Figure: Global Temperature Anomaly from Arbitrary Reference Period (°C) versus Year. The pink plot is the month-by-month anomalies. The blue plot is the year-by-year anomalies.
This page serves as a summary of what my friends and I have discovered on the web in our debates about the global climate. We add to it as we have time. We don't make measurements ourselves. We just gather other people's measurements, compare them, and examine their conclusions. It is our habit to be skeptical of all claims by all scientists, including ourselves. But we hope very much that nothing we write here shows any sign of disrespect to anyone working in the field of climate science, to whom we are in debt for all their hard work gathering data, and their further hard work making that same data available to the public.
Despite rumors we have read on the internet about climate scientists trying to keep their data secret, in our experience, every climate science institute has gone out of its way to make its data available to amateur, armchair climate scientists like us. Furthermore, they have posted their papers on the web for us to view, without paying fees to journals. As far as our experience goes: that's better freedom of information than we have in Physics or Electrical Engineering.
We use several simple concepts and phrases in our analysis. Although they are simple, they are nevertheless difficult to understand. Well, maybe you can understand them easily, but it took us years to understand them properly. For a guide to our terms of order, precision, accuracy, and calibration, see here.
We begin with a discussion of global surface temperature. This discussion quickly becomes detailed and rather complicated. It is impossible to avoid these details and complications. The concept of "global temperature" can be vague only until we try to measure it. If we want to measure "global temperature" to 0.1°C, we must be so extremely specific in our definition of "global temperature" that complicated detail becomes absolutely necessary. The purpose of our Global Surface section is to show you how these complicated details arise, and show you how the details allow us to estimate the accuracy of our final measurement.
You will find our large data files and an Exel spreasheet with our graphs and calculations combined in a zip file Climate.zip.
The Climate Research Unit (CRU) in England estimate the average global temperature from the year 1850 until the present day. They maintain their data on their website, and answer basic questions about their methods here. The original scientific paper presenting their measurements is Jones, P.D., New, M., Parker, D.E., Martin, S. and Rigor, I.G., 1999: Surface air temperature and its variations over the last 150 years. Reviews of Geophysics 37, 173-199. The paper is available for download here. The paper concludes that the average temperature of the earth has risen by 0.6°C in the last fifty years.
We downloaded the global mean temperature data from CRU, which you will find here. We re-formatted the data to make it easier to plot, here. We took the average of their monthly anomalies (we'll explain what an anomaly is later) and made a table of yearly anomalies as well, which you will find here. We plotted both in the graph below.
Jones et al of CRU collected the measurements made by many land-based weather stations. For a map of the locations of all their weather stations, see here. Below is a graph showing the number of stations available each year, which we obtained here. For a graph of the total number of stations available in each year, including those that CRU rejected, and counting all duplicate stations, see here.
They started with around 250 stations, built up to 1700 in 1950. The period between 1970 and 2000, sees the number of stations dropping from 1600 down to 400. During that same period, the CRU global temperature estimate rises by 0.6°C.
We downloaded the monthly global mean temperature data available from the National Climatic Data Center (NCDC). We obtained the data file from here, and add their monthly anomaly corrections to get this data, which we plot below.
As you can see, the global temperature varies by 4°C during the year. We can greatly reduce this cyclic variation by subtracting the average January temperature from all the January measurements, and the average February temperature from all the February measurements, and so on, to obtain temperature anomalies. When we do this to the NCDC data, we get the a graph similar to that published in Jones et al. Phil Jones of CRU confirms that the two data sets are the same. There are differences in the way the data is combined, and CRU used older measurements in the data to extend their record back another thirty years. You will find the NCDC paper on their analysis here.
Jones et al address many potential sources of error in the way they combine temperature measurements. For example, one source of error is the warming of weather stations as cities build up around them. This effect can be up to +10°C on a hot day. The urban effect would tend to give the impression that the global temperature has risen. Jones et al site work by other scientists that claims these urban effects will contribute less than 0.1°C to Jones et al's observed 0.6°C rise in global temperature. Let us accept this claim for now, but we dispute it below in Disappearing Stations.
Suppose we consider picking a place on the surface of the globe at random. What will its temperature be? The hottest place in the world we could find is El Aziza, where it can get to 60°C on a summer day. The coldest place we could find was Antarctica, where the temperature once dropped to −90°C. Just before we pick a place on the globe at random, the instantaneous temperature we will soon obtain with our thermometer that place is, so far as we are concerned, a random quantity with a near-gaussian distribution. (If you doubt the near-gaussian distribution, please consult the Central Limit Theorem). This random quantity has a maximum, and very rare, value of 60°C, and a minimum, and very rare, value of −90°C. When the spread of very rare values is 150°C, the standard deviation of a guassian distribution is roughly six times smaller, or 25°C. (See here for a graph off the guassian distribution, showing that a six-sigma spread encloses 99.8% of all values.) We define the instantaneous global temperature as the expected value of annual temperature. In other words, if we covered the globe uniformly with an infinite number of accurate thermometers, the average value of all their measurements would be the instantaneous global temperature.
