3D Radiative Transfer in Cloud Resolving Models

Fabian Jakub, Carolin Klinger

LMU - Meteorological Institute Munich

November 16, 2015

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Does 3D Radiative Transfer impact cloud evolution?

Earlier studies suggest radiation may affect

I cloud evolution and lifetime

I microphysical processes (condensation, nucleation)

I precipitation onset/amount

I convective organization

Can we model radiative transfer in the atmosphere?

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Does 3D Radiative Transfer impact cloud evolution?

Earlier studies suggest radiation may affect

I cloud evolution and lifetime

I microphysical processes (condensation, nucleation)

I precipitation onset/amount

I convective organization

Can we model radiative transfer in the atmosphere?

2 / 26

HD(CP)2 project (www.hdcp2.eu)

I run hindcasts over Central Europe

I 100m horizontal resolution

I grids consisting of 10.000 x 15.000 x 300 voxels

I first develop a model capable of running it (ICON)

I . . . with the goal to develop improved parameterizations for

weather and climate predictions

3 / 26

History of Radiative Transfer

Radiative Transfer theory well established

I radiative transfer equation (1960 Chandrasekhar)

dL

kext · ds= −L+

ω0

4π

∫4π

p(Ω′,Ω) L(Ω

′)dΩ

′+(1−ω0)BPlanck(T )

I surprisingly well working 1D approximations

I sophisticated 3D models since the 90’s (e.g. MonteCarlo)

I . . . but orders of magnitude too slow to run in atmospheric

models

4 / 26

History of Radiative Transfer

Radiative Transfer theory well established

I radiative transfer equation (1960 Chandrasekhar)

dL

kext · ds= −L+

ω0

4π

∫4π

p(Ω′,Ω) L(Ω

′)dΩ

′+(1−ω0)BPlanck(T )

I surprisingly well working 1D approximations

I sophisticated 3D models since the 90’s (e.g. MonteCarlo)

I . . . but orders of magnitude too slow to run in atmospheric

models

4 / 26

History of Radiative Transfer

Radiative Transfer theory well established

I radiative transfer equation (1960 Chandrasekhar)

dL

kext · ds= −L+

ω0

4π

∫4π

p(Ω′,Ω) L(Ω

′)dΩ

′+(1−ω0)BPlanck(T )

I surprisingly well working 1D approximations

I sophisticated 3D models since the 90’s (e.g. MonteCarlo)

I . . . but orders of magnitude too slow to run in atmospheric

models

4 / 26

Approximations for Radiative Transfer

Radiative transfer describes photon interactions with atmosphere.MonteCarlo modeling of scattering and absorption:

simplify to solve:

I Plane Parallel approx.

I Independent Column approx.

I Twostream solvers

I diagonal band-matrix (5)

5 / 26

Approximations for Radiative Transfer

Radiative transfer describes photon interactions with atmosphere.MonteCarlo modeling of scattering and absorption:

simplify to solve:

I Plane Parallel approx.

I Independent Column approx.

I Twostream solvers

I diagonal band-matrix (5)

5 / 26

Approximations for Radiative Transfer

Radiative transfer describes photon interactions with atmosphere.MonteCarlo modeling of scattering and absorption:

simplify to solve:

I Plane Parallel approx.

I Independent Column approx.

I Twostream solvers

I diagonal band-matrix (5)

5 / 26

A walk through the ages

3D parameterizations – a tradition at MIM:

I Tilted-ICA (Gabriel and Evans 1996,

Varnai 1999)

I Non-local ICA (Marshak 1998)

I displaced shadow regions (Schumann 2002)

I TICA in EULAG (Wapler 2008)

I NICA with automatic kernel

size (Wissmeier 2012)

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A walk through the ages

3D parameterizations – a tradition at MIM:

I Tilted-ICA (Gabriel and Evans 1996,

Varnai 1999)

I Non-local ICA (Marshak 1998)

I displaced shadow regions (Schumann 2002)

I TICA in EULAG (Wapler 2008)

I NICA with automatic kernel

size (Wissmeier 2012)

6 / 26

A walk through the ages

3D parameterizations – a tradition at MIM:

I Tilted-ICA (Gabriel and Evans 1996,

Varnai 1999)

I Non-local ICA (Marshak 1998)

I displaced shadow regions (Schumann 2002)

I TICA in EULAG (Wapler 2008)

I NICA with automatic kernel

size (Wissmeier 2012)

6 / 26

Why care for 3D radiation now? – a matter of resolution

Complex cloud radiation interaction

Visualization done with libRadtran.org/MYSTIC (Montecarlo code for the phYSically correct Tracing of photons In Cloudy atmospheres)

