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 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)

Box AMF and profile retrieval 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

Box AMF and profile retrieval 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 didi aiai 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 v v,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, O 4 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

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 investigation of total AMFs in relation to scattering parameters

AMF investigation example BrO AMF P1,P2: AMF highest for 2° elev. P3:?

Results: AMF AMF->f(Albedo), O4 AMF 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.

AMF investigation example Number of scatterings 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 LSA for small elevations between 300 and 400 m =>decreases light path within lowest boxes as comp. to 1/sin(ε)

AMF investigation example LSA -> AMF(i) LSA LSA for small elevations < 1 km A(i) for boxes above 1 km decrease for low elevations

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 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  influence of multiple scattering on the way to & within the layer  incl. albedo, clouds  2000 PU was used for the calculations to follow.

Balloon-borne limb geometry Altitude variation Line 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

Balloon-borne limb geometry 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

Balloon-borne limb geometry Elevation variation LOS 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

Balloon-borne limb geometry Elevation variation LOS 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

Balloon-borne limb geometry Azimuth variation LOS 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

Balloon-borne limb geometry Aperture variation LOS 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 discretization  changing elevation (scanning) equals a higher effective ap. angle

Balloon-borne limb geometry Cloud cover variation LOS Parameters: -4° elevation, 90° azimuth, 0.5° aperture, altitudes 10 and 30 km  cloud cover:  1. grid cell filled with Mie particles - high CPU time  2. layer with altitude, coverage, albedo, transmission  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

Balloon-borne limb geometry Cloud cover variation: O 4, radiance LOS Parameters: -4° elevation, 90° azimuth, 0.5° aperture, altitude 10 km  radiance: smooth increase with cloud cover  O 4 : decrease due to lower troposphere shielding

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

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

Investigation: Influence of aerosol LSA 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%

Investigation: Influence of aerosol how to retrieve aerosol data - O 4 ? 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

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)=p 0 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 p0p0