Strahlungs-Seminar

A new Radiative Transfer Solver

for fast computation of 3D Heating Rates

for use in LES models

Fabian Jakub

5. Juni 2014

1 / 24

Does 3D Radiative Transfer impact cloud evolution?

Very likely:

• Schumann [2002]

• Frame et al. [2009]

• Wapler & Mayer [2007]

• O’Hirok [2005,ARM Meeting]

Until today, no operational 3D RT scheme available!

2 / 24

Does 3D Radiative Transfer impact cloud evolution?

Very likely:

• Schumann [2002]

• Frame et al. [2009]

• Wapler & Mayer [2007]

• O’Hirok [2005,ARM Meeting]

Until today, no operational 3D RT scheme available!

2 / 24

Does 3D Radiative Transfer impact cloud evolution?

Very likely:

• Schumann [2002]

• Frame et al. [2009]

• Wapler & Mayer [2007]

• O’Hirok [2005,ARM Meeting]

Until today, no operational 3D RT scheme available!

2 / 24

Does 3D Radiative Transfer impact cloud evolution?

Very likely:

• Schumann [2002]

• Frame et al. [2009]

• Wapler & Mayer [2007]

• O’Hirok [2005,ARM Meeting]

Until today, no operational 3D RT scheme available!

2 / 24

Does 3D Radiative Transfer impact cloud evolution?

Very likely:

• Schumann [2002]

• Frame et al. [2009]

• Wapler & Mayer [2007]

• O’Hirok [2005,ARM Meeting]

Until today, no operational 3D RT scheme available!

2 / 24

Why bother with 3D RT for Heating Rates?

As a consequence of efficiency:

• all NWP/LES models use Independent Pixel Approximation

• usually employ two-stream solver

• sparse temporal sampling

If model resolution < 1km need 3D RT!

3 / 24

Why bother with 3D RT for Heating Rates?

As a consequence of efficiency:

• all NWP/LES models use Independent Pixel Approximation

• usually employ two-stream solver

• sparse temporal sampling

If model resolution < 1km need 3D RT!

3 / 24

Why bother with 3D RT for Heating Rates?

As a consequence of efficiency:

• all NWP/LES models use Independent Pixel Approximation

• usually employ two-stream solver

• sparse temporal sampling

If model resolution < 1km need 3D RT!

3 / 24

Why bother with 3D RT for Heating Rates?

As a consequence of efficiency:

• all NWP/LES models use Independent Pixel Approximation

• usually employ two-stream solver

• sparse temporal sampling

If model resolution < 1km need 3D RT!

3 / 24

IPA vs. 3D RT

4 / 24

Exemplary cloud field

• solar zenith: 60◦

• resolution: dx = 70m,dz = 40m

5 / 24

IPA compared to 3D calculation

Main differences at ground:

• Shadows translated

• Irradiance locally bigger than in

clear sky

• RMSE: 62%

• Bias: +4%

(IPA → more Irradiance at ground)

0 1 2 3 4 5 60

1

2

3

4

5

6

y [

km]

3D

080160240320400480560640720800

Irra

dia

nce

[W

m2

]

0 1 2 3 4 5 6x [km]

0

1

2

3

4

5

6

y [

km]

IPA

080160240320400480560640720800

Irra

dia

nce

[W

m2

]

;6 / 24

IPA compared to 3D calculation

Main differences at ground:

• Shadows translated

• Irradiance locally bigger than in

clear sky

• RMSE: 62%

• Bias: +4%

(IPA → more Irradiance at ground)

0 1 2 3 4 5 60

1

2

3

4

5

6

y [

km]

3D

080160240320400480560640720800

Irra

dia

nce

[W

m2

]

0 1 2 3 4 5 6x [km]

0

1

2

3

4

5

6

y [

km]

IPA

080160240320400480560640720800

Irra

dia

nce

[W

m2

]

;6 / 24

IPA compared to 3D calculation

Main differences at ground:

• Shadows translated

• Irradiance locally bigger than in

clear sky

• RMSE: 62%

• Bias: +4%

(IPA → more Irradiance at ground)

0 1 2 3 4 5 60

1

2

3

4

5

6

y [

km]

3D

080160240320400480560640720800

Irra

dia

nce

[W

m2

]

