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Tidal Corrector Application (TCARI)

What is TCARI?

Tidal Constituent And Residual Interpolation (TCARI) is a quick, accurate method of providing tidal corrections to hydrographic data.

What are tidal corrections and why are they necessary?

Tidal corrections are the measure of the differences in the instantaneous water level from mean lower low water (MLLW), the datum* that is used for National Ocean Service (NOS) charts. The difference of the instantaneous water level from MLLW is due to variations in the phase of the astronomic tide, residual (or non-tidal) effects caused primarily by winds and river flows, and to the datum difference between the long-term Mean Sea Level (MSL) and MLLW. Tidal corrections are essential to the hydrographic survey process so that water depths presented on the chart are referenced to the same point.

What is the Coast Survey Development Laboratory (CSDL) doing with TCARI?

The Coast Survey Development Laboratory (CSDL) has created a GUI-driven, user-friendly version of TCARI which went operational in 2008.

How will this GUI-driven, user-friendly version of TCARI work?

TCARI works by separating the astronomic tide, residual, and datum difference components and treating them differently. First, the method spatially interpolates each tidal constituent's amplitude and phase throughout the region, based on data at the water level stations and makes a tidal prediction. The amplitude and phase of constituents at water level stations must have been previously determined by analysis of historical records. This predicted tide is then added to the residual component, which is computed by spatially interpolating the non-tidal values observed at the water level stations at the time of the survey. Finally, the datum offset, or difference between MSL and MLLW based on historical data, is interpolated throughout the region and added to the prediction.

All spatial interpolation is performed by a set of weighting functions. The weighting functions are computed before the survey by creating a grid mesh for the coastal region of interest and acquiring the historical data. As an example, the coastline and tidal station data for mid-Chesapeake Bay has been selected (see Figures 1 and 2), and a grid mesh of triangular elements is generated.


 Figure 1: Water level stations and coastline for central Chesapeake Bay.  Figure 2: Grid mesh for central Chesapeake Bay.
Figure 1: Water level stations and coastline for central Chesapeake Bay. Figure 2: Grid mesh for central Chesapeake Bay.

Next, the weighting functions for the harmonic constants, tidal datums, and the residual are computed. In the field, a prediction of the instantaneous tide, relative to MLLW, is made using the stored weighting function, datum fields, and harmonic constants as well as observed water levels at the tide stations. The predicted value is subtracted from the sounding to give the water depth relative to chart datum of MLLW.

This figure is a color coded picture of upper Upper Chesapeake Bay showing a sample weighting function for harmonic contants. 
 A sample weighting function for harmonic constants.

This is a color coded picture of Chesapeake Bay showing predicted instantaneous water leveling central Chesapeake Bay relative to MLLW. 
Predicted instantaneous water leveling central Chesapeake
Bay relative to MLLW.

*What is a datum? A datum is a reference point on the earth’s surface against which position measurements are made. MLLW and MSL are both examples of vertical datums that reference a point some height above sea level.

Hess, K., R. Schmalz, C. Zervas, and W. Collier, 2004. 'Tidal Constituent and Residual Interpolation (TCARI): A New Method for the Tidal Correction of Bathymetric Data'. NOAA Technical Report NOS CS 4, Silver Spring, MD, 112 pp.
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