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 (