0 1 2 3 4 5 6x [km]

0

1

2

3

4

5

6

y [

km]

IPA

080160240320400480560640720800

Irra

dia

nce

[W

m2

]

;6 / 24

IPA compared to 3D calculation

Main differences at ground:

• Shadows translated

• Irradiance locally bigger than in

clear sky

• RMSE: 62%

• Bias: +4%

(IPA → more Irradiance at ground)

0 1 2 3 4 5 60

1

2

3

4

5

6

y [

km]

3D

080160240320400480560640720800

Irra

dia

nce

[W

m2

]

0 1 2 3 4 5 6x [km]

0

1

2

3

4

5

6

y [

km]

IPA

080160240320400480560640720800

Irra

dia

nce

[W

m2

]

;6 / 24

IPA compared to 3D calculation

Main differences in atmosphere:

• Heating on cloud side faces

• Elongated cloud shadows

• RMSE: 74%

• Bias: −12%

(3D → more absorption)

0 1 2 3 4 5 60.0

0.5

1.0

1.5

2.0

2.5

h [

km]

3D

08162432404856647280

HR

[K

/day]

0 1 2 3 4 5 6x [km]

0.0

0.5

1.0

1.5

2.0

2.5h [

km]

IPA

08162432404856647280

HR

[K

/day]

;

7 / 24

IPA compared to 3D calculation

Main differences in atmosphere:

• Heating on cloud side faces

• Elongated cloud shadows

• RMSE: 74%

• Bias: −12%

(3D → more absorption)

0 1 2 3 4 5 60.0

0.5

1.0

1.5

2.0

2.5

h [

km]

3D

08162432404856647280

HR

[K

/day]

0 1 2 3 4 5 6x [km]

0.0

0.5

1.0

1.5

2.0

2.5h [

km]

IPA

08162432404856647280

HR

[K

/day]

;

7 / 24

IPA compared to 3D calculation

Main differences in atmosphere:

• Heating on cloud side faces

• Elongated cloud shadows

• RMSE: 74%

• Bias: −12%

(3D → more absorption)

0 1 2 3 4 5 60.0

0.5

1.0

1.5

2.0

2.5

h [

km]

3D

08162432404856647280

HR

[K

/day]

0 1 2 3 4 5 6x [km]

0.0

0.5

1.0

1.5

2.0

2.5h [

km]

IPA

08162432404856647280

HR

[K

/day]

;

7 / 24

IPA compared to 3D calculation

Main differences in atmosphere:

• Heating on cloud side faces

• Elongated cloud shadows

• RMSE: 74%

• Bias: −12%

(3D → more absorption)

0 1 2 3 4 5 60.0

0.5

1.0

1.5

2.0

2.5

h [

km]

3D

08162432404856647280

HR

[K

/day]

0 1 2 3 4 5 6x [km]

0.0

0.5

1.0

1.5

2.0

2.5h [

km]

IPA

08162432404856647280

HR

[K

/day]

;

7 / 24

A trip down memory lane

Tilted Independent Pixel Approx.

Zuidema and Evans [1998] & Wissmeier [2013]

8 / 24

A trip down memory lane

0 20 40 60 80

0

20

40

60

80

0 20 40 60 80

0

20

40

60

80

Diffuse Downward Irradiance at Ground

IPA Non-Local IPA

Marshak et al. [1998] & Wissmeier [2013]

9 / 24

Master Thesis

• combine TIPA and NIPA ( Wissmeier )

• physically parametrize smoothing width

• apply to atmosphere

10 / 24

Master Thesis

• combine TIPA and NIPA ( Wissmeier )

• physically parametrize smoothing width

• apply to atmosphere

10 / 24

Master Thesis

• combine TIPA and NIPA ( Wissmeier )

• physically parametrize smoothing width

• apply to atmosphere

Good for fluxes.

Not so for Absorption!

Parallelizes poorly!

10 / 24

PhD Thesis

Time for a new concept!

11 / 24

Concept for a new Solver

• two-stream → N-stream

• Minimum

• 3 for direct radiation → S0,S1,S2

• 10 for diffuse radiation → Edn,Eup,Ele . . .

