├── LICENSE ├── README.md ├── erratum ├── ERRATUM.txt ├── chap09_corrections111.png └── chap09_corrections112.png ├── pics ├── bookcover.pdf └── bookcover.png └── presentations ├── 2022_04_07_UNIBO.pdf ├── 2022_05_19_UNIBO.pdf ├── course2022.txt ├── course2023.txt ├── eve19b.pdf ├── evensen2009_scalar_ex.pdf ├── slides.pdf ├── slides_Cluj_FV_1.pdf ├── slides_Cluj_FV_2.pdf ├── slides_Cluj_GE.pdf └── uibcourse.pdf /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2021 Geir Evensen 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Data-Assimilation-Fundamentals 2 | 3 | This repository is a resource complementary to the Springer book: Data Assimilation Fundamental: A unified formulation for state and parameter estimation 4 | 5 | The book is Open Access and is available from 6 | https://link.springer.com/book/10.1007/978-3-030-96709-3 7 | 8 | Please rise an issue if you discover typos or errors in the book, or just wish to discuss one of the book's topics. 9 | 10 |

11 | 12 |

13 | 14 | -------------------------------------------------------------------------------- /erratum/ERRATUM.txt: -------------------------------------------------------------------------------- 1 | Typos and errors in the book: 2 | 3 | Eq. 2.21 2.22 Missing the past measurements in the prior for the last update f(z_L | d_{L-1}, \ldots, d_1) 4 | 5 | Eq. 4.41 "++" should be "+" : fixed 6 | 7 | Addeed indices "4DVar!strong constraint", 4DVar!weak constraint", "variational methods", "Euler-Lagrange equations", "En4DVar". 8 | 9 | Sec. 9.3 "Fokker-Plank" should be "Fokker-Planck" : fixed 10 | 11 | In Approximation 5: The reference to Eq. (6.1) should be Eq. (3.11). 12 | 13 | Eq 6.33 and 6.38 and once in the text: error in placement of ^a on C^a_{zz}: fixed in definition of \Czza in extras.tex 14 | 15 | Eq. 6.22: Added definition of Hessian as Del Del J = 16 | 17 | Eqs. 6.29 and 6.22: wrong font on transpose superscript ^T -> ^\rmT 18 | 19 | Eq. 6.30: Changed constant to \textrm{constant} 20 | 21 | Eq. 6.31: \calJ (\bmz^\rma) -> \calJ (\bmz) 22 | 23 | After Eq. 8.25: superscript i on \bmOmega 24 | 25 | Eq: 8.28: the division on the \sqrt{N-1} in the middle line should be removed 26 | First line following Eq. 8.28: where we have used $\bmW^i/\sqrt{N-1} = \bmPI \bmW^i$, which we get from Eq.~(\ref{eq:Wi}) using $\bmS^\rmT/\sqrt{N-1}=\bmPI\bmS^\rmT$. 27 | 28 | Algorithm 7 lines 2-4: input D_l inside loop over assimilation windows. 29 | Algorithm 8 lines 2-4: input d and C_dd inside loop over assimilation windows. 30 | Algorithm 8 line 5: Loop over MDA steps 31 | Algorithm 8 line 19: It should be Z=X_K 32 | All algorithms should use a comma and not a colon in for loops, e.g., for i=1,N. Applies to Algorithms 1, 2, 3, and 4. 33 | 34 | Eq 8.52 and around ^+ changed to ^\dagger 35 | 36 | Eq: 9.40: (ln f/f +1) 37 | 38 | Eq: 9.41: (1+ln f/f) and a minus sign in front 39 | 40 | Eq: 9.42: should read: 41 | - \int f_s ( m_s \cdot \nabla_z ln f(z|d) + \nabla_z \cdot m_s ) dz 42 | 43 | Eq: 9.44: should read: 44 | - < \int f_s ( K(.,z) \cdot \nabla_z ln f(z|d) + \nabla_z \cdot K(.,z) ) dz , m_s(.) > 45 | 46 | Eq: 9.46: should read 47 | - \int f_s ( K(.,z) \cdot \nabla_z ln f(z|d) + \nabla_z \cdot K(.,z) ) dz 48 | 49 | Eq: 9.49 should read: 50 | - B 1/N sum ( K(zj,zl) \cdot \nabla_zl ln f(zl|d) + \nabla_zl \cdot K(zj,zl) ) 51 | 52 | 10.4.1: first line Space missing in Hammil etal and Bishop etal. 53 | 54 | Sec 13.5 (sixt line) ^+ changed to ^\dagger 55 | 56 | Chap 16.1 $\beta=8/3$ 57 | 58 | 59 | Eq. 18.2 sin(x) should be sin(pi*x) 60 | 61 | -------------------------------------------------------------------------------- /erratum/chap09_corrections111.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/erratum/chap09_corrections111.png -------------------------------------------------------------------------------- /erratum/chap09_corrections112.