Correlation Maps

You'll learn: what Pearson r means on gridded data, how correlate's two modes ask two different questions, how vector layers work (component), and how the editor's live validation catches a type error the moment you create one.

The question: "Does wind cool the sea surface?" Physically it should — wind drives evaporation and stirs cool water up from below — so where the two are genuinely coupled, months with stronger wind should be months with cooler water.

Temporal correlation: a map of r#

1. Open the Graph tab and build:

   • layer → layer: sst, start: 2023-01, stepMonths: 2
   • layer → layer: wind, start: 2023-01, stepMonths: 2, and — because wind is a vector layer — component: speed. Forget the component and the run stops with a structured error naming the node: vector layers need to know which scalar you want (speed, u, or v).
   • correlate (under combine) → mode: temporal; connect the SST layer to input a and wind to b.
   • display and answer, both fed by the correlate node.

2. ▶ Run. The wind months stream from the live GFS feed, so the first run takes a while (watch the status line); they're cached afterwards.

3. Reading the result:

   • The map is r per cell, on a fixed ±1 balance scale — the engine knows r and always displays it the same way. Broad blue across the tropics and subtropics: negative correlation, wind up → temperature down. Exactly the physics we guessed.
   • The answer: correlation of sst vs wind: mean -0.18 · p5 -0.72 · p95 0.53 · 66% coverage, plus the caveat line (gridded r — read as association, not significance).

4. What r means here: at each cell, take the ~20 date-paired (SST, wind) month-values and ask how consistently they move together. r = −1: every windier-than-usual month was cooler-than-usual, proportionally. r = 0: no linear relationship. The per-cell requirement of ≥ 8 pairs is why short windows produce gray cells.

5. And what it doesn't mean: not causation (a shared season can correlate two strangers), and not "significance" — neighboring cells move together, so the 64 800 cells are far fewer than 64 800 independent samples. That's why the engine reports n and refuses to print p-values.

Break it on purpose: switching to spatial#

6. Change the correlate node's mode to spatial. The display node instantly turns red. Hover it: "input value of display expects field | stack, got scalar" — spatial correlation produces a single number, and you can't draw a number as a map. This is the type system working: the editor told you at edit time, not at run time.

7. Right-click the display node → ✕ delete node. The graph is valid again (the answer sink is still there — every program needs at least one sink).

8. ▶ Run. One number: the spatial correlation between the two time-averaged maps. It answers a totally different question — not "do they move together over time" but "do their geographies look alike?" Windy regions (the Southern Ocean) and warm regions (the tropics) are mostly different places, so expect a negative number here too — but for an unrelated reason. Keeping the two modes straight is the main skill of this tutorial:

   	temporal	spatial
   Pairs	frames over time, per cell	cells across the map
   Output	a map of r	one number
   Question	do they wiggle together in time?	do their patterns coincide?

The positive counterpart#

9. Rebuild the temporal version (put mode back and re-add the display — or load the built-in SST × wind coupling from the graphs… dropdown), then change the first layer to waves. Wave height vs wind speed is the same program shape with opposite physics: the map comes back strongly positive nearly everywhere, because wind makes waves. Comparing the two maps — same code, mirrored sign — is the fastest way to build intuition for what a correlation map is showing you. (This pair ships as the built-ins SST × wind coupling and Wind makes waves.)

The finished temporal program#

{ "nodes": [
  { "id": "sst", "op": "layer", "params": { "layer": "sst", "start": "2023-01", "stepMonths": 2 } },
  { "id": "wind", "op": "layer", "params": { "layer": "wind", "component": "speed", "start": "2023-01", "stepMonths": 2 } },
  { "id": "r", "op": "correlate", "inputs": { "a": "sst", "b": "wind" }, "params": { "mode": "temporal" } },
  { "id": "map", "op": "display", "inputs": { "value": "r" }, "params": { "title": "r · SST × wind speed" } },
  { "id": "ans", "op": "answer", "inputs": { "value": "r" }, "params": { "label": "per-cell r: SST vs wind speed" } }
] }

Experiments: correlate airtemp × humidity (GFS layers cover land too); insert a mask node with a region preset between a layer and the correlate to focus one basin; try mode: spatial between chl and sst — the built-in Warm seas are deserts — and see why one number is sometimes exactly enough.

Next: El Niño Composites — graphs that branch.