The following image is a look at each December’s monthly average temperature, beginning in 1995.  The black line represents the temperature trend over the seventeen years that this school has collected data – an estimated increase of .1601°C over the 17 year period.

A timeseries showing December monthly temperatures from 1995-2011 for Zakladni Skola – Ekolog. Praktikum in Jicin, Czech Republic;
All data is GLOBE student collected data.

Using this knowledge, and setting the base 10 year reference period of 1998-2007, it is easy to calculate the short-term average for this station to determine the departure from that average.  The average temperature for December is 0.211°C.  This average is easy to calculate.  First, you calculate the average daily temperature by averaging the observed maximum and minimum temperatures.  Then, you average the daily average temperatures together to obtain the average temperature for the month of December.  Once you’ve done that for each of the Decembers from 1998-2007, you can average those together to get your average December temperature.  From here you can examine how each December departs from that average, and put it into graphical format, like below.

Departure from 10 year (1998-2007) average December temperature for Zakladni Skola – Ekolog. Praktikum in Jicin, Czech Republic; All data is GLOBE student collected data

Notice that at the beginning of the time period the occurrence of below normal temperatures was more common.  As time progressed, temperatures became more above normal, which supports the trend in monthly temperature.  Globally, the month of December 2011 was the 322^nd consecutive month where global average temperature was above the 20^th century normal – the last month that was below normal across the globe was February 1985.

Another school, Primarschule Neufeld in Thun, Bern Switzerland, has been collecting atmosphere data since 1998.  The graph below shows the monthly average temperature for each December since 1998, which indicates a positive temperature trend of 0.088°C over the entire time period.

A timeseries showing December monthly temperatures from 1998-2012 for Primarschule Neufeld in Thun, Bern Switzerland;
All data is GLOBE student collected data

Using the same base 10 year reference period of 1998-2007 as we did for the school from the Czech Republic, it is found that the average temperature for December for the school in Switzerland is 1.101°C.

Departure from the 10 year (1998-2007) average December temperature for Primarschule Neufeld in Thun, Bern Switzerland; All data is GLOBE student collected data.

It is very important, as a member of the GLOBE community, to continue building this observational record for your site.  Every data point is important in describing the bigger picture.

Suggested activity: Over the next 12 years, GLOBE students will collect enough data to be able to examine long-term changes in variables such as air temperature.  However, you can start examining your data, or data of a nearby school now.  You can even examine the data from these two schools to look at the trends for June.  What do you think you will find? We’d love to hear from you.  Leave us a comment, send us an email or get in touch on our Facebook Page.

Figure 1. Map showing location of Boulder and CASES-99. The colors represent contours. The Rocky Mountains are yellow, orange, and red on this map. The colors denote elevation, with yellows, oranges and reds indicating higher terrain.

How does the air temperature relate to the surface temperatures that the students measured during Dr. C.’s field campaign? To answer this question, I looked at how the surface temperature related to the air temperature at our house.

The air temperature at our house was measured at 1-1.5 meters in our carport, and also on a thermometer I carried with me on our early-morning walk around the top of our mesa. That temperature, as noted above, was -21 degrees Celsius. To get the surface temperature, I put the thermometer I was carrying on the surface after I finished my walk. I am assuming that this temperature is close to the temperature that would be measured by a radiometer like the one used in GLOBE. I took the reading ten minutes later.

Just for fun, I also measured the temperature at the bottom of our snow (now 10 cm deep) and at the top of the last snow (about in the middle of the snow layer). At these two places, I put the snow back on top of the thermometer, waited ten minutes, and then uncovered the thermometer and read the temperature. The new snow was soft and fluffy, while the old snow was crusty; so it was easy to find the top of the old snow.

All of the measurements were taken close to sunrise, when the minimum temperature is normally reached, and the area where I took the measurements was in the shade.

Figure 2 shows the temperatures that I measured.

Figure 2. Temperature measurements at the snow surface, between the old and new snow, at the base of the snow layer, and at 1-1.5 meters above the surface at 7:30 in the morning, local time.

That is, the temperature was coolest right at the top of the snow. The temperature was warmer at the top of the old snow, and warmest at the base of the snow. As noted in earlier blogs, the snow keeps the ground warm.

The temperature at the top of the snow was also cooler than the air temperature. The surface temperature is often cooler than the air temperature in the morning, especially on cold, clear, snowy mornings like this one. However, on hot, clear, days in the summertime, the ground is warmer than the air.

Here are two sets of measurements taken in the Midwestern United States in October of 1999. Could you guess which measurements were taken at night, and which measurements were taken during the day even if the times weren’t on the labels? The first plot is from data taken after sunset, while the second plot was from data taken at noon.

Figure 3. Data from the 1999 Cooperative Atmosphere Exchange Study (CASES-99) program in the central United States, courtesy of J. Sun, NCAR.

Figure 1. Rain gauge used for observations in my backyard. Normally, there is a funnel and small tube inside, but it doesn’t fit very well, so we pour the rain into the small tube after each rain event. This gauge is similar to those used by the U.S. National Weather Service. This gauge is about 25 cm in diameter.

Figure 2. Plastic raingauge matching GLOBE specs. This gauge is about 12 cm in diameter. Note the tall tree in the background.

Neither gauge is in an ideal location. In both cases, there are nearby trees (Fig. 2, map) which might impact the measuring of the rain. This is a problem a lot of schools have: there is just no ideal place to put a rain gauge. We were particularly worried about the plastic gauge, which was closer to trees than the metal gauge.

Why do we have two gauges? The metal gauge was hard to use: its funnel didn’t fit easily into the gauge, so we had to pour the rain from the large gauge into the small tube after every rainfall event. We got the plastic gauge to replace the metal one. We put the gauge on the fence because it was well-secured. But the first six months we used the new gauge, the rainfall seemed too low compared to totals in other parts of Boulder. So, I put the metal gauge back outside and started comparing rainfall data.

