## Weather versus climate

If you don't like the springtime weather in Chicago, just wait a few days. It's a gray 5°C out there now, but the forecast for the weekend puts it up to 15°C, which is a little more like spring. The 10-day forecast says showers the weekend after that, but no one believes the end of a 10-day forecast anyway. They're better than they used to be, but 10 days is still something of a crap shoot. And here I am sitting down to write about forecasting the climate 100 years from now. I suppose some would feel that an explanation might be in order.

It is indeed tricky to forecast the weather too far in advance because weather is chaotic. To a scientist, the word chaotic brings to mind an extreme sensitivity to initial conditions, so that small differences between two states tend to amplify, and the states diverge from each other. This behavior is called the butterfly effect, the reference being to a puff of air from a butterfly's wing eventually resulting in a giant storm somewhere that wouldn't have happened if the butterfly had never existed. The butterfly effect was first observed in a weather simulation model. The model computer run stopped, and the researcher Edward Lorenz restarted it by typing in the values of model variables like temperatures and wind speeds, but with a small seemingly insignificant change of initial conditions. It didn't take long for the restarted simulation to diverge from the results of the initial simulation. The weather is forecast by constructing an initial condition from meteorological data and past model results, and running this initial condition forward into time using a model. The initial condition will never be perfect, and these imperfections tend to blow up, so that by about 10 days the prediction becomes meaningless. One way to cope with this situation is to run the model lots of times with tiny variations in initial conditions; an ensemble of model runs. Then you can see something of the range of what's possible in the forecast. It doesn't fix the problem exactly but it does result in a more reliable forecast.

The climate is defined as the time average of the weather. One could speak of a clima-tological January, which would be the average of many Januaries, let's say 10 Januaries. Forecasting climate is not as difficult as forecasting weather because it doesn't matter whether the rain you predict comes on a Tuesday or a Thursday. The butterfly can't foil our climate prediction with her storm, if the model gets the large-scale tendency for storminess right. If the model doesn't follow a storm trajectory this time, it will the next time; the butterflies average out. You would also like your climate model to get the frequency of the most extreme events, etc., what climatologists would call getting the statistics right. Even the decade and longer timescale "climate" output from models is sensitive to initial conditions, however, and so the ensemble technique is used

— Sunlight Infrared Total

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Hour in day

Fig. 6.2 The surface of the Earth only receives incoming solar radiation during the daytime (heavy solid line), but it radiates IR light all the time (thin solid line). The energy budget for this location (dashed line) is only in balance when it is averaged over 24 h.

Fig. 6.3 The Earth's tilt is responsible for the seasons. This is southern hemisphere summer, northern hemisphere winter.

for climate forecasting, predictions to 2100, for example, just as they do for weather forecasting.

The heat-input forcing to the real world does not sit unchanged at the eternal average value, but rather bounces around pretty wildly. On the day-night cycle, for example, the night-time side of the Earth receives no solar input at all, while infrared (IR) energy loss to space continues around the clock (Fig. 6.2).

The heat input varies over the seasonal cycle as well. The seasons are caused by the tilt of the Earth's axis of rotation (Fig. 6.3). The issue is not the intensity of the incoming sunlight at the top of the atmosphere, Isolar, because the size of the Earth is negligible compared with the distance from the Sun. The Earth's orbit is elliptical, rather than circular, with the Earth closer to the Sun in southern hemisphere summer. However, if the distance from the Sun caused the seasons, the whole world would get cold and warm at the same time. The fact that the seasons are opposite each other in the two hemispheres proves that it is the tilt of the Earth, not the distance from the Sun, that causes the seasons.

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Daily average sunlight energy flux (W/m2)

Daily average sunlight energy flux (W/m2)

Fig. 6.4 The Earth's tilt determines how much heat the surface receives from the Sun each day, as a function of latitude (vertical axis) and time of year (horizontal axis).

The summertime hemisphere, the south in Fig. 6.3, gets more than its share of the solar energy, and the winter hemisphere gets less. Figure 6.4 shows a sort of map of the intensity of solar heating as a function of latitude and day of the year. The contours show us the intensity of sunlight for every square meter on the ground averaged over 24 h. Because the Earth completes one rotation in 24 h, any location on some line of latitude, say 42°N which goes through Chicago, will get the same solar influx as any other at that same latitude, like Barcelona or Vladivostok. A map of solar influx in regular latitude and longitude would look like a bunch of horizontal stripes. Therefore, we are showing two "dimensions" over which the solar influx does vary; latitude and day of the year.

The beginning of the year is southern hemisphere summer, and we see high heat fluxes in the south and low fluxes in north. Northern hemisphere summer is the middle of the year, centered around day 180. The pattern arises by two mechanisms. First, the intensity of sunlight per square meter of ground area is greater at noon in the summer than in the winter because the ground is at less of an angle to the Sun in the summer (recall Fig. 6.3). Second, days are longer in summer, and this increases the 24-h average energy influx.

It is interesting to note that the highest daily-average energy fluxes you find anywhere are at the north or south pole during north or south summer. The Sun never sets in midsummer at the poles, it just whirls around in a circle over the horizon. In winter the poles gets no sunlight for months on end. The poles do not turn into tropical garden spots in summer because it takes time for temperatures to respond to changes in heat forcing. This thermal inertia tends to damp out the temperature swings of the day-night cycle, the seasonal cycle, and any global warming temperature trends

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 Net incoming solar Outgoing IR Heat transport by winds and currents

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Fig. 6.5 The energy budget between incoming solar and outgoing IR radiation does not balance locally because heat is transported on Earth by winds and currents. The equator receives more solar energy than it radiates as IR, while high latitudes lose more IR than they receive from sunlight.

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as well. The liquid ocean, it turns out, has much greater temperature stabilizing power than land or ice does because water mixes bringing a much greater mass of water into thermal exchange with the atmosphere than land can bring. Cooling of surface waters drives convection, in the same way that warming of surface air brings convection in the atmosphere. The seasonal cycle of temperatures in soils reach only a few feet down, while the temperatures farther down, in caves for example, reflect the yearly average, about 10°C in my part of the world. The seasonal cycle of temperature changes at the ocean reaches a 100 m down and more. For this reason, the seasonal cycle is much more intense in the middle of large continents than it is in "maritime" areas impacted by the temperature stabilizing effects of liquid water.

Even if we average out the seasonal cycle, the energy budget of a local region of the Earth maybe far from being in balance because heat energy is redistributed around the Earth's surface by wind and water currents (Fig. 6.5). There is a net influx of heat in the tropics; sunlight brings in energy faster than it is radiated back to space. Heat is carried poleward by flow in the atmosphere and the ocean. In high latitudes, the Earth vents the excess tropical heat as excess radiative heat loss to space over direct solar heating.