Weighting functions (Box AMFs) for Limb measurements of stratospheric trace species

Weighting functions (Box AMFs) for Limb measurements of stratospheric trace species

using 3D Monte Carlo RTMChristoph v. Friedeburg, A. Butz, F. Weidner, S. Sanghavi, K. Pfeilsticker, U. Platt and T. Wagner

•Box AMF and profile retrieval

•3D Monte Carlo RTM „AMFTRAC“

•AMF investigation example

•Balloon-borne limb geometry

•Outlook

[email protected]

IUP University of Heidelberg

Box AMF and profile retrieval

•Discretization of atmosphere into boxes i=1,..,n

•SCD box-wise

•AMF box-wise: A(i)

•Weighting Function

•S(i) = c(i) * d(i)

•V(i) = c(i) * v(i)

•S(i) = V(i) * A(i)

•SCD = Σ S(i)

•SCD = Σ c(i) * v(i)* A (i)

•=> into equation system C [cm-3]

Altd [m]

v(i)

•SCD and AMF do not tell us where along the light path the trace gas is located

•But this is what we’d like to know.

d(i) c(i),σ(c,i)


C [cm-3]

Altd [m]

v(i)

d(i) c(i),σ(c,i)

Box AMF defined as:

•sum over all intensity having traversed the layer/cell

•divided by total intensity received by detector

•divided by layer‘s/cell‘s vertical extension


θ

ε

•Multiple scattering increases retrieval difficulty since

•geometrical approximations/estimations not valid and misleading

•AMF and A(i) must be modelled with RTM

•Behaviour of A(i) with relevant parameters must be investigated & understood

3D Monte Carlo RTM „AMFTRAC“ (working title)e.g. v. Friedeburg EGS 2002

di

ai

detector

features

•spherical 3D geometry

•supports arbitrary platform positions and viewing geometries

•full MS by Rayleigh, aerosols, clouds, albedo

•refraction, polarization and solar CLD (limb)

principle

•backward Monte Carlo technique

•N photon launched out of telescope

•random numbers, scatt. centre ND & c/s govern light path => establish path sun->detector

•molecular absorption calculated analytically

•AMF computed from modelled av. intensity with/without absorber

vv,i

3D Monte Carlo RTM „AMFTRAC“

output

•SCDs, SODs, AMFs, Box AMFs (A(i)) for a specified set of boxes/layers

•abs. radiances

•geometrical path length, traversed air column, O4

•number of Rayleigh, Mie and albedo scattering events

•altitudes of first and last scattering event, distance detector-last scattering event

•entry angle of light into atmosphere, first scattering angle

•Solar CLD effect parameter, polarization (under testing)

•parameters as intensity weighted means

•errors as intensity weighted std dev.

3D Monte Carlo RTM „AMFTRAC“

radiance validation

•In addition to validation against AMF by other RTMs:

•validation against measurements with calibrated spectro-radiometer

60 65 70 75 80 85 900.0

1.0x10-8

2.0x10-8

3.0x10-8

4.0x10-8

5.0x10-8

6.0x10-8

7.0x10-8

Radia

nce

[W

cm-2nm

-1sr

-1]

SZA [°]

Radiance 22.2.2003 roof IUP Heidelbergfrom 5° around zenith

measured 420 nm modelled 420 nm measured 350 nm modelled 350 nm

AMF investigation example

ground based MAX DOAS scenario•λ = 352 nm

•atmosphere: 1 km vertical discret., 0-70 km

•ε = 2°, 5°, 10°, 20°, 45°, 90°;

•azimuth α to sun 90°, aperture 0.1°

•albedo values 0%, 30%, 50%, 70%

•standard aerosol scenario

•BrO near ground: 3 profiles

0

1

2

3

4

5

0.0 2.0x108 4.0x108 6.0x108 8.0x108 1.0x109

[BrO] [cm-3]

Altd

[km

]

