# Optimization of Aerosol Model Selection for TROPOMI/S5P

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## Abstract

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## 1. Introduction

## 2. Methodology

- ${\delta}_{\mathrm{mes}}$ is a Gaussian random vector with zero mean and covariance matrix ${\mathbf{C}}_{\mathrm{mes}}={\sigma}_{\mathrm{mes}}^{2}{\mathcal{C}}_{\mathrm{mes}}$, where ${\sigma}_{\mathrm{mes}}^{2}$ is the measurement error variance and ${\mathcal{C}}_{\mathrm{mes}}$ a normalized measurement error covariance matrix;
- ${\delta}_{\mathrm{aer}m}$ is a Gaussian random vector with zero mean and covariance matrix ${\mathbf{C}}_{\mathrm{aer}m}={\sigma}_{\mathrm{aer}m}^{2}{\mathbf{I}}_{M}$, where ${\sigma}_{\mathrm{aer}m}^{2}$ is the aerosol model error variance and ${\mathbf{I}}_{M}$ the identity matrix; and
- ${\delta}_{\mathrm{mes}}$ and ${\delta}_{\mathrm{aer}m}$ are independent random vectors,

## 3. Aerosol Models

- non-absorbing (NONABS) aerosols, generated from fossil fuel combustion in urban-industrial areas;
- moderately absorbing (MODABS) aerosols;
- absorbing (ABS) aerosols, generated from biomass burning; and
- desert dust (DUST), originated from desert and transported by wind.

- weakly absorbing (WA),
- biomass burning (BB),
- desert dust (DD),
- marine (MA), and
- volcanic (VO).

## 4. Tests with Synthetic Data

#### 4.1. Test 1

- The relative errors corresponding to the maximum solution estimate (${\epsilon}_{\mathrm{max}}^{\tau}$ and ${\epsilon}_{\mathrm{max}}^{h}$) are considered to be acceptable according to the scientific requirements defined in the pre-launch characterization tests and significantly smaller than those corresponding to the mean solution estimate (${\epsilon}_{\mathrm{mean}}^{\tau}$ and ${\epsilon}_{\mathrm{mean}}^{h}$). Thus, the retrieval algorithm can recognize correctly the exact aerosol model.
- For the maximum solution estimate, the retrieved aerosol optical depth achieves a higher accuracy than the retrieved aerosol layer height.
- Different aerosol models could have similar a posteriori densities as the inversion process is not ideally perfect. An inappropriate aerosol model may occasionally be identified, which can result in unexpected errors (${\tau}_{\mathrm{e}}=1,\phantom{\rule{0.166667em}{0ex}}1.25$).

#### 4.2. Test 2

- the relative errors are larger than those in the first test example,
- the relative errors corresponding to the maximum solution estimate (${\epsilon}_{\mathrm{max}}^{\tau}$ and ${\epsilon}_{\mathrm{max}}^{h}$) and the mean solution estimate (${\epsilon}_{\mathrm{mean}}^{\tau}$ and ${\epsilon}_{\mathrm{mean}}^{h}$) are comparable, and
- on average, the retrieved aerosol layer height obtains a higher accuracy than the retrieved aerosol optical depth.

- ${h}_{\mathrm{mean}}$ and ${h}_{\mathrm{max}}$ are both not too far from ${h}_{\mathrm{e}}$; thus, for aerosol layer height retrieval, the maximum solution estimate and the mean solution estimate (${\epsilon}_{\mathrm{mean}}^{\tau}$ and ${\epsilon}_{\mathrm{mean}}^{h}$) have similar accuracies;
- ${\tau}_{\mathrm{mean}}$ is relatively closer to ${\tau}_{\mathrm{e}}$ than ${\tau}_{\mathrm{max}}$; thus, for aerosol optical depth retrieval, the mean solution estimate performs better than the maximum solution estimate;
- aerosol layer height retrievals have wide a posteriori densities that cover the exact layer height; and
- aerosol optical depth retrievals have multi-peaked densities, in which the exact optical depth does not have the highest probability.

