Assuming the point of measurement is at the boat, the dominant effect is that it goes up and down in a decaying sinusoidal pattern due to the ripples caused by

Assuming the point of measurement is at the boat, the dominant effect is that it goes up and down in a decaying sinusoidal pattern due to the ripples caused by the anchor hitting the water (it was thrown, right?) The centre point of the sinuisoidal decay is the new, lower, level as noted by other people. But I would imagine (someone going to calculate?) that effect would be at least 1 or 2 order of magnitude below the ripple effect, given reasonable assumptions.