In the above presentation of the tideway the vertical scale is -4 to 8 metres ODN (Ordnance Survey Newlyn).
Note that seafarers and boatmen will be used to CD (Chart Datum) which is at about 0m lowest normal tide. (Shown by the short black lines)
But this varies widely on the tideway - so to understand what is happening all the figures are changed to ODN.
There is no horizontal scale! The gauge stations are spaced equally.
The barrier is between Charlton and Silvertown - and the drop between them is the only indication of the barrier state available.
The tidal movement is always right to left (east to west). The high water and low water points are marked.
The high water and low water times are shown.
This next graph shows the maths behind an experimental attempt to find formulae for places above Southend.
The heights relative to Southend are plotted against river flow.
The vertical scale is 0 to 2 metres (above the relative High Water at Southend).
The horizontal scale is the river flow in cubic metres/second.
The straight best fit line through them defines the formula to apply for each place.
Where the line starts on the left is the fixed amount to add to the Southend High Water.
The slope of the line defines a factor which is the effect of the flow.
Each high water at each station relative to the Southend HW is added and changes the results very slightly.
The best fit lines are calculated by LEAST SQUARES REGRESSION METHOD.
This is all on the assumption that the formula is linear. So far it might be!
The variations are probably caused by wind and sudden changes in river flow.