## 5. Case Study with TROPOMI Data

- the mean solution estimates show a slightly smoother spatial pattern than the maximum solution estimates, and
- despite the differences in the micro-physical properties of the aerosol models from Sets 1 and 2, the spatial distributions of the mean retrieval results are comparable.

## 6. Conclusions

- When the exact aerosol model, for which synthetic data are generated, is included in the set of candidate models, the relative errors corresponding to the maximum solution estimate are relatively small. When this is not the case, it is likely that several aerosol models are able to fit the data equally well. In such situations, the mean solution estimate has a smaller bias than the maximum solution estimate.
- For the real measurements on 4 July 2019, the absorbing aerosol model from Set 1 and the biomass burning aerosol type from Set 2 are found to be the most plausible. This result is in agreement with the thick smoke observed in the true-color image. For the thinner smoke scenario on 5 July 2019, the above models together with the dust aerosol model are found to be the most probable aerosol models. Actually, no dominant aerosol model, but rather a less absorbing mixture of different aerosol types, is identified in this case. The mean and maximum solution estimates have a similar spatial distribution, but the mean solution estimates have a more continuous spatial pattern.
- The two TROPOMI cases on 6 June 2020 and 10 February 2020 for desert dust and urban aerosols, respectively, have demonstrated the promising performance of the proposed algorithm under various aerosol loading scenarios.
- A definite choice between Sets 1 and 2 for possible candidate models may not exist and a suitable one could be problem dependent.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ALH | Aerosol Layer Height |

AOD | Aerosol Optical Depth |

GE_LER | Geometry-dependent Effective Lambertian Equivalent Reflectivity |

MODIS | Moderate-resolution Imaging Spectroradiometer |

NIR | Near-infrared |

OMI | Ozone Monitoring Instrument |

OMAERO | OMI Multi-wavelength |

S5P | Sentinel-5 Precursor |

TROPOMI | Tropospheric Monitoring Instrument |

ABS | Absorbing (Set 1) |

DUST | Desert dust (Set 1) |

MODABS | Moderately absorbing (Set 1) |

NONABS | Non-absorbing (Set 1) |

BB | Biomass Burning (Set 2) |

DD | Desert Dust (Set 2) |

MA | Marine (Set 2) |

VO | Volcanic (Set 2) |

WA | Weakly absorbing (Set 2) |

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**Figure 1.**Relative errors ${\epsilon}_{\mathrm{mean},\mathrm{max}}^{\tau ,h}({\tau}_{\mathrm{e}}=0.5,{h}_{\mathrm{e}})$ for the aerosol models from Set 1. ALH represents the aerosol layer height.

**Figure 2.**Relative errors ${\epsilon}_{\mathrm{mean},\mathrm{max}}^{\tau ,h}({\tau}_{\mathrm{e}},{h}_{\mathrm{e}}=3.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{km})$ for the aerosol models from Set 1. AOD represents the aerosol optical depth.

**Figure 3.**The a posteriori densities $p(\mathbf{x}=[\tau ,h]\mid {\overline{\mathbf{y}}}^{\delta},m)$ for $m=$ NONABS, MODABS, ABS, and DUST, and the mean a posteriori densities ${p}_{\mathrm{mean}}(\mathbf{x}=[\tau ,h]\mid {\overline{\mathbf{y}}}^{\delta})$ in the case ${m}_{\mathrm{e}}=$ MODABS, ${\tau}_{\mathrm{e}}=1.25$, and ${h}_{\mathrm{e}}=3.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}$. The black curve indicates the mean a posterior density. In each plot, the red vertical dashed line corresponds to the exact values to be retrieved (${\tau}_{\mathrm{e}},{h}_{\mathrm{e}}$), the blue vertical dashed line to the maximum solution estimate (${\tau}_{\mathrm{max}},{h}_{\mathrm{max}})$, and the green dashed line to the mean solution estimates (${\tau}_{\mathrm{mean}},{h}_{\mathrm{mean}}$).

