Our rule of thumb downunder for air drying timber in thick board dimensions is this.
1 years air drying time per 1 inch thickness thru the thinnest dimension plus a year.
Hence a 2 x 4 would take 3 years to air dry to a little above 13% EMC (Equilibrium Moisture Content).
I like to kiln dry my timbers down to 10% and then allow to reabsorb up to 12% EMC for furniture.
It's likely a high % for those of you in the Northern hemisphere, with snowfall and hence low relative humidity - for whom a much lower EMC% would be desirable no doubt.
Something to recognize with air drying is that a lot of the free moisture will come out and most of the intercellular moisture - but the intracellular (in the cell wall) will not, without kiln drying in most instances.
The Intercellular moisture has to diffuse out thru the lumens (pores) in the cell walls. It does this too fast if the free moisture is removed too quickly (i.e. if left in the hot sun while green straight off the saw..you will see and hear it surface check in front of your eyes and ears).
What happens is this - the air movement evaporates moisture from the surface of the freshly sawn green lumber. As a result - free moisture from between the cells is wicked to the surface, to in turn be evaporated away by dry air movement.
As a result the moisture drops throughout the wood on a gradient from the insides to the outsides.
As the free moisture is wicked to the surface it creates a slight vacuum between the cells. If there is sufficient time and low enough vacuum and enough heat - the moisture trapped within the cells (inter cellular moisture) turns to a gas (steam) and is forced out of the lumens (pores) in the cell wall, into the vacuum spaces left by the removal of free moisture (sap), and in turn wicks it's way to the surface of the board and is evaporated.
If the free moisture is removed too fast under high temperatures, the gaseous moisture inside the cells burst thru the cell wall to fill the vacuum in the free moisture spaces, and we get what's known as "structural collapse" of the timber - and this is usually seen as a depressed powdery texture to the wood in the centre of the board full of long checks thru to the surface.
This condition and this form of drying applies to both kiln and air drying if not adequately controlled - I'd imagine in snow country with zero relative humidity it could also be an issue in winter.
With kiln drying - the last type of moisture within the timber - that trapped in the cell walls made of cellulose - (intracellular moisture) can be removed with vacuum dehumidifying kilns over time. usually this moisture doesn't come out with air drying unless undertaken in almost desert like conditions of very high heat and very low relative humidity for prolonged periods.
We work it this way - we can air dry down to a suitable EMC for Joinery work (door Frames, solid doors, window frames & sashes etc) where some limited movement after manufacture and during installation etc is acceptable, (Joinery usually is exposed to weather extremes while the bricks are laid, and roof put on until lockup).
All that protects them after manufacture during the building phase is a light spray of linseed oil straight after manufacture until lockup..so removing that last Intracellular moisture from inside the cell walls is wasted time effort and $...Air dried is sufficient for Joinery.
However for solid timber furniture manufacture where stability is more important (critical?) we do kiln dry to remove intracellular moisture since hopefully the furniture will never see exposure to weather.
I personally used a non destructive wood moisture encounter made by Tramex.
https://www.tramexmeters.eu/Wood-Moisture-Encounter
You should allow for Hot wood (+1.5%) up to 21degrees C plus 1% for every 11 degrees C above 21 degrees with these meters.
Also - most meters are graduated for Oregon so dense timbers like Walnut will likely need a correction factor due to their high SG (Specific Gravity) probably adding another 5 or 6%..
So for example, a reading of 4% on the meter if the woods hot straight from an oven / kiln could be a proper reading of 4% reading + 1.5% Temp to 21 degrees C + say 2% for temp to 43 degrees C, plus say 6% correction factor for density of walnut = say, 13.5% moisture content reading.
my 2c.