Figure 3. Map of our backyard. Left to right (west to east), the yard is about 22 meters across. The brown rectangular shape is our house; the circles represent trees and bushes. The numbers denote the height of the trees and bushes. The 10-m tree is an evergreen; the remaining trees and bushes are deciduous. The southeast corner of the house is about 3 m high.

How did the gauges compare?

Starting this summer, I started taking data from both gauges. Unfortunately, it didn’t rain much. And sometimes, we were away from home: so this is not a complete record. But I don’t need a complete record to compare the rain gauges.

Table: Rain measurements from the two rain gauges

The results (in the table, also plotted in Figure 4) look pretty good. With the exception of the one “wild” point on 6 October 2008, the measurements are close to one another. We think that the plastic gauge was filled when the garden or lawn next door was watered. This would not be surprising: we have found rain in the plastic gauge when there was no rain at all.

I learned after writing this blog that Nolan Doeskin of CoCoRaHS (www.cocorahs.org) has compared these two types of gauges for 12 years, finding that the plastic gauge measures slightly more rain (1 cm out of 38 cm per year, or about 2.6%).

Figure 4. Comparison of rainfall from the two rain gauges in our back yard. Points fall on the diagonal line for perfect agreement.

I learned two things from this exercise.

First, I probably should have used the two gauges before I stopped using the metal one. That way, my rainfall record wouldn’t be interrupted if the new gauge was totally wrong. (I was worried that the trees were keeping some rain from falling into the gauge. This would have led to the plastic gauge having less rainfall than the metal gauge. And, since the blockage by the trees would depend on wind direction and time of year, I wouldn’t have been able to simply add a correction to the readings.) Fortunately, the new and old gauges agreed.

In the same way, if you want to replace an old thermometer with a new one, it’s good to take measurements with both for awhile, preferably in the same shelter. Suppose the new thermometer gives higher temperatures than the old one. If you want to know the temperature trend, you can correct the temperatures for one of the two so that the readings are consistent.

The second thing I learned is that it is o.k. to reject data if there is a good reason (such as people watering their lawns). It’s also important to note things going wrong – like my spilling a little bit of water on 15 August. If you keep track of things going slightly wrong (or neighbors watering the lawn), you can often figure out why numbers don’t fit the pattern.

I will continue to compare records for awhile, to see whether the readings are close to one another on windy days. If they continue to be similar, I will be able to try a method to keep birds away from the rain gauge that was developed by a GLOBE teacher – Sister Shirley Boucher in Alabama. Keep posted!

Last time, we calculated an average adult human breathes out between 0.7 and 0.9 kg of carbon dioxide each day. This is based on lots of assumptions, with people of all ages and nationalities counted as processing 0.5 liters of air, 16 times an hour, for 24 hours.

Let’s compare this rough estimate to some other numbers.

The amount of carbon dioxide given off by an automobile in a mile (1.6 kilometers)

I’ve heard a number quoted for this one, but thought it would be good to estimate to find out how close I was, and then I will convert the number to metric units. We start from some facts.

• Density of gasoline is 0.71-0.77 grams per cubic centimeter (that’s 0.71-0.77 kg per liter)
• Gasoline is 85% carbon by mass

So there is approximately 0.74 times 0.85 = 0.63 kg carbon per liter.

This converts to 0.63 kg C x 3.79 liter/gallon or 2.39 kg C per gallon (C=Carbon).

If our car drives 20 miles on one gallon of gas (this is clearly not a very efficient car!), the car burns 2.39 kg per gallon x 1 gallon per 20 miles, or 0.12 kg of carbon per mile.

This is equivalent to 0.12 x 44 divided by 12 = 0.44 kg per mile, or 0.96 pounds (~1) pound of carbon dioxide per mile. Or, in metric units, 0.28 kg per kilometer.

And, driving this car for two miles (3.2 km) produces 0.88 kg carbon dioxide – as much as we produce by breathing all day! (What if the car could travel twice as far per gallon?)

Carbon dioxide released by going from Point A to Point B.

I’m going to suppose someone wants to travel two miles or 3.2 kilometers. That’s a distance many of us would be willing to walk (and about the distance between where I live and where I work).

That means:

If we walk three miles per hour, it would take us 40 minutes to reach Point B walking 3 miles an hour.

If we ride a bicycle at 8 miles (12.8 kilometers) per hour on average, it would take 15 minutes to get to Point B.
The Web is full of charts listing the number of Calories (kCal, abbreviated kCal) used in different types of exercise. I’ll select the following values. For a 155-pound (70 kg) person:

• Walking at 3 miles per hour (4.8 km/hr) burns 250 kCal
• Riding a bicycle at 8 miles per hour (12.8 kilometers per hour) burns 280 kCal

Which means the number kCal burned going from Point A to Point B is:

• 167 kCal walking for 40 minutes compared to 56 kCal for 40 minutes at rest
• 70 kCal riding a bicycle for 15 minutes compared to 21 kCal for 15 minutes at rest

The “at rest” numbers are based on the previous blog, where we used energy production to estimate carbon dioxide output. We assumed a human produced 2000 kCal of energy (equal to the amount eaten) and found that roughly equivalent to 0.7 kilograms of carbon dioxide a day. (0.9 kg a day could be used as well. We used 0.7 simply because that was the number associated with the 2000 kCal.

