{"id":9045,"date":"2020-02-05T00:00:16","date_gmt":"2020-02-04T15:00:16","guid":{"rendered":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/?p=9045"},"modified":"2020-02-05T00:00:55","modified_gmt":"2020-02-04T15:00:55","slug":"samuel-p-shen-richard-c-somerville-2019-climate-mathematics","status":"publish","type":"post","link":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/?p=9045","title":{"rendered":"Samuel P. Shen &#038; Richard C. Somerville (2019) Climate Mathematics"},"content":{"rendered":"<ul>\n<li>Samuel P. <strong>Shen<\/strong> &#038; Richard C. <strong>Somerville<\/strong>, 2019: <em>Climate Mathematics: Theory and Applications<\/em>. Cambridge UK: Cambridge University Press. ISBN 978-1-108-47687-4 (Hardback). DOI: 10.1017\/9781108693882 . \u30a6\u30a7\u30d6\u30b5\u30a4\u30c8www.cambridge.org\/9781108476874 <\/li>\n<\/ul>\n<p>2019\u5e74\u306e\u65b0\u520a\u3002\u308f\u305f\u3057\u306f\u305d\u306e\u5e74\u306e\u5e74\u672b\u306b\u6771\u4eac\u306e\u6d0b\u66f8\u5c4b\u306e\u5e97\u982d\u3067\u307f\u3064\u3051\u305f\u3002\u5927\u5b66\u9662\u751f\u306e\u6307\u5c0e\u3092\u3057\u3066\u3044\u305f\u3089\u3059\u3050\u8cb7\u3063\u3066\u8aad\u307e\u305b\u3088\u3046\u3068\u601d\u3063\u305f\u3060\u308d\u3046\u304c\u3001\u81ea\u5206\u3060\u3051\u304c\u8aad\u3080\u306e\u306b\u306f \u304b\u3055\u3070\u3089\u306a\u3044\u307b\u3046\u304c\u3088\u3044\u306e\u3067\u3001\u30c7\u30a3\u30b8\u30bf\u30eb\u7248 (\u308f\u305f\u3057\u306e\u7fd2\u6163\u3067 Amazon 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\u3055\u3093\u306f\u3001\u6570\u5024\u30e2\u30c7\u30eb\u3092\u3064\u304b\u3063\u305f\u6c17\u5019\u306e\u7814\u7a76\u3067\u306f\u77e5\u3089\u308c\u305f\u4eba\u3067\u3001\u540d\u8a89\u6559\u6388\u306b\u306a\u3063\u3066\u3044\u308b\u304c\u3001UCSD\u3067\u306e\u6559\u80b2\u306b\u306f\u304b\u304b\u308f\u3063\u3066\u3044\u3066\u3001\u8fd1\u304f\u306eSan Diego State University\u3067\u6559\u3048\u3066\u3044\u308bShen\u3055\u3093\u306b\u975e\u5e38\u52e4\u3067\u6388\u696d\u3092\u3084\u3063\u3066\u3082\u3089\u3044\u3001\u3044\u3063\u3057\u3087\u306b\u672c\u3092\u307e\u3068\u3081\u308b\u3053\u3068\u306b\u3057\u305f\u3089\u3057\u3044\u3002Shen\u3055\u3093\u306f\u4e2d\u56fd\u3067\u5b66\u58eb\u3001\u30a2\u30e1\u30ea\u30ab\u3067\u535a\u58eb\u3092\u3068\u308a\u3001\u30ab\u30ca\u30c0\u306a\u3069\u306e\u5927\u5b66\u3067\u6570\u5b66\u30fb\u7d71\u8a08\u5b66\u3092\u6559\u3048\u308b\u8077\u306b\u3064\u304d\u306a\u304c\u3089\u3001\u7814\u7a76\u5bfe\u8c61\u3068\u3057\u3066\u306f\u6c17\u5019\u5909\u5316\u3092\u3068\u308a\u3042\u3052\u3066\u304d\u305f\u3002\u6771\u5927\u306e(\u5f53\u6642\u306e\u540d\u307e\u3048\u3067)\u6c17\u5019\u30b7\u30b9\u30c6\u30e0\u7814\u7a76\u30bb\u30f3\u30bf\u30fc(CCSR)\u306b\u5ba2\u54e1\u3068\u3057\u3066\u3044\u305f\u3053\u3068\u3082\u3042\u308b(\u3053\u3068\u304c\u3001\u30a2\u30fc\u30ab\u30a4\u30d6\u3068\u3057\u3066\u6b8b\u3055\u308c\u3066\u3044\u308bCCSR\u306e\u30da\u30fc\u30b8\u3092\u898b\u305f\u3089\u308f\u304b\u3063\u305