The world's leaders are having a tough time figuring out how to solve global warming. This week, UN officials all but admitted it was unlikely that any new climate deal would avoid 2°C (3.6°F) of warming — the agreed-on limit.

Think you can do better? Then try playing around with this unbelievably detailed Global Calculator, a joint project from the UK government, the IEA, and others. It lets you fiddle with a whole slew of scenarios and assumptions about energy, food, transportation, and farming to see how they'd affect future emissions and global warming (based on climate modeling).

Here are 5 things I found while fiddling around with it:

1) Right now, we're on pace for 3°C or more of global warming

First I asked the calculator to model the International Energy Agency's 4DS pathway. This is very, very roughly what UN negotiators are groping toward in the ongoing climate talks. It's ambitious, but not overwhelmingly so.

In this scenario, global greenhouse-gas emissions peak sometime in the next few decades and then flatline (first column). Fossil-fuel use rises. Nuclear power roughly doubles by mid-century. Renewable energy rises even faster. And policies are put in place to bolster efficiency. All told, the world uses roughly 50 percent more energy in 2050 than it did in 2011, as countries like India keep developing.

The IEA's scenario would require a large number of new and fairly difficult policy changes to constrain emissions. And even after all that, it still puts us on track for around 3°C (5.4°F) of warming or more by the end of the century — considered a pretty drastic increase. Can we do better?

2) Small shifts in meat-eating can make a big difference

One place to look for changes is with diet.

The IEA scenario I started with assumed that, by mid-century, the average person will be eating 2,330 calories per day, including 220 calories of meat. It also assumes we'll be eating more beef — that is, about 25 percent of the world's meat will come from ruminants like cows, up from 22 percent today. Since cows produce a lot of methane, this is significant.

But what if we tweaked those assumptions? I told the calculator to assume that in 2050, the average person was only consuming 152 calories of meat per day — which is the WHO's target for a healthy diet. I also assumed that the mix of meat stayed similar to what it was today — marginally less beef, more chicken and pork.

The result? Global greenhouse-gas emissions dropped significantly. We're now on pace for around 2.5°C of global warming, give or take:

We still haven't solved the climate problem. But we're getting closer. And I wasn't even asking everyone to become a vegetarian. Just eat less beef and stick to health guidelines for meat eating.

3) Slower population growth would reduce warming a lot

I've written before about how demographers are constantly adjusting their population forecasts for the coming decade. This also makes a huge difference for climate change.

Right now, there are 7 billion people on Earth. The IEA scenario I mentioned above assumed this would rise to 9.6 billion people in 2050. That's about what the UN is currently forecasting. But what if that's wrong?

If we assume there will be fewer people by mid-century, then solving climate change becomes dramatically easier. In fact, if you stick with the IEA's (moderately ambitious) policies on clean energy and energy efficiency, throw in my assumptions about meat-eating, and then assume there will only be 8.3 billion people by 2050 (which is actually the low end of UN projections), we've almost met the target. We're now on pace for around 2.1°C of warming:

Not bad.

Of course, uncertainty can swing both ways. I also asked what would happen if we end up at the high end of the UN projections: 10.9 billion people by mid-century. Keeping all other IEA assumptions the same, the results are not good. We're back at high levels of global warming — around 3°C:

The IEA's 4DS scenario, plus assumptions about slightly less meat-eating, plus assumptions about higher population growth, put us on track for 1.3°C to 4.5°C of warming (Global Calculator)

Modern-day environmentalists don't like to talk about population very much. That's partly because some green groups have an unsavory history of flirting with eugenics and partly because policies to reduce population growth are often coercive (like China's one-child policy).

But clearly, population is a big part of the climate-change story. And some of the policies that can change the trajectory here are relatively uncontroversial. As this recent paper in Population and Development Review points out, the world's population is expected to grow much more slowly if education rates in the developing world rise (particularly among women and particularly in Africa).

4) Slight setbacks to nuclear, coal efficiency, or mass transit make tackling climate even harder

Now, I'm still making lots of assumptions in my calculations above — nuclear power will expand, coal plants will get more efficient, mass transit will improve in cities. What if this doesn't pan out? I took a look:

Nuclear: The IEA scenario I mentioned above assumed that nuclear power would double by mid-century. Maybe you think that's unrealistic, given that nuclear power is currently declining worldwide. So I asked what would happen if nuclear power stayed flat. Global temperatures increased by about 0.2°C at century's end. Not catastrophic, but not good.

Coal efficiency: My IEA scenario assumes that 50 percent of the world's coal-power stations will be highly efficient by mid-century, using ultra- or super-critical technology. When I lowered that to just 45 percent, I also got a 0.2°C increase in temperature. Slight improvements in coal plant efficiency make nearly as big a difference as doubling nuclear power.

Car travel: The IEA also assumes that 43 percent of all travel in cities will be done by car in mid-century. That would require a pretty ambitious scaling up of public transit. By contrast, if you assume that car travel makes up 65 percent of trips, you get another 0.2°C of temperature increase.

5) Many climate plans rely on debatable assumptions

Fiddling with these assumptions lets you test out different scenarios for tackling global warming. And one thing that becomes clear is how heroic certain assumptions are in various plans.

For instance: Here's Shell's plan for keeping global warming to a bit above 2°C by the end of the century:

As the calculator reveals, this scenario assumes that carbon capture and storage (CCS) for power plants works and becomes incredibly widespread by mid-century (reaching 3,700 gigawatts of capacity by mid-century, up from very little today). It also assumes that nuclear power will triple worldwide. Are these assumptions realistic? Who can say for sure, but you can see what happens if these assumptions happen to falter. Suddenly, tackling global warming gets much, much tougher.

Further reading

-- The folks behind the calculator wrote a longer report about insights they gleaned from creating it.

-- Read David Roberts' post: "We can solve climate change, but it won't be cheap or easy." It has more about the assumptions embedded in many of these climate scenarios.

-- Thanks to Brian Kahn of Climate Central for the pointer to the Global Calculator. He's got some more commentary here.