Introduction
Amidst the record-breaking wildfires being experienced in Europe over summer 2026, many people believe the solution is to reduce the number of causes - and in fact attach agency, such as arson, to those causes in preference to the scientific explanation, global warming.
The Climate Science argument is that the critical issue is global warming itself, because it supercharges wildfires: heatwaves get more common and intense. Then land gets drier and therefore easier to combust. Once a fire starts, conditions make fires burn harder, faster and hotter.
This article explores one major reason why this property is the critical one, over and above that of the number of fires - and it's due to some fairly simple maths. People who can understand and communicate the maths, will have an advantage over climate science deniers who will repeatedly pick the wrong solution.
The Problem
The problem occurs because there is essentially a finite amount of resources we can apply to extinguishing (denoted by 'x' here) wildfires. As the speed of a wildfire front (denoted by 'f' here) increases, it has a disproportionate impact on the rate of progress (denoted by 'p' here) at which fires can be put out.
We can understand some of this intuitively. x can be measured as a speed: the rate at which we can put a fire out given reasonable resources, in m/s. Similarly, f represents the speed of the front of a wildfire, also measured in m/s. Thus if f = 0, i.e. the fire is not moving (but is still burning), then we know that as long as x is greater than 0, we can put the fire out. And the general rule here is that f≥x means the fire can never be put out. If the fire already has an extent, then for every metre of fire we put out, the fire has advanced by over 1m. So, this establishes hard limits.
Early Stages
The early stages of a fire is a front that would tend to expand outwards in a circle from its source at a constant rate. In this model we'll ignore wind speed and wind direction, in order to simplify the maths.
One thing we can observe is this: the initial part of the fire will be slower than when the fire is more mature. And this is because when the fire starts, there's a substantial curvature at the front and this means that the heat distribution at any one point at the front has to set light to a wider span ahead of it, that is: the fire is fanning out. But because it's setting light to a wider span ahead it means that there's less heat being applied to any point ahead of the front, because it has to be distributed to the span ahead.
This means that the fire will initially travel slower and is therefore easier to extinguish. It's possibly also why in the early stages of a wildfire, people believe they can stop the fire relatively easily - because it's slower and the temperature curve ahead of the front is less intense. And this is partly true, it will be easier to stop.
That's why we ignore this in our model.
Maturity
When the fire is mature, the front is essentially a straight line. Obviously terrain will affect this, but this will be a reasonable approximation. The fire is hotter now and is travelling faster, because there is no fan-out.
So, as the front advances by f metres, the amount extinguished will be along the hypotenuse of a right-angled triangle (because the fire-fighters want to move along the fire, but also outward as it advances). The amount of progress must be p.
Thus we can see that p=√(x²-f²), by a simple application of Pythagoras' theorem. So, the key question is this: as f approaches x, what's the ratio of x:p, the amount we extinguish, vs the amount of progress? So, if we normalise it, by making x=1, we get p=√(1-f²) and so we want to know 1/√(1-f²) .
Results
The results are actually quite shocking. At low rates of f, e.g. f=0.1, x/p is also very small (in this case 1.005). But as f gets increasingly close to x, even tiny changes in f result in large changes to x/p. Thus at this stage, as global warming increases, even tiny increases in local temperatures and burn rates in a wildfire result in worse than exponentially more land burned than as a result of direct human causes such as barbecues or cigarettes (which is linear).
Conclusion
Climate Science deniers always ascribe agency to anything they disagree with: Climate Scientists just say what their bosses tell them to; floods happen because people don't dredge rivers (dredging rivers doesn't really help in fact); wildfires happen because of arsonists. Conversely, they use "common sense" to determine policy, which allows them to bypass all the science they want, but in turn means their policies are driven by human agency rather than objective criteria, by definition.
But this kind of thinking means they can't plan properly for climate extremes, because they'd never trust the models that predict the future.
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