f)\u3002<\/p>\n<p>\u65e5\u672c\u8a9e\u7248\u3082\u3042\u308b\u3068\u3088\u3044\u3068\u601d\u3046\u304c\u3001\u308f\u305f\u3057\u304c\u7387\u5148\u3057\u3066\u7ffb\u8a33\u3057\u3088\u3046\u3068\u3044\u3046\u307b\u3069\u3067\u306f\u306a\u3044\u3002(\u3044\u3064\u3082\u3088\u3044\u65b9\u6cd5\u3067\u306f\u306a\u3044\u306e\u3060\u304c\u3001\u3053\u306e\u672c\u306e\u3070\u3042\u3044\u306f)\u5b66\u751f\u304c\u304a\u304a\u305c\u3044\u3044\u308b\u7814\u7a76\u5ba4\u3067\u5206\u62c5\u3057\u3066\u7ffb\u8a33\u3059\u308b\u3068\u3088\u3044\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n<p>\u6298\u308a\u304b\u3048\u3057\u306e\u3042\u3068\u306b \u304f\u308f\u3057\u3044\u76ee\u6b21\u3092\u3064\u3051\u308b\u3002Kindle\u7248\u3092\u3082\u3068\u306b\u3057\u305f\u3002MS Windows\u7528\u306eKindle\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u3067\u3001\u672c\u306e\u306a\u304b\u307f\u304b\u3089\u306e\u30b3\u30d4\u30fc(\u305d\u3057\u3066Windows\u4e0a\u306e\u30a8\u30c7\u30a3\u30bf\u306b \u306f\u308a\u3064\u3051)\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u3063\u305f\u306e\u3067\u3001\u305d\u308c\u3092\u5229\u7528\u3057\u305f\u3046\u3048\u3067\u7de8\u96c6\u3057\u305f\u3002\u305f\u3060\u3057\u3001\u7ae0\u30fb\u7bc0\u306e\u756a\u53f7\u3068\u984c\u540d\u304c\u304f\u3063\u3064\u3044\u3066\u3057\u307e\u3063\u3066(tab\u30b3\u30fc\u30c9\u304c\u306c\u3051\u305f\u306e\u3060\u3068\u601d\u3046)\u3001\u3042\u3068\u3067\u7a7a\u767d\u3092\u3044\u308c\u308b\u4fee\u6b63\u3092\u3057\u305f\u3002<br \/>\n<!--more--><br \/>\n== \u76ee\u6b21\u3000==<br \/>\nCover page<br \/>\nHalf Title page<br \/>\nTitle page<br \/>\nCopyright page<br \/>\nDedication<br \/>\nContents<br \/>\nPreface<br \/>\nAcknowledgements<br \/>\nMain Symbols and Acronyms<br \/>\n1 \u200bDimensional Analysis for Climate Science<br \/>\n &#8211; 1.1 \u200bDimension and Units<br \/>\n &#8211; 1.2\u200b Fundamental Dimensions: LMT \u03b8I-class<br \/>\n &#8211; 1.3\u200b Dimensional Analysis for a Simple Pendulum<br \/>\n &#8211; 1.4\u200b Dimensional Analysis for the State Equation of Air<br \/>\n &#8211; 1.5\u200b Dimensional Analysis of Heat Diffusion<br \/>\n &#8211; 1.6\u200b Dimensional Analysis of Rossby Waves and Kelvin Waves<br \/>\n &#8211; &#8211; 1.6.1 \u200bParameters for Rossby Waves<br \/>\n &#8211; &#8211; 1.6.2\u200b Non-Dispersive Properties of Kelvin Waves<br \/>\n &#8211; 1.7\u200b Estimating the Shock Wave Radius of a Nuclear Explosion by Dimensional Analysis<br \/>\n &#8211; 1.8\u200b Chapter Summary<br \/>\n &#8211; References and Further Readings<br \/>\n &#8211; Exercises<br \/>\n2\u200b Basics of R Programming<br \/>\n &#8211; 2.1 \u200bDownload and Install R and RStudio<br \/>\n &#8211; 2.2\u200b R Tutorial<br \/>\n &#8211; &#8211; 2.2.1 \u200bR As a Smart Calculator<br \/>\n &#8211; &#8211; 2.2.2\u200b Define a Sequence in R<br \/>\n &#8211; &#8211; 2.2.3\u200b Define a Function in R<br \/>\n &#8211; &#8211; 2.2.4\u200b Plot with R<br \/>\n &#8211; &#8211; 