Airborne imaging remote sensing is increasingly used to map the spatial distribution of nitrogen dioxide (
Nitrogen oxides (
Airborne imaging spectrometers are passive remote sensing instruments from which we can retrieve
The aim of this study is to quantify, for the first time, the impact of these 3D radiative transfer (RT) effects in the presence of spatially variable surface properties and
MYSTIC is operated as a RT solver of the libRadtran package
AMFs are obtained by dividing the mean photon path length in each layer or box by its height. For a layer or box
To calculate a total AMF that can be used to convert measured SCDs to VCDs, an a priori VCD (VCD
The urban canopy was implemented in libRadtran as a triangular mesh, where each triangle can be assigned different optical and physical properties. Information on vertex positions and optical properties are read from an input file that has to be generated from a 3D building data set prior to the simulation. Using a ray-tracing algorithm newly integrated into the model, MYSTIC detects if and where a photon hits a triangle. The interaction of the photon with the surface (absorption or reflection) is then simulated using preexisting MYSTIC functions.
To create a triangular mesh for each building, a Python script was written that converts buildings stored in an ESRI shapefile into triangles. A building consists of one or several flat roofs and several vertical walls. To create triangles for the roof, we connect the polygon centroid to each polygon corner.
Wall triangles are created by splitting each wall diagonally into two triangles.
Each triangle surface carries information about its albedo and skin temperature. The skin temperatures are used for thermal simulations, a feature that is not used in this publication.
The triangular mesh is stored in a NetCDF file readable by MYSTIC. An example file layout is shown in the Supplement. The file contains the variable
In MYSTIC, each photon is traced stepwise along its optical path from one interaction to the other. To interact with the urban canopy, a ray-tracing code searches for hits with one of the triangles during each step. We use the Star-3D library (
In the case that a ray hits a surface, a Lambertian reflection happens, and a new direction is attributed to the photon, which will continue its path until its next interaction. Absorption on surfaces is accounted for by reducing a photon weight by
To study radiative transfer effects on airborne measurements for a realistic scene, we selected a 1 km
We used 3D building data from a shapefile obtained from the Swiss Federal Office of Topography (swisstopo). Each building is defined as a polygon with
We created a simple but quite realistic 3D
The vertical distribution was modeled as a linear decrease from the surface value to the background value of 0.65
Our scenario corresponds to an airborne imaging spectrometer flying across the model domain from south to north (
The simulations were conducted for a standard atmosphere and for a wavelength of 490 nm, which is the center of the
To resolve the spatial variability of surfaces and elevations within each 50 m
To study the sensitivity of a single measurement to the surrounding of the ground pixel, we simulated the horizontal distribution of 3D-box AMFs close to the ground for a single observation scenario. The simulations were conducted without aerosols and for a typical urban aerosol scenario with an aerosol optical depth (AOD) of 0.1. For the scenario, the sensor was placed at
To obtain a map of the close-to-ground
In this section we first show the instrument incoming radiance calculated with MYSTIC over the selected study area. Second, we analyze the 3D-box AMFs for a single
An airborne imaging spectrometer measures radiance from back-scattered and reflected solar irradiance.
Figure
Radiance seen by a downward-viewing instrument placed in the center of the 1 km
Since building surfaces have higher reflectance in this example, the bright building roofs clearly stand out. Some bright walls illuminated by the sun can be seen in the east of the domain. Shadows are also clearly visible in the east of the buildings with taller buildings producing longer shadows. This radiance field is closely related to the close-to-ground
3D-box AMFs have a distinct 3D distribution for each ground pixel. Figure
Since 3D-box AMFs inform about the sensitivity to
The total AMF for the observation presented in this example computed with Eq. (
To further illustrate the horizontal sensitivity of an airborne spectrometer to layers close to the ground, Fig.
Figure
Figure
Figure S7 in the Supplement shows the footprint for the aerosol scenario. The aerosol scattering increases the sensitivity contribution from outside the ground pixel to 55 % for both the scenario without and with buildings. The contribution from outside the main optical path is increased to 25 % and 32 % without and with buildings, respectively, compared to 18 % and 24 %, when not including aerosols.
The main effect of the 3D optical path of the photons is thus to smear out the sensitivity of a measurement into the direction of the main optical path, which is determined by the viewing and illumination geometry. The presence of buildings further modifies the sensitivity by adding a complex pattern of enhancements and reductions due to the shielding effects of buildings and multiple reflections in street canyons.
