Tidal Predictions

1. Tidal Predictions

2. Harmonic Analysis & Tide Prediction TIDE PREDICTION harmonic constants harmonic constants observed tide Predicted tide HARMONIC ANALYSIS

3. Height of Tide at Any Time (harmonic method) h = Ho + Σ ƒH cos [at + (Vo + u) - κ] where: h height of tide at any time t Ho mean height of water level above datum used for prediction H mean amplitude of any constituent A ƒ factor for reducing mean amplitude H to year of prediction a speed of constituent A t time reckoned for some initial epoch (beginning year of predictions) (Vo + u) value of equilibrium argument of constituent A when t= 0 κ epoch constituent A

4. The Harmonic Prediction Equation • h(t) = H o + 3i =1 to nf i Hi cos (a i t + {Vo + u} i - 6i ) • where • h(t) = height (above some reference datum) of the tide at any time t • n = the number tidal constituents being used to make the prediction • H o = mean height of water level above the datum • Hi = amplitude of tidal constituent i • a i = angular speed of tidal constituent i (i.e., its frequency) [in degrees/hour] • t = time, reckoned from some initial epoch (e.g., t=0 at the beginning of the year) [in hours] • 6i = epoch (phase lag) of tidal constituent i [in degrees] • f i = node factor for tidal constituent i • {Vo+u} i = equilibrium argument for tidal constituent i at t=0. [in degrees] • (a i t + {Vo + u} i - 6i ) = the phase at any time t (sometimes called the argument)

5. Tide Predictions • OBSERVE THE TIDE AT A TIDE STATION, COMPUTE DATUMS, • AND TABULATE HOURLY HEIGHTS • PERFORM HARMONIC ANALYSES USING HOURLY HEIGHTS AS • INPUT AND OBTAINING HARMONIC CONSTANTS AS OUTPUT • (AMPLITUDES AND PHASES FOR HARMONIC CONSTITUENTS) • USING A TIDE PREDICTION EQUATION AND THE HARMONIC • CONSTANTS, PREDICT THE TIDE FOR A FUTURE TIME FRAME • KNOWING THE POSITION OF THE EARTH-MOON-SUN SYSTEM • IN THE FUTURE

7. Baltimore, MD - 365day Harmonic Analysis

10. Galveston Pier 21, TX - 365 day harmonic Analysis

12. Galveston Pier 21, TX - 365 day harmonic Analysis

14. Boston, MA - 365 day Harmonic Analysis

16. Boston, MA - 365 day Harmonic Analysis

18. Seattle, WA - 365 day Harmonic Analysis

20. Seattle, WA - 365 day Harmonic Analysis

21. COMPARISON OF TIDAL VS. NON-TIDAL EFFECTSREDUCTION OF VARIANCE STATISTICS(FROM ONE-YEAR HARMONIC ANALYSIS) STATIONTIDALNON-TIDAL BOSTON, MA 98.2% 1.8% BALTIMORE, MD 44.8% 55.2% CHARLESTON, SC 91.2% 8.8% KEY WEST, FL 74.5% 25.5% PENSACOLA, FL 45.4% 54.6% GALVESTON, TX 39.5% 60.5% SAN FRANCISCO, CA 98.6% 1.4% SEATTLE, WA 98.8% 1.2%

22. Total reduction of variance from least-squares harmonic analyses : 98%

23. Total reduction of variance from least-squares harmonic analyses : 75%

24. Total reduction of variance from least-squares harmonic analyses : 58%

25. Total reduction of variance from least-squares harmonic analyses : 98%

26. Total reduction of variance from least-squares harmonic analyses : 27%

27. Total reduction of variance from least-squares harmonic analyses : 97%

28. Harmonic Analysis of Water Level Data 4.3 Assessing the Quality of the Predicted Tide Series -- how well is the tide predicted, not the total water level (which includes nontidal water level changes) -- produce a residual time series (observed time series minus predicted time series) -- carry out a spectral analysis of the residual series to see how much energy is left at the various tidal frequencies -- if there still is tidal energy, not enough the tidal constituents may have been calculated, or for a short analysis perhaps some constituents were not inferred correctly for a shallow-water station look for more shallow-water constituents to include -- a self prediction may look good, but a prediction for the following year might not look as good, so -- if one has the data, carry out a spectral analysis of the residual series for a different time period -- examine the actual residual time series for periods when tidal oscillation appear and then disappear (because a nontidal event has temporarily changed the tide regime, and the harmonic constants from the entire analysis time period are not good for the period of this nontidal event) -- compare high and low waters in the predicted series versus the observed series (a standard method, especially for stations in Tide Tables) -- most nontidally caused differences (due to wind, pressure, river flow, etc.) will average out, but -- the differences can still contain seasonal asymmetries -- the standard deviations (sq. root of the average of the squared differences) include all nontidal effects (they don’t average out) -- the 90% distribution level (i.e., 90% of the absolute differences are less than or equal to the value) (again includes all nontidal effects involves absolute differences; they are not averaged out) -- see Table 8

29. Table from Tide Tables supposedly showing “tide prediction accuracy”, based on comparing predicted and observed high and low waters, but it doesn’t eliminate nontidal influences. [It’s actually showing how well the tide predictions compare with the variation in total water level.