2.2.5\u200b Symbolic Calculations by R<br \/>\n &#8211; &#8211; 2.2.6\u200b Vectors and Matrices<br \/>\n &#8211; &#8211; 2.2.7\u200b Simple Statistics by R<br \/>\n &#8211; 2.3\u200b Online Tutorials<br \/>\n &#8211; &#8211; 2.3.1\u200b YouTube Tutorial: For True Beginners<br \/>\n &#8211; &#8211; 2.3.2\u200b YouTube Tutorial: For Some Basic Statistical Summaries<br \/>\n &#8211; &#8211; 2.3.3\u200b YouTube Tutorial: Input Data by Reading a csv File into R<br \/>\n &#8211; 2.4\u200b Chapter Summary<br \/>\n &#8211; References and Further Readings<br \/>\n &#8211; Exercises<br \/>\n3\u200b Basic Statistical Methods for Climate Data Analysis<br \/>\n &#8211; 3.1 \u200bStatistical Indices from the Global Temperature Data from 1880 to 2015<br \/>\n &#8211; &#8211; 3.1.1 \u200bMean, Variance, Standard Deviation, Skewness, Kurtosis, and Quantiles<br \/>\n &#8211; &#8211; 3.1.2\u200b Correlation, Covariance, and Linear Trend<br \/>\n &#8211; 3.2\u200b Commonly Used Statistical Plots<br \/>\n &#8211; &#8211; 3.2.1 \u200bHistogram of a Set of Data<br \/>\n &#8211; &#8211; 3.2.2\u200b Box Plot<br \/>\n &#8211; &#8211; 3.2.3\u200b Scatter Plot<br \/>\n &#8211; &#8211; 3.2.4\u200b Q-Q Plot<br \/>\n &#8211; 3.3\u200b Probability Distributions<br \/>\n &#8211; &#8211; 3.3.1 \u200bWhat Is a Probability Distribution?<br \/>\n &#8211; &#8211; 3.3.2\u200b Normal Distribution<br \/>\n &#8211; &#8211; 3.3.3\u200b Student\u2019s t-distribution<br \/>\n &#8211; 3.4\u200b Estimate and Its Error<br \/>\n &#8211; &#8211; 3.4.1\u200b Probability of a Sample inside a Confidence Interval<br \/>\n &#8211; &#8211; 3.4.2\u200b Mean of a Large Sample Size: Approximately Normal Distribution<br \/>\n &#8211; &#8211; 3.4.3\u200b Mean of a Small Sample Size t-Test<br \/>\n &#8211; 3.5\u200b Statistical Inference of a Linear Trend<br \/>\n &#8211; 3.6\u200b Free Online Statistics Tutorials<br \/>\n &#8211; 3.7 \u200bChapter Summary<br \/>\n &#8211; References and Further Readings<br \/>\n &#8211; Exercises<br \/>\n4\u200b Climate Data Matrices and Linear Algebra<br \/>\n &#8211; 4.1 \u200bMatrix as a Data Array<br \/>\n &#8211; 4.2\u200b Matrix Algebra<br \/>\n &#8211; &#8211; 4.2.1 \u200bMatrix Equality, Addition, and Subtraction<br \/>\n &#8211; &#8211; 4.2.2\u200b Matrix Multiplication<br \/>\n &#8211; 4.3\u200b A Set of Linear Equations<br \/>\n &#8211; 4.4\u200b Eigenvalues and Eigenvectors of a Square Space Matrix<br \/>\n &#8211; &#8211; 4.4.1 \u200bMatrices of Data Anomalies, Standardized Anomalies, Covariance, and Correlation<br \/>\n &#8211; &#8211; 4.4.2\u200b Eigenvectors and Their Corresponding Eigenvalues<br \/>\n &#8211; 4.5\u200b An SVD Representation Model for Space\u2013Time Data<br \/>\n &#8211; 4.6\u200b SVD Analysis of Southern Oscillation Index<br \/>\n &#8211; &#8211; 4.6.1 \u200bStandardized SLP Data and SOI<br \/>\n &#8211; &#8211; 4.6.2\u200b Weighted SOI Computed by the SVD Method<br \/>\n &#8211; &#8211; 4.6.3\u200b Visualization