Meridian

The climate charges by the mile.

The only question is how much, and that is answerable. Nine findings from published research run against Meridian’s model on every change. Eight pass. The one that does not is on this page, with the reasoning.

The question

How much does hot air cost a runner?

It has been studied properly, in large samples, over decades. The answers are consistent enough to build on and uncertain enough that anyone claiming a single exact number is selling something.

Meridian's model reproduces nine published findings. It matches eight of them. The ninth it disagrees with, on purpose, and that is on this page too.

What the research says

Marathon times fall roughly 2.8% across a 15°C swing

Seven marathons, up to 36 years of results each, hundreds of thousands of finishers. The effect is larger for slower runners, who are out in it for longer — which is why Meridian scales the penalty with time on feet rather than distance.

Ely, Cheuvront, Roberts & Montain (2007), Medicine & Science in Sports & Exercise

The cost rises faster than the temperature does

Stockholm Marathon finishers across many years show a gradient that steepens as conditions worsen. Doubling the heat does considerably more than double the damage. Meridian's heat term is quadratic for this reason, not because a curve looked better than a line.

Vihma (2010), International Journal of Biometeorology

Altitude costs about 6.3% of aerobic capacity per 1,000 m — from sea level up

The received wisdom was that nothing happens below about 600 m. It does. The decline is linear and it starts almost immediately, which is why Meridian's altitude threshold sits at 300 m rather than the traditional figure.

Wehrlin & Hallén (2006), European Journal of Applied Physiology

Heat acclimation is worth more than most runners think

A meta-analysis of 96 studies and 1,048 participants. Ten to fourteen days of regular heat exposure recovers a substantial fraction of what the heat takes. This is why Meridian works out where you actually train instead of asking you how tough you are.

Tyler, Reeve, Hodges & Cheung (2016), Sports Medicine

Running uphill and downhill has a measured energy cost

Treadmill work across gradients from −45% to +45% produced the polynomial Meridian uses for elevation. It is one of the few parts of the model that is close to settled physics rather than statistics.

Minetti, Moia, Roi, Susta & Ferretti (2002), Journal of Applied Physiology

Where we disagree with a paper

One study says the cost per degree is about a third of what we use

A pooled analysis across endurance running puts the marginal cost near 0.2–0.4% per degree of heat index. Meridian predicts roughly 0.7% for a marathoner, which is close to double.

We think the gap is real and mostly explained: that analysis pooled events far shorter than a marathon, where heat costs much less, so the average is diluted by races our model is not describing. The marathon-specific research points the other way and we have gone with it.

Two peer-reviewed sources genuinely disagree here. We picked a side and wrote down why. If real runner data lands nearer the other one, the duration curve is the first thing we will change.

Mantzios et al. (2022), Frontiers in Physiology — the finding we do not match
Energy cost of running by gradient: a 5 percent climb costs about 30 percent more, a 5 percent descent saves only about 24 percent 0.6×0.8×1.0×1.2×1.4×1.6×1.8× down 5% gives back 24% up 5% costs 30% -12%-8%-4%0%+4%+8%+12% gradient
Hills are not symmetrical. A five percent climb costs about 30 percent more energy per mile. The same five percent going back down gives you only about 24 percent back. That gap is why an out-and-back on rolling ground is slower than the same distance on the flat, and why a course profile matters even when it finishes where it started.

How it is checked

Nine anchors drawn from that literature run against the model automatically. Any change to any constant has to keep passing them.

AnchorWhat it testsResult
Ely marathon slowdownCost across a 15°C swingpass
Ely elite marginalFaster runners suffer lesspass
Vihma gradientSlower runners suffer morepass
Wehrlin 1,500 mAerobic loss at altitudepass
Wehrlin 2,500 mSame, higher uppass
Gore transferCapacity lost vs pace lostpass
Tyler acclimationAdapted vs unadapted at 32°Cpass
Minetti gradientEnergy cost of a hillpass
Mantzios per-degreeMarginal cost per degreedisagrees
The model's predicted heat cost against the cost measured in 170 of Max's own runs, with a 95 percent confidence band +0s+15s+30s+45s+60s model my runs 12°C17°C22°C27°C33°C air temperature
The model, checked against one real runner. The green line is what Meridian predicts heat costs a fully heat-adapted runner over ten miles. The red line is what it actually cost across 170 of my own runs between 12°C and 33°C, with heart rate held constant; the shaded wedge is the range that data can honestly support. The model sits at the top of that range — plausible, but very likely a little pessimistic for me specifically. Which is the entire argument for personalising it.

Modeled, then calibrating, then personalized

The word on the screen is a measurement, not a mood.

Before Meridian has seen you run, the heat adjustment comes entirely from published research on runners in general. Every qualifying run you connect moves a little of that answer from the population onto you. This is the actual blend the engine uses, not an illustration of one: your share is your run count divided by your run count plus ten.

How much of the heat adjustment comes from your own runs rather than from published research, as your history grows 0%25%50%75%100% calibrating personalized 86% yours 0102030405060your qualifying runs
It never reaches a hundred percent, on purpose. Five qualifying runs earns the word calibrating and about a third of the answer; twelve earns personalized and just over half. Even at sixty runs the population prior still holds a seventh of it, because a runner who has a strange summer should not have the model rewritten around it. Meridian also refuses to say personalized if all your runs happened in similar humidity — without contrast there is nothing to learn from, however many runs there are.

The thing we are least sure about

Dew point.

Meridian is built on the idea that humidity matters as much as heat — that 75°F air over a 70°F dew point is a different run from 75°F over 45°F. Every coach knows this. Every runner has felt it.

But three large studies looking for dew point as an independent predictor of marathon performance did not find one. The effect kept collapsing into temperature. That is uncomfortable, and pretending otherwise would make this page worthless.

Our position: the studies measured field marathons where temperature and humidity move together, which makes the two nearly impossible to separate. The way to settle it is real runners' own histories across genuinely different conditions. That is the work in front of us, and if it says we are wrong, this page will say so.

One number matters more than all the others

A sensitivity analysis over every constant in the model found one that dominates: the threshold where heat starts costing anything. Its influence is about ten times the next largest.

It is a coaching heuristic. It is not measured. If something in Meridian is wrong, it is most likely that, and we would rather you heard it from us.

Get it when it opens

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