Projected Temperatures for Worldwide Locations

Here's another exercise involving temperature records to project what temperatures will be in the future. The GISS people have been kind enough to put lots of station data for lots of stations around the world on their web site.

Here's the procedure: go to HERE
http://data.giss.nasa.gov/gistemp/

Then click on Station Data, which takes you to the STATION DATA
http://data.giss.nasa.gov/gistemp/station_data/

Note that the temperatures reported for the stations are mean (average) annual temperatures for those stations, not the temperature anomaly (Temperature Difference) we've talked about before.

For US locations, click on the map for a state. Here's a random example. Click on Nebraska, then look for stations that have records at least from 1900-2010. Take the first station (Minneapolis - Nebraska, not Minnesota!), click on the station name, and the mean annual temperatures will come up. You can be fancy and do a regression to predict the mean annual temperature in 2050. What's easier is just to use a ruler and eyeball the best-fit line for the points. My guesstimate is that the predicted mean annual temperature in 2050 is about 14.3 °C . This is well within the range of temperatures that show up on the graph - in other words, significant climate change isn't expected to happen by 2050 in Minneapolis, NE. Here's the graph:



If you think this station may not be representative, try a few more. I randomly clicked on Tecumseh. From the graph, it appears that the slope of the line is negative; that is, the mean annual temperature in Tecumseh is going down rather than up.

If you want to look at other countries, click on the map. Here's an example. I clicked on the tip of South Africa, about the location of Capetown. The Capetown Safr station has records from 1880-2010. The temperatures appear essentially to form a wave, with no clear direction. There's no reason to expect the temperature in 2050 to be significantly higher than at present. The Kimberly station has records from 1897-2010, and there appears to be a slight positive slope, but the projected temperature in 2050 isn't expected to be significantly higher than at present.

So far, I haven't found ANY stations with long-term records where the 2050 temperatures are projected to be significantly higher than the long-term average temperature for that station and/or the average temperature for the last 10 years. I'm sure there are such stations; I just haven't tried very hard to find them.

An interesting question is why the global warming people say the average temperatures are going up substantially (global warming) when it appears that the temperatures at the individual stations aren't going up significantly. Perhaps that's a subject for another day.

Below is the graph of Temperature Differences (in °C) versus year. Sorry the image is so fuzzy (the problems with uploading images in Blogger). You can view the graph in pdf format or its equivalent in the spreadsheet; see below. You see that the projected Temperature Difference in 2050 (the red dot on the right of the graph) is about 0.75 °C - the result of the regression analysis (the center of the vertical axis is 0, the other entries going up the scale from 0 are 0.5, 1, and 1.5).





















If you're interested in the analysis, as an exercise in playing with Google Docs I've uploaded the spreadsheet in Google Docs format. The link to the Google Docs is HERE

The spreadsheet is also more-or-less available in Excel format, including the diagram above. The reason for "more-or-less" is that you probably won't be able to open the spreadsheet unless you're signed into your gmail account. This appears to be one of the quirks of Google Docs - maybe Google wants everybody in the world to have a gmail account ("Well, Duh"). The link to the Excel spreadsheet is HERE. In the Excel spreadsheet, the Chart is the diagram above.

Here's a work-around that someone found for the Excel format problem. The link to the spreadsheet is HERE. With luck, you should be able to download and then open this spreadsheet whether or not you are signed into a gmail account.

I've also uploaded the Chart sheet to Google Docs in pdf format. The pdf Chart also should open even if you're not signed in to your gmail account. The Chart is HERE

In any of the spreadsheets, the Results sheet is the result of the regression, and the USTemps09142010xls sheet is the data. Enjoy.

Update - projected US temperatures in 2050

An update on the answer to the question: "What will US temperatures be in 2050?"