of the ENSO Mode Computed from the SVD Method<br \/>\n &#8211; 4.7\u200b Mass Balance for Chemical Equations in Marine Chemistry<br \/>\n &#8211; 4.8\u200b Multivariate Linear Regression Using Matrix Notations<br \/>\n &#8211; 4.9\u200b Chapter Summary<br \/>\n &#8211; References and Further Readings<br \/>\n &#8211; Exercises<br \/>\n5\u200b Energy Balance Models for Climate<br \/>\n &#8211; 5.1 \u200bEBM for Modeling the Moon\u2019s Surface Temperature<br \/>\n &#8211; &#8211; 5.1.1 \u200bMoon\u2013Earth\u2013Sun Orbit and Lunar Surface<br \/>\n &#8211; &#8211; 5.1.2\u200b Moon\u2019s Surface Temperature<br \/>\n &#8211; &#8211; 5.1.3\u200b EBM Prediction for the Moon Surface Temperature<br \/>\n &#8211; 5.2\u200b EBM for the Global Average Surface Temperature of the Earth: A Zero-Dimensional Climate Model<br \/>\n &#8211; &#8211; 5.2.1 \u200bThe Incoming Power from the Solar Radiation to the Earth<br \/>\n &#8211; &#8211; 5.2.2\u200b The Outgoing Power from Long-Wave Radiation Emitted by the Earth<br \/>\n &#8211; &#8211; 5.2.3\u200b EBM as a Power Balance<br \/>\n &#8211; 5.3\u200b EBM for the Global Average Surface Temperature of an Earth with a Nonlinear Albedo Feedback<br \/>\n &#8211; 5.4\u200b Time-Dependent Zero-Dimensional EBM for the Earth\u2019s Global Average Surface Temperature<br \/>\n &#8211; &#8211; 5.4.1 \u200bAn EBM Including Time Dependence<br \/>\n &#8211; &#8211; 5.4.2\u200b Stability Analysis of the Multiple Solutions of the EBM with a Nonlinear Albedo Feedback<br \/>\n &#8211; &#8211; 5.4.3\u200b Energy Flow Budget and Greenhouse Effect for the Earth\u2019s Climate<br \/>\n &#8211; 5.5\u200b Increasing the Complexity of Climate Models<br \/>\n &#8211; 5.6\u200b Chapter Summary<br \/>\n &#8211; References and Further Readings<br \/>\n &#8211; Exercises<br \/>\n6\u200b Calculus Applications to Climate Science I: Derivatives<br \/>\n &#8211; 6.1 \u200bStefan\u2013Boltzmann Law and Budyko\u2019s Approximation<br \/>\n &#8211; 6.2\u200b Linear Approximation<br \/>\n &#8211; 6.3\u200b Bisection Method for Solving Nonlinear Equations<br \/>\n &#8211; 6.4\u200b Newton\u2019s Method<br \/>\n &#8211; 6.5\u200b Examples of Higher-Order Derivatives<br \/>\n &#8211; 6.6\u200b Pressure Gradient Force and Coriolis Force<br \/>\n &#8211; 6.7\u200b Spatiotemporal Variations of the Atmospheric and Oceanic Temperature Fields<br \/>\n &#8211; 6.8\u200b Taylor Polynomial as a High-Order Approximation<br \/>\n &#8211; &#8211; 6.8.1 \u200bTaylor\u2019s Theorem<br \/>\n &#8211; &#8211; 6.8.2\u200b Taylor Series Example: Exponential Function<br \/>\n &#8211; &#8211; 6.8.3 \u200bNumerical Integration Using Taylor Expansion<br \/>\n &#8211; 6.9\u200b Chapter Summary<br \/>\n &#8211; References and Further Readings<br \/>\n &#8211; Exercises<br \/>\n7\u200b Calculus Applications to Climate Science II: Integrals<br \/>\n &#8211; 7.1 \u200bGeopotential and Atmospheric Pressure<br \/>\n &#8211; &#8211; 7.1.1 \u200bVertical Forces