Better Climate Models and Weather Forecasts End, but Climate Forecasts Continue

The energy from the sun that reaches the top of Earth’s atmosphere is sometimes labeled S, in units such as Watts per square meter (W/m²⁾, and is approximately S=1370 W/m². Most of the energy leaving the sun misses the Earth and goes streaming off into space, but we intercept a little of it. This total energy reaching the whole Earth is just the Earth’s cross-sectional area multiplied by S, or $\pi r^{2}S$, where r is the radius of the Earth.

But, because the Earth is a sphere rotating under the Sun, this energy must be spread around the whole surface area of the planet, including the side facing away from the Sun, with a total area of $4\pi r^2$. Hence, the energy available per square meter of Earth’s surface is $\pi r^{2}S/4\pi r^2=S/4$.

However, recall that some of this energy is reflected back to space without warming the planet. We call the reflected part the albedo, and for the whole Earth it is roughly 30%, or A=0.3. The absorbed energy is 1-A=0.7. The average energy going to warm the planet is then S(1-A)/4.

The Earth radiates energy back to space, and this can be approximated by “black-body” physics. In this approximation, the outgoing radiation increases with the fourth power of the absolute temperature T (which is how many degrees you are above absolute zero), so outgoing radiation is $\sigma T^4$, where the constant σ, which is often called the Stefan-Boltzmann constant, has a particular numerical value = $5.67\ast {10}^{-8}W/m^2/K^4$ (that is, 5.67 times 10 to the negative eighth power), with temperature in Kelvins (K).(Some people like to write “degrees Kelvin” or “^oK”, and the same for “degrees Fahrenheit or ^oF” or “degrees Celsius or ^oC”, but it is OK to just use K, F or C.)

Incoming and outgoing energy come into balance, so we have the equation $S(1-A)/4=\sigma T^4$. You can substitute the numbers given just above for S, A, and σ, and then calculate T, the average surface temperature of the Earth. This will give you about 255 K, or -18 C or 0 F, which is well below freezing; the actual average surface temperature is close to 288 K, or 15 C, or 59 F. Our very simple model omitted the greenhouse effect, which keeps the Earth’s average surface temperature above freezing.

Because radiation increases as the fourth power of absolute temperature, the climate is very strongly stabilized. A 1% increase in average temperature causes approximately a 4% increase in radiated power, which means that even a relatively large change in the brightness of the sun, or in other factors affecting the climate, will have a moderately small effect on the temperature. Without this strongly stabilizing effect giving us the climate we have, we might not even be here!

Better Climate Models

Climate models may be the part of the science that most people know the least about. Be very clear-scientists do not tell their computers to produce global warming, and then get excited when global warming comes out of the computer!

The simplest climate model we just discussed shows you a tiny bit of what goes into a real climate model. The starting point is physics. This includes the rules that mass and energy are not created or destroyed but just changed around. The physics also includes interactions between mass and energy-how much energy is needed to evaporate an inch of water per week, for example, or to warm the atmosphere by a degree. Interactions of radiation and greenhouse gases are specified from the fundamental physics worked out by the US Air Force after World War II, and other such studies.

The model also must “know” about the Earth-how much sunshine we get, how big the planet is and how fast it rotates, where the land and oceans are, how much air we have and what it is made of. (Climate models are applied to other planets, and very clearly give different answers because of the differences between the planets.)

All of this information is written down in equations, translated into computer language, and then the computer is turned on. What happens next is remarkable-the computer simulates a climate that looks like the real one. Air rises and rains in the tropics, then sinks and dries over the Sahara and Kalahari. Storms scream out of the west riding the jet stream, and snow grows and shrinks with the seasons across the high-latitude lands.

The model will not be perfect, of course. Suppose you are interested in wind speed. You know from personal experience that you can hide behind a windbreak for relief on a windy day. A forest can serve as a windbreak, giving weaker winds than on a prairie. So, the model must be “told” about the distribution of forests and grasslands (or else must calculate where they grow), and about the “roughness” of the forest and the grass. Scientists have conducted studies on the effects of forests and grasslands on winds, but all studies include some uncertainty. So, the modelers know that the surface roughness in this region must be about this much, but could be a little less or a little more within the range allowed by the data.

