what does averge temperature actually mean

What does Average Temperature Actually mean?Belleville Example.

By J. Richard WakefieldUpdated Jan. 18 2010.

AbstractThose who promote human caused global warming (AGW) claim the world average temperature is increasing. It is then claimed that the planet is going to get hotter as more CO2 is added to the atmosphere. However, the average yearly temperature is an average of mean daily temperatures over the course of the year. In temperate zones this includes deep winter colds, hot summer days and cool summer nights. 1300 Canadian weather station data was downloaded from Environment Canada’s website and evaluated for internal trends on a number of key ranges in temperatures. Thus preliminary study on one station in Ontario shows that indeed the average temperature since 1900 has been increasing just as the AGW proponents claim. However, that average increase was due to warmer shorter winters with no increase in summer temperatures, in fact, the hotter summer temperatures have dropped. The average mean yearly temperature is highly correlated to the number of days a year is above 30C (hot days), the number of days in a year the temperature is below –20C (very cold days) and the length of winter in days. All three of these are decreasing, meaning more moderated yearly climate today as compared to the period before 1950. Thus, the concept of average temperature has no physical meaning since in reality one can get an increasing average by different physical changes in temperature trends. The true nature of the climate is far more complex than a simple average temperature.

Introduction:Software was written to cycle through each station, for each month for each year which fired off a URL request to Environment Canada’s historical temperature website. The returned file was in CSV format, altered into a tabbed format and stored in a text file, one file for each station.

Software was written to cycle through these files and make an Access MDB file for each station, with the text data imported into that file. Queries were fired to clear the raw data of headers and legends that was embedded in the text files.

Software was also written to cycle through all the mdb files and fire off queries that gathered the number of valid records and the first date of a valid record, and stored in a master mdb file for the stations.

Of the first batch of 250 stations, 70% of them have no data prior to 1960 (80% after 1945). The vast majority of stations started in the 1960s and 1970s. Only 7 stations have data from 1900, and many of them have incomplete data before 1920.

Belleville Ontario, Station #4859, was chosen from the initial batch of 250 stations because it has one of the earliest continuous dates of temperatures. The data is continuous since 1921 with two missing years, 1930 and 1931. Strangely, records after 2006 are missing from their database.

These daily records included maximum, mean and minimum temperatures, as well as precipitation data.

The following graphs are from the Belleville data set only. The plan is to eventually, once all the stations have been downloaded, to compile the date into distinct regions and do the same analysis to see if what has happened in Belleville has happened elsewhere in the country, which then can be used to inspire others to check world temperatures to see if the same pattern discovered here holds true for the rest of the planet.

Preamble:

Here is the graph of daily average temperatures for each year. Understand that this is the average of the daily mean temperatures for each year. This average hides the natural daily and monthly variation. The climate is far more complex than what an average of the mean temperatures can tell.

This graph very closely follows that which is used to show the world is heating up. Even the cool trend from 1950 to 1975 is clearly visible. But what does this actually mean? What is physically happening with the daily temperature trend that is causing this graph? Does this show that the planet is indeed heating up?

There is a definite semantics game being played by the warmists. They claim that the planet is heating up due to our CO2 emissions. Claims as wild as the planet is going to eventually “cook” (like Venus) because of our CO2, or even Lovelock’s claim that in the not so distant future we will only be able to exist in the polar regions because the rest of the planet would be too hot. So the message from these people is the planet is getting hotter. But is that what an increase in average mean temperature means?

There are 4 ways in which the average mean yearly temperature can increase:1) Increase the summer maximum temperatures and increasing the winter minimum

temperatures.

Figure 1: Plot of daily average temperatures since 1921. The smoothed line is a ten-year moving average. Data does not exist for 1930-1931.

2) Increase the summer maximum temperatures but no change in the winter minimum temperatures

3) No increase the summer maximum temperatures but increase the winter minimum temperature

4) Decrease the summer temperatures a little, but increase the winter minimum temperatures more.

All four can give the exact same average mean temperature. Thus detail of what is physically going on is lost using the average mean temperature. (We will soon see that #4 is what has actually happened.) Here is an analogy. You set your home temperature to 23C all day with climate control. Throughout the year if you averaged all the daily temperatures you will get 23C. If however, you decide to save some money and during the winters you allow your nighttime temperature to drop to 10C. You have just pulled the average temperature for the year down to around 18C.

