Impact of the choice of the satellite AOD product in a sub-regional dust emission inversion

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Atmospheric aerosols (with an emphasis on dust)

Definitions and interest

Aerosols are solid or liquid particles suspended in a gaseous medium. The gas itself is part of the aerosol, but for the sake of clarity in this work we follow the common usage of excluding both hydrometeors and gas from the definition of atmospheric aerosols. Aerosol physical and chemical properties are diverse and can vary considerably in space and time. An aerosol population is a collection of aerosols that usually share similar physical or chemical characteristics.
Aerosol size can range from a few nanometres of diameter to several tens of microns. It is common to group aerosol populations in size modes with the usual terminology of (from smaller to larger): nucleation mode, Aitken mode, accumulation mode, coarse mode and super-coarse mode. It is usual to represent an aerosol population with several modes that can overlap with each other.
Aerosol morphology varies between simple and regular geometrical forms (such as spheres or spheroids) to more complex non-regular shapes. As an illustrative example, particles resulting from high-temperature combustion processes can be described as aggregates of smaller particles formed from unburned or uncompletely burned material; aerosols resulting from the condensa-tion of gaseous chemical species are usually spherical; asbestos particles usually have a cylindrical shape and (dry) sea salt particles may be roughly described by a parallelepiped shape. More complex morphologies can be found, for example, in biogenic particles (e.g. pollen) or aggregates of heterogeneous smaller particles. Dust particles are highly non-spherical and their shape de-pends on the composition and mixture of the particle. Figure 1.1 shows dust particles collected during the SAMUM I (Saharan Mineral Dust Experiment I) campaign.
In terms of aerosol formation process, two types of aerosol are commonly described; primary aerosols are directly emitted into the atmosphere, while secondary aerosols are formed by conden- dust particles of northern Africa collected during the SAMUM I campaign in Morocco. At the bottom of the images, the major elements analyzed by energy-dispersive X-ray technique (EDX) are labelled. In the following, common atmospheric minerals with the specified com-position (and matching the morphology of the particle) are given in parenthesis. (a) Si-rich particle (quartz), (b) Na-bearing aluminosilicate (albite), (c) K-bearing aluminosilicate (illite), (d) Mg-dominated silicate (palygorskite), (e) Ca sulfate and Ca-dominated mineral (gypsum on calcite), (f) Fe-dominated mineral (iron oxide or iron hydroxide), (g) complex internally mixed aluminosilicate with individual Fe-dominated phase (bright spot in center), (h) Ca-P-S-bearing particle (biological?), (i) Si-dominated particle (opaline diatom), (j) aluminosilicate (kaolin group?) with Ca(Na) sulfate (gypsum, thenardite, glauberite?), and (k) Si-rich particle (quartz) with sulfate coating (overview). (l) Detail of coating with EDX spectra for rim and core of the particle.

ATMOSPHERIC AEROSOLS (WITH AN EMPHASIS ON DUST) 

