Flood Risk Assessment: Flood Frequency Analysis Flashcards
What are the three main learning goals of flood frequency analysis?
Understand its purpose, develop a cumulative distribution function, relate CDF to return period.
What is a flood frequency curve?
A plot relating peak discharge to a measure of frequency.
What are the two key questions flood frequency estimation answers?
- How rare was that flood?
- How big a flood should infrastructure be designed for?
POT → __
AM (Annual Maxima) → __
- Values over a threshold, more data
- One peak per year, simpler
True/False
Annual maxima series includes all floods per year.
False (only the largest)
What is the hydrological year start month in the UK?
October
If record < 14 years and POT = AM length, use ____ to estimate Q.
POT
True/False
Annual maxima should be used if you have long records.
True
What are the two rules for independent POT events?
3× average rise time between peaks and inter-peak minimum < ⅔ first peak
If average rise time is 15 hrs, peaks must be ≥ __ hrs apart to be independent.
45 hrs
Constructing the Flood Frequency Curve (n large)
Formula :
P(q > qd) ≈
1 − m/n
Where: m = cumulative frequency, n = total samples
CDF is obtained by dividing cumulative frequency by __.
sample size (n)
Formula
Return period: T =
1 / P(q > qd)
What is the probability a 10-year flood does not occur in 1 year?
0.9 (1 − 1/10)
P(no flood in N years) =
(1 − 1/T)^N
P(flood at least once) =
1 − (1 − 1/T)^N
Formula
P(x floods in n years) =
nCx · p^x · (1 - p)^(n - x)
Where p = P(q > qd)
For POT sampling:
T = _____
(n / t) × 1 / (1 − F(qd))
Where: n = years, t = POT samples
If F(qd) = 0.9, t = 40, n = 20, what’s the return period?
5 years
What problems arise with small n?
Flat sections between points, P(q > qmax) = 0
Plotting Position Formulas
Formula
Weibull:
Pm(q ≤ qm) = m / (N + 1)
Formula
Gringorten:
Pm(q ≤ qm) = (m − 0.44) / (N + 0.12)
Why not use P = m/N directly?
Leads to T = ∞ for largest value → physically meaningless
True/False
Plotting positions give a continuous probability curve.
False
What is a limitation of plotting positions?
Cannot extrapolate beyond observed max value
What distribution is fitted for flood frequency extrapolation?
The Gumbel distribution (Extreme Value Type I)
To estimate floods with return periods longer than your record, you must ______ data.
extrapolate
What are possible distributions for extrapolation?
Log-normal, Beta, Gamma
What distribution is typically used for extreme floods?
Gumble
Gumbel Distribution Basics
Formula
CDF:
F(qₐ) = exp( -exp( (a - qₐ) / b ) )
Transformation
Gumbel variate:
z = -ln( -ln[ F(qₐ) ] ) ⇒ qₐ = bz + a
What is the Gumbel variate z used for?
It linearises the distribution for regression
List the 4 Gumbel parameter estimation methods.
Linear regression, Moment matching, L-moment matching, Maximum likelihood
True/False
Hydrologists typically prefer maximum likelihood methods.
False (they prefer L-moments)
What plotting position formula is used to estimate F(qd)?
Gringorten formula
Formula
Sample mean:
m = (1 / N) × Σ qₐ
Formula
Sample variance:
s² = (1 / (N - 1)) × Σ (qₐ - m)²
Gumbel Moment Equations
b = (√6 / π) × s
a = m - 0.5772 × b
Why is the L-moment method more robust?
It reduces sensitivity to outliers by avoiding squaring deviations.
True/False
Outliers can significantly bias Gumbel parameters.
True
List 3 checks to ensure data quality before fitting a distribution.
- Inspect time series for errors
- Remove serial dependence
- Plot fitted CDF and remove outliers
What two methods should be used to estimate Gumbel parameters>
Method of moments and L-moments
What two approaches help when flow data is scarce?
- Use regional flood frequency analysis
- Generate synthetic flow using hydrological models
L-Moment Matching
Formula Recall
b = L₂ / ln(2)
a = L₁ − 0.5772 × b
Regional Flood Frequency Analysis
Formula
0.0213 × AREA^0.94 × STMFRQ^0.27 × S1085^0.16 × SOIL^1.23 × RSMD^1.03 × (1 + LAKE)^-0.85
Regional Flood Frequency Analysis
RSMD →
S1085 →
LAKE →
- wetness index
- channel slope
- % of catchment routed through lake/reservoir
What is the “index flood” in regional analysis?
The median or mean peak flow, used to scale the growth curve.
The Flood Estimation
Formula
Q_Med = 3.4451 × AREA^0.3062 × SAAR^0.1536 × FARL^0.0460 × BFIHOST^0.8510
SAAR →
FARL →
BFIHOST →
- average annual rainfall
- fraction of area through lakes/reservoirs
- baseflow index
Rainfall frequency is summarised using ______ curves.
Depth-Duration-Frequency (DDF)
What two factors define a rainfall event’s rarity?
Depth and duration
What approach is used when no reliable flow data exist?
Use of historical maximum flood or regional/global datasets
Why might L-moment estimates be preferred?
More robust to outliers and better suited for skewed data