P1 P2 P3

investigation of total AMFs in relation to scattering parameters


BrO AMF

0 20 40 60 80 1000

2

4

6

8

10

12

14

AM

F [

]

Elev. [°]

Albedo 0 % P1 P2 P3

0 20 40 60 80 1000

2

4

6

8

10

12

14

Elev. [°]

AM

F []

Albedo 30 % P1 P2 P3

0 20 40 60 80 1000

2

4

6

8

10

12

14

AM

F [

]

Elev. [°]


0 20 40 60 80 1000

2

4

6

8

10

12

14

Elev. [°]

AM

F []


P1,P2: AMF highest for 2° elev.

P3:?

Results: AMF

AMF->f(Albedo), O4 AMF

0 20 40 60 80 100

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

AM

F [

]

Elev. [°]

AMF P3Albedo

0 % 30 % 50 % 70 %

0 20 40 60 80 1002

3

4

5

6

AM

F [

]

Elev. [°]

O4 AMF

Albedo 0 % 30 % 50 % 70 %

•P3: AMF increases with albedo, but behaviour pertains:

•AMF for smallest elevations not highest

•same effect for O4 - looks like P1 & 2, but higher proportion (~3/4) located above 1 km.


Number of scatterings

0 20 40 60 80 1000.0

0.5

1.0

1.5

2.0

2.5

3.0

Num

ber

Elev. [°]

NO of Rayleigh scatteringsAlbedo

0 % 30 % 50 % 70 %

NO of Aerosol scatteringsAlbedo

0 % 30 % 50 % 70 %

•Single scattering approx. („1/sin(τ)“, „1/cos(θ)“) heavily limited

•similar investigations for higher wavelengths useful


Last Scattering Altitude LSA

0 20 40 60 80 100102

103

104

LSA

[m]

Elev. [°]

Last Scattering Altitude 0 % 30 % 50 % 70 %

LSA

•LSA for small elevations between 300 and 400 m

=>decreases light path within lowest boxes as comp. to 1/sin(ε)


LSA -> AMF(i)

LSA

•LSA for small elevations < 1 km

•A(i) for boxes above 1 km decrease for low elevations

0

2

4

6

8

10

2 4 6 8 10 12 14AMF(i)

Altd

(i) [k

m]

2 ° Elev. 10 ° Elev.

error ~5%

Balloon-borne limb geometry

•relevant to SCIAVAL balloon operations

•SCIAMACHY limb mode

SZA (at altd 0 below instrument position): 70°

atmosph. discret. 1 km

Variation of

•altitude

•elevation angle

•azimuth angle

•aperture angle

•cloud cover


Error investigation

0 2000 4000 6000 8000 100000.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

BO

X A

MF

re

l err

or

PU modelled

0-1 km 9-10 km 10-11 km 19-20 km 29-30 km 39-40 km 49-50 km 59-60 km 69-70 km

Box AMF error’s absolute value depends on:Number of pathslayer’s/grid cell’s shape & extensionlayer’s/grid cell’s distances from the instrument

influence of multiple scattering on the way to & within the layerincl. albedo, clouds

2000 PU was used for the calculations to follow.


Altitude variationLine Of Sight Parameters:-4° elevation, 90° azimuth, 0.5° aperture, 30% albedo

above instrument: Box AMF governed by SZA

below instrument: Box AMF increases due to LOS geometry,at altd<25 km LOS hits ground

below altitude of highest Box AMF: fall-off depends on aperture (see aperture var.)

near ground AMFs dependent on multiple scattering

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35 40 45 50

Box AMF

Altd

[km

]

floating altd 10 km 15 km 20 km 25 km 30 km 35 km 40 km


Altitude variation: scattering parameters

NRS (MS importance) decreases with increasing altitude

Last Scattering Distance (LSD) affected by MS

LSA complies well with altitude of highest Box AMF

10000 15000 20000 25000 30000 35000 400001.35

1.40

1.45

1.50

1.55

1.60

1.65

1.70

1.75

1.80

Altd [km]