If, on the other hand, we put a number of thermometers at random places around the globe, and take the average of their measurements, we get an estimate of the instantaneous global temperature that itself has a gaussian distribution. Jones et al start off with roughly 250 measurements of global temperature in 1880, so let's consider what happens if we use 250 measurements distributed around the globe. The average of 250 measurements each with standard deviation 25°C is a measurement with standard deviation 25°C/√250 ≈ 1.6°C.
The instantaneous temperature at any place includes its day-night variation and its summer-winter variation. Suppose we take the average of temperature measurements every hour throughout the year, and call this the annual temperature. We pick places on the globe at random and calculate the average of their annual temperatures instead of their instantaneous temperatures. The annual temperature in Death Valley is 25°C, and at the South Pole it's −55°C. These are the hottest and coldest places on Earth. One is 80°C colder than the other. Let us once more divide the maximum variation by six to obtain our standard deviation: the standard deviation of annual temperature across the globe is 13°C. We define the annual global temperature as the expected value of annual temperatures. In other words, if we covered the globe uniformly with an infinite number of accurate thermometers, took measurements for a year to obtain the annual temperature at each of our infinite number of locations, the average value of all their measurements would be the annual global temperature.
If we pick 250 thermometers at random places around the globe (once again, we are using 250 because that is the number Jones et al started with in 1880), record their measurements for a year, calculate each location's annual temperature, and then take the average of all 250 annual temperatures, we arrive at an estimate of the annual global temperature. This estimate has standard deviation 13°C/√250 ≈ 0.8 C.
But if you look at the figure above, you will see that the distribution of thermometers in the data used by CRU and NCDC is not random. They are clustered together, and these clusters change as time goes by. In 1850, there were far more weather stations in the northern hemisphere than the southern, and we can imagine that there were far more in Europe than there were in Africa. Given that our 250 thermometer locations are not chosen randomly, we will not get the factor of √250 improvement in accuracy by averaging all of their measurements together.
If we don't get an improvement of √250, what improvement do we see when we average the 250 measurements? We look at the clusters and ask ourselves, if we distributed thermometers randomly, how many could we distribute before they started to look more evenly-distributed than our actual clusters. This gives us a measure of the actual randomness in our clusters. So, we looked at the clusters. The south pole gets left out, Brazil, Australia, and Russia are hardly measured. But we could easily distribute 25 thermometers across the globe and have them under-represent three or four large areas, as does the distribution of the available stations. We're guessing the effective number of independent measurements from our existing clusters is something like 25, in which case our global average temperature has error 13°C/√25 = 3°C because of poor distribution of stations. This error is not random from year to year, but varies as the set of stations grows and shrinks.
Jones et al do not claim to know the annual global temperature to 0.1°C. Instead, they claim to be able to measure changes in the annual global temperature to 0.1°C. To see how these two claims are different, suppose you have a home thermometer and it tells you that the temperature in your house is 30°C, when you know perfectly well that it's closer to 20°C. What does it mean when your home thermometer tells you that the temperature in your house is 29°C? Most likely, it means that the temperature went down. Your thermometer may measure the temperature to only 10°C accuracy, but it can measure changes with 1°C resolution.
We will now take a paragraph or two to explain how Jones et al combined their weather station measurements to obtain their estimate of the change in annual global temperature.
For each month of measurements obtained from each station, Jones et al calculated the average temperature for the month, and subtracted from it the average temperature in that same location for that same month during an arbitrary reference period. This difference they call the station's monthly anomaly. For their arbitrary reference period, they chose 1961 to 1990.
The reason that Jones et al choose 1961-1990 for their reference period is because this is the period has the largest number of active land-based weather stations. In the Anomaly Versus Absolute Temperature of their paper, they say:
In this analysis, 12,092 station estimates of mean temperature for 1961-1990 are used to construct a 0.5° latitude by 0.5° longitude climatology for global land areas excluding Antarctica.
Consider, for example, a weather station on the coast of Australia in 1850 that operated for twenty years. We use the 1961-1990 temperature map to obtain the average temperature at the weather station's location from 1961-1990. We subtract this temperature from the weather station's measurements to obtain its anomalies. Every year, we have hundreds to thousands of anomalies from stations all over the world. We take the average of all of them to obtain our estimate of global anomaly. The global anomaly is what we show plotted in the graphs above. We show both the monthly and annual global anomaly.
If we assume that our weather stations in the reference period are well-distributed, then the method of anomalies helps remove errors that arise from poor spatial distribution of weather stations outside the reference period. If we have only a few weather stations in 1850, we don't have to worry so much that they are in mostly hot areas or mostly cold areas. We are comparing each station to the climate in the same location a hundred and twenty years later, when we have many more weather stations.