**Figure 4.**Relative errors ${\epsilon}_{\mathrm{mean},\mathrm{max}}^{\tau ,h}({\tau}_{\mathrm{e}}=0.5,{h}_{\mathrm{e}})$ for the aerosol models from Set 2.

**Figure 5.**Relative errors ${\epsilon}_{\mathrm{mean},\mathrm{max}}^{\tau ,h}({\tau}_{\mathrm{e}},{h}_{\mathrm{e}}=3.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{km})$ for the aerosol models from Set 2.

**Figure 6.**The mean a posteriori densities ${p}_{\mathrm{mean}}(h\mid {\overline{\mathbf{y}}}^{\delta})$ for ${m}_{\mathrm{e}}=$ NONABS, MODABS, ABS, DUST, ${\tau}_{\mathrm{e}}=0.5$, and ${h}_{\mathrm{e}}=3.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}$. In each plot, the red vertical dashed line correspond to the exact values to be retrieved (${\tau}_{\mathrm{e}},{h}_{\mathrm{e}}$), the blue vertical dashed line to the maximum solution estimate (${\tau}_{\mathrm{max}},{h}_{\mathrm{max}})$, and the green dashed line to the mean solution estimates (${\tau}_{\mathrm{mean}},{h}_{\mathrm{mean}}$).

**Figure 7.**The same as in Figure 6 but for the mean a posteriori densities ${p}_{\mathrm{mean}}(\tau \mid {\overline{\mathbf{y}}}^{\delta})$.

**Figure 9.**(

**a**) The aerosol model with the highest evidence from Set 1, and (

**b**) the aerosol type containing the aerosol model with the highest evidence from Set 2. The TROPOMI spectra were recorded on 4 July 2019.

**Figure 10.**The model evidence for each aerosol model from Set 1. The TROPOMI spectra were recorded on 4 July 2019.

**Figure 11.**The sum of the first 10 best aerosol model evidences for each aerosol type from Set 2. The TROPOMI spectra were recorded on 4 July 2019.

**Figure 12.**The same as in Figure 9 but for the data on 5 July 2019.

**Figure 13.**The same as in Figure 10 but for the data on 5 July 2019.

**Figure 14.**The same as in Figure 11 but for the data on 5 July 2019.

**Figure 15.**The maximum solution estimates (${h}_{\mathrm{max}}$, ${\tau}_{\mathrm{max}}$) and the mean solution estimates (${h}_{\mathrm{mean}}$, ${\tau}_{\mathrm{mean}}$) for Set 1 and data on 4 July 2019.

**Figure 16.**The maximum solution estimates (${h}_{\mathrm{max}}$, ${\tau}_{\mathrm{max}}$) and the mean solution estimates (${h}_{\mathrm{mean}}$, ${\tau}_{\mathrm{mean}}$) for Set 2 and data on 4 July 2019.

**Figure 17.**The same as in Figure 15 but for the data on 5 July 2019.

**Figure 18.**The same as in Figure 16 but for the data on 5 July 2019.

**Table 1.**Micro-physical properties of aerosols models of Set 1. Each model is composed of a fine and coarse mode. The median radius of the volume distribution ${r}_{\mathrm{v}}$, standard deviation $\sigma $, the volume of particles ${V}_{0}$, and complex refractive index m of each mode are listed in the table.

