Flood Risk Assessment: Flood Frequency Analysis

Question 1

What is a flood frequency curve?

Answer 1

A plot relating peak discharge to a measure of frequency.

Question 2

What are the two key questions flood frequency estimation answers?

Answer 2

1. How rare was that flood?
2. How big a flood should infrastructure be designed for?

Question 3

POT → __
AM (Annual Maxima) → __

Answer 3

• Values over a threshold, more data
• One peak per year, simpler

Question 4

True/False
Annual maxima series includes all floods per year.

Answer 4

False (only the largest)

Question 5

What is the hydrological year start month in the UK?

Answer 5

October

Question 6

If record < 14 years and POT = AM length, use ____ to estimate Q.

Answer 6

POT

Question 7

True/False
Annual maxima should be used if you have long records.

Answer 7

True

Question 8

What are the two rules for independent POT events?

Answer 8

1. Two indepedent peaks must be separated by at least 3× average time to rise
2. The minimun flow between two peaks must be < 2/3 of the first peak

Question 9

If average rise time is 15 hrs, peaks must be ≥ __ hrs apart to be independent.

Answer 9

45 hrs

Question 10

Constructing the Flood Frequency Curve (n large)
Formula :
P(q > qd) ≈

Answer 10

1 − m/n
Where: m = cumulative frequency, n = total samples

Question 11

CDF is obtained by dividing cumulative frequency by __.

Answer 11

sample size (n)

Question 12

Formula
Return period: T =

Answer 12

1 / P(q > qd)

Question 13

What is the probability a 10-year flood does not occur in 1 year?

Answer 13

(1-1/T)^N =>
(1-1/10) = 0.9

Question 14

P(no flood in N years) =

Answer 14

(1 − 1/T)^N

Question 15

P(flood at least once) =

Answer 15

1 − (1 − 1/T)^N

Question 16

Formula
P(x floods in n years) =

Answer 16

nCx · p^x · (1 - p)^(n - x)
Where p = P(q > qd)

Question 17

For POT sampling:
T = _____

Answer 17

(n / t) × 1 / (1 − F(qd))
Where: n = years, t = POT samples

Question 18

If F(qd) = 0.9, t = 40, n = 20, what’s the return period?

Answer 18

5 years

Question 19

What problems arise with small n?

Answer 19

Flat sections between points, P(q > qmax) = 0

Question 20

Why not use P = m/N directly?

Answer 20

Leads to T = ∞ for largest value → physically meaningless

Question 21

True/False
Plotting positions give a continuous probability curve.

Answer 21

False

Question 22

What is a limitation of plotting positions?

Answer 22

• Give discrete estimates not continuous frequency curve
• Cannot extrapolate beyond observed max value

Question 23

What distribution is fitted for flood frequency extrapolation?

Answer 23

The Gumbel distribution (Extreme Value Type I)

Question 24

To estimate floods with return periods longer than your record, you must ______ data.

Answer 24

extrapolate

Question 25

What are possible distributions for extrapolation?

Answer 25

Log-normal, Beta, Gamma

Question 26

What distribution is typically used for extreme floods?

Answer 26

Gumble

Question 27

Transformation Gumbel variate:

Answer 27

z = -ln( -ln[ F(qₐ) ] ) ⇒ qₐ = bz + a

Question 28

What is the Gumbel variate z used for?

Answer 28

It linearises the distribution for regression

Question 29

List the 4 Gumbel parameter estimation methods.

Answer 29

Linear regression, Moment matching, L-moment matching, Maximum likelihood

Question 30

True/False Hydrologists typically prefer maximum likelihood methods.

Answer 30

False (they prefer L-moments)

Question 31

What plotting position formula is used to estimate F(qd)?

Answer 31

Gringorten formula

Question 32

Formula Sample mean:

Answer 32

µ = (1 / N) × Σ qₐ

Question 33

Formula Sample variance:

Answer 33

s² = (1 / (N - 1)) × Σ (qₐ - m)²

Question 34

Why is the L-moment method more robust?

Answer 34

It reduces sensitivity to outliers by avoiding squaring deviations.

Question 35

True/False Outliers can significantly bias Gumbel parameters.

Answer 35

True

Question 36

List 3 checks to ensure data quality before fitting a distribution.

Answer 36

- Inspect time series for errors - Remove serial dependence - Plot fitted CDF and remove outliers

Question 37

What two methods should be used to estimate Gumbel parameters>

Answer 37

Method of moments and L-moments

Question 38

What two approaches help when flow data is scarce?

Answer 38

1. Use regional flood frequency analysis 2. Generate synthetic flow using hydrological models

Question 39

Regional Flood Frequency Analysis Formula

Answer 39

0.0213 × AREA^0.94 × STMFRQ^0.27 × S1085^0.16 × SOIL^1.23 × RSMD^1.03 × (1 + LAKE)^-0.85

Question 40

Regional Flood Frequency Analysis RSMD → S1085 → LAKE →

Answer 40

- wetness index - channel slope - % of catchment routed through lake/reservoir

Question 41

What is the "index flood" in regional analysis?

Answer 41

The median or mean peak flow, used to scale the growth curve.

Question 42

The Flood Estimation Formula

Answer 42

Q_Med = 3.4451 × AREA^0.3062 × SAAR^0.1536 × FARL^0.0460 × BFIHOST^0.8510

Question 43

SAAR → FARL → BFIHOST →

Answer 43

- average annual rainfall - fraction of area through lakes/reservoirs - baseflow index

Question 44

Rainfall frequency is summarised using ______ curves.

Answer 44

Depth-Duration-Frequency (DDF)

Question 45

What two factors define a rainfall event's rarity?

Answer 45

Depth and duration

Question 46

What approach is used when no reliable flow data exist?

Answer 46

Use of historical maximum flood or regional/global datasets

Question 47

Why might L-moment estimates be preferred?

Answer 47

More robust to outliers and better suited for skewed data