sation of gases (such as sulphuric acid, nitric acid, and low-volatility organic compounds) in the atmosphere. By source, aerosols can be differentiated if they are emitted by a natural (e.g. ma-rine, vegetation fire, desert) or by an anthropogenic (e.g. industrial, urban, agricultural) source. By chemical composition, it is common to identify inorganic aerosols (e.g., sulphate, nitrate, ammonium, sea salt as a major component of sea spray), organic aerosols (whether primary or secondary, also called carbonaceous aerosols) and mineral aerosols among others. The degree of mixture between the different chemical compounds in an aerosol population could range between an external mixture and an internal mixture, including special cases like coated particles or chain particles consisting of aggregates of smaller aerosols.
Aerosol populations can be described using different criteria either by the physical and chem-ical characteristics of the aerosol itself or by the capability of the aerosol population to interact with the environment in relevant atmospheric processes. For instance aerosols can be hydrophilic or hydrophobic depending on their ability to grow in size with relative humidity, and their degree of hygroscopicity is a key property. In relation to their hygroscopicity, aerosols can be grouped by their efficiency to act as cloud condensation nuclei (CCN) or ice nuclei (IN). Finally they can also be characterised by their efficiency in absorbing or scattering radiation for a given part of the electromagnetic spectrum (e.g. visible, infrared). Here the absorbing or non-absorbing character of the aerosols is quite important.
Aerosols present in the lower part of the atmosphere, the troposphere, are called tropospheric aerosols, while in the stratosphere are called stratospheric aerosols. Most of the aerosol descrip-tions above are inter-related, and a general classification for the purpose of aerosol climate effects can be done as in Boucher et al. (2013) by distinguishing sulphate, nitrate, black carbon, organic aerosol, mineral dust and sea spray aerosols. While such a classification may be too simple in light of observed aerosol degree of mixture, it is useful at least from a modelling perspective.
In the atmosphere, aerosols play a crucial role in radiation and cloud processes, which are key processes for weather and climate. Aerosols also impact the whole climate system through their interactions with atmospheric chemistry (e.g., actinic fluxes, heterogeneous chemistry, formation of polar clouds), or with their interaction with the biosphere (e.g., fertilization effect in the Amazon forest because of phosphorus deposition) or with the cryosphere (e.g., through deposition of black carbon in the Artic).
At the moment, there is a large uncertainty in the quantification of aerosol impact in weather and climate (e.g. Boucher et al., 2013). Along with the current lack of knowledge in some of the physical and biogeochemical processes involving aerosols; the quantification of the global aerosol mass balance is still highly uncertain. In terms of global aerosol mass, natural emissions provide the largest source of aerosol, and within them, sea spray over ocean and mineral dust over continent are the most important contributors to the global burden. It is worthy to note that both sea spray and mineral dust emissions, are driven by near surface wind speed (depending on the local atmospheric conditions) along with local surface characteristics complexifying the study and understanding of both processes of emissions, which results in a large uncertainty of their respective contributions at global and local scales.
Linked with the uncertainties in the sources, transport, transformations and sink processes of aerosols in the atmosphere are still not well characterized. All these factors together pose difficulties in estimating the lifetime of aerosols in the atmosphere (see Huneeus et al. (2011) for a comparison of dust lifetime in different models). In fact, the lifetime (τ) of aerosols in the atmosphere can be defined by τ=BS=BR where B is the aerosol burden, that is, the column integrated mass of aerosols, S is the source flux (in terms of mass per time) and R is the sink flux (in the same unit). When all the sink and/or source processes are included in the S and R terms of the previous equation, τ is often called residence time. For aerosols, the sink term includes wet and dry deposition. The latter includes the dry deposition for small aerosols (mainly driven by brownian motion) and sedimentation for coarser particles (mainly driven by gravitational settling). For coarser aerosols as mineral dust or sea spray, the sedimentation rate is highly dependent on the size of the particles. Thus the residence time of these coarser aerosols depends on the cutoff size considered (larger aerosols will have shorter residence time).
Radiative forcing and radiative effect are important concepts to describe and quantify per-turbations to the climate system, as they diagnose changes in the energy balance in the system, which then impact on the climate system. Conceptually, the aerosol-radiation radiative forcing (RF) can be decomposed into four terms (Schulz et al., 2006), as is shown in Equation (1.1.1).
The first term (A) is the radiative efficiency of the aerosol; the second (B) is related to the aerosol microphysics (mass extinction efficiency). Aerosol residence time can be identified in term C of Equation (1.1.1), while the emission rate represents term D. The aerosol chemical composition is important for terms A, B (by their optical properties) and C (by their chemical reactions). The size distribution is crucial for the aerosol residence time (C) and for term B of Equation (1.1.1). Emissions are directly related to the aerosol residence time and to the RF. Radiative forcing due to aerosol-cloud interactions is also sensitive to these parameters. In brief, uncertainties in sources and sinks of aerosols propagate to all aerosol radiative forcing and radiative effect calculations due to its high sensitivity of this quantity to the aerosol size distribution, spatial distribution and composition (among others). Therefore, increasing the accuracy of aerosol emission estimates is a necessary step to improve the current knowledge on the effects and interactions of aerosols in the climate system.
As was mentioned before, the largest contributor to continental aerosols is mineral dust, but their emission flux remains highly uncertain at the global scale. This work will focus on the largest mineral dust emission region of the world, Africa, with the aim of narrowing uncertainties in flux estimates.

