The Storm-Surge Modelling Capabilities ofD-Flow Flexible Mesh

An Assessment Based on Exact Benchmarks

Giordano Lipari

Watermotion | WaterbewegingConsultancy Dissemination Marketing Research

3 November 2015

www.watermotion.eu | www.waterbeweging.nl@hydrodynamics | www.watertu.be

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 1 / 27

Context and Objectives

On Being Right and Doing Right — with Models

Wind moves about water in wondrous ways — We attach value to estimating this innumbers, whether stark or accurate — For analysis, design, etc.How far shall we trust a computer model to quantify such wondrousways?

Choose the Right ToolIssue of scope — A computer model solves for a particular set of equations, e.g.shallow-water typeHow far can these equations explain the whole going?How assertive can we be about our expectations?

Solve the Problem RightIssue of precision — Computer models follow instructions — Hard-coded errors persistDoes the computer program work out the numbers right?

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 2 / 27

Context and Objectives

To Err Is Human. To Persist with Error Is the Work of the Computer

Edward Smith

Errors of Execution — from AviationCommission Do what you ought not — Omission Not do what you ought — SlipsMinor errors — Lapses Distraction, incomplete tasks, omitted steps — MistakesActions conform to an inadequate plan — Violations Deviation from safe procedures,standards or rulesLike aeroplanes, programs ‘explode’, ‘crash’ or fail the scheduled missionErrors in conception, formulation, implementations, etc.

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 3 / 27

Physics | Formalities

Forces → ( Equation → Solution ) → Movement

Shallow-Water Equations → Gauging the DemandsEquations are a written form of force balance — D-Flow FM solves the‘shallow-water’ balance — We restrict the nature of the forces applied to the water!— Results only explain the net motion of the water columns and long wavesWe cannot ask more than this, but can leverage a lot

Shallow-Water Solutions → Grasping the AnswerWater levels and velocity = solution — Variety of basins (shape), forcings (wind,currents, density), fluidity itself — Calculus doesn’t help hack the equations, usealgorithms — The number-crunching burden is shifted to computershow to ensure to stay close to the solution if you don’t know it?

Shallow-Water Benchmarks → Building the TrustNothing is sufficient and all is necessary — Measurements from laboratory and field,not free of error though — Analytical solutions do exist for simplified, specific, notobvious situations — Acid test: the computer recalculates that situationAre the instructions devised and coded to the intended aim?

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 4 / 27

Physics | Solutions

Analytical Solution for Storm Tide Codes

TunablesThe depth and length of a rectangular basin open to the sea — The bed roughness —The wind velocity and front speed — Grid spacing (and time step)Enough to link this up with salt marshes, harbours, marginal seas...

Chosen Benchmarks1. Sudden uniform steady wind – 2. Wind pulse travelling over the basin

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 5 / 27

Physics | Solutions

Analytical Solution for Storm Tide Codes

Partially-open basinOpen sea boundary upwind — Closed wall downwind — Wind blows parallel to thebasin’s side — Expect water raising, oscillations, in- and outflux, etc.

A question of giving and taking...

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 6 / 27

Physics | Solutions

Analytical Solution for Storm Tide Codes

Partially-open basinSobey’s parameters: L = 5000 m — H = 2 m — T = 3-6 h — λ = 10-4 s-1

Discretization: ∆x = 25 m — ∆t = 5 s, Nyquist/Courant compliant — θ = 0No sensitivity analysis

Testing the gridsCartesian (squares) — Triangular (quasi-structured)

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 7 / 27

Benchmarks | Uniform and Steady Wind

1. Sudden Uniform Steady Wind | Time Evolution of Profile

Sobey’s Solution — Side View (← sea | land →) — Wind 25 m/s

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 8 / 27

Benchmarks | Uniform and Steady Wind

1. Sudden Uniform Steady Wind | Water Level at Wall Side

0 5000 10000 15000 20000T [s]

