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Coastal Land vs Sea Level Rise An Exercise in Mathematical Modeling
Juan Apolinario ReyesAssistant ProfessorLyceum of the Philippines University Batangas, Lyceum International Maritime AcademyCoastal Land vs Sea Level RiseA Land Inundation Model for Small Communities
Definition of TermsModel (Mathematical Model) a paradigm, a statement that describes interrelationships between objects and events using mathematical structures
Coastal Land land near the coastline not yet impacted by the sea
Definition of TermsCoastal Zone region where the interaction between sea and land processes occur.
Mean Sea Level is the midpoint between average low and average high tides
Sea Level Rise the rise in mean sea level relative to fixed mean sea level measured at a particular area. (Newly, Cornwall, UK between 1915 1921)
Questions of interest:
How much land area will be impacted by rising sea level?
What is the spatial extent of such impact?Coastal Land vs Sea Level RiseA Land Inundation Model
Figure 1 Coastal land
Objectives
To construct a Mathematical Model that estimates estimate the spatial impact of land inundation on a specific coastal land (Anilao Beach Resort) due to sea level rise ( impact: area and visual spatial occupation)To provide a guide by which local communities can develop a localized model for land inundation
AssumptionsAverage sea level rise is 3.2 mm/year (Intergovernmental Panel on Climate Change UN), Commonwealth Scientific and Industrial Research Organization (CSIRO), Average rise in sea level is constant.The model is constructed ceteris paribus
Coastal Land vs Sea Level RiseAn Exercise in Mathematical Modelling
d. The model is sensitive to assumed average sea level rise.
e. The model is sensitive to elevation data. (Shuttle Radar Topography Mission, Google Earth, GPS)
Coastal Land vs Sea Level RiseAn Exercise in Mathematical Modelling
Model ConstructionCompare a coastal land to a matrix whose entries contain the elevation of various points in the land.
Figure 2 Elevation data superimposed as a matrix on a section of coastal land
Model ConstructionDefine the following:x to be the elevation of a point C on the plainr the rate by which average sea level rises each yearThe new elevation of point C after t years is
Model ConstructionIn Matrix Form
r average sea level riset time in years
Model Construction
Figure 3 Land Inundation at r = 1 unit, t - timeBlue impacted Peach - land
Model ConstructionLand Area Impacted
Figure 4 Land area impacted as area of an inclined rectangular plane
Model Construction
L total land arear average sea level risex horizontal distance of the coastline from a fixed point inlandy elevation of a fixed point inlandFigure 5 Land area impacted as area of an inclined rectangular plane
Land Inundation Model
r average sea level riset time in yearsL total land arear average sea level risex horizontal distance of the coastline from a fixed point inlandy elevation of a fixed point inland
Simulation ResultsFigure 6 Anilao Beach Resort, Mabini, Batangas
Simulation ResultsFigure 7 Land Inundation at
Year 2114 0.32 m sea-level rise after 100 years
Simulation ResultsFigure 8 Land Inundation at
Year 2114 1.00 m sea-level rise after 100 yearsUniversity of Colorado Sea Level Research Group
Simulation ResultsFigure 9 Land Inundation at
Year 2114 2.00 m sea-level rise after 100 years
Simulation ResultsFigure 10 Sea level rise, 0.32 m, 1.00 m, 2.00 m
Simulation ResultsAverage Sea-level rise r (meter/year)Land Area Inundated0.003211.57%0.0138.5 %0.0277.00%
Table 1 Land Area Inundated ( %) after 100 years
RecommendationsTransform the mathematical model into one that takes advantage of computing abilities available from GPS and Google Earth
Figure 11 GPS and Google Earth
RecommendationsPartition the Philippine coastline into sub-coastal regions and assign each region to students.
Collect and organize the special projects into one land inundation model for the entire province.
Make Land Inundation Simulation a Special Project to college students majoring in computer science or applied mathematics.
Figure 12 Batangas coastal land
Juan Apolinario ReyesAssistant ProfessorLyceum of the Philippines University Batangas, Lyceum International Maritime Academy
Thank You!Coastal Land vs Sea Level RiseA Land Inundation Model for Small Communities