Atmospheric Satellite Observations: Variation Assimilation and Quality Assurance

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Atmospheric Satellite Observations: Variation Assimilation and Quality Assurance
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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
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