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

P(no flood in N years) =

Answer 13

(1 − 1/T)^N

Question 14

P(flood at least once) =

Answer 14

1 − (1 − 1/T)^N

Question 15

Formula
P(x floods in n years) =

Answer 15

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

Question 16

For POT sampling:
T = _____

Answer 16

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

Question 17

What problems arise with small n?

Answer 17

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

Question 18

Why not use P = m/N directly?

Answer 18

Leads to T = ∞ for largest value → physically meaningless

Question 19

True/False
Plotting positions give a continuous probability curve.

Answer 19

False

Question 20

What is a limitation of plotting positions?

Answer 20

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

Question 21

What distribution is fitted for flood frequency extrapolation?

Answer 21

The Gumbel distribution (Extreme Value Type I)

Question 22

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

Answer 22

extrapolate

Question 23

What are possible distributions for extrapolation?

Answer 23

Log-normal, Beta, Gamma

Question 24

What distribution is typically used for extreme floods?

Answer 24

Gumble

Question 25

Transformation Gumbel variate:

Answer 25

z = -ln( -ln[ F(qₐ) ] ) ⇒ qₐ = bz + a

Question 26

What is the Gumbel variate z used for?

Answer 26

It linearises the distribution for regression

Question 27

List the 4 Gumbel parameter estimation methods.

Answer 27

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

Question 28

True/False Hydrologists typically prefer maximum likelihood methods.

Answer 28

False (they prefer L-moments)

Question 29

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

Answer 29

Gringorten formula

Question 30

Formula Sample mean:

Answer 30

µ = (1 / N) × Σ qₐ

Question 31

Formula Sample variance:

Answer 31

s² = (1 / (N - 1)) × Σ (qₐ - µ)²

Question 32

Why is the L-moment method more robust?

Answer 32

It reduces sensitivity to outliers by avoiding squaring deviations.

Question 33

True/False Outliers can significantly bias Gumbel parameters.

Answer 33

True

Question 34

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

Answer 34

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

Question 35

What two methods should be used to estimate Gumbel parameters>

Answer 35

Method of moments and L-moments

Question 36

What two approaches help when flow data is scarce?

Answer 36

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

Question 37

Regional Flood Frequency Analysis RSMD → S1085 → LAKE →

Answer 37

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

Question 38

What is the "index flood" in regional analysis?

Answer 38

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

Question 39

SAAR → FARL → BFIHOST →

Answer 39

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

Question 40

Rainfall frequency is summarised using ______ curves.

Answer 40

Depth-Duration-Frequency (DDF)

Question 41

What two factors define a rainfall event's rarity?

Answer 41

Depth and duration

Question 42

What approach is used when no reliable flow data exist?

Answer 42

Use of historical maximum flood or regional/global datasets

Question 43

Why might L-moment estimates be preferred?

Answer 43

More robust to outliers and better suited for skewed data