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

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

1. Key components of the hydrologic cycle

Which components are important to engineers designing storm water systems?

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

2. Precipitation

Time-series of daily precipitation at USU http://climate.usurf.usu.edu/products/data.php

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

Precipitation Depth-Duration-Frequency Curves for Layton, UT Source: NOAA, 2008, http://www.nws.noaa.gov/oh/hdsc/index.html

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

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

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

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

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

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