Development of co-tidal model for Gulf of Khambhat, Gujarat

Dr. K.M. Sivakholundu, Dr. B.K. Jena, Mr. J. RajkumarNational Institute of Ocean Technology(Ministry of Earth Sciences, Govt. of India)

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Physical setup & Tidal propagation in Gulf of Khambhat

Amplification of range in GoK

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Stn:1

Stn:9

Instantaneous variation in Water surface elevation [10x10km block at 14:30 26/6/13]

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- 0.4m variation in height within 10km distance may be noted - Applying observed tide for sounding reduction beyond couple of km becomes inappropriate- chart datum definition for large area may be untenable

Observations & limits of modelNIOT observations: 15INCOIS : 9JNPT : 1

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-The model domain is curtailed north of Bhavnagar.- The tidal waveform is no more amenable for harmonic analysis beyond this limit .- More tidal observation along coast and offshore is required to further improve prediction and validation of model.

Observations at MSL and below CD

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Datum connected time trace

Tidal Harmonics

where

(t) : water levelηai : amplitude of constituent iωi : frequency of constituent ifi : phase of constituent iAi(t) : amplitude correction to constituent iFi(t) : phase correction to constituent i

Based on the observations at 15 stations, a minimum of 36 constituents have been obtained.For each of these constituents a theoretical surface was approximated over the model domain using cubic spline interpolation scheme

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Variation of constituents

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User interface

With co-tide program the usage steps are as follows:

- constituents dataset using observations is created

- a surface for amplitude and phase variation over the model domain is approximated

-Using graphical front end, the user can input a location and time span of interest.

- The model synthesizes the tide using the constituents amplitude and phase pertaining to this point

Graphical user interface developed in NIOT (Co-tide) in MATLAB uses an existing open source code (t_tide) at back end. The cubic spline interpolation scheme is adopted after testing other options

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Output options

Longitute : 72.21551724 E Latitute : 20.47867514 N From : 11-May-2013 00:00:00To : 12-May-2013 00:00:00Interval(min): 10Time Zone : IST Interpolation: cubicDatum : MSLNote:-High and Low water level updated below the tide data----------------------------------------------------------Date&Time Tide(m)11-May-2013 00:00:00 0.0511-May-2013 00:10:00 0.1411-May-2013 00:20:00 0.2311-May-2013 00:30:00 0.32----11-May-2013 23:40:00 -0.5211-May-2013 23:50:00 -0.4112-May-2013 00:00:00 -0.31----------------------------------------------------------Date&Time Tide(m) WL11-May-2013 02:50:00 0.99 HWL11-May-2013 09:20:00 -1.85 LWL11-May-2013 15:40:00 2.09 HWL11-May-2013 22:00:00 -1.13 LWL

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Validation   Amplitude(m) Phase(deg)

  Linear Cubic

Nearest neighbor hood Linear Cubic

Nearest neighbor hood

M2 3.29 3.27 3.18 134.13 136.81 129.45

S2 1.19 1.17 1.23 179.46 179.08 176.96

O1 0.29 0.29 0.30 76.13 85.49 73.98

K1 0.65 0.67 0.61 93.65 99.66 95.26

Comparison between interpolation schemes

Observation Vs prediction (cubic spline) 13

Utility of model

Rapid amplification in Gulf of Khambhat renders conventional tidal reduction for sounding error prone. Co-tide model enables surveyor/navigator to predict tide continuously along the track (interpolation in time AND space).

Hydrodynamic models need boundary conditions to be defined with elevation forcing. Existing open ocean models define only astronomical constituents that requires the model domain to be extended upto deep water. Co-tide model can substantially improve such definition for high resolution small domain models. The boundaries can be just sufficient to cover the area of interest –saving in grid size and computational efforts, while avoiding additional bathymetry related issues. Cotide model can provide upto 36 constituents while deep ocean tidal models provide typically 12 or so.

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Thank you 15