The carbon dioxide we produce by going two miles on foot or on a bicycle is then, if we count the total:

• 0.7 kg CO2 per 2000 kCal times 167 kCal: 0.058 kg CO2 walking
• 0.7 kg CO2 per 2000 kCal times 70 kCal: 0.025 kg CO2 biking

But the “extra cost” of traveling the distance should be the difference between the “exercising” number and the “at rest” number, namely:

• 0.7 kg per 2000 kCal times (167-56) kCal = 0.039 kg of extra CO2 walking
• 0.7 kg per 2000 kCal times (70-21) kCal = 0.017 kg of extra CO2 riding a bike

Thus: traveling the 2 miles (3.2 kilometers) produces this amount of CO2 above what was produced by respiration at rest:

Traveling 2 miles (3.2 kilometers)

By car: 0.88 kg CO2
Walking: 0.039 kg CO2
Riding a bike: 0.017 kg CO2

While the numbers aren’t exact, the large factor – 20 or more, is probably close. Walking or riding a bicycle does reduce the production of CO2 relative to driving. And – these modes of transportation provide healthful exercise as well! If we have to drive, putting more people in the car reduces the impact of driving. And, driving a car that uses half as much gasoline per unit distance would also help.

Standing for much of two days with groups of students at the base of the weather tower at the GAWS site at Cape Point, I found myself wondering how much we were contributing to the carbon dioxide in the atmosphere. I returned home, resolving to estimate how much carbon dioxide an average human gives off in a given day simply by breathing.

Figure 1a. 30-meter tall Global Atmosphere Watch Station (GAWS) tower from a distance. It is located almost at the southern tip of Africa.

Figure 1b Close-up of GAWS tower. The air is pumped in from the top of the tower into the laboratory building, when it is analyzed for the fraction of carbon dioxide and other trace gases.

I will estimate this in two ways. First, based on how many Calories a “typical” human consumes. And secondly, based on how much carbon dioxide is released with each breath.

Based on how much we eat

I start with some rather gross assumptions:

1. The average human eats 2000 Calories (kiloCalories) of food a day
2. 100% of this food is processed, with all the carbon returning to the atmosphere
3. All of the food eaten is in the form of sugars with carbon:hydrogen:oxygen ratios of 1:2:1.

And some information:
Atomic weight of carbon: 12
Atomic weight of hydrogen: 1
Atomic weight of oxygen: 16
Molecular weight of carbon dioxide (2 x 16 + 12 = 44)

This means that:
By mass, the sugars are 40% carbon
By mass, carbon dioxide is 27% carbon

Sugar provides 4 kiloCalories of energy per gram, meaning that our human eats 500 grams of sugar each day. 40% of this or 200 grams is carbon. Assuming all this carbon is released as part of carbon dioxide, our human releases 733 grams of carbon dioxide (200 grams x 44/12).

So, let’s just call our estimate 700 grams of carbon dioxide a day, recognizing that the number is an approximate one.

There are a number of reasons this is probably an overestimate. Our human wouldn’t eat all sugar. He/she would eat some fat as well, which has 9 kiloCalories per gram. We are assuming our human to be in steady state – so that net uptake by the body would be zero. But our human would release carbon in other forms (feces, dried skin, shed hair, etc.) So there would be some solid waste as well as gas – but over long term, there would be some carbon dioxide released from that.

Based on carbon dioxide released through breathing (respiration)

Let’s try another way to estimate the amount of carbon dioxide our human releases. But this time we focus on breathing. Again, some facts:

A human adult breathes 15 times a minute, on average (Reference 1). While I am writing this, my respiration rate is 16 breaths per minute, so this number seems reasonable. And, just for fun, I’ll use my respiration rate.

Each breath exchanges 500 cubic centimeters of air (Reference 2)

Assuming an air density of 1 kilogram per cubic meter, we can find out how many kilograms of air are exchanged for each breath:

500 cm x cm x cm x 0.01 m/cm x 0.01 m/cm x 0.01 m/cm
= 0.0005 cubic meters

0.0005 cubic meters x 1 kilogram per cubic meter
= 0.0005 kilograms of air per breath.

We now use this to estimate the kilograms of air processed each day, which is

0.0005 kilograms per breath x 16 breaths per minute x 1440 minutes per day
= 11.52 kilograms per day “processed” by breathing

To find out how much carbon dioxide is put into the atmosphere, we compare the amount of carbon dioxide (0.038% by volume) inhaled to the amount (4.6-5.9% by volume exhaled, Reference 3.), from the same web site. But first we need to allow that “by volume” means (using carbon dioxide as an example)

0.038 carbon dioxide molecules per 100 air molecules, or
3.8 carbon dioxide molecules per 10000 air molecules.

From above, we know that the molecular weight for carbon dioxide is about 44. The molecular weight for moist air is about 28, which means that the air we inhale contains about

3.8 x 44 divided by 28 x 10000 = or 0.0006 grams carbon dioxide per gram of air

The number “.0006″ is really a fraction – which I am labeling in grams per gram. It could just as easily be pound per pound.

Similarly, the fractional amount of carbon dioxide exhaled, by mass is, assuming 5% by volume:

0.05 x 44 divided by 28 x 100 or 0.0786

So the net fractional change in carbon dioxide for each breath is

0.0786 – 0.0006 or 0.0.078

Now we convert this to a mass by multiplying the fraction times the mass per breath, namely:

11.52 kilograms of air exchanged each day x 0.078 fractional increase in carbon dioxide,

= 0.9 kilograms of carbon dioxide for each day per human.

Again, we made assumptions to make things simple. Our human wasn’t exercising. Our human was an adult. And our human was exchanging a typical amount of air. Recognizing that the number is a crude estimate, I will again round the number to one significant figure, so that we have 0.9 kilograms of carbon dioxide released each day per human.

Isn’t it exciting that we came up with roughly the same answer! For comparison, Wickipedia (http://en.wikipedia.org/wiki/Breathing) quotes an estimate of 900 grams of carbon dioxide a day by the United States Department of Agriculture (USDA).

