Physical oceanography, tides and coastal flooding the science behind it all

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Physical oceanography, tides and coastal flooding
the science behind it all

• Dr Kevin Horsburgh
• Head of the National Tidal and Sea Level Facility
• Physics Teachers Conference
• 26 June 2008

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Proudman Oceanographic Laboratory

• Is a component laboratory of the Natural
  Environment Research Council (NERC), and is based
  in Liverpool
• In partnership with the Met Office, we supply the
  coastal flood forecasts that are used
  operationally for the UK
• POL science helps develop improved coastal
  forecasting systems
• Sea level research
• Shelf sea physics
• Statistics of extremes
• Effect of climate change on extreme sea level
  events
• Wave modelling wave climate research
• Real-time monitoring

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Outline

• Context coastal flood forecasting, operational
  oceanography, real-time marine monitoring
• Physics underlying some key oceanographic
  phenomena
• Forecasting models
• Climate change and its implications
• Sea level rise
• Importance of observations (empiricism)

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• Insurance companies pay about 1 billion annually
  due to coastal flooding
• Without sea defences this figure would rise to
  3.5 billion
• Defences costly! New sea wall at Blackpool cost
  60 m

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• Increased flooding due to sea level rise, or
  larger storm surges and waves due to increased
  storminess, could impact on economic and social
  systems, as well as fragile ecosystems
• An important tool in the management of episodic
  flood events is a reliable forecasting capability
• Improved operational models lead to better risk
  management, and inform high-level policy
  decisions

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North Sea storm surge of 1953
Sea Palling, Norfolk (1 Feb 1953)
Oosterscheldekering (part of Delta works)
Thames Barrier (1987- )
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Components of the UK coastal flood warning system
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Tides

• Tides are one of the most important dynamical
  phenomena in continental shelf seas
• The earliest evidence of knowledge of tidal
  motion dates back to the Indian Vedic period
  (1500 BC)
• The scientific civilizations of the Mediterranean
  didnt know much about the tide we now know
  that this is because the Mediterranean basin
  responds only slightly to the tide generating
  forces
• The English monk Bede was aware of tidal
  behaviour around the Northumbrian coast in 730 AD
  
• Steps towards a proper understanding of tides
  were taken by European scientists in the 16th and
  17th centuries. The key physical law is the Law
  of Universal Gravitation (Newton, 1687)

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The equilibrium tide

• The notion of a tidal bulge of water aligned with
  tidal forces- the equilibrium tide was
  suggested by Newton
• The gravitational pull of the Sun is only 0.46
  that of the moon
• Every fortnight, when the moon is full or new,
  the solar and lunar tides combine to give spring
  tides
• The behaviour of the real ocean is far more
  complicated than this due to land masses,
  friction and inertia

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The harmonic method of prediction

• Practical methods of tide prediction are based on
  the principle (Laplace, 1755) that, for every
  frequency in the equilibrium tide there exits a
  constituent in the real tide with the same
  frequency
• Harmonic analysis finds the amplitude (size) and
  phase (timing) of each constituent
• The tide at any place is the sum of a large
  number of constituents, each of which is
  associated with a distinct (usually astronomical)
  cause
• Tide tables were first produced by precision
  mechanical machines, but are nowadays computed
  rapidly by computer

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Storm surges

• Deviations from predicted tidal heights are
  (largely) due to meteorological effects. A storm
  surge is the effect of the weather on the sea
  surface due to
• atmospheric pressure
• wind stress
• A surge is defined as
• Height of observed sea level - height of
  predicted tide
• Statistical analysis at UK ports shows that tidal
  predictions give
• 90 of HW height to within 20 cm
• 95 of HW times to within 10 minutes
• Residuals (surge) gt 50 cm occur 10 times per
  year

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Images from Katrina
Levee overtopping Bay St Louis
H90,Gulfport, FL
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Surges in Bangladesh
Notable storm surges impacting the coast of
Bangladesh since 1974
Cyclone 02B April 1991