The modeler (or more typically, the modeling team) can now “tune” the model. If the winds in the model are a little stronger in some places than in the real world, the modeler may increase the roughness a little, although without going outside the uncertainties. To avoid any biases, different groups in different countries with different funding sources build different models, and tune them in different ways; when all of them agree closely, it is evident that the tuning hasn’t controlled the answer.

Some of the models are used for weather forecasting and for climate studies, and work fine for both. There are differences between weather and climate (see Weather Forecasts End, But Climate Forecasts Continue) - many climate models are simulating changes in vegetation, for example, but if you’re worried about the weather for next week, you don’t really care whether global warming endangers the Amazonian rainforest over the coming decades.

As a general rule, in talking to the public or policymakers, climate modelers rely especially on those results that:

• are exhibited by a range of models from simple to complex run by different scientific groups;
• are understood based on the physics;
• are observed in the history of climate; and
• are confirmed by recent instrumental observations.

Weather Forecasts End, But Climate Forecasts Continue

No one has succeeded in forecasting the weather more than a week or two into the future, and we’re confident that such forecasts are impossible because of “chaos”. But, this difficulty does not interfere with the ability to project climate changes much, much further into the future.

For weather forecasting, you need to start with the current state of the atmosphere. If there is a cold front sweeping eastward across North Dakota in the US, areas just to the east in Minnesota are likely to experience the effects of that cold front soon. However, if the cold front has already passed across Minnesota, a different forecast will be more accurate.

This difficulty arises from the fact that no one can ever perfectly know the current state of the atmosphere everywhere (nor can we calculate perfectly, but let’s focus on the data here). If you give a good forecasting model the best available data, the model will produce a forecast that is demonstrably skillful for the next week or two, but the further you look into the future, the lower the skill, until the model is not able to predict the details of the weather. The model still produces “reasonable” forecasts—for summer in North Dakota, it will produce summertime conditions, not wintertime ones—but there is no skill for forecasting whether a cold front is coming in 26 days, or 27.

Suppose you now take your best data, and “tweak” them within the known uncertainties in the original measurements and the interpolations between the measurement stations. If the temperature in Fargo at noon on June 23, 2012 was 87.1 F, you don’t really know whether that was 87.100 or 87.102 or 87.009, nor do you know the exact temperature in all of the suburbs of Fargo that lack thermometers. So, take the 87.1 and try replacing it with the possible value 87.102, fully consistent with the available data. Make similar tweaks to other stations. Then, run the model again. What happens?

For the first few days, the forecast is almost unaffected. But, as you look further into the future, the forecast becomes more and more different from the original one. If you do this again, with different tweaks to the data (say, 87.009 rather than 87.100), you again will get almost the same forecast for a few days, but further out the forecast will differ from both of the prior ones. Do this a lot of times, and the odds are good that one of the runs will end up being close to what happens in the future, and that the average of the runs will be similar to the average behavior of the weather over a few decades (unless climate is changing rapidly!). But, you won’t know which individual run is the right one. This “sensitivity to initial conditions” is often called “chaos” in public discussions, and it means that weather forecasts can’t be accurate too far into the future. In the same way, you cannot predict the outcome of the roll of dice in a game until the dice have almost stopped moving.

Note that you can predict the average outcome of many rolls of dice, and you can predict the average behavior of weather over many years, which is climate. You may have met someone who argued that failure of a weather forecast casts doubt on climate-change projections, but that is like using one roll of dice to argue that if you keep gambling you’ll beat the casino. People who make that mistake at casinos are usually known as “poor” or “broke”.