Here are some questions to think about:

The respiration rate I used was for an average adult. When I measured my respiration, I was sitting, so I’m thinking this is for an average adult at rest. How would these numbers be changed for someone who was exercising? Children breathe faster (Reference 3) but have smaller lungs. How would each of these factors affect the result? Finally, if you wanted a more accurate number, how would you change the calculations?

Comparison to carbon dioxide uptake by plants

How does that compare to some other things?

Prairie near Mandan, ND during the growing season (24 Apr – 26 October) 1996-1999, (reference 4)
1.85 grams CO2 per square meter taken from the atmosphere on average
(Meaning that 380 square meters of land would cancel out the effect of our human) – but remember – this in only during the growing season!

A generic tree (reference 5)

This tree (I’m assuming this is a big one) is said to take up 21.8 kilograms of carbon dioxide a year. For a year, our human produces about 365 x 0.7 kilograms a year, or 255 kilograms. So we’d need 10 of these threes to cancel the carbon dioxide we exhale. This site unfortunately does not quote a source.

Pine forest in Finland (Reference 6)

During the period of measurement, this forest took up
2.4 grams carbon dioxide per square meter per day during July/August, and
1.7 grams carbon dioxide per square meter per day during September

In “human units”, taking 0.7 kg/day, this means we’d need
290 square meters to offset our exhaled carbon dioxide in July and August, and 410 square meters to offset our exhaled carbon dioxide in September.

So – we are part of the carbon cycle, too! At Cape Point, we were breathing out carbon dioxide, but the atmosphere sampled was 30 meters above us – so we probably did not affect the measurements there. But I hear stories from scientists who are measuring carbon dioxide uptake about how they avoid contaminating their measurements. Some of the things they do – push their cars when they get close to the instruments instead of driving them, and leaving their dogs inside the car instead of letting them wander around the site. For more about the carbon cycle, visit the carbon cycle pages on the GLOBE web site.

References

1. p. 151, Berkow, , R., et al., 1997: The Merck Manuel for Medical Information: Home Edition. Merck & Co, publishers, 1509 pp.

2. p. 44, Kapit, W., et al., 1987: The Physiology Coloring Book. HarperCollins. 154 pp.

3. The five percent was decided on based on several references. The Argonne National Laboratory “Ask a Scientist” (http://www.newton.dep.anl.gov/askasci/zoo00/zoo00065.htm) lists 5.3 per cent by volume for “alveolar air” in response to a question about how much CO2 is exhaled. This is slightly lower than the range of values for arterial blood gases derived from p. 907, Taylor, C., C. Lillis, and P. LeMone, 1989: Fundamentals of Nursing. J. B. Lippincott Company, Philadelphia. 1356 pp. On the other hand, http://en.wikipedia.org/wiki/Breath writes exhaled air has 4-5% carbon dioxide by volume, with the BBC listing 4%.

4. Frank, A.B., and A. Dugas, 2001: Carbon dioxide fluxes over a northern, semiarid. mixed-grass prairie. Agricultural and Forest Meteorology. 108, 317-326,

5. http://www.coloradotrees.org/benefits.htm#10

6. U. Rannik et al, 2002 fluxes of carbon dioxide and water vapour over Scots pine forest and clearing. Agricultural and Forest Meteorology, 111, 187-202

Acknowledgments. I talked about this blog a great deal with colleagues. I am indebted to Jimy Dudhia and Greg Holland for contributing useful ideas and information. Also, our sincere thanks to the staff at the Cape Point GAWS station for sharing their facility with the students at the GLE.

Have you ever arrived at a school event, movie, or concert, shivering in a cold auditorium at first, but then feeling too warm by the time the auditorium was full? (For an earlier discussion, see the blog, Human Metabolism: What is That?, posted 23 February 2007).

The opening day of the GLOBE Learning Expedition offered a perfect opportunity to show the effect of people on the temperature of a large room, Jameson Hall at the University of Cape Town (Figure 1).

Figure 1. Jameson Hall; photo by Jan Heiderer. The GLE banners in front are slightly less than 9 meters high.

In order to measure the temperature, Jamie Larsen of GLOBE installed the temperature sensor on the speaker’s podium on the stage. This kept the sensor away from the doors to the outside, and put the sensor in full view of the audience. The sensor was supplied to us by Robyn Johnson of Vernier Software and Technology, one of the GLE sponsors. The sensor was installed while the auditorium was still empty, so that we would know the temperature of the room before many people came in. It was attached to a data logger, which was attached to a computer, so that the audience could see what happened to the temperature of the hall from the time it was empty, to when the approximately 500 people attending came in and sat down, and through several welcoming talks.

Thanks to Jamie and Robyn, my welcome talk could include a science question, “How much had the room warmed up during the time people came in?” Most of the people in the audience thought that the room was warmer. And the graph did in fact show that the temperature had warmed – about 3 degrees Celsius. Unfortunately, the data logger was turned off without storing the data (there were more talks and a performance before Jamie could get back to the logger), but the warming curve looked very much like the one in Figure 2, which is basically a sketch of the curve rather than actual data.

Based on our memories, the photograph in Figure 1, and some pictures of Jameson Hall on the Web, we estimated the size of the Jameson Hall Auditorium to be about 30 meters high on average, and about 40 m by 40 meters inside. So that there were about 48,000 cubic meters of air in the auditorium. The room started out empty, but by the time it was full, there were 500 people.

Each person was giving off about 100 Watts* (one Joule of energy each second). A Joule is a measure of energy. To get a feel for the rate of energy release, think of a 100-Watt light bulb.

Figure 2. Sketch of the observed warming of Jameson Hall before and during the GLOBE Learning Expedition Opening Ceremony at Jameson Hall, University of Cape Town.

