Fixing the Level of the Sea – Not so long ago an interesting marine boundary called ordinary low water appeared in Virginia law. Its legal definition was “not spring, not neap, but ordinary low water”. So as long as you were not out looking for the low water mark on your property during a spring tide or any other extra-ordinary tidal condition, you’d be sure to find the boundary in question. Or so the lawyers said.
Water level measurements at primary tide stations show that the problem is somewhat more complex than that. For one thing, mean sea level measured relative to the land - is changing. At the Chesapeake Bay Bridge Tunnel in lower Chesapeake Bay, annual mean sea level and its recent trend looks like this:
But in Juneau, Alaska, mean sea level and its recent trend looks like this:
Today, global sea level rise is occurring everywhere due to increases in water volume in the world’s oceans. But the chief reason for the difference in trend shown above lies within the earth’s crust. Chesapeake Bay, along with most of the U.S. East Coast, falls within a region where the crust is sinking – adding to the effect of a global rise in sea level. However, in many parts of the U.S. West Coast, and especially in Alaska, the crust is actually emerging faster than the global sea level rise rate.
Tidal Datums and Tidal Epochs – Obviously nothing is going to prevent sea level from changing in response to these and other factors. However, we can take sea level averages over several years to obtain a tidal datum - a vertical reference based on some phase of the tide - to slow the process if only temporarily. This is a workable idea because, in addition to sinking crusts and melting ice, tidal variations also have their effect on sea level. One such effect is the 18.6-year cycle of the lunar nodes – a cycle accompanied by variations in tidal range. Another force for change is the annual variation in solar declination that modulates solar heating and density of ocean waters. To account for both, a 19-year period of water level averaging – the National Tidal Datum Epoch (NTDE) – has been established by NOAA/NOS in the United States. NTDEs have included the years 1924-1942, 1941-1959, 1960-1978, and most recently, 1983-2001. NTDEs thus are being updated roughly every twenty years.
Here are the basic definitions for tidal datums commonly used in the U.S. and its territories:
Mean Sea Level (MSL) – Arithmetic mean of hourly water levels observed during current NTDE.
Mean Higher High Water (MHHW) – Mean of higher high water heights during current NTDE.
Mean High Water (MHW) – Mean of all high water heights observed during current NTDE.
Mean Low Water (MLW) – Mean of all low water heights observed during current NTDE.
Mean Lower Low Water (MLLW) – Mean of lower low water heights during current NTDE.
Mean Tide Level (MTL) – A datum located midway between MHW and MLW; i.e.,
MTL = ½ (MHW+MLW).
That last bit of algebra is intended to underscore the fact that all tidal datums have elevations above some arbitrary but well-protected reference – usually the station datum or staff zero (see Tide Measurement module). The intersection of any of these tidal datum elevations with the land produces a line or contour bearing the name of the datum; e.g., Mean High Water Line (MHWL), Mean Low Water Line (MLWL), etc.
Tidal Datum Transfers – How to get them from here to there is important for two reasons: 1) Tidal datum elevations vary from place to place as dictated by tide wave hydrodynamics (see Long Waves module) – transfer by leveling is not an option, 2) establishing the datum by direct means (19-year series every 20 years) is an exacting and expensive operation conducted at a relatively small number of primary tide stations. Fortunately, there’s an easier way called simultaneous comparisons. Here’s how it works:
At a primary tide station (A in figure below), get the NOS tidal datum elevations for the current NTDE.
Obtain a month of tidal observations at station B matched by simultaneous observations at station A.
Calculate monthly mean tide level at both stations (MMTLA, MMTLB).
Calculate the monthly mean range (MMRA = MMHWA-MMLWA, MMRB = MMHWB-MMLWB) and the range ratio between the stations (RR = MMRB/MMRA).
Now, if stations A and B are connected by a tidal waterway and we assume that both experience similar monthly deviations from mean tide level, then
Applying the range ratio, and
Mean higher high water and mean lower low water transfer from A to B in the same way using a new mean tide level elevation midway between them.
If you want to generate tidal predictions relative to a tidal datum such as MLLW, simply add the offset (MSL-MLLW) to your astronomical model output – output which always assumes a base elevation independent of the tide; i.e., MSL. The tidal datum of MSL transfers from A to B in the way previously demonstrated for the MTL tidal datum.