Video: Chaos and Phil the Groundhog (PSUrockvideo) (3:50)

Carbon Dioxide is more Important than Water Vapor as a Greenhouse Gas

This may seem strange. If you track what happens to the radiation leaving the Earth's surface, some is absorbed on the way, and some goes straight out to space. Water vapor, carbon dioxide, and clouds dominate the absorption, with all the others (methane, ozone, chlorofluorocarbons, nitrous oxide, etc.) also enough to be important if taken together. (Clouds also have a slightly more important role in blocking the sun, with the net effect of clouds being slight cooling under modern conditions.) Because some radiation is blocked almost entirely by only one gas type, but other wavelengths may interact with both water vapor and carbon dioxide, there is a bit of uncertainty in the bookkeeping of the exact importance of a single type of greenhouse gas. Overall, though, it is fairly accurate to say that water vapor supplies close to half of the total greenhouse effect, clouds and carbon dioxide each a little under a quarter, and all others just under a tenth.

But, the amount of water vapor in the air is equal to the amount of rain that falls on the Earth in just over a week. As water vapor rains out very rapidly, it is replaced by evaporation of more water. Any extra water vapor we put in the air from burning of fossil fuels or irrigating crops just doesn't stay up there very long. And, because the natural source of water vapor is so huge (evaporation from a giant ocean and a lot of plants that together cover almost the entire Earth), the human source is actually tiny in comparison. The only practical way we know of to greatly change water vapor in the air is to change the temperature. A hair dryer has a heater for good reasons, and warming the air will allow it to pick up and carry along more water vapor, whether the warming is caused by carbon dioxide, or a brighter sun, or some sort of heat ray from space aliens, or anything else.

Some research has looked at what would happen if carbon dioxide were removed from the atmosphere. Loss of the carbon dioxide cools the planet, but that condenses some of the water vapor, which cools the planet more, and the Earth turns into an ice-covered snowball. If water vapor is removed, a lot more evaporates quickly before the Earth can freeze.

So, yes, water vapor is blocking more energy than carbon dioxide today. But, carbon dioxide is much more important for changing the climate than is water vapor. Carbon dioxide can be a forcing—add it to the air, and you force the climate to change. Carbon dioxide also can be a feedback—change something else (such as reducing oxygen in the ocean to allow more fossil-fuel formation), and that changes carbon dioxide in the air, which in turn changes the temperature. But, water vapor is almost entirely a feedback because there aren't any natural or human processes other than changing the temperature that can put water vapor up fast enough to make a big difference to climate.

Humans are primarily responsible for the rise in CO2

Bookkeeping by itself shows that humans are responsible. We produce roughly 100 times more CO₂ than volcanoes do (maybe only 50 times, maybe closer to 200 times, if you include the uncertainties, but something like 100). Nature was producing its CO₂ for a long time, but humans have increased from being a very small source to being much more important than volcanoes.

Furthermore, several tracers in the atmosphere confirm the bookkeeping. These include:

• Dropping oxygen. The level of oxygen in the air is dropping as CO₂ rises. You'll still be able to breathe with no trouble, but this shows that the rise in CO₂ is caused by fire, which uses oxygen, and not by melting beneath a volcano or CO₂coming out of the ocean, which don't use oxygen.
• Falling carbon-13. Plants preferentially use CO₂ containing the lighter and faster-diffusing carbon-12 rather than the heavier carbon-13, so CO₂ formed by burning living plants or fossil fuels is more enriched in carbon-12 than is CO₂emitted by volcanoes or coming from chemicals dissolved in the ocean. The CO₂ in the air is becoming more enriched in carbon-12 and less enriched in carbon-13, which shows that the extra CO₂ comes from living or dead plants.
• Falling carbon-14. Carbon-14 is made in the atmosphere by cosmic rays, then taken quickly into living plants, but decays radioactively over about 50,000 years. (Half of the carbon-14 decays in just about 5730 years, half of the remainder in the next 5730 years, and by 50,000 years or so almost none remains.) Thus, living plants contain carbon-14, but fossil fuels don't. Carbon-14 is becoming less common in the atmospheric CO₂, much more rapidly than can be explained by radioactive decay, showing that the extra CO₂ in the air is coming from plants that have been dead a long time.