30. Enhancing Navigation Providing the Nation’s Tide and Tidal Current Predictions • 3,142 Tide Predictions Published Annually • 2,821 Tidal Current Predictions Published Annually

32. How are Predicted Currents Derived? • Tides and Tidal Currents are predictable because theyare caused by the gravitational forces of the sun and moon, which are thoroughly understood. • The majority of estuarine currents in the USare tidally-dominated, hence they are highly predictable. • Measurements are obtained for at least 29 days to span an entire lunar month (NOAA uses 35 days to better resolve some constituents) . • For Reference Stations 45 days are needed. • Current speed and direction data are harmonically analyzed, similar to the water levels. Tides and Water Levels for Surveying and Mapping

33. Analysis (not instrument specific) Data are analyzed. • Greenwich Intervals (timing) • Principal directions (ebb and flood) • Harmonic Analysis (Constituents) Tides and Water Levels for Surveying and Mapping

34. Analysis • Predictions are made using the constituents determined by Harmonic Analysis. • Residuals (Observed currents – predicted (tidal currents) = non-tidal components, or residual currents). Tides and Water Levels for Surveying and Mapping

35. Real-time Tides and Water Levels for Surveying and Mapping

36. Special Reports/Products Tides and Water Levels for Surveying and Mapping

37. The main focus for this initial release is to develop a web-based application which will allow users, inside and outside of NOAA, to easily obtain accurate tide predictions in a form which is convenient for use. - Map-based displays and text views for station selection - “On-the-fly” predictions based on harmonic constituents where available - Tabular and graphical displays of tide predictions for a user-specified time interval and datum - Output options which will allow users to import the tide predictions into other tools - Programmatic access to all predictions, constituents and updates via a web services portal

38. COMMERCE & TRANSPORTATION GOAL NATIONAL COASTAL MODELING PROGRAM BENEFITS:Prevents Ship GroundingsIncreases EconomicViability of MarineCargo Shipping Industry9 Operational Forecast ModelsOperability of Models on NCEP HPC Simulated and Forecasted Water Levels and Currents USERS:Navigation Community, Coastal Community, NWS Forecast Offices

39. COMMERCE & TRANSPORTATION GOAL NATIONAL COASTAL MODELING PROGRAM BENEFITS:Prevents Ship GroundingsIncreases EconomicViability of MarineCargo Shipping Industry5 Operational Great Lakes Forecast Models Simulated and Forecasted Great Lakes USERS:Navigation Community, Coastal Community, NWS Forecast Offices, USACE

40. The Use of Numerical Hydrodynamic Models For Predicting Tides and Tidal Currents A major purpose of harmonic tidal analysis is to be able to predict the tide and tidal current, but there are situations where it is better to make such predictions using a numerical hydrodynamic model. Advantages of Using a Numerical Hydrodynamic Model (1) Can provide predictions at hundreds (or thousands) of locations (most where there is no data) -- this is not a great advantage for tides, since the tide regime changes slow enough that one could do reasonably well by linearly interpolating between two nearby tide stations, but -- this is a great advantage for tidal currents, which vary dramatically with distance, both horizontally and vertically. (even using HF radar and towed ADCPs one could not get as detailed description of the tidal current structure as from a high-resolution numerical model)

41. The Use of Numerical Hydrodynamic Models For Predicting Tides and Tidal Currents Advantages of Using a Numerical Hydrodynamic Model (2) Can handle complex dynamic situations where there is rapid spatial change in harmonic constants (for which not enough data could possibly be obtained and analyzed, and which the Tidal Current Tables could not possibly handle) [can use a digital product produced with a numerical model]; For a situation such as in the Strait of Juan de Fuca, San Juan Islands, Strait of Georgia region. Great spatial variation in the diurnal-to-semidiurnal speed ratios in the tidal currents. Would take dozens of reference stations in the Tidal Current Tables to try to handle predictions for this area. K1/M2 tidal current amplitude ratios

