coastal land vs sea level rise

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

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

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)

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

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

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

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

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

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

Model Construction

In Matrix Form

trjicjic tt ,,1

r –average sea

level rise

t – time in years

Model Construction

Figure 3 Land Inundation at r = 1 unit, t

- time

Blue – impacted Peach -

land

Model Construction

Land Area Impacted

Figure 4 Land area impacted as

area of an inclined rectangular

plane

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

iii

y

yxwrL

22

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

iii

y

yxwrL

22

Simulation Results

Figure 6 Anilao Beach Resort, Mabini,

Batangas

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

Simulation Results

Figure 8 Land

Inundation at

m/yr) (0.01mm/year .0102 rYear 2114 1.00 m sea-level rise after

100 years

University of Colorado Sea Level

Research Group

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

Simulation Results

Figure 10 Sea level rise, 0.32 m, 1.00

m, 2.00 m

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

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

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

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 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