The gnomes that keep the temperature data add new years and massage/tweak/fudge/adjust (take your choice) the data from time to time. That is, the figure they give for the Temperature Difference in, for example, 1934 decreased from 1.25 to 1.20 between 2007 and 2010 (??). Also, according to their new figures, the average Temperature Difference in the years 1995-2005 increased from 0.53 C to 0.67 C between 2007 and 2010. Go figure. (Hint: adjusting/fudging the older temperatures downward, and the newer temperatures upward, makes it appear that current temperatures are relatively high by historical standards.)

Anyway, let's use their current data posted at http://data.giss.nasa.gov/gistemp/graphs/Fig.D.txt
and go through the same regression as before. I won't bother with the details of the calculations; see the August 19, 2007 post for these. Here's the results, using their data from 1880-2009:
In 2050, the Temperature Difference is now projected to be 0.74 °C (1.3 °F).
The Temperature Difference is expected to rise by 1 °C (1.8 °F) about every 160 years (that is, the slope of the temperature vs. year line is 0.0063.

The 2007 regression projected the 2050 Temperature Difference to be 0.58 °C (1.06 °F)with the 95% confidence interval 0.35 °C to 0.82 °C (0.64 °F to 1.48 °F). So the new prediction is well within the uncertainty of the 2007 projection.

Here's the conclusion from the 2007 projection:
"The linear regression predicts that the US temperature difference in 2050 (0.58 °C or 1.06 °F) will be essentially the same as it was in the years 1995-2005 (0.53 °C or 0.95 °F). A bit warmer than the average since 1880, but not exactly a big deal."

And here's the conclusion from the current projection (remembering that the 1995-2005 figures were adjusted/fudged upwards by the gnomes who do these things):
The linear regression predicts that the US Temperature Difference in 2050 (0.74 °C or 1.3 °F) will be essentially the same as it was in the years 1995-2005 (0.67 °C or 1.2 °F). A bit warmer (about 1 °F) than the average since 1880, but not exactly a big deal.

So if a global warming (oops! - the term is now "climate change") advocate comes to you and says that the Himalayan glaciers will disappear by 2035 (oops again! - they've already retracted that prediction) or that the US temperatures in 2050 will be radically higher than now, ask them to put their money where their mouth is. Suggest they bet you, say, $1 million in inflation-adjusted dollars at even odds that the average Temperature Difference in 2045-2055 will be more than 3 °C or 5 °F higher than in 1995-2005, with the bet being binding on the heirs of both of you. Then sit back and wait to collect your money, or to give your children or grandchildren a nice nest egg.

US climate change??

August 19, 2007
Projected US temperatures in 2050 - U.S. and/or global warming?

What will US temperatures be in the year 2050?
Many have predicted that ongoing global warming, due in large part to human activity, will produce a US meltdown by the year 2050, with much of Florida under water, rampant tropical diseases such as malaria, and the US essentially going to Hell temperature-wise. What’s actually most likely to happen?


The Bottom Line
In 2050, the US temperature is projected to be essentially the same as it was in the period 1995-2005.
In other words, a yawner. Keep reading for the details.

Background
The US government publishes standardized temperatures for the US through the years, trying to compensate for heat effects of urbanization, etc. These temperatures are called “temperature anomalies” but we’ll call them “temperature differences“ - the word “anomalies“ has an implication of being unusual. These are some sort of average of temperature readings all across the continental US. The temperature differences are relative to the average for 1950-1980. That is, a temperature of 1 °C doesn‘t mean the average temperature was 1°Celsius; it means the temperature for that year was 1° Celsius hotter than the 1950-1980 average. These temperature differences can be found at the following web site:
http://data.giss.nasa.gov/gistemp/graphs/Fig.D.txt
Note: when going to this site, type it in exactly as shown. For example, fig.d.txt (lower case) gives an error message.
More information can be obtained by moving backward through the site; e.g.,
http://data.giss.nasa.gov/gistemp/graphs/

Note: The temperatures were recently updated because of a Y2K glitch, caught by an outsider, not by the government scientists who produced them. (Is anybody surprised?) It is not known how many additional errors are in their data and interpretations, because the source code and original data are not available to the public. But we’ll use these data as the best currently available.