The use of anomalies also helps us remove errors that arise from changes in our set of available weather stations. Suppose we have nine weather stations aroudn the world, whose average annual temperature is 10°C from 1900 to 2000. We want to combine these measurements with those of a weather station in Antarctica that was founded in 1950. We can't add Antarctic measurements before 1950, because they don't exist. The moment we start adding the Antarctic measurements, our average annual temperature will drop by 5°C, because the annual temperature in Antarctica is around −50°C. The method of anomalies avoids this −5°C.
The method of anomalies greatly reduces errors due to changes in our set of available weather stations. It greatly reduces errors due to temperature offsets between weather stations. With these two errors greatly reduced, we might hope to see only changes in the global annual temperature, and this is indeed the claim made by Jones et al. They claim to be able to measure changes in global annual temperature with 0.1°C precision. Let us estimate for ourselves the accuracy with which the method of anomolies can measure trends in global annual temperature.
Consider the central England temperature over the last three hundred years, which we present elsewhere. Suppose we had only a ten-year stretch of data from Central England, and we used the anomalies from this ten-year stretch in our estimate of the global anomaly. The figure below shows the trend in°C/decade we would obtain using the previous ten years of Central England measurements, plotted against the year. The standard deviation of the ten-year anomaly trend is 0.7°C/decade.
If we plot the same graph for shorter or longer periods, we find that the standard deviation of the trend is close to 0.7°C/T, where T is the length of the period. So the half-century trend has standard deviation 0.7°C/half-century.
Let us suppose Central England is representative of temperature variations around the globe. If we have twenty-five weather stations distributed evenly about the world and we combine ten continuous years of measurements with the method of anomalies, we will obtain an estimate of the decade-long global temperature trend that has standard deviation 0.7/√25 = 0.14°C/decade. If we combine fifty continuous years of measurements we will obtain an estimate of the half-century-long global temperature trend with will have standard deviation 0.14°C/half-century.
We can understand how CRU and NCDC believe it is possible to use their method of monthly anomalies to determine changes in global temperature with 0.1°C resolution. But they have not proven their accuracy by comparing their method with another, independent method that is accurate to 0.1°C for the same time period.
The distribution of weather stations in the CRU and NCDC data set is non-uniform across the globe and with time. Because of poor distrubution, the effective number of stations can be hundreds of times smaller than the total number of stations.
Another reason to doubt the accuracy of the CRU and NCDC trends is that the data from almost all stations is incomplete. The addition and subtraction of stations from the calculations is bound to introduce systematic errors. When we look at the CRU graph of global temperature, we see a clear correlation between the number of weather stations used and the rise in temperature in the last fifty years. As the number of weather stations drops from 1955 to 2005, their estimated global temperature rises. We look into this correlation in more detail below, and show that it appears to introduce a false warming of order 0.2°C.
The fact that CRU and NCDC trends agree suggests that their application of the anomaly method to the same set of data is free of errors. Indeed, we come up with almost exactly the same results from the same data set, but using a very much simplified analysis, as we present below, so we are convinced that they have both done their analysis accurately. But this agreement does not verify the anomaly method itself. We cannot confirm the CRU and NCDC trends by comparing them to a more accurate measurement method. There is no more accurate measurement method. Climate scientists tend to use the CRU and NCDC measurements to calibrate their own trend measurements. Nor can we even determine the precision of the method by measuring the global temperature for a century during which it remained constant. There is no century during which we know the global temperature was constant.
Perhaps as a result of our own ignorance, or perhaps out of a contrary disposition, we remain skeptical that the resolution of the CRU and NCDC measurements is 0.1°C. We see no mention of the correlation in Jones et al's paper, and no effort to show the correlation is mere coincidence. We estimate that their global trend contains systematic errors of order 0.1°C/decade.
We are not alone in our skeptisism. The paper Unresolved Issues with the Assessment of Multi-Decadal Global Land Surface Temperature Trends (available here) argues that the effects of new buildings, loss of vegetation, change in instrument elevation, and changes in the instruments themselves, produce systematic errors in the global trends that could easily be of order 1°C. For example, they show how a change in land-use and land-cover (they say LULC) causes the sudden apperance of positive trends in a collection of a hundred or so neighboring stations (see their Table 5).
We resolved to look at the raw data ourselves. For our results, see below. Our home analysis allowed us to estimate the systematic error caused by the disappearance of weather stations.
Let us suppose that Jones et al of the Climate Research Unit are correct, and their measurement of global temperature is indeed accurate to 0.1°C. Can we look at their graph and predict a trend? How do we know that the fluctuations in global temperature are not random?
What we see in the Jones et al graph are variations from year to year of around 0.1 C, variations from decade to decade of 0.2 C, and variations from century to century of 0.4 C. This looks like the 1/f noise we see in many physical systems.
The only way to prove that global temperature does not behave like 1/f noise is to present a long period of time, something like a thousand years, during which the global climate did not behave like 1/f noise. We have no such period of time.
Before we can say that a rise in temperature is a trend caused by anything, we have to first prove that it is not random. To prove that it's not random, we need a lot of accurate data. We don't have that data. We cannot draw any conclusions about the future of the climate from the Jones et al graph.