0.0

0.5

1.0

1.5

2.0η/η x

Station x =5000.0 m | ηx = 0.3832 m

0.02

0.01

0.00

0.01

0.02

(N−A

)/η x

Cartesian GridRed Exact solution — Blue dashed D-Flow FM — Grey Residual (secondary axis)

normalized values — scale shown in the plot title

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 9 / 27

Benchmarks | Uniform and Steady Wind

1. Sudden Uniform Steady Wind | Water Level at Wall Side

0 5000 10000 15000 20000T [s]

0.0

0.5

1.0

1.5

2.0η/η x

Station x = 5000.0 m | ηx = 0.3832 m

0.02

0.01

0.00

0.01

0.02

(N−A

)/η x

Triangular GridRed Exact solution — Blue dashed D-Flow FM — Grey Residual (secondary axis)

normalized values — scale shown in the plot title

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 10 / 27

Benchmarks | Uniform and Steady Wind

1. Sudden Uniform Steady Wind | Water Level at Wall Side

Connecting the Dots | Water Levels Around Error Peak

0 10 20 30 40 50

time [s] +2.122e4

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

y [m]

Time Evolution

0.300.350.400.450.500.550.600.650.70

target [m]

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

hit [m]

Scatter Targets v Hits

error [m]

−0.008

−0.006

−0.004

−0.002

0.000

0.002

0.004

0.006

0.008Error Distribution

Situation at time 21245.0 s

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 11 / 27

Benchmarks | Uniform and Steady Wind

1. Sudden Uniform Steady Wind | Water Level at Wall Side

Connecting the Dots | Water Levels Around Error Peak

0 10 20 30 40 50

time [s] +2.122e4

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

y [m]

Time Evolution

0.300.350.400.450.500.550.600.650.70

target [m]

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

hit [m]

Scatter Targets v Hits

error [m]

−0.008

−0.006

−0.004

−0.002

0.000

0.002

0.004

0.006

0.008Error Distribution

Situation at time 21245.0 sGiordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 11 / 27

Benchmarks | Uniform and Steady Wind

1. Sudden Uniform Steady Wind | Velocity at Sea Side

0 5000 10000 15000 20000T [s]

1.0

0.5

0.0

0.5

1.0u/u

x

Station x =0.0 m | ux = 0.8466 m/s

0.02

0.01

0.00

0.01

0.02

(N−A

)/ux

Velocity — Cartesian GridSolid red Exact solution — Dashed green D-Flow FM — Grey Residual (secondary axis)

normalized values — scale shown in the plot title

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 12 / 27

Benchmarks | Uniform and Steady Wind

1. Sudden Uniform Steady Wind | Velocity at Sea Side

0 5000 10000 15000 20000T [s]

1.0

0.5

0.0

0.5

1.0u/u

x

Station x = 0.0 m | ux = 0.8466 m/s

0.02

0.01

0.00

0.01

0.02

(N−A

)/ux

Velocity — Triangular GridSolid red Exact solution — Dashed green D-Flow FM — Grey Residual (secondary axis)

normalized values — scale shown in the plot title

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 13 / 27

Benchmarks | Uniform and Steady Wind

1. Sudden Uniform Steady Wind | Other Probing Stations

0 5000 10000 15000 20000T [s]

1.0

0.5

0.0

0.5

1.0

u/u

x

Station x = 0.0 m | ux = 0.8466 m/s

0.02

0.01

0.00

0.01

0.02

(N−A

)/ux

0 5000 10000 15000 20000T [s]

0.0

0.5

1.0

1.5

2.0

η/η x

Station x = 5000.0 m | ηx = 0.3832 m

0.02

0.01

0.00

0.01

0.02

(N−A

)/η x

0 5000 10000 15000 20000T [s]

1.0

0.5

0.0

0.5

1.0

u/u

x

Station x = 2512.5 m | ux = 0.4212 m/s

0.02

0.01

0.00

0.01

0.02

(N−A

)/ux

0 5000 10000 15000 20000T [s]