The curve showed steady and rather cool temperatures before people came in, a rapid warming phase as the hall filled, and then the temperature was steady again as the air adjusted to the number of people in the hall. It was surprising that the temperature didn’t continue to warm – the people were still releasing heat, but they kept the doors open to keep the hall from getting too warm. This suggests a new “equilibrium” with the heat escaping to the outside the same as the heat given off by those of us in the hall. (There did not seem to be any heating or air conditioning operating at the time.) The actual curve was so “perfect” many found it hard to believe it was real data!

So does the temperature increase make sense?

From the earlier blog, the heating per unit time by the 500 people is given by:

500 people times 100 Watts per person = 50,000 Watts.

50,000 Watts is equal to the change in heat content in the air per unit time (here seconds), written

Heat content change per second =
specific heat
times volume
times density of air
times temperature change per second

The specific heat is around 1000 Joules per kilogram per degree Celsius. (Specific heat is a nearly-constant number that relates heating of a given mass to its change in temperature.)

Let’s use this relationship to figure out what the temperature change should be over the roughly one hour or 3600 seconds the temperature climbed.

Temperature change = total heat input, divided by (volume x air density x specific heat)

Total heat input is 50,000 Watt times about 3600 seconds, or 180,000,000 Joules

Specific heat times volume times air density = 1000 K per Joule per degree C times 48,000 cubic meters x 1 kg air per cubic meter = 48,000,000 Joules per degree C

Temperate change in degree C = 180,000,000 Joules divided by 48,000,000 Joules per degree C, or about 3.8 degrees Celsius!

This is amazingly close to the measured temperature change.

You could try this experiment in your school. All you need is a thermometer (or perhaps more than one) to take temperatures before and during an event. The results might not always look like Figure 2, since heating and air conditioning systems are designed to keep the temperature the same. What does it mean if the temperature stays the same? If you had thermometers in different parts of the auditorium, would they show the same temperature changes? (Note: since the temperature change is important rather than the actual temperature, it is o.k. if the thermometers aren’t starting out at the same temperature).

*A nice discussion of the amount of heat release by an individual can be found in Energy, Environment, and Climate, by Richard Wolfson. (published 2008, by W.W. Norton and Company)

The effect of extreme values on the trend line

Let’s start with the Jicin, Czech Republic, annual average temperatures. But this time, we will include 1996:

Figure 1. For GLOBE data at 4. Zakladni Skola in Jicin, the Czech Republic, change of trend from leaving out the first point.

In the figure the red points are those used for Fig. 2 of the previous blog. You see the trend, 0.04 degrees Celsius per year. If we add the point from 1996, the trend more than doubles – to 0.1 degrees Celsius per year – 1 degree Celsius per decade.

But 1996 might be a cold year. Remember – weather and climate vary from days to weeks to years to decades.

2001 was a cold year, too, relative to the surrounding points. What if we left 2001 out? How much would you expect 2001 to affect the trend? Note in Figure 2 that there is almost no effect. This is because 2001 is close to the middle of the data record. This makes sense: if you drew a straight line through the points by eye, you would be influenced more by the points at the beginning and end of the time series.

Figure 2. For same dataset, but ignoring the cold point in 2001.

Now, you might think that you should get rid of both years. Maybe they are not representative of the long term trend. Something happened in the Jicin area to make it a really cold year in 1996, and a really warm year in 2001. So, you plot the data without either of the two points.

Figure 3. Same data as for Figures 1 and 2, but minus the averages for 1996 and 2001.

Now we are back to the trend in the first graph – 0.04 degrees Celsius per year!

Someone might look at Figure 3, and say that the average temperatures are just going up and down with time, like the seasons. And, that the trend is just because you didn’t have two (or three, or four) complete oscillations! You couldn’t really say this person isn’t right without having temperature measurements from before 1996.

Obviously, the actual value of the temperature trend depends on how you look at the data! You might try this exercise for other stations in the data provided in the last blog.

Let’s try this exercise for the global points in Figure 7 of the last blog:

Table: Global Annual Average Temperature minus the 1961-1990 Mean. Source, Climate Research Unit, Hadley Centre, UK.

(The alert reader will notice that Figure 7 in the previous blog is slightly different now – I had accidentally included data for 2008, which is incomplete.)

Figure 4. For the most recent 12 years of the Hadley Climate Research Unit data, the effect of ignoring “extreme” points in the time series.

Note from Figure 4 that the slope varies depending on the data selected, but that the trends remain positive.

Reducing the influence of extreme points by smoothing

Recall last time that I took out the seasons because I thought they might affect the trend. Climate scientists average in time to get rid of the effect of large year-to-year changes like the ones in 1996 and 2001.

To show the effect of smoothing the data for Jicin, I will do a “three-point running mean average.” This means that I will average the first three temperatures and the first three years. That is, I will average

7.7500
8.8500
9.2300 to get 8.61

And I will average the years, too

1996
1997
1998 to get 1997

Then I will average the next three temperatures for 1997, 1998, and 1999 to get the temperature for 1998, and so on. Let’s say how this smoothing affects the data

Figure 5. For Jicin data, change in trend from smoothing the data.

And you might want to try four-point averages or five-point averages. The fact that the trend is positive, no matter what we do, gives us a little more confidence that there is a warming trend. Just as adding more stations would. But no matter how good the data in Figure 4, this is a trend only for one place – and only for 12 years.

Defining the average temperature

Unlike trends, which are affected by where the numbers are in time, the year doesn’t matter when you take an average. The larger the number of points, the less difference an odd year makes. Let’s do the averages for Jicin, starting with 2 years, then three years, then four years, and so on, for the complete record, to see how each new year affects the average temperature. The results are in Figure 6

Figure 6. For the Jicin data set, the average as a function of the number of points. To take the average, we start by averaging 1996 and 1997 (two points), then 1996, 1997, and 1998 (3 points), and so on.

