Valentin Debarnot

Pierre Weiss

DEEPBLUR: BLIND IDENTIFICATION OF SPACE VARIANT PSF

Keywords: blur identification, neural network, nonuniform blur, blind debluring, blind inverse problem

We propose to train a neural network to estimate space varying blur operators from a single blurry image. The key assumption is that the operator lives in a subset of a known subspace, which is a reasonable assumption in many microscopes. We detail a specific sampling procedure of the subset to train a Resnet architecture. This allows a fast estimation. We finally illustrate the performance of the network on deblurring problems.

INTRODUCTION

Optical systems often produce observations blurred 1 by the various optical components. Most existing deblurring algorithms require the knowledge of the blur operator to improve the image quality. This assumption is critical to produce accurate reconstructions. There are three main methods for estimating a blur operator: i) using a theoretical model, which is prone to calibration errors, ii) imaging point sources: unfortunately, this step should often be reproduced before each acquisition, iii) solving a blind inverse problem, i.e. looking for both the original signal and the blur operator. In this paper, we are interested in the latter approach.

Existing works

Blind inverse problems have received continual attention for the last four decades. The approach that has prevailed is to estimate the original signal and the blur operator using an alternating minimization procedure. Under regularity assumptions on the image and the operator, each sub-problem boils down to a standard inverse problem [START_REF] Fergus | Removing camera shake from a single photograph[END_REF][START_REF] Levin | Understanding and evaluating blind deconvolution algorithms[END_REF][START_REF] Sun | Edge-based blur kernel estimation using patch priors[END_REF][START_REF] Perrone | Total variation blind deconvolution: The devil is in the details[END_REF]. In the last few years, machine learning approaches have begun to emerge and outperform older methods, in particular in the field of computer vision where motion blurs are estimated [START_REF] Sun | Learning a convolutional neural network for non-uniform motion blur removal[END_REF][START_REF] Gong | From motion blur to motion flow: a deep learning solution for removing heterogeneous motion blur[END_REF]. These blurs This work was supported by the Fondation pour la Recherche Médicale (FRM grant number ECO20170637521 to V.D.). P.W. acknowledges support from the ANR JCJC OMS and from ANR 3IA ANITI. 1 In this paper, we deal with spatially varying blurs, and therefore prefer the term deblurring to deconvolution (i.e. spatially invariant operator).

a

Image dataset

Operator dataset b Observation model have characteristic (slow Fourier decay) which are not directly applicable to microscopic blurs. Recently [START_REF] Shajkofci | Spatially-variant cnn-based point spread function estimation for blind deconvolution and depth estimation in optical microscopy[END_REF] proposed to use a neural network to estimate the blur parameter from a single blurry image. This work is closely related to our contribution, with the following differences: i) their operators are convolutions and ii) a central assumption in our work is that the operator live in a low-dimensional subspace.

y = H 0 u 0 + η H 0 ∼ L H u 0 ∼ L u c Training procedure Resnet neural network (y, H 0 ) Ĥ ≈ H 0

Observation model

Let y ∈ R m denote the observed signal, H 0 : R m → R m denote the linear blur operator and u 0 ∈ R m denote the original image. We have

y = H 0 (u 0 ) + η, (1)
where η ∈ R m is an additive random perturbation. Without further assumption, estimating H 0 and u 0 from y is an ill-posed problem. In the next paragraphs, we will detail the structure of the admissible operators.

Product-convolution expansion

Optical blurs are very often modeled by a convolution operator, and can only capture stationary degradations. We overcome this limitation by using the product-convolution expansions [START_REF] Denis | Fast approximations of shift-variant blur[END_REF][START_REF] Escande | Approximation of integral operators using product-convolution expansions[END_REF]. They are efficient models of space varying blurs, have good approximation properties if the PSF (Point Spread Function) varies smoothly, and can be computed rapidly using fast Fourier transforms.

A product-convolution expansion H has the following form:

H(u) = K k=1 e k * (f k u), ∀u ∈ R m , (2)
where * denotes the convolution product, denote the Hadamard (element-wise) product and (e k ) k and (f k ) k denote two families of R m . The family (e k ) can be interpreted as a basis to describe the PSFs of H while the family (f k ) describes the PSF variations.

To clarify the definition, we provide an example with K = 2 in Fig. 2. The family (e k ) is computed by selecting 2 anisotropic Gaussian kernels with standard deviations randomly chosen in [START_REF] Fergus | Removing camera shake from a single photograph[END_REF][START_REF] Perrone | Total variation blind deconvolution: The devil is in the details[END_REF], see Fig.

Subspace of operators

We now detail the assumptions on the space of admissible blur operators.

Assumption 1.1 (Subspace of operators). Let (e k ) and (f k ) denote two known families. The blur operators live in a lowdimensional subspace H ⊂ {H : R m → R m } of productconvolution operators of the form:

H[γ](u) = K k=1 γ k e k * (f k u) (3)
We will refer to an operator in H either by H, γ or H[γ].

Assumption 1.1 is realistic in many microscopes. The space H can be estimated by imaging fluorescent micro-beads [START_REF] Debarnot | Learning low-dimensional models of microscopes[END_REF], or provided that we have access to a collection of operators [START_REF] Debarnot | A scalable estimator of sets of integral operators[END_REF].

Assumption 1.2 (A conical hull in H). We are given a collection (γ p ) of P admissible operator parameterizations. Assuming that this set represents the set of operators sufficiently densely, we can construct the conical hull of the coefficients γ p :

C def. = cone (γ p , 1 ≤ p ≤ P ) , (4)
which we will use as a proxy to describe the set of all admissible operators.

Contributions

The objective of this paper is to recover an estimate Ĥ of H 0 and an estimate û of u 0 given the observation y. Given the previous assumptions, a natural approach to attack this issue would consist in solving

inf u∈R m , H∈H[C] 1 2 Hu -y 2 2 + R(u), (5)
where R : R m → R + is a regularization function promoting desired properties of the signal u. Imposing H ∈ H[C] is a strong regularization on the admissible operators that preserve properties of the admissible operators (e.g. positivity or barycenter). Optimizing H and u jointly makes the problem (5) nonconvex and numerically involved.

In this paper, we therefore follow a different route and consider a two-step procedure: First, estimate the blur operator Find Ĥ ∈ C an estimate of H 0 using y.

Second, solve a non-blind inverse problem assuming that H 0 = Ĥ.