• Transport coefficients from MonteCarlo

model

• Couple boxes in linear equation system

12 / 24

Concept for a new Solver

• two-stream → N-stream

• Minimum

• 3 for direct radiation → S0,S1,S2

• 10 for diffuse radiation → Edn,Eup,Ele . . .

• Transport coefficients from MonteCarlo

model

• Couple boxes in linear equation system

12 / 24

Concept for a new Solver

• two-stream → N-stream

• Minimum

• 3 for direct radiation → S0,S1,S2

• 10 for diffuse radiation → Edn,Eup,Ele . . .

• Transport coefficients from MonteCarlo

model

• Couple boxes in linear equation system

12 / 24

Concept for a new Solver

• two-stream → N-stream

• Minimum

• 3 for direct radiation → S0,S1,S2

• 10 for diffuse radiation → Edn,Eup,Ele . . .

• Transport coefficients from MonteCarlo

model

• Couple boxes in linear equation system

12 / 24

Recalling the two-stream form

E+up

E−dn

E−dir

=

a11 a12 a13a12 a11 a230 0 a33

E−up

E+dn

E+dir

(E+up

E−dn

)=

(a11 a12a12 a11

)(E−up

E+dn

)+

(a13 · E+

dira23 · E+

dir

)

1 −a11 −a12−a12 1

1 −a11−a11 −a12 1

Eiup

Eidn

Ei+1up

Ei+1dn

=

biupbidnbi+1up

bi+1dn

13 / 24

Recalling the two-stream form

E+up

E−dn

E−dir

=

a11 a12 a13a12 a11 a230 0 a33

E−up

E+dn

E+dir

(E+up

E−dn

)=

(a11 a12a12 a11

)(E−up

E+dn

)+

(a13 · E+

dira23 · E+

dir

)

1 −a11 −a12−a12 1

1 −a11−a11 −a12 1

Eiup

Eidn

Ei+1up

Ei+1dn

=

biupbidnbi+1up

bi+1dn

13 / 24

Recalling the two-stream form

E+up

E−dn

E−dir

=

a11 a12 a13a12 a11 a230 0 a33

E−up

E+dn

E+dir

(E+up

E−dn

)=

(a11 a12a12 a11

)(E−up

E+dn

)+

(a13 · E+

dira23 · E+

dir

)

1 −a11 −a12−a12 1

1 −a11−a11 −a12 1

Eiup

Eidn

Ei+1up

Ei+1dn

=

biupbidnbi+1up

bi+1dn

13 / 24

Non-zero pattern of 3x3x3 10-stream Matrix

• Matrix is huge but

very sparse

• Direct Solver requires

too much memory

• → Solve iteratively

• Parallelization results

in non-local product

(PETSc library)

14 / 24

Non-zero pattern of 3x3x3 10-stream Matrix

• Matrix is huge but

very sparse

• Direct Solver requires

too much memory

• → Solve iteratively

• Parallelization results

in non-local product

(PETSc library)

14 / 24

Non-zero pattern of 3x3x3 10-stream Matrix

• Matrix is huge but

very sparse

• Direct Solver requires

too much memory

• → Solve iteratively

• Parallelization results

in non-local product

(PETSc library)

14 / 24

Non-zero pattern of 3x3x3 10-stream Matrix

• Matrix is huge but

very sparse

• Direct Solver requires

too much memory

• → Solve iteratively

• Parallelization results

in non-local product

(PETSc library)

Local computation Non-local computation

14 / 24

Transport Coefficients

• Use simple MonteCarlo Raytracer

• Transport Coefficients depend on:

• dz/dx aspect ratio

• βscatter scattering coefficient

• βabsorption absorption coefficient

• g asymmetry parameter

• θ, φ sun angles

• save in LookUpTable

• Linear Interpolation

15 / 24

Transport Coefficients

• Use simple MonteCarlo Raytracer

• Transport Coefficients depend on:

• dz/dx aspect ratio

• βscatter scattering coefficient

• βabsorption absorption coefficient

• g asymmetry parameter

• θ, φ sun angles

• save in LookUpTable

• Linear Interpolation

15 / 24

Transport Coefficients

• Use simple MonteCarlo Raytracer

• Transport Coefficients depend on:

• dz/dx aspect ratio

• βscatter scattering coefficient

• βabsorption absorption coefficient

• g asymmetry parameter

• θ, φ sun angles

• save in LookUpTable

• Linear Interpolation

15 / 24

Transport Coefficients

• Use simple MonteCarlo Raytracer

• Transport Coefficients depend on:

• dz/dx aspect ratio

• βscatter scattering coefficient

• βabsorption absorption coefficient

• g asymmetry parameter

• θ, φ sun angles

• save in LookUpTable

• Linear Interpolation

15 / 24

Transport Coefficients

• Use simple MonteCarlo Raytracer

• Transport Coefficients depend on:

• dz/dx aspect ratio

• βscatter scattering coefficient

• βabsorption absorption coefficient

• g asymmetry parameter

• θ, φ sun angles

• save in LookUpTable

• Linear Interpolation

15 / 24

Transport Coefficients

• Use simple MonteCarlo Raytracer

• Transport Coefficients depend on:

• dz/dx aspect ratio

• βscatter scattering coefficient

• βabsorption absorption coefficient

• g asymmetry parameter

• θ, φ sun angles

• save in LookUpTable

• Linear Interpolation

15 / 24

Transport Coefficients

• Use simple MonteCarlo Raytracer

• Transport Coefficients depend on:

• dz/dx aspect ratio

• βscatter scattering coefficient

• βabsorption absorption coefficient

• g asymmetry parameter

• θ, φ sun angles

• save in LookUpTable

• Linear Interpolation

15 / 24

Transport Coefficients

10-3 10-2 10-1 100

βscattering [m−1 ]

0.0

0.2

0.4

0.6

0.8

1.0

Tra

nsm

issi

onco

effici

ent

Direct 2 Direct: sza =20° g =.91

βabsorption =10−6 m−1

boxsize =70m

S +0 →S−0

S +0 →S−1

S +1 →S−0

S +1 →S−1

16 / 24

Transport Coefficients

10-3 10-2 10-1 100

βscattering [m−1 ]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Tra

nsm

issi

onco

effici

ent

Diffuse 2 Diffuse: g =.91

βabsorption =10−6 m−1

boxsize =70m

E+dn→E+

up

E+dn→E−dn

E+dn→E−le

E+dn→E+

le

16 / 24

Algorithm Outline

17 / 24

Algorithm Performance for I3RC cloud scene

0 20 40 60 80

Solar zenith angle θ

0

50

100

150

RM

SE

Hea

ting

Rat

es[%

]

RMSE(θ=80°) =379%

MC-IPA vs MC 3D10str vs MC 3D

18 / 24

What does it cost computationally?

Runtime increase compared to two-stream solver

0 20 40 60 80

Solar zenith angle θ

1

2

3

4

5

6

7

8

9

10

Runtim

efa

ctor

direct Radiation

zero-guess

0 20 40 60 80

Solar zenith angle θ

2

4

6

8

10

12

14

diffuse Radiation

zero-guess

0 20 40 60 80

Solar zenith angle θ

2

4

6

8

10

12total Computation

zero-guess

Two-stream ≈15-20% of NWP-model runtime.Ten-stream → worst case factor ≈3

19 / 24

What does it cost computationally?

Runtime increase compared to two-stream solver

0 20 40 60 80

Solar zenith angle θ

1

2

3

4

5

6

7

8

9

10

Runtim

efa

ctor

direct Radiation

2str-guess

zero-guess

0 20 40 60 80

Solar zenith angle θ

2

4

6

8

10

12

14

diffuse Radiation

2str-guess

zero-guess

0 20 40 60 80

Solar zenith angle θ

2

4

6

8

10

12total Computation

2str-guess

zero-guess

Two-stream ≈15-20% of NWP-model runtime.Ten-stream → worst case factor ≈3

19 / 24

What does it cost computationally?

Runtime increase compared to two-stream solver

0 20 40 60 80

Solar zenith angle θ

1

2

3

4

5

6

7

8

9

10

Runtim

efa

ctor

direct Radiation

perfectguess

2str-guess

zero-guess

0 20 40 60 80

Solar zenith angle θ

2

4

6

8

10

12

14

16diffuse Radiation

perfectguess

2str-guess

zero-guess

0 20 40 60 80

Solar zenith angle θ

2

4

6

8

10

12total Computation

perfectguess

2str-guess

zero-guess

Two-stream ≈15-20% of NWP-model runtime.Ten-stream → worst case factor ≈3

19 / 24

What does it cost computationally?

