Stochastic Event Flood Model (SEFM) Stochastic Modeling of Extreme Floods A Hydrological Tool for Analysis of Extreme Floods Mel Schaefer Ph.D. P.E. MGS Engineering Consultants, Inc. Olympia, WA NRC Workshop Probabilistic Flood Hazard Assessment (PFHA) Jan 213 Stochastic Modeling of Extreme Floods PURPOSE Develop Magnitude -Frequency Relationships (Hydrologic Hazard Curves) for: Flood Inflow Discharge (Peak, Max 6-hr, 24-hr, 72-hr, etc) Flood Runoff Volume Maximum Reservoir Level ( primary interest ) Maximum Reservoir Outflow Depth of Overtopping Flows Duration of Spillway Flows exceeding a discharge threshold MGS Engineering Consultants, Inc. 1
Stochastic Modeling of Extreme Floods APPLICATIONS Hydrologic Hazard Curves for Risk Analysis Conduct Global Sensitivity Analysis Assess Conservatism of Proposed PMF Provide Information for Decision Making about: Flood Magnitude-Frequency Seasonality of Floods Reservoir Operations for Floods Advances That Make Stochastic Flood Modeling Possible Increases in Computational Power of PC 2, simulations in 1-hour GIS Spatial Mapping Products and Methods particularly for Precipitation (PRISM) Regional Analysis Methods and L-Moment Statistics for developing basin-specific specific precipitation-frequency relationship including extreme events Long record lengths for precipitation data 35+ years records in mountains (SNOTEL) MGS Engineering Consultants, Inc. 2
History of SEFM Development started in 1996 Used by USBR for Hydrologic Risk Analyses since 1998 Bumping Lake Dam Bumping River, WA A.R. Bowman Dam Crooked River, OR Cle Elum Dam Cle Elum River, WA Keechelus Dam Yakima River, WA Minidoka Dam Snake River, ID Whiskeytown Dam Clear Creek, CA Trinity Dam Trinity River, CA Altus Dam North Fork Red River, OK History of SEFM BC Hydro Mica Dam (787-ft), Upper Columbia River, BC received International Peer Review - 21 US Corps of Engineers Folsom Dam, American River, CA SEFM Accepted by USCOE for Analysis of Extreme Floods and PMF - 25 Puget Sound Energy Baker River Project, Baker River, WA FERC Licensed Project - 29 BC Hydro Campbell River System, Vancouver Island BC 3 Dams in series 1,5-km 2 watershed - 212 MGS Engineering Consultants, Inc. 3
Current Projects 212-213 - SEFM USBR and Southern California Edison Friant Dam and Mammoth Pool Dam, San Joaquin River, CA 6 SCE Dams in Upper Watershed - 1,6-mi 2 watershed BC Hydro Bridge River System, Coastal Mountains, BC 3 dam system - 3,5-km 2 watershed SEFM Primary Deliverable Magnitude-Frequency Curve for Maximum Reservoir Level (Hydrologic Hazard Curve) MA AX RESERVOIR ELEV (ft) 75 745 74 735 73 725 72 715 71 75 7 Extreme Value Type 1 Plotting Paper West Pass Dike 737.77 ft NAVD88 PMF Estimate 739.19 ft NAVD88 Stochastic Model Results Top of Flood Control Pool 727.77 ft NAVD88 Top of Dam 735.77 ft NAVD88 Upper Baker Project Regulated Frequency Curve.5 1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 ANNUAL EXCEEDANCE PROBABILITY 1-9 1-1 Integrates Frequency Information Flood Peak Discharge Runoff Volume Hydrograph Shape Initial Reservoir Level Reservoir Operations while Preserving Seasonality of Events MGS Engineering Consultants, Inc. 4
SEFM Other Outputs Magnitude-Frequency Curves for Flood Discharge -HOUR DISCHARGE (cfs) 72 Thousands 72 66 6 54 48 42 36 3 24 18 12 6 Extreme Value Type 1 Plotting Paper 1-1 1-2 1-3 1-5 ANNUAL EXCEEDANCE PROBABILITY 1-6 Model Outputs for Reservoir Inflow Instantaneous Peak Max 6-hr Discharge Max 24-hr Discharge.5 1-4 Max 72-hr Discharge SEFM Structure SEFM Engine conducts stochastic simulations and many rainfall-runoff runoff and snowmelt computational tasks Watershed Model conventional watershed modeling tasks that were not conducted by SEFM engine; for HEC-1, primarily used as network model for routing of streamflow from sub-basins Post Processor processes watershed model output to develop flood-frequency frequency relationships, stores all simulation inputs and outputs, flood hydrographs, etc MGS Engineering Consultants, Inc. 5