Later you realize that that 10C is just too cold at night so you raise it to 15C. Doing this has pulled the average temperature up, to around 20C. Is your house “hotter”? No. It’s less cold. Big difference in the meaning. You would have to increase the daytime temp up (say to 25) to make the house “hotter.” But raising the minimum temperature up, which increases the average temp, does not make your house, or the planet, “hotter.”

Another example of the warmists manipulation of semantics is in their use of graphs that show the temperature “anomaly”. What this is is they take the average mean yearly temperature and plot it as a difference from some arbitrary flat line. Thus temps above the line are positive anomaly from that line. The use of the temp anomaly may be understood in the scientific community, but to the public and policy makes, anomaly means “an incongruity or inconsistency” as defined in the dictionary. That is, the temperature above the flat line should not happen and we are to blame for this “inconsistency” in the recent temperatures.

There is no underlying scientific reason for using anomaly. One can simply just plot the average mean temperature raw numbers. But of course doing that does not give the implication the warmists want.

Being clear and precise in one’s choice of words is vital in science. The usage of vague terminology in science, this linguistic smoke and mirrors, is nothing more than a deliberate attempt to confuse the public and policy makers.

Results:

This study focuses on the extreme temperatures during the years as the possible mechanism that gives the average mean temperature the shape it has in Figure 1. But why just the extreme temperature ranges and not all the temperatures taken throughout the year? Because it is the summer maximum temperatures and the winter minimum temperatures that pull the average up or down, not the temperatures that falls within the standard deviation of the range of temperatures throughout the days of the year. Just because we have a few more days in March above 20C today than we did in the 1930’s does not mean the planet is getting “hotter.” It would only get “hotter” if the maximum

temperatures in the year (summer) were to increase (you will soon see it’s actually going down).

One of the claims of the AGW proponents is that, because of this increase in average temperature, there will be more hotter summer days. That’s easy enough to test. If this claim is true then the number of days above 30C in each year should be increasing to give us more heat waves.

The question is, above what temperature makes for a “heat wave”? Mathematically, the upper standard deviation of the maximum temperatures should be used. The average of the maximum temperatures for June, July and Aug is 25.4C with a standard deviation of 3.7, which makes a “hot day” anything over 29C. Hence the number of days 30C or more is quite valid for this criteria.

This is a plot of the number of days in each year that were 30C or more.

Note that there are three clear episodes. The first is between 1933 to 1955 where there were 332 (4.1% of time) hot days above 30C. This shows a clear trend of fewer days 30C or more. The second is a cooler time of less hot days from 1956 to 1982 where only 159 (1.7%) days above 30C and was stable. The third is the current period from 1983 to 2006 where there were 286 (3.4%) hot days, which shows an increase in the count for the first third and then leveling off with a slight decline.

A straight-line trend is clearly for fewer hotter days in the summers, and that the current group of more days since 1983 is for fewer than the group between 1933 to 1955. The “cooler” 60’s and 70’s is quite clear with as much as half the number of days above 30C than now and in the previous group.

Thus, from this location, the claim that more people are going to die because of more heat waves is clearly NOT the trend. There are in fact, FEWER hot days.

Figure 2: Number of days above 30C. Trend line is ten year moving average. There is no data for 1930-1931.

Next we need to look at the number of days below zero, the other extreme of the mean temperature. Two plots for this. Daytime maximum and nighttime minimum temperatures, which is one way of getting the duration and severity of winter.

Notice the clear drop in the number of days below freezing. Winters in Belleville are getting less severe even though the number of hot days are getting fewer.

Defining cold snaps suffers the same definition problem as heat waves. The average of the minimum of the winter temperatures (Dec, Jan and Feb) is –10.36C with a standard deviation of 7.68. So a cold snap is any day that is below –18C. Which is rounded up to any day that is –20C or colder.

Figure 3: Number of days below zero. Upper line is maximum temps in the winters while the lower line is the minimum temperatures. Data is scarce for 1930-1931

This plot shows the number of days below –20C, which you will see connected to the days above 30C is important in how Figure 1 has the shape it has:

Notice that the number of days that the temperature was below –20C has had a dramatic drop -- less really cold days. This graph, coupled with Fig. 1 and Fig. 2 will be very important.

Figure 4: Number of days where the temperature is below –20C. Trend line is the ten-year moving average.

