Air mass factors (AMFs) are used in passive trace gas remote sensing for converting slant column densities (SCDs) to vertical column densities (VCDs). AMFs are traditionally computed with 1D radiative transfer models assuming horizontally homogeneous conditions. However, when observations are made with high spatial resolution in a heterogeneous atmosphere or above a heterogeneous surface, 3D effects may not be negligible. To study the importance of 3D effects on AMFs for different types of trace gas remote sensing, we implemented 1D-layer and 3D-box AMFs into the Monte carlo code for the phYSically correct Tracing of photons In Cloudy atmospheres (MYSTIC), a solver of the libRadtran radiative transfer model (RTM).
The 3D-box AMF implementation is fully consistent with 1D-layer AMFs under horizontally homogeneous conditions and agrees very well (

Ground-based, space-based and airborne remote sensing of air pollutants and greenhouse gases from scattered sunlight are increasingly used for air pollutant monitoring

A physically more meaningful quantity that is independent of the measurement geometry is the vertical column density (VCD), which is the integrated trace gas concentration from the ground to the top of the atmosphere. The ratio between SCD and VCD is called air mass factor (AMF)

Layer AMFs assume horizontal homogeneity, which is not valid when the parameters affecting scattering and absorption along the path of the photons vary also horizontally, for example, in limb geometry near the polar vortex

To account for horizontal inhomogeneity, one-dimensional (1D) layer AMFs need to be extended to three-dimensional (3D) box AMFs. Notice that in previous studies

Atmospheric trace gases can be measured with ground-, aircraft- and space-based spectrometers that measure solar irradiance scattered into the line of sight of the instrument (see Fig.

Illustration of the difference between

Similarly, the atmosphere can be divided into boxes in all three dimensions

The libRadtran RTM (available at

AMFs depend on absorption and scattering processes affecting the light path in the atmosphere. AMFs can be readily calculated from the photon paths simulated by a Monte Carlo radiative transfer model. The Monte Carlo technique traces the paths of individual photons by describing the effects of absorption, scattering and reflection as random events with specific probabilities

SCDs, VCDs and AMFs can be computed for the whole atmosphere, for individual vertical layers or for individual 3D boxes.
For the general case of an atmospheric box

The implementation of the 1D-layer and 3D-box AMF module in MYSTIC was evaluated against the results of different RTMs presented in an extensive RTM comparison study

For the comparison, we computed 1D-layer and 3D-box AMFs with MYSTIC in plane-parallel geometry as well as 1D-layer AMFs in spherical geometry for all scenarios presented in

1D-layer and 3D-box AMFs were computed for five wavelengths (310, 360, 440, 477, 577 nm), seven elevation angles (1, 2, 3, 6, 10, 20, 90

The comparison of 1D-layer AMF profiles calculated with the MYSTIC 1D modules with SCIATRAN for the 67 observation scenarios used in

Scatter plots of MYSTIC 1D-layer AMFs computed with

Upper row: MAX-DOAS AMF profiles for MYSTIC 1D spherical geometry (s), 1D plane-parallel geometry (pp) and 3D plane-parallel geometry (pp) for two selected elevation angles of 3 and 90

Upper row: MAX-DOAS AMF profiles for MYSTIC 1D spherical geometry (s), 1D plane-parallel geometry (pp) and 3D plane-parallel geometry (pp) for two selected elevation angles of 3 and 90

To illustrate the differences in AMF profiles between the two RTMs, we selected four scenarios with a wavelength of 577 nm, because at this wavelength we observe comparatively large differences between the two models. To illustrate a usual scenario with low difference, we also selected the same scenarios but with a 360 nm wavelength.
The upper row of Fig.

In the upper atmosphere, the 1D-layer AMFs decrease with altitude in all scenarios (Figs.

1D-layer AMFs computed with spherical and plane-parallel geometry show noticeable differences for long wavelengths and low aerosol extinction, especially at altitudes above 5 km where extinction coefficients are small (see upper- and lower-left part in Fig.

AMF profiles calculated with MYSTIC generally agree very well with those calculated with SCIATRAN with relative differences mostly smaller than 5 %. However, significant differences (up to 23 % relative difference) are seen between the plane-parallel solutions of the two models above 5 km for the scenarios without aerosols at 577 nm (Fig.

The simulations for the same scenarios but with 360 nm wavelength agree very well with SCIATRAN for both spherical and plane-parallel geometries (relative difference

Overall, MYSTIC agrees very well with SCIATRAN with differences mainly smaller than 5 %. An exception is the high elevation scenario without aerosols, where the plane-parallel solutions of MYSTIC and SCIATRAN differ by up to 23 % for a wavelength of 577 nm at altitudes above 5 km. It should be noted that for these cases the 1D-layer AMFs are very small, and therefore the absolute differences, which are relevant for most applications, are also small. The 1D-layer AMFs computed with MYSTIC also agree very well with the other models presented in

MAX-DOAS is a ground-based passive remote sensing technique allowing the retrieval of vertical concentration profiles of trace gases and aerosols

To illustrate the 3D distribution of 3D-box AMFs for a typical MAX-DOAS measurement, we simulated 3D-box AMFs at 450 nm for two scenarios with low and high aerosol optical depth, which correspond to a visibility of 50 and 10 km in the planetary boundary layer (PBL), respectively. A value of 450 nm is a typical wavelength for light absorption by

Cross section of 3D-box AMFs for a MAX-DOAS scenario with an instrument (black triangle) at the ground (

Figure

Top: vertically integrated 3D-box AMFs in the PBL (

To illustrate the horizontal spread of the sensitivity of the MAX-DOAS measurements in the PBL, Fig.

