2.9 Tides: Tables, Datums & Height of Tide

Tides, Datums and the Height of Tide

Tide is the vertical rise and fall of the sea surface caused by the gravitational pull of the moon and sun on the oceans, modified by the shape of the coastline. As a captain you rarely predict tides from first principles - you read a tide table - but you must command the vocabulary and be able to compute the height of tide at a moment between the printed high and low waters, because that number decides whether you clear a shoal or ground on it.

The language of tides

• High Water (HW) and Low Water (LW) - the crest and trough of the tidal curve.
• Range - the vertical difference between one HW and the adjacent LW.
• Stand - the brief period of little vertical change at the top and bottom.
• Spring tides - the largest ranges, at new and full moon, when sun and moon pull in line.
• Neap tides - the smallest ranges, at the quarter moons, when sun and moon pull at right angles.

Tides fall into three patterns: semidiurnal (two nearly equal highs and lows each day, typical of the U.S. East Coast); diurnal (one high and one low each day, parts of the Gulf of Mexico); and mixed (two unequal highs and lows a day, the U.S. West Coast). The difference between the two daily lows in a mixed tide is the diurnal inequality, and it is exactly why the datum is built on the lower low water.

The chart datum: MLLW

Charted soundings (depths, printed in feet, fathoms, or meters as stated in the chart title block) are measured downward from a reference plane called the datum. Since 1980 the U.S. tidal datum has been Mean Lower Low Water (MLLW) - the average of the lower of the two daily low waters over the 19-year National Tidal Datum Epoch. Because the datum sits at a low-water plane, the real water is usually deeper than the printed number, and the tide table almost always adds a positive height of tide:

Actual depth = Charted depth + Height of tide

A negative tide (a height printed with a minus sign, common at spring lows) means less water than charted - a genuine grounding hazard where you have the least margin.

The overhead-clearance trap

Vertical clearances under bridges and overhead cables are not referenced to MLLW. They are given above Mean High Water (MHW). So at any tide lower than MHW you actually have more clearance than the chart prints:

Actual clearance = Charted clearance + (MHW - present height of tide)

Mixing the two datums - subtracting tide from a clearance, or adding a clearance to a depth - is a classic exam trap. Depth works from the low-water plane; clearance works from the high-water plane.

Interpolating with the Rule of Twelfths

Between printed HW and LW, the practical mariner estimates height with the Rule of Twelfths, which approximates the tidal curve (a rough sine wave) over about six hours. The range is added, hour by hour, in this sequence:

The water moves slowest near the turns and fastest at mid-cycle - which is why the two middle hours each carry 3/12.

Worked example

Tide table: Low water 0600 at 1.0 ft, High water 1212 at 7.0 ft. Range = 7.0 - 1.0 = 6.0 ft, so one twelfth = 6.0 / 12 = 0.5 ft.

At 0900 the height of tide is 4.0 ft. Over a shoal charted at 3 ft, the actual depth is 3 + 4.0 = 7.0 ft. A vessel drawing 5 ft therefore carries 2 ft of water under the keel - thin, but afloat.

Now the same instant at a bridge: the chart prints 55 ft vertical clearance (above MHW), and MHW is 7.0 ft. At 0900 the height is 4.0 ft, i.e. 3.0 ft below MHW, so actual clearance = 55 + (7.0 - 4.0) = 58 ft. When the tide is below MHW you gain clearance; a rising spring tide near MHW gives you the least.

Reference and subordinate stations

Printed tables list a few reference stations in full and give subordinate stations as time and height corrections to the nearest reference - so many marinas are found by applying "HW +0h48m, height x0.9" to the reference port. Modern practice is to pull the prediction directly from NOAA for the exact station, but the correction method is still tested.