Mayer,

B., 2009. Radiative transfer in the cloudy atmosphere (EPJ Web of Conferences)

7 / 26

Why care for 3D radiation now? – a matter of resolution

Global models

Visualization done with libRadtran.org/MYSTIC (Montecarlo code for the phYSically correct Tracing of photons In Cloudy atmospheres)

Mayer,

B., 2009. Radiative transfer in the cloudy atmosphere (EPJ Web of Conferences)

7 / 26

Why care for 3D radiation now? – a matter of resolution

Weather models today

Visualization done with libRadtran.org/MYSTIC (Montecarlo code for the phYSically correct Tracing of photons In Cloudy atmospheres) Mayer,

B., 2009. Radiative transfer in the cloudy atmosphere (EPJ Web of Conferences)

7 / 26

Why care for 3D radiation now? – a matter of resolution

Next-gen models

Visualization done with libRadtran.org/MYSTIC (Montecarlo code for the phYSically correct Tracing of photons In Cloudy atmospheres) Mayer,

B., 2009. Radiative transfer in the cloudy atmosphere (EPJ Web of Conferences)

7 / 26

Why care for 3D radiation now? – a matter of resolution

Next-gen models

Visualization done with libRadtran.org/MYSTIC (Montecarlo code for the phYSically correct Tracing of photons In Cloudy atmospheres) Mayer,

B., 2009. Radiative transfer in the cloudy atmosphere (EPJ Web of Conferences)

7 / 26

The Tenstream solver

A new concept for a solver – what do we want?

I3RC cloud scene, benchmark heating rate

calculation with MYSTIC (MonteCarlo code)

I accurately approximate 3D

effects

I has to be several orders of

magnitude faster than state

of the art 3D solvers

I parallelizable on modern

machines

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The TenStream solver

Finite Volume formalism:Discretization of energy transport – spatially and by angle

ST↓

SL→

SR→

SB↓

(a) direct streams (θ=40)

EB↑

ET↓

ERւEL

ց

ERտEL

ր

(b) diffuse streams

Fabian Jakub and Bernhard Mayer, 2015. A three-dimensional parallel radiative transfer model for atmospheric

heating rates for use in cloud resolving models – The TenStream solver (JQSRT)

9 / 26

The TenStream solver

Setup equation system for one voxel:

ET↑

EB↓

EL

ER

EL

ER

SB↓

SR→

=

γ1 γ2 γ3 γ3 γ4 γ4 β01 β11

γ2 γ1 γ4 γ4 γ3 γ3 β02 β12

γ5 γ6 γ7 γ8 γ9 γ10 β03 β13

γ5 γ6 γ8 γ7 γ10 γ9 β04 β14

γ6 γ5 γ9 γ10 γ7 γ8 β05 β15

γ6 γ5 γ10 γ9 γ8 γ7 β06 β16

0 0 0 0 0 0 α00 α10

0 0 0 0 0 0 α01 α11

EB↑

ET↓

ER

EL

ER

EL

ST↓

SL→

Coupling voxels in 3

dimensions. . .

. . . gives huge but sparse matrix.

=⇒ solve with PETSc!

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The TenStream solver

Setup equation system for one voxel:

ET↑

EB↓

EL

ER

EL

ER

SB↓

SR→

=

γ1 γ2 γ3 γ3 γ4 γ4 β01 β11

γ2 γ1 γ4 γ4 γ3 γ3 β02 β12

γ5 γ6 γ7 γ8 γ9 γ10 β03 β13

γ5 γ6 γ8 γ7 γ10 γ9 β04 β14

γ6 γ5 γ9 γ10 γ7 γ8 β05 β15

γ6 γ5 γ10 γ9 γ8 γ7 β06 β16

0 0 0 0 0 0 α00 α10

0 0 0 0 0 0 α01 α11

EB↑

ET↓

ER

EL

ER

EL

ST↓

SL→

Coupling voxels in 3

dimensions. . .

. . . gives huge but sparse matrix.

=⇒ solve with PETSc!

10 / 26

Energy transport coefficients

We need to determine the energy transport

from one stream to another:

EB↑

ET↓

ERւEL

ց

ERտEL

ր

→ solve radiative transfer equation with

MonteCarlo method

. . . and put them into LookUpTable

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Energy transport coefficients

We need to determine the energy transport

from one stream to another:

EB↑

ET↓

ERւEL

ց

ERտEL

ր

→ solve radiative transfer equation with

MonteCarlo method

. . . and put them into LookUpTable

11 / 26

Does it work?