0.0

0.5

1.0

1.5

2.0

η/η x

Station x = 2512.5 m | ηx = 0.193 m

0.02

0.01

0.00

0.01

0.02

(N−A

)/η x

Triangular Grid — Checking on propagation of errorsTop left Velocity at the sea boundary — Top right Elevation at the wall

Bottom left Velocity at mid basin — Bottom right Elevation at mid basin

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 14 / 27

Benchmarks | Travelling Wind Pulse

Analytical Solution | Wind Pulse and Squall Lines

Squall Lines

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 15 / 27

Benchmarks | Travelling Wind Pulse

2. Sudden Uniform Steady Wind | Time Evolution of Profile

Sobey’s Solution — Side View (← sea | land →) — Wind 25 m/s, Pulse 5 m/s

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 16 / 27

Benchmarks | Travelling Wind Pulse

2. Wind Pulse and Squall Lines | Comparison at Wall Side

0 2000 4000 6000 8000 10000T [s]

1.0

0.5

0.0

0.5

1.0η/η

Station x = 5000 m | η = 0.3832 m

0.06

0.04

0.02

0.00

0.02

0.04

0.06

(N−A

)/η

Water Level — Cartesian GridRed Exact solution — Blue dashed D-Flow FM — Grey Residual (secondary axis)

normalized values — scale shown in the plot title

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 17 / 27

Benchmarks | Travelling Wind Pulse

2. Wind Pulse and Squall Lines | Comparison at Wall Side

0 2000 4000 6000 8000 10000T [s]

1.0

0.5

0.0

0.5

1.0η/η

Station x = 5000 m | η = 0.3832 m

0.06

0.04

0.02

0.00

0.02

0.04

0.06

(N−A

)/η

Water Level — Triangular GridRed Exact solution — Blue dashed D-Flow FM — Grey Residual (secondary axis)

normalized values — scale shown in the plot title

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 18 / 27

Benchmarks | Travelling Wind Pulse

2. Wind Pulse and Squall Lines | Comparison at Wall Side

Connecting the Dots | Water Levels Around Error Peak

10 20 30 40 50

time [s] +1.062e4

−0.4

−0.3

−0.2

−0.1

0.0

0.1

0.2

0.3

0.4

y [m]

Time Evolution

−0.4−0.3−0.2−0.1 0.0 0.1 0.2 0.3 0.4

target [m]

−0.4

−0.3

−0.2

−0.1

0.0

0.1

0.2

0.3

0.4

hit [m]

Scatter Targets v Hits

error [m]

−0.04

−0.03

−0.02

−0.01

0.00

0.01

0.02

0.03

0.04Error Distribution

Situation at time 10650.0 s

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 19 / 27

Benchmarks | Travelling Wind Pulse

2. Wind Pulse and Squall Lines | Comparison at Wall Side

Connecting the Dots | Water Levels Around Error Peak

10 20 30 40 50

time [s] +1.062e4

−0.4

−0.3

−0.2

−0.1

0.0

0.1

0.2

0.3

0.4

y [m]

Time Evolution

−0.4−0.3−0.2−0.1 0.0 0.1 0.2 0.3 0.4

target [m]

−0.4

−0.3

−0.2

−0.1

0.0

0.1

0.2

0.3

0.4

hit [m]

Scatter Targets v Hits

error [m]

−0.04

−0.03

−0.02

−0.01

0.00

0.01

0.02

0.03

0.04Error Distribution

Situation at time 10650.0 sGiordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 19 / 27

Benchmarks | Travelling Wind Pulse

2. Wind Pulse and Squall Lines | Velocity at Sea Side

0 2000 4000 6000 8000 10000T [s]

1.0

0.5

0.0

0.5

1.0u/u

Station x = 0 m | u = 0.958 m/s

0.06

0.04

0.02

0.00

0.02

0.04

0.06

(N−A

)/u

Velocity — Cartesian GridRed Exact solution — Blue green D-Flow FM — Grey Residual (secondary axis)

normalized values — scale shown in the plot title

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 20 / 27

Benchmarks | Travelling Wind Pulse

2. Wind Pulse and Squall Lines | Velocity at Sea Side

0 2000 4000 6000 8000 10000T [s]

