Sea level rise, global warming, mathematical modelling

1. Juan Apolinario Reyes
Assistant Professor
Lyceum of the Philippines University
Batangas, Lyceum International
Maritime Academy
Coastal Land vs Sea Level Rise
A Land Inundation Model for Small
Communities

2. Definition of Terms
Model (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

3. Definition of Terms
Coastal 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)

4. Questions of
interest:
1) How much land
area will be
impacted by
rising sea level?
2) What is the
spatial extent of
such impact?
Coastal Land vs Sea Level Rise
A Land Inundation Model
Figure 1 Coastal
land

5. 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

6. Assumptions
a. Average sea level rise is 3.2 mm/year
(Intergovernmental Panel on Climate
Change UN), Commonwealth Scientific
and Industrial Research Organization
(CSIRO),
b. Average rise in sea level is constant.
c. The model is constructed ceteris
paribus
Coastal Land vs Sea Level Rise
An Exercise in Mathematical
Modelling

7. 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 Rise
An Exercise in Mathematical
Modelling

8. Model Construction
Compare 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

9. Model Construction
Define the following:
• x to be the elevation of a point C on the
plain
• r the rate by which average sea level
rises each year
The new elevation of point C after t years
is trxxt 

10. Model Construction
In Matrix Form
    trjicjic tt  ,,1
r –average sea
level rise
t – time in years

11. Model Construction
Figure 3 Land Inundation at r = 1 unit, t
- time
Blue – impacted Peach -
land

12. Model Construction
Land Area Impacted
Figure 4 Land area impacted as
area of an inclined rectangular
plane

13. Model Construction
L – total land area
r – average sea level rise
x – horizontal distance of
the coastline from a fixed
point inland
y – elevation of a fixed
point inland
Figure 5 Land area
impacted as area of an
inclined rectangular plane



i
ii
i
y
yx
wrL
22

14. Land Inundation Model
    trjicjic tt  ,,1
r –average sea
level rise
t – time in years
L – total land area
r – average sea level rise
x – horizontal distance of
the coastline from a fixed
point inland
y – elevation of a fixed
point inland



i
ii
i
y
yx
wrL
22

15. Simulation Results
Figure 6 Anilao Beach Resort, Mabini,
Batangas

16. Simulation Results
Figure 7 Land
Inundation at
m/yr)(0.0032mm/year.231 r
Year 2114 0.32 m sea-level rise after
100 years

17. Simulation Results
Figure 8 Land
Inundation at
m/yr)(0.01mm/year.0102 r
Year 2114 1.00 m sea-level rise after
100 years
University of Colorado Sea Level
Research Group

18. Simulation Results
Figure 9 Land
Inundation at
m/yr)(0.02mm/year.0203 r
Year 2114 2.00 m sea-level rise after
100 years

19. Simulation Results
Figure 10 Sea level rise, 0.32 m, 1.00
m, 2.00 m

20. Simulation Results
Average Sea-level
rise r (meter/year)
Land Area
Inundated
0.0032 11.57%
0.01 38.5 %
0.02 77.00%
Table 1 Land Area Inundated ( %) after
100 years

21. Recommendations
Transform the mathematical model into
one that takes advantage of computing
abilities available from GPS and Google
Earth
Figure 11 GPS and Google
Earth

22. Recommendations
Partition 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
Make Land Inundation Simulation a Special Project
to college students majoring in computer science or
applied mathematics.
Figure 12 Batangas
coastal land

23. Juan Apolinario Reyes
Assistant Professor
Lyceum of the Philippines University
Batangas, Lyceum International Maritime
Academy
Thank You!
Coastal Land vs Sea Level Rise
A Land Inundation Model for Small
Communities