nach oben

2010 | Buch

Kapitel lesen Erstes Kapitel lesen

Climate Time Series Analysis

Classical Statistical and Bootstrap Methods

verfasst von: Dr. Manfred Mudelsee

Verlag: Springer Netherlands

Buchreihe : Atmospheric and Oceanographic Sciences Library

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Einloggen, um Zugang zu erhalten

Über dieses Buch

Climate is a paradigm of a complex system. Analysing climate data is an exciting challenge, which is increased by non-normal distributional shape, serial dependence, uneven spacing and timescale uncertainties. This book presents bootstrap resampling as a computing-intensive method able to meet the challenge. It shows the bootstrap to perform reliably in the most important statistical estimation techniques: regression, spectral analysis, extreme values and correlation.

This book is written for climatologists and applied statisticians. It explains step by step the bootstrap algorithms (including novel adaptions) and methods for confidence interval construction. It tests the accuracy of the algorithms by means of Monte Carlo experiments. It analyses a large array of climate time series, giving a detailed account on the data and the associated climatological questions. This makes the book self-contained for graduate students and researchers.

Inhaltsverzeichnis

Frontmatter

Fundamental Concepts

Frontmatter

Chapter 1. Introduction

Abstract

“Weather is important but hard to predict”—lay people and scientists alike will agree. The complexity of that system limits the knowledge about it and therefore its predictability even over a few days. It is complex because many variables within the Earth’s atmosphere, such as temperature, barometric pressure, wind velocity, humidity, clouds and precipitation, are interacting, and they do so nonlinearly. Extending the view to longer timescales, that is, the climate 1 system in its original sense (the World Meteorological Organization defines a timescale boundary between weather and climate of 30 years), and also to larger spatial and further processual scales considered to influence climate (Earth’s surface, cryosphere, Sun, etc.), does not reduce complexity. This book loosely adopts the term “climate” to refer to this extended view, which shall also include “paleoclimate” as the climate within the geologic past.

Manfred Mudelsee

Chapter 2. Persistence Models

Abstract

Climatic noise often exhibits persistence (Section 1.3). Chapter 3 presents bootstrap methods as resampling techniques aimed at providing realistic confidence intervals or error bars for the various estimation problems treated in the subsequent chapters. The bootstrap works with artificially produced (by means of a random number generator) resamples of the noise process. Accurate bootstrap results need therefore the resamples to preserve the persistence of X _noise(i). To achieve this requires a model of the noise process or a quantification of the size of the dependence. Model fits to the noise data inform about the “memory” of the climate fluctuations, the span of the persistence. The fitted models and their estimated parameters can then be directly used for the bootstrap resampling procedure.

Manfred Mudelsee

Chapter 3. Bootstrap Confidence Intervals

Abstract

In statistical analysis of climate time series, our aim (Chapter 1) is to estimate parameters of X _trend(T), X _out(T), S(T) and X _noise(T). Denote in general such a parameter as θ. An estimator, \( \hat{\theta } \), is a recipe how to calculate θ from a set of data. The data, discretely sampled time series \( \{t\left( i \right),x\left( i \right)\}_{{i=1}}^{n} \), are influenced by measurement and proxy errors of x(i), outliers, dating errors of t(i) and climatic noise. Therefore, \( \hat{\theta } \) cannot be expected to equal θ. The accuracy of \( \hat{\theta } \), how close it comes to θ, is described by statistical terms such as standard error, bias, mean squared error and confidence interval (CI). These are introduced in Section 3.1.

Manfred Mudelsee

Univariate Time Series

Frontmatter

Chapter 4. Regression I

Abstract

Regression is a method to estimate the trend in the climate equation (Eq. 1.1). Assume that outlier data do not exist or have already been removed by the assistance of an extreme value analysis (Chapter 6). Then the climate equation is a regression equation

Manfred Mudelsee

Chapter 5. Spectral Analysis

Abstract

Spectral analysis investigates the noise component in the climate equation (Eq. 1.2). A Fourier transformation into the frequency domain makes it possible to separate short-term from long-term variations and to distinguish between cyclical forcing mechanisms of the climate system and broad-band resonances. Spectral analysis allows to learn about the climate physics.

Manfred Mudelsee

Chapter 6. Extreme Value Time Series

Abstract

Extreme value time series refer to the outlier component in the climate equation (Eq. 1.2). Quantifying the tail probability of the PDF of a climate variable—the risk of climate extremes—is of high socioeconomical relevance. In the context of climate change, it is important to move from stationary to nonstationary (time-dependent) models: with climate changes also risk changes may be associated.

Manfred Mudelsee

Bivariate Time Series

Frontmatter

Chapter 7. Correlation

Abstract

The correlation measures how strong a coupling is between the noise components of two processes, X _noise(i) and Y _noise(i). Using a bivariate time series sample, \( \left\{ {t\left( i \right),x\left( i \right),y\left( i \right)} \right\}_{{i=1}}^{n} \), this measure allows to study the relationship between two climate variables, each described by its own climate equation (Eq. 1.2).

Manfred Mudelsee

Chapter 8. Regression II

Abstract

Regression serves in this chapter to relate two climate variables, X(i) and Y(i). This is a standard tool for formulating a quantitative “climate theory” based on equations. Owing to the complexity of the climate system, such a theory can never be derived alone from the pure laws of physics—it requires to establish empirical relations between observed climate processes.

Manfred Mudelsee

Outlook

Frontmatter

Chapter 9. Future Directions

Abstract

What changes may bring the future to climate time series analysis? First we outline (Sections 9.1, 9.2 and 9.3) more short-term objectives of “normal science” (Kuhn 1970), extensions of previous material (Chapters 1, 2, 3, 4, 5, 6, 7 and 8). Then we take a chance (Sections 9.4 and 9.5) and look on paradigm changes in climate data analysis that may be effected by virtue of strongly increased computing power (and storage capacity). Whether this technological achievement comes in the form of grid computing (Allen 1999; Allen et al. 2000; Stainforth et al. 2007) or quantum computing (Nielsen and Chuang 2000; DiCarlo 2009; Lanyon et al. 2009)—the assumption here is the availability of machines that are faster by a factor of ten to the power of, say, twelve, by a mid-term period of, say, less than a few decades.

Manfred Mudelsee

Backmatter

Titel: Climate Time Series Analysis
verfasst von: Dr. Manfred Mudelsee
Verlag: Springer Netherlands
Electronic ISBN: 978-90-481-9482-7
Print ISBN: 978-90-481-9481-0
DOI: https://doi.org/10.1007/978-90-481-9482-7