Understanding Mathematical and Statistical Techniques in Hydrology E-Book

Harvey J. E. Rodda

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 192

Veröffentlichungsjahr: 2015

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Title Page

Preface

How to use this book

CHAPTER 1: Fundamentals

1.1 Motivation for this book

1.2 Mathematical preliminaries

Reference

CHAPTER 2: Statistical modelling

2.1 The Central European Floods, August 2002

2.2 Extreme value analysis

2.3 Simple methods of return period estimation

2.4 Return periods based on distribution fitting

2.5 Techniques for parameter estimation

2.6 Bayesian parameter estimation

2.7 Resampling methods: bootstrapping

References

CHAPTER 3: Mathematics of hydrological processes

3.1 Introduction

3.2 Algebraic and difference equation methods

3.3 Methods involving exponentiation

3.4 Rearranging model equations

3.5 Equations with iterated summations and products

3.6 Methods involving differential equations

3.7 Methods involving integrals

References

CHAPTER 4: Techniques based on data fitting

4.1 Experimental and observed data

4.2 Rating curves

4.3 Regression with two or more independent variables

4.4 Demonstration of decaying quantities

4.5 Analysis based on harmonic functions

References

CHAPTER 5: Time series data

5.1 Introduction

5.2 Characteristics of time series data

5.3 Testing for time dependence

5.4 Testing for trends

5.5 Frequency analysis

5.6 Other analysis methods

5.7 Smoothing and filtering

5.8 Linear smoothing and filtering methods

5.9 Nonlinear filtering methods

5.10 Time series modelling

5.11 Hybrid time series/process-based models

5.12 Detecting non-stationarity

References

CHAPTER 6: Measures of model performance, uncertainty and stochastic modelling

6.1 Introduction

6.2 Quantitative measures of performance

6.3 Comparing measures

6.4 The Nash–Sutcliffe method

6.5 Stochastic modelling

6.6 Monte Carlo simulations

6.7 Non-uniform Monte Carlo sampling

6.8 Uncertainty in hydrological modelling

6.9 Uncertainty in combined models

6.10 Assessing uncertainty given observed data: Bayesian methods

References

Glossary

Index

End User License Agreement

List of Tables

Chapter 02

Table 2.1 Return period estimates for flows during the August 2002 floods.

Table 2.2 Ten largest return periods for observed flows on the Vltava at Prague, 1827–2002 (including the events of 2002), estimated using the Weibull plotting formula (2.1).

Table 2.3 Ten largest return periods for observed flows on the Vltava at Prague, 1827–2001 (excluding the events of 2002), estimated using the Weibull plotting formula (2.1).

Table 2.4 Return periods to two significant figures for observed flows on the Vltava at Prague, estimated by fitting the Gumbel extreme value distribution to the annual maximum daily flow, 1827–2002.

Table 2.5 Example bootstrap computations to estimate standard deviation of the average depth of rainfall from a synthetic time series.

Chapter 03

Table 3.1 Load calculation using Equation (3.16) based on concentration and flow data.

Table 3.2 SPRHOST values in Equation (3.17) for different soils for the hypothetical catchment shown in Figure 3.1.

Chapter 05

Table 5.1 An example of a soil water balance time series, computed using Equation (5.14), and starting with a day 0 soil moisture deficit of 0 mm.

Chapter 06

Table 6.1 Comparing results of measures quantifying the accuracy of predictions from models A and B, for the catchment sediment load data shown in Figure 6.1.

Table 6.2 Statistical properties of the catchment sediment load data and predictions shown in Figure 6.1.

Table 6.3 Example computation of the Nash–Sutcliffe efficiency for a set of observed and modelled data, using Equation (6.7).

Table 6.4 Example uniform random number combinations within known ranges of rainfall and snow depth.

Table 6.5 Example slices for 2-day rainfall ranging from 0 to 250 mm, using non-uniform random stratified sampling to emphasize extremes.

List of Illustrations

Chapter 01

Figure 1.1 Approximate integration of the area under the curve

x

2

(black) using rectangles (grey), over the interval 0–1, with coarse partition (top) and finer partition (bottom).

Chapter 02

Figure 2.1 Annual maximum flows on the Vltava at Prague, 1827–2006.

Figure 2.2 Gumbel plot of the annual maximum daily flows on the Vltava at Prague, 1827–2006. The dotted line is the best straight line obtained by least-squares fitting.

Figure 2.3 An example of the flow (

y

axis) plotted against reduced variate (

x

axis) and return period.