The trends for just February and just July, the two extreme ends of the year, were also plotted. This is the yearly trend for February:

Notice the temperature trend is not simple. The warmest maximum temperature is undulating and slightly warmer today than the late 1950’s. There has been an increase in the cooler maximum temperatures. That means, less swinging in the highest winter temperatures. Figure 5b shows the same. The warmest minimum temperature has stayed flat, while the coldest minimum temperature has clearly been increasing since at least the 1950’s. Getting less cold.

Figure 5a: Highest and lowest of the maximum daily temps for each year for February. Trend line is ten year moving average. No data for 1930-1931.

Figure 5b: Highest and lowest of the minimum daily temps for each year for February. Trend line is ten year moving average. No data for 1930-1931.

Here is the same set of temperature trends for July.

Notice that the maximum temperatures recorded for Julys is flat. There is no over all trend in the hottest temperatures. Minimum temperature shows a clear increase. Summers are getting less variable in their extremes, but not getting hotter.

Figure 6a: Highest and lowest of the maximum daily temps for each year for July. Trend line is ten year moving average. No data for 1930-1931.

Figure 6b: Highest and lowest of the minimum daily temps for each year for July. Trend line is ten year moving average. No data for 1930-1931

To see the statistics of the July temperatures I ran a regression and standard deviation on these numbers.

Notice the definite narrowing of the highest July temperatures (daytime) and the lowest July temperatures (nighttime).

Figure 6c. Standard deviations and regression trends for maximum and minimum July temperatures since 1921. Note the over all range is definitely narrowing.

Last trend is to see the span of daily temperatures for each year. That is, the yearly range of variation of maximum to minimum temperatures. If the warmists are right, this should be increasing.

This plot is the yearly maximum and yearly minimum temperature range for each vertical line. The rest of the year’s temperature falls within one vertical line. The center dot is the mean average temperature. This graph tells the whole story. Summer temperatures have not gotten hotter at all. In fact, the number of hot days (as in Figure 2) has been dropping slightly. However, what is clear is the number of cold days has dramatically been dropping, which one can see with the bottom of each vertical line.

To see if there is indeed a mathematical confirmation of this narrowing, the following plot shows it.

Figure 7a: Range of variation in yearly temperatures. Scant data for 1930-1931.

Figure 7b: Standard deviations of the summer max and winter min temps

Figure 7b is the standard deviation of just the summer maximum temperatures and the winter minimum temp of each year. These correspond to the very ends of each vertical bar in Figure 7a. Notice the trend is dropping for both, which means the variation for both is statistically narrowing. The winter min temperatures have a higher variation and is narrowing twice as fast as the summer max temperatures.

The following is a selection of months for the winter, spring and summer of the 10 day moving average of daily temperatures for selected years to compare what is happening recently with what has happened in the past.

When viewed like this, 2006 is much colder than any of the other selected years in mid Jan, but not at the beginning of Jan. Feb minimum temperatures for Feb for these years are will within range of each other. Note 1998’s profile however. El Nino year.

Figure 8a. Ten day moving average of the winter months (Dec, Jan, and Feb) of the minimum temperature for selected years.

Figure 8B. The transition months in spring. All years are well within the same range. Note 1998 stands out at the top again.

Figure 8C. Spring max temperature trends.

It is clear from these two graphs that 2006 is not unusual compared to other years. What you can see is that the onset of spring is happening sooner in 1998 and 2006 compared to 1945.

Figure 8d is very interesting indeed. 1921 stands above the others for the beginning of the summer months. Followed by 1945 at the end. The El Nino year, 1998, is not unusual, though it was in the winter. 2006 ranks at the bottom.

To do these for all years would require a 3D plane, difficult to display here and is too congested to pinpoint any trends.

Figure 8d: Summer temperature trends for selected years.

Data Analysis.Now we can determine how the shape of Figure 1 occurred.

Figure 9 merges the number of days above 30C in the top plot, with the number of days below –20C in the bottom plot compared to the average of the mean yearly temperatures in the middle. Notice three distinct phases in all three plots. Phase 1 is the time period 1933-1955 where the number of days above 30C was the highest, while the number of days below –20C was also the highest. Thus, during this period this area suffered extreme temperatures at both ends. Very hot summers and very cold winters.

Figure 9: The three temperature phase changes that give rise to an increase in average mean temperatures.

Phase 2 shows a significant drop in the number of hot days by more than half. The number of days of below –20C has dropped a bit and leveled off, giving rise to the plateau during 1956-1982.