Dust and African dust

As mentioned above, mineral dust is mostly emitted by natural processes (Ginoux et al., 2012). Aeolian erosion of arid and semi-arid soils can produce mineral dust emissions, depending on several factors including the wind speed, soil texture, soil moisture, the presence of available erodible material, etc. Conceptually, mineral dust is the result of three main physical processes (Ch. 5 from Knippertz and Stuut, 2014). First, the aeolian erosion is only reached when the wind momentum is strong enough to lift particles from the soil. This threshold is usually defined by a minimum friction velocity, which may depend on the size distribution of soil particles, the crusting effects, soil moisture and the surface roughness. Secondly, the so called creeping and saltation processes take place when the particles moves close to the ground either by “rolling” on the surface or by making small jumps, impacting other particles in the soil. The fraction of particles injected into the boundary layer through the saltation processes is estimated to be small (Ch. 5 from Knippertz and Stuut, 2014), but the impact of the saltation on the soil can release more particles available for this process, or break the binding energies of soil particles themselves into smaller ones that can be injected into the boundary layer. This last process is called sandblasting. Figure 1.2 shows a schematic representation of these processes. A detailed description of the dust production module used in this work which includes the three aforementioned processes can be found in Section 2.1.3.
Figure 1.3 shows picture of a haboob, a dust storm generated by a strong downward flux of air related to convective activity. A satellite view of a dust outbreak is also shown in Figure 1.4. In this figure the dust plume can be noticed over the Atlantic Ocean.
It is worthy to note that dust emission is a process that primarily occurs on a very local scale (of the order of centimetres to meters). Due to the large variability of surface conditions, the estimation of global or regional emission flux is therefore a difficult task. On the regional scale, satellite-based observational studies have been successful in estimating the frequency of dust events (over an emission threshold) (e.g. Schepanski et al., 2007) or directly estimating regional dust emissions flux from satellite and model data as in Evan et al. (2014). For the first approach, satellite imagery was used to track all recognizable dust plumes to the source pixel. The work by Schepanski et al. (2007) is a good example on how to determine dust emission regions and their frequency of emission, but it is only valid for dust that can be manually identified from satellite images, which implicitly sets a threshold on the emission rate. With this methodology, it is not possible to directly estimate the emitted flux. Evan et al. (2014) use dust emissions and aerosol burden from models with aerosol burden estimated from satellite optical depth measurements. This valuable first order approximation cannot well distinguish contributions of dust and sea spray aerosols in the observationally-estimated dust burden.
Modelling studies have also been used to estimate emissions (Huneeus et al., 2011). Estimates of dust emission over North Africa can range between hundreds to thousands of teragrams per year (Tg yr−1), depending on the estimation methodology and tools used. Figure 1.5 shows the estimated annual average dust emission flux over the globe by Ginoux et al. (2012). In the work by Ginoux et al. (2012) they derived a preferential dust source map using AOD retrievals from MODIS Deep Blue, and then they computed the emissions using the dust emission model proposed in Ginoux et al. (2001). Despite the fact that the use of MODIS Deep Blue could be less accurate than other methods (Schepanski et al. (2012) show that the afternoon sampling of the MODIS/Aqua satellite impacts negatively the geographical identification of dust emission sources with this method), Figure 1.5 shows that the largest region of mineral dust emission is the Sahara Desert. However, non-negligible dust sources can be identified in Asia, North America, South America and Australia. Table 1.1 shows the total dust emissions for the median of the models analysed in Huneeus et al. (2011).
The importance of North Africa and the Arabian Peninsula in the global balance. can be inferred from Table 1.1 and Figure 1.5. Additionally, the impact of the dust emitted in these regions on the climate puts forward the need of improving our understanding and knowledge on this topic.
Despite our incomplete knowledge on some key physical processes affecting mineral dust, it has been shown that mineral dust plays an active role in the Earth system. Feldespar-rich mineral dust is one of the most effective aerosols that could serve as ice nuclei (IN) (Atkinson et al., 2013). Deposition of dust containing soluble iron over the ocean can be a limiting factor in the marine productivity, with impacts in the oceanic biogeochemical cycles and potential impacts in the climate system (Jickells et al., 2005). Mineral dust deposited over the Amazon rainforest provides phosphorus to the vegetation (Yu et al., 2015). Yu et al. (2015) propose that the Saharan dust deposition over the rainforest is necessary to avoid the depletion of phosphorus in tropical ecosystems in the long term. Dust interactions with short-wave and long-wave radiation have effects on the surface temperature and the vertical profile of temperature which could modulate a large range of atmospheric variables (e.g., evaporation, vegetation, atmospheric stability, winds, etc.), impacting clouds and the global radiative budget.
On the human dimension, dust can affect agriculture by the erosion of soils (removing fine particles and nutrients from the soil) when dust is emitted and by the abrasion and deposition of dust over crops and natural vegetation (Goudie and Middleton, 2006). Airborne dust reduce the shortwave solar radiation flux at the surface, which decreases the production of electricity of solar power plants. Dust particles, like other aerosols, also have an impact on human health, which is potentially important for local African populations. Inhalation and ingestion of dust are the most important routes of entrance of aerosols into the human body. Once deposited in the human body, they can react with fluids and tissues (Knippertz and Stuut, 2014). Dust increases the incidence of respiratory disease, eye infections, and cardiovascular mortality (Morman and Plumlee, 2013); and has been associated to deadly epidemics of meningococcal meningitis in the African Sahel (Martiny and Chiapello, 2013; P´erez Garc´ıa-Pando et al., 2014) and to coccidioidomycosis (valley fever) in North America (e.g. Kirkland and Fierer, 1996; Goudie, 2014).
In the previous paragraph we have spoken about aerosols and dust in the atmosphere, giving the rationale and the interest of the dust emission estimation problem. We will continue this chapter with a second topic, more related to the methodology that we have applied, and which is present throughout all this thesis: data assimilation in atmospheric sciences.

