Atmospheric aerosols (with an emphasis on dust)

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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.

Data assimilation and numerical models of the atmosphere

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.
Data assimilation techniques have been developed since the pioneering works of Panofsky (1949) and Cressman (1959). They have proven very successful to estimate the fundamental variables of the atmosphere (temperature, pressure, …) as shown by the accuracy of weather forecasts (e.g., Buizza et al., 2005) and the quality of atmospheric reanalyses (e.g. Saha et al., 2010; Dee et al., 2011). In the last decades data assimilation techniques have been used to estimate the chemical state of the atmosphere (e.g. Bocquet et al., 2015, for a review). In this work, we will focus on the variational approach.
In data assimilation (DA) the real state is unknown, but it can be approximated by a prior (or first guess) and by the observations. The aim is to find the best estimate of the real state, using these two approximations and descriptions of their statistical errors. To this effect, in variational DA, a variable called control vector (or state vector) is controlled in the model domain, and the best estimate of the state of the atmosphere is determined by the result of the minimization of a cost function.
The formulation of a DA problem relies on two different spaces. The control vector is defined in a subspace of Rn, i.e., it is a vector of n components corresponding to n model variables, while the observation vector y is defined in Rp where p is the number of observations. In a typical 6-hour window of a numerical weather prediction assimilation, the number of model variables is O(107 − 108) and the observations are O(105 − 106) (Nichols, 2010).
If x is the true continuous state of the atmosphere, we will denote by xt the projection of x into the space of the control vector x through a projection operator Π, that is, xt = Π(x). The prior (or background) represents the a priori information and it is denoted by xb (with xb ∈ Rn). The prior is assumed unbiased and can be expressed as xb = xt + εb, with εb a random variable with mathematical expectancy equal to zero (E(εb) = 0). The assumption that the prior is unbiased is an important one, which we will come back to later in this work. The covariance matrix of εb is denoted by B.
Observations y have an instrumental error denoted by εi. In other words, there exists a map h such that y = h(x) + εi (Bocquet, 2014). Elements in the control vector space are compared with the observations using an observation operator H : Rn → Rp. The observations y can be written as y = H(xt) + εo. The error εo is called the observational error, it is also assumed unbiased with covariance matrix R, and it can be written as the sum of two errors: the instrumental error εi and the representativeness error εr as in Bocquet (2014):
εo = εi + εr ,
with εr = h(x) − H(xt) = (h − H ◦ Π)(x).
The representativeness error includes the discretization errors of the observations (e.g., sam-pling and model grid approximation) and errors of the observation operator (e.g., errors or unre-solved physical processes in the model) while the instrumental error basically corresponds to the measurement and retrieval errors.
Non-diagonal terms of R are the covariances between the different elements of the observa-tional error, while non-diagonal terms of B are the covariances between the different elements of background error. It is usual to assume independence between the observational and background errors probability density functions. In this work we will implicitly use this assumption. In data assimilation, one of the main challenges is to properly estimate the covariance matrices B and R, including their non-diagonal terms. Later in this thesis we will work on this topic, for both covariance matrices.
With the definitions above, it is possible to define the cost function J as:
J(x) = 1 (x − xb)T B−1(x − xb) + 1 (y − H(x))T R−1(y − H(x)) . (1.2.1)
The solution of the minimization of Equation (1.2.1) over a feasible domain of x is called the analysis and it is denoted by xa. The analysis is the best estimate of the state of the system, but only under well defined assumptions such as unbiased errors and well defined error covariance matrices.
In this work, we will perform the data assimilation minimizing Equation (1.2.1) in Chapter 4 and Chapter 5.