on a Small Parcel of Atmosphere<br \/>\n &#8211; &#8211; 7.1.2\u200b Geopotential<br \/>\n &#8211; 7.2\u200b Hypsometric Equation: Exponential Decrease of Pressure with Respect to Elevation<br \/>\n &#8211; &#8211; 7.2.1 \u200bThe General Hypsometric Equation<br \/>\n &#8211; &#8211; 7.2.2\u200b An Application of the Hypsometric Equation: Calculate the Elevation of Mount Mitchell<br \/>\n &#8211; &#8211; 7.2.3\u200b Hypsometric Equation for an Isothermal Layer<br \/>\n &#8211; &#8211; 7.2.4\u200b Error Estimate of the Linear Approximation to the Hypsometric Equation<br \/>\n &#8211; &#8211; 7.2.5\u200b Applications of Geopotential Height in Radiosonde Measurements<br \/>\n &#8211; 7.3\u200b Work Done by an Air Mass in Expansion<br \/>\n &#8211; 7.4\u200b Internal Energy, Enthalpy, and Entropy<br \/>\n &#8211; &#8211; 7.4.1 \u200bInternal Energy and Enthalpy<br \/>\n &#8211; &#8211; 7.4.2\u200b Entropy<br \/>\n &#8211; 7.5\u200b Use of Integrals to Derive Stefan\u2013Boltzmann\u2019s Blackbody Radiation Formula from Planck\u2019s Law of Radiation<br \/>\n &#8211; 7.6\u200b Chapter Summary<br \/>\n &#8211; References and Further Readings<br \/>\n &#8211; Exercises<br \/>\n8\u200b Conservation Laws in Climate Dynamics<br \/>\n &#8211; 8.1 \u200bConservation of Mass<br \/>\n &#8211; &#8211; 8.1.1 \u200bBasic Elements of the Continuum Mechanics Method for Climate Modeling<br \/>\n &#8211; &#8211; 8.1.2\u200b Lagrangian and Eulerian Observers, and Mass Conservation in the Lagrangian Framework<br \/>\n &#8211; &#8211; 8.1.3\u200b Total Derivative<br \/>\n &#8211; &#8211; 8.1.4\u200b Mass Conservation in the Eulerian Framework<br \/>\n &#8211; 8.2\u200b Conservation of Momentum Over a Grid Box: F = ma<br \/>\n &#8211; 8.3\u200b The Equations of Momentum Conservation in x, y, z, t Coordinates<br \/>\n &#8211; 8.4\u200b Geostrophic Approximation of the Momentum Equations<br \/>\n &#8211; &#8211; 8.4.1 \u200bMathematical Description of the Geostrophic Approximation<br \/>\n &#8211; &#8211; 8.4.2\u200b Flow Direction Perpendicular to the PGF under the Geostrophic Approximation<br \/>\n &#8211; 8.5\u200b The Potential Vorticity Conservation Equation<br \/>\n &#8211; &#8211; 8.5.1 \u200bAbsolute Vorticity and Relative Vorticity<br \/>\n &#8211; &#8211; 8.5.2\u200b Potential Vorticity and Its Conservation<br \/>\n &#8211; &#8211; 8.5.3\u200b Mathematical Derivations of the Conservation of Potential Vorticity<br \/>\n &#8211; 8.6\u200b Chapter Summary<br \/>\n &#8211; References and Further Readings<br \/>\n &#8211; Exercises<br \/>\n9\u200b R Graphics for Climate Science<br \/>\n &#8211; 9.1 \u200bTwo-Dimensional Line Plots and Setups of Margins and Labels<br \/>\n &#8211; &#8211; 9.1.1 \u200bPlot Two Different Time Series on the Same Plot<br \/>\n &#8211; &#8211; 9.1.2\u200b Figure Setups: Margins, Fonts, Mathematical Symbols, and More<br \/>\n &#8211; &#8211; 9.1.3\u200b Plot Two or More Panels on the Same Figure<br \/>\n &#8211; 