The main contribution of this paper is to provide a robust methodology to solve the first step. We identify the blur operator from a blurry-noisy image by training a neural network. This requires a specific sampling procedure of the set H[C]. We then train a Resnet neural network to estimate a spatially variant blur operator from a single blurry image. This procedure appears to be robust if trained with a large enough dataset. In particular, we show that the network trained with natural images still performs well on unseen biological images. A summary of the approach is shown in Fig. 1.

METHOD

Modeling and sampling blur operators

In order to train a neural network, we will need to sample operators at random within H[C]. If P is large, a uniform sampling on the (P -1)-dimensional simplex would result in the fact that the extreme rays of the cone C are not explored. To avoid this flaw, we propose two complementary solutions: i) Simplify the cone by keeping only a subset of extreme rays. ii) Do not draw the coefficients α uniformly, but rather favor sparse distributions.

Cone simplification

Simplifying a conical hull is a difficult problem related to nonnegative matrix factorization. We refer the interested reader to [START_REF] Van Buskirk | Sparse approximate conic hulls[END_REF] for instance. In this work, we propose a simple greedy algorithm described in Algorithm 1.

Algorithm 1 A cone simplification algorithm

Require: A set of normalized vectors (γ p ).

Require: A number of extreme rays N . Find the circumcenter [START_REF] Henrion | Inradius and circumradius of various convex cones arising in applications[END_REF] γ of cone(γ p , 1 ≤ p ≤ P ).

Initialize the set of kept rays to R = {γ}. Initialize the set rays to explore to S = {γ p , 1 ≤ p ≤ P }. for all n = 0 → N -1 do Find γ ∈ S that maximizes the minimum angle with the rays in R. Remove this vector from S and add it to R. end for Set R = R\{γ}. return R and cone(R).

Sampling the operators at random

By Caratheodory theorem, any point within a conical hull can be expressed as a conical combination of K extreme rays. In this work, we propose a heuristic method to favor the extreme rays. This is detailed in Algorithm 2.

Algorithm 2 Sampling procedure in C Require: The subspace dimension K and the cone cone(γ q , 1 ≤ q ≤ |R|). Weights α min < α max . Draw a random integer J uniformly in {1, . . . , K}.

Pick J integers {z 1 , . . . , z J } at random on the set {1, . . . , |R|}. Draw a random vector β uniformly distributed on the (J -1)-dimensional simplex. Draw a random weight α uniformly in [α min , α max ]. return Coefficient vector α J j=1 β[j]γ zj .

Learning procedure

The coefficient γ is drawn from a distribution L H defined in Algorithm 2. This ensures that γ ∈ C. In order to compute y from the model (1), we need an image u. In this work, we select u using the uniform distribution L u over the STL-10 data-set of natural images [START_REF] Coates | An analysis of singlelayer networks in unsupervised feature learning[END_REF]. This data-set is composed of 10000 images for the training procedure, and 1000 different images for the testing procedure. Finally, we train a Resnet convolutional neural network (CNN) [START_REF] He | Deep residual learning for image recognition[END_REF] to retrieve γ using the blurry-noisy observation y. We use the relative Frobenius norm between the true operator and the estimation as a cost function. We train the convolutional neural network with 100 iterations of the ADAM algorithm, using 2, 048 images drawn from the distribution L u , with a batch size of 64 and a learning rate equal to 10 -3 .

NUMERICAL ILLUSTRATION

In this section, we work with square images m = 128 × 128.

The subspace H and the convex set C are computed using the estimation procedure described in [START_REF] Debarnot | Learning low-dimensional models of microscopes[END_REF]. We use the operators described in Section 1.2.1. The resulting subspace is composed of K = 20 elementary operators. The learning procedure is performed using the parameters described in Section 2.2. The average relative Frobenius norm between the true operator and the estimation produced by the network is less than 5% at the end of the training phase (on the test data-set).

To illustrate the proposed methodology, we solve the following total variation deblurring problem with a proximal gradient descent algorithm:

inf u∈R m T V (u) + λ 2 Ĥu -y 2 2 . (7)
In Fig. 3, we display the true and estimated operators applied to a Dirac comb, and the result of the deblurring algorithm using the estimated operator with total variation regularization for various images. In Fig. 3a-d, we use natural images of the STL-10 test data-set. As expected, the network -that has been trained on similar images -outputs an accurate estimate of the true operator. Solving the deblurring Problem (7) leads to sharp results, and allows to recover hidden details. In Fig. 3e and Fig. 3f, we observe how the trained network behaves on other images. In Fig. 3e, we use a real image of microscopy from the dataset [START_REF] Ljosa | Annotated high-throughput microscopy image sets for validation[END_REF]. In Fig. 3f, we use a simulated image of single molecule localization microscopy, i.e. points sources at random locations. In both problems the network performs well and retrieves the operator with high accuracy. More importantly, solving the deblurring Problem [START_REF] Shajkofci | Spatially-variant cnn-based point spread function estimation for blind deconvolution and depth estimation in optical microscopy[END_REF] with the estimated operator allows to better discriminate the biological elements, such as the cells in Fig. 3e. In the last experiment, we replace the total variation regularization term by a 1 penalty on the signal. It allows to retrieve sparse elements and greatly improves the resolution of fluorescent proteins. Notice that these deblurring results are simply a proof of concept since better deblurring algorithms could be used (e.g. a variational network). The SNR with the blurry and the estimated images is given in the sub-captions.

CONCLUSION

We have presented a learning based method to estimate spatially varying blur from a blurry-noisy image. This methodology is robust in the sense that even if the neural network is trained on a set of natural images, it still performs well on biological images not seen during the training. We will extend this work to blur operators adapted to large images estimated from microscopes in [START_REF] Debarnot | Learning low-dimensional models of microscopes[END_REF]. We expect this approach to provide a turnkey tool for biologists to improve their image quality.

COMPLIANCE WITH ETHICAL STANDARDS

This is a numerical simulation study for which no ethical approval was required.

Fig. 1 :

 1 Fig.1: a, Image and operator dataset used to train the proposed neural network. The image dataset is composed of 10000 natural images, and the operator dataset is composed of space varying blur operator. b, Observation model, the unknown blur operator H0 and the unknown signal u0 are drawn from an arbitrary distribution. c, Estimation procedure, the blurry-noisy image is given to the Resnet neural network. It outputs Ĥ an estimate of the original blur operator H0.

Fig. 2 :

 2 Fig. 2: Example of product-convolution. a) 24 × 24 anisotropic Gaussian filters e1, e2, b) 128 × 128 coefficients maps f1, f2, c) Product-convolution operator applied to a Dirac comb (128 × 128).

