Coastal Erosion Risks - Beaches. Objectives

Transcription

1 Coastal Erosion Risks - Beaches Risk Management in Civil Engineering, Advanced Course Lisbon, November 21 st, 2008 Objectives To briefly introduce coastal processes governing sediment transport and beach change To discuss coastal erosion, including its main causes and effects, associated with storms, man-made structures and activities, and sea-level rise To review approaches to model the different types of coastal erosion with a risk-based perspective To examine different methods for employing risk-based estimates of coastal erosion in integrated coastal zone planning and management

2 Overview Introduction to coastal processes Coastal sediment transport and erosion at different scales Modeling coastal erosion induced by: Storms (dune erosion and overwash) Man-made structures and activities (shoreline change) Sea level rise (beach profile retreat) Erosion estimates in coastal zone management and planning Concluding remarks Wave Generation and Propagation Superposition of sinusoidal waves Ocean surface C a = Wave Amplitude Ocean wave spectrum Wave properties: H, L, T, dir

3 Wave Statistics Statistical wave measures: Mean wave height ( H ) Significant wave height (H s ): average of the 1/3 highest waves H 10 : average of the 1/10 highest waves H 1 : average of the 1/100 highest waves Statistical wave measures used in different calculation procedures to assess impact. Rayleigh Distribution For narrow-banded sea, consisting of sinusoids (Longuet-Higgins, 1952): 2 ˆ ( ˆ H PH> H) = exp H rms Normal pdf Rayleigh pdf Lord Rayleigh

4 Spectrum of Random Waves Surface elevation time series Spectrum Frequency spectrum Frequency-direction spectrum Wave Transformation and Currents in the Nearshore Nearshore wave transformation: refraction shoaling breaking diffraction reflection Breakwater

5 Longshore Current Long-crested, breaking waves v, = 2.7u sin α cos α lmid m b b Obliquely incident waves generating a longshore current Cross-Shore Currents mass transport undertow ( gd ) (boundary layer streaming) Gives vertical structure to the coastal circulation. Stokes drift (mass transport) Duck, NC

6 Water Level Variations astronomical tides tsunamis seiches wave setup wind setup storm surge climatological variations Water Level Variations mean sea level + tide + surge + runup

7 Wave Run-up Structure Run-up/Overtopping Beach/Dune Processes Hunt s formula: R = tanβ HL o o Time Morphological features Space

8 Characteristics Scales in Sediment Transport and Morphology microscale (sec - min; mm - cm) mesoscale (hr - day; m - km) macroscale (mon - yr; km - 10km) megascale (10yr - 100yr; 10km - 100km) Coastal Sediment Transport Longshore transport:. _... v l.. I l q l c 1 1 = ε VP 1 a ρ ρ gw s.. u m Transport mechanism Coarse sediment Fine sediment

9 Cross-shore shore Transport - Profile Change Profile A Beach shaped by normal wave action t = hours-days Profile B Storm wave attack Profile C After storm, normal wave action rebuilds new berm t = weeks-months Profile D Under normal wave action beach returns to berm profile Longshore Transport - Planform Change Seasons to years

10 Time and Space Scales of Morphological Modeling TIME SCALE MICRO sec-min MESO hr-day MACRO mon-yr MEGA decade-century SPACE SCALE MICRO mm-cm MESO m-km MACRO km-10 km MEGA sub-regional regional Fully 3D Profile Change Schematic 3D Multi-line One-line Analytical Cascade turbulence wind tides coastal currents sea level rise waves seasonal waves and tides wave climate grains scour shoals large-scale ripples bars sand banks morphology change RESPONSE, SPACE FORCING, TIME Mathematical Modeling Procedure formulation evaluation application 1. Process identification 2. Equation selection 3. Numerical technique selection 1. Verification 2. Calibration 3. Validation 4. Sensitivity analysis 5. Uncertainty estimate 1. Analysis 2. Prediction 3. Design

11 Case I: Impact of Storms High waves and water levels may cause: Erosion Overwash Breaching Morphological features such as coastal dunes and barrier islands are particularly exposed. Methods to Predict Dune Response Equilibrium profile theory (Bruun 1962, Kriebel and Dean 1993) Wave impact theory (Fisher and Overton 1984, Nishi and Kraus 1996)

