## 22.2.14

### IT TAKES A THEORY TO BEAT A THEORY.

The Old Farmers Almanac missed the DeKalb winter.
Winter will be slightly milder than normal, with near-normal precipitation and below-normal snowfall in most of the region. The coldest periods will be in mid- to late December, early and mid-January, and in early to mid-February. The snowiest periods will be in mid- and late December and in late January.
No.

The Climate Prediction Center missed it too.
“Not one of our better forecasts,” admits Mike Halpert, the Climate Prediction Center’s acting director. The center grades itself on what it calls the Heidke skill score, which ranges from 100 (perfection) to -50 (monkeys throwing darts would have done better). October’s forecast for the three-month period of November through January came in at -22. Truth be told, the September prediction for October-December was slightly worse, at -23. The main cause in both cases was the same: Underestimating the mammoth December cold wave, which brought snow to Dallas and chilled partiers in Times Square on New Year’s Eve.
The problem: three months is too long an interval for a weather forecast, but too short an interval for a climate forecast.
The limit on useful weather forecasts seems to be about one week. There are inaccuracies and missing information in the inputs, and the models are only approximations of the real physical processes. Hence, the whole process is error prone. At first these errors tend to be localized, which means the forecast for the short term (a few days) might be wrong in places, but is good enough in most of the region we’re interested in to be useful. But the longer we run the simulation for, the more these errors multiply, until they dominate the computation. At this point, running the simulation for longer is useless. 1-day forecasts are much more accurate than 3-day forecasts, which are better than 5-day forecasts, and beyond that it’s not much better than guessing.
Put simply:

wt = f(wt-1) + e,

where wt is the weather at observation t, f is the forecasting function, and e is the error, which may suffer from all the statistical contaminants.

Climate forecasts, on the other hand, are all about calibration of the model.
Climate science has the opposite problem. Using pretty much the same model as for numerical weather prediction, climate scientists will run the model for years, decades or even centuries of simulation time. After the first few days of simulation, the similarity to any actual weather conditions disappears. But over the long term, day-to-day and season-to-season variability in the weather is constrained by the overall climate. We sometimes describe climate as “average weather over a long period”, but in reality it is the other way round – the climate constrains what kinds of weather we get.

For understanding climate, we no longer need to worry about the initial values, we have to worry about the boundary values. These are the conditions that constraint the climate over the long term: the amount of energy received from the sun, the amount of energy radiated back into space from the earth, the amount of energy absorbed or emitted from oceans and land surfaces, and so on. If we get these boundary conditions right, we can simulate the earth’s climate for centuries, no matter what the initial conditions are. The weather itself is a chaotic system, but it operates within boundaries that keep the long term averages stable. Of course, a particularly weird choice of initial conditions will make the model behave strangely for a while, at the start of a simulation. But if the boundary conditions are right, eventually the simulation will settle down into a stable climate.
The researchers have ample opportunities to design boundary conditions and stability ranges consistent with their priors.
To handle this potential for initial instability, climate modellers create “spin-up” runs: pick some starting state, run the model for say 30 years of simulation, until it has settled down to a stable climate, and then use the state at the end of the spin-up run as the starting point for science experiments. In other words, the starting state for a climate model doesn’t have to match real weather conditions at all; it just has to be a plausible state within the bounds of the particular climate conditions we’re simulating.

To explore the role of these boundary values on climate, we need to know whether a particular combination of boundary conditions keep the climate stable, or tend to change it. Conditions that tend to change it are known as forcings. But the impact of these forcings can be complicated to assess because of feedbacks. Feedbacks are responses to the forcings that then tend to amplify or diminish the change. For example, increasing the input of solar energy to the earth would be a forcing. If this then led to more evaporation from the oceans, causing increased cloud cover, this could be a feedback, because clouds have a number of effects: they reflect more sunlight back into space (because they are whiter than the land and ocean surfaces they cover) and they trap more of the surface heat (because water vapour is a strong greenhouse gas). The first of these is a negative feedback (it reduces the surface warming from increased solar input) and the second is a positive feedback (it increases the surface warming by trapping heat). To determine the overall effect, we need to set the boundary conditions to match what we know from observational data (e.g. from detailed measurements of solar input, measurements of greenhouse gases, etc). Then we run the model and see what happens.

Observational data is again important, but this time for making sure we get the boundary values right, rather than the initial values. Which means we need different kinds of data too – in particular, longer term trends rather than instantaneous snapshots. But this time, errors in the data are dwarfed by errors in the model. If the algorithms are off even by a tiny amount, the simulation will drift over a long climate run, and it stops resembling the earth’s actual climate. For example, a tiny error in calculating where the mass of air leaving one grid square goes could mean we lose a tiny bit of mass on each time step.
There's still room, though, for further research.
The models also fail to get details of the past climate right. For example, most of the observed warming over land in the past century occurred at night. The same models used to predict future warming models showed day and night warming over the last century at nearly the same rates.

Past models also missed the dramatic recent warming found in observations in the Arctic. With this information as hindsight, the latest, adjusted set of climate models did manage to show more warming in the Arctic. But the tweaking resulted in too-warm predictions—disproved by real-world evidence—for the rest of the planet compared with earlier models.

Shouldn't modelers be more humble and open to saying that perhaps the Arctic warming is due to something we don't understand?
And, perhaps, these commenters suggest, to understand the value of specialization and division of labor.
The climate-change consensus is not endangering lives, but the way it imperils economic growth and warps government policy making has made the future considerably bleaker. The recent Obama administration announcement that it would not provide aid for fossil-fuel energy in developing countries, thereby consigning millions of people to energy poverty, is all too reminiscent of the Sick and Health Board denying fresh fruit to dying British sailors.

We should not have a climate-science research program that searches only for ways to confirm prevailing theories, and we should not honor government leaders, such as Secretary Kerry, who attack others for their inconvenient, fact-based views.
Indeed. Economists recognize, every day, the risk of engaging in mathematical politics, to endorse or to undermine established ways of doing things. Policy scientists in other disciplines require the same consciousness of those risks.