• November 1970 300,000 fatalities
• April 1991 138,000 fatalities

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Dynamics of storm surges

• The response of the sea surface to atmospheric
  pressure can be estimated from the so-called
  inverted barometer effect
• A change in atmospheric pressure of 1 mb
  corresponds to a rise in sea level of about 1 cm.
  During an extreme low, sea level can rise in
  places by up to 0.5 m due to pressure alone
• Sea level rise due to wind effect is inversely
  proportional to the depth. The wind effect is
  most severe in shallow water
• With some typical values for strong winds, sea
  level rise in the southern North Sea due to wind
  alone is 1.5-2.5m

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The equations of motion for fluids

• a.k.a. the momentum equations, the dynamical
  equations or (incorrectly) the Navier-Stokes
  equation.
• Newtons 2nd Law a F/m
• If m 1 (unit mass), then the acceleration on
  this 1 kg parcel of water is simply the sum of
  forces acting on it
• From this simple beginning, some rather complex
  equations can be derived that describe the flow
  of fluids on a rotating Earth
• In the vertical, a simplification leads to the
  hydrostatic approximation
• The oceanographic pressure field is usually in
  hydrostatic balance, but there are exceptions
  (e.g. upwelling, convective overturning, deep
  water formation)

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Alternative forms of these equations

• In the most general case, the friction terms are
  written as gradients of stress
• In real flows, these stresses are the Reynolds
  stresses, and viscous stress due to the fluids
  molecular viscosity can be ignored. The equation
  for the mean flow is then
• Finally, we may choose to parameterise the
  Reynolds stresses using an eddy viscosity
  coefficient and the velocity shear of the main
  flow (by analogy with viscous stress in a
  Newtonian fluid)

F ma
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The Coriolis force

• Newtons Laws apply to an inertial frame of
  reference (subject to no acceleration - fixed
  relative to distant stars).
• Transformation to rotating axes gives rise to an
  apparent force called the Coriolis force which
  causes a deflection to the right of motion in the
  northern hemisphere, and to the left of motion in
  the southern hemisphere (cum sole).
• In the northern hemisphere, northwards movement
  (positive v) contributes acceleration towards the
  east.
• f is called the Coriolis parameter and f 2?
  sin? where ? is the Earths angular rotation
  rate (7.29 x 10-5 rad s-1) and ? is latitude.
  Hence f is maximum at the poles but zero at the
  equator.

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Simple demonstration of the Coriolis force

• Imagine a cannon at the north pole, firing at a
  target to the south. The missile moves in a
  straight line in an inertial frame (obeys
  Newtons 1st Law). The target is moving eastward
  as Earth spins, and the shot appears to veer to
  the right
• Earths spin is a vector quantity. Just like
  velocity it can be resolved into component
  directions. In this case, spin about Earths axis
  is broken up into spin in the local horizontal
  plane and spin normal to this (a rolling action)
• At the poles, all of Earths spin O is in the
  local horizontal plane (around the local vertical
  axis). At the equator, none of it is.

North
?
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Geostrophic flow

• If the flow is steady (i.e. no accelerations) and
  frictional forces can be neglected then the only
  terms in the equations of motion are the pressure
  gradient and the Coriolis force. This is called
  geostrophic balance
• The geostrophic flow is at right angles to the
  pressure gradient. A good example of geostrophic
  flow is the wind above the atmospheric boundary
  layer (where friction is negligible)
• The Gulf Stream is also in geostrophic balance to
  a good approximation, with a sea surface slope
  balancing a geostrophic current. This is
  expressed by the gradient equation, fv g tan?

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North Sea storm surge of 9 November 2007
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Synoptic situation on Friday 9 November 2007
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Real-time data operational model performance
Immingham
Lowestoft
Sheerness
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Clean-up begins after the typhoon that never
wasBy DAVID DERBYSHIRE

• Seawalls were breached at Walcott in Norfolk
• Sea levels around Lowestoft were about 0.7m below
  defences
• Some overtopping around Great Yarmouth

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Comparison with 1 February 1953
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Architecture of the ensemble surge system
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Output from the MOGREPS ensemble surge suite
18Z run on 8/11/08
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Spatial difference between extreme ensemble
member and deterministic forecast
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• On this occasion there was no significant change
  in inundation with the extreme member
• Topography exposes all low-lying areas to risk at
  moderate extreme levels.
• Wherever local topography implies a series of
  critical threshold levels, inundation mapping can
  set multiple warning levels which the ensemble
  system can then target probabalistically

