tide modelling

Dr. Parluhutan ManurungNational Coordinating Agency for Survey and Mapping (BAKOSURTANAL)

INDONESIA

INTRODUCTION TO TIDE MODELLING

Training Course on Satellite Altimetry and Its ApplicationCibinong, 12-16 October 2009

Outline

• Observed sea level• Mean Sea Level• Tidal Level• Extreme Level• Exercise: Sea Level Processing

Time Varying Sea Level

X (t) = Zo (t) + T (t) + S (t)

• T (t) = Tidal Level

• X (t) = Observed sea level

• Zo (t) = Mean Sea Level

• S (t) = Surge (extreme) Level

Basic Equation of Sea Level

How do we observe?X (t) = Observed sea level

Tsunami December 26th, 2004

Indonesia Tide Gauge Network

Before• 54 stations• 34 analog and 20 digital • Delayed mode communication

After• 90 stations• 10 analog and 80 digital• 57 tsunami capable (real time)• 22 near real time

German Support for InaTEWS

USA/NOAA – IOC/UNESCO Support for InaTEWS

Sea Level Recording

Pressure gauge based on measure of water level column difference

Radar gauge; direct measure to sea surface

Digital float gauge; capable of performing real time data transmission

Graphical float gauge; direct measurement via floating mass

InstrumentationsBasic Concept

Platform Transmission rate

Coverage in Indonesia

Com. direction

PowerConsumption

Cost/yr (USD)

VSAT IP C-band flexible good 2-ways high 6,000

GTS/Meteosat 15’ (5’?) good 1-way low free

BGAN flexible good 2-ways low > 3,000GSM/GPRS flexible none in remote 2-ways low < 400

PSTN flexible none in remote 2-ways low 1000

Radio flexible inter visibility 2-ways high No air time cost

• VSAT is currently the best choice for a real time data transmission and its flexibility to add data transmission of other sensors: GPS and Meteo Sensor

• PASTI/BGAN would be the most preferable if a special rate is available

• Radio requires tower due to inter station visibility

GTS/Meteosat Pasti Radio

Data Communication Options

Database Server

OBSERVATION PROCESSING CENTER DISPLAY

InaTEWS CentreSea Level Centre

VSAT PASTI

GSM

BGAN

GTS

VSAT/VPN IP

InaTEWS Sea Level Data Work Flow

Public Access

Dedicated Access

Station distribution

Data Communication

Real Time Multigraph Display

Zo (t) = Mean Sea Level

• Tidal Datum • Sea level rise due to Global change

Where the sea level refer to?

Tsunami ; an extreme sea level..

Tidal Datum

Chart Datum = Lowest Astronomic Height

Long Term Datum Change

Global sea level rise ~ 10-20 cm for 100 years Semarang

Jepara

Tanjung Priuk

Sorong

T (t) = Tidal Level

• Astronomical Generating Force• Tide Prediction

Tide Generating Force

MoonEarth

Astronomical constellation of Moon, Sun and other planets toward the Earth generating sea tide

Tidal Description

• High Water : a water level maximum (High Tide)• Low Water : A water level minimum (Low Tide)• Mean Tide Level : the mean water level, relative to A reference point , averaged over a long ttime• Tidal Range: High and Low Tide difference• Daily Inequality: two successive low or high tide difference• Spring Tide: the tide following full and new Moon• Neap Tide: the tide following the first and last quarter of the Moon phases

Tide as function of time

Tides produced by the Moon• M2 (semidiurnal Lunar) ½ Lunar

day= 12 H 25 Min• O1 (Diurnal Lunar) 1 Lunar DAY=

12 h 25 min

Tides produced by the Sun• S2 (Semidiurnal Solar) ½ Solar

day= 12• K1 (Diurnal Solar) 1 Solar day=

24

Tidal Types (cont)

F Category

0 - 0.25 Semidiurnal: two high and low waters each day

0.25-1.5 Mixed, mainly semidiurnal two high and low waters each day during most of the time, only one high and low water during neap tides

1.5-3 Mixed, mainly diurnal 1 dominant high and low water per day, 2 high and low waters during spring tide.

>3 Diurnal one high and low water each day

F = (K1 + 01)/(M2 + S2)

Tidal Analysis

• Tides can be represented as the sum of tidal constituents, each has its amplitude, period and phase

• The amplitude, period and phase of each tidal constituent can be extracted from observations by harmonic analysis

• Practical tidal prediction uses more then 60 of tidal constituents derived from 1 year observations

Name DescriptionZ0 Mean Sea Level (MSL)M2 Principal lunar

semidiurnal constituent. S2 Principal solar

semidiurnal constituent.K1 Lunisolar diurnal

constituentO1 Lunar diurnal constituent. N2 Larger lunar elliptic semi

diurnal constituent. K2 Smaller lunar elliptic

semi diurnal constituent.

Harmonic Constants Description

MSM, MM, MSF, MF Long period

ALP1, Q1, SIG1, Q1, RHO1, O1, TAU1,BET1, NO1, CHI1, P1, K1, PHI1, THE1J1, SO1, OO1

,Diurnal

OQ2, EPS2, 2N2, MU2, N2, NU2, M2,MKS2, LDA2, L2, S2, , MSN2, ETA2

Semi diurnal

MO3, M3, SO3, MK3, SK3 Third Diurnal

MN4, M4, SN4, MS4, MK4, S4, SK4 Fourth Diurnal

MK5, SK5 Fifth DiurnalMN6, M6, MS6, MK6, SM6, MSK6 Sixth Diurnal

Harmonic Constants

Major Constants

Tide Prediction

• Quality data time series results in good model• Better identification of error budget

JAKARTA

S (t) = Surge (extreme) level

Tsunami, extreme sea level

• Tsunami; extreme and destructive sea level• Storm surge, other less destructive sea level

Showing Tsunami Signals

• Sea state during tsunami: Sea Level = tide + (atmospheric + current + local factor + tsunami signal)

• Removing tide effect from the record• Need to introduce low pass digital filters• The remaining is approximately turbulence

generated by tsunami• MATLAB Script is written by: Walters, R. A. and Heston,

C., 1982. Removing the tidal-period variations from time-series data using low-pass digital filters. Journal of Physical Oceanography, 12 112-115

• The source is available in:http://woodshole.er.usgs.gov/operations/sea-mat/index.html

Tend to occur at least once in a year

POL Liverpool, 3 December 2008

2004

2005

2006

2007

2008

17 Nov 2008

It happens at least once in a year……

2009

The Latest Tsunami: Manokwari’s Earthquake

3rd January 2009

Exercise: Sea Level Data Processing

Sample of Hourly Tide Data Harmonic Constants after tide data processing

Data Processing

Tide Processing

Graphics of Tide Processing

Tide Prediction

Thanks …..