Phase 3 shows the dramatic increase in the average mean temperatures, which clearly corresponds to a drop in the number of days below –20C and a rise in the number of days above 30C (but not at hot as Phase 1). Much more moderate temperature swings than Phase 1.

Correlation between the number of days and average temp seems quite clear. If there is a real physical correlation between them, then the correlation should be apparent on a scatter graph and see a line that the trend follows. This would need to be a three-dimensional scatter plot of days above 30C on the X axis, days below –20 on the Z axis and average temperature on the Y axis. The relationship, if any, would be a line that flows, in a specific direction, in space inside that cube. If there is no correlation, the points would be scattered with no line trend.

Unfortunately Excel cannot do 3D scatter plots, so the Z and X axis have to be combined. This was done as a Pythagorean. The new X axis would be Sqrt(X^2 + Z^2). This can then be plotted on a 2D graph as such.

Figure 10. 3D scatter plot as a 2D graph.

Of course, Nature again shows she is not so simple. The three phases are quite clearly distinct. The trend is also clear, though meandering. The over all trend is that the smaller the difference between the number of hot days and the number of cold days, a smaller swing in variation in the year, results in an increase in average temperature. In Phase 1, the run up to the widest difference between the two extremes has the trend move from left to right until 1942 when it completely reversed direct and trended right then up (This means 1942 had the hottest summer with the coldest winter). During the years around 1945 there was no net change in the extremes, but the temperature increased anyway before darting left into Phase 2.

Phase 2 clearly shows back and forth narrow osculation as the range in days of the extreme ends varies little and there is also little change in temperatures until Phase 3 starts somewhere around 1988.

Since 1998, in Phase 3, the very year that the hottest temperature of the last 60 years due to an El Nino, the temp increased even though the range between the extreme days did not narrow or widen. Some other factor is increasing the average temp during this period.

Nature is far more complex than this simple relationship, something else is going on.

Next is to see if there is any shift in the beginning and ending of winter. The criteria for what starts and ends winter was the last freezing night in spring and the first freezing night in fall. This is a measure of the growing season. The results are dramatic.

Figure 11: Graph of first and last of frost nights (min temp) for each year. Trend lines are 10 year moving averages.

Figure 11 shows a very interesting trend. Spring is definitely coming sooner since 1921. What is interesting is the wide variation in the onset of spring until 1990 when the last frost since then until 2006 was in early April.

The onset of winter, measured by the first frost night, has undulated in a long frequency, currently in an upturn trend since around 1995.

The over all length of winter in the number of days is:

Don’t confuse this length in winter, as defined as the number of days from first frost to last frost, with the number of days below zero. Often during winter, temperatures can and do go above zero, even in the depths of January and February.

The trend here is clear. Including the spring and fall days to get the number of days in winter (the reverse is the number of days of the growing season.) one can see that the trend is definitely to shorter winters, shorter by some 30 days.

Now a question arises about tree ring proxy data as an indicator of the warmth of the year (they cannot tell us anything about the winter temperatures). If you increase the growing season does that increase the size of the year’s ring, even if the temperature does not change?

Figure 12: Number of days of winter, since the first night frost in fall to the last night frost in spring. Trend line is 10 year moving average.

Combining the length of winter in days to Figure 10 we get this remarkable graph.

Figure 13, what explanation needs to be said?! This graph is very clear, the trend is for cooler summers, warmer shorter winters having a direct affect on increasing the average mean temperature. The correlation coefficient for that plot is –0.84, with a P value of essentially zero (10^-98).

The question now is, what is causing this movement from extreme changes in yearly temperatures in Phase 1, to the jump and steady state of Phase 2, and the migration in Phase 3? Is this from CO2 emissions? There is no way to know. We have no such analysis prior to the Industrial Revolution because no such detailed daily temperatures exist. Thus we cannot compare this to prior to 1850. Hence we cannot compare to how the daily temperature influenced the average temperature. Even if we did, that prior time was in the Little Ice Age and hence would not be a valid comparison to the current warm period. We would have to compare this to the Medieval Warm Period, and of course no such data exists.

Some factor, some natural phenomena, is clearly pushing for more moderated yearly temperatures.

Figure 13: Correlation between trends and average mean temperature. X axis is the component of the days above 30C, days blow –20C and length of winter.

It should be noted that around 1998 is when the sun entered a new quieter phase. Coincidence that this graph is trending in the direction it is after 1991?