Indeed, if it were that easy to predict trends from chaotic-looking graphs like the global temperature history, the we'd all be millionaires in the stock market by now. Just look at the graph above, and see if you can tell what the stock is going to do next. To see what happened next, click here.
This example shows the absurdity of fitting a straight line to a chaotic-looking plot and claiming that the straight line somehow represents an underlying trend.
When we perform an experiment, we usually start with a hypothesis about what the results will be. If the result matches our expectation, we stop working and present our results. If our result does not match our expectation, we look for errors in our measurements. When we find an error, we correct it. The errors we are looking for are ones that cause our results to deviate from our expectations.
You can see an example of this expectation-driven search for errors below. The scientists at Michigan State University expected their measurements to agree with those of the Climate Control Unit, and when the results disagreed, they looked for ways to alter the results. They found one way, and applied it. The book How Experiments End gives further examples of the same phenomenon occuring in experimental physics.
There's no way to avoid this expectation-driven search for errors. On the one hand, we are busy, so we won't look for errors when there don't appear to be any. On the other hand, when our results are wrong, we are inclined to check our work. But it we must not allow our expectation-driven search for errors to escalate to outright data-manipulation, which we call data massage. The following actions are data massage, and once you start doing them, your conclusions do not qualify as science.
Data massage is not the same as scientific dishonesty. It's merely one of the many mistakes we can make as we try to do the best job we can with our data. We try to identify corrupted data, but there's always a risk that our expectations will lead us to mistake good data for corrupt data, despite our best efforts to the contrary. Well, that's our experience: we claim to know a thing or two about data massage, simply because we have been guilty of it ourselves many times.
Here's a graph that strikes us as a good example of data massage. If someone presented the graph to us in a conference, we would have a few questions to ask about it. It's the hockey-stick temperature composite, made up of several different global temperature estimates. (We obtained the graph from here.)
The measurements agree with one another in the past fifty years, but disagree everywhere else. It is impossibly unlikely that five independent temperature measurements would agree to within 0.1°C in the past fifty years, but disagree as much as 0.6°C everywhere else. The measurements are not independent. They have been massaged until they agree with one another during that fifty-year period.
We can't be sure exactly how the massaging took place, but we can guess. Two groups came up with two independent temperature measurements. They disagreed. They called in a third group, and tried to figure out what was wrong. Some time later, a fourth and fifth groups joined the discussion. They were most disappointed by their disagreement over the past fifty years, because that's the period for which they had the richest data. They started to look for errors in their methods, and identify corrupted data points. They adjusted weighting factors and calibration constants in ways that made sense in the light of their shared discussions. They investigated data points that were far removed from others, and often found reasons to doubt and reject those data points. After a while, their measurements agreed well over the past fifty years, and that's when they let themselves get some rest. Their measurements still didn't agree over the long-term, but they had done all they could, as diligent scientists, to set things right.
The reason data massage is so dangerous to science is that it's hard for people who did not do the work to spot it. The way we defeat data massage is to encourage lively debate, fund contrary scientists who wish to disprove new results, and check every result we can by duplicating it in an experimental setting.
There are some weather stations that were rural when they were founded, and remain rural today. One such center is the Armagh Observatory in Northern Ireland. The record of Armagh temperatures for the last two hundred years is here. The Armagh Observatory shows no significant rise or fall in temperature over the past two hundred years.
The Hadley Center maintains an average Central England Temperature for the past three hundred years. The figure below plots the monthly and annual average central England temperature from data we obtained here.
You can judge for yourself if you think central England is significantly warmer now than it was a century ago.
Even if we had a hundred weather stations like Hadley and Armagh, we would be hard-pressed to produce a global average temperature estimate accurate to 0.1°C in the way the Climate Research Unit and the National Climate Data Center have done (see above). But we don't have anything near as good as one hundred centers. We have hundreds of disparate, short-lived, and urbanized weather stations.
By pulling ice out from the polar ice caps, we can measure the temperature of the ice caps hundreds of thousands of years ago, and the atmospheric concentration of carbon dioxide (CO2). These lumps of ice are called ice cores. The temperature measurement comes from the relative concentration of isotopes in ice crystals, and the carbon dioxide content comes from gas bubbles trapped in the ice.
As you can see, carbon dioxide concentration rises when the world is warmer.
So far as we can tell, the temperature measurement is a thousand-year average. It is insensitive to century-long fluctuations in temperature. The same is true for the carbon dioxide concentration. But the dates of the two measurements are hard to match up, because gas bubbles rise up through the ice, so that the gas measurements tends to pre-date the temperature measurement as we drill down into the ice. Nevertheless, ice core scientists have worked hard to account for these effects, and recent work suggests that changes in carbon dioxide concentration lag behind changes in temperature by a few hundred years to a few thousand years.
The concentration of carbon dioxide in the atmosphere is now at around 0.038% by volume. A few hundred years ago, it was 0.028%. According to most estimates, such as this one, carbon dioxide concentration a few billion years ago was over one hundred times higher than it is today. (Please note that the article we link to contains a typo when it says former concentrations were 10,000 time higher than today.)