  Operator relative error: 4.8%. SNR: 15dB to 21dB. (b) Operator relative error: 3.4%. SNR: 19dB to 27dB. (c) Operator relative error: 6.8%. SNR: 18dB to 24dB. (d) Operator relative error: 4.9%. SNR: 19dB to 28dB. (e) Operator relative error: 6.5%. SNR: 7.6dB to 15dB. (f) Operator relative error: 8.4%. SNR: -7dB to 0.64dB.

Fig. 3 :

 3 Fig. 3: From left to right. True and estimated operator, blurry-noisy image, original image and estimated one by solving problem (7) with total variation regularization for (a)-(e) and 1 regularization for (f)).The SNR with the blurry and the estimated images is given in the sub-captions.


Florian Moreau

Nathalie Audebrand

Cyril Poriel

9,9'-spirobifluorene based zinc coordination polymers: a play on linker geometry and topology

We report four Zn-based coordination polymers (CPs), synthesized from three spirobifluorene (SBF) tetracarboxylate ligands, possessing different topologies and dimensionalities. Zn-SBF-1, Zn-SBF-2 and Zn-SBF-3 CPs have 2D crystal structures with sql topology built from square planar ligands (L1 and L3) and paddle-wheels for Zn-SBF-1 or original dimers of zinc for Zn-SBF-2 and Zn-SBF-3. Zn-SBF-4 is built from a ligand with a distorted tetrahedron geometry (L2) and inorganic octahedral building unit resulting in a non-interpenetrated 3D porous framework with toc topology. Structural relationships evidence that meta (L2) versus para (L1, L3) position of the carboxylic functions on the benzoate group of the SBF ligand increases the connectivity of the inorganic building unit and then the dimensionality of the framework.

Introduction

Metal-Organic Frameworks (MOFs) or Porous Coordination Polymers (PCPs) have emerged as an important class of materials over the past twenty years, at first due to their fascinating crystal structures, mainly because they allow the control of porosity and its combination with various other properties making them suitable for a variety of applications such as gas storage and separation, heterogeneous catalysis, sensing, drug delivery and more recently as electronic or protonic conductors, valence tautomerism systems and for mixed matrix membranes. [START_REF]Special issue on the 'Chemistry and applications of MOFs[END_REF] These coordination polymers (CPs) are built from inorganic secondary building units (SBU) and bridging organic linkers. Polycarboxylate linkers are most commonly used due to their ability to form suitable inorganic SBUs and to promote high dimensionality of the resulting frameworks. In this context we have been interested in the topology of PCPs and in the design and synthesis of ligands, in particular those based on the spirobifluorene (SBF) core. SBF is constituted of two orthogonal fluorene units connected through a shared spiro carbon. Thanks to this particular 3D geometry, SBF fragment has played a key role in the development of emerging technologies of organic electronics as it is a commonly used building unit in functional materials. 2 The very specific geometry of the SBF scaffold has also allowed its use in many other applications such as fluorescent marker for biomolecules, 3 homogeneous 4 or heterogeneous 5 catalysis of various chemical reactions (epoxidation, sulfoxidation…). Attaching anchoring functions to the backbone of the SBF fragment hence appears as an interesting strategy to construct 3D PCP with shape persistent structures.

However, only ten coordination polymers built from SBF-based di-or tetracarboxylate ligands have been reported to date, 6,7,8,9,10,11,12,13,14,15 six of them showing potential or permanent porosity. [8][9][10][11]13,15 In the course of our study on SBF-based CPs, we reported a Cu II based compound with a tetrabenzoïc SBF ligand designed for that aim. 15 Inorganic SBUs are often formed in situ without any real rationalisation, which limits the topological prediction of the PCP, whereas the organic building units stay robust during the assembly procedure. In this context, and in order to tune the topologies and then the porosity of the resulting PCP, we have designed in this work differently substituted SBF-based tetracarboxylic ligands with their anchoring functions localized at different positions of the molecular fragment. Four Znbased CPs with different topologies and dimensionalities were successfully obtained. The structural relationships between these CPs are discussed. It is evidenced that the association of square planar ligands of different sizes with inorganic SBUs like paddle-wheels or dimers leads to 2D structures with the sql topology. For two of the reported 2D structures, the layers are built from original distorted paddle-wheel zinc dimers and the stacking of the layers depends on the molecule occupying the apical position of the zinc polyhedra governing the weak interactions between the layers. On the other hand, switching from para-to metabenzoate units generates different inorganic SBUs with higher connectivity and allows the formation of a framework with higher dimensionality, in that case, a non-interpenetrated 3D PCP with a toc underlying net topology. The structural relationships between the four new CPs and related SBF-based CPs reported in the literature highlights the predominant role of the ligand geometry on the topology of the resulting coordination polymers.

Experimental General techniques, materials and methods

Commercially available reagents and solvents were used without further purification other than those detailed below. Light petroleum refers to the fraction with b.p. 40-60 °C.

Dichloromethane was distilled from P 2 O 5 drying agent Sicapent (Merck). Semiconductor grade toluene has been used. Reactions were magnetically stirred. Analytical thin layer chromatography was carried out using aluminium backed plates coated with Merck Kieselgel 60 GF254 and visualized under UV light (at 254 and/or 365 nm). Chromatography was carried out using silica 60A CC 40-63 mm (SDS). [START_REF]Special issue on the 'Chemistry and applications of MOFs[END_REF] H and 13 C NMR spectra were recorded using Bruker 300 MHz instrument ( 1 H frequency, corresponding 13 C frequency is 75 MHz); chemical shifts were recorded in ppm and J values in Hz. The residual signals for the NMR solvents are: CDCl 3 , 7.26 ppm for the proton and 77.00 ppm for the carbon; [D6]DMSO, 2.50 ppm for the proton and 39.52 ppm for the carbon. The following abbreviations have been used for the NMR assignment: s for singlet, d for doublet, sd for doubled singlet, t for triplet, m for multiplet and br for broad.

High-resolution mass spectra were recorded at the Centre Regional de Mesures Physiques de l'Ouest (Rennes) on a Bruker MicrO-Tof-Q2 and reported as m/z. Names of chemicals have been determined according to systematic nomenclature rules agreed upon by the International Union of Pure and Applied Chemistry.

Synthesis

Syntheses of ligands H 4 L1, H 4 L2 and H 4 L3.

