Tide Modelling
IB Mathematics Standard Level Portfolio Assignment Task I
Tide Modeling
Kelvin Kwok
In this modeling assignment, I will develop a model function for the relationship between time of day and the height of the tide. I will first show the data in a table form copied from the assignment sheet. Then I will use the data to construct a scatter graph of time against height, then I will develop a function that models the behavior noted in the graph analytically, and describe any variables, parameters or constraints for the model. In the end I will modify the same model using the regression feature of graphing software to develop a best-fit function for the data. This modeling task will allow me to find out what is the best time that a good sailor should launch their boat. For all the diagrams, I am using autograph to plot my graphs and find the regression model.
Table 1 below shows the height of tide at different time from 27 December 2003 using Atlantic Standard Time(AST), the heights were taken at Grindstone Island.
Time(AST) | 00.00 | 01.00 | 02.00 | 03.00 | 04.00 | 05.00 | 06.00 | 07.00 | 08.00 | 09.00 | 10.00 | 11.00 | Height(m) | 7.5 | 10.2 | 11.8 | 12.0 | 10.9 | 8.9 | 6.3 | 3.6 | 1.6 | 0.9 | 1.8 | 4.0 |
Time(AST) | 12.00 | 13.00 | 14.00 | 15.00 | 16.00 | 17.00 | 18.00 | 19.00 | 20.00 | 21.00 | 22.00 | 23.00 | Height(m) | 6.9 | 9.7 | 11.6 | 12.3 | 11.6 | 9.9 | 7.3 | 4.5 | 2.1 | 0.7 | 0.8 | 2.4 |
Source: http://www.lau.chs-shc.dfo-mpo.gc.ca
Method 1: Using Autograph, plotted a scattered graph of time against height from the data collected on 27 December 2003
Diagram1 Scatter graph of hours after midnight against height of tide
The data points form a sinusoidal shape, high tide occurred at 03.00 and 15.00 which are 12.0m and 12.3m respectively. And the low tide occurred at 09.00 and 21.00 which are 0.9m and 0.7m respectively. If we look at the two crest(12.0m&12.3m) we can see a period of 12 hours from 03.00 to 15.00,
Tide Modeling
Kelvin Kwok
In this modeling assignment, I will develop a model function for the relationship between time of day and the height of the tide. I will first show the data in a table form copied from the assignment sheet. Then I will use the data to construct a scatter graph of time against height, then I will develop a function that models the behavior noted in the graph analytically, and describe any variables, parameters or constraints for the model. In the end I will modify the same model using the regression feature of graphing software to develop a best-fit function for the data. This modeling task will allow me to find out what is the best time that a good sailor should launch their boat. For all the diagrams, I am using autograph to plot my graphs and find the regression model.
Table 1 below shows the height of tide at different time from 27 December 2003 using Atlantic Standard Time(AST), the heights were taken at Grindstone Island.
Time(AST) | 00.00 | 01.00 | 02.00 | 03.00 | 04.00 | 05.00 | 06.00 | 07.00 | 08.00 | 09.00 | 10.00 | 11.00 | Height(m) | 7.5 | 10.2 | 11.8 | 12.0 | 10.9 | 8.9 | 6.3 | 3.6 | 1.6 | 0.9 | 1.8 | 4.0 |
Time(AST) | 12.00 | 13.00 | 14.00 | 15.00 | 16.00 | 17.00 | 18.00 | 19.00 | 20.00 | 21.00 | 22.00 | 23.00 | Height(m) | 6.9 | 9.7 | 11.6 | 12.3 | 11.6 | 9.9 | 7.3 | 4.5 | 2.1 | 0.7 | 0.8 | 2.4 |
Source: http://www.lau.chs-shc.dfo-mpo.gc.ca
Method 1: Using Autograph, plotted a scattered graph of time against height from the data collected on 27 December 2003
Diagram1 Scatter graph of hours after midnight against height of tide
The data points form a sinusoidal shape, high tide occurred at 03.00 and 15.00 which are 12.0m and 12.3m respectively. And the low tide occurred at 09.00 and 21.00 which are 0.9m and 0.7m respectively. If we look at the two crest(12.0m&12.3m) we can see a period of 12 hours from 03.00 to 15.00,