Plants build their bodies out of carbon dioxide and water with the help of sunlight. A billion years ago, before the evolution of plants, carbon dioxide in the atmosphere was in equilibrium with that dissolved in the ocean and other reservoirs. The concentration of carbon dioxide in those days seems to have been of order 3%. Carbon dioxide entered the cold oceans and left the warm oceans. Cold water can hold more carbon dioxide than warm water. (Here are some calculations.) The equilibrium between the atmosphere and the ocean is complex.
Once plants evolved, they captured carbon dioxide and converted it into the hydrogen-with-carbon compounds that make up plant matter. With plants consuming carbon dioxide, the concentration of carbon dioxide in the atmosphere appears to have dropped by a factor of one hundred, to around 0.03%. We are not certain that plants are responsible for this drop in carbon dioxide concentration. We have not yet found any work that proves plants were responsible. It may be the drop in carbon dioxide concentration occurred before the evolution of plants, and is instead a feature only of the complex equilibrium between the atmosphere and the oceans.
Rotting plant matter was buried underground by movements of the earth's techtonic plates. Under pressure, the plant matter turned into coal and oil. Now we are digging the coal and oil out of the ground and burning it, which converts its hydrogen-with-carbon compounds into carbon dioxide and water. As a result of this burning, it appears that the concentration of carbon dioxide has risen to 0.04%. Once again, we cannot be certain that our burning of fossil fuels is responsible for the rise in carbon dioxide concentration. The rise could instead be a fluctuation in the equilibrium between the atmosphere and the oceans.
One thing we can say for sure about the carbon dioxide we release into the atmosphere by burning fossil fuels: it's going back where it came from.
When you burn hydrocarbons (compounds of carbon and hydrogen), you get carbon dioxide and water. When bacteria and animals digest plant and animal matter, they combine it with oxygen, which is equivalent to burning it: you get carbon dioxide and water also. Methane is the simlest hydrocarbon. Here's what happens when you combine it with oxygen.
CH4 + 2O2 --> CO2 + 2H2O
One way of looking at the carbon dioxide in the atmosphere is to think of it as one place where the element carbon exists in and around the Earth. The atmosphere is a carbon resevoire. So are the reserves of coal, oil and gas in the ground, which we can group together as fossil fuels. The bodies of all animals and plants, as well as rotting vegetation in soil, is another resevoir, which we can group together as the world's biomass. The oceans are a carbon resevoir, by virtue of the carbon dioxide dissolved in them. We downloaded the following figure here, from Woods Hole. It shows the Earth's carbon resevoirs, and gives their estimates of the rate at which carbon is moving from one to another every year. The ocean is divided into two parts, which we believe are the surface layer of the ocean and the deep layer.
You will find a more complicated graphic, with similar numbers, here, at the IPCC site. The human contributions to the carbon cycle are the burning of fossil fules and deforestation. Together these represent, according to the Wood's Hole estimates, around 8 Pg (eight pentragrams, or 8×1015g or 8×1012kg). Meanwhile we have roughly 100 Pg entering the world's biomass every year as new plants and animals grow, and another 100 Pg leaving as old plants and animals decompose. Another 100 Pg is dissolved in the ocean in some places, while 100 Pg comes out of solution in other places.
The total release of carbon into the atmosphere is around 200 Pg. The total absorption is 200 Pg. And so we have equillibrium, or near-equillibrium. The human contribution is 8 Pg, which amounts to a 4% addition to the flow into the atmosphere.
Let's try to put an upper limit on how strongly carbon dioxide contributes to the warmth of the world. The carbon dioxide concentration a billion years ago was 3%. The temperature of the Earth was roughly the same. But the sun was weaker. We're not sure by how much, but more than 10% less bright than today, and perhaps as much as 50% less bright. The sun on its own warms planets. It warms the moon. The moon gets very cold at night, and warm during the day. The earth itself is a ball of molten rock, and heat emerges from it through the crust. The Earth was itself hotter a billion years ago. All these factors make it difficult for us to put an upper limit on how strongly carbon dioxide contributes to the warmth of the world. All we can say is: there used to be a hundred times as much of it, and the world was not much warmer.
Ice cores allow us to measure carbon dioxide concentration hundreds of thousands of years ago. As we noted above, the ice-core carbon dioxide measurement is a thousand-year average. It is misleading to add to the end of an ice-core measurement our recent year-to-year carbon dioxide concentration measurements, as someone has done here. The graph suggests that there were no short-term fluctuations in carbon dioxide concentration before the modern era, but the ice-core measurement is insensitive to short-term fluctuations. Many such fluctuations could have occurred in the past.
According to ice cores, carbon dioxide concentration changes lag behind temperature changes by around a thousand years. Therefore, we must reject the claim made by many climate scientists that carbon dioxide is a potential cause of global warming. If one thing is going to cause another, it must occur first.