2,2',7'7'-tetrabromo-9,9'-spirobifluorene (1) and 4,4',4'',4'''-(9,9'spirobifluorene-2,2',7,7'tetrayl)tetrabenzoic acid (H 4 L1) were synthesized as previously described 15 .

3,3',3'',3'''-(9,9'spirobifluorene-2,2',7,7'-tetrayl)tetrabenzoic acid (H 4 L2) 1 (0.95 mmol, 600 mg), 3-(methoxycarbonyl)phenylboronic acid (4.75 mmol, 855 mg) and potassium carbonate (3.25 mmol, 450 mg) were added to a mixture of toluene and deionized water (70 mL/15 mL). The resulting mixture was degassed, stirred under an Ar atmosphere and heated at 80 °C. While stirring at 80 °C, under argon stream, tri-tert-butylphosphine (0.26 mmol, 63 μL) (P(t-Bu) 3 ) and tris(dibenzylideneacetone)dipalladium (0.2 mmol, 180 mg) (Pd 2 (dba) 3 , CH 2 Cl 2 ) were carefully added. The Schlenk tube was sealed and the resulting mixture was stirred at 80°C under an Ar atmosphere for 20 h. After the mixture was cooled to room temperature, a saturated aqueous solution of ammonium chloride (50 mL) was added and the resulting mixture was extracted with dichloromethane (3 × 80 mL). The combined extracts were dried on magnesium sulfate, and the solvent removed in vacuo. Purification by column chromatography on silica eluting with light petroleum/ethyl acetate (7:3) gave tetramethyl 3,3',3'',3'''-(9,9'spirobifluorene-2,2',7,7'-tetrayl)tetrabenzoate (2) as a colourless solid (480 mg, 56 % yield).

Sodium hydroxide (40 mmol, 1.6 g) was added to a suspension of 2 (0.56 mmol, 480 mg) in ethanol and deionized water (100 mL/15 mL). The resulting mixture was stirred at reflux for 12 h. After it was cooled to room temperature, ethanol was removed under vacuo. The resulting aqueous solution was diluted with deionized water, acidified to pH = 2 using concentrated hydrochloric acid, and extracted with ethyl acetate (380 mL). The combined organic layers were dried on magnesium sulfate, the solvent removed under vacuo to afford H 4 L2 as a colorless solid (440 mg, 99 % yield). M.p. > 300°C; [START_REF]Special issue on the 'Chemistry and applications of MOFs[END_REF] To a degassed solution of 1 (300 mg, 0.475 mmol) in anhydrous DMF (15 mL) was added copper cyanide under an argon atmosphere (425 mg, 4.75 mmol). The resulting mixture was degassed and stirred at reflux under an argon atmosphere for four days. The reaction was monitored by TLC (eluant: petrol/ethyl acetate: 4/1). After cooling to room temperature, a solution of iron III chloride hexahydrate (6.8 g, 25.2 mmol) in a mixture of water/ethanol (4.5 mL/4.5 mL) was added. The resulting mixture is heated at reflux for 10 min, cooled down to room temperature then carefully added to dilute HCl (37 mL, 1%) at 0°C. The mixture was then extracted with dichloromethane and the combined organic layers were washed with an aqueous saturated solution of ethylenediaminetetraacetic acid tetrasodium salt and dried (MgSO 4 ). The solvent was removed in vacuo and the crude mixture was taken up with dichloromethane and filtered on silica eluting with a mixture of petrol/ethyl acetate (4/1). The crude mixture was suspended in ethylene glycol (10 mL) in the presence of potassium hydroxide (0.6 g, 10.7 mmol) and the resulting mixture was heated at 200°C for 12h. After cooling to room temperature, water was added and concentrated HCl was added until pH = 1.

After filtration and drying (oven at 80°C-48 H), the title compound was obtained as a colourless solid (yield =68%). The spectroscopic analyses and purity are in perfect accordance with reported data. 7

Syntheses of coordination polymers Zn-SBF1-4

Synthesis of Zn 2 (L1)(H 2 O) 2 .(solv) x (Zn-SBF-1)

H 4 L1 (1.25×10 -2 mmol, 10.0 mg) was dissolved in a solution of ZnCl 2 in N,N'diethylformamide (DEF) (2.5 mL, 0.02 M). Ethanol (2.5 mL) and hydrochloric acid aqueous solution (1 mL, 0.05 M) were added to the resulting solution, which was placed in a tightly capped PFA (perfluoroalkoxy copolymer resin) flask in an oven at 80 °C for 96 h. Long rodlike colorless crystals were collected by filtration, washed ethanol, and dried in air.

Synthesis of Zn 2 (L3)(DEF) 2 (solv) x (Zn-SBF-2) and Zn 2 (L3)(H 2 O) 2 .(solv) x (Zn-SBF-3)

H 4 L3 (1.30×10 -2 mmol, 16.0 mg) was dissolved in a solution of ZnCl 2 in DEF (2.5 mL, 0.02 M). Ethanol (2.5 mL) and hydrofluoric acid aqueous solution (1 mL, 0.1 M) were added to the resulting solution, which was placed in a Teflon-lined 23 mL autoclave in an oven at 100 °C for 60 h, then cooled down to room temperature at a rate of 0.1 °C.h -1 . 2 and 3 crystallize together and attempts to separate them in large quantities were unsuccessful due to close densities. Plate-like colorless crystals of 2 and rod-like colorless crystals of 3 suitable for single crystal X-Ray diffraction were collected and quickly drown into Paratone oil.

Synthesis of Zn 6 (L2) 3 (H 2 O) 4 .(solv) x (Zn-SBF-4)

H 4 L2 (2.5×10 -2 mmol, 20.0 mg) was dissolved in a solution of ZnCl 2 in DMF (2.5 mL, 0.01 M). Ethanol (2.5 mL) and hydrochloric acid aqueous solution (1 mL, 0.05 M) were added to the resulting solution, which was placed in a tightly capped PFA flask in an oven at 80 °C for five days. Large colorless crystals (highest size greater than 1 mm) were collected by filtration, washed with DMF and ethanol, and dried in air.

