Weighting functions (Box AMFs) for
Limb measurements of stratospheric trace species
using 3D Monte Carlo RTM
Christoph 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
•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.
•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)
Altd
[m] c(i),σ(c,i) d(i)
v(i)
•SCD = Σ S(i)
•SCD = Σ c(i) * v(i)* A (i)
•=> into equation system
C [cm-3]
Box AMF and profile retrieval
Box AMF defined as:
•sum over all intensity
having traversed the
layer/cell
•divided by total
intensity received by
detector
Altd
[m] c(i),σ(c,i) d(i)
•divided by layer‘s/cell‘s
v(i)
vertical extension
C [cm-3]
Box AMF and profile retrieval
•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
θ
ε
3D Monte Carlo RTM „AMFTRAC“ (working title)
features
e.g. v. Friedeburg EGS 2002
•spherical 3D geometry
•supports arbitrary platform positions and
viewing geometries
ai
•full MS by Rayleigh, aerosols, clouds, albedo
•refraction, polarization and solar CLD (limb)
principle
vv,i
di
•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
detector
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“
-2
-1
-1
Radiance [Wcm nm sr ]
radiance validation
7.0x10
-8
6.0x10
-8
5.0x10
-8
4.0x10
-8
3.0x10
-8
2.0x10
-8
1.0x10
-8
Radiance 22.2.2003
roof IUP Heidelberg
from 5° around zenith
measured 420 nm
modelled 420 nm
measured 350 nm
modelled 350 nm
0.0
60
65
70
75
80
85
90
SZA [°]
•In addition to validation against AMF by other RTMs:
•validation against measurements with calibrated spectro-radiometer
AMF investigation example
•λ = 352 nm
ground based MAX DOAS scenario
•atmosphere: 1 km vertical discret., 0-70 km
•ε = 2°, 5°, 10°, 20°, 45°, 90°;
5
•azimuth α to sun 90°, aperture 0.1°
4
•albedo values 0%, 30%, 50%, 70%
•BrO near ground: 3 profiles
3
Altd [km]
•standard aerosol scenario
P1
P2
P3
2
1
0
0.0
8
2.0x10
8
4.0x10
8
6.0x10
8
8.0x10
-3
[BrO] [cm ]
investigation of total AMFs in relation to scattering parameters
9
1.0x10
AMF investigation example
Albedo 0 %
P1
P2
P3
12
AMF []
10
8
10
P3:?
4
8
6
4
2
2
0
0
20
14
40
60
Elev. [°]
80
0
100
0
10
8
6
40
60
Elev. [°]
80
100
Albedo 70 %
P1
P2
P3
12
AMF []
10
20
14
Albedo 50 %
P1
P2
P3
12
AMF []
Albedo 30 %
P1
P2
P3
12
P1,P2: AMF highest for 2° elev.
6
14
BrO AMF
AMF []
14
8
6
4
4
2
2
0
0
0
20
40
60
Elev. [°]
80
100
0
20
40
60
Elev. [°]
80
100
Results: AMF
AMF->f(Albedo), O4 AMF
6
5.5
AMF P3
Albedo
0%
30 %
50 %
70 %
4.5
AMF []
4.0
3.5
O4 AMF
Albedo
0%
30 %
50 %
70 %
5
AMF []
5.0
3.0
2.5
4
3
2.0
1.5
0
20
40
60
Elev. [°]
80
2
1000
20
40
60
80
Elev. [°]
•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.
100
AMF investigation example
Number of scatterings
3.0
O
N of Rayleigh
scatterings
Albedo
0%
30 %
50 %
70 %
O
N of Aerosol
scatterings
Albedo
0%
30 %
50 %
70 %
2.5
Number
2.0
1.5
1.0
0.5
0.0
0
20
40
60
80
100
Elev. [°]
•Single scattering approx. („1/sin(τ)“, „1/cos(θ)“) heavily limited
•similar investigations for higher wavelengths useful
AMF investigation example
Last Scattering Altitude LSA
LSA [m]
10
4
10
3
10
2
Last Scattering Altitude
0%
30 %
50 %
70 %
LSA
0
20
40
60
80
Elev. [°]
•LSA for small elevations between 300 and 400 m
=>decreases light path within lowest boxes as comp. to 1/sin(ε)
100
AMF investigation example
LSA -> AMF(i)
10
Altd(i) [km]
8
LSA
2 ° Elev.