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Aerosol data assimilation

Measurements of the amount of aerosols in the atmosphere can be assimilated into models through filtering or variational approaches. Observational information of the amount of aerosols may come from ground-based, airborne or spaceborne instruments.
Ground-based observations include direct measurements, such as surface aerosol mixing ratios, and indirect (remote-sensing) measurements, such as the Aerosol Optical Depth (AOD) from sunphotometers which represent the column aerosol amount, or vertically- resolved aerosol extinction coefficients retrieved from lidar systems.
Passive instruments on board satellites can measure the reflection of solar radiation by the atmosphere and the surface at several wavelengths. Qualitative retrievals of the amount of aerosol in the atmospheric are, for example, the aerosol index (AI) from the satellite-borne instruments Total Ozone Mapping Spectrometer (TOMS) and Ozone Monitoring Instrument (OMI). Aerosol optical depth is a quantitative measure of the aerosol burden and it can be retrieved by satellite-borne instruments as the Moderate Resolution Imaging Spectroradiometer (MODIS), the Mul-tiangle Imaging Spectroradiometer (MISR), the Advanced Infrared Radiation Sounder (AIRS), the Infrared Atmospheric Sounder Interferometer (IASI), the Polarization and Directionality of the Earth’s Reflectances instrument (POLDER) among others. Spaceborne active instruments can also retrieve aerosol vertical profiles (e.g., Cloud-Aerosol Lidar with Orthogonal Polariza-tion,CALIOP) but the current state of play makes it difficult to invert a consistent AOD given the characteristics of current spaceborne lidars.
The aforementioned instruments are on-board low earth orbit (LEO) satellites with sub-synchronous polar orbits. Instruments on-board LEO satellites typically cross the equator at the same local time everyday, and thus they visit a point in the equator at most one time per day and other at night. Depending on the instrument swath, a global coverage can be done in a few days (one day for Visible/Infrared Imaging Radiometer Suite, VIIRS, 2 days for MODIS, 9 days for MISR, etc.). AOD can be also derived from measurements of instruments onboard geostationary satellites, for example from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) instrument onboard Meteosat Second Generation (MSG) and the Advanced Himawari Imager (AHI) onboard the Japanese geostationary meteorological satellite Himawari-8. These measurements can be done at a high temporal frequency (15 minutes) but only cover a fixed portion of the globe.
At the current state, AODs derived from satellite measurements are the most widely used products in aerosol data assimilation. It can be assimilated at several wavelengths or from several instruments simultaneously. Although AOD is a column integrated piece of information with relatively large uncertainty at the pixel level, the large temporal and spatial coverage of satellite retrievals can counteract these disadvantages. On the contrary, aerosol concentration measurements at surface level can report a more detailed and accurate measurements than AOD including, for example, size distribution or aerosol composition (but only at surface level). The local nature of these measurements hampers their use in large scale studies, unless there exists a dense observational network. Such measurements have been assimilated in chemical transport models as well.
Instead of assimilating AOD, it is possible to directly assimilate the measured radiances. This implies including the retrieval process in the observation operator, and consequently lessening the possible inconsistencies between the aerosol model (in the observation operator) and the retrieval algorithm. This approach also needs a more complex radiative transfer code, because the measured radiances at the top of the atmosphere are also influenced by gases, clouds, surface properties and viewing angles. Additionally and depending on the instrument, the radiative transfer code should be able to handle polarized radiances at the top of the atmosphere (e.g., POLDER) or radiances measured in several viewing angles and wavelengths (e.g., MISR).
Such observational aerosol information can be assimilated in models at the global or regional scale. Depending on the choice of the control vector, aerosol data assimilation can be used to improve initial conditions in chemical weather forecast, improve modelled aerosol concentrations for observed states (“reanalysis”) or estimate emissions using a top-down approach.
The control vector can be either the aerosol concentrations or aerosol emissions, or both. In the former case, the size of the control vector is usually large (the order of magnitude of the number of gridboxes in the model). In the case of AOD assimilation, it is necessary to make assumptions on the aerosol vertical profile and the aerosol composition in the observation operator. In this thesis, we will assimilate AOD by defining a control vector related to the aerosol emissions. More precisely, we will use correction factors of the prior emissions for all the aerosols and gaseous precursors simulated by the model.

Inversion of dust fluxes

The overall emission rate of mineral dust is estimated to range from hundreds to thousands of teragrams per year (e.g. Huneeus et al., 2011), with a large associated uncertainty. As we stated in previous sections, the knowledge about the amount of atmospheric aerosols in the climate system is required for a better understanding of our environment. The estimation of these emissions is not an easy task. Direct measurements of emissions are unpractical in large source regions, so an indirect estimation has to be done.
Additionally, emissions of natural aerosols have a large temporal variability, and are modulated on time scales from seconds to decades. There are several factors at different time and spatial scales affecting dust production. The dust emission process itself has a scale of seconds, and can be triggered by wind gusts and turbulence close to the surface. Diurnal cycle of winds and boundary layer stability, with temporal scale from minutes to hours, are important for the characteristics of near surface winds. Soil moisture is a variable that can decrease the soil capacity to produce dust, with a variability from hours to months. It also influence the presence and growing of vegetation in semi-arid or transition regions, having impacts on dust emissions from the seasonal to the inter-annual scale. Meteorological conditions at the synoptic and seasonal scales also have an impact onto the dust emission flux, through precipitation and near surface winds. Finally, long-term changes in the climate system affects the meteorology and thus the ensemble of variables mentioned below.
A large amount of observations is therefore needed to capture the sporadic nature of emissions of natural emissions. If the aerosol is measured downwind of its source region, other aerosol related processes (such as transport or deposition) that are driven by complex physical mechanisms need to be accounted for when estimating the source strength.
In this work we intend to tackle the issue of dust aerosol source in a systematic way, using tools from data assimilation and thus including a large amount of satellite observations. We have deliberately reduced the degrees of freedom of the problem by controlling regional emissions. To this end, we have defined appropriate regions, in which an improved model of dust emissions provides prior emission fields.
The main aim of this work is to perform dust inversions, giving new estimates of mineral dust fluxes. However another aim is to study the quality of the assimilation system and the scope of our estimates. Some work has been performed to compare the quality of the different satellite retrievals of AOD and the feasibility to use them for aerosol data assimilation purposes, with a special attention on their potential biases. We illustrate our methodology for dust source inversion, but the methodology that we present here can easily be applied to a more general assimilation framework with other aerosol species and for other regions.

Outline of this thesis

This thesis comes in 7 chapters. Chapter 2 describe the main tools used in this thesis: the assimilated observations and the most important aspects of the observation operator, i.e., the dust emissions, aerosol and meteorological model. Chapter 3 describes the choice of control vector and the data assimilation system.
A first dust source inversion is shown in Chapter 4 and the sensitivity of the dust fluxes inversion to the assimilated observation is discussed in Chapter 5. A proposed and implemented bias correction scheme is shown in Chapter 6. Final conclusions and remarks follow in Chapter 7

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

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