NRS

05000

100001500020000

25000

100000

200000

300000

400000

LSA

[m]

LS

D [m

]

NR

S

LSD LSA

(last sctrg distance)


Elevation variationLOS Parameters:90° azimuth, 0.5° aperture, altitudes 10 and 30 km

strong variation in sensitivity for tangent altitude

tangent altitude moves upwards

important for limb scanning geometry - total Box AMF as weighted average

below tangent altitude Box AMF largely unaffected

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 60 80 100Box AMF

Altd

[km

]

fltg altd 30 km -4° elev. -2° elev. 0° elev. +2° elev. +4° elev.



Elevation variationLOS Parameters:90° azimuth, 0.5° aperture, altitudes 10 and 30 km

strong variation in sensitivity for tangent altitude

tangent altitude moves upwards

important for limb scanning geometry - total Box AMF as weighted average

below tangent altitude Box AMF largely unaffected

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 60 80 100Box AMF

Altd

[km

]




Azimuth variationLOS Parameters:-4° elevation, 90° azimuth, 0.5° aperture, altitudes 10 and 30 km

impact small as compared to e.g. elevation influence

for az. 90° Box-AMF largest in tangent alt, above for az 180° “sun beam” has to travel longer distance to reach LOS intersection point

0

5

10

15

20

25

30

35

40

0 15 20 25 30 35

Box AMF

Altd

[km

]

fltg altd 30 km 0° az 20° az 45° az 90° az 180° az

fltg altd 10 km 0° az 20° az 45° az 90° az 180° az


Aperture variationLOS Parameters:-4° elevation, 90° azimuth, 0.5° aperture, altitudes 10 km

fall-off below tangent altd influenced by aperture for geometrical reasons

for ap. angles <1° effect small but:

depends on chosen discretizationchanging elevation (scanning) equals a higher effective ap. angle

0

5

10

15

20

25

30

0 2 4 16 18 20

Altd

[km

]

Box AMF

fltg altd 10 km ap 0.2° ap 0.3° ap 0.4° ap 0.5° ap 1° ap 5°


Cloud cover variationLOS Parameters:-4° elevation, 90° azimuth, 0.5° aperture, altitudes 10 and 30 km

cloud cover: 1. grid cell filled with Mie particles - high CPU time2. layer with altitude, coverage, albedo, transmission

multiple layers, vertical cloud surfaces easy to implementaccuracy depends on cloud effects impact on measurement

cloud layer altitude 5 km albedo 80%, transmission zero

0

2

4

6

8

10

12

20

30

0 5 10 15 20 25 30

Box AMF

Altd

[km

]

altd 30 km cloud cov 1 altd 10 km cloud cov 1 altd 10 km cloud cov 0.5 altd 10 km cloud cov 0.2 altd 10 km cloud cov 0


Cloud cover variation: O4, radiance

LOS Parameters:-4° elevation, 90° azimuth, 0.5° aperture, altitude 10 km

radiance: smooth increase with cloud coverO4: decrease due to lower troposphere shielding

0.0 0.2 0.4 0.6 0.8 1.0

7.0x10-11

7.5x10-11

8.0x10-11

8.5x10-11

9.0x10-11

9.5x10-11

1.0x10-10

radi

ance

[W c

m-2

nm s

r-1

]

Cloud cover []

Rad

3.0

3.5

4.0

4.5

5.0

5.5

6.0

O4 A

MF

[]