3D MYSTIC 1D independent-column Twostream

Computations done with libRadtran (Library for Radiative Transfer, libradtran.org)

12 / 26

Does it work?

3D MYSTIC TenStream

Computations done with libRadtran (Library for Radiative Transfer, libradtran.org)

12 / 26

Thermal Radiative Transfer

Thermal spectral range (Wallace and Hobbs 2006, p.114).

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3D Solar vs. Thermal Radiative Transfer

3D Solar 3D Thermal

Heating Rate [K/d]Surface Flux [W/m2]

0 30 60 90 120700 595 463 283 0 - - - -

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Monte Carlo Variance Reduction Techniques

Emission–Absorption

dT

dt= − 1

ρ cp(qem−qabs)

0.0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Sta

ndard

Devia

tion

[K/d

]

1 2 5 10 2 5 102

Optical Thickness

(1) Emission - Absorption

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Monte Carlo Variance Reduction Techniques

Emission–Absorption

dT

dt= − 1

ρ cp(qem−qabs)

0.0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Sta

ndard

Devia

tion

[K/d

]

1 2 5 10 2 5 102

Optical Thickness

(1) Emission - Absorption

(1b) Emission - Absorption (Variance Reduction)

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Monte Carlo Variance Reduction Techniques

Net Flux Divergence

dT

dt= − 1

ρ cp∇ ~Enet

0.0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Sta

ndard

Devia

tion

[K/d

]

1 2 5 10 2 5 102

Optical Thickness

(1) Emission - Absorption

(1b) Emission - Absorption (Variance Reduction)

(2) Net Flux Divergence

15 / 26

Monte Carlo Variance Reduction Techniques

CombiningEmission–Absorptionand Net FluxDivergence toHYBRID

0.0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Sta

ndard

Devia

tion

[K/d

]

1 2 5 10 2 5 102

Optical Thickness

(1) Emission - Absorption

(1b) Emission - Absorption (Variance Reduction)

(2) Net Flux Divergence

(3) HYBRID

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3D vs. 1D Thermal Radiative Transfer

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Neighboring Column Approximation NCA

MYSTIC NCA ICA

17 / 26

Neighboring Column Approximation NCA

MYSTIC NCA ICA

17 / 26

Neighboring Column Approximation NCA

MYSTIC NCA

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Neighboring Column Approximation NCA

MYSTIC NCA

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Neighboring Column Approximation NCA

MYSTIC NCA

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Neighboring Column Approximation NCA

MYSTIC NCA

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NCA vs. 1D - NCA vs. 3D MYSTIC

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NCA vs. 1D - NCA vs. 3D MYSTIC

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Couple Paramterizations to Atmospheric Model

TenStream solver and NCA coupled to the UCLA-LES

I use LES to model atmospheric flow with resolutions from

10 m to 1 km

I consider dynamics, turbulence, microphysics and radiation

I TenStream solver increases total model runtime by factor 3-5

I NCA only factor 1.5-2 more expensive

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Cloud Evolution With 3D Thermal Radiation

Shallow Cumulus Cloud Field

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Cloud Evolution With 3D Thermal Radiation

Shallow Cumulus Cloud Field

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Cloud Evolution With 3D Thermal Radiation

Single CloudNo Radiation 1D Thermal ICA 3D Thermal NCA

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Cloud Evolution With 3D Thermal Radiaton

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Flying through a Cloud Field

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Current state and a glimpse at whats to come..

Conclusions

I Development of 2 parallel solvers

I Implemented in UCLA-LES

I Unprecedented large and extensive simulations

Outlook

I Further investigation of simulations (cloud organization)

I RCE simulations

I Get ready for large scale computations in ICON – HD(CP)2-Project

I Systematic analysis of 3D effects and impact on large scale flow –

W 2W -Project

25 / 26

Thank you!

Carolin Klinger and Bernhard Mayer, 2014. Three-dimensional Monte Carlo calculation of atmospheric thermal heating rates (JQSRT)

Fabian Jakub and Bernhard Mayer, 2015. A three-dimensional parallel radiative transfer model for atmospheric heating rates for use incloud resolving models – The TenStream solver (JQSRT)

Carolin Klinger and Bernhard Mayer, 2015. The Neighboring Column Approximation (NCA) - A fast approach for the calculation of 3Dthermal heating rates in cloud resolving models (JQSRT)

Fabian Jakub and Bernhard Mayer, 2015. 3-D radiative transfer in large-eddy simulations - experiences coupling the TenStream solver tothe UCLA-LES (GMDD)

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