As you can see, even the large changes at the end don’t really show up much in the average. And I think you can also see that, the more points in the average, the less one difference one more point will make.

Climatologists have chosen to take their average over 30 years. Thus the HAD.CRUT3 curve in Figure 7 of the last blog is relative to a thirty-year average – from 1961 to 1990.

With the upcoming GLOBE Student Research Campaign on Climate Change in mind, I thought it might be interesting to check for temperature trends in the data from GLOBE schools. (A preliminary version of the yearly-averaged GLOBE student data is included at the end of this blog.)

GLOBE was founded in 1995. By 1996, some schools were already recording temperature data regularly. This provides us with up to 12 years of data from some schools.

Figure 1 shows an example of a long record of monthly mean temperature.

Figure 1. Monthly average temperatures from 4. Zakladni Skola in Jicin, the Czech Republic. The straight line through the data in a “best fit” linear trend determined by least-squares regression.

Figure 1 shows strong seasonal changes, with monthly average temperatures ranging from below freezing to around 20 degrees Celsius. While there is a long-term trend, the large departures from the trend line indicate that the estimate of warming rate is rather uncertain.

I decided to re-compute the trends by taking yearly averages. If a month was missing, I assigned a mean temperature equal to the average of the data from the two surrounding months (Fortunately, such gaps occurred in the spring or autumn, when filling in the data like this makes some sense). If too many months were missing, I didn’t include the year in the averages. Figure 2 shows the yearly-averaged data for 4. Zakladni Skola.

Note that the “best-fit” line in Figure 2 still shows a warming – but a different value. This is the result of the uncertainty in the linear trend, from a purely statistical point of view. This is not surprising – even the yearly averages don’t fit on a straight line. In fact the warmest year is 2000, near the beginning of the record.

Figure 2. Average annual temperatures for the data in Figure 1. Note that the “best-fit” line still shows a warming, but a larger value.

We can reduce the uncertainty by adding more data. So I include data from five other schools in Europe in Figure 3.

Figure 3. Temperature trends for six schools in Europe, selected so that no two schools are in the same country. Represented are Belgium, Estonia, Finland, Germany, and Hungary, as well as the Czech Republic.

In Figure 3, the best-fit trend lines for all six schools show warming. Note that the most rapid warming rates are at the farthest-north latitudes. Figure 3 gives us some confidence that Europe has been warming for the last decade, but there are year-to-year changes that are much larger than the 10-year trend. These short-term changes tell us there is a lot of uncertainty in the trend lines, but the fact that there are six lines instead of one gives us a little more confidence that the result might be “real” for the roughly 10 years data were collected.

For comparison, we take three sites in the United States, selected for having a continuous data record (Figure 4). In this case, two out of the three sites actually show cooling! This is quite different from Europe. However, as in the case of Europe, the year-to-year changes are greater than the long-term trend.

Figure 4. As for Figure 2, but for three schools in the United States.

Such differences could be real. The maps of temperature changes in Figure 5 show that the trends over 30 and 100 years show a lot of variation. For both time periods, the figure shows that Europe is getting warmer. Both periods also show more warming at higher northern latitudes. Results for the United States are mixed. Between 1905 and 2005, temperatures were warming over the northwest United States but cooling over the southeast United States. However, temperatures were warming over most of the United States between 1979 and 2005, with the possible exception of part of Maine (northeast corner of the United States).

Figure 5. Linear trend of annual temperature for 1905-2005 (top) and 1979-2005 (bottom). Areas in gray don’t have enough data to get a good trend. The data were produced by the National Climate Data Center (NCDC) from Smith and Reynolds (2005, J. Climate, 2021-2036). This figure and an excellent commentary on recent climate change are found at www.ncdc.noaa.gov/oa/climate/globalwarming.html.

In this blog, I have avoided using statistics to estimate the uncertainty in the trends, but I think you can see two things. First, even with all this carefully-collected data, there is uncertainty in the local trends; but the uncertainty can be reduced by including more data in the same region. And second, the trends can be quite different in different parts of the world.

To close, I include two more plots. The first is a version of the well-known curve that shows Earth’s average temperature warming with time. I plotted the curve from data from the Climate Research Unit (CRU) of the Hadley Centre in the United Kingdom

Figure 6. Annual average temperature, averaged over the globe. From the UK Hadley Centre (www.cru.uea.ac.uk/cru/data/temperature/hadcrut3gl.txt).

Figure 7. Data from Figure 6, with linear trend based on data from 1996-2007, on the same scale as for Figure 2 and 3.

The second plot is based on data since 1996 and plotted on the same scale as for the GLOBE schools. Notice how tiny the change is! This is, of course, because some parts of the Earth were cooling or warming less rapidly. But there is much more information included in that curve – and hence a lot more statistical certainty. Also, the scientists who worked on the data worked very hard to remove the effects of changing thermometers or station location, beginning and ending of observations, and many other things that can cause artificial trends. (By the way, a plot of the averages of the nine GLOBE sites produces a very slight warming with time of 0.0018 degrees Celsius per year – with the temperature peak in the year 2000 really standing out).

Clearly, this simple-looking curve took a lot of careful work to produce!

GLOBE STUDENT DATA

Below are the data used for Figures 1-4. For details in processing see the text.

xxxx – missing data (see below)

Documentation of the data

Summary of Sites

GLOBE school locations

1. Hartland, Maine, USA
2. Utajarvi, Finland
3. Tahlequah, Oklahoma, USA
4. Karcaq, Hungary
5. Eupen, Belgium
6. Waynesboro, Pennsylvania, USA
7. Hamburg, Germany
8. Jicin, Czech Republic
9. Tartumaa, Estonia
10. Average of Temperatures 1-9

Yearly averaging

Missing months are “filled in” by averaging the surrounding months. This was done when one month was missing or two months was missing (very rare). Fortunately, the missing data tended to occur in the spring or autumn, when the missing temperatures would be expected to be between the temperatures of the neighboring months. The average was then computed by summing up the data for all 12 months and then dividing by 12.