The troposphere is the lowest layer of the atmosphere. It is of order 10 km thick. The temperature of the troposphere drops by approximately 7°C per 1 km you ascend from the earth.
The University of Alabama at Huntsville uses satellite-based radar to estimate the temperature of the lower troposphere. Their raw data is on their website here, and on our website here. We plot four of the columns from their data in the graph below.
We invite you to look at the UAH data plotted in various other places like Wikipedia. We're not sure what data they plotted to get their graph. Our plots show no sign of warming, but their plots do.
When you transmit microwaves towards the earth from a satellite, most of the microwave energy passes through the intervening atmosphere and reflects off the earth. But some of it reflects off the intervening air, and some very small portion of that reflected energy returns to the satellite, where we can measure it. Microwaves reflected by the stratosphere return one hundred microseconds (one ten-thousandth of a second) before microwaves reflected by the troposphere, because the stratosphere is of order 30 km closer to the satellite. The radar records the amount of energy returning to the satellite as the microseconds go by. In theory, therefore, we can obtain an estimate of the amount of energy reflected by, for example, the troposphere, or even the lower parts of the troposphere, or lower troposphere.
Air reflects more microwave energy if is it more dense, and it is more dense if it is colder. The energy reflected by the troposphere could, in theory, be used to measure the temperature of the troposphere. But we must keep in mind that the troposphere temperature drops by roughly 70°C from the bottom to the top, so it's not clear how meaningful taking an average temperature of the troposphere is going to be. To make a global measurement, we repeat our troposphere measurement millions of times as our satellite orbits the earth. The temperature of the earth varies at any given time by of order 40°C from the poles to the equator, and the colder air is more dense than the warmer air, so we still have to do some thinking before we combine the millions of measurements into a meaningful measurement of average global temperature.
Nevertheless, that's what the scientists at the University of Alabama have been doing: using satellite radar to measure the average temperature of the world, and you see the results above. Many other scientists have done the same. Here is the abstract from a report by Michigan State University.
"The retrieval of the satellite radiant temperature for global climate monitoring is a complex task. It requires strong processing of the raw data, because various corrections are applied to the measurements to solve instrumental inhomogeneities. The lower troposphere signal is derived from the difference of two large quantities thus amplifying errors and noise in the record. The data represents the air temperature averaged over the lower 8 km of the troposphere. A strong debate has arisen over the years because of the discrepancies in the trend between satellite and surface temperature records. Many causes are suggested to explain the differences. Anyway, it is important to consider that the two records are only partially comparable, because the surface and the lower troposphere are two distinct physical entities. For this reason, it is believed that part of the discrepancies is real."
Despite these difficulties, the troposphere measurement appears to be stable to ±2 C from one year to the next, which makes it likely that the precision of the yearly measurements is 1°C or better. If we want to claim better precision than 1°C, we need to show that the variations we observe from one year to the next are real variations. To do that, we must compare the satellite measurements to those made by another method that we are certain of to much better than 1° C.
At Michigan State University, they compared their satellite measurements to what they believed to be more accurate land-based measurements by the Climate Research Unit, which we show above. They found that their satellite measurements and the land-based measurements disagreed. The land-based measurements showed an increasing global temperature. The satellite measurements did not. They corrected their troposphere measurements for an effect they call stratospheric cooling, knowing that such a correction would bring their measurements more in line with the land-based measurements. But the two measurements still do not agree, although the satellite measurements now showed a slight warming trend, as shown in below.
We are not baffled by the discrepancy between the satellite and land-based measurements. Our analysis suggests that the land-based results are not accurate enough to calibrate the satellite measurements. We think it likely that the two disagree because their errors don't agree.
We resolved to look at the raw measurements used by CRU and NCDC to obtain their surface temperature trends. We wrote to CRU, and promptly received this gracious reply, in which Phil Jones points us to the raw data in two places, and invites us to analyze it for ourselves.
The data from all known weather stations is stored by GHCN (Global Historical Climatology Network) here. Their ftp download side is here. We downloaded v2.mean.Z and v2.temperature.readme. We unzipped the first file and re-formatted it with the following steps. Each line in the data file contains data from one weather station for one year, as twelve monthly average temperatures, as described here. When there are several recording stations very close to one another, GHCN refers to these multiple measurements of the same location as duplicates. You will find a more detailed description of the data in An Overview of the Global Historical Climatology Network Temperature Database, which you will find here. We remind you that the distribution of these stations looks like this.
The result is our own data file, called GMA.txt, which you can download in zip file here. You can look a sample of the data here. The first number on each line is the GHCN station code. The next number is the years. The following twelve numbers are the January to December monthly average temparatures at the station.
We creating a new data file, called GYA_1.txt, containing the same lines as GMA.txt, except the monthly average temperatures are replaced by a single annual average temperature, which is the average of the twelve monthly measurements. For each year starting with 1800 and ending with 2006, we searched through GYA_1.txt for all available station measurements, counted them, and calculated their average. (We try to perform all our re-formatting in TCL/TK, but analyzing these large files, we switched to Pascal so it would run faster. You will find our Pascal code for our first analysis here.)
