Why does Cold Air Advection cause backing winds with height?

And, I suspect that the answer will also tell why Warm Air Advection causes veering winds with height.

I’ve seen this mentioned In multiple basic meteorology resources, but I haven’t seen an explanation of the physics that causes it, and I haven’t been able to intuitively imagine a hypothesis of my own either.
 

Jeff Duda

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There is not a causal relationship here. The relationship is associative. In other words, having one (assuming geostrophic balance is not violated) is equivalent to having the other.

First big lesson there. Do not confuse correlation with causation.

Back to your larger question - the association is called the "thermal wind relationship" and is basically what happens when you have vertical shear of the geostrophic flow. The idea being that geopotential heights give you a sense of layer mean temperature, and coupled with geostrophic winds will give you a picture of WAA = veering

Note: this general principle is only valid on the synoptic scale, and only when winds are geostrophic. That means that in highly curved flow, or on smaller scales, this relationship does not hold. No, not the opposite...there is just no longer an explicit relationship.
 
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Thank you, Jeff! Your explanations are always helpful.

Your last point is extremely important in preventing me from potentially getting further confused. The fact that there’s not a relationship that holds on small scales is not the same as saying that there is an opposite effect. I definitely could have fallen into the trap of thinking that those two things were the same while learning more about Thermal Wind.