1. Hydrology and Precipitation (a review and application)
CEE 6/5460
David Rosenberg

2. Learning Objectives
Identify hydrologic cycle components and equations important to manage storm water
Infer the appropriate rainfall intensity and hytograph from a depth-duration-frequency chart
Recall basic probability principles
Calculate the risk of a detention basin overtopping during it’s design life
CEE 6/5460 – Water Resources Engineering

3. 1. Key components of the hydrologic cycle

4. Which components are important to engineers designing storm water systems?

5. 1. Hydrologic cycle (cont.)
 How do we quantify flow through cycle components?
CEE 6/5460 – Water Resources Engineering

6. 2. Precipitation

7. Time-series of daily precipitation at USU

8. Precipitation intensity
The rate at which rain or snow occurs [L/T]
What rainfall intensity should we use?
Depends on the storm duration and precipitation
Likelihood of the event
Often specified in design criteria
Read depth from a rainfall depth-duration-frequency curve
Intensity (i) = depth / duration
CEE 6/5460 – Water Resources Engineering

9. Precipitation Depth-Duration-Frequency Curves for Layton, UT
Source: NOAA, 2008,

10. Rainfall intensity (cont.)
Example 1. What is the expected rainfall intensity of a 3-hour storm with a 10-year recurrence interval?
Example 2. Draw the hourly storm hytograph (intensity versus time).
CEE 6/5460 – Water Resources Engineering

11. 4. Probabilities Purpose Basic properties
To quantify and represent uncertainty in an uncertain world
Basic properties
0 ≤ pi ≤ 1, for all possible outcomes i
Probability of jointly occurring independent events
P(A∩B) = P(A) P(B) (product rule; intersection)
What do probabilities represent?
Relative frequency of outcomes (repeatable events) C A B
CEE 6/5460 – Water Resources Engineering

12. 4. Probabilities (cont.) Return Period (T) Reliability Risk
Expected time T to wait for the next event size Q or larger [years]
Probability that event Q will occur in any year = P(0) = 1/T
Reliability
Probability that a design/structure will safely pass
Probability that structure will not fail (no catastrophic event Qs)
Probability that Q will NOT occur over an n-year period
Probability that Q will NOT occur in any year = 1 – P(0) = 1 – 1/T
Probability that Q will not occur in n-years = (1 – P(0))n
Risk
Probability that at least one Q will occur
= 1- Reliability = 1 – (1 – 1/T) n
CEE 6/5460 – Water Resources Engineering

13. System risk for different magnitude events over various observation periods
Risk = 1 – (1 – 1/T) n
CEE 6/5460 – Water Resources Engineering

14. Risk (cont.)
Example 3. A 3-hour storm generates 2 inches of precipitation and will overtop a Layton, UT storm water detention basin. What is the risk a 3-hour storm will overtop the basin during the 25-year life of the basin?
CEE 6/5460 – Water Resources Engineering

15. Wrap up Today’s key points and learning objectives
Thursday: rainfall-runoff
CEE 6/5460 – Water Resources Engineering