The graph below shows the number of stations available in each year. Our number of available stations rises to 8314 in 1967, while GHCN says the total number of distinct stations in the data set is only 7280. That's because we counted what they call duplicate stations as separate stations. In other words, if there are three weather stations within a hundred meters of one another, we count them as three separate weather stations. Our total number of stations is 13289.
The graph below shows the annual global temperature we obtained by taking the average of all available stations in each year. The graph is wrong. It does not agree with individual rural stations (see above). There is no place in the world that has warmed up by 5°C in the past 150 years. Nevertheless, the graph goes some way to explaining the 1970's theory we now call Global Cooling.
We can safely assume that the upward trend in temperature over the last two hundred years is no more than 1°C/century. The 5°C/century trend in our Annual Global Temperature is the systematic error introduced into our global average by changes in the set of weather stations. (We discussed this error above.) The above graph is a measurement of the systematic error that our method of anomalies must eliminate for us to see the global temperature trend, if there is one.
You will recall from our discussion above that we expect the annual global temperature, calculated by taking the average of a changing set of weather stations, to contain large systematic errors. If we add new stations in the tropics, for example, the new stations, with their higher than average temperatures, will raise the average of all available measurements. Climatologists use what they call anomalies to reduce these errors. To calculate their anomolies, they first make a reference map of global average temperature for a reference period during which they have a large number of weather stations available. The CRU reference period is 1961-1990, during which they have continuous measurements from over twelve thousand weather stations.
To calculate global anomalies from the data ouselves, we need a reference map. For that we need a file mapping our weather station numbers to global positions. We are confident that we can obtain such a map. In the meantime, however, we would like to try an alternative analysis suggested by Julian Hjortshoj (right after he debunked my impressive-sounding Method of Self-Referencing Anomalies).
For each year, and for each station, we subtract the previous years's annual temperature from the current year's annual temperature. If the previous year's annual temperature does not exist, we ignore the station. By this means, we obtain as many estimates of year-to-year change in global temperature. We will call these the station derivatives. Each year, we take the average of all these estimates to form the global derivative. We can plot this in a graph. It will be interesting. But then we integrate the global derivative, and in theory, we get the global temperature minus a constant. We should be able to see the global trend. Our concern will be any systematic offset in our derivatives, so that we end up integrating a small constant error from year to year, giving rise to a fake trend.
We calculate the station derivatives and the global derivative using this program. We plot the global derivative below. For a graph of the number of derivatives per year, see here
Now we integrate this curve and subtract its average value to get the global trend centered about zero. We also plot the Jones et al anomaly trend for comparison.
The two graphs are almost identical.
We claim that, given a new set of data, our method will arrive at almost exactly the same result as either the CRU or NCDC methods would if applied to the same new data. That is to say, we claim that our method of integrated derivatives is a valid proxy for the methods of CRU and NCDC.
Our method is a proxy for the CRU and NCDC methods, and our method makes not effort to compensate for the poor distribution of weather stations across the world. We conclude that the CRU and NCDC methods do nothing to compensate for the poor distribution of weather stations across the world. We can see this is the case if se take the time to examine the CRU and NCDC methods, but time is valuable, and the CRU and NCDC methods take several hours to understand in detail. Our proxy method, on the other hand, takes only five minutes to understand in detail.
In the following section, we alter the set of weather station measurements, and show how the global trend changes as a result of our alteration. We claim that the CRU and NCDC global trends would change in the same way if they were re-calculated from the same altered data.
Imagine a weather station in a field just outside metrapolitan New York City one hundred years ago. The breeze wafts gently across the field, passing through the grass, over a little stream, and through the station. Fifty years later, the second world war is over, and New York City expands. A developer buys land up to the edge of the field containing the station. The breeze wafts through the car park of a new apartment building, passing over the hot black tarmac in summer. The temperature recorded by the station rises. After another ten years, a developer buys the field containing the weather station, and the weather station is dismantled. It no longer provides measurements for our global trend.
The rise in surface temperature caused by urban development is well-known. It's called the Urban Heat Island effect. Surface temperatures in cities are of order 2°C higher than they would be in the same place if the city were absent. If a city builds up around a weather station, pressing close about it, we can expect the weather station to show a warming trend of order 2°C in the process. If the process takes twenty years, we might see a +0.1°C/yr trend. The weather station disappears at the end of the twenty years, when someone buys the land out from under it to make space for a building.
Many people have looked into the potential effect of urban heat upon the global trend, and concluded that the effect is small. Their arguments are based upon observations of stations that did not disappear from the temperature record, and which can therefore be compared to rural temperature measurements over the past fifty years. They found that urban weather stations tend to reside in parks and on coastlines, which are cooler than the city. They call these urban locations cool islands
But our concern is not with weather stations that remain in cities. Our concern is with the weather stations that disappeared from the cities. We do not know for sure that the dramatic drop in the number of weather stations over the last fifty years is entirely due to urban development around and ultimately on top of the disappearing weather stations. But we are certain that an analysis of the remaining weather stations in their cool islands does not help us estimate the effect of disappearing weather stations upon the global trend. Our suspicion is that these disappearing stations were not in permanent cool islands, but rather were overtaken by urban development.