Runtime increase compared to two-stream solver

0 20 40 60 80

Solar zenith angle θ

1

2

3

4

5

6

7

8

9

10

Runtim

efa

ctor

direct Radiation

perfectguess

2str-guess

zero-guess

0 20 40 60 80

Solar zenith angle θ

2

4

6

8

10

12

14

16diffuse Radiation

perfectguess

2str-guess

zero-guess

0 20 40 60 80

Solar zenith angle θ

2

4

6

8

10

12total Computation

perfectguess

2str-guess

zero-guess

Two-stream ≈15-20% of NWP-model runtime.Ten-stream → worst case factor ≈3

19 / 24

How does wind affect convergence?

0 1 2 4 8 16 ∞

opt.prop.horizontalshift

2

4

6

8

10

12

Runtim

efa

ctor

total Computation

20 / 24

And a glimpse at what’s to come. . .

• Include algorithm in UCLA-LES / PALM

• Merge with thermal solver from Carolin Klinger

• Check if there are differences in cloud physics / evolution

• Ultimate goal is to include and test solver in ICON for

HDCP2 project

21 / 24

Thank you!

0 1 2 3 4 5 60.0

0.5

1.0

1.5

2.0

2.5

h [

km]

3D

08162432404856647280

HR

[K

/day]

0 1 2 3 4 5 6x [km]

0.0

0.5

1.0

1.5

2.0

2.5

h [

km]

IPA

08162432404856647280

HR

[K

/day]

0 1 2 3 4 5 60

1

2

3

4

5

6

y [

km]

3D

080160240320400480560640720800

Irra

dia

nce

[W

m2

]

0 1 2 3 4 5 6x [km]

0

1

2

3

4

5

6

y [

km]

IPA

080160240320400480560640720800

Irra

dia

nce

[W

m2

]

10-3 10-2 10-1 100

βscattering [m−1 ]

0.0

0.1

0.2

0.3

0.4

0.5

Tra

nsm

issi

onco

effici

ent

Direct 2 Diffuse: sza =20° g =.91

βabsorption =10−6 m−1

boxsize =70m

S +0 →E+

up

S +0 →E−dn

S +0 →E−le

S +0 →E+

le

S +1 →E+

up

S +1 →E−dn

S +1 →E−le

S +1 →E+

le

0 20 40 60 80

Solar zenith angle θ

1

2

3

4

5

6

7

8

9

10

Runtim

efa

ctor

direct Radiation

perfectguess

2str-guess

zero-guess

0 20 40 60 80

Solar zenith angle θ

2

4

6

8

10

12

14

16diffuse Radiation

perfectguess

2str-guess

zero-guess

0 20 40 60 80

Solar zenith angle θ

2

4

6

8

10

12total Computation

perfectguess

2str-guess

zero-guess

0 20 40 60 80

Solar zenith angle θ

0

50

100

150

RM

SE

Hea

ting

Rat

es[%

]

RMSE(θ=80°) =379%

MC-IPA vs MC 3D10str vs MC 3D

22 / 24

0 20 40 60 800

10

20

30

40

50

60

70solar3D + thermal3D RMSE: 0%

10080604020

020406080100

0 20 40 60 800

10

20

30

40

50

60

70solar3D + thermal IPA RMSE: 982%

10080604020

020406080100

0 20 40 60 800

10

20

30

40

50

60

70solar IPA + thermal3D RMSE: 540%

10080604020

020406080100

0 20 40 60 800

10

20

30

40

50

60

70solar IPA + thermal IPA RMSE: 866%

10080604020

020406080100

23 / 24

10-3 10-2 10-1 100

βscattering [m−1 ]

0.0

0.1

0.2

0.3

0.4

0.5T

ransm

issi

onco

effici

ent

Direct 2 Diffuse: sza =20° g =.91

βabsorption =10−6 m−1

boxsize =70m

S +0 →E+

up

S +0 →E−dn

S +0 →E−le

S +0 →E+

le

S +1 →E+

up

S +1 →E−dn

S +1 →E−le

S +1 →E+

le

24 / 24