Single-crystal data collections and structure determinations

Suitable single-crystals of Zn-SBF-1-4 were mounted on a four-circle APEX II Bruker-AXS diffractometer (Centre de Diffractométrie X, UMR CNRS 6226, Rennes), using Mo K radiation ( = 0.71073 Å). Intensities were collected at 150 K by means of the program Bruker SMART included in the APEX2 programs suite. [START_REF] Bruker-Nonius | SMART in APEX2 programs suite version 2.1-0[END_REF] The scaling of the integrated intensities of equivalent reflections was performed with the program SADABS. [START_REF] Sheldrick | SADABS version 2.03[END_REF] Reflection indexing, Lorentz-polarization correction, peak integration and background determination were carried out with the program SAINT. [START_REF] Bruker-Nonius | SAINT version 7.23A[END_REF] Unit-cell parameters refinement and frame scaling were performed with the program SADABS. [START_REF] Sheldrick | SADABS version 2.03[END_REF] Numerical absorption corrections were performed using a multi-scan absorption correction. [START_REF] Blessing | [END_REF] Structures of Zn-SBF-1-4 have been determined using direct methods with the program SIR97 20 and models have been completed by Fourier difference calculations and refined with SHELXL-2018. [START_REF] Sheldrick | SHELXL-2018: Programs for Crystal Structure Refinement[END_REF] For Zn-SBFs 1, 3 and 4, atomic positions of hydrogen atoms linked to sp 2 C of ligands, as well as hydrogen atoms from DEF solvent in 2, have been calculated with HFIX command of SHELXL-2018. Restrains on distances and angles in DEF molecule in 2 have also been introduced with DFIX command of SHELXL-2018. For Zn-SBFs 1-3, the solvent molecules contributions have been removed by using the PLATON Squeeze routine. [START_REF] Spek | A Multipurpose Crystallographic Tool[END_REF] Crystallographic data and details on data collection are listed in Table 1. Structure drawings were carried out with Diamond 3, supplied by Crystal Impact. [START_REF] Brandenburg | Diamond (version 3), Crystal Impact[END_REF] The pore sizes values were estimated by considering the largest sphere that can fit in the voids taking into account the van der Waals radius of the atoms of the various frameworks. The synthesis of the target spirobifluorene-based ligands H 4 L1, H 4 L2 and H 4 L3 is presented in Scheme 1. The synthetic approach uses a common intermediate, i.e. 2,2',7,7'-tetrabromo spirobifluorene 1, in order to easily obtain various ligands with different geometries.

Results and Discussion

Compound 1 was then first synthesized, as we previously reported through an efficient catalyst free tetrabromination of 9,9'-spirobifluorene. 15 Introduction of the four aryl arms has been further achieved through Suzuki-Miyaura cross coupling reaction with either 4-or 3-(methoxycarbonyl)phenylboronic acid using Pd 2 (dba) 3 ,CH 2 Cl 2 /P( t Bu) 3 [START_REF] Thirion | [END_REF] as catalytic system, sodium carbonate as the base in a mixture of THF and water (3/1) leading to their corresponding esters with moderate yields around 56 % (it should be noted that the poor reactivity of 1 in Suzuki-Miayura cross coupling reactions has been pointed out in literature 15,25 ). Finally, hydrolysis of the methyl carboxylate groups easily leads to the tetracarboxylic acid H 4 L1 and H 4 L2 with a quantitative yield.

The synthesis of the target ligand H 4 L3, with the four carboxylic acids directly connected to the spirobifluorenyl core has been previously reported by Clews and co-workers, involving a key carboxymethylation step of 2,2',7,7'-tetraiodo spirobifluorene derivative (48% over two steps). 7 In our case, the synthesis of H 4 L3 has been carried through a different synthetic approach starting from the tetrabromo analogue 1 (Scheme 1). The Rosenmund-von Braun cyanation of 1 in the presence of an excess of copper(I) cyanide at the reflux of DMF leads to the expected tetracyanide derivative along with a mixture of products incorporating nitriles and amide functions. Indeed, these compounds both crystallize in the monoclinic crystal system, space-group P2/c, with very close unit-cell parameters. The asymmetric unit of Zn-SBF-1 contains one zinc atom, half a L1 ligand with its spiro carbon C1 sit on the 2e Wickoff position, one oxygen atom and highly disordered solvent molecules. As Cu 2 L1(H 2 O) 2 .(EtOH) 4 , 15 the structure of Zn-SBF-1 consists of corrugated layers with a square planar net topology (sql, point symbol 4 4 ) (Fig. 1), previously reported for other paddle-wheels based CPs as the archetypal MOF-2. 26 The nodes of the nets are alternatively occupied by zinc paddle-wheels, which are very common SBUs for 3d metals 27 , and SBF cores connected through benzoate groups of the ligands. The ligand L1 has a rigid geometry and consists in the junction via the spiro carbon of two orthogonal aryl-fluorene-aryl arms with carboxylate groups in the para position of each aryl groups 15 . Considering the upper and lower arms it appears that the upper arm is bent towards the bottom, while the lower arm is bent up (Fig 1), so that the four carbon atoms of the carboxylate functions are almost coplanar. Then, L1 can be considered as an organic building unit with a square planar geometry. (Zn-SBF-2) is constructed with H 4 L3 ligand, which can be seen as a shorter version of H 4 L1, without the phenyl units. Zn 2 (L3)(DEF) 2 (solv) x crystallizes in the monoclinic crystal system, space-group C2/c. The asymmetric unit contains one zinc atom, half L3 ligand with its spiro carbon C1 sit on the 4e Wickoff position, and a highly disordered DEF molecule. On the contrary to Zn-SBF-1, the inorganic SBU in Zn-SBF-2, Zn 2 (RCOO) 4 (DEF) 2 , is not a paddlewheel but a dimer of zinc cations which are four-fold coordinated in a tetrahedral geometry.

As depicted in Fig. 2, two trans equatorial carboxylate functions (O1, O3, O1 i , O3 i ) from two independent ligands are bridging the zinc atoms in chelating bidentate µ 2 - 1 : 1 coordination mode, and the last two trans oxygen atoms (O5 ii , O5 iii ) belong to  0 : 1 monodentate carboxylate functions from two other independent ligands. Two oxygen atoms from DEF molecules occupy the apical positions of the building unit. The four spiro carbon atoms from the ligands connected to the same inorganic SBU are strictly coplanar due to their position on the c glide plane and they are equidistant to the centroïd of the SBU (spiro Ccentroïd: 7.16 and 7.18Å) which is located on the 2-fold axis.

Then, the inorganic unit can be considered as a square planar secondary building unit (Fig. 3) as in the case of paddle-wheel. To the best of our knowledge, this type of SBU has never been described. The inorganic SBUs are connected through the tetracarboxylate L3 ligands. Considering one ligand, the two monodendate carboxylate functions are in cis positions and then the two bridging functions also are in cis positions regarding the central spiro carbon atom (Fig. 3).

