Solar radiative transfer parameterizations for three-dimensional effects in cloudy atmospheres [Elektronische Ressource] / Matthias Peter Jerg

Matthias Peter Jerg

Informations

• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2006
• Nombre de lectures: 17
• Langue: English
• Poids de l'ouvrage: 17 Mo

Extrait

Solar radiative transfer
parameterizations for three-dimensional
effects in cloudy atmospheres
Matthias Peter Jerg
Munc¨ hen 2006Solar radiative transfer
parameterizations for three-dimensional
effects in cloudy atmospheres
Matthias Peter Jerg
Dissertation
an der Fakult¨at fur¨ Physik
der Ludwig–Maximilians–Universit¨at
Munc¨ hen
vorgelegt von
Matthias Peter Jerg
aus Ludwigshafen am Rhein
Munc¨ hen, den 14.09.2006Erstgutachter: Prof. Dr. Susanne Crewell
Zweitgutachter: Prof. Dr. Thomas Trautmann
Tag der mundlic¨ hen Prufung¨ : 11.12.2006Fur¨ meine Eltern.
To my parents.viContents
Contents vii
List of Figures viii
List of Tables xii
Zusammenfassung xv
Abstract xvii
1 Introduction 1
1.1 Motivation of the Conducted Work . . . . . . . . . . . . . . . . . . . . . . 1
1.2 State-of-the-art of Science . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Outline of the Thesis and Applied Methods and Models . . . . . . . . . . . 6
2 Radiative Transfer Fundamentals 9
2.1 Definition of Radiative Properties . . . . . . . . . . . . . . . . . . . . . . . 9
2.2n of Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Optical Properties of the Atmosphere . . . . . . . . . . . . . . . . . . . . . 17
2.4 Deriving Cloud Optical Properties . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 Radiative Transfer Equation for 1D and 3D Problems . . . . . . . . . . . . 31
2.6 Discrete Ordinate Method for 1D Problems . . . . . . . . . . . . . . . . . . 35
3 Adjoint Radiative Transfer and the Perturbation Theory 39
3.1 Adjoint Radiative Transfer Equation . . . . . . . . . . . . . . . . . . . . . 39
3.2 Linear Perturbation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4 Treatment of Lambertian Surface Reflection . . . . . . . . . . . . . . . . . 47
3.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6 Multiple Base Cases and Interpolation . . . . . . . . . . . . . . . . . . . . 50
3.7 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.8 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54viii Table of Contents
4 3D radiative transfer parameterizations 57
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 Tilted Independent Pixel Approximation . . . . . . . . . . . . . . . . . . . 64
4.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4 Nonlocal Independent Pixel Approximation. . . . . . . . . . . . . . . . . . 70
4.5 Diffusion Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.6 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.7 Nonlocal Tilted Independent Pixel Approximation . . . . . . . . . . . . . . 84
4.8 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.9 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5 Application of the Methods and Results 95
5.1 1D Radiative Transfer Perturbation Theory . . . . . . . . . . . . . . . . . 95
5.1.1 Example 1: INSPECTRO stratocumulus . . . . . . . . . . . . . . . 96
5.1.2 2: FIRE stratus . . . . . . . . . . . . . . . . . . . . . . . 102
5.1.3 Example 3: ARM cumulus . . . . . . . . . . . . . . . . . . . . . . . 104
5.1.4 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2 3D Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2.1 High Resolution Clouds . . . . . . . . . . . . . . . . . . . . . . . . 108
5.2.2 Medium Resolution Cloud . . . . . . . . . . . . . . . . . . . . . . . 128
5.2.3 Coarse Resolution Clouds . . . . . . . . . . . . . . . . . . . . . . . 135
6 Discussion and Conclusions 149
6.1 Review of the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.2 Future Research and Improvements . . . . . . . . . . . . . . . . . . . . . . 157
A First Order Perturbation Expansion 161
B Expressions for the Albedo Related Perturbation Integral 163
Symbols 165
Acronyms 169
Bibliography 171
Acknowledgment 179List of Figures
1.1 Cloud-radiation interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Annual global mean energy budget of the earth . . . . . . . . . . . . . . . 3
1.3 Global mean radiative forcing. . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Definition of the solid angle Ω created by the surface A at distance r. . . . 10
2.2n of the general Cartesian coordinate system. . . . . . . . . . . . . 11