SEFM Operational Modes Completely Deterministic Mode Completely Stochastic Mode Mixed Mode - Some Inputs are Set (Fixed) Other Inputs Treated as Variables (Stochastic) Stochastic Approach GOAL Simulate the hydrologic behavior of the watershed in a manner that provides an unbiased measure of the magnitude-frequency characteristics of floods (looking for reality/truth, not conservative estimates) SEFM draws heavily on the analysis of historical data using regional analysis methods Historical data are analyzed to obtain a better understanding of the actual behavior of the hydrometeorological components to assist in the realistic simulation of floods MGS Engineering Consultants, Inc. 6
Stochastic Approach 1) Use Deterministic Rainfall-Runoff Runoff Model HEC-1,UBCWM, WATFLOOD, (HEC-HMS HMS in future) 2) Treat Hydrometeorological Inputs as Variables 3) Stochastically Generate Multi-Thousand Years of Storms and Dates of Storm Occurrence 4) Select Hydrometeorological Inputs to Accompany Storms and Maintain Seasonal Characteristics and Dependencies Stochastic Approach 5) Compute Multi-Thousand Flood Annual Maxima using Hydrologic Model and Input Datasets Conduct Sufficient Simulations to Exceed Flood Magnitudes of Interest 6) Rank Flood Outputs in Descending Order of Magnitude and Assign Exceedance Probabilities using a Plotting Position Formula 7) Construct Probability-Plots Plots for Flood Characteristics of Interest No Need to Fit a Probability Distribution, Floods Characteristics of Interest Found from Interpolation Not Extrapolation MGS Engineering Consultants, Inc. 7
Stochastic Simulation Storm Related Variables Magnitude of Basin-Average Precipitation (24-hr, 72-hr) PRECIPITATION (in) 72-HOUR 48 Extreme Value Type 1 Plotting Paper 44 American River Watershed 9% Uncertainty Bound 4 36 Best Estimate 32 28 24 2 16 9% Uncertainty Bound 12 8 4.99.9.7.5.3.2.1.4.1 1-3 1-4 ANNUAL EXCEEDANCE PROBABILITY Spatial Distribution of Precipitation over Watershed 1-5 Temporal Distribution of Precipitation over Watershed variable storm duration. HOURLY PRECIPITATION (in) 1.4 1.2 1..8.6.4.2 Friant Watershed Basin-Average Dec 18-27, 1955 Scaled Storm 72-Hour Maxima = 27.-in 72 96 12 144 168 192 ELAPSED TIME (Hours) Stochastic Simulation Hydrometeorological Variables Antecedent Precipitation Spatially Distributed Antecedent Snowpack (spatially distributed snow depth and density) Antecedent Soil-Moisture (spatially distributed by soil type) Freezing Level and Air Temperature Temporal Pattern Initial Streamflow Initial Reservoir Level MGS Engineering Consultants, Inc. 8
Stochastic Simulation Rainfall-Runoff Runoff Modeling Runoff Modeled on Distributed Basis Surface Runoff Response Interflow Runoff Response Snowmelt Runoff Computation includes Snow Water Accounting within Snowpack and Energy-Budget Approach Watershed Model Calibration Watershed Model Calibrated to Historical Floods DISCHARGE (cfs) Folsom Dam 28 Dec 25 - Jan 4, 1997 Observed 24 Simulated 2 16 12 8 4 25 26 27 28 29 3 31 1 2 3 4 5 TIME (Days) 3-DAY DISCHARGE (cfs) Thousands 3 Log-Normal Plotting Paper 2 American River at Folsom Dam 15 NO Upstream Regulation 1 8 6 4 2 1 Systematic Record 195-24 2 Stochastic Flood Model 5 1 2 5 1 RECURRENCE INTERVAL (Years) 2 Stochastic Model Calibrated to Historical Flood-Frequency Frequency Curves at Multiple Durations (24-hr, 72-hr) MGS Engineering Consultants, Inc. 9