12 Dune Erosion due to Wave Impact Dune Describe average retreat of dune Ds uo, ho us zo Foreshore bf Dune erosion mechanisms: sliding and flowing impact and layer separation notching and slumping rotaional slumping Governing Equations Transport relationship: Δ W = C F E (eroded weight related to wave impact force) Δ W =ΔVρ (1 p) g s (weight of eroded material) F 1 1 u = ρ u h = ρ 2 2 gc 2 o o o 4 o 2 u (impact force, single wave) 1 u F = ρ 2 gc 4 o 2 u Δt T (impact force, many waves)

13 Average transport rate: q D dv = = dt 2 C g T (1 p) 4 1 CE ρ uo u ρs u = u 2gz (front speed of wave) 2 2 o s o 2 u s R = 2g C s 1 C ρ 1 = E 2 2 Cu ρs (1 p) (transport coefficient) dv dt = 4C s ( R z ) 2 T o Coastal Overwash Definition: Overwash is the flow of water and sediment over the crest of the beach that does not directly return to the water body (ocean, sea, bay, or lake) where it originated. Overwash may occur at dunes, barrier islands, and spits.

14 Analytical Model of Overwash Schematize dune or barrier island with a triangular cross section => three parameters to describe the evolution: x o, x B, and s DV B q B DV o Bay b B s bo q o Ocean x s Dx B Dx o x Evolution of the cross section occurs with constant seaward and bayward slopes Sediment Conservation Equations Sediment eroded from wave impact is transported either offshore or over the beach crest (overwash): dv dt o = q + q o B Sediment deposited on the backside due to overwash: dv dt B = q B From geometry: Δ V =Δx s B o o B Δ V =Δx s Δ VD =ΔVB ΔVo 1 VD xb xo s 2 Dune volume: = ( )

15 Analytical Solution Solution (q o and q B assumed constant): 2VDo qot s = 1 l V (dune/barrier height) Do Do q B qt o xo = xoo + ldo q o V Do (seaward beach foot) q B qt o xb = xbo + ldo 1 1 q o VDo (shoreward beach foot) Method for Assessing Probability of Storm Impact Storm impact may be characterized in terms of key morphological parameters such as: eroded volume overwash volume duration of overwash recession distance Classical approach to estimate probability of an impact: Storm with a certain return period yields impact with same return period. But, not one-to-one correspondence. Better approach: simulate long time series of morphological impact and perform statistical analysis (fit theoretical distribution)

16 Model Simulation Objectives: Estimate the statistical properties of subaerial response to storms in terms of dune erosion and overwash. Needed model input System characteristics: dune properties parameter values Forcing data: wave height and period water level (surge + tide) Long-term Data Set Ocean City (MD), United States: Hourly values of waves, water level, and wind (January 1930 December 1999) Beach morphologies high dune (north of Ocean City inlet) low-crested barrier island (northern Assateague Island south of Ocean City inlet)

17 Ocean City Study Site North Fenwick Island Dune height: 2 m Dune foot el.: 3 m Assateague Island Dune height: 2 m Dune foot el.: 1 m Empirical Distribution Functions, Ocean City Eroded volume (m 3 /m) z o = 3.0 m s = 2.0 m Erosion Event Duration (hr) z o = 3.0 m s = 2.0 m Probability of Non-Exceedance Eroded volume (about 20 events/year) Probability of Non-Exceedance Erosion event duration High Dune (north of Ocean City)

18 Empirical Distribution Functions, Ocean City 100 z o = 1.0 m z o =1.0 m Overwash Volume (m 3 /m) 10 1 s = 2.0 m Overwash Event Duration (hr) s = 2.0 m Probability of Non-Exceedance Overwash volume (about 10 events/year) Probability of Non-Exceedance Overwash event duration Low-Crested Barrier (south of Ocean City) Maximum Value of Parameters Significant wave height: 6.2 m (Jan 1938) Water level: 2.1 m (Sep 1960) Surge level: 1.6 m (Sep 1960) Largest overwash events, high dune (calculated): Sep 1933 (29 m 3 /m) Opening of OC inlet Mar 1962 (33 m 3 /m) Ash Wednesday storm Nov 1981 (21 m 3 /m) Oct 1991 (9 m 3 /m) Halloween storm Dec 1992 (30 m 3 /m) Largest events from a combination of factors!