Model | Mode | ${\mathit{r}}_{\mathbf{v}}$ (μm) | $\mathit{\sigma}$ | m = (Re(m), Im(m)) | ${\mathit{V}}_{0}\phantom{\rule{3.33333pt}{0ex}}(\mathsf{\mu}{\mathbf{m}}^{3}/\mathsf{\mu}{\mathbf{m}}^{2})$ |
---|---|---|---|---|---|

NONABS | fine | $0.160+0.0434\tau $ | $0.364+0.1529\tau $ | (1.42, $0.004-0.0015\tau $) | $0.1718{\tau}^{0.821}$ |

coarse | $3.325+0.1411\tau $ | $0.759+0.0168\tau $ | $0.0934{\tau}^{0.639}$ | ||

MODABS | fine | $0.145+0.0203\tau $ | $0.374+0.1365\tau $ | (1.43, $0.008-0.002\tau $) | $0.1642{\tau}^{0.775}$ |

coarse | $3.101+0.3364\tau $ | $0.729+0.098\tau $ | $0.1482{\tau}^{0.684}$ | ||

ABS | fine | $0.134+0.0096\tau $ | $0.383+0.0794\tau $ | (1.51, 0.02) | $0.1748{\tau}^{0.891}$ |

coarse | $3.448+0.9489\tau $ | $0.743+0.0409\tau $ | $0.1043{\tau}^{0.682}$ | ||

DUST | fine | $0.1416{\tau}^{-0.052}$ | $0.7561{\tau}^{0.148}$ | ($1.48{\tau}^{-0.021}$, $0.0018{\tau}^{-0.08}$) | $0.087{\tau}^{1.026}$ |

coarse | 2.2 | $0.554{\tau}^{-0.052}$ | $0.6786{\tau}^{1.057}$ |

**Table 2.**Micro-physical properties of aerosols models of Set 2. The median radius of the number size distribution ${r}_{\mathrm{mod}}$, stand deviation $\sigma $, and complex refractive index m of two modes are listed in the table. ${w}_{\mathrm{coarse}}$ is the fraction of coarse mode in number concentration. The two lines of m for MA mod. abs. and MA abs. aerosol model are the refraction index of fine and coarse modes, respectively.

Type | Model | Fine Mode | Coarse Mode | m = (Re, Im) | ${\mathit{w}}_{\mathbf{coarse}}$ | ||
---|---|---|---|---|---|---|---|

${\mathit{r}}_{\mathbf{mod}}$ | ${\mathbf{e}}^{\sigma}$ | ${\mathit{r}}_{\mathbf{mod}}$ | ${\mathbf{e}}^{\sigma}$ | ||||

WA | WA1101 | 0.078 | 1.499 | 0.497 | 2.160 | $(1.4,5.0\times {10}^{-8})$ | $(4.36\times {10}^{-4})$ |

WA1102 | 0.088 | 1.499 | 0.509 | 2.160 | $(1.4,5.0\times {10}^{-8})$ | $(4.04\times {10}^{-4})$ | |

WA1103 | 0.137 | 1.499 | 0.567 | 2.160 | $(1.4,5.0\times {10}^{-8})$ | $(8.10\times {10}^{-4})$ | |

WA1104 | 0.030 | 2.030 | 0.240 | 2.030 | $(1.4,5.0\times {10}^{-8})$ | $(1.53\times {10}^{-2})$ | |

WA1201 | 0.078 | 1.499 | 0.497 | 2.160 | $(1.4,4.0\times {10}^{-3})$ | $(4.36\times {10}^{-4})$ | |

WA1202 | 0.088 | 1.499 | 0.509 | 2.160 | $(1.4,4.0\times {10}^{-3})$ | $(4.04\times {10}^{-4})$ | |

WA1203 | 0.137 | 1.499 | 0.567 | 2.160 | $(1.4,4.0\times {10}^{-3})$ | $(8.10\times {10}^{-4})$ | |

WA1301 | 0.078 | 1.499 | 0.497 | 2.160 | $(1.4,1.2\times {10}^{-2})$ | $(4.36\times {10}^{-4})$ | |

WA1302 | 0.088 | 1.499 | 0.509 | 2.160 | $(1.4,1.2\times {10}^{-2})$ | $(4.04\times {10}^{-4})$ | |

WA1303 | 0.137 | 1.499 | 0.567 | 2.160 | $(1.4,1.2\times {10}^{-2})$ | $(8.10\times {10}^{-4})$ | |