Stochastic Simulations Each flood simulation represents an annual maxima flood based on historical behavior of the hydrometeorological inputs and the observed flood response of the watershed Sufficient flood simulations conducted so there is no need to fit a probability distribution to the flood outputs flood-frequency frequency relationship can be depicted via a probability-plot plot Flood simulations reflect flood hazards based on current climatic characteristics effects of climate change can be assessed through sensitivity analysis or uncertainty analysis SEFM Output Primary Outputs are Magnitude-Frequency Curves (Hydrologic Hazard Curves) RES SERVOIR STAGE (Feet) 49 48 47 46 45 44 43 42 41 4 Extreme Value Type 1 Plotting Paper American River at Folsom Dam Top of Flood Control Pool 1997 Flood 1986 Flood ANNUAL EXCEEDANCE PROBABILITY Stochastic Flood Model Curve Extension Method Regulated Frequency Curve.5 1-1 1-2 1-3 1-4 1-5 Hydrologic loading for extreme floods are of primary interest 1-6 MGS Engineering Consultants, Inc. 1
SEFM Example Output Safe Channel Capacity within the Levee System is a Concern in the Sacramento Valley RESERVOIR OUTFLOW (cfs) nds Thousan 15 14 Extreme Value Type 1 Plotting Paper 13 American River at Folsom Dam 12 Regulated Frequency Curve 11 1 Stochastic Flood Model 9 8 Curve Extension Method 7 6 Safe Channel Capacity 115, cfs 5 4 3 2 1.5 1-1 1-2 1-3 1-4 1-5 ANNUAL EXCEEDANCE PROBABILITY Magnitude-Frequency Relationships for Maximum Reservoir Level and Reservoir Discharges are Typically Very Non-Linear - Due to Operations 1-6 SEFM Example Output Strathcona Dam - Vancouver Island BC Various Reservoir Elevations Are Often of Interest for Evaluating Potential Failure Modes MGS Engineering Consultants, Inc. 11
Selected Examples of Interest Watershed Layout for Distributed Rainfall-Runoff Runoff Modeling Seasonality of Storms Precipitation-Frequency Relationships for Watershed Diversity of Temporal Patterns for Storms Distributed Rainfall-Runoff, Runoff, Snowmelt Modeling 11 Zones of Mean Annual Precipitation American River, CA Mean Annual Precipitation varies from 2-inches (zone 1) to 72-inches (zone 11) MGS Engineering Consultants, Inc. 12
Distributed Rainfall-Runoff, Runoff, Snowmelt Modeling American River, CA 9 Elevation Zones Elevation varies from 3-feet (zone 1) to 12,-feet (zone 9) Distributed Rainfall-Runoff, Runoff, Snowmelt Modeling 7 Zones for Describing Soil Characteristics Soil Characterization from NRCS Merged to produce 7 Soil Zones with similar hydrologic characteristics MGS Engineering Consultants, Inc. 13
Distributed Rainfall-Runoff, Runoff, Snowmelt Modeling Hydrologic Runoff Units (HRUs) are polygons of land formed from the intersection of Zones of Mean Annual Precipitation, Elevation and Soil Type 263 unique HRUs in American River Watershed for: Soil moisture accounting Snow-water water accounting Spatial allocation of snowpack Rainfall-runoff modeling Snowmelt modeling Stochastic Hydrometeorological Inputs Seasonality of Storms FREQUENCY.24 21.21.18.15.12.9.6.3. WEST FACE SIERRA MOUNTAINS 4 Storms 72 Hour Duration Storms exceeding 1-year event Historical Storms Normal Distribution SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG MONTH E NUMERICAL STORM DATE American River Watershed 18. Normal Plotting Paper 17. 16. 72-Hour Extreme Storms 15. 14. Normal Distribution 13. 12. 11. 1. 9..1.1.2.5.1.2.3.4.5.6.7.8.9.95.98.99.999 NON-EXCEEDANCE PROBABILITY Studies in western US and British Columbia Show Storm Seasons to be Normally Distributed MGS Engineering Consultants, Inc. 14