° O1

The ligands act also square planar building blocks since the centroïds of the four inorganic SBUs linked to each ligand are coplanar and equidistant to the spiro carbon. The resulting combination of square planar organic and inorganic SBUs leads to 2D grids with sql topology as in Zn-SBF-1 (Fig. 4).

The rows of the layers consist of inorganic SBUs connected through fluorene arms of the ligands with on one hand, alternating bidentate (B) and monodentate (M) carboxylate functions in a B-B-M-M sequence, and on the other hand, with upper (U) and lower (L) arms (Fig. 4a). Identical rows are generated by symmetry in the two directions of the layers. The nets are piled up in a staggered manner. Indeed, by translation along [-1 0 1] direction, inorganic SBUs replace SBF cores of the adjacent layer, and vice-versa, which generates a halite-like topological network (Fig. 4b). This stacking generates weak hydrogen bonds between the layers, involving the four hydrogen atoms from the SBF core of one ligand and the two oxygen atoms from carboxylate functions of the upper and lower inorganic SBUs (see SI). Thus, one dimensional channels are generated along the [-1 0 1] direction. These 10.35 Å wide channels are largely occupied by the disordered ethyl groups of DEF molecules (see SI), which blocks the porosity of the framework.

Crystal structure of Zn 2 (L3)(H 2 O) 2 .(solv) x (Zn-SBF-3)

Interestingly, Zn-SBF-3, a CP based on the same H 4 L3 ligand but with a slightly different crystal structure can be obtained. Zn 2 (L3)(H 2 O) 2 .(solv) x crystallizes in the triclinic crystal system, space-group P-1. The asymmetric unit consists of one ligand L3, with its spiro carbon C8 sit on the 2i Wickoff position, two zinc atoms and two oxygen atoms from coordinating water molecules. Structures of Zn-SBF-2 and Zn-SBF-3 are strongly related. The inorganic building unit of Zn-SBF-3 differs from that of Zn-SBF-2 by the apical positions of the zinc dimer. Indeed, in the case of Zn-SBF-3, these positions are occupied by oxygen atoms from water molecules instead of the disordered and cumbersome DEF molecules in Zn-SBF-2. As only the apical molecules of the dimmers change, they can also be considered as square planar SBUs (Fig. 5a). In the crystal structure of Zn-SBF-3, the coordinate modes of the ligands are the same as in Zn-SBF-2, but the bridging bidentate carboxylate functions are in trans positions of the ligand (Fig. 5b). In Zn-SBF-2, the symmetry of the system generates identical rows in the two directions of the grids, with alternating monodentate and bidentate coordination modes of the carboxylate functions. However, in Zn-SBF-3, the lower symmetry of the structure generates two different kinds of rows in the two directions of the grid: one with only bidentate carboxylate functions, and the other one with only monodentate carboxylate functions (Fig. 6). Another feature of Zn-SBF-3 is that it possesses much stronger interactions between the layers than Zn-SBF-2. Indeed, the apical water molecule of zinc SBUs, which is much less cumbersome than a DEF molecule, allows a greater proximity of zinc SBUs of adjacent layers, and a stacking of the nets in a AB manner, in such a way that SBF cores from the neighboring layers come close to each other (Fig. 7a). As a consequence the 3D cohesion of the material is held by two types of weak interactions: on one hand, the formation of hydrogen bonds between a water molecule of one SBUs and the oxygen atom from a carboxylate function of the neighboring zinc SBU (Fig. 7b) and, on the other hand, the existence of a π stacking phenomenon between SBF cores of the ligands (Fig. 7c) (see SI). The PCP we aim to describe herein has been obtained with H 4 L2 ligand. H 4 L2 is a positional isomer of H 4 L1. Thus, the switching from para substituted benzoate in H 4 L1 to meta benzoate in H 4 L2 leads to a drastically different CP structure. Positional isomerism is an important concept in organic chemistry, which has drastic consequences on the electronic and structural properties of the resulting materials. 28 This has been previously used in MOF chemistry 1e,h but not with the SBF scaffold. The association of large tetrahedral organic building units and octahedral inorganic SBUs in a ratio 3:2 generates a three-dimensional network with a toc topology with the resulting point symbol for this binodal network {4 4 .6 2 } 3 {4 6 .6 6 .8 3 } 2 (Fig. 9). Zn-SBF-4 has a large potential porosity of 51 % as calculated by means of PLATON with a diameter of the pores around 20 Å. Attempts to activate the material were unfortunately unsuccessful since the treatment under vacuum triggers the collapse of the framework, presumably due to the departure of to the labile apical water molecules of the SBU. In H 4 L1, phenyl spacers between the SBF core and carboxylate functions allow these functions to be almost coplanar. This quasi planarity of the ligand generates a 2D stable structure in the case of Zn-SBF-1 because it allows all the carboxylate functions to be bridging and thus to form paddle-wheel SBUs. On the contrary, carbon atoms from the carboxylate functions of H 4 L3 are situated more than one Angström away from the mean plane of the molecule in the structures of Zn-SBF-2 and Zn-SBF-3, compared to 0.48 Å for Zn-SBF-1, which is due to the C carboxylate -C spiro -C carboxylate angle within the ligand (Figure 10).

This deviation from planarity prevents the existence of the same kind of coordination modes as in Zn-SBF-1. Indeed, in Zn-SBF-2 and Zn-SBF- 11 Secondly, the association of zinc dimers, which are not organized in a paddle-wheel in that case, connected to four ligands L1 leads to a two-fold interpenetrated 4,4-connected framework and a resulting 3D structure with the qzd topology. 12 In order to increase dimensionality of the framework, the use of SBUs with higher connectivity is necessary. Indeed, the framework of Zn-SBF-4, built from ligand L2 with carboxylate functions in meta position of the benzoate groups, has an underlying 3D net with framework with larger void space. Therefore, it can be concluded that, for a given metal, the connectivity, and the resulting overall topology of the coordination polymers is strongly influenced by the geometry of the ligand and its interplay with the nature of the formed inorganic SBUs.

Associated Content

Accession Codes CCDC 1939810, 1939811, 1939812, 1939833

Scheme 1 .

