Understanding Mathematical and Statistical Techniques in Hydrology

An Examples-based Approach

Harvey J. E. Rodda, Max A. Little

• Publisher: Wiley-Blackwell
• Year: 2015
• Print ISBN: 9781444335491
• eBook ISBN: 9781119076605
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Environmental Management
• Index: Technology & Engineering

Pick up any hydrology textbook and it will not be long before you encounter pages listing sequences of equations representing complex mathematical concepts. Students and practitioners of hydrology will not find this very helpful, as their aim, generally, is to study and understand hydrology, and not to find themselves confronted with material that even students of mathematics would find challenging. Often, equations appear to be copied and pasted into hydrological texts in an attempt to give a more rigorous scientific basis to the narrative. However, they are commonly wrong, poorly explained, without context or background, and more likely to confuse and distance the reader than to enlighten and engage them in the topic.

Understanding Mathematical and Statistical Techniques in Hydrology provides full and detailed expositions of such equations and mathematical concepts, commonly used in hydrology. In contrast to other hydrological texts, instead of presenting abstract mathematical hydrology, the essential mathematics is explained with the help of real-world hydrological examples.

CHAPTER 1
Fundamentals

1.1 Motivation for this book

Hydrology is the study of water, and in the International Glossary of Hydrology (UNESCO/WMO 1992) it is defined as ‘Science that deals with the waters above and below the land surfaces of the Earth, their occurrence, circulation and distribution, both in space and time, their biological, chemical and physical properties, their reaction with their environment, including their relation to living beings’. The movement and transformation of water within these processes as described in the definition, as a fluid, will obey the physical rules of fluid mechanics. Fluid mechanics, being a quantitative topic, requires heavy use of mathematical concepts, and these concepts are therefore naturally found in hydrology. These quite basic physical principles can be used effectively to model and hence predict and understand the behaviour of water under many useful circumstances.

Nonetheless, despite the essentially predictable behaviour of water that justifies the use of mathematical principles, often, the flow of water in practice is subject to forces that are beyond our ability to measure with any precision: for example, water in the atmosphere is heated, cooled, mixed with numerous gasses, and transported across large distances under the action of turbulent winds. Eventually, water condenses out of the atmosphere in the form of precipitation but exactly when, where, and how much water falls to the ground under gravity is often extremely uncertain. This uncertainty usually makes it useless to apply the basic physical principles of fluid mechanics to the flow of water in these circumstances. For this reason, hydrologists often turn to statistics, which can be considered as the application of mathematics to uncertain phenomena.

Quantitative hydrology is, therefore, based on an interesting mix of the two great branches of applied mathematics: physical laws (mathematical physics) and probability (mathematical statistics).

Mathematics is, perhaps, the archetypal example of a composite subject. This means that more complex concepts are built from many simpler ones, and so, in order to properly understand the more complex topic, it is necessary to understand the simpler ones from which it is constructed. Not all subjects are like this: it is possible to gain a deep understanding of many aspects of plant biology without having to know anything about mammals, for instance. But mathematics is unforgiving: one cannot understand the true meaning of equations of fluid transport without knowing calculus. Unfortunately, for many reasons, the chance to learn the basic mathematical concepts is not afforded to every student or practitioner of hydrology, and many find themselves at a loss when presented with more complex mathematical concepts as a result.

This book is therefore, intended as a guide to students and practitioners of hydrology without a formal or substantive background in either mathematical physics, or mathematical statistics, who need to gain a more thorough grounding of these mathematical tech...

Table of contents

• Cover
• Title Page
• Table of Contents
• Preface
• How to use this book
• CHAPTER 1: Fundamentals
• CHAPTER 2: Statistical modelling
• CHAPTER 3: Mathematics of hydrological processes
• CHAPTER 4: Techniques based on data fitting
• CHAPTER 5: Time series data
• CHAPTER 6: Measures of model performance, uncertainty and stochastic modelling
• Glossary
• Index
• End User License Agreement