# predicting low tide

At 18:03 PDT at La Jolla Cove the lifeguard's bulletin board stated predicted low tide at 5:36 (17:36 PDT?). In fact, it was already after 6:00 and the sun had not yet set. The moon was a waxing crescent, about 2 days old. I infer that the moon would be setting in about 2 hours so the tide should be low in about 3 hours, that is, around 21:00 PDT. How can the discrepancy be explained?

I infer that the moon would be setting in about 2 hours so the tide should be low in about 3 hours, that is, around 21:00 PDT. How can the discrepancy be explained?

Your inference is based on multiple misconceptions. The key misconception is that the tides at La Jolla are solely due to the Moon's position in the sky. A secondary misconception is that the time of moonset is a key indicator with regard to the tides at La Jolla.

With regard to the latter, we're often told that the Moon rises and sets 50 minutes later than it did the day before. While this is the average behavior, it is rarely the actual behavior1. The time between subsequent moonrises/moonsets can vary quite a bit from this mean, with the variation depending on the phase of the Moon, the time of the year, the latitude of the observer, and other influences. For La Jolla, the times between subsequent moonrises/moonsets just for October 2018 varies from 36 minutes to 68 minutes later than on the previous day.

With regard to the former, the tides at La Jolla result from several cyclical influences, plus non-cyclical variations caused by things such as weather. The key cyclical influences, from Harmonic Constituents - NOAA Tides and Currents for La Jolla are

Name   Amplitude (ft)  Phase(°)  Speed (°/hr)
M2      1.64           270.1     28.984104
K1      1.089           86.6     15.041069
O1      0.699           80.2     13.943035
S2      0.669          258.5     30.0
N2      0.384          254.1     28.43973
P1      0.344           83.4     14.958931
SA      0.259          175.3      0.0410686
Q1      0.125           77.2     13.398661


The above shows that the M2 tidal constituent is dominant at La Jolla, but it also shows that it is not overwhelmingly so. The predicted tides result from the composition of these constituents, plus a bunch of smaller constituents that I did not list. The predicted tide levels for La Jolla CA for October 2018 is shown below. Note the complex pattern of beats in the graph.

1Three statisticians went duck hunting. Two shot at a duck. Both missed, one ten feet to the left, the other ten to the right. The third proclaimed "We hit, on average!"