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## MISR observations

The Multiangle Imaging SpectroRadiometer instrument (MISR, Diner et al., 1998) on-board the Terra satellite is a spectroradiometer with 36 channels, with four visible and near-infrared spectral bands. It can measure radiances from a given target with up to nine viewing angles (Kahn and Gaitley, 2015). At nadir, the swath of MISR is 380 km and the Level 2 AOD retrieval is reported at approximately 17.6 km resolution. The instrument observes the same atmospheric column from different viewing angles and for several air mass factors in a short period of time, which allows the retrieval algorithm to distinguish contributions from the surface and the atmosphere in the observed reflectance. Thus more information regarding the aerosol microphysics (Kahn et al., 2005) can be retrieved than for nadir-only instruments (e.g., MODIS). Level 3 products are calculated from Level 2 AOD gridded in a regular latitude- longitude mesh of 0.5 degrees of resolution. Total AOD in Levels 2 and 3 are reported for the following wavelengths: 446, 557, 672 and 867 nm. The 557 nm wavelength is usually considered equivalent to 555 nm. The retrieval AOD is split into the AOD due to spherical and non-spherical aerosols, and into the AOD due to small (less than 0.35 m of radii), medium (between 0.35 m and 0.7 m of radii) and large (more than 0.7 m of radii) aerosols. For the total AOD, Kahn et al. (2005) estimate the EE at 555 nm by EE = ±max(0.05, 0.2 A).

### SEVIRI-AERUS observations

The above-mentioned instruments are carried by low orbiting satellites in sun-synchronous orbits. They overpass a point of the Earth over the Equator at most once during daylight and once during nighttime (keeping in mind that passive instruments cannot retrieve visible AOD in nighttime). On the contrary, the SEVIRI instrument on-board the geostationary satellite MSG (Meteosat Second Generation) captures a full-disk image of the Earth each 15 minutes; covering Europe, Africa and the eastern Atlantic Ocean.

All the above-mentioned satellite derived AOD products use the spectral signature of aerosols and surface reflectance to estimate the AOD. In contrast, Carrer et al. (2010) and Carrer et al. (2014) take advantage from the high temporal and spatial resolution of the SEVIRI images to produce an AOD product at 630 nm. The algorithm uses the multiple radiance measurements for different solar angles to derive, using only the 630 nm SEVIRI channel, surface reflectance and AOD simultaneously. Over land, the surface is modelled with a Bidirectional Reflectance Distribution Function (BRDF) and over ocean is assumed Lambertian. The parameters of the surface reflectance models are calculated for each day (along with the AOD), with assumptions on their timescales. For each day, the final AOD product is calculated with a filtering method using the 15-minute acquired images. The variance of the AOD error reported in the daily AOD is the variance of the analysis errors from this filter. We will use this error estimate in Chapter 5. In this work, we filter the SEVIRI AOD products by only using the AOD calculated with information from the same day of the measurements; i.e., only using pixels when the flag “ZAge” is equal zero (D. Carrer, personal communication). This filter eliminates suspicious large and isolated AOD values over the tropical Atlantic Ocean.

#### Satellite interpolation procedure

To be compared with the model outputs, all observations are gridded into the model grid, which is a latitude–longitude grid with a zoom in it, which means that the grid size is not the same in all the pixels. Figure 4.2 shows the model grid used in this work. The source (observational) grid is usually finer than the model grid.

There are several standard interpolation procedures for meteorological data which can be used for our purposes. The “nearest neighbour” method finds the closest grid center of the source grid to the new grid and assigns this value to the new field. This could be highly inaccurate if the two grids have different resolutions, in addition with the potential large information loss. Linear and bilinear interpolation are a common choices for interpolating meteorological model data. For each grid point in the new grid, these methods need valid data from all the source grid points that provide information to the new grid point (close in latitude and longitude). Satellite observations usually show large amounts of pixels with missing data, which propagates the missing data to the new grid if it is coarser than the source grid, leading to an important information loss.

The general interpolation procedure for satellite observations used in this work is similar to the bilinear method, but it can handle the quantity of missing data in the new grid. We have written a weighted-average interpolation method that we will describe in the following paragraph. For each model gridbox (blue lines in Figure 2.8), the area contribution of each source gridbox (green lines in Figure 2.8) to the model gridbox (most of them will be zero but not if both gridboxes overlap) is calculated. If the area covered by valid data in the source grid (green filled squares in Figure 2.8) is larger than a (configurable) threshold, then the value of the observation in the model grid is the average of the observations in the source grid, weighted by their relative contribution to the covered area of the model grid. If the threshold is not reached, the model observation is set to missing data.

**MISR AOD redefinition of bins**

As stated earlier, the standard MISR Level 3 product reports AOD for three aerosol size ranges: small, medium and coarse. Regrettably, the cut-off sizes of these bins do not match with the SPLA bins, with the cut-off between coarse and fine modes being close to the center of the MISR medium size classification.

The MISR algorithm finds the best fit between the simulated radiances given by 74 aerosol mixture models (Kahn and Gaitley, 2015) and the radiances observed by the satellite. The mixture models are themselves combinations of 8 basic aerosol types.

Fortunately, the key parameters of these models are well documented, and they are part of the standard Level 2 products. Additionally, optimum fit parameters for each model are also reported in the Level 2 products, along with the optical properties and parameters of the size distributions of the aerosol models. With this information, it is possible to calculate the contribution of each of the 8 basic aerosol types to the optimal fit given by the MISR algorithm.