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IPCC WG1 of 4AR (February 2007)
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Effects of climate change on coastal sea level

• When water depth changes, and when also there are
  coupled changes in regional meteorology, there
  will be changes in storm surges, tides, waves and
  extreme water levels
• Most records show evidence for rising mean sea
  levels (MSL) during the past century
• IPCC Fourth Assessment Report (Summary for
  Policymakers) concluded that there has been
  global MSL rise of
• 1.8 ( 0.5) mm/year from tide gauge data
  (1961-2003)
• 3.1 ( 0.7) mm/year from satellite altimetry
  (1993-2003)
• Latest predictions for the decade 2090-2099 from
  a range of numerical models, and excluding rapid
  changes in ice flow, advise a MSL rise of 20-60cm
• These rates will be regionally different due to
  ocean circulations and regional land movements

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Ensemble projections of change in extreme sea
levels
Uncertainty in large scale atmospheric forcing
Run surge model simulations to estimate
uncertainty range in local extreme water levels
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• Annual maximum skew surges and 50-year return
  levels with time-trend (from 5 largest per year)

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MSL Changes in Last 100 Years
Is the rate of rise increasing ? Not clear. On
basis of 20th century tide gauge data alone. Yes.
On basis of altimeter data from the 1990s.
But there is large decadal variability in
all geophysical signals
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Tools for Measuring Sea Level Changes
Tide Gauges Satellite Altimetry
Sea Floor Systems
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The UK National Tide Gauge Network
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Geodetic Tools for Measuring Land Level Changes
GPS
Absolute Gravity

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Current measurement the Acoustic Doppler
Current Profiler (A.D.C.P.)

• Measures currents at all depths by emitting
  acoustic pulses and determining the Doppler shift
  of the return signal reflected by passive
  particles
• ADCPs can be vessel-mounted (looking down), or
  placed on the bed (looking upwards) in a
  recoverable frame.
• The Doppler effect. When an acoustic signal of
  frequency f0 is reflected by a target moving
  relative to the source/receiver, at relative
  speed V, the backscattered signal is frequency
  shifted by an amount ?f 2f0V / c (c
  speed of sound)
• To derive velocity components in the x, y, z
  coordinate directions required, ADCPs have four
  acoustic beams

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Measurement of suspended particulates
Path length

• Suspended particulate material (S.P.M.) can be
  measured with an optical beam transmissometer.
  The attenuation of a beam of light over a known
  path length can be accurately related to S.P.M.
  concentrations (as low as 1 mg/l).
• A 660 nm light source (rapidly absorbed in
  seawater) ensures that sunlight does not
  contaminate the received signal, and eliminates
  attenuation due to gelbstoff.

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Biological measurements - fluorometers

• Fluorometers use the principle of fluorescence to
  estimate the amount of chlorophyll in a volume of
  water.
• Chlorophyll (and other fluorescent materials),
  when excited by a source of light, absorb light
  in one region of the visible spectrum and then
  re-emit a portion of the energy at longer
  wavelengths.
• Chlorophyll is excited by blue light at 455 nm
  and re-emits red light at 685 nm.

455 nm
685 nm
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• The small amount of red light produced by the
  blue light source is blocked by a suitable
  filter, as is any scattered blue light reaching
  the detector.
• A detector (photo-diode) measures the amount of
  fluorescent light emitted
• The estimated concentration of chlorophyll can be
  used as an indicator of phytoplankton biomass.
• Optical properties of phytoplankton are functions
  of size, shape, species and phytoplankton health!

Blue LED
Red-removing filter
Blue-removing filter
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Concluding remarks

• Oceanography is a physical science, and is
  replete with fundamental physics
• Classical mechanics is at the heart of the
  complex computer models used for predicting
  coastal flooding, ocean currents, meteorology and
  climate change
• By refining such models we can provide effective
  coastal flood warning that is so essential to
  protect lives, property and infrastructure
• Uncertainties remain in any forecasting system.
  Their quantification through ensemble forecasting
  and statistical methods is a subject of much
  current research
• All models need validation with accurate,
  repeatable observations. Observation is the
  bedrock of science.
• The precision instrumentation of the
  oceanographer makes use of hydrostatics, optics,
  Doppler effect, electronics, gravity and many
  aspects of the electromagnetic spectrum