How Wrong is Your Flood Model? Bill Syme, Senior Principal, BMT Water & Environment

Transcription

1 How Wrong is Your Flood Model? Bill Syme, Senior Principal, BMT Water & Environment

2 Always! Really Accurate How Accurate is my Model? Sufficiently Accurate Young Modeller (or Salesperson!) Old Modeller Experience

3 Flood Modelling Uncertainties Prime Areas of Uncertainty Accuracy Dependency/Target Rainfall quantity and distribution ±10 or 50+% Historical Record Topography (e.g. Ground elevations) ±5 to 30+% Data Quality Hydrologic (catchment runoff) modelling ±10 to 50% Calibration Level Hydraulic software s mathematical solution ±5 to 100+% Should be <10% Hydraulic model mass/timestep convergence ±0 to 3% Target <1% Hydraulic model mesh size convergence ±0 to 50+% Target <5% Modelling experience/quality ±5 to 50+% Should be <10% Parameters (e.g. Manning s n) ±5 to 20% Calibration Level (Within Industry Standards)

4 Mathematical Solution Solving the Equations!!! Momentum How Velocity changes over time Inertia Term Coriolis Force Gravity Bed Resistance Atmospheric Pressure Turbulence External Forces (Wind ) v t v v + u + v + c x y fu + g h + gv u2 +v 2 u 2 v + 2 v y C 2 H x 2 y 2 + h ρ p y = F y Can solve using different orders of approximation (e.g. 1 st, 2 nd, 3 rd, order)

5 Mathematical Solution What is Order of Approximation? In engineering, orders of approximation refer to how precise an approximation is in increasing order of precision, a zeroth-order approximation, a firstorder approximation, a second-order approximation, and so forth. it is simply the level of precision used to represent quantities not perfectly known

6 Velocity Mathematical Solutions What is Order of Approximation? 1 st Order Error causes numerical diffusion (A rounding or blurring of results) Last Calculation 2 nd Order Time Exact Answer (not known) Why choose 1 st Order? Easier to code Faster More numerically stable Why not 3 rd Order? Not beneficial (for long wave hydraulics)

7 Mathematical Solutions Does Order of Approximation Matter? 1 st Order Can exhibit numerical diffusion (smoothing) causing unnatural energy losses in complex flows Imposes an artificial viscosity 2 nd Order 1 st Order 2 nd Order 2 nd (no Order turbulence Non-Diffusive term) 1 st Order (no turbulence 1 st Order Diffusive term)

8 Mathematical Solutions Does Order of Approximation Matter? 1 st Order Spatial compared with 2 nd Order Spatial 1 st Order typically generates more energy losses and steeper water level gradients ~1.5 m higher in this case Yes, it can matter Only use 1 st Order spatial if consistent with 2 nd Order Well calibrated model

9 Mathematical Solutions What Physical Processes Matter? How Velocity changes over time Inertia Term Coriolis Force Gravity Bed Resistance Atmospheric Pressure Turbulence (Eddy Viscosity) External Forces (Wind ) v t v v + u + v + c x y fu + g h + gv u2 +v 2 u 2 v + 2 v y C 2 H x 2 y 2 + h ρ p y = F y

10 Benchmarking Physical Processes Test Case 6A UK EA 2D Benchmarking Flume model ~3 m wide with 6 gauges measuring water level and velocity Hydraulic jump forms in front of building Eddy shedding downstream of building Jump propagates upstream as flow eases

11 Benchmarking Physical Processes Test Case 6A UK EA 2D Benchmarking Audience Survey Which result is least wrong?

12 Benchmarking Test Case 6A With turbulence (eddy viscosity) Without turbulence (eddy viscosity) Location 1 Location 2 Location 3

13 Benchmarking Physical Processes Test Case 6A UK EA 2D Benchmarking Beware the Pretty Image!

14 Mathematical Solutions Different Solution Method 2 nd Order Implicit Finite Difference compared with 2 nd Order Explicit Finite Volume FD and FV equally accurate Depths within 2% (<0.2m difference in 30m water depth) Well calibrated model Tended to find that 1 st order versus 2 nd order, and missing key physical processes, cause greater differences

15 Mesh Size Convergence

16 Mesh Size Convergence

17 Mesh Size Convergence

18 Mesh Size Convergence

19 Mesh Size Convergence Does it Matter? Sensitivity Test Run for different mesh resolutions, different timesteps Ascertain any dependencies Are these of importance? Look out for the Picasso effect! 1 st order solutions tend to show poorer convergence Yes, it can matter

20 Don t Despair! Me! (circa. 1980s)

21 What Should We Do? 1. Appreciate all models are simplifications of a complex physical process 2. Accept models are wrong, but an accurate model is very useful 3. Understand accuracy dependent on input data (terrain, inflows, etc.) Garbage In, Garbage Out 4. Know that a model developed for one purpose may not be suitable for another 5. Calibrate, Calibrate, Calibrate to historic data

22 Understand How Wrong? Where s the evidence of being right? Input data sufficiently accurate Mathematical solution is appropriate Calibration reproduces reality Parameters are within industry norms If not, something is wrong! How to quantify wrong? Sensitivity Testing Test mesh and timestep convergence Compare with other solutions Levee Breach Model Software A Software B Software C Software A: 1D Solver over a 2D grid Software B & C: 2D 2 nd Order Solvers

23 Conclusion So, models are always wrong Minimise Wrong by ensuring Input data of adequate accuracy for objectives 1 st order spatial solution does not cause unacceptable numerical diffusion test 1 st vs 2 nd Solution accurately reproduces key physical processes Making mesh resolution finer does not unreasonably change results or is accounted for Reducing time-stepping does not change results Should be negligible change Parameters are within industry norms If not, strong indicator something is wrong! Comparing/calibrating to historical events can t stress this enough! Quantify uncertainties by Sensitivity testing and comparing with other solution schemes/approaches And, don t be mislead by a nice looking image or flood map!

24 Thank You Questions? Q A