Streamflow measurement

1
CE461 Hydrology
Unit 9 Peak Discharge Frequency Analysis
2
Peak Discharge

• Hydrograph plot of discharge Vs time

Peak
Shape
discharge
Volume
time
3
Peak Discharge Design

• From a design perspective, there are several
  types of hydraulic structures that can be
  designed solely on the basis of the peak
  discharge of an associated hydrograph
• Bridges
• Levees
• Open Channels
• Culverts

4
Peak Discharge

• The peak discharge for a given design application
  will always be associated with a given design
  probability (frequency).

Qp f (P)
5
Peak Discharge Determination

• Direct Method (gaged sites)
• Frequency Analysis
• Extrapolation Analysis
• Area Analysis
• Regional Analysis
• Regression Analysis
• Indirect Method
• Design Intensity Method
• Design Storm Method

6
1. Frequency Analysis

• In using frequency analysis, a relationship
  between streamflow and probability (frequency) is
  developed which can then be used to obtain a
  design discharge for an associated design
  probability.

Q
Q
Time
Probability or Frequency
7
Probability
Probability is the measure of how likely an event
is.
The probability of event A is the number of ways
event A can occur divided by the total number of
possible outcomes.
P(A) No. of ways Event A can occur
the total number of possible outcomes
8
Random Variable

• A random variable is a function that assigns a
  number to an event

E3
X ( )
E2
E4
E1
0
9
Random Variable

• A random variable is a parameter (e.g. stream
  flow, rainfall, stage) that cannot be predicted
  with certainty.
• Such variables can either be
• Discrete, or
• Continuous
• Most hydrologic data is continuous and is
  analyzed probabilistically using continuous
  frequency distributions.

10
Random Variables (Discrete and Continuous)
Discrete random variables are used to describe
random phenomena in which only integer values can
occur. Continuous random variables can be used
to describe random phenomena in which the
variable can take on any value in some interval
11
Probability Function

• A probability function is a function that assigns
  a probability to a number

1
P ( ) probability
0
0
12
Probability Distributions
Probability Density Function (pdf) Cumulative
Distribution Function (cdf) The pdf and cdf give
the complete description of the probability
distribution of a random variable.
13
Probability Functions
a
b
1 0
P (a lt q lt b) P2 (b) - P2 (a) p
(q)
CDF Cumulative Density Function
Probability
P2 (Q lt q)
Random Variable q
0
PDF Probability Density Function
Probability Density
b
a
Probability Density Function
Random Variable q
14
Return Interval

• An alternative way to express probability is to
  use the concept of a return interval. If a
  random event (e.g. flood) of magnitude q occurs
  (on average) once in T years, the probability of
  a second random event Q having a magnitude
  greater than the first event may be expressed as

P1(Q gt q) 1/Tq where Tq the return interval q
where P1
complementary cumulative probability function
15
Return Interval (Cont.)

• Mathematically, the return interval Tq may be
  expressed as

Tq 1/ P1(Q gt q) 1/ 1-P2(Q lt
q)
Where Tq is normally expressed in terms of
years, and P2 is a cumulative hydrologic
probability function that yields a value of
probability between 0 and 1 for a given value
of a random variable q (e.g. a stream discharge).