For the different scenarios, we evaluated which part of the signal originated from a 0.25 km wide region centered on the northward pointing line of sight (referred to as main line in the following) and which part crossed boxes outside this range. For the low-aerosol scenario, between 63 % and 70 % originated from the main line. Thus, up to 37 % of the signal originated from photons crossing neighboring boxes. For the high-aerosol scenario with enhanced scattering, the part of the signal originating from the main line was correspondingly lower, between 30 % and 41 %. The lower values correspond to the scenarios with higher relative azimuth angles.

Depending on the viewing direction of the instrument relative to the position of nearby emission sources, this temporally varying spatial sensitivity could introduce a diurnal cycle in the measurement even when the trace gas concentration field was constant in time. Understanding the horizontal distribution of the sensitivity to

In this section, we demonstrate the effect of the spatial variability in 3D-box AMFs on airborne

The

Using MYSTIC, we computed the SCDs that would be observed from an airborne push-broom spectrometer flying parallel to the plume axis from south to north at an altitude of 6 km. The field of view in the across-track direction of the instrument covers the full

As an example, Fig.

The 3D-box AMFs cross section at

Airborne remote sensing of an

The column AMFs (Fig.

3D-box AMFs and corresponding SCDs were computed for four different solar zenith angles and four different relative azimuth angles between the sun and the plume axis (and flight direction). We used a default aerosol scenario with a rural-type aerosol representative of spring–summer conditions in the PBL (0–2 km) and a background aerosol above 2 km (visibility of 50 km in the PBL). The parameters used for the AMF calculation are summarized in Table

MYSTIC input parameters for the emission stack scenario.

The SCDs computed for the scenario with the sun illuminating the scene from the west at a solar zenith angle of 40

Schematic of the across-track measurement by the aircraft measuring a

For each scenario, total AMFs were also computed from 1D-layer AMFs, which requires a

Figure

Figure

Absolute difference between total VCD from synthetic SCD and 1D box AMF with solar zenith angles (SZA) of

Absolute difference between total VCD from synthetic SCD and 1D box AMF with solar azimuth angle of

The displacement of the calculated VCD plume and the magnitude of the bias depend on the position of the sun as demonstrated in Figs.

A possible application of airborne imaging spectroscopy is the estimation of

Plume VCD cross section at

We computed line densities 300 m downstream of the source for the true VCD field and for fields computed with 1D-layer AMFs for different solar zenith and azimuth angles. The VCD cross sections are shown in Fig.

Estimated

Table

This study demonstrates the importance of 3D radiative transfer effects for a range of trace gas remote sensing applications such as ground-based MAX-DOAS and airborne imaging spectroscopy. To study these effects, 1D-layer and 3D-box AMFs were implemented in the Monte Carlo solver MYSTIC of the libRadtran RTM. The computation of AMFs is a central component in most trace gas retrieval algorithms to convert observed SCDs into VCDs, but so far these algorithms were limited to 1D RTMs. In the case of a horizontally homogeneous atmosphere and in plane-parallel geometry, the 3D-box and 1D-layer AMFs perfectly agree within the statistical noise of the Monte Carlo method. They also agree very well with 1D-layer AMFs calculated with other RTMs presented in a previous model intercomparison study by

The importance of 3D effects was demonstrated for two examples. For a ground-based MAX-DOAS instrument, we showed that 3D-box AMFs are highest along the line of sight of the instrument (representing photons that have mostly scattered only once) but that the contribution from outside is not negligible and depends on sun position and aerosol optical depth. The spatial distribution of the vertically integrated 3D-box AMFs depends on the sun position, which can be important for interpreting MAX-DOAS observations, especially in urban areas or, more generally, in the vicinity of pollution sources. The spatial variability in the

As second example, trace gas retrievals were studied for an airborne imaging spectrometer using simulations of a

Our study showed that even for simple examples, 3D effects are not negligible if the trace gas field has a high spatial variability. This finding is particularly relevant for ground-based and airborne remote sensing in cities, where considering 3D effects is likely indispensable to reduce systematic errors. This will be addressed in a followup study where the potential impact of 3D radiative transfer effects on the horizontal smoothing of the retrieved trace gas fields will also be studied. The 3D effects are also important for tomographic inversion

The libRadtran package including the 1D version of MYSTIC is freely available on

The data used for this study are available at

The supplement related to this article is available online at:

MS implemented the 3D-box AMF module and validated the implementation, designed and simulated the 3D scenarios, and wrote the paper with input from all coauthors. CE implemented 1D-layer AMF module, implemented the 3D-box AMFs together with MS, provided assistance with study design and reviewed the paper. TW provided the 1D-layer AMF data used for the validation and reviewed the paper. DB, BB and AB provided critical feedback to the study and reviewed the paper; RM conducted and provided the GRAL simulation; GK supervised the study, designed together with MS the case studies and reviewed the paper.

The authors declare that they have no conflict of interest.

This research has been supported by the Swiss National Science Foundation (SNSF, grant no. 172533).

This paper was edited by Folkert Boersma and reviewed by Frederik Tack and one anonymous referee.