Hydrologic Design and Design Storms Readings: Applied Hydrology Sections /18/2005

2 Hydrologic extremes Extreme events – Floods – Droughts Magnitude of extreme events is related to their frequency of occurrence The objective of frequency analysis is to relate the magnitude of events to their frequency of occurrence through probability distribution It is assumed the events (data) are independent and come from identical distribution

3 Hydrologic design Water control – Peak flows, erosion, pollution, etc. Water management – Domestic and industrial use, irrigation, instream flows, etc Tasks – Determine design inflow – Route the design inflow – Find the output check if it is sufficient to meet the demands (for management) Check if the outflow is at safe level (for control)

4 Hydrologic design scale Hydrologic design scale – range in magnitude of the design variable within which a value must be selected Design considerations – Safety – Cost Do not design small structures for large peak values (not cost effective) Do not design large structures for small peak values (unsafe) Balance between safety and cost.

5 Estimated Limiting Value (ELV) Lower limit on design value – 0 Upper limit on design value – ELV ELV – largest magnitude possible for a hydrologic event at a given location, based on the best available hydrologic information. – Length of record – Reliability of information – Accuracy of analysis Probable Maximum Precipitation (PMP) / Probable Maximum Flood (PMF)

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7 TxDOT Recommendations

8 Hydrologic design level Hydrologic design level – magnitude of the hydrologic event to be considered for the design or a structure or project. Three approaches for determining design level – Empirical/probabilistic – Risk analysis – Hydroeconomic analysis

9 Empirical/Probabilitic P(most extreme event of last N years will be exceeded once in next n years) P(largest flood of last N years will be exceeded in n=N years) = 0.5 Drought lasting m years is worst in N year record. What is the probability that a worse drought will occur in next n years? – # sequences of length m in N years = N-m+1 – # sequences of length m in n years = n-m+1

10 Example If the critical drought of the record, as determined from 40 yrs of data, lasted 5 yrs, what is the chance that a more severe drought will occur during the next 20 yrs? Solution: N = 40, m = 5 and n = 20

11 Risk Analysis Uncertainty in hydrology – Inherent - stochastic nature of hydrologic phenomena – Model – approximations in equations – Parameter – estimation of coefficients in equations Consideration of Risk – Structure may fail if event exceeds T–year design magnitude – R = P(event occurs at least once in n years) Natural inherent risk of failure

12 Example Expected life of culvert = 10 yrs Acceptable risk of 10 % for the culvert capacity Find the design return period What is the chance that the culvert designed for an event of 95 yr return period will not have its capacity exceeded for 50 yrs? What is the chance that the culvert designed for an event of 95 yr return period will not have its capacity exceeded for 50 yrs? The risk associated with failure of culvert when the flow exceed 95 yr flood in the next 95 years is: The chance that the capacity will not be exceeded during the next 50 yrs is = 0.59

13 Hydroeconomic Analysis Probability distribution of hydrologic event and damage associated with its occurrence are known As the design period increases, capital cost increases, but the cost associated with expected damages decreases. In hydroeconomic analysis, find return period that has minimum total (capital + damage) cost.

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Beargrass Creek Case Study Description of the Study Area Hydrology & Hydraulics Economic Analysis Project Planning Assessment of the Risk Based Analysis Methodology From “Risk Analysis and Uncertainty in Flood Damage Reduction Studies”, NRC Report:

Beargrass Creek Study Area North Fork Middle Fork South Fork Buechel Br Ohio River 61 mi 2 Drainage Area

Levee on the Ohio River

Pump Station at the Levee (Capacity 7800 cfs!)

Concrete-Lined Channel

Detention Pond Inlet Weir

Beargrass Creek at the Detention Pond Pond Outlet Pipe

Buechel Branch (2.2 miles) South Fork Beargrass Creek (12 miles) Damage Reaches 9 Example Reach SF-9

Beargrass Creek Case Study Description of the Study Area Hydrology & Hydraulics Economic Analysis Project Planning Assessment of the Risk Based Analysis Methodology

Flood Frequency Curve (SF-9) Separate curve for each reach and each plan

Uncertainty in Frequency Curve Reach SF-9, Without Plan Conditions ProbMean (cfs) Mean +2 SD Mean -2 SD Log 10 (SD)

Buechel Branch (61 cross-sects) South Fork Beargrass Creek (202 cross-sects) Water Surface Profiles 9

Uncertainty in Stage-Discharge SD= 0.5 ft at 100 yr flow Constant Reduces prop. to depth