 1 Scheme 1. Synthesis of H 4 L1, H 4 L2 and H 4 L3. Reagents and conditions: a) 4-(methoxycarbonyl)phenylboronic acid, [Pd 2 dba 3 ], P(t-Bu) 3 , K 2 CO 3 , THF/H 2 O, 80 °C; b) NaOH, H 2 O/EtOH reflux; c) 3-(methoxycarbonyl)phenylboronic acid, [Pd 2 dba 3 ], P(t-Bu) 3 , K 2 CO 3 , THF/H 2 O, 80 °C; d) CuCN, DMF, reflux, 4 days; e) KOH, ethylene glycol, 200°C; f) HCl, H 2 O.

  Zinc atoms are surrounded by four oxygen atoms belonging to chelating bidentate carboxylate functions and one water molecule in a square-based pyramid polyhedron. The layers are piled up in a AA manner along the [001] direction, leading to monodimensional pores (  17 Ǻ).The channels are filled by the disordered solvent molecules (48 % solvent accessible void as calculated by PLATON). Although the O-Cu15 and O-Zn (see SI) distances slightly differ, van der Waals interactions between the layers of Zn-SBF-1 are the same as in the structure of Cu 2 L1(H 2 O) 2 .(EtOH) 4 .15 On one hand, apical water molecules of the paddle-wheels form hydrogen bonds with two carboxylate oxygen atoms from the adjacent layer, and on the other hand, SBF cores from neighboring layers generate π stacking of the grids.

Figure 1 .

 1 Figure 1. Crystal structure of Zn-SBF-1: projection showing channels along the [001] direction and representation of a single grid and one of its corrugated rows. Solvent molecules have been omitted for clarity

Figure 2 .

 2 Figure 2. Inorganic SBU of Zn-SBF-2: (i) -0,5-x, -0,5-y, 1-z; (ii) -0,5+x, 0,5-y, -0,5+z; (iii)x, -1+y; 1,5-z.

Figure 3 .

 3 Figure 3. Representation of the square geometries of the (a) inorganic and (b) organic SBUs in Zn-SBF-2; M: monodentate; B: bidentate.

Figure 4 .

 4 Figure 4. (a) Representation of one layer along [100] direction and one row in Zn-SBF-2 with alternating bidentate carboxylate function (B), lower arm of the ligand (L), monodentate carboxylate function (M), upper arm of the ligand (U). (b) topology of the staggered layers in a AA manner with halite-type structure in Zn-SBF-2: inorganic and organic SBUs are displayed with yellow and black nodes, respectively.

a b Figure 5 .

 b5 Figure 5. Representation of the square geometries of the (a) inorganic and (b) organic SBUs in Zn-SBF-3; M: monodentate; B: bidentate.

Fig. 6 .

 6 Fig. 6. (a) Representation of one layer along [001] direction and of the two kinds of rows in Zn-SBF-3, one with bidentate carboxylate function (B) alternating with lower arm of the ligand (L), and the other one with monodentate carboxylate function (M) alternating with upper arm of the ligand (U).

a b c Figure 7 .

 c7 Figure 7. (a) Topology of the layers in a AB manner in Zn-SBF-3: inorganic and organic SBUs are displayed with yellow and black nodes, respectively; (b) hydrogen bonds in between inorganic SBUs belonging to neighboring layers; (c)  interaction between SBF cores from neighboring layers.

Zn 6 (Figure 8 .

 68 Figure 8. Representations (a) of the inorgnic SBU with Zn coordination polyhedra in Zn-SBF4, (b) of the inorganic SBU with octahedral geometry, (c) of the ligand L2 with the meta conformation, (d) of the organic SBU with tetrahedral geometry.

Figure 9 . 1 and

 91 Figure 9. Representation of one unit cell of Zn-SBF-4 and of the toc topology of the net.

Figure 10 .

 10 Figure 10. Structural characteristics of aryl/fluorene/aryl arms of L1 (left) and L3 (right) showing angles C carboxylate -Cspiro-C carboxylate' .

4, 6 - 13 Conclusions

 613 c toc topology. Meta position of the carboxylate function in L2 allows different conformations of the ligand. As a consequence, in Zn-SBF4 the connectivity of the inorganic SBU increases to 6 when compared to a connectivity of 4 for paddle-wheels in Zn-SBF-1 or cations dimers in Zn-SBF-2 and Zn-SBF-3. This illustrates again the influence of the linker geometry, with meta versus para position of the carboxylic functions on the benzoate group, on the nature of the inorganic SBU. The increase of the dimensionality of the framework due to a high connectivity of the inorganic SBUs is also observed in the structures of other L1 or L3 based coordination polymers with Zr or Ca based 8-connected SBUs.11,We have developed efficient routes towards three SBF-based ligands possessing different sizes and geometries. This synthetic approach involving a common intermediate is simple and adaptable to the synthesis of various SBF-based ligands of interest for CPs elaboration. 2D frameworks with sql net are obtained when square planar linkers L1 and L3 are associated with paddle-wheel type SBUs, and as far as we are aware, the distorted paddle-wheel zinc dimers in Zn-SBF-2 and Zn-SBF-3 had not been previously reported. When using other inorganic SBUs with higher degrees of connectivity, 3D frameworks can also be obtained with the same L1 and L3 ligands, showing the versatility of these systems. It has also been illustrated in this work that introducing a level of conformational freedom by introducing meta-benzoate groups on spirobifluorene-based ligand L2 instead of para substituted L1 allows an increase of the connectivity of the inorganic SBUs from 4 for a paddle-wheel in Zn-SBF-1 to 6 for an octahedral trimer in Zn-SBF-4, leading to a non-interpenetrated 3D

Table 1 .

 1 Hydrolysis of this mixture (KOH, ethylene glycol, 200°C) cleanly leads the target ligand H 4 L3 with an overall yield of 68%. Therefore, we have developed efficient routes towards SBF-based ligands possessing different geometric profiles. This synthetic approach involving a common intermediate is simple and adaptable to the synthesis of various tetracarboxylate SBF-based ligands of interest for the elaboration of CPs. Crystallographic data and structure refinement parameters for Zn-SBF1-4.