The number of available weather stations used by NCDC and CRU in the calculation of their global trend dropped from roughly 1700 in 1960 to 400 in 1990, as shown above. To the first approximation, we lost 5% of our weather stations per year for thirty years. Let us suppose that 10% of these disappearing stations were subject to +0.1°C/yr warming for tweny years prior to their disappearance, as a result of urban heating. At any time during these thirty years, a total of 10% of our stations are experiencing 0.1°C/yr warming. Our combined trend will be affected by 0.01°C/yr. Over thirty years, this false trend would give us an apparant warming of 0.3°C, caused soley by urban heating.
We noted earlier the striking correlation between the number of weather stations used to obtain the global surface temperature and the apparant 0.6°C rise in global temperature between 1960 and 1990. Now we see a perfectly straightforward manner in which the drop in the number of weather stations could be the cause of this 0.6°C rise.
Let us test our hypothesis by removing the final twenty years of measurements from all weather stations that existed prior to 1950 but disappeared some time between 1950 and 2006. We re-calculate the global trend using our method of Integrated Derivatives, which we described above.
You will find our analysis code here. We plot the resulting trend below, and compare it to our original trend.
As you can see, the corrected trend is consistently lower than the original trend starting from about 1970. During the 36-year period from period 1970 to 2006, the slope of the original trend is 0.027°C/yr and that of the corrected trend is 0.021°C/yr. Below is a graph showing how the number of weather stations we used varied with year, compared to our original data.
Our Integrated Derivative Method produces the same results as the NCDC and CRU methods when applied to the complete set of weather station measurements. We think it likely that both NCDC and CRU would obtain the same drop of 0.006°C/yr in their own global trends if they were to exclude the same measurements we did. Over the period 1970 to 2006, this drop causes a drop in the global warming of 0.2°C from 0.97°C to 0.76°C. Looking at the graph above, it appears to us that over the fifty years of our study, we excluded an average of half the stations. The excluded half must have contained a trend of roughly 0.4°C. It might be that the remaining half of the temperature sensors also included a false trend of 0.4°C due to urban heating. Therefore, we expect a 0.4°C positive error due to urban heating in the un-corrected graph. This leaves us with a real trend of 0.5°C, or roughly half of the un-correctd trend.
Below is a graph of the average temperature on the continental United States, plotted from data we obtained directly from NASA here.
The standard deviation of the annual anomaly is 0.5°C. There is variation from year to year. This variation could be random. If it is random, we don't know what type of random distribution if follows. Is it the guassian distribution we encounter in thermal noise, the 1/f distribution we encounter in thermal drifts of semiconductor components, or the kolmogorov distribution we encounter in atmospheric turbulence?
It's not clear to us what we can learn from looking at the hottest year or the coldest year. The hottest year is 1934. The coldest year was 1917. If we were living through 1934, would we fear that 1935 was going to be even hotter? Perhaps, but it's not clear that the summer of 1934 was particularly hot. It could be that the winter was particularly mild. It could be that the summer of 1933 was very hot, followed by a very cold winter, making the annual anomaly come out close to zero.
Because 1934 is the hottest year, does that mean the world is cooling down? We don't think so. The year 1998 was almost as hot. The graph is so variable that the hottest and coldest years are of little help in figuring out a long-term trend.
If the hottest and coldest years are not much help, how about a running average? If we take the ten-year average, maybe that will help us. But we will then be faced with the hottest ten-year average and the coldest ten-year average. How will we know if these are significant? We don't have enough data to judge the significance of the ten-year average.
We conclude that we can't predict the future of the climate by looking at the graphs alone. The graphs are too random in appearance. We need some fundamental understanding of the climate, and its long-term behavior before we can predict the future. Before we can rely upon a climate model, we would have to test it for many years, to make sure that it works. It's no use just going back and finding a model that matches the data. We can always find a model that matches the data. The correct model is the one that predicts the unknown data.
As a result of our investigations, and after much thought, we propose the following climate model:
Climate Model: Next year, it is 95% likely that the global temperature anomoly will be within 1°C of its hundred-year mean.
Our climate model is simple. It fits the data very well. It predicts the climate ten years from now to within 1°C. We challange anyone to produce a more accurate climate model along with empirical proof of its accuracy. There are many climate models out there that claim to be more accurate. They claim to be able to tell whether the world will be hotter or colder fifty years from now. We see no empirical evidence to support the claims of the modellers. All we see is claims that the principles the model is built upon are sound. So far as we are concerned, sound principles are necessary for us to begin testing a model, but they are certainly not sufficient for us to trust the model.
Therefore, we claim that our climate model is the best you can find.