10 ° Elev.
error ~5%
6
4
2
0
2
4
6
8
AMF(i)
10
•LSA for small elevations < 1 km
•A(i) for boxes above 1 km decrease for low elevations
12
14
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
Balloon-borne limb geometry
Error investigation
influence of multiple
scattering on the way to &
within the layer
incl. albedo, clouds
BOX AMF rel error
Box AMF error’s absolute
value depends on:
Number of paths
layer’s/grid cell’s shape &
extension
layer’s/grid cell’s distances
from the instrument
0.14
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
0.12
0.10
0.08
0.06
0.04
0.02
0.00
2000 PU was used for the
calculations to follow.
0
2000
4000
6000
PU modelled
8000
10000
Balloon-borne limb geometry
Altitude variation
Line Of Sight Parameters:
-4° elevation, 90° azimuth, 0.5°
50
aperture, 30% albedo
45
above instrument: Box AMF
governed by SZA
below altitude of highest Box
AMF: fall-off depends on
aperture (see aperture var.)
floating altd
10 km
15 km
20 km
25 km
30 km
35 km
40 km
35
Altd [km]
below instrument: Box AMF
increases due to LOS geometry,
at altd<25 km LOS hits ground
40
30
25
20
15
10
5
0
0
5
10
15
20
25
Box AMF
near ground AMFs dependent
on multiple scattering
30
35
40
45
50
Balloon-borne limb geometry
Altitude variation: scattering parameters
LSD
LSA
(last sctrg distance)
300000
1.70
200000
1.65
LSA complies well with
altitude of highest Box AMF
100000
1.60
1.55
400000
LSD [m]
1.75
NRS
Last Scattering Distance
(LSD) affected by MS
1.80
NRS
1.50
1.45
1.40
1.35
10000 15000 20000 25000 30000 35000 40000
Altd [km]
25000
20000
15000
10000
5000
0
LSA [m]
NRS (MS importance)
decreases with increasing
altitude
Balloon-borne limb geometry
LOS Parameters:
90° azimuth, 0.5° aperture,
altitudes 10 and 30 km
Elevation variation
50
strong variation in sensitivity
for tangent altitude
fltg altd 30 km
-4° elev.
-2° elev.
0° elev.
+2° elev.
+4° elev.
fltg altd 10 km
-4° elev.
-2° elev.
0° elev.
+2° elev.
+4° elev.
45
40
tangent altitude moves
upwards
important for limb scanning
geometry - total Box AMF as
weighted average
below tangent altitude Box
AMF largely unaffected
Altd [km]
35
30
25
20
15
10
5
0
0
5
10 15 20 25 30
Box AMF
60
80 100
Balloon-borne limb geometry
LOS Parameters:
90° azimuth, 0.5° aperture,
altitudes 10 and 30 km
Elevation variation
50
strong variation in sensitivity
for tangent altitude
fltg altd 30 km
-4° elev.
-2° elev.
0° elev.
+2° elev.
+4° elev.
fltg altd 10 km
-4° elev.
-2° elev.
0° elev.
+2° elev.
+4° elev.
45
40
tangent altitude moves
upwards
important for limb scanning
geometry - total Box AMF as
weighted average
below tangent altitude Box
AMF largely unaffected
Altd [km]
35
30
25
20
15
10
5
0
0
5
10 15 20 25 30
Box AMF
60
80 100
Balloon-borne limb geometry
Azimuth variation
LOS Parameters:
-4° elevation, 90° azimuth, 0.5°
aperture, altitudes 10 and 30 km
40
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
35
impact small as compared to
e.g. elevation influence
25
Altd [km]
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
30
20
15
10
5
0
0
15
20
Box AMF
25
30
35
Balloon-borne limb geometry
Aperture variation
LOS Parameters:
-4° elevation, 90° azimuth, 0.5°
aperture, altitudes 10 km
for ap. angles <1° effect small
but:
fltg altd 10 km
ap 0.2°
ap 0.3°
ap 0.4°
ap 0.5°
ap 1°
ap 5°
25
20
Altd [km]
fall-off below tangent altd
influenced by aperture for
geometrical reasons
30
15
10
5
0
depends on chosen
discretization
changing elevation (scanning)
equals a higher effective ap.
