Atmospheric Satellite Observations: Variation Assimilation and Quality Assurance

Description

Atmospheric Satellite Observations: Variation Assimilation and Quality Assurance provides an invaluable reference for satellite data assimilation. Topics covered include linear algebra, frequently used statistical methods, the interpolation role of function fitting, filtering when dealing with real observations, minimization in data assimilation systems, 3D-Var and the inverse problem it solves, 4D-Var and adjoint techniques, and much more. The book concludes with satellite observation of hurricanes. Contains mathematical concepts from several branches of study, including calculus, linear algebra, probability theory, functional analysis, and minimizationIllustrates quality assurance for satellite observations using real data examplesIncludes a dedicated chapter on how different satellite instruments see hurricanesReviews theory, system development, and the numerical experiments of three- and four-dimensional variational data assimilation (3D-Var/4D-Var) Cover Atmospheric Satellite Observations: Variation Assimilation and Quality Assurance Copyright Contents Preface 1 Introduction to data assimilation 1.1 What does data assimilation do? 1.2 Thermodynamic variables and the equation of state 1.3 Atmospheric governing equations for numerical weather prediction 2 Linear algebra and statistics 2.1 Introduction 2.2 Inner product and adjoint of linear mapping 2.3 Least-squares fit 2.4 Gaussian distribution 2.5 Maximum likelihood estimate 2.6 Error of the fit 2.7 Linear regression 2.8 Lagrangian multiplier 2.9 Minimum variance estimate 2.10 Concluding remarks 3 Interpolation 3.1 Introduction 3.2 Polynomial function fitting 3.3 Local fitting 3.4 Regional fitting 3.5 Adding background fields 3.6 Successive correction 3.7 Optimal interpolation 3.8 Background error covariance of geopotential field 3.9 Concluding remarks 4 Filtering 4.1 Introduction 4.2 Fourier transform 4.3 Variance contributions from different scales 4.4 Aliasing 4.5 Nonrecursive filters 4.6 Filter design 4.7 Recursive filters 4.8 Empirical ensemble mode decomposition 4.9 Concluding remarks 5 Minimization 5.1 Introduction 5.2 Extrema of functional 5.3 Scalar function, gradient, and Hessian matrix 5.4 Iterative minimization, line search, and rate of convergence 5.5 Steepest descent and Newton’s methods 5.6 Conjugate gradient method 5.7 Rank-one update formula for search direction 5.8 Rank-two update formula for search direction 5.9 The L-BFGS method 5.10 Method of line search 5.11 Concluding remarks 6 Adjoint model 6.1 Introduction 6.2 Adjoint in ordinary differential equation 6.3 Nonlinear model 6.4 Tangent linear model 6.5 Adjoint model 6.6 Equivalence between adjoint variables and Lagrangian multipliers 6.7 Analytic adjoint equations 6.8 Computer programming of adjoint models 6.9 Adjoint sensitivity and relative sensitivity 6.10 Concluding remarks 7 Microwave temperature sounding observations 7.1 Introduction 7.2 Polar-Orbiting Operational Environmental Satellites missions carrying microwave temperature sounders 7.3 Polar-Orbiting Operational Environmental Satellites orbital characteristics 7.4 Absorption and emission of radiation 7.5 Two-point calibration equation and observation errors 7.6 Absorption and emission weighting functions 7.7 A fast radiative transfer model 7.8 Channel characteristics, scan pattern, field-of-view, and weighting function 7.9 Advanced Technology Microwave Sounder striping noise analysis and mitigation 7.10 Fengyun-3 microwave temperature sounders 7.11 Relative sensitivity of Advanced Microwave Sounding Unit-A brightness temperatures 7.12 Concluding remarks 8 Three-dimensional variational data assimilation 8.1 Introduction 8.2 Deterministic mathematical formulation 8.3 Statistic formulation 8.4 The National Meteorological Center method for constructing B matrix 8.5 Recursive filters for constructing B matrix 8.6 Comparison between 3D-Var and the Kalman filter 8.7 AMSU-A cloud liquid water path retrieval and cloud detection 8.8 Bias estimate and bias correction 8.9 Impacts of AMSU-A data assimilation on quantitative precipitation forecasts 8.10 Additional remarks 9 Four-dimensional variational data assimilation 9.1 Introduction 9.2 Four-dimensional variational formulation and gradient calculation using adjoint model 9.3 Penalty method for controlling gravity-wave oscillations 9.4 Adjoints of physical parameterization schemes with “on–off” switches 9.5 Development of a full-physics global four-dimensional variational system 9.6 Development of two regional adjoint modeling systems 9.7 Parameter estimation 9.8 Incremental four-dimensional variational and its equivalence to the Kalman filter 9.9 Comparison of four-dimensional variational with extended and ensemble Kalman filters 9.10 Additional remarks 10 Global positioning system radio occultation observations 10.1 Introduction 10.2 GPS and LEO satellite orbital features and GPS RO missions 10.3 Excess phase delay and excess Doppler shift 10.4 Bending angle and impact parameter 10.5 Refractivity retrieval 10.6 Two local observation operators 10.7 A ray-tracing observation operator of bending angle 10.8 A tangent-link observation operator of excess phase 10.9 Multipath occurrence and detection 10.10 Observation error sources 10.11 Impacts of liquid and ice clouds 10.12 Temperature, pressure, and water vapor retrievals 10.13 Postlaunch calibration of satellite microwave temperature sounders data 10.14 Concluding remarks 11 Geostationary Operational Environmental Satellite imagers 11.1 Introduction 11.2 Geostationary Operational Environmental Satellite satellite altitude 11.3 GOES missions and IGFOV characteristics 11.4 Advanced Himawari Imager and Advanced Baseline Imager instrument characteristics 11.5 Cloud detection 11.6 Advanced Baseline Imager bias characterization 11.7 Geostationary Operational Environmental Satellite imager data assimilation 11.8 Simultaneous assimilation of GOES and POES sensors measurements 11.9 Concluding remarks 12 Satellite observations for tropical cyclones 12.1 Introduction 12.2 A general description of tropical cyclones 12.3 Typhoon Maria (2018) observed by Advanced Himawari Imager 12.4 Warm-core retrieval from AMSU-A and ATMS data 12.5 Conical-scanning microwave radiometers AMSR2 and MWRI 12.6 Microwave humidity sensors MHS, ATMS, MWHS, and MWHS2 12.7 Satellite total column ozone data from TOMS and OMPS 12.8 Hyperspectral infrared sounders AIRS, IASI, and CrIS 12.9 Vortex initialization 12.10 Additional remarks Bibliography Index Back Cover