Average of all nine sites

The average is found by summing up the temperatures in columns 1 through 9 and then dividing by 9. If a temperature is missing (as in the first row, 1996), an average is not computed. Why do you think we did it this way? Two out of the three sites (3 – Tahlequah and 6 – Waynesboro) are the two warmest of the nine, and the third (8 – Jicin) is in the middle of the temperature range. If we used the average of those three points, it would make the average temperature in 1996 too warm.

NOTE: The data here are reported to two decimal places, while some of the data used for the graphs has three or four decimal places, so results might vary slightly from the results shown here.

What can be done to “improve” the dataset? We will be calculating averages for other schools with long temperature records and adding them.

Cricket temperature in degrees Fahrenheit = number of chirps in 15 seconds + 37.

I measured the actual temperature by taking the average from two thermometers. One is mounted on the house at about eye level (1.5 m) beneath the overhang where we park our car. The second lies on the table on our deck, at about 1.5 m above the ground. A louvered sun-roof on the deck keeps the thermometer from cooling too much. In both places, there is enough wind for ventilation. But I had to ignore the house-mounted thermometer if our car was warm (i.e., recently driven). Though I did not have a GLOBE instrument shelter, the height matches that for the GLOBE air temperature protocol.

It took me a week or two to figure out how to count cricket chirps. 15 seconds was too short a time — I kept ending up with numbers like 30-and-a-half chirps. Or I would lose track or start too early or too late. So I tried 30 seconds. That way if I was between 60 and 61 chirps, the resulting error would be divided by two.

Then I discovered that the crickets didn’t always chirp together (CHIRP CHIRP CHIRP) but sometimes got out of synch (chir-rurp chir-rurp chir-rurp). In this case, I would count the chirps when they were in unison, and try to maintain the beat until they got back in unison again. To make things more accurate, I’d count chirps for five 30-second periods, average the number, and then divide the average by two. If there were two sets of crickets that weren’t always chirping at the same time (say an “alto” group and a “soprano” group), I’d count the alto chirps for one 30-second period and then count the soprano chirps for the next 30-second period.

I ended up with a lot of data for temperatures above 70 degrees. But getting numbers at the cooler temperatures was harder.

Since temperatures are the coolest around sunrise, I had to start getting up around 2:00-3:00 a.m. and 5:00 a.m. to get data for the cooler temperatures.
How well did the formula work? You can see from the first graph, in Figure 1. If everything (the formula, my counting, the thermometers) worked perfectly, all the red dots would fall on the black line. That is — along the black line the “cricket temperature” is equal to the measured air temperature.

Figure 1. Air temperature measured from cricket chirps. For this graph, the number of chirps during 15 seconds is added to 37 to get the air temperature. The highlighted temperature readings are for the red “best-fit” line.

In the graph, the data are close to the black line, but not always on it. The red line is the straight line that best fits the data. Notice that the red line drops below the black line for high temperatures. Thus from the red line, for a “cricket temperature” of 80 degrees Fahrenheit, the measured air temperature is only 78 degrees Fahrenheit. Similarly, from the red line, a cricket temperature of 50 degrees Fahrenheit corresponds to a measured temperature of 52 degrees Fahrenheit — not exactly right.

So I plotted cricket chirps against air temperature to get a better method: Count cricket chirps for 13 seconds, and then add 40 degrees. Using this method, the points (and the red line) are much closer to the black line.

Figure 2. Air temperature measured using cricket chirps. For this graph, the number of chirps during 13 seconds is added to 40 to get the air temperature. As in Figure 1, the black line is where the points would fall if the method was perfect, and the red line is the line that best fits the data.

Clearly the approach in Figure 2 works slightly better. The red “best-fit” line through the data lies almost on top of the “perfect fit” black line. I later found this method was also on the Web.

If you find it hard to count chirps for 13 seconds, count chirps for a longer period (say 30 seconds) and then multiply by 13/30 to get the chirps in 13 seconds. Or if you are really patient, count chirps for a full minute and multiply by 13/60.

Notice that both the “cricket temperature” and the measured temperature stay above 50 degrees Fahrenheit. Both my husband (who helped collect data when I was gone) and I heard no cricket chirps at all when the measured temperature was 49 degrees Fahrenheit or lower. This suggests that 50 degrees Fahrenheit is at about the lower limit for when crickets chirp.

I had suspected that the lowest temperature for chirping crickets would be 50 degrees Fahrenheit or less. Why? Because meteorologists who study winds using radar have noticed that insects stop flying (and producing radar echoes) at 50 degrees Fahrenheit (or 10 degrees Celsius). I reasoned that it would take about the same energy — or less — to chirp than to fly, since chirps are produced by crickets rubbing their wings together, which should consume less energy than flying.

For comparison, a posted article from Dartmouth College lists 55 degrees as the minimum temperature for cricket chirps. Both my husband and I noticed fewer crickets (one or two) were chirping when the temperatures were in the lower 50s, so some crickets probably did stop chirping at that temperature, but not all.

Finally, let’s plot the data to show the relationship between cricket chirps and the temperature in Celsius degrees. Figure 3 shows this relationship. Again, the “best-fit” red line and the data are close to the “perfect fit” black line.

Figure 3. Relationship between cricket chirps and the temperature in degrees Celsius. As in Figures 1 and 2, the black line is where the points would fall if the method was perfect, and the red line is the line that best fits the data.