9.2\u200b Color Contour Maps<br \/>\n &#8211; &#8211; 9.2.1 \u200bBasic Principles for an R Contour Plot<br \/>\n &#8211; &#8211; 9.2.2\u200b Plot Contour Color Maps for Random Values on a Map<br \/>\n &#8211; &#8211; 9.2.3\u200b Plot Contour Maps from Climate Model Data in NetCDF Files<br \/>\n &#8211; 9.3\u200b Plot Wind Velocity Field on a Map<br \/>\n &#8211; &#8211; 9.3.1 \u200bPlot a Wind Field Using arrow.plot<br \/>\n &#8211; &#8211; 9.3.2\u200b Plot a Surface Wind Field from netCDF Data<br \/>\n &#8211; 9.4\u200b ggplot for Data<br \/>\n &#8211; 9.5\u200b Animation<br \/>\n &#8211; 9.6\u200b Chapter Summary<br \/>\n &#8211; References and Further Readings<br \/>\n &#8211; Exercises<br \/>\n10\u200b Advanced R Analysis and Plotting: EOFs, Trends, and Global Data<br \/>\n &#8211; 10.1 \u200bIdeas of EOF, PC, and Variances Computed from SVD<br \/>\n &#8211; 10.2 2Dim Spatial Domain EOFs and 1Dim Temporal PCs<br \/>\n &#8211; &#8211; 10.2.1 \u200bGenerate Synthetic Data by R<br \/>\n &#8211; &#8211; 10.2.2\u200b SVD for the Synthetic Data EOFs, Variances, and PCs<br \/>\n &#8211; 10.3\u200b From Climate Data Download to EOF and PC Visualization: An NCEP\/NCAR Reanalysis Example<br \/>\n &#8211; &#8211; 10.3.1 \u200bDownload and Visualize the NCEP Temperature Data<br \/>\n &#8211; &#8211; 10.3.2\u200b Space\u2013Time Data Matrix and SVD<br \/>\n &#8211; 10.4\u200b Area-Weighted Average and Spatial Distribution of Trend<br \/>\n &#8211; &#8211; 10.4.1 \u200bGlobal Average and PC1<br \/>\n &#8211; &#8211; 10.4.2\u200b Spatial Pattern of Linear Trends<br \/>\n &#8211; 10.5\u200b GPCP Precipitation Data: Analysis and Visualization by R<br \/>\n &#8211; &#8211; 10.5.1 \u200bRead and Write GPCP Data<br \/>\n &#8211; &#8211; 10.5.2\u200b GPCP Climatology and Standard Deviation<br \/>\n &#8211; 10.6\u200b Chapter Summary<br \/>\n &#8211; References and Further Readings<br \/>\n &#8211; Exercises<br \/>\n11\u200b R Analysis of Incomplete Climate Data<br \/>\n &#8211; 11.1 \u200bThe Missing Data Problem<br \/>\n &#8211; 11.2\u200b Read NOAAGlobalTemp and Form the Space\u2013Time Data Matrix<br \/>\n &#8211; &#8211; 11.2.1 \u200bRead the Downloaded Data<br \/>\n &#8211; &#8211; 11.2.2\u200b Plot the Temperature Data Map of a Given Month<br \/>\n &#8211; &#8211; 11.2.3\u200b Extract the Data for a Specified Region<br \/>\n &#8211; &#8211; 11.2.4\u200b Extract Data from Only One Grid Box<br \/>\n &#8211; 11.3\u200b Spatial Averages and Their Trends<br \/>\n &#8211; &#8211; 11.3.1 \u200bCompute and Plot the Global Area-Weighted Average of Monthly Data<br \/>\n &#8211; &#8211; 11.3.2\u200b Percent Coverage of the NOAAGlobalTemp<br \/>\n &#8211; &#8211; 11.3.3\u200b Compare Trends and Variances at Two Different Locations<br \/>\n &#8211; &#8211; 11.3.4\u200b Which Month Has the Strongest Trend?