Figure 2.4 An illustration of selecting peaks over a threshold for a period of observations.

Chapter 03

Figure 3.1 SPR values for different soil types 1–4 within a hypothetical catchment.

Figure 3.2 Calculation of channel flow by combining subdivision measurements of width, depth and velocity.

Chapter 04

Figure 4.1 An example of water level monitoring.

Figure 4.2 The effects of increasing water levels on the area and flow of water in a natural river channel.

Figure 4.3 Rating curves and equations for the Glomma at Nor for (a) levels below 0.75 m and (b) levels between 0.75 and 10.5 m.

Figure 4.4 A scatter plot of log of

Q

2

against log of area for example data (not that used to derive Eq. (4.7)).

Figure 4.5 The decay of inorganic nitrogen (N) in the soil during autumn and winter drainage for two different soil types.

Figure 4.6 Variation of soil moisture deficit over time from January (1) to December (12) for Croydon, near London.

Figure 4.7 3D scatter plot of the data from Figure 4.6 showing how the data lies approximately on a circle embedded in a plane in 3D.

Figure 4.8 Data from Figure 4.6 plotted from the start of the data collection period showing the harmonic fit.

Chapter 05

Figure 5.1 Surface runoff measured at 1 minute resolution from experimental 1 ha plots at North Wyke Research, UK (Rodda and Hawkins 2012), for 13 May 2007, from 09:00 to 12:00.

Figure 5.2 Observed daily rainfall during 1998 near Hancheng, China.

Figure 5.3 Maximum annual discharge on the Morava River, Czech Republic, 1916–1972.

Figure 5.4 Number of meteorological droughts observed at Oxford, UK, per decade from 1853 to 2002.

Figure 5.5 A 3-year running mean of maximum annual flows for the Morava River, shown in solid, with the original data shown as the dashed line. This is the centred running mean (mean of three values: previous, current and following) as opposed to a lagged running mean taking the previous 2 years and the current one.

Figure 5.6 The application of filtering to produce a digital ground surface model from LiDAR elevation data, where trees and other spurious elevation values in (a) (dark spots) have been removed to form the bare earth model in (b).

Figure 5.7 Mean sea levels for Oslo, 1910–2005.

Chapter 06

Figure 6.1 Hypothetical model predictions from two different sediment load models compared with observed sediment load for a catchment.

Figure 6.2 A histogram derived from stochastic stratified sampling using the data ranges and sampling slices (10 values per slice) as shown in Table 6.5.

Guide

Cover

Table of Contents

Begin Reading

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Understanding Mathematical and Statistical Techniques in Hydrology

An Examples-Based Approach

Harvey J. E. Rodda

Max A. Little

This edition first published 2015 © 2015 by Harvey Rodda and Max Little

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Library of Congress Cataloging-in-Publication Data

Rodda, Harvey. Understanding mathematical and statistical techniques in hydrology : an examples-based approach / Harvey Rodda, Max Little.  1 online resource. Includes index. Description based on print version record and CIP data provided by publisher; resource not viewed.

 ISBN 978-1-119-07659-9 (pdf) – ISBN 978-1-119-07660-5 (epub) – ISBN 978-1-4443-3549-1 (cloth)1. Hydrology–Mathematical models. 2. Hydrology--Statistical methods. I. Title. GB656.2.M33 551.4801′51–dc23

    2015023562

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Cover image: The River Avon at Upavon, Wiltshire, UK © Harvey J. E. Rodda

Preface

Understanding Mathematical and Statistical Techniques in Hydrology: An Examples-Based Approach is primarily intended as a textbook to assist undergraduate and postgraduate students with courses or modules in hydrology. In higher education, hydrology as a subject is not usually taught in its entirety as a separate course at undergraduate level but is generally included as a module of geography, environmental science or earth science courses. It can also be included in civil engineering courses which deal with river engineering, drainage, water supply and sewage treatment. More specialized postgraduate courses such as water resources management focus on hydrology. Such undergraduate and postgraduate courses do not generally include any supplementary mathematics and in many cases an advanced school leaving qualification in mathematics is not an essential entry requirement. However, many of the current hydrology textbooks for undergraduate and postgraduate courses assume a high level of mathematical expertise, such as that attained when studying for a mathematics degree. For example, textbooks often present a sequence of differential equations which are impossible to comprehend without having this high level of mathematical knowledge. Instead of assisting the students with their studies these texts when full of mathematical notations are of little interest to the reader. They can also distance students from using mathematics to the extent that they are discouraged from attempting any mathematical-based questions in final exams.