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Data assimilation and numerical models of the atmo-sphere

Numerical weather prediction models are numerical implementations of the equations governing the dynamics and the physics of the atmosphere. The equations themselves represent approxi-mations of atmospheric processes and are therefore an integral part of such models. Atmospheric models aim to solve, at least, the most important equations from fluid dynamics applied to the atmosphere. These are the momentum equation, the continuity equation and thermodynamics equations, where the variables are the so-called “state” or prognostic variables (i.e., wind field, temperature, surface pressure) and mixing ratio of some important atmospheric trace gases or particles (e.g., water vapour) among others. Numerically it is usual to split the process of solv-ing the (discretized) equations into the “dynamics” (momentum and continuity equations) and the “physics” parts of the model, the latter consisting of radiative transfer, boundary layer and surface exchange, convection and other cloud processes.
Atmospheric observations consist of in situ and remote sensing measurements of the atmo-sphere. Typically atmospheric remote sensing rely on measuring radiative quantities which can be translated into relevant atmospheric variables (e.g., temperature) through a “retrieval scheme” that is based on fundamental physical laws. If the source of the electromagnetic radiation em-ployed by the sensor is a natural source (e.g., radiation emitted by the sun or terrestrial radiation emitted by the Earth system), then the remote sensing is called passive. This is, for example, the case of sunphotometers and of a range of passive satellite-borne (spectro)radiometers. When the emitted source is artificial, then the retrieval technique is called active. Lidars and radars are examples of this type of instruments (Liou, 2002). Information about the state or the composition of the atmosphere can be retrieved by using remote sensing. In this case, the electromagnetic spectrum is sampled depending on the variables of interest. For example, the visible and in-frared parts of the spectrum are commonly used in cloud detection, the ultraviolet is useful to determine ozone concentrations. Aerosols are usually retrieved by using the visible part of the electromagnetic spectrum, but infrared radiation can also be useful to detect coarse mode aerosols such as dust. Operational products developed for dust detection rely on visible (e.g., Levy et al., 2013) or infrared (e.g., Peyridieu et al., 2013) electromagnetic radiation. In particular, infrared dust retrievals can give information about dust size distribution and the height of the dust layer (Peyridieu et al., 2013). We will describe the observations used in this thesis in Chapter 2.
Observations typically provide discrete information on the state of the atmosphere, while models try to provide a comprehensive and almost continuous view of the state of the atmosphere. To achieve realistic forecast, models need observations. Weather and chemical weather forecasting is modelled as a partial differential equation system, which includes the equation themselves, the domain where the variables needs to be solved, the initial conditions and the boundary conditions. Boundary conditions at the surface can be artificially imposed or they can be extracted from observations, land and ocean models (also driven by observations) or a combination of both. At the top of the atmosphere, the solar radiation is the most important boundary condition, which is typically acquired from astronomical knowledge. For realistic forecasts, the initial conditions have to be close to the real state of the atmosphere, and thus the incorporation of observations of the atmosphere is fundamental.
Models are not perfect, and observations neither. How can we estimate the real state of the atmosphere taking into account model and observational errors in a physically consistent estimate? That is the principal subject of study of data assimilation, which we now discuss.

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

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