Monte Carlo Simulations for Probabilistic Flood Hazard Assessment

Transcription

1 Monte Carlo Simulations for Probabilistic Flood Hazard Assessment Jemie Dababneh, Ph.D., P.E., 1 and Mark Schwartz, P.E. 1 1 RIZZO Associates, Monroeville, Pennsylvania Presentation to PSA 2017 International Topical Meeting on Probabilistic Safety Assessment and Analysis Pittsburgh, PA; September 24-28,

2 Purpose Illustrate series of calculations involved in a potential uncertainty analysis for flood protection, involving Monte Carlo simulations to evaluate potential levee failure. 2

3 Definitions Probabilistic Flood Hazard Assessment (PFHA) is a tool for quantifying the flood hazard potential probabilistically including an evaluation of uncertainty. Flood Hazard Curves are graphs of peak flow and volume or flood levels versus annual exceedance probabilities (BOR, 2004). - FHC are developed using PFHA. Fragility Curves describe the conditional probability of structure or system failure as a function of load (USACE, 2010). - Fragility curves depend on the FHCs. 3

4 Definitions Aleatory: Able to allocate a cause and describe statistical variability (irreducible). Those uncertainties with a return period Epistemic: Systemic variability, with the statistical variability not described (even if it could be with more data or study). Also known as knowledge-based uncertainty. Those uncertainties that do not have a return period (or are uncertainties within a return period) 4

5 Example : Failure of a Levee A fragility curve indicates the probability of failure of some specified load. What is failure? - First Movement of riprap at the crest of the levee - Catastrophic release This example is provided as an illustration of the PSA for a specific failure mode. 5

6 Proposed Approach For this example, overtopping associated with static water levels and waves, is the failure mode. What are the loads associated with this failure mode? - Significant wave height - Wave period - Freeboard ID Loads & Failure Modes Collect Data Categorize Uncertainties Evaluate Select Models Select Parameters Build Logic Tree Fragility Curves Document & Peer Review 6

7 Consideration of Steps An amalgamation of hydrologic/hydraulic modeling with MCS techniques are utilized in this example to compute flood levels, wave run-up, run-up depths and flow velocities. 7

8 Rainfall NOAA s Atlas 14 is utilized for this illustration example. A normal distribution is assumed for this parameter for simplicity in this illustrative example, with a standard deviations equal to 90% confidence interval/ Data combinations of 10 rainfall recurrence intervals ranging from 1 to 1000 years, and 19 durations ranging from 5 minutes to 6 days. 8

9 9 How certain are you?

10 Hydrologic Model Setup Choice of Models: HEC-HMS, ICPR, FLO-2D 10 SITES Program 100 simulations are made for each combination of rainfall frequency and duration as part of the MCS to determine the frequency associated with runoff rates.

11 Sources of uncertainty in the Rainfall-Runoff Model Map data: - Seasonal conditions - Atmospheric conditions - Land development - Photographic errors and anomalies - Site specific and difficult to quantify - Data processing overlapping/gaps Time of concentration: - Estimated flow path length increases with finer DEM resolution The uncertainty associated with these parameters are considered to be addressed through the uncertainty associated with the parameters developed using the map data (e.g., TOC and CN). 11

12 Basin Parameters Antecedent Moisture Conditions, Accuracy and Resolution of Topography, Accuracy of Calculated Watershed Area, Impact of Roads and Depressions Not Represented, Manning s Roughness, and Runoff Calculation Method. Selection of Alternative Probability Density Functions? 12

13 LOGIC TREE 13

14 Standard Deviation Runoff Through Reach (100 trials/box) 14

15 15

16 Number of Simulations 16

17 Simulated Runoff for 24-hr Rainfall Events with Highest Peak Discharge Simulated Runoff for 1000-yr/24-hr Rainfall Events (A total of 100 of these events are simulated in the Monte Carlo Simulation). 17

18 Hydraulic Model Schematic Sources of uncertainty include TOB elevations which are determined based on the DEM 18

19 Return Water Levels 19

20 Wind Speed L-moments methodology used to estimate probabilities for extreme winds at the site - The following PDFs are selected to approximate the extreme wind distribution: LN, GEV, PIII, and GL. - Data from 4 weather stations covering a period of 59 years. - Goodness of fit values for these distributions are used to weight the estimated mean, 5% and 95% CI. - The maximum wind speeds are compared to the ASCE reported values to evaluate the reasonability of the calculated return period. 20

21 Return Wind speeds L-moment methods used to determine 10-minutes sustained wind speeds 21

22 Waves Equations II-2-36 of Coastal Engineering Manual: significant wave height, friction velocity, drag coefficient Wave run-up, depth of run-up Overtopping Erosion 22

23 Return Period for Significant Wave Height and Wave Period 23

24 Overtopping Erosion Determine flow rates, velocities over the levee. Determine required design rip-rap size to prevent erosion for that velocity. Compare the computed rip-rap size to the actual in-place rip-rap size. If D 50actual > D 50 computed, then levee failure with some overtopping is not anticipated. 24

25 Logic Tree 25

26 Overtopping Erosion Uncertainty in the estimated values of some parameters is considered in the MCS. A total of 5000 trials are included in the MCS for each method of estimating overtopping rates. 26

27 Probability of Failure 27

28 Probability of Levee Failure 28

29 Probability of Levee Failure 29

30 Conclusions Alternative equations and models could be selected. Other failure modes possible Additional refinements could be implemented, decreasing the probability of levee failure 30

31 QUESTIONS 31