angle
0
2
4
Box AMF
16
18
20
Balloon-borne limb geometry
Cloud cover variation
LOS Parameters:
-4° elevation, 90° azimuth, 0.5°
aperture, altitudes 10 and 30 km
multiple layers, vertical cloud
surfaces easy to implement
accuracy depends on cloud
effects impact on measurement
cloud layer altitude 5 km
albedo 80%, transmission zero
30
20
Altd [km]
cloud cover:
1. grid cell filled with Mie
particles - high CPU time
2. layer with altitude,
coverage, albedo, transmission
12
10
8
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
6
4
2
0
0
5
10
15
20
Box AMF
25
30
Balloon-borne limb geometry
Cloud cover variation: O4, radiance
-10
9.5x10
-11
9.0x10
-11
8.5x10
-11
8.0x10
-11
7.5x10
-11
6.0
Rad
5.0
4.5
4.0
3.5
7.0x10
-11
0.0
0.2
0.4
0.6
Cloud cover []
0.8
3.0
1.0
O4 AMF []
-1
5.5
-2
radiance:
smooth increase with cloud
cover
O4:
decrease due to lower
troposphere shielding
1.0x10
O4AMF
radiance [W cm nm sr ]
LOS Parameters:
-4° elevation, 90° azimuth,
0.5° aperture, altitude 10 km
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
   ( )  c( s )ds
•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
MAX-DOAS, AMF and profile retrieval
•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,...
θ
ε
Investigation: Influence of aerosol
how to retrieve aerosol data - radiance?
1.6x10
-2
-1
radiance [Wcm sr ]
-11
1.4x10
-11
1.2x10
-11
1.0x10
-12
8.0x10
-12
6.0x10
1.0
rel. radiance (Elev. 90° = 1)
no aerosols
-1
aerosols 0.03 km ext coeff 0 km
-1
aerosols 0.05 km ext coeff 0 km
-11
0.9
0.8
0.7
0.6
0.5
0.4
no aerosols
-1
aerosols 0.03 km ext coeff 0 km
-1
aerosols 0.05 km ext coeff 0 km
0.3
0.2
0.1
0.0
0
20
40
60
Elev.[°]
80
100
0
20
40
60
Elev.[°]
80
100
•radiance series R(ε) : Spectrographs not usually absolutely calibrated
•dR/dε not significantly different to allow for concl. on aerosol
Investigation: Influence of aerosol
LSA
aerosols
Albedo
10 %
30 %
50 %
70 %
no aerosols
Albedo
10 %
30 %
50 %
70 %
1000
aerosols
Albedo
10 %
30 %
50 %
70 %
no aerosols
Albedo
10 %
30 %
50 %
70 %
LSA [°]
LSA [°]
10000
1000
100
0
20
40
60
80
100
5
Elev. [°]
10
Elev. [°]
•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
Investigation: Influence of aerosol
albedo in many cases known; aerosol load not.
investigation on AMF->f(aerosol) for albedo 30%
18
16
aerosols
P1
P2
P3
no aerosols
P1
P2
P3
14
AMF []
12
10
8
6
4
2
0
0
20
40
60
Elev. [°]
80
100
Investigation: Influence of aerosol
how to retrieve aerosol data - O4?
6.0
no aerosols
-1
aerosols 0.03 km ext coeff 0 km
-1
aerosols 0.05 km ext coeff 0 km
5.5
O4 AMF
5.0
4.5
4.0
3.5
3.0
2.5
2.0
0
20
40
60
Elev. [°]
80
100
•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 ?
MAX model scenario
•aerosols:
•continental scenario (F. Hendrick, IASB, pers. comm.)
•ext. coeff. Value for 0 km varied for investigation
1.6
60
Altd [km]
50
40
Extinct. coeff
Type1
Type2
Type3
30
20
Phase Fct. Value (a.u.)
70
10
0
1E-7
1.4
1.2
Phase function
Type 1
Type 2
Type 3
1.0
0.8
0.6
0.4
0.2
1E-6
1E-5
1E-4
-1
Ext. Coeff. [km ]
1E-3
0.01
0.0
0
20
40
60
80
100 120 140 160 180
 [°]
Monte Carlo Approach for MS
•
calculation of distance d to next voxel
boundary
1.
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
d
p‘
1
p0
X
d