Taken together, bookkeeping says that the rise in atmospheric CO₂ is coming from human burning of fossil fuels. And, the atmosphere says that the rise in CO₂ is coming from burning of plants that have been dead a long time. The agreement is beautiful, confirming that we are responsible for what is occurring.

There is a bit more complexity to this, linked to our burning of forests, but also letting some forests grow back and fertilizing others, and linked to us releasing some CO₂ while making cement. But overall, the biggest source of CO₂ is our fossil fuels, and this will become more and more important in the future if we continue on our present path.

Global Warming Did Not Stop Recently

The main text presented some of the evidence that temperature is rising. But, the climate is influenced by the 11-year sunspot cycle, the occasional sun-blocking influence of particles from big volcanic eruptions, and also by the sloshing of water in the tropical Pacific Ocean associated with El Nino and La Nina-when the hot waters spread along the equator in an El Nino event, some heat moves from the ocean to the air, and when the cold waters of La Nina follow, heat flows back into the ocean. An extra El Nino, or an extra-strong one, in a decade can make global warming look very fast, whereas an extra La Nina can temporarily slow the upward march of temperature from the rising CO₂. This sort of sloshing cannot ultimately change the warming of the planet, but can make it appear more variable, and control whether the air warms fast and the ocean much slower, or whether faster warming of the ocean slows the atmospheric warming a bit.

Think for a minute about a neighbor taking a very active dog for a walk. Watch the person, and you can see steady progress down the street. Watch the dog, and you may have to study carefully for a while to even know which way they are going. You may find it useful to think of the year-to-year temperature changes as the dog, and the average behavior as the person.

Animated gif demonstrating trends.

Click for a text description of Global mean temp Celsius vs year graph.

This animated GIF displays a graph of global mean temperature (°C) over time from 1960 to 2010, with temperature fluctuations shown in red. The x-axis represents the years, while the y-axis represents global mean temperature in degrees Celsius, ranging from 14°C to 15.5°C.

Frame 1 (Early 1960s to 1970s)

• The graph initially shows data only from the 1960s to late 1970s.
• The red temperature line fluctuates, but appears to decline slightly.
• A black trend line slopes downward, suggesting cooling.
• Text displayed: "Dr. Alley was born in 1957, at the start of cooling?"

Frame 2 (Extending into the 1980s)

• The graph expands, now including temperature data up to the early 1980s.
• The red line still fluctuates, but some warmer years start appearing.
• The black trend line slightly flattens, though cooling is still implied.
• Text changes to: "Oh wait... we forgot some data."

Frame 3 (More 1980s Data Appears)

• Additional data from the mid-to-late 1980s appears.
• The red temperature line rises more visibly.
• The black trend line flattens further, reducing the cooling trend.
• Text now reads: "Oops... forgot some more data."

Frame 4 (1990s Data Added)

• The timeline now extends through the 1990s<.
• The red temperature line shows a noticeable warming trend.
• The black trend line is nearly flat.
• Text changes again to: "Hmmm... looks like it's getting warmer."

Frame 5 (Early 2000s Data Appears)

• Data from the early 2000s appears, reinforcing warming.
• The red temperature line climbs further, surpassing earlier fluctuations.
• The black trend line now slopes slightly upward.
• Text now reads: "Maybe the cooling was just a fluke?"

Frame 6 (Late 2000s Data Added)

• The graph extends into the late 2000s.
• The red temperature line is now clearly trending upward, confirming warming.
• The black trend line now visibly slopes upward.
• Text changes to: "Yeah, definitely a fluke."

Frame 7 (Final Frame - Full Data to 2010)

• The graph completes the dataset, extending into 2010.
• The red temperature line reaches its highest points, solidifying the warming trend.
• The black trend line fully reverses, now clearly showing long-term warming.
• Final text displayed: "Never mind!

