## Q. 4.5

Given the following information for observed ocean tide levels (semidiurnal) at an established gauge and a new survey site, calculate the sounding datum for the new site.

 Established Gauge 1 (m) New Site Gauge 2 (m) LW 0.5 1.2 HW 3.7 3.6 LW 0.8 1.4 HW 3.6 3.3 LW 0.4 1.0 HW 3.9 3.9 LW 0.7 1.3 MHWS 3.5 – MLWS 0.5 –

## Verified Solution

Following the steps outlined in the section above:

$(OMLW)_{1}$ = (0.5 + 3 × 0.8 + 3 × 0.4 + 0.7)/8 = 0.51
$(OMHW)_{1}$ = (3.7 + 2 × 3.6 + 3.9)/4 = 3.70
$(OMR)_{1}$ = 3.70 − 0.51 = 3.19
$(OMTL)_{1}$ = (3.70 + 0.51)/2 = 2.10
$(TMTL)_{1}$ = (3.5 + 0.5)/2 = 2.00
$(OMLW)_{2}$ = (1.2 + 3 × 1.4 + 3 × 1.0 + 1.3)/8 = 1.21
$(OMHW)_{2}$ = (3.6 + 2 × 3.3 + 3.9)/4 = 3.52
$(OMR)_{2}$ = 2.31
$(OMTL)_{2}$ = 2.36
The correct sounding datum at the new site should be
2.36 − (2.10 − 2.0) − (2.0 × 2.31)/3.19 = 0.81 m.
Had $(TMTL)_{1}$ been unknown the next best estimate would have been
2.36 − (2.10 × 2.31)/3.19 = 0.84 m.