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a little related to this question:
How many "Munro" revisions has there been?
Leads me to wonder do mountains change height? or is this because the equipment is more precise these days?
I understand that erosion will (very gradually) lower a mountain. I suppose I mean geologically and I suppose specifically in relatively un-active areas such as the Cairngorms/Scotland.
If they do change height by how much? (roughly)
While heights do change slowly by natural processes such changes are likely to be on the order of centimeters barring any extreme events.
Most changes in published heights of hills since people started measuring these things accurately (only the last couple of hundred years) are due to improvements/investments in technology.
Measuring the height of a hill is surprisingly hard. One of the earliest ways to determine hill height was trigonometry. If you have two points with a known distance between them and one known height (sea-level works well here) then by careful measurement of angles you can determine the height (and distance) of a third point. The accuracy here will depend on the the ability to measure an accurate angle and the distance to the third point. I haven't done any accurate calculation but with tools of the late 19th/early 20th c. I reckon accuracy of a few meters is reasonable. Possibly a bit higher with careful repeated measurements.
Interestingly this is what lead to the introduction of the system of trig points in the UK and other places. Which used this principle to map out distances and heights across the country.
Even in modern times calculating heights is not trivial. Here is an interesting article but the ordnance survey describing the process.
Primarily, they use photogrammetry (and probably related techniques such as LIDAR) to measure height by air. This is a quick way to cover large areas by is limited to accuracy of a couple of meters.
If you want to measure height accurately you need to leave a fixed GPS receiver in place for several weeks. While the accuracy here can be a few centimeters it is too expensive to be used in most situations.
Therefore there is significant uncertainty about some Munros height considering how close they are to the 3000' (914m) cut-off. The two post 1997 Munro re-classifications have both been due to interested parties hiring an team of surveyors to do very accurate measurements of some mountains which are more accurate than what the OS would normally do and they found that these two are just below the cut-off.
Mountains change height on geologic time scales. If a list of mountains above a certain height changes in one or two human lifetimes, then very likely this is due to measurement errors or refinements. I remember a decade or two ago when GPS first became widely available that someone made a big deal of claiming K2 was higher than Everest. That turned out to be false, by hundreds of feet. The original measurements done by the Everest team using theodolites turned out to be quite good.
Mountains wear down by erosion, but also go up and down as parts of the earth's crust move relative to each other. For example, India is still moving northeast relative to Asia at about 2 inches a year. That's really fast for continental plate movement. This same movement is what created the Himalayas when India slammed into Asia and the crust buckled and crunched at the impact zone. Since this process is still going on, the Himalayas are still rising. Mt Everest is getting a few 10s of mm higher each year.
On the flip side, some older mountains are relics from long ago plate movements and are wearing down over time. The Appalachians in the eastern US are good examples of this.
The most common reason for a mountain to 'change height' is because it's been remeasured. Erosion, rockslides and other natural causes can change the height of a mountain however in comparison they're relatively minor.
The main reason that the Munros are reclassified is because they have been measured to a far greater degree of accuracy. Ordnance Survey and several amateur groups periodically survey the UK, when errors are found the SMC updates it's list.
Reclassification is fairly unique to Munros, the Wainwrights for example are not reclassified as they are set on guide books rather than a set criteria of inclusion.
TLDR
The most common way for a mountain to change it's height is because it was incorrectly measured previously.
Some mountains change height at a surprisingly fast rate. For example, the magma chamber beneath the Yellowstone caldera is currently inflating. This is causing some of the nearby mountains to grow by as much as an inch or two per year.
