Scope is rode length divided by depth measured from the bow. Depth changes with the tide; rode length does not.
The arithmetic
Anchor in 10 feet at low water with a bow height of 4 feet. The vertical distance is 14 feet, and 100 feet of rode gives a scope of about 7:1.
Six hours later the tide has risen 6 feet. The vertical distance is now 20 feet, the rode is still 100 feet, and the scope is 5:1.
In a ten-foot range it falls to 4:1, which is short in anything but calm conditions. Nothing was done wrong; the water arrived.
Calculate for the maximum
Work out scope against the depth at the next high water, not the depth under the keel when you drop.
That means knowing the range for that day, which is the tide table, and adding it to the sounded depth. It also means adding the bow height, which people forget in both cases.
rode needed = (charted depth + tide rise to next HW + bow height) × desired scope
Erring long costs nothing except swinging room. Erring short costs the night.
Swinging room grows too
More rode means a larger circle, and the circle grows again as the tide floods. A boat that clears a moored yacht at low water on 100 feet of rode may not clear it at high water on the same rode with the boat lying further off.
Assess room at maximum rode and maximum tide, and be conservative in a crowded anchorage where neighbours may be on different rode types. A boat on all chain and one on rope-and-chain swing differently in the same wind, and they can converge.
Depth under the keel at low water
The other half of the problem. Anchoring at high water in what looks like plenty of depth can leave a boat aground at low water, and the calculation is the mirror image:
depth at LW = sounded depth − fall to next low water
Compare that against draught plus a safety margin. In a large range this is the constraint that decides where you can anchor at all.
Tidal streams reverse the boat
In an anchorage with tidal stream, the boat turns as the stream reverses and lies to the current rather than the wind for much of the cycle. Two consequences.
The anchor is loaded from a different direction several times a day, and an anchor that resets well matters more here than raw holding power.
Wind against tide produces the worst motion and the highest loads, because the boat is pushed one way by the water and the other by the air. Anchorages that are comfortable on a fair tide can be unpleasant an hour later.
What to do in practice
Check the tide table before choosing the spot, not after. Note the times and heights of the next high and low water in the log.
Set rode for high water, verify swinging room at that rode, and confirm depth at low water clears the keel. If any of the three does not work, the answer is a different spot rather than a compromise on scope.
Snubbers and tide
A snubber sized for the depth at low water becomes short as the tide rises, and a short snubber does less to absorb shock loads. In a large tidal range, allow enough snubber length that it still hangs in a useful curve at high water.
This matters more on all-chain rode, where the snubber is doing all the shock absorption that a rope rode would provide on its own.
Anchor alarms in a tidal anchorage
An alarm radius set for the swing circle at low water will trigger repeatedly as the tide rises and the boat lies further off, and an alarm that cries wolf gets turned off.
Set the radius for the maximum circle — rode length plus boat length plus a margin — and accept that it will not detect a small drag. A tighter alarm and a transit check before turning in together do more than either alone.
Writing it down
Note the sounded depth, the state of tide when you dropped, the rode paid out, and the times of the next high and low water. Three lines in the log, and they are the information anyone waking at 3am needs in order to decide whether the boat is where it should be.