2.3.2 Kohno_Storm_Surge_Prediction - Boram LEE

[email protected]. Preliminary reference for ... Expression of storm surges. ▫ Storm tide ... Storm surges are used for expression of the magnitude of ...
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Preliminary reference for the 8th JCOMM/TCP Workshop on Storm Surge and Wave Forecasting

Nairobi, Kenya 19 – 23 /Nov / 2012

An Introduction to Storm Surge Prediction

Nadao Kohno Office of Marine Prediction, Global Environment and Marine Department, JMA [email protected]

Contents Introduction Mechanism

of storm surges Prediction method (storm surge model) Some cases

1. Introduction Definition of storm surges 

 

Abnormal rise of sea level caused by meteorological phenomena (typhoons, hurricanes, cyclones, extratropical cyclones). Sea level changes are caused by strong winds and pressure depressions. From a hydro-dynamical point of view, storm surges are classified to external gravity waves, especially shallow water waves (long waves) as their large horizontal scale, as well as tsunamis.

Expression of storm surges Storm tide Maximum sea level including variation of astronomical tides. Storm tides are used for expression of the magnitude of disasters. Also used for disaster prevention practically. 

observation astronomical tide

storm tide

sea level



storm surge

Storm surge Maximum sea level anomaly from (estimated) astronomical tide. Storm surges are used for expression of the magnitude of phenomena.

time →

Strom surge = maximum anomaly = observed sea level - astronomical tide

An example of storm surge caused by TY BART 400 observation astronomical tide

sea level [ cm ]

300 200 100 0 -100 -200

storm surge [ cm ]

200

100

0

-100 9/23 18:00

9/24 00:00

9/24 06:00

9/24 12:00

9/24 18:00

9/25 00:00

date & time (JST)

The record at Yatsushiro tide station (Kumamoto) and storm surges

The path of TY BART(9918)

2.Mechanism of storm surges Storm surges - caused by developed tropical cyclones etc. What decides the magnitude? a. Inverse Barometer effect b. Wind set-up

a. Inverse Barometer effect The static balance the sea level and the surface pressure pressure depression

ρ : sea water density g

ρg∆h = ∆p ∆h =

∆p 1.0[hPa] = ≅ 1.0[cm] ρg 1.0[g/cm−3 ] × 9.8[m/s−2 ]

1hPa pressure decrease ≒ 1cm sea level rise

Δp

gravity

: gravitational acceleration, Δh : sea level rise, Δp : pressure depression

ρgΔh

Surge Δh

b. Wind set-up Wind force (Stress) to sea Wind stress

τ:wind stress ∝V2 L :fetch (horizontal scale) h :water depth g

∂η τ = ∂x ρh

η =



L 0

τ ρ gh

 ∂η τ  = ρ gh  ∂x dx =

τ ρ gh

− g   

∂η ∂x

τ ρh Gradient force

Surge

η

⋅L

η: ∝V2 (square of wind speed) ∝L (horizontal scale of wind) ∝1/h (inverse of water depth)

Depth h

Horizontal length L

W

wind

τ τx

surge η

τy

Coriolis force f・v current v

wind stress τ

bottom friction y

τbty

water depth h

g・∂η/∂x surface gradient

x

Integrating in x

Balance in x direction : τx ∂η + {fv = g ρh {∂ x Coriolis force {

(1)

surface gradient

surface stress

Balance in y direction : τ y = τ bty τ bty = ρ C w v 2

(2) (3)

from equations (2) and (3) v = ±

τy ρCw

∂η f τx = ± ∂x ρgh g

τy ρCw τy ρCw

   (x − x 0 )  

Comparison of the right two terms: normal component parallel component

≈ ≈

(4)

deleting v with equations (1) and (4)

∂η τx g = ±f ∂x ρh

  f τx τy ± η =  g ρ gh ρC w  { 1 4 2 43  normal to coast parallel to coast

τx ρ gh 1 fh

f g C wτ

ρ

τy ρCw ∝

W h

In condition of h → 0 or large W



wind setup >> Ekman pumping

τx ⋅L ρgh sea level change ∝ wind stress・L / h ∝ V2 ・L / h η=

Sea bathymetry of Afreca (NGDC ETOPO2 data)

Shallow water areas are vulnerable to storm surges.

Another factors influence of astronomical tide  Ocean waves (wave set-up, wave run-up)  river flows 

Influence of astronomical tide Storm tide the high tide of the spring tide is dangerous



The low tide of the neap tide might be also notable (water level does not fall in neap tide) Spring tide

Spring tide Neap tide

Neap tide

Wave set-up

Estimation of wave set-up 04UTC 20/Oct/2004





wave set-up occurs at beaches, within several hundreds meters from land. (The ‘sub-grid’ scale phenomena) The parameterized estimation way, which considers offshore wave heights, sea topography etc, is now under development

river flows In estuary part, river flow also enlarges surges

Prediction method (storm surge model) Non divergent Navier–Stokes equation without viscousity. Coriolis force and gravity are included. Equations of motion ∂u ∂u ∂u ∂u 1 ∂P 1 ∂τ x + u + v + w − fv = − + ∂t ∂x ∂y ∂z ρ 0 ∂x ρ 0 ∂z ∂v ∂v ∂v ∂v 1 ∂P 1 ∂τ y + u + v + w + fu = − + ∂t ∂x ∂y ∂z ρ 0 ∂y ρ 0 ∂z ∂w ∂w ∂w ∂w 1 ∂P +u +v +w =− −g ∂t ∂x ∂y ∂z ρ 0 ∂z

Continuity equation ∂u ∂v ∂w + + =0 ∂x ∂y ∂z

(x, y), z: horizontal / vertical directions (u, v), w: velocity components P: pressure, ρ0: density, τ:stress, f : Coriolis parameter, g: gravitational acceleration.

simplification We often use 2 dimensional vertically integrated model. (For further simplicity, linearized version is also used.)

