Development of co-tidal model for Gulf of Khambhat, Gujarat Dr. K.M. Sivakholundu, Dr. B.K. Jena, Mr. J. Rajkumar National Institute of Ocean Technology (Ministry of Earth Sciences, Govt. of India)

Physical setup & Tidal propagation in Gulf of Khambhat

Amplification of range in GoK Stn:9 Amplification of range in GoK Stn:1

Instantaneous variation in Water surface elevation [10x10km block at 14:30 26/6/13] 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 model NIOT observations: 15 INCOIS : 9 JNPT : 1 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

Datum connected time trace

Tidal Harmonics where η(t) : water level ai : amplitude of constituent i ωi : frequency of constituent i fi : phase of constituent i Ai(t) : amplitude correction to constituent i Fi(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

Variation of constituents

User interface 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 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

Output options Longitute : 72.21551724 E Latitute : 20.47867514 N From : 11-May-2013 00:00:00 To : 12-May-2013 00:00:00 Interval(min): 10 Time Zone : IST Interpolation: cubic Datum : MSL Note:-High and Low water level updated below the tide data ---------------------------------------------------------- Date&Time Tide(m) 11-May-2013 00:00:00 0.05 11-May-2013 00:10:00 0.14 11-May-2013 00:20:00 0.23 11-May-2013 00:30:00 0.32 -- 11-May-2013 23:40:00 -0.52 11-May-2013 23:50:00 -0.41 12-May-2013 00:00:00 -0.31 Date&Time Tide(m) WL 11-May-2013 02:50:00 0.99 HWL 11-May-2013 09:20:00 -1.85 LWL 11-May-2013 15:40:00 2.09 HWL 11-May-2013 22:00:00 -1.13 LWL

Validation Comparison between interpolation schemes   Amplitude(m) Phase(deg) 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 0.30 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)

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.

Thank you