You can find several approaches on the Web, but it is not certain where they came from, and the raw data aren’t available, so you don’t know how many measurements were taken to determine the approach. Here I provide the data set so that you can play with it — or add your own observations. Have fun! It will be interesting to see whether chirps from crickets in the other parts of the U.S. and world relate to temperature in the same way.

Cricket Chirp Data – Boulder Colorado, USA. All dates 2007

On 29 May 2002, we took observations of the heating and moistening of the lower atmosphere using an aircraft and surface sites observations in the Oklahoma Panhandle (The Western Track in Figure 1). Two days before we took our data, a heavy rain brought 80 mm of rain to the point labeled 1, with the points labeled 2, 3, and 10 getting 30 mm or less.

Figure 1. Map showing the location of aircraft flight tracks (white lines) and sites where we took special measurements (numbered 1-10). The observations I write about are along the Western Track, on the left side of the picture. The long white lines outline part of the state of Oklahoma.

We have been trying to see how well a land surface model would do in predicting the observed heating and moistening, given the weather conditions – temperature, solar radiation, wind, rainfall, and so on as input. And the model didn’t work very well near Site 1. No matter what we did.

We have an idea why: Puddles.

As you can see from Figure 2, there were puddles near the southern end of the flight track. In fact, one road was blocked by water. And the land surface model didn’t account for evaporation from puddles. We think this could explain why the measurements showed more moistening (and less heating) of the air than the model did.

Figure 2. On 29 May 2002, photograph of puddles near the southern end of the Western Track, shown in Figure 1. The spots are on the aircraft windshield.

I decided that I had better learn more about puddles. So the first day there were puddles outside my office, I went outside and took puddle temperatures with a GLOBE infrared sensor (see the GLOBE Surface Temperature Protocol).

I was surprised – the puddles were warm compared the ground around them. This is not what I expected. Puddles like those in Figure 2 were cooler than the surrounding ground on 29 May. So I became even more excited about puddles. There is nothing more fun – and sometimes more awful! – than taking measurements you don’t understand.

I’m starting this project by just trying to figure out how fast the puddle disappears. On an asphalt surface, this tells me how fast the puddle evaporates. I’m also measuring the temperatures of the surface around the puddles.

Figure 3 is a picture of the puddle that I measured. The chalk rings are drawn around the puddle so that I can see how fast it is drying out.

Figure 3. Puddle with outlines of water’s edge. The lines alternate between light yellow and light pink. Yellow or pink dashed lines are where the chalk is too light to see easily. By the time this picture was taken, the puddle was almost gone, with shallow water in a few places in the small left circle. Times are when the lines were drawn. UTC = MDT + 6 hours.

What did I learn? Figure 4 showed results more like what I had expected. As the sun got higher in the sky, the asphalt surrounding the puddle warmed more than the puddle itself. And the difference between the puddle temperature and the asphalt temperature got bigger, until around 11 a.m., when it started to get cloudy. After that, the temperature difference became smaller.

Figure 4. Temperature of the puddle in Figure 3 as a function of time. The skies were mostly clear until about 11 a.m. MDT. After that, the sky got cloudier with time. It was overcast by 11:50. Local solar noon (when the Sun is highest in the sky) is around 13 MDT.

Does this offer a clue to why the first puddle I looked earlier at was warmer than the surrounding surface? I think it does. That day, it was also cloudy in the afternoon.

If this puddle had lasted longer, AND if this puddle cooled more slowly than the dry asphalt once the skies were cloudy, then this puddle might have ended up warmer than the asphalt. And maybe it has something to do with the fact that water stores heat well.

So I need to look at more puddles. And, while doing this simple experiment, I noticed that I could have done some things better:

• I didn’t want to use the oven mitt on the radiation thermometer, as recommended for the GLOBE Surface Temperature Protocol, so I kept the radiation thermometer outside so that its temperature was the same as the air temperature. But I soon discovered that the air temperature where I kept the radiation thermometer was different enough from the puddle site that the measured surface temperature changed rather rapidly for about five minutes (the differences weren’t that bad). So I’m not too sure about the temperatures before 8 a.m. After 8 a.m., I still left the instrument outside but oven mitt on – and the measurements were more consistent.
• Toward the end of the observations, I realized that I had made a bad assumption: that all the asphalt outside the puddle was the same. It wasn’t. The puddle was in a place that had been repaired. You can see the difference in Figure 5. The area to the north of the puddle was up to 3 degrees cooler than the area to the south of the puddle! ). So I only use the temperatures on the south side in Figure 4.
• I had carefully drawn chalk rings around the puddle, so that I could see how fast it evaporated. But I forgot to take an important observation – how deep the puddle was! So – even though I could tell that the puddle was evaporating, I couldn’t tell how much water was evaporating – and I wanted to know that.
• If clouds are important, as they would be if the puddle stays warm after the skies cloud over, but the surface around it cools off – I need to be more careful about writing down when there were clouds.
• Fourth, once the puddle got quite shallow, it was basically wet asphalt. I should have taken the temperature of the wet asphalt as well.

Figure 5. The puddle and its environment. Note the puddle lies on the south (right) end of an asphalt square that was slightly warmer than the darker asphalt to the right. (Although dark things are usually warmer than white things, the warm temperature could have something to do with different materials being used, or the thickness of the asphalt layer.)

I have some of the other data below. You’ll notice I may have made a few mistakes! (It’s important to keep track of them, so you can learn from them). The times are important because I might want to check other weather data I can get from the Web or from the automatic weather station on top of our building.

Next time I will be more thorough. I’ll let you know what happens. In the meantime, think about how you can use measurements or simple observations to describe some things that are happening around your home or school.

Table: Puddle measurements on 6 May 2007.