Beargrass Creek Case Study Description of the Study Area Hydrology & Hydraulics Economic Analysis Project Planning Assessment of the Risk Based Analysis Methodology

Computation of Expected Annual Damage (EAD) Stage (H) Discharge (Q) Exceedance Probability (p) Discharge (Q) Stage (H) Damage (D) Exceedance Probability (p) Damage (D)

Damage Categories Single-family residential Multi-family residential Commercial buildings Public buildings Automobiles Cemeteries Traffic disruption Utilities

p=0.999 p=0.1 p=0.01 p=0.002 Structures

Index Location Each damage reach has an index location All structures are assumed to exist there First floor elevation adjusted to reflect the change in location within the reach Rm Rm Rm Index for SF-9 Invert p=0.01 p=0.1 p=0.5

Building Damage Value of the structure, V Value of the contents, C = kV k=V/C, contents to value ratio (~40%) Damage is a function of depth of flooding, expressed as ratio,r(h), of value First Floor Elevation h Depth, hr 1 (h)r 2 (h) 3ft27%35% 6ft40%45%

Uncertainty in Building Damage Value of structure, – SD=10% of V for residential – Commercial distribution described by Value of contents (SD of k in C=kV) Uncertainty in first floor elevation, SD=0.2ft Uncertainty in damage ratios, r(h) First Floor Elevation h

Stage-Damage Curve Multi-family Residential, Reach SF-9

Stage-Damage Curves Each structure is treated individually Stage-damage curve with uncertainty is produced for each damage category for each reach Added together to give the total stage- damage curve for the reach(?)

Beargrass Creek Case Study Description of the Study Area Hydrology & Hydraulics Economic Analysis Project Planning Assessment of the Risk Based Analysis Methodology

Planning Team Three key people: – Planner: formulates project alternatives, works with local sponsor – Hydraulic Engineer: determines discharge and stage data – Economist: estimates damage, costs, benefits and does the risk analysis

Planning Methodology Identify potential project components (detention ponds, levees, …) – 22 initially proposed, 11 on Beargrass Creek, and 11 on Buechel Branch Evaluate them all individually to see if net benefits are positive – 8 components on Buechel Branch eliminated Combine components into plans, incrementally – 10 components in NED plan: 8 detention ponds, 1 floodwall, 1 channel improvement

Buechel Branch Three Plan Development Reaches

Risk of Flooding Establish a target stage at each damage reach index point Find annual probability of exceeding that stage Find reliability of passing design floods Target Stage

Assessment of Engineering Risk Conditional probability – Assumes a particular flood severity Annual probability – Integrates over all flood severities Risk measures actually used – Annual exceedance probability – Conditional nonexceedance probability Target Stage H F(h) 0 1 Nonexceedance probability Exceedance probability

Computation of Engineering Risk Measures from the Stage-Frequency Curve Annual exceedance probability – Find p e for target stage at each Monte Carlo replicate – Get expected value and median of p e values over all simulations – Get long term risk as 1-(1-p e ) n Conditional nonexceedance probability –Find H* for given p* at each replicate –Find % of replicates for which H* < Target stage Q Q* f 2 (H|Q) H* p f 1 (Q|p) p* Q* H p f 3 (H|p) p* H* H pepe Target Stage Q

Beargrass Creek Case Study Description of the Study Area Hydrology & Hydraulics Economic Analysis Project Planning Assessment of the Risk Based Analysis Methodology

Overall Assessment The core methodology is solid and is an advance in engineering practice of flood risk assessment Focus is completely on damage reaches considered as statistically independent entities Whole project risk and 25%,50%,75% damage values cannot be built up this way Can specification of standard deviations of analysis variables be improved?

Beargrass Creek 100 year Flood Plain Map Middle Fork South Fork

Spatial Subdivision of the Region Spatial UnitUsed for Whole River Expected Annual Damage (EAD), Benefit-Cost analysis 3 Main River ReachesIncremental analysis to get NED plan 22 Damage Reaches Basic unit for analysis using HEC-FDA 263 Hydraulic Cross- sections Water surface elevation profile computation 2150 Structures Structure inventory

Whole Project Risk Assessment Take a flood of severity, p, and integrate the damage along the reach – Without any plan (o) – With a plan (w) – Benefit of plan is B = D o - D w Randomize the flood discharge and stage for the whole project rather than for each reach Compute project-based damage values for each randomization and use them to get B 25, B 75 values