AnalysisSuppose one wants to predict the temperature for some year. The absolutely simplest form of analysis imaginable is to do a linear regression of temperatures versus time
Y= a + b X, where Y is temperature and X is the year
with the year for which the temperature is being predicted set to X=0 in the regression equation. The intercept of the regression line is the temperature of the year of interest, and the slope is how rapidly the temperature is changing.

The regression analysis is equivalent to finding the best-fit straight line for a graph of temperature differences vs. year and then extrapolating the line to find the temperature for the year in which you’re interested. See Fig. D (“U.S. Temperature”) on the site
http://data.giss.nasa.gov/gistemp/graphs/

Here’s a simple example of such a regression calculation. Suppose in 1934 Al Gore’s grandfather had the temperature data available only for the years 1924-34, and decided to predict the temperature for 2004. The data would look like:

Actual ...........Year (for ..............Temperature
Year ..............regression) ..........(°Celsius)
1924 ...............-80......................... -0.74
1925 ...............-79 ...........................0.36
1926 ...............-78 ...........................0.04
1927 ................-77 ...........................0.15
1928 ...............-76 ............................0.07
1929 ...............-75 ...........................-0.58
1930 ..............-74 .............................0.16
1931 ...............-73 ............................1.08
1932 ...............-72 ...............................0
1933 ...............-71 ...........................0.68
1934 ...............-70 ...........................1.25

Put these numbers into an Excel spreadsheet, crank up the Tools\Data Analysis package, and regress “Temperature” against “Year (for regression),” and you get the following results - and lots more statistical information as well. Temperatures are given in both °Celsius and
°Fahrenheit, because a typical US citizen hasn‘t got a clue what a Celsius temperature is.
Predicted average US temperature difference in 2004: 9.1 °C (16.4 °F)
95% confidence interval: 1.2 °C to 17.1 °C (2.1 °F to 30.7 °F)
Slope (change in temperature per year): 0.12 °C/year (0.21 °F/year) - that is, the regression equation says the temperature increases 1 °F every 5 years
Significance level of F-statistic: 0.031 (without being too fancy about it, the significance level indicates a significant relationship at the 97% confidence level between temperature and year)

So Al Gore’s grandfather could have made a movie and gone out on the lecture circuit talking about how the US would be impossibly hot in the year 2004. The predicted temperature in 2004 would be about 9 °C (16 °F) hotter than the average during the 1924-1934 period (0.2 °C or 0.4 °F temperature difference) and perhaps as much as 17 °C (30 °F) hotter. A truly frightening possibility of a truly frightening calamity by 2004!! Back to reality: The actual 2004 US temperature difference was 0.44 °C (0.79 °F). OOPS!

This example was just to show how the regression process works - try it yourself to see if you get the same numbers. It’s obviously silly to extrapolate too far from the actual observations. For example, it would be downright stupid to extrapolate from the US temperatures in 2000-2006 to say the sky will be falling and Florida will disappear into the ocean by 2050. OOPS again! That’s what people do.

But let’s try a serious analysis. We want to predict temperatures in 2050, using temperatures through 2006; that is, 44 years in the future. So let’s see how good a job we can do at predicting temperatures 44 years in advance.

We’ll try predicting the temperature difference in 2004 using temperature data from 1880-1960. The reason for choosing 2004 is that it’s the last year we can look at the 5-year average for 2002-2006 as what we’re really trying to predict. There are enough year-to-year variations that it’s better to predict the 2004 temperature difference, and see how closely the predicted temperature compares with the 2002-2006 5-year average, not just with 2004 itself - although we can also make that comparison.

