🌊 PUGET-TIDES: The Tides of Puget Sound, in FORTRAN

This is the third of my old-language weather and water projects. SIERRA-FLOW does Sierra Nevada rivers in COBOL, and CASCADIA-WX reads the Northwest’s weather balloons in FORTRAN. I wanted one more that I could check against something real every single day, and I live a few miles from the water. So PUGET-TIDES follows the tide in from the Pacific at eight NOAA gauges, from Neah Bay at the tip of the Olympic Peninsula, through the Strait of Juan de Fuca, past the San Juans and Port Townsend, and down the Sound to Seattle and Tacoma.

Making a tide table

A tide looks like one wave that comes and goes twice a day, but it’s really the sum of dozens of smaller, steady waves, each keeping time with something the moon or the sun does. The biggest, called M2, follows the moon’s twice-a-day pull. Others follow the moon swinging north and south of the equator, the moon coming closer and going farther, the sun, and the 18.6-year wobble of the moon’s orbit. NOAA has measured the size and timing of 37 of these at every gauge. Add them up for any moment and you have the tide.

That’s how tide tables have always been made. Lord Kelvin built a brass machine of pulleys and gears to add the waves up in 1872, and the Coast and Geodetic Survey printed America’s tide tables on one, nicknamed Old Brass Brains, until the mid-1960s. PUGET-TIDES does it in FORTRAN: it works out where the moon and sun are from scratch, applies the corrections for the moon’s 18.6-year cycle, and adds up all 37 waves at every gauge, every six minutes, a year ahead. All eight gauges take it about two seconds.

Checking its homework

The fun part is that NOAA publishes its own predictions, so every run checks itself. On the first run, FORTRAN found the same 257 high and low tides NOAA lists for the coming week at the eight gauges, every one within 0.8 minutes and a hundredth of a foot. NOAA rounds to the minute, so that’s about as close as two tide tables can agree. Over whole years, FORTRAN’s hourly tide matches NOAA’s to two thousandths of a foot on average.

It took one bit of detective work to get there. At first FORTRAN was off by up to a third of a foot in some years, always in the same small wave, M1. Fitting a year of NOAA’s predictions showed the difference was exactly the position of the moon’s nearest point on January 1. NOAA starts that one wave each year without it, then lets it run at a speed that includes it. Once FORTRAN did the same, the two lined up. I’d never have found that without a whole year to compare against.

One more small thing: where the tide just stands for an hour, with a “high” and a “low” a hundredth of a foot apart, NOAA’s tables leave the pair out, so FORTRAN does too, and the check counts any extras it finds.

What the weather adds

The measured water level is almost never exactly the tide. The difference is the surge: wind piling water up, low air pressure letting the sea rise (about a foot for every 30 hectopascals), river water pouring in. FORTRAN subtracts its tide from every six-minute reading for the last month, and a second program, NORMALS, did the same for 1.78 million hours of readings from 1991 to 2020, so each day’s surge can be compared with thirty years of the same weeks.

This afternoon the water at Seattle, Tacoma and Port Townsend was running about a third of a foot above the tide, a little more than usual for early October. The biggest surge on record here came on the morning of December 27, 2022. The tide alone was due to reach 12.90 feet at Seattle; the storm added another 2.2 feet, and the gauge read 15.12 feet, the highest water in a record that goes back to 1899. Friday Harbor, Port Townsend, Bremerton and Tacoma all set their records the same day.

Looking ahead

King tides. FORTRAN looks a year ahead for the highest tides. Seattle’s biggest this winter is January 25 at 7:15 in the morning, 13.1 feet, with December 26 close behind. Put a winter storm on top of one of those and the waterfront floods.

Minus tides for the tide pools. My favorite part. FORTRAN finds every low tide below zero that comes while the sun is up, using its own sunrise and sunset. Right now the answer for Seattle is none until March 12, because in fall and winter the big low tides come in the middle of the night. By summer they’ve swung round to midday, and the lowest of the year is the morning of the Fourth of July: 3.9 feet below zero at 11:36. That’s a beach walk worth planning.

The tide comes in

The tide is a wave, and you can watch it travel. It reaches Port Angeles about two hours after Neah Bay, Port Townsend in three and a half, and Seattle and Tacoma about four and a third. Along the way it shrinks in the Strait, where the main lunar tide is only two-thirds of the ocean’s, then grows again as Puget Sound’s long inlets funnel it, until at Tacoma it’s almost half again as big as at Neah Bay.

Sea level is moving too. FORTRAN fits a trend to every monthly mean at each gauge, and they come out within 0.05 millimeters a year of NOAA’s published trends. Seattle is up 2.1 millimeters a year since 1899, about eight inches a century. Neah Bay is going the other way, down 1.7 millimeters a year, because the land there is rising faster than the sea.

The page

The live page is a cyan cousin of CASCADIA-WX’s amber terminal. It plays back the latest job log, shows each gauge’s water level, tide and surge, draws the week of measured water over FORTRAN’s tide, lists the highs and lows beside NOAA’s, and has the king tides, the minus tides and sea level since 1899. The report comes off a line printer on blue-bar paper, and the loop that adds up the 37 waves is copied live onto a 1957 FORTRAN coding form.

How it runs

Every six hours a GitHub Action on Ubuntu runs the batch job: a stdlib-only Python script asks NOAA’s free Tides & Currents API for the constituents, datums and the last month of water levels, GFortran 13 compiles the program, and FORTRAN runs and sets a return code. The normals took about three minutes to build and only need rebuilding once. Bremerton is the one gap: its gauge has no record between 1978 and 2021, so it has no normals or trend, and the page says so rather than guessing. All free, no keys, and not for navigation.

Lord Kelvin’s machine needed a person to turn the crank. This one runs itself, and checks its own answers against the people who still make the official tables.

Code: github.com/bdgroves/puget-tides. The method is Schureman’s Manual of Harmonic Analysis and Prediction of Tides (1958), with the moon’s and sun’s positions from Meeus’s Astronomical Algorithms.

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