Credit: Richard B. Alley @ Penn State is licensed by CC-BY-NC-4.0

Next, take a look at the figures, which highlight events from Dr. Alley’s career. In each case, the jagged red line connects the temperatures from year to year, using data from NASA’s Goddard Institute for Space Studies, and the smoother black line is the best fit to the data over the interval selected. You will see that in each case, Dr. Alley has carefully picked the end points so that the best-fit line slopes downward, indicating a cooling trend. For the last 20 years, Dr. Alley has met important people in Washington, DC who declared that global warming stopped. It is very easy to do so; be quiet during a year with strong warming, and then the next year go back to claiming that global warming stopped.

Over a century ago, the Guinness brewery in Ireland hired an Oxford mathematician, W.S. Gosset, to develop ways to separate actual trends from short-term variability. The techniques were published with a pseudonym (A. Student), presumably to help people without telling competitors how valuable it was for a business to avoid self-delusion. If you apply techniques derived from that research, global warming has not stopped; all time intervals long enough to show a statistically significant trend do show warming.

By 2016, the temperature had risen enough that it barely fit in the chart above, aided by the ongoing human warming and by a strong El Nino event. This strong El Nino was warmer than the previous one, which was warmer than earlier ones, mostly because of human CO2. But, temperature was dropping a bit in late 2016 as the El Nino faded. And, some inaccurate voices were already, again, declaring that global warming had stopped.

Some Better Climate Models

Climate models may be the part of the science that most people know the least about. Be very clear — scientists do not tell their computers to produce global warming, and then get excited when global warming comes out of the computer!

The simplest climate model we just discussed shows you a tiny bit of what goes into a real climate model. The starting point is physics. This includes the rules that mass and energy are not created or destroyed, but just changed around. The physics also includes interactions between mass and energy — how much energy is needed to evaporate an inch of water per week, for example, or to warm the atmosphere by a degree. Interactions of radiation and greenhouse gases are specified from the fundamental physics worked out by the US Air Force after World War II, and other such studies.

The model also must “know” about the Earth-how much sunshine we get, how big the planet is and how fast it rotates, where the land and oceans are, how much air we have and what it is made of. (Climate models are applied to other planets, and very clearly give different answers because of the differences between the planets.)

All of this information is written down in equations, translated into computer language, and then the computer is turned on. What happens next is remarkable — the computer simulates a climate that looks like the real one. Air rises and rains in the tropics, then sinks and dries over the Sahara and Kalahari. Storms scream out of the west riding the jet stream, and snow grows and shrinks with the seasons across the high-latitude lands.

The model will not be perfect, of course. Suppose you are interested in wind speed. You know from personal experience that you can hide behind a windbreak for relief on a windy day. A forest can serve as a windbreak, giving weaker winds than on a prairie. So, the model must be “told” about the distribution of forests and grasslands (or else must calculate where they grow), and about the “roughness” of the forest and the grass. Scientists have conducted studies on the effects of forests and grasslands on winds, but all studies include some uncertainty. So, the modelers know that the surface roughness in this region must be about this much, but could be a little less or a little more within the range allowed by the data.

The modeler (or more typically, the modeling team) can now “tune” the model. If the winds in the model are a little stronger in some places than in the real world, the modeler may increase the roughness a little, although without going outside the uncertainties. To avoid any biases, different groups in different countries with different funding sources build different models, and tune them in different ways; when all of them agree closely, it is evident that the tuning hasn’t controlled the answer.

Some of the models are used for weather forecasting and for climate studies, and work fine for both. There are differences between weather and climate (see Weather Forecasts End, But Climate Forecasts Continue) - many climate models are simulating changes in vegetation, for example, but if you’re worried about the weather for next week, you don’t really care whether global warming endangers the Amazonian rainforest over the coming decades.

As a general rule, in talking to the public or policymakers, climate modelers rely especially on those results that:

• are exhibited by a range of models from simple to complex run by different scientific groups;
• are understood based on the physics;
• are observed in the history of climate; and
• are confirmed by recent instrumental observations.