Earth Data School/Signal vs. noise: SNR, the noise floor & BACI
Lesson 3.3 · 8 of 17

Signal vs. noise: SNR, the noise floor & BACI

When is a measured change a real effect, and when is it just the natural wobble of the world? This is the idea behind the bars on the deforestation result — the change has to 'clear the tick' to count.

In one lineNature is jittery. Before believing "deforestation made it warmer", first measure how much the temperature wobbles in untouched forest nearby — and demand the cut sites change by more than that wobble.

BACI — a natural experiment

You can't re-run history with and without deforestation, so you do the next best thing: Before-After-Control-Impact.

  • Impact sites — pixels where forest was actually lost.
  • Control sites — nearby pixels that stayed forested.
  • Before / After — the same windows for both.

The trick: subtract the controls' change from the impact sites' change. Whatever happened regionally (a hot decade everywhere) hits both groups, so subtracting it leaves only what's specific to the cutting. That difference-of-differences is the BACI effect. It's evidence, not a prediction — observed contrast across similar places, not a forecast for one plot.

The noise floor — how much wobble is "normal"

Even untouched forest isn't perfectly steady year to year. We measure that natural variability as the standard deviation (SD) of the change across control pixels, and set a bar — the noise floor — at half of it:

noise floor = ½ × SD(change in control pixels)

An effect smaller than the floor is indistinguishable from the forest just breathing. This is measured from the data, not guessed — and building it honestly once corrected a hand-set guess (a land-surface-temperature floor jumped from 0.05 °C to a measured 0.185 °C, ~4× higher).

SNR — signal-to-noise ratio

SNR = |effect| / SD(controls)

SNR > ~1 means the effect stands above the wobble. On /verify you saw SNR 2.59 for warming (trustworthy) vs SNR 0.04 for rainfall (basically noise). One more guardrail: pixel count. A coarse 28 km grid might give a region only ~25 control pixels — too few to trust, so it's flagged. Fine 1 km grids give tens of thousands. More pixels → a more reliable floor.

Play with it

This is the bar from /verify. Raise the control wobble and the floor (the tick) moves out — the same effect can go from "real signal" to "no clear change". Drop the pixel count and you lose confidence even when the bar clears the tick.

land surface temperature
effect: noise floor: SNR:

Do it yourself

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The disciplineA null is a real result. When the effect doesn't clear the tick, the honest answer is "no clear change" — not silence, and not a number dressed up as a finding. That's what makes the word "verified" mean something.