Equations of motion ∂M ∂ 2 ∂ 1 h ∂P 1 + u + uv − fN = − ∫z =− D dz + (τ sx − τ bx ) ρ0 ρ0 ∂t ∂x ∂y ∂x ∂N ∂ ∂ 1 h ∂P 1 + uv + v 2 + fM = − ∫z =− D dz + (τ sx − τ by ) ∂t ∂x ∂y ∂y ρ0 ρ0

Continuity equation ∂h ∂M ∂N + + =0 ∂t ∂x ∂y

where M ≡ ∫z =− D udz , N ≡ ∫z =− D vdz , h

h

∂ 2 ∂ h 2 ∂ ∂ h u ≡ ∫z =− D u dz , uv ≡ ∫z =− D uvdz ,Λ ∂x ∂x ∂y ∂y

Stresses at the surface and bottom τ s = (τsx, τsy ) = ρair Cd W (Wx, Wy )   τ b = (τbx, τby ) = ρwater Cdw V (u , v) τs :surface stress, τb :bottom stress, W : wind speed, V : current speed Cd, Cdw : drag coefficients (2.5~3.5×10-3)

Meteorological conditions Pressure profiles (some formulae) P −P Fujita P(r ) = P − ∞

Myers

c

1 + (r / r0 ) 2



P(r) = Pc + (P∞ − Pc ) ⋅ exp(− r0 r )

Pc;central pressure, P∞ ;circumstantial pressure, r0;radius of gale wind

Gradient wind relation 1 ∂P v2 − − fv = − r ρ ∂r

Estimated wind field     1   



 r   W = C V g + C ⋅ exp  − π   re   

Case studies 

Typhoon Chaba in 2004  storm



Typhoon Tokage in 2004  large



storm surge by wave set-up in Japan

Hurricane Katrina in 2005  large



surge occurred in Seto Inland Sea

storm surge in USA

Cyclone Nargis in 2008  large

storm surge in Myanmer

The best track of Typhoon Chaba(0416)

Disaster by Ty Chaba 14(3)

The dead The causality

serious

35(0)

slight

232(6)

The injured Razed

29(1)

partially damaged

95(8)

The houses inundation

The loss

above floor

16,799 (8,393)

blow floor

29,767 (13,424) \10,540,000,000

(Fire and Disaster Management Agency) ※The values in ( ) are those in Kagawa Prefecture, where Takamatsu City is located.

Storm tides observed

The observed sea levels: solid line The astronomical tide: broken line The arrows show the time of the minimum surface pressure.

Sea topography in the Seto Inland Sea

Simulated storm surge

Storm surge and wave by Ty Tokage(2004)

Nabae beach (Kochi)

Typhoon track

The Max wave (obs) death Broken houses

> 13m 3 5

Observed tide level Kochi 250

350 300 250 200 150 100 50 0

tide level (cm)

tide level (cm)

Murotomisaki

200 150 100 50 0

18

19

20

21

18

22

19

20

Shirahama

storm surge (cm)

tide level (cm)

200 150 100 50 0 20

21

22

200

250

19

22

day

day

18

21

21

22

150 100 50 0 -50 18

19

day

20

day Murotomisaki

Kochi

Shirahama

Simulated storm surge

Simulation to observed storm surge Shirahama

100 80 60 40 20 0 -20

storm surge(cm)

storm surge(cm)

Kochi

obs cal

18

19

20

21

22

100 80 60 40 20 0 -20

obs cal

18

19

20

day

22

day Murotomisaki

Murotomisaki 200

200 150 100

obs cal

50 0

storm surges(cm)

storm surge(cm)

21

150 100 50 0 -50

-50 18

19

20

21

22

19

20

21

22

day

day obs

cal

invers barometric

wind setup

Simulated ocean wave condition

Comparison of calculation errors to waves

6

12

18

0

6

12

14 12 10 8 6 4 2 0

70 60 50 40 30 20 10 0 0

18

6

12

18

wave height(cal)

error

wave height(obs)

15

100

10

50

5

0

0 12

18

0

6

12

18

errors(cm)

150

6

wave height(cal)

18

wave height

120 100 80 60 40 20 0

30 25 20 15 10 5 0 0

hour(UTC) error

12

Murotomisaki

Wave Heights(m)

errors(cm)

Murotomisaki

0

6

hour(UTC)

hour(UTC) error

0

6

12

18

0

6

12

18

hour(UTC)

wave height(obs)

error

wave period(cal)

wave period(obs)

Wave period(s)

0

errors(cm)

14 12 10 8 6 4 2 0

Wave Heights(m)

errors(cm)

60 50 40 30 20 10 0

Wave Heights(m)

Shirahama

Kochi

Storm Surge by Hurricane Katrina in 2005

Track and intensity of Katrina

Storm surges and inundation  

The wide range of beach area is quite shallow. NA is located in low land and the estuary part of the Mississippi River.

Sea topography (NGDC ETOPO2 data)

Central part of the Gulf of Mexico

The water depth along the coast is shallow (