Lastly, we need to clear up some statistical analysis to verify that we are indeed looking at a narrowing of temperatures. If we are getting hotter in the last 30 years compared to the previous 100 years, we should be able to clearly see that in a graph that contains both datasets.

Figure 14 shows the difference between the two year ranges. You will note that the blue line (1998-2006) is well within the vertical lines (1921-1998). Thus we are not “heating up” for any month. What we do have is the blue line for the highest max temperatures for 1998-2006 lower than the highest max temperatures for the entire range of 1921-1998. All months show the highest temperatures have dropped. The lowest of the max temperatures also shows a clear narrowing. Thus the highest temperatures we see each month of the year in the past 30 years is less than what it has been previously. The

Figure 14: Vertical lines represent the temp ranges for each month from 1921 to 1998. The blue curved line is temperature range for each month from 1998 to 2006.

lowest of the max temperatures has raised recently, thus the max temperatures for each month for the past 30 years has narrowed compared to the previous years.

The lowest of the minimum temperatures in the bottom graph shows the same trend of narrowing. The past 30 years shows a clear increase in the minimum temperatures than in the previous years.

Thus, we are seeing an over all narrowing of the range of temperatures for every month of the year. Warmer shorter winters with fewer heat waves in the summer.

The above graphs are for the extremes of the maximum and minimum temperatures. If there is a true narrowing we should be able to see it in the difference in the standard deviations of the 4 datasets. That is, the magnitude of the standard deviation should be smaller now than in the past. If we take the standard deviation for monthly maximum and minimum temperatures from 1921 to 1998, and subtract the standard deviation for monthly maximum and minimum temperatures from 1998 to 2006 we should see increasing numbers (larger difference due to narrowing).

Figure 16 clearly shows the range of standard deviation (variation) in both the maximum and minimum temperatures for the period 1998-2006 subtracted from the standard deviation for period 1921-1998. The current period has a markedly narrower range, especially in the winter months, and a bigger number for the minimum. Both of which would be expected.

Figure 16: Subtraction of the 1998-2006 standard deviation from the 1921-1998 standard deviation for each month.

CO2’s Influence:

This analysis would not be complete with out including the CO2 numbers for comparison. NOAA’s daily CO2 measurements (averaged into months) can be found here: ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt. Unfortunately it only goes back to 1958, thus Phase 1 is not represented.

Here is the plot of the mean yearly CO2 vs average mean temperature.

The correlation coefficient for this plot is 0.61. However, notice the last two phases are well represented. Phase 2 shows that CO2 rose, but the average mean temperature fluctuated back and forth. You can run a vertical line right through those points.

Phase 3 is also clearly presented, which again a vertical line drawn through those points. Thus one can argue that the average mean temperature has no correlation to CO2 levels at all. Some natural shift in the planet’s climate moved the vertical line over and widened the variation of the average temperature compared to Phase 2.

Figure 17: CO2 concentration vs Average Mean Temperature. Note the distinct 2 phases show up. CO2 data starts in 1958.

ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt

Conclusion.

Those promoting human caused global warming claim the planet is getting hotter due to the increase in world average temperature since the 1980’s. However this average temperature calculation has no physical meaning. What is actually, physically, happening, as shown in this detailed Belleville temperature data, is that there is a narrowing of the variability in temperatures with no net change in summer temperatures, except that there are fewer hotter days. This narrowing in variability is primarily due to warmer shorter winters.

Apply this to the rest of the world and what we are seeing is an over all global narrowing of yearly temperature variation while not changing summer temperatures. Thus the planet is not heating up at all, it’s seeing warmer and shorter winters.

This means, that even if our CO2 emissions are causing this trend, which there is no correlation there is, the future of the planet is not one of warmer, harsher climate, but less variability in yearly temperatures below a summer normal that is not increasing, more tolerable winters, longer growing seasons, and less heating bills.

Now image for a moment this scenario. Go back 20 years and climate scientists come to the consensus that the planet’s temperature range is narrowing, that with no increase in summer temperatures, winters are getting warmer and shorter due to emissions of human CO2. There would be no alarmism. There would not have been a Kyoto Accord. There would not be any call for extreme action to change our society. And there would likely be no reason for the IPCC. And there wouldn’t be the tens of billions of taxpayer’s money wasted on AGW that would have instead been used to solve our real pollution and energy problems.

Disclaimer:I have not received a penny from any fossil fuel company or right wing lobby organization to write this paper.

Data is available to anyone who requests it by emailing me at

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