<br \/>\n &#8211; &#8211; 11.3.5\u200b Spatial Average of Annual Data<br \/>\n &#8211; &#8211; 11.3.6\u200b Nonlinear Trend of the Global Average Annual Mean Data<br \/>\n &#8211; 11.4\u200b Spatial Characteristics of the Temperature Change Trends<br \/>\n &#8211; &#8211; 11.4.1 \u200bThe Twentieth-Century Temperature Trend<br \/>\n &#8211; &#8211; 11.4.2\u200b Twentieth-Century Temperature Trend Computed under a Relaxed Condition<br \/>\n &#8211; &#8211; 11.4.3\u200b Trend Pattern for the Four Decades of Consecutive Warming: 1976\u20132016<br \/>\n &#8211; 11.5\u200b Chapter Summary<br \/>\n &#8211; References and Further Readings<br \/>\n &#8211; Exercises<br \/>\nAppendix A. Dot Product of Two Vectors<br \/>\n &#8211; A.1\u200b Two Definitions for the Dot Product<br \/>\n &#8211; A.2\u200b Solar Power Flux to the Earth\u2019s Surface and Seasonality<br \/>\n &#8211; A.3\u200b Divergence Theorem for the Mass Continuity Equation in Climate Models<br \/>\nAppendix B. Cross Product of Two Vectors<br \/>\n &#8211; B.1\u200b Definition of the Cross Product of Two Vectors<br \/>\n &#8211; B.2\u200b Coriolis Force<br \/>\n &#8211; B.3\u200b Vorticity<br \/>\n &#8211; B.4\u200b Stokes\u2019 Theorem<br \/>\nAppendix C. Spherical Coordinates<br \/>\n &#8211; C.1\u200b Transform between the Spherical Coordinates and Cartesian Coordinates<br \/>\n &#8211; C.2\u200b Area and Volume Differentials in Spherical Coordinates<br \/>\nAppendix D. Calculus Concepts and Methods for Climate Science<br \/>\n &#8211; D.1\u200b Descartes\u2019 Direct Calculus for Functions of a Single Variable<br \/>\n &#8211; D.2\u200b Calculus from a Statistics Perspective<br \/>\n &#8211; D.3\u200b Differentiation Methods and Higher Derivatives<br \/>\n &#8211; D.4\u200b Calculus for Functions of Two and More Variables<br \/>\n &#8211; References and Further Readings Exercises<br \/>\nAppendix E. Sample Solutions to the Climate Mathematics Exercises<br \/>\nGlossary<br \/>\nIndex<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Samuel P. Shen &#038; Richard C. Somerville, 2019: Climate Mathematics: Theory and Applications. Cambridge UK: [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-9045","post","type-post","status-publish","format-standard","hentry","category-dokusyo-memo-"],"_links":{"self":[{"href":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/index.php?rest_route=\/wp\/v2\/posts\/9045","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9045"}],"version-history":[{"count":2,"href":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/index.php?rest_route=\/wp\/v2\/posts\/9045\/revisions"}],"predecessor-version":[{"id":9047,"href":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/index.php?rest_route=\/wp\/v2\/posts\/9045\/revisions\/9047"}],"wp:attachment":[{"href":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9045"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9045"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/macroscope.world.coocan.jp\/yukukawa\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9045"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}