Book contents
- Time Series Data Analysis in Oceanography
- Time Series Data Analysis in Oceanography
- Copyright page
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Introduction to MATLAB
- 3 Time and MATLAB Functions for Time
- 4 Deterministic and Random Functions
- 5 Error and Variability Propagation
- 6 Taylor Series Expansion and Application in Error Estimate
- 7 Spherical Trigonometry and Distance Computation
- 8 A System of Linear Equations and Least Squares Method
- 9 Base Functions and Linear Independence
- 10 Generic Least Squares Method and Orthogonal Functions
- 11 Harmonic Analysis of Tide
- 12 Fourier Series
- 13 Fourier Transform
- 14 Discrete Fourier Transform and Fast Fourier Transform
- 15 Properties of Fourier Transform
- 16 More Discussion on the Harmonic Analysis and Fourier Analysis
- 17 Effect of Finite Sampling
- 18 Power Spectrum, Cospectrum, and Coherence
- 19 Window Functions for Reducing Side Lobes
- 20 Convolution, Filtering with the Window Method
- 21 Digital Filters
- 22 Rotary Spectrum Analysis
- 23 Short-Time Fourier Transform and Introduction to Wavelet Analysis
- 24 Empirical Orthogonal Function Analysis
- References
- Index
5 - Error and Variability Propagation
Published online by Cambridge University Press: 21 April 2022
Book contents
- Time Series Data Analysis in Oceanography
- Time Series Data Analysis in Oceanography
- Copyright page
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Introduction to MATLAB
- 3 Time and MATLAB Functions for Time
- 4 Deterministic and Random Functions
- 5 Error and Variability Propagation
- 6 Taylor Series Expansion and Application in Error Estimate
- 7 Spherical Trigonometry and Distance Computation
- 8 A System of Linear Equations and Least Squares Method
- 9 Base Functions and Linear Independence
- 10 Generic Least Squares Method and Orthogonal Functions
- 11 Harmonic Analysis of Tide
- 12 Fourier Series
- 13 Fourier Transform
- 14 Discrete Fourier Transform and Fast Fourier Transform
- 15 Properties of Fourier Transform
- 16 More Discussion on the Harmonic Analysis and Fourier Analysis
- 17 Effect of Finite Sampling
- 18 Power Spectrum, Cospectrum, and Coherence
- 19 Window Functions for Reducing Side Lobes
- 20 Convolution, Filtering with the Window Method
- 21 Digital Filters
- 22 Rotary Spectrum Analysis
- 23 Short-Time Fourier Transform and Introduction to Wavelet Analysis
- 24 Empirical Orthogonal Function Analysis
- References
- Index
Summary
The objective of this chapter is to discuss the error propagation through computation from the error contained in the original data. We are not focusing on the measurement errors themselves, although the propagation of computational error is related to measurement errors. We also discuss the variability propagation with given mathematical relationships, or sensitivity of a system to a given parameter, which are all closely related to error propagation.
Keywords
- Type
- Chapter
- Information
- Time Series Data Analysis in OceanographyApplications using MATLAB, pp. 90 - 109Publisher: Cambridge University PressPrint publication year: 2022