19 Case II: Shoreline Erosion Induced by Structures Detached breakwaters Seawalls and revetments Groins Shore Protection Measures * REVETMENT * BULKHEAD * SEAWALL * DETACHED BREAKWATER * GROIN * PROTECTIVE BEACH * PROTECTIVE DUNES & EARTH DAMS Gradients in longshore transport and shoreline change (erosion) * VEGETATION * SLOPE ADJUSTMENT * PERCHED BEACH Hard and soft measures * COMBINATIONS

20 Shoreline Change Model (one-line model) Q y + DC = 0 x t Q = Q o sin 2α b y α b =αo arctan x Sand continuity equation Sand transport equation Geometric condition DB DC Analytical Solution to Shoreline Change Linearize governing equation: y t =ε s 2 y 2 x ε = s 2Q o D C (diffusion equation) y Accumulation Updrift Groin: Q b = 0 = tan αo x Solution: εt x 2 /4εt x x yxt (, ) = 2 tan αo e erfc 2 π 2 εt

21 Probabilistic Shoreline Evolution Employ a Monte-Carlo simulation approach: 1. Develop input wave time series from measured/hincasted data 2. Simulate shoreline evolution for selected time series 3. Repeat step 1 and 2 a sufficiently large number of times 4. Compute statistical properties of the shoreline response from the N realizations 5. If possible, fit theoretical distributions to probabilistic shoreline response 6. Utilize statistical properties within a coastal management system Case III: Impact of Sea Level Rise Overwash Flooding Erosion

22 Bruun Rule for Erosion due to Sea Level Rise Bruun, 1962 Study Site Objectives: assess the impact of sea level rise on flooding and erosion until 2050 at the Falsterbo Peninsula

23 Measured Water Levels Sea level relative to Mean Sea Level (MSL) between y = x Trend: cm/yr (or 0,006cm/month) Sea level ( cm.) Year data points! Annual High Water Levels (corrected for MSL change) Water level above MSL (cm) Trend = 0.45 cm/yr Antal dagar/år > 21 m/s 35 Uppmätta 30 Trend Year dagar/år 5 Källa: SMHI (1989) År

24 Distribution of Detrended NHW Levels Water Level Rel Trend (cm) Meas - trend -35 Trend (MHV) Year Conditions ? 0.80 P (Annual high > Level) MV = 0.09 SD = Measurements Normal distr NHW Level Rel Trend (cm) Alternative Future MSL Trends: Present or IPCC Sea-level rise (cm) High Mid (Best estimate) Low Present trend (IPCC, 1995)

25 Forecasting to 2050? P (Annual high > Level) trend (50 yrs + MSL) +50 yr trend + gr h eff +25 yr trend + gr h eff Level above present MSL (cm) Forecasting to 2050? P (Annual high > Level) trend (50 yrs + MSL) +50 yr trend + gr h eff +25 yr trend + gr h eff Water level above MSL (cm) Level above present MSL (cm) cm/yr 0.45 cm/yr Year

26 Forecasting to 2050? P (Annual high > Level) trend (50 yrs + MSL) +50 yr trend + gr h eff +25 yr trend + gr h eff Water level above MSL (cm) Year 0.75 cm/yr 0.45 cm/yr Level above present MSL (cm) Sea-level rise (cm) Mid (Best estimate) 36 High Low (IPCC, 1995) Forecasting to 2050? P (Annual high > Level) trend (50 yrs + MSL) +50 yr trend + gr h eff +25 yr trend + gr h eff Water level above MSL (cm) Year 0.75 cm/yr 0.45 cm/yr Level above present MSL (cm) Sea-level rise (cm) Mid (Best estimate) 36 High Low (IPCC, 1995)

27 Digital Elevation Model New Data Based on 18,000 known points (x, y, z) Vertical scale exaggerated to enhance 3D-effekt Digital Elevation Model - Scenarios Flooding of housing areas in Skanör/Falsterbo at ,0 m: 00%

28 Digital Elevation Model - Scenarios Flooding of housing areas in Skanör/Falsterbo at ,5 m: 18%...+2,0 m: 42% Ljunghusen: 4% Concluding Remarks Probabilistic and risk-based approaches are becoming more frequent in coastal erosion studies, but still not common Complex simulation models do not easily permit probabilistic approaches (tendencies are towards the use of such models) Available data series on erosion are typically short and unevenly spaced making it difficult to derive statistical properties through direct analysis Measured/hindcasted wave and water level data typically avaliable that combined with a sediment transport and beach evolution model allows for probabilistic approaches