FLOOD01900

• County: Statewide
• Community: Nationwide
• Title: Techniques of Weather-Resources Investigations of the USGS Book 4, Chapter A1
• Date: 1/1/1968
• Floodplain - Doc Type: Educational/Technical/Reference Information

.

.

.

SOME STATISTICAL TOOLS IN HYDROLOGY

By H. C. Riggs

Abstract

This chapter of "Techniques of Water-Resources
Investigations" provides background material needed
for understanding the statistical procedures most use-
ful in hydrology; it furnishes detailed procedures, with
examples, of regression analyses; it describes analysis
of variance and covariance and - discusses the char~
actenstics of hydrologic data.

Introduction

As hydrologic analyses become more sophis-
ticated, the proper design and interpretation
of these analyses require a greater knowledge
of statistical methods. In fact, two long-used
hydrologic tools, the flood-frequency curve and
the duration curve, require an understanding
of the theory of statistics for proper evaluation.
The more elaborate statistical methods are
mathematical, but graphical methods are ex-
tremely useful and adequately accurate for
many purposes, if made with an understanding
of the underlying assumptions and if properly
interpreted.
Until recent years most statistics texts em-
phasized procedures applicable to normally
distributed data because the assumption of
normality is appropriate to many types of
biological and agricultural data. But much of
the data used in hydrology either is not nor-
mally distributed or does not have a prob-
ability distribution at all. Most hydrologists
learned statistics from texts or courses directed
toward analysis of normally distributed data.
Consequently some early hydrologic analyses
were either incorrectly done or incorrectly
interpreted.
This chapter of "Techniques of Water-
Resources Investigations" provides the back-
ground material needed for understanding the

statistical procedures most useful in hydrology.
Although it starts with the basic concept of a
distribution, many elementary details are
omitted. The reader is assumed to have some
familiarity with statistical terminology, com-
putation procedures, and elementary prob-
ability such as would be obtained from n. class-
room course in statistics for engineers or from
the U.S. Geological Survey correspondence
course "Elementary Statistics in Hydrology."
Although theory is emphasized in this chap-
ter, the treatment is intuitive rather than
rigorous. Many practical approaches to graph-
ical regression are given, and the pitfalls as-
sociated with computation of least-squares lines
are located. The chapter concludes with a
discussion of the statistical characteristics of
hydrolo~ic data.

Distributions

The concept of a population' of objects
having a distribution of sizes (or of some other
characteristic.) is basic to the statistical method.
It is not possible to collect enough datn to
define a frequency distribution exactly, but the
existence of a particular one can be proven to
the desired degree of confidence by repeating
an experiment many times.
Kendall (1952, p. 23) reported the results of
a dice-tossing experiment in which 12 dice were
tossed simultaneously and the number of sixes
was recorded f~r each toss. The dice were
tossed 4 096 times with the results shown in
table 1. Also shown are the relative frequency
computed from the experimental results and
the theoretical relative frequency computed
from the binomial distribution. The close agree-
ment between the theoretical and experimental
1