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/erratum/chap09_corrections112.png -------------------------------------------------------------------------------- /pics/bookcover.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/pics/bookcover.pdf -------------------------------------------------------------------------------- /pics/bookcover.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/pics/bookcover.png -------------------------------------------------------------------------------- /presentations/2022_04_07_UNIBO.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/presentations/2022_04_07_UNIBO.pdf -------------------------------------------------------------------------------- /presentations/2022_05_19_UNIBO.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/presentations/2022_05_19_UNIBO.pdf -------------------------------------------------------------------------------- /presentations/course2022.txt: -------------------------------------------------------------------------------- 1 | Scalar case: presentations/evensen2009_scalar_ex.pdf 2 | Chapter 1: Introduction 3 | Chapter 2: Bayes and problem formulation 4 | Chapter 3: MAP solution and Gauss-Newton iterations 5 | Chapter 4: 4.1 6 | Chapter 5: 5.1 and 5.2 7 | Chapter 6: Kalman Filters 8 | Chapter 7: RML sampling 9 | Chapter 8: 8.1-8.6 (ensemble methods EnKF and EnRML) 10 | Chapter 11: A summary of approxiations and methods. 11 | Chapter 14: EnKF with advection equation 12 | Chapter 15: EnKF, EnKS, ES with Lorenz equations 13 | Figures 17.3 and 17.4 to illustrate strong vs. weak constraint 14 | -------------------------------------------------------------------------------- /presentations/course2023.txt: -------------------------------------------------------------------------------- 1 | Scalar case: presentations/evensen2009_scalar_ex.pdf 2 | Chapter 1: Introduction 3 | Chapter 2: Bayes and problem formulation 4 | Chapter 3: MAP solution and Gauss-Newton iterations 5 | Chapter 4: 4.1 6 | Chapter 6: Kalman Filters 7 | Chapter 7: RML sampling 8 | Chapter 8: 8.1, 8.2, 8.5, 8.6, 8.7 9 | Chapter 11: A summary of approxiations and methods. 10 | Chapter 14: EnKF with advection equation 11 | Chapter 15: EnKF, EnKS, ES with Lorenz equations 12 | Figures 17.3 and 17.4 to illustrate strong vs. weak constraint 13 | -------------------------------------------------------------------------------- /presentations/eve19b.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/presentations/eve19b.pdf -------------------------------------------------------------------------------- /presentations/evensen2009_scalar_ex.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/presentations/evensen2009_scalar_ex.pdf -------------------------------------------------------------------------------- /presentations/slides.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/presentations/slides.pdf -------------------------------------------------------------------------------- /presentations/slides_Cluj_FV_1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/presentations/slides_Cluj_FV_1.pdf -------------------------------------------------------------------------------- /presentations/slides_Cluj_FV_2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/presentations/slides_Cluj_FV_2.pdf -------------------------------------------------------------------------------- /presentations/slides_Cluj_GE.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/presentations/slides_Cluj_GE.pdf -------------------------------------------------------------------------------- /presentations/uibcourse.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/geirev/Data-Assimilation-Fundamentals/44221e996fc66462b634a44bab67d045fc514e04/presentations/uibcourse.pdf --------------------------------------------------------------------------------