Hydrologic Probability and Statistics

Joseph V. Bellini, PE, PH, DWRE, CFM

Course Outline

Interested in knowing what is meant when we hear “100-year flood” or 25-year rainfall”?  This course is intended to provide a technical understanding of the data and methodologies used to estimate probabilities and frequencies of extreme hydrologic events.

This course discusses the following topics:

• Hydrologic Statistics
• Probabilistic Treatment of Hydrologic Data
• Frequency and Probability Functions
• Statistical Parameters
• Probability Distribution for Hydrologic Variables
• Probability/Frequency Analysis
• Return Period
• Extreme Value Distributions
• Frequency Analysis using Frequency Factors
• Probability Plotting
• Confidence Limits
• Application to Stream Flow
• USGS PEAK-FQ Example
• Application to Rainfall

This course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of the course materials.

Learning Objective

At the conclusion of this course, the student will learn:

• How to estimate the probability of events using measured data;
• How to fit a probability distribution function when measured data is limited;
• Which probability functions apply to which hydrologic events;
• How to estimate statistical parameters of hydrologic data (i.e. mean, median, variance, standard deviation, and skewness);
• Understand terms used in flood-frequency;
• How to apply probability functions to peak annual stream flow;
• How to use probability plotting to “linearize” a probability distribution for estimating purposes;
• How to compute confidence limits and intervals to account for uncertainty;
• An example application of the USGS Peak-FQ software; and
• How to find rainfall and stream flow data on the internet.

Intended Audience

This course is intended for civil and water resources engineers, hydrologists, environmental scientists, and watershed planners.

Benefit to Attendees

Attendee of this course will be able to understand the basis for estimating risk due to extreme hydrologic events; particularly flooding.

Course Introduction

In general, extreme hydrologic events are largely random and unpredictable.  Therefore, deterministic approaches have limited application in estimating the magnitude and frequency of such events.  As such, output from hydrologic processes can be treated using “stochastic” (non-deterministic) methodologies.  Probabilistic and statistical methods are used to analyze stochastic processes and involve varying degrees of uncertainty.  This course will address such methods for quantifying the magnitude, frequency, and probability of extreme hydrologic events; particularly stream flow and rainfall.

Course Content

This course is in the following PDF document:

Hydrologic Probability and Statistics

Course Summary

In general, extreme hydrologic events are largely random and unpredictable.  Therefore, deterministic approaches have limited application in estimating the magnitude and frequency of such events.  As such, output from hydrologic processes can be treated using “stochastic” (non-deterministic) methodologies.  Probabilistic and statistical methods are used to analyze stochastic processes and involve varying degrees of uncertainty.  This course will address such methods for quantifying the magnitude, frequency, and probability of extreme hydrologic events; particularly stream flow and rainfall.