42. The Use of Numerical Hydrodynamic Models For Predicting Tides and Tidal Currents • Advantages of Using a Numerical Hydrodynamic Model • (3) Can handle the effect of tide nontidal phenomena (such as river flow and storm surges) • on the tide through nonlinear interaction in shallow water • these nontidal phenomena can modify the harmonic constants during strong events, so that they cannot be used to make tide or tidal current predictions for other time periods (and they are generally not even usable for the time period of the nontidal event, because such events are too short for a reliable harmonic analysis to be done. • A numerical hydrodynamic model can model the tide, the various nontidal phenomena and their interactions, and predict the total water level and the total currents. • If the model includes the appropriate equations for salinity and water temperature, it can also include all the • transient baroclinic effects on the tide and tidal current (such as internal tide waves); it can also include the • gravitational circulation due to salinity gradients up the waterway, another nontidal effect.

43. The Use of Numerical Hydrodynamic Models For Predicting Tides and Tidal Currents • Proper Tidal Forcing of a Numerical Hydrodynamic • Theaccuracy of the predictions inside the waterway from a numerical hydrodynamic model is critically dependent of the forcing at the entrance, • At least one water level station with at least one year’s worth of data for each ocean entrance (two on both sides if the entrance is reasonably wide) • The water level data time series for such a station should be at least a year long in order to be able to use as many tidal constituents as possible in the harmonic analysis; the most recent data should be used (especially in small waterways) in case there have been bathymetric changes which may have affected the tide regime. • The ideal place for an open boundary condition is at a location that will not be affected by the dynamics of the waterway itself; for waterways with deep entrances directly to the ocean, at the entrance may be fine; but for a waterway whose entrance is shallow and connects to a shallow continental shelf, there are likely to be some local hydrodynamic effects, and putting the forced boundary there might not produce as good results asone would like. For this reason, some modelers move the open boundary offshore of the entrance onto the continental shelf. That usually solves the problem of local hydrodynamic effects at the open boundary, but it presents another problem, which can be much worse. Offshore there are unlikely to be any long water level data time series for the points along this new open boundary on the continental shelf, from which accurate harmonic constants can be derived for tide predictions.

44. The Use of Numerical Hydrodynamic Models For Predicting Tides and Tidal Currents • Proper Tidal Forcing of a Numerical Hydrodynamic • -- several approaches to developing a good offshore tidal forcing boundary condition for the numerical hydrodynamic model of a bay or estuary • put several water level measuring devices out on the continental shelf at the locations appropriate for the extended model grid. (bottom pressure sensors or GPS on buoys); • use satellite altimetry data; even though the sampling interval is very large (on the order of a day or more at cross-over points), one can still extract tidal constituents from these data using special least squares techniques; but results have actually been better in the deep ocean compared with over the continental shelves and near the coasts, because of the shorter tidal wavelengths over the shelf, which require better spatial resolution in the data, and there is also less data over the shelves; • use the output from a shelf model. An often-used approach is to use such a model with altimetry data analyzed for the tides. It is also likely be forced with an ocean or global tide model. Another approach is to start with a such a shelf or coastal model and then use some type of data assimilation technique (using the tides predicted from accurate harmonic constants at stations along the coast) to improve the model.

45. Tidal Current Analysis and Predictions • Ingestion • Analysis • Output • Products • Tabular • Real-time

46. Ingestion (ADCP) Data are collected in UTC with magnetic headings (compass is calibrated prior to deployment). • Data are downloaded from the ADCP and uploaded to CO-OPS network. • Data files are then converted from binary to ASCII and compass headings are adjusted to °True.

47. How are Predicted Currents Derived? • Tides and Tidal Currents are predictable because theyare caused by the gravitational forces of the sun and moon, which are thoroughly understood. • The majority of estuarine currents in the USare tidally-dominated, hence they are highly predictable. • Measurements are obtained for at least 29 days to span an entire lunar month (NOAA uses 35 days to better resolve some constituents) . • For Reference Stations 45 days are needed. • Current speed and direction data are harmonically analyzed, similar to the water levels.

48. Analysis (not instrument specific) Data are analyzed. • Greenwich Intervals (timing) • Principal directions (ebb and flood) • Harmonic Analysis (Constituents)

49. Analysis • Predictions are made using the constituents determined by Harmonic Analysis. • Residuals (Observed currents – predicted (tidal currents) = non-tidal components, or residual currents).

50. ProductsTables • Published Annually and required on commercial vessels operating in the U.S. • Areas of coverage: • Atlantic Coast of N. America. • Pacific Coast of N. America. • Each Book is Composed of 5 tables • Reference stations with daily predictions. • Secondary stations with correction to reference stations • Interpolations “Currents at any Time” • Slack Durations • Rotary Stations • Stations are now available online at tidesandcurrents.noaa.gov