Frequency Analysis

Question 1

Name five problems that make discharge information derived from a rating curve
uncertain.

Answer 1

DATA - measurement errors, processing and transcription errors

NATURAL - changes in the channel due to bed movement and weed growth, non-modular flows

RATING CURVE - extrapolation of the rating curve, out of bank flows

HUMAN - changes to the gauging station, flow regulation

Question 2

When is it necessary to re-calibrate a rating curve? Why?

Answer 2

When changing river catchment because different river catchments respond differently to rainfall

Question 3

How is “return period” defined?

Answer 3

the average recurrence interval (average time between occurrences) between events that equal or exceed a specific magnitude.

Question 4

Why is it often difficult to distinguish between variability and trends in hydrological time
series?

Answer 4

Most of our time series are too short for direct calculation of the return periods

Question 5

Name two data series of peak flow that are considered by hydrologists for the frequency analysis.

Answer 5

1) the Annual Maximum series (often called the AMAX series)

2) the Partial Duration or Peaks-over-Threshold series

Question 6

The stage-discharge relationship has to be calibrated, what is used to measure discharge of a river?

Answer 6

ADCP - Acoustic Doppler Current Profiler

Question 7

Frequency analysis is an information problem, what is an information problem?

Answer 7

if one had a sufficiently long record of flood flows, rainfall, or low flows, then a frequency distribution for a site could be precisely determined.

Question 8

What 2 assumptions do we make in frequency analysis?

Answer 8

• We have to assume that no change (e.g. urbanization, climate change) occurs within the period of record.
• In most situations, available data sets are insufficiently long to define the risk of extreme events.

Question 9

For a period of 10yrs+ which data series do we use for peak flow?

Answer 9

For return periods of 10 years and more, the differences are minimal and the annual maximum series is the one most usually analysed.

Question 10

2 strategies for using the random samples of peak flow data

Answer 10

1) graphical/empirical

2) distribution based

Question 11

Why do we use equations such as Weibull or Gringorten to estimate plotting positions?

Answer 11

P(X) is calculated for X, according to a plotting position formula devised to overcome the fact that when N is not large, r/N is not a good estimator of P(X) if X is equaled or exceeded r times in N years.

Question 12

Name three issues that make frequency analysis difficult. (Limitations of FA)

Answer 12

1) as a general rule, frequency analysis should be avoided in estimating frequencies of expected hydrologic events greater than twice the record length.” This general rule is followed rarely because of the regulatory need to estimate the 100-year flood

The problem with extrapolation in frequency analysis can be referred to as the tail wagging the dog. In this case, the “tail” is the annual floods of relatively high frequency (1- to 10-year events), and the “dog” is the estimation of extreme floods needed for design (e.g., the floods of 50-, 100-, or even higher-year return periods). When trying to force data to fit a mathematical distribution, equal weight is given to the low end and high end of the data series when trying to determine high-return-period events.

Question 13

We can use a graphical approach or fit a distribution to an AMAX series to figure out the probability of exceedance. Which method is more reliable? Why?

Answer 13

It is more reliable (and less subjective) to fit a distribution to the data, e.g. Gumbel