	Crystal structures and properties of Zn-SBFs
		Zn-SBF-1	Zn-SBF-2	Zn-SBF-3	Zn-SBF-4
	Empirical formula	C 26.5 H 14 O 5 Zn	C 39 H 34 N 2 O 10 Zn 2	C 29 H 12 O 10 Zn 2	C 53.33 H 27.08 O 9.33 Zn 2
	Ligand	H 4 L1	H 4 L3	H 4 L3	H 4 L2
	Molecular weight	477.75	821.42	651.13	947.9
	Crystal system	Monoclinic	Monoclinic	Triclinic	Cubic
	Space group	P2/c	C2/c	P	Fd c
	Topolgy	sql	sql	sql	toc
	Z	4	4	2	48
	a (Å)	13.360(4)	18.556(1)	10.750(3)	44.210(2)
	b (Å)	17.200(4)	10.339(6)	13.933(5)	44.210(2)
	c (Å)	14.314(4)	23.224(1)	14.348(5)	44.210(2)
	α (°)	90.0	90.0	73.69(1)	90.0
	β (°)	94.69(1)	119.006(2)	74.14(1)	90.0
	γ (°)	90.0	90.0	68.27(1)	90.0
	V (Å 3 )	3278(2)	3899.0(4)	1881(1)	86410(12)
	Calculated density (g. cm -3 )	0.968	1.399	1.150	0.874
	F (000)	972	1688	652	23124

Crystal structure of Zn 2 (L1)(H 2 O) 2 .(solv) x (Zn-SBF-1)

It is first important to mention that Zn 2 L1(H 2 O) 2 .(solv) x and the previously reported Cu-SBF, Cu 2 L1(H 2 O) 2 .(EtOH) 4

15

are isostructural, leaving aside the disordered solvent molecules.

  3, monodentate carboxylate functions compensate the lack of planarity of the ligand, but the formed SBUs are necessarily less robust than paddle-wheels in which all carboxylate groups are bidentate. This comparison shows that the resulting inorganic SBUs depend greatly on the nature and geometry of the ligand and not only on the synthesis conditions.The organic building units, L1 and L3, with different lengths, can still be considered on average as square planar. When associated with square-planar inorganic SBU as the paddle-

wheel in Zn-SBF-1, or dimers in Zn-SBF-2 and Zn-SBF-3, the resulting PCPs have 2D sql underlying nets. One can notice that Clews et al. also reported a 2D coordination polymer, in a (4,4) topology, with layers stacked in AB manner

7

which is built from ligand L3 with Co atoms in four-fold environment.

Only three 3D coordination polymers built from L3 or L1 ligands have been reported in the literature and they all involve inorganic building units different from paddle-wheels. A 3D coordination polymer built from L3 and tetramers of 7-fold coordinated calcium cations has been recently synthesized by Duan's group:

13

the non-interpenetrating framework with a 4,8connected flu net topology and 45% of void space is built from tetranuclear oxoclusters linked by eight L3 ligands. Apart from Cu 2 L1(H 2 O) 2 .(EtOH) 4 15 which is isostructural to Zn-SBF-1, two other coordination polymers based on the L1 linker have been reported. First, Park et al. reported a MOF with a 4,8-connected scu net topology, built from hexa-Zr(IV) nodes connected to eight L1.

  contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by email data_request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre, 12, Union Road, Cambridge CB2,

1EZ, UK; fax: +44 1223 336033.

Acknowledgments

Grateful thanks are expressed to Dr. T. Roisnel (Centre de Diffractométrie, UMR CNRS 6226) for his assistance in single-crystal data collection, Damien Thirion (Sciences Chimiques de Rennes UMR 6226 CNRS, Université de Rennes 1) for his fruitful advices in organic chemistry and to MENSR for financial support.

Authors' information

Corresponding Authors * E-mail: nathalie.audebrand@univ-rennes1.fr * E-mail : cyril.poriel@univ-rennes1.fr

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.


El Hadji

Thierno Doumbia
email: thiernodoumbia@yahoo.fr

Catherine Liousse

Sekou Keita

Louise Granier

Claire Granier

Christopher D Elvidge

Nellie Elguindi

Kathy Law

Flaring emissions in Africa: Distribution, evolution and comparison with current inventories

Keywords: Defense Meteorological Satellite Program (DMSP), nighttime light, flaring, Africa

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

During the past few decades, crude oil/gas explorations have been shown to have large socioeconomic, environmental and health impacts on local populations [START_REF] Waldner | Associations between oiland gas-well sites, processing facilities, flaring, and beef cattle reproduction and calf mortality in western Canada[END_REF][START_REF] Nwaogu | Environmental impact of gas flaring on Ebocha-Egbema, Niger Delta, Nigerian[END_REF][START_REF] Wilk | Ozone effects on the emission of pollutants coming from natural gas combustion[END_REF][START_REF] Nwankwo | Effects of Gas Flaring on Surface and Ground Waters in Delta State Nigeria[END_REF].

One of the major issues linked to these activities is gas flaring. Flaring is a process during which natural gas or associated gas (which co-exists with oil in a primarily oil field) that is deemed uneconomical to collect and sell is burned at a high temperature [START_REF] Johnson | A Characterization of Solution Gas Flaring in Alberta[END_REF] ; [START_REF] Talebi | The Estimation and Evaluation of New CO, CO2, and NOx Emission Factors for Gas Flares Using Pilot Scale Flare[END_REF]. It is also used to burn gases that would otherwise present a safety problem. For example, natural gas that contains hydrogen sulfide (H2S) is routinely flared in order to convert the highly toxic H2S gas into less toxic compounds. These processes, used extensively in oil/gas refineries, may lead to large emissions of air pollutants consisting of unburned fuel components (e.g. methane (CH4), non-methane volatile organic compounds (NMVOCs)), by-products of combustion (e.g. black carbon (BC), organic carbon (OC) and partially combusted substances such as carbon monoxide (CO), carbon dioxide (CO2), nitrogen oxides (NOx)) and sulfur dioxide (SO2) [START_REF] Mcewen | Black carbon particulate matter emission factors for buoyancy-driven associated gas flares[END_REF][START_REF] Johnson | A Generalized Sky-LOSA Method to Quantify Soot/Black Carbon Emission Rates in Atmospheric Plumes of Gas Flares[END_REF][START_REF] Davoudi | The major sources of gas flaring and air contamination in the natural gas processing plants: A case study[END_REF]. An estimated 140-150 billion cubic meters (BCM) of gas is flared or vented globally each year, representing approximately 70 % of the natural gas production in Africa in 2011 (IEA, 2016). The economic loss due to these practices is about $30-35 billion per year worldwide, and about $2.5 billion in Nigeria (Ite and Ibok, 2013).

Africa, particularly in the Niger Delta and northern regions, has many natural resources that include large crude oil/gas reserves which has attracted the interest of international petroleum companies since the 1950s. Six African countries (Nigeria, Algeria