So we take the 1880-1960 data, set 1960 as year -44, 1959 as year -45, etc., and do the regression with the intercept being the predicted temperature difference for 2004. Here’s what we find:
Predicted average US temperature difference in 2004: 0.66 °C (1.18 °F)
95% confidence interval: 0.30 °C to 1.01 °C (0.55 °F to 1.82 °F)
Significance level of F-statistic: 0.0003 (significant at the 99.97% confidence level)
The actual temperature differences in 2002-2006:
2002 0.53 °C (0.95 °F)
2003 0.50 °C (0.90 °F)
2004 0.44 °C (0.79 °F)
2005 0.69 °C (1.24 °F)
2006 1.13 °C (2.03 °F)
And the actual 5-year average for 2002-2006: 0.66 °C (1.18 °F)

Obviously, the agreement to within 0.01° between the predicted 2004 temperature difference and the average of the 5 years around 2004 is sensationally good. In fact, much, much better than one would reasonably expect. And the agreement between the predicted and actual 2004 temperatures (within about 0.2 °C or 0.4 °F) isn’t shabby.

Now that the model for the temperature estimation has been validated way beyond any reasonable expectations, let’s address the multi-trillion-dollar question: What will the US temperature be in 2050?

What we’ll do is to take all the data we have (1880-2006), and do the linear regression for the 2050 temperature. (In the regression, 2006 is year -44, 2005 is year -45, down to 1880 is year -170). Here’s the result:
Predicted average US temperature difference in 2050 (the intercept): 0.58 °C (1.06 °F)
95% confidence interval: 0.35 °C to 0.82 °C (0.64 °F to 1.48 °F)
Change in temperature per year (the slope): 0.0048 °C/year (0.0087 °F/year) - the regression predicts the temperature will increase 1 °C about every 200 years or 1 °F every 115 years.
Significance level of F-statistic: 0.00001

Let’s compare this result to some recent temperatures. The average temperature in the period 1995-2005 was 0.53 °C ( 0.95 °F).
In other words, the linear regression predicts that the US temperature difference in 2050 (0.58 °C or 1.06 °F) will be essentially the same as it was in the years 1995-2005 (0.53 °C or 0.95 °F). A bit warmer than the average since 1880, but not exactly a big deal.

A few quibbles, caveats, etc.1. There are as many ways of fitting data to equations as there are statisticians. The easiest way to begin is with the simple linear equation. That’s always the first place to start, and most of the time does about as well as much fancier equations. Although, of course, there are data for which a linear equation either doesn’t work or can be improved upon.
Anybody can use any equation, and see if that equation produces a significantly better fit than the simple linear equation. There are straightforward statistical tests to see if a fancier equation improves the fit. We’ve tried a few without much success, but anybody is welcome to try any other equation.
2. Whether it will be successful to do a straight-line extrapolation of previous temperatures for 44 years into the future is an open question. The extrapolation worked sensationally successfully 44 years in the “future” to 2004. What will happen going forward to 2050 is unknown. Perhaps a gigantic meteor will hit the Earth, even more gigantic volcanoes will erupt, or the cataclysmic tipping point events predicted by the global warming crowd will come to pass. Who knows?
3. The prediction here is only for US temperatures. Somebody might want to try the equivalent exercise for temperatures in other parts of the world.
4. The advantage of the linear extrapolation of temperatures is that the data and analysis are completely transparent - anybody can reproduce the calculation or look up the data. But ask any climatologist who has a climate model to show you the source code - lots of luck getting it. It’s a closely-held secret whether or not the code contains a line
IF ((T2050 - T2006) < 2.5) THEN (((T2050 - T2006) = 2.5) AND CALL AL GORE)
In modern science, data are considered proprietary trade secrets, even when the data are gathered on government contracts and grants.
The general rule is that you should take with a very large grain of salt any projection showing major effects on temperature due to human activity when the projection is done by somebody whose grant funding depends on getting results showing that human activity causes temperature changes. Too many scientists are more than happy to sing for their suppers whatever tune strikes the fancy of the person paying for the supper.
5. And a question to which we’ve never heard a very good answer: What will be the temperature effect of injecting, say, 1,000 kg of carbon dioxide into the atmosphere? 0.0000001 °C or 0.0000000000001 °C or what? Does anybody have an answer and, more important, will they let other people check their calculations?

That's all for now.