11. Flood Frequency Analysis Flashcards
What is ARI?
Average Recurrence Interval:
an annual maximum event has an ARI of T years if on average its magnitude is equalled or exceeded once every T years
What is AEP?
Annual Exceedance Probability:
the probability that the event is equaled or exceeded in any one year
What is the relationship between ARI and AEP
AEP = 1 / ARI = 1 / T
What is the formula for the probability of Q being between values A and B
P(A≤Q≤B) = ∫ p(Q) dQ with upper bound = B & lower bound = A
What is the formula for the probability that Q equals or exceeds X
P(Q≥X) = ∫ p(Q) dQ with upper bound = ∞ & lower bound = X
What is the complement of P?
F(X) = 1 - P(X) F(X) = ∫ p(Q) dQ with upper bound = X & lower bound = 0
What is the Californian formula for AEP, and when should it be used?
AEP = r/N
N: number of years recorded
- used for very large sets of observations
How do you determine the ranking of values?
Rank is in descending order of magnitude i.e. rank 1 corresponds to the highest value
What is the Weibull formula for AEP and when should it be used?
AEP = r / (N+1)
- used when N is not large
In the formulae for AEP, what are the parameters r and N?
r: rank of the magnitude
N: number of years of record
What is the Gringorten formula for AEP and when should it be used?
AEP = (r - a) / (N + 1 - 2å)
where a = 0.44 (Gumbel value)
- used when N is not large
What is the Gumbel value for alpha?
a = 0.44
What is the method of plotting position?
- list flows in descending order and rank from 1 to N
- estimate P(Q≥X) for each X using e.g. Gringorten
- calculate complement F = P(Q<X) = 1 - P(Q≥X)
- plot on probability paper e.g. log normal and plot a straight line
- use fitted line to interpolate and extrapolate data
What are the method of moments and maximum likelihood method used for?
Used to derive fitting parameters when applying PDFs to hydrological data
What is the purpose of the X^2 (chi-squared) method?
To evaluate the ‘goodness’ of fit of a PDF fitted to hydrological data