BB | BB2101 | 0.074 | 1.537 | 0.511 | 2.203 | $(1.5,1.0\times {10}^{-2})$ | $(1.70\times {10}^{-4})$ |

BB2102 | 0.087 | 1.537 | 0.567 | 2.203 | $(1.5,1.0\times {10}^{-2})$ | $(2.06\times {10}^{-4})$ | |

BB2103 | 0.124 | 1.537 | 0.719 | 2.203 | $(1.5,1.0\times {10}^{-2})$ | $(2.94\times {10}^{-4})$ | |

BB2201 | 0.074 | 1.537 | 0.511 | 2.203 | $(1.5,2.0\times {10}^{-2})$ | $(1.70\times {10}^{-4})$ | |

BB2202 | 0.087 | 1.537 | 0.509 | 2.203 | $(1.5,2.0\times {10}^{-2})$ | $(2.06\times {10}^{-4})$ | |

BB2203 | 0.124 | 1.537 | 0.719 | 2.203 | $(1.5,2.0\times {10}^{-2})$ | $(2.94\times {10}^{-4})$ | |

BB2102 | 0.087 | 1.537 | 0.509 | 2.203 | $(1.5,3.0\times {10}^{-2})$ | $(2.06\times {10}^{-4})$ | |

BB2103 | 0.124 | 1.537 | 0.719 | 2.203 | $(1.5,3.0\times {10}^{-2})$ | $(2.94\times {10}^{-4})$ | |

DD | BB2101 | 0.074 | 1.537 | 0.511 | 2.203 | $(1.5,3.0\times {10}^{-2})$ | $(1.70\times {10}^{-4})$ |

DD3101 | 0.042 | 1.697 | 0.670 | 1.806 | $(1.53,4.0\times {10}^{-3})$ | $(4.35\times {10}^{-3})$ | |

DD3102 | 0.052 | 1.697 | 0.670 | 1.806 | $(1.53,4.0\times {10}^{-3})$ | $(4.35\times {10}^{-3})$ | |

DD3201 | 0.042 | 1.697 | 0.670 | 1.806 | $(1.53,1.0\times {10}^{-2})$ | $(4.35\times {10}^{-3})$ | |

DD3202 | 0.052 | 1.697 | 0.670 | 1.806 | $(1.53,1.0\times {10}^{-2})$ | $(4.35\times {10}^{-3})$ | |

MA | MA mod. abs. | 0.030 | 2.030 | 0.240 | 2.030 | $(1.4,4.0\times {10}^{-3})$ | $(1.55\times {10}^{-4})$ |

$(1.4,5.0\times {10}^{-8})$ | |||||||

MA abs. | 0.030 | 2.030 | 0.240 | 2.030 | $(1.4,1.2\times {10}^{-2})$ | $(1.55\times {10}^{-4})$ | |

$(1.4,5.0\times {10}^{-8})$ | |||||||

VO | VO4101 | 0.230 | 0.800 | 0.240 | 2.030 | $(1.45,7.5\times {10}^{-8})$ | 0.5 |

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## Share and Cite

**MDPI and ACS Style**

Rao, L.; Xu, J.; Efremenko, D.S.; Loyola, D.G.; Doicu, A. Optimization of Aerosol Model Selection for TROPOMI/S5P. *Remote Sens.* **2021**, *13*, 2489.
https://doi.org/10.3390/rs13132489

**AMA Style**

Rao L, Xu J, Efremenko DS, Loyola DG, Doicu A. Optimization of Aerosol Model Selection for TROPOMI/S5P. *Remote Sensing*. 2021; 13(13):2489.
https://doi.org/10.3390/rs13132489

**Chicago/Turabian Style**

Rao, Lanlan, Jian Xu, Dmitry S. Efremenko, Diego G. Loyola, and Adrian Doicu. 2021. "Optimization of Aerosol Model Selection for TROPOMI/S5P" *Remote Sensing* 13, no. 13: 2489.
https://doi.org/10.3390/rs13132489