Does saturation mixing ratio change during adiabatic ascent/descent? I think the mixing ratio ($r_v = \rho_v/\rho_d$) is constant as long as no water vapor is condensed out, but saturation mixing ratio always confuses me a little.
The saturation mixing ratio is not how much water vapor the air has in it... but how much it could have, based upon the temperature. Since adiabatic ascent/descent means cooling or heating, the saturation mixing ratio will change. The actual mixing ratio on the other hand won't change unless you lift the parcel so much that it cools to the dewpoint and beyond and starts condensation.
When you're working with a skew-T or such, anytime you see the word saturation, it signals to refer to the temperature part of the profile (the right/red line) and not the dew point part (the left/green line).
Anytime you see that word saturation, it's a different entity... (unless $T=T_d$) saturation mixing ratio is different than mixing ratio, saturation vapor pressure is different than vapor pressure, etc. And each are so tied to the temperature/possibility of what can exist at that point and not the dew point/current existing moisture.
On a skew T, the saturation mixing ratio is the same shape, up and to the right, along/parallel to the example mixing ratio lines usually given (in dashed light green on this image). But they aren't the same line (unless $T = T_d$):
The saturation mixing ratio line starts from the temperature, the regular mixing ratio starts from the dew point.
I think the mixing ratio (rv=ρv/ρd) is constant as long as no water vapor is condensed out, but saturation mixing ratio always confuses me a little.
Indeed the (regular) mixing ratio is constant as long as there's no condensation and no outside change to the parcel... for the moisture you stay with the same mixing ratio in ascent (until saturation), such as when calculating the LCL. But you follow the dry adiabat (lines going up to the left on a skewt like this one) for the temperature for condensation-less ascent (so never use the saturation mixing ratio line, the one coming from just the temperature).