Stochastic Hydrometeorological Inputs Magnitude of 72-Hour Precipitation Annual Maxima (in) 72-HOUR PRECIPITATION 48 44 4 36 Extreme Value Type 1 Plotting Paper American River Watershed Best Estimate 9% Uncertainty Bound 32 28 24 2 16 12 9% Uncertainty Bound 8 4.99.9.7.5.3.2.1.4.1 1-3 1-4 1-5 ANNUAL EXCEEDANCE PROBABILITY Precipitation-Frequency for American River Watershed 1,862-mi 2 Slightly More Positive Skew than Extreme Value Type 1 PMP Estimate Revised Dam Goes from Safe to Unsafe? MGS Engineering Consultants, Inc. 15
Large Storms occur on Campbell River Watershed when Moist Inflow Winds are from the East and ESE Orographic Precipitation occurs from Upslope Winds on what is typically the Leeward Mountain Face Duration of Heavy Precipitation dependent upon sustaining moist inflow winds from East and ESE Duration of Upslope Winds is Transient Condition During Storm Passage Result: Large Volume Storms/Floods are Rare for Campbell River Watershed Relative to Windward Face Stochastic Hydrometeorological Inputs Scalable Spatial and Temporal Storm Patterns 72-Hour Precipitation (inches) Hourly Precipitation (in) 1..9.8.7.6.5.4.3.2.1. Dec 28, 1996 - Jan 3, 1997 American River Watershed, CA 12 24 36 48 6 72 84 96 18 12 132 144 156 168 18 192 TIME (hours) Total storm duration not limited to 72-hours Each of 33 sub-basins has a separate temporal pattern, scalable by the selected 72-hour basin-average precipitation MGS Engineering Consultants, Inc. 16
Stochastic Hydrometeorological Inputs Scalable Spatial and Temporal Storm Patterns 72-Hour Precipitation (inches) Hourly Precipitation (in) American River Watershed, CA 1. Feb 12-2, 1986.9.8.7.6.5.4.3.2.1. 12 24 36 48 6 72 84 96 18 12 132 144 156 168 18 192 24 216 TIME (hours) 24 Prototype Temporal and Spatial Templates developed from historical storms observed on the watershed HOURLY PRECIPITATION (m mm) HOURLY PRECIPITATION (mm) 32 28 24 2 16 12 8 4 32 28 24 2 16 12 8 4 Scaled Storm 72-Hour = 5-mm Strathcona Basin Basin-Average Mar 5-14, 1983 Strathcona Basin 5 mm 72 hour precipitation 1: 5, AEP 24 48 72 96 12 144 168 192 216 24 TIME (Hours) Scaled dstorm 72-Hour = 5-mm Strathcona Basin Basin-Average Jan 13-23, 25 24 48 72 96 12 144 168 192 216 24 264 TIME (Hours) Note Diversity: Temporal Patterns Multi Pulse Storms Max Intensities Storm Duration MGS Engineering Consultants, Inc. 17
HOURLY PRECIPI ITATION (mm) Strathcona Basin Basin-Average Oct 2-12,1984 32 Scaled Storm 28 72-Hour Maxima = 5-mm 24 2 16 12 8 4 24 48 72 96 12 144 168 192 216 24 264 288 TIME (Hours) Strathcona Basin Basin-Average Nov 25- Dec 5, 1993 m) HOURLY PRECIPITATION (m 32 Scaled Storm 28 72-Hour Maxima = 5-mm 24 2 16 12 8 4 24 48 72 96 12 144 168 192 216 24 264 288 TIME (Hours) HOURLY PRECIP PITATION (mm) Strathcona Basin Basin-Average Nov 1-7, 26 32 Scaled Storm 28 72-Hour = 5-mm 24 2 16 12 8 4 24 48 72 96 12 144 168 TIME (Hours) Strathcona Basin Basin-Average Nov 1-2, 29 HOURLY PRECIPITATION (m mm) 32 Scaled Storm 28 72-Hour = 5-mm 24 2 16 12 8 4 24 48 72 96 12 144 168 192 216 24 264 TIME (Hours) MGS Engineering Consultants, Inc. 18
HOURLY PRECIP ITATION (mm) HOURLY PRECIPITATION (m mm) Strathcona Basin Basin-Average Nov 11-21, 1995 32 Scaled Storm 28 72-Hour = 5-mm 24 2 16 12 8 4 24 48 72 96 12 144 168 192 216 24 264 TIME (Hours) Strathcona Basin Basin-Average Oct 14-22, 23 32 Scaled Storm 28 72-Hour = 5-mm 24 2 16 12 8 4 24 48 72 96 12 144 168 192 216 TIME (Hours) Diversity of Storm Temporal Patterns Provides for Robust Assessment of Inflow Flood Characteristics and Reservoir Responses Summary SEFM provides a Hydrological Tool for Developing Flood-Frequency Frequency Relationships (Hydrologic Hazard Curves) for Flood Discharges, Runoff Volumes and Maximum Reservoir Level and for Assessing the Annual Exceedance Probability (AEP) of Extreme Floods including IDFs and the PMF MGS Engineering Consultants, Inc. 19
SEFM Description and Examples End-of-Slides MGS Engineering Consultants, Inc. 2