O4AMF

Conclusion/Outlook

•AMFTRAC capable of handling limb geometry in relevant LOS parameters

•output parameters help understanding AMF‘s and A(i)‘s behaviour quantitatively

•Investigation of use of polarization and CLD effects

•Implementation of realistic clouds and aerosols

•Inclusion of basic LES-based retrieval module

MAX-DOAS, AMF and profile retrieval

•DOAS: Differential Optical Absorption Spectroscopy

•Measured quantity: optical density τ of trace gases investigated

•integrated over light path

•σ(λ) absorption cross section c(s) concentration

•along “slant” light path : Slant Column Density SCD = τ(λ) / σ(λ)

•along vertical path from location: Vertical Column Density VCD

•related by Air Mass Factor AMF

•VCD=SCD / AMF

•Measure of sensitivity

for the trace gas profile

dssc )()(

MAX-DOAS, AMF and profile retrieval

θ

ε

•Solar light enters atmosphere on straight path

•gets scattered by e.g. Rayleigh, Mie, albedo

•enters telescope => AMFs depend on:

•Solar Zenith Angle (SZA θ) and Solar Azimuth Angle

•scattering centre number density, cross section, phase fct.

•elevation ε, aperture angle,...

Investigation: Influence of aerosol

how to retrieve aerosol data - radiance?

•radiance series R(ε) : Spectrographs not usually absolutely calibrated

•dR/dε not significantly different to allow for concl. on aerosol

0 20 40 60 80 100

6.0x10-12

8.0x10-12

1.0x10-11

1.2x10-11

1.4x10-11

1.6x10-11

radi

ance

[Wcm

-2sr

-1]

Elev.[°]

no aerosols

aerosols 0.03 km-1 ext coeff 0 km


0 20 40 60 80 1000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Elev.[°]

rel.

radi

anc

e (

Ele

v. 9

0°

= 1

)

no aerosols




LSA

0 20 40 60 80 100100

1000

10000

LSA

[°]

Elev. [°]

aerosolsAlbedo

10 % 30 % 50 % 70 %

no aerosolsAlbedo

10 % 30 % 50 % 70 %

5 10

1000

Elev. [°]LS

A [°

]

aerosolsAlbedo

10 % 30 % 50 % 70 %

no aerosolsAlbedo

10 % 30 % 50 % 70 %

•without aerosol impact effect present, but much weaker

•aerosol scenario largely governs AMF -> f(ε)

•use of std. scen. Risky => need hard data on local aerosol


albedo in many cases known; aerosol load not.

investigation on AMF->f(aerosol) for albedo 30%

0 20 40 60 80 1000

2

4

6

8

10

12

14

16

18

AM

F []

Elev. [°]

aerosols P1 P2 P3

no aerosols P1 P2 P3


how to retrieve aerosol data - O4?

•But O4-AMF->f(ε) signif.tly different for large aerosol ld. differences

•parametrize the O4-AMF(ε) behaviour as f(aerosol ext. coeff.) => scale aerosol ext. coeff.

•uncertainties: effect of phase function ?

0 20 40 60 80 1002.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

O4

AM

F

Elev. [°]

no aerosols



MAX model scenario•aerosols:

•continental scenario (F. Hendrick, IASB, pers. comm.)

•ext. coeff. Value for 0 km varied for investigation

0

10

20

30

40

50

60

70

1E-7 1E-6 1E-5 1E-4 1E-3 0.01

Ext. Coeff. [km-1]

Altd

[km

]

Extinct. coeff Type1 Type2 Type3

0 20 40 60 80 100 120 140 160 1800.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Ph

ase

Fct

. V

alu

e (

a.u

.)

[°]

Phase function Type 1 Type 2 Type 3

Monte Carlo Approach for MS

• calculation of distance d to next voxel boundary

• extinctors (Rayleigh, Mie particles) yield probability p(x) for free passage up to x

• p(d)=p0 prob. of unscattered passage along d

• map random number p‘ to x by the inverse of function p(x):

• determines location of scattering event [0,d]

• use a second random number to decide between scatterers according to the relative probabilities

X d

p‘

1

d

p0

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Weighting functions (Box AMFs) for Limb measurements of stratospheric trace species

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