Tidal Characteristics April 30, 2012

1. Tidal Characteristics April 30, 2012

2. 2. Theory Behind Tidal Analysis and Prediction 2.1 Short Introductory Overview – the Big Picture 2.1.1 Some Definitions Tides Astronomy & Hydrodynamics Tide (vertical movement; scalar) Tidal Current (horizontal; vector) Tide Range (HW –LW) Tidal Period Tidal Frequency Angular Speed Mean Sea Level Tidal energy at many astronomical frequencies Mean Sea Level Tidal Period (average) = 12.4206 hours [actually M2 constituent] Tidal Frequency (average) = 1/12.4206 hours = 1.932 cycles per day (cpd) Angular Speed (average) = 28.9841o/hour (Lunar day = 28.8412 hours; solar day = 24.0000 hours)

3. Higher High Higher High MHHW MHW High Observed Water Level Low MLW Lower Low Low MLLW Lower Low Day 1 Day 2 LMSL = avg. of hourly levels MTL = avg. of MHW and MLW DTL = avg. of MHHW and MLLW Water level record of 19 years (Tidal Epoch) 1983-2001

4. Some Definitions • mean high water (MHW) – average of all the high waters over some time period (e.g., 19 years) • mean low water (MLW) – average of all the low waters over some time period • mean rangeof tide (Mn) – the difference between mean MHW and mean MLW • (the average of all the tidal ranges over some time period) • mean high water springs (MHWS) – average height of the high waters at spring tide (or spring high water) • mean low water springs (MLWS) – average height of the low waters at spring tide (or spring low water) • (mean) spring range (Sg) – MHWS minus MLWS (the average range occurring at the time of spring tides) • – larger than the mean range • – used only if the type of tide does not have a strong diurnal signal • (mean) perigean range (Pn) – average range occurring at the time of perigean tides. When there is a significant diurnal inequality, use: mean higher high water(MHHW) – average of all the higher high waters for some time period (e.g., 19 years) mean lower low water (MLLW) – average of all the lower low waters for some time period mean lower high water (MLHW) – average of all the lower high waters for some time period mean higher low water (MHLW) – average of all the higher low waters for some time period (great) diurnal range – difference in height between MHHW and MLLW. (mean) tropic higher high water – average of the higher high waters occurring at times of maximum lunar declination (mean) tropic lower low water – average of the lower low waters occurring at times of maximum lunar declination (great) tropic range (Gc) – difference in height between tropic higher high water and tropic lower low water.

5. Some Definitions • The timing of high waters (and low waters) has always been referenced to the moon’s transit, • either over the location of the tide gauge or over a time meridian (local or Greenwich). • lunitidal interval – interval between the moon's transit (upper or lower) over the local time meridian • (or the Greenwich meridian) and the following high or low water. • (transit is designated as: upper transit when it crosses the time meridian near the tide gauge, and • lower transit when it crosses the meridian that is 180 degrees from the tide gauge location.) • (mean) high water lunitidal interval (HWI) – average of all intervals between the moon’s • transit and the following high waters • (mean) low water lunitidal interval (LWI) – average of all intervals between the moon’s • transit and the following low waters • When there is a diurnal inequality in the tide, separate intervals are calculated for HHW, LHW, HLW, and LLW: • higher high water interval (HHWI), lower high water interval (LHWI), • higher low water interval (HLWI), lower low water interval (LLWI). • Need to distinguish between the upper and lower transit of the Moon with reference to its declination: • – Intervals referenced to the moon's upper transit at the time of its north declination, or • to the lower transit at the time of south declination are usually marked a. • – Intervals referenced to the moon's lower transit at the time of its north declination or • to the upper transit at the time of south declination are usually marked b. • establishment of the port (also called the vulgar establishment) • – the average high water interval on days of the New Moon and Full Moon • – the term high water full and change (HWF&C) is sometimes used today. • HWF&C is typically ten or fifteen minutes earlier than HWI.

6. TypesofTides ( classification schemes are only approximate and do not cover entire month) Semidiurnal Mixed Mixed Diurnal

7. Tidal Currents (horizontal current due to tide) • Reversing Tidal Current • in narrow waterways • one-dimensional scalar • (like the tide) But more typical

8. ---------------------Tidal Current flows in offshore areas--------------------------- Mixed Diurnal Semidiurnal • TIDALCURRENTS • horizontal current flow • rotary flow , i.e., direction of • flow rotates around compass • two-dimensional vector data • time series (break data up into • 2 component time series) • energy at the same • frequencies as the tide • (but maybe more overtides) Tidal Current flow in a waterway with irregular shoreline and/or bathymetry Tidal Current flow in a narrow channel

9. WIND Tidal phenomena in data time series, are deterministic; the data are truly periodic. [ unique in oceanography – allows for a special type of analysis and prediction that takes advantage of the known frequencies at which the tidal energy will be found] Nontidal phenomena in data time series are stochastic; the data are random. [wind, atmospheric pressure, river discharge, salinity, water temperature, wind waves, etc.] [Some nontidal effects are temporarily periodic, such as land breeze-sea breeze, or inertial currents or the effects of the daily or annual variation in solar radiation. In the much more chaotic atmospheric system, such meteorologically generated periodicities do not have a strong and consistent effect on the ocean’s water levels or currents.].

10. While it is the astronomical forcing of the tide that is the basis for the tide’s predictability, it is the hydrodynamics of the tide determines: the size of the tide range, the timing of high and low waters the type of tide the speed and timing of the tidal current etc. hydrodynamics is controlled by the length, width, and depth of the bay or river (and of any adjoining waterways) Because of the hydrodynamics, tide ranges, times/phase lags of high and low tides, the tide regime, and the relationship between the tide and tidal current vary with horizontal (geographic) distance throughout a waterway, especially in shallower water.

11. Tide Ranges > 40’ around the world Ungava Bay, Canada (50’) Gulf of St. Malo, France Bristol, UK Cook Inlet, AK Bay of Fundy, Canada (50’) Gulf of Cambia, India Southern Argentina (continental shelf) Magellan Strait, Chile

12. Saltstraumen Strait (>15 knots) South Indian Pass, SE Alaska (15 knots) Seymour Narrows, BC, Canada (15 knots) Kanmon Strait (10 knots) Fast Tidal Currents Around the World

13. Fast Tidal Currents Can lead to Tidal Whirlpools Malstrom between southern Loften Islands, Norway Scylla and Charybdis in Homer’s Odyssey (and yet negligible tide range)

14. Types of Tides in the U.S.

15. Observations to Products