2.3 Definition of the local coordinate system. . . . . . . . . . . . . . . . . . . . 12
2.4 The τ-coordinate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Shortwave irradiance as a function of wavelength. . . . . . . . . . . . . . . 18
2.6 Size distributions of clouds. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7 Time series and energy spectrum of liquid water content. . . . . . . . . . . 24
2.8 Surface elevation of the LM domain. . . . . . . . . . . . . . . . . . . . . . 27
2.9 Transformation from η to Cartesian coordinates. . . . . . . . . . . . . . . . 29
2.10 Comparison of original and transformed partial cloud cover. . . . . . . . . 31
3.1 The pseudo problem for adjoint radiative transfer. . . . . . . . . . . . . . . 42
3.2 Perturbation of the extinction coefficient for Example 1. . . . . . . . . . . 46
3.3 Example 1: Perturbation result for the net flux-density. . . . . . . . . . . . 47
3.4 2: Result for the net flux-density for a perturbation of the asym-
metry factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Example 3: Result for the pure albedo superposition. . . . . . . . . . . . . 51
3.6 4: Result for the net flux-density for perturbation and albedo
superposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.7 Example 5: Result for the net flux-density for linear and interpolated esti-
mates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.8 Errors for the net flux-density for linear and interpolated estimates. . . . . 54
4.1 Realistic behavior of photons in an heterogeneous medium. . . . . . . . . . 58
4.2 Example for independent pixel radiative transport. . . . . . . . . . . . . . 59
4.3 Trapping of photons inside clouds. . . . . . . . . . . . . . . . . . . . . . . . 59
4.4 Leaking of photons through cloud sides.. . . . . . . . . . . . . . . . . . . . 60
4.5 Interaction of cloud layers by scattering of photons. . . . . . . . . . . . . . 60
4.6 Shadowing by propagation of photons through cloud gaps. . . . . . . . . . 61x LIST OF FIGURES
4.7 Penetration of photons through cloud sides. . . . . . . . . . . . . . . . . . 61
4.8 Interaction of cloud top and cloud side. . . . . . . . . . . . . . . . . . . . . 62
4.9 Plane-parallel radiative transfer. . . . . . . . . . . . . . . . . . . . . . . . . 62
4.10 Reflection as a function of total optical depth. . . . . . . . . . . . . . . . . 63
4.11 Scale break due to radiative smoothing. . . . . . . . . . . . . . . . . . . . . 64
4.12 Concept of the TIPA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.13 Vertical coordinates of TIPA . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.14 Example profiles of the downwelling flux-density for the example with pure
absorption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.15 HistogramsandcumulativedistributionsforΔT andΔR forthemixedcase
cloud. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.16 Schematic convolution of a 2D field. . . . . . . . . . . . . . . . . . . . . . . 71
4.17 Example of 2D Gaussian convolution kernels for different values of σ. . . . 72
4.18 Diffusion approximation of the intensity. . . . . . . . . . . . . . . . . . . . 73
4.19 ComparisonofthedensityderivedfromDiAwith3DMCforahomogeneous
cloud. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.20 2D field of U /T at the lower boundary of the homogeneous cloud. . . . . . 77d
4.21 2D field of the total optical depth of the sinx×cosy example. . . . . . . . 79
4.22 Distributions of absolute errors ΔR and ΔT derived from IPA and 3DMC
for the sinx×cosy example. . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.23 Functional dependence of the absolute errors ΔT and ΔR derived from IPA
and 3DMC on optical depth for the sinx×cosy example. . . . . . . . . . 81
4.24 Functional dependence of the absolute errors ΔT and ΔR derived from IPA
and 3DMC on area for the sinx×cosy example.. . . . . . . . . . . . . . . 82
4.25 Distributions of absolute errors ΔR and ΔT derived from NIPA and 3DMC
for the sinx×cosy example. . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.26 Functional dependence of the errors ΔT and ΔR of NIPA on the optical
depth for the sinx×cosy example. . . . . . . . . . . . . . . . . . . . . . . 83
4.27 Functional dependence of the absolute errors ΔT and ΔR deduced from
NIPA and 3DMC on averaging area for the sinx×cosy example. . . . . . 83
4.29 Histograms of transmission and reflection errors of NTIPA for t