that the weight decreases exponentially as we go back in time.
It is said that process control using the EWMA control chart makes it easier to detect small shifts (changes) in the process. Therefore, in the following, it is shown above. twenty three About the average temperature in Kyoto in the month EWMA I will draw.
JMP 16 of EWMA control chart
In JMP for a long time EWMA I was able to draw a control chart, JMP 16 The interface has changed and significantly better features have been added. The main additional functions are as follows.
- With EWMA control chart X A control chart and a control chart of residuals are also displayed.
- According to the control panel in the report, λ (lambda) And σ ( sigma ) Is changed and reflected in the control chart interactively.
- The starting point of change can be detected.
Against the average temperature in Kyoto EWMA control chart( 2,3 Month)
First of all 2 Of the moon EWMA It is a control chart.
The figure is from top to bottom 3 One is drawn, but in order from the top EWMA control chart, X It is a control chart (control chart using the temperature value itself) and a control chart of residuals.
The residual control chart is at a certain point in time. X From the value of the control chart 1 Before the point EWMA It is a plot of the residuals calculated by subtracting the values in the control chart. For example 2010 The residual of the year is 2020 From the year value 2019 Of year EWMA It can be calculated by subtracting the value of.
The values entered in the "Settings panel" on the left are as follows.
Target value : Average value of data. (EWMA control chart, X Green line on the control chart )
Sigma : Value indicating variation (σ). Estimated from the data.
Lambda : Weights described above (default is 0.2 )
The red line is 3 It is a control limit line calculated by σ (sigma).
In the middle X Looking at the control chart, it is not possible to discover such trends by appearance. But at the top EWMA Looking at the control chart, 70,80 Downtrend over the ages, 2018 You can see the uptrend since the year. However, the management limit has not been exceeded in any year.
By the way EWMA The blue dots plotted in the upper right corner of the control chart are 2022 This is the predicted value for the year.
next 3 Of the moon EWMA It is a control chart. You can see the easy-to-understand trends.
X control chart 2021 It is out of the upper control limit in the year. EWMA In the control chart 2010 An uptrend can be seen in the 1980s, 2020 It is out of control limits in the year.
The purple line drawn on the EWMA chart indicates the starting point where the shift occurred. 2 It could not be detected by the average monthly temperature, Small changes can be detected in the average temperature in March.
Although not shown here, a control chart showing the same tendency is drawn for the average temperature in Tokyo. recent years 3 The feeling that the moon is warm and the cherry blossoms bloom early is EWMA The trend towards the top of the control chart will be evidence.
JMP 16 EWMA In the control chart, from the "setting panel" on the left, the target value, sigma, lambda If you change the setting of, the control chart will be drawn with that setting immediately. The figure below is 3 Of the moon EWMA In the control chart Lambda To 0.1 It is the one when it was changed to. In other words, increasing the reliance on historical data results in this year ( 2021 Year) goes out of the upper control limit.
Considering it as an environmental problem
For those who are not good at cold, it may be nice to get warm quickly, but considering the result of global warming, we cannot be happy to let go.
Regarding current international environmental efforts ” Paris Agreement ” Is famous, but as an agreement before that, it was decided in Kyoto, which was the topic of this time. ” Kyoto Protocol ” there is. The Kyoto Protocol 1997 It was adopted as a measure against global warming in 2011, but since then 20 Even now, more than a year later, we still have to say that effective measures have not been taken.
President Biden takes office in the United States this year 2 I returned to the Paris Agreement in March, and I feel that the future is an important phase to stop global warming.