With this disaggregated AOD by aerosol type and with the size distribution and optical aerosol parameters it is possible to approximately calculate the contribution arbitrary defined size bins to the total AOD. The approximation is because the size dependent extinction coefficients for each model are not reported in the Level 2 products and only the bulk extinction coefficients are given. In this step we assume homogeneity of the extinction coefficient over all the aerosol model size range. The error produced by the extinction coefficient assumption is in practice less than 5% of the total AOD value, for less than the 5% of the recalculated pixels.

The size bins were defined by the SPLA size bins limits, and then the MISR Level 2 AOD were calculated for these size bins. The last step is to filter the AOD by the quality flags reported in the MISR product, and regrid the data from the native Level 2 MISR grid (Space Oblique Mercator projection) to a regular latitude-longitude grid.

**Covariance matrix of the observation errors**

In Chapter 1 we defined the covariance matrix of the observation errors (R matrix) by the covariance matrix of the random variable « o, where y = H(xt) + « o .

with y the observations, H the observation operator and xt the true correction factors (in the control vector space). For the moment, the observations are assumed unbiased. We will discuss this assumption later in Chapter 6.

Two different definitions were used for the diagonal elements of the R matrix. In Chapter 4 only MODIS/Aqua total 550 nm AOD is assimilated. Here we follow the AOD error estimates used in Huneeus et al. (2013) for this satellite product, that is, to define a constant value of 0.2 as the standard deviation of the MODIS/Aqua AOD errors over land and a value of 0.1 over ocean. For the experiments in Chapter 5 we follow the error estimated given in the literature and shown in Section 2.2.1. Table 5.1 summarizes the pixel-wise AOD errors used.

In both cases, the model error was defined with a standard deviation of 0.02, thus the total error in R is the sum of the model and the observational AOD error. Huneeus et al. (2012) show the low sensitivity of their analysis with respect to the model error, ranging between 0.02 to 0.5 in AOD.

For the results shown in Chapter 4 and Chapter 5 the R matrix is assumed diagonal. This assumption is not necessarily true because several sources of correlation in the AOD errors could exist. For example, collocated total and fine AOD from MODIS/Aqua should be correlated because both retrievals are calculated using the same radiance measurements, the same algorithm with similar assumptions. AOD errors from nearby pixels in a retrieval could also be correlated, as the AOD error could depend on the viewing geometry and/or surface properties.

Similarly, for the experiments in Chapter 5 would be necessary to include the correlations between simulated fine and total AOD errors. These errors should be included as part of the representativeness error (cf. Section 1.2), which is included in the model error in the R matrix. The above mentioned correlations were not included in this thesis due to the high complexity on their estimation.

**Table of contents :**

**1 Introduction **

1.1 Atmospheric aerosols (with an emphasis on dust)

1.1.1 Definitions and interest

1.1.2 Dust and African dust

1.2 Data assimilation and numerical models of the atmosphere

1.3 Aerosol data assimilation

1.4 Inversion of dust fluxes

1.5 Outline of this thesis

**2 Observation operator and observations **

2.1 Observation operator

2.1.1 LMDZ model

2.1.2 SPLA model

2.1.3 Dust emission model

2.1.3.1 Soil texture and size distribution

2.1.3.2 Wind velocity

2.1.3.3 Horizontal flux

2.1.3.4 Vertical flux

2.1.4 Other emissions

2.2 Observations

2.2.1 Satellite observations

2.2.1.1 MODIS observations

2.2.1.2 MISR observations

2.2.1.3 PARASOL observations

2.2.1.4 SEVIRI-AERUS observations

2.2.1.5 Satellite interpolation procedure

2.2.1.6 MISR AOD redefinition of bins

2.2.2 Ground-based observations

**3 Emission fluxes inversion system **

3.1 Cost function and control vector

3.1.1 Control vector sub-regions

3.1.1.1 Dust sub-regions

3.1.2 Cost function

3.2 Error covariance matrices

3.2.1 Covariance matrix of the background errors

3.2.2 Covariance matrix of the observation errors

3.2.3 Desroziers diagnostics

3.3 Minimization

3.3.1 Technical aspects of the sensitivity matrix computation

3.3.2 Cost function minimization

**4 Article: Subregional inversions of North African dust sources **

4.1 Published article

4.1.1 Introduction

4.1.2 Data and Methods

4.1.2.1 LMDz-SPLA Model

4.1.2.2 Observations

4.1.2.3 Data Assimilation System

4.1.2.4 Experimental Configuration

4.1.3 Results

4.1.3.1 Cost Function Decrease

4.1.3.2 Correction Factors

4.1.3.3 Comparison with MODIS

4.1.3.4 Comparison with AERONET

4.1.3.5 Emission Fluxes

4.1.4 Discussion

4.1.5 Conclusions

4.2 Further information

4.2.1 Near surface winds

4.2.2 Dust outbreak

4.2.3 Vertical profile

**5 Article: Impact of the choice of the satellite AOD product in a sub-regional dust emission inversion **

5.1 Submitted article

5.1.1 Introduction

5.1.2 Inversion system

5.1.2.1 Observation operator

5.1.2.2 Control vector

5.1.2.3 Observations

5.1.2.4 Error covariance matrices and assimilation configuration

5.1.3 Results

5.1.3.1 Some words about the observations

5.1.3.2 Assimilation results: Departures

5.1.3.3 Analysis AOD

5.1.3.4 Mineral dust flux

5.1.4 Conclusions

5.1.5 Appendix: Comparison with AERONET

5.2 About the linear approximation

5.3 Coarse and fine AOD assimilation

5.3.1 Results

**6 Inversion with bias correction **

6.1 Motivation

6.2 Cost function with bias correction

6.3 Implementation

6.4 Results

6.5 Conclusions

**7 Conclusions and perspectives **

7.1 Summary

7.2 Perspectives

**A List of acronyms **

**References **