1.0

0.5

0.0

0.5

1.0u/u

Station x = 0 m | u = 0.958 m/s

0.06

0.04

0.02

0.00

0.02

0.04

0.06

(N−A

)/u

Velocity — Triangular GridRed Exact solution — Green dashed D-Flow FM — Grey Residual (secondary axis)

normalized values — scale shown in the plot title

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 21 / 27

Benchmarks | Travelling Wind Pulse

2. Wind Pulse and Squall Lines | Comparison at Sea Side

Connecting the Dots | Velocity Around Error Peak

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 22 / 27

Benchmarks | Travelling Wind Pulse

2. Wind Pulse and Squall Lines | Comparison at Sea Side

Connecting the Dots | Velocity Around Error Peak

10 20 30 40 50

time [s] +9.97e3

−0.5

0.0

0.5

y [m/s]

Time Evolution

−0.5 0.0 0.5

target [m/s]

−0.5

0.0

0.5

hit [m/s]

Scatter Targets v Hits

error [m/s]

−0.08

−0.06

−0.04

−0.02

0.00

0.02

0.04

0.06

0.08Error Distribution

Situation at time 10000.0 s

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 23 / 27

Comparison | Conclusions

Conclusion | Context

Context of the Assessment• Assessment — partial and objective — simplified shallow-water equations

• No advection term — complicative effect, deserves separate attention• Linear friction — little complicative limitation• No Coriolis force — unchallenging limitation• ‘Custom’ wind shear — likes of large-scale storms and squall lines

• Benchmark solution — all but a trivial flow arrangement• Variations in time and space, even rapid ones• Standing-wave behaviour and memory effects• Tunable to have all terms at play• All in all realistic

• Solving algorithms — extensively put to the test• Momentum and mass conservation• Time-marching algorithm — ‘chasing the target’• Boundary conditions — check on spurious reflections• Reproducibility — one edit of source code, of little generality• No imposed diffusion (θ = 0)• 2000-4400 time steps

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 24 / 27

Comparison | Conclusions

Conclusion | Results

Evidence of the Assessment• Residuals

• Probed at relevant output points• Peaks at moment of abrupt changes — expected• Phase difference at moment of abrupt changes — conceivable• Don’t build up or accumulate — desired• Range (well) within 10% for non-trivial values, max order of cm (cm/s)

• Triangular and Cartesian behave similarly• Mostly difference of detail, not of character – no propagation/amplification

• Analysis — see contribution to Validation Document (under revision)

In view of the necessary assumptions, anticipated behaviours and chosensettings . . . subject to the additional consideration of non-linear processesneglected or simplified here . . . the results lend a high degree of confidence thatD-Flow FM can correctly simulate these long-wave component in storm-surgesituations acted on by steady and uniform as well as spatially and rapidlyvariable wind fields.

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 25 / 27

Comparison | Conclusions

Conclusion | Appreciation

PeopleWim van Balen | Arthur van Dam | Erik de Goede | Herman Kernkamp | EdwardMelger | Sander van der Pijl | Rodney Sobey

Computer ToolsFortran | D-Flow FM | LATEX| Python

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 26 / 27

Comparison | Conclusions

Contacts

Watermotion | WaterbewegingRegistered in the Netherlands no. 6105 8998

advancing understandingclarifying targetsdevising solutionsenriching skills

e glnl@ymail.com | OpenPGP public key: 0x2ACD7EDC

m 0031 (0)687 256 643

w www.watermotion.eu | www.waterbeweging.nl

@hydrodynamics

www.watertu.be

Giordano Lipari ( Watermotion | Waterbeweging Consultancy Dissemination Marketing Research)D-Flow FM Wind Validation 3 November 2015 27 / 27