In the previous section we have shown how 3D radiative transfer effects and buildings smear out and modify the sensitivity of a single observation. Here we demonstrate how a complete image of
Figure
AMFs for a simulation with SAA of 90
AMFs derived from 1D-layer AMFs (Fig.
AMFs calculated with 3D-box AMFs but without buildings (Fig.
Sketch of two main optical paths for an airborne spectrometer pointing at (1) a road in grey and (2) at a pixel aside the road.
The mean difference between SCD
AMFs calculated with the 3D-box AMFs module including the urban canopy (Fig.
The results presented above were obtained for the special situation where viewing and illumination directions were along the same east–west direction. In this case, the smearing effects are most prominent along this axis but relatively small in the perpendicular direction. Here, we also analyze the situation where the sun is in the south and thus viewing and illumination directions are perpendicular to each other. As shown in Fig.
SCDs for simulations with a SAA of 0
To investigate the reduced SCDs over buildings observed in the former paragraphs, we analyze the spatial distribution of SCDs within the 50 m
At this resolution, we can better resolve the spatial distribution of
At 5 m resolution, we distinguish four types of ground pixels.
The ground pixel is on the surface and the geometric path to the sun and the instrument is not obscured by buildings. In this case, the 3D-box AMFs are only affected by buildings through multiple scattering either increasing the AMF when buildings reflect photons towards the ground pixel or reducing the AMF when buildings block photons from reaching the ground pixel. In our example, the effect results in a small but hardly visible reduction of AMFs (see Fig. The reflecting point of the geometric path is located on top of a building. The case is similar to the first case, but 3D-box AMFs are smaller, because photons cannot reach the ground. Since we assume that a priori VCDs are fixed regardless of the presence of a building, SCDs are reduced above buildings. However, the effect is very small, because only about 3 % of the total VCD is below a 10 m building. In the third case, the ground pixel is located on the sunlit side of a building, but the direct path to the instrument is blocked by the buildings. Since the VZAs of the simulated instrument are very small, we do not find these cases in our example with rather small buildings. In the final case, the ground pixel is located in the shadow of the buildings blocking the direct path towards the sun. In this case, photons can only reach the instrument after multiple scattering or simple atmospheric scattering directly into the direction of the instrument, which drastically reduces the 3D-box AMFs near the surface. As a result, SCDs are significantly lower in the shadows of buildings (Fig.
We can therefore conclude that the reduction of SCDs over buildings (Fig.
SCDs over a small subdomain computed from high-resolution 3D-box AMFs simulated without
In imaging remote sensing,
The VCDs computed with 1D-layer AMFs fail to correct for the spatial smoothing induced by the complex 3D optical path of the photons (Fig.
The codes developed for this study can also be applied to real observations, e.g., to the campaigns conducted with APEX imaging spectrometer. A major challenge is to obtain the required input data. The 3D building data are available for many cities, but albedos for ground, roof and walls are generally not available. In addition, to compute the total AMFs, realistic 3D
To minimize 3D effects when using 1D-layer AMFs, it would be recommendable to obtain the airborne spectrometer measurement around local noon when the SZA is lowest and avoid large viewing zenith angles. However, around noon, turbulent atmospheric mixing will be strong, and the
The computation of 3D-box AMFs with buildings is computationally quite expensive but still manageable for current airborne campaigns. For example, the computation of the 3D-box AMF field for a single APEX pixel (e.g., in Fig.
Airborne imaging spectrometers are increasingly used for high-resolution mapping of
Our case study shows that the footprint of a single observation is only partly located over the observed ground pixel and that there is a “tail” in the direction of the main optical path. In the presented simulations with a SZA of 60
The 3D radiative transfer simulations show that 3D effects introduce significant spatial smearing of high
Generalizing our results to other cities is challenging, because many relevant parameters such as building shapes, surface reflectances and a priori
In conclusion, our case study demonstrates that 3D effects explain the smooth
The libRadtran package including the 1D version of MYSTIC is freely available at
The data used for this study are available on
The supplement related to this article is available online at:
MS designed and implemented the urban canopy module, designed and simulated the 3D scenarios, and wrote the article with input from all co-authors. FJ designed and implemented the urban canopy module together with MS and CE. DB, BB and AB provided critical feedback to the study and reviewed the article; GK supervised the study, designed (together with MS) the case studies and reviewed the article.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
We obtained building data from the Swiss Federal Office of Topography (swisstopo) and the traffic emission inventories from the city of Zurich.
This research has been supported by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (SNSF, grant no. 172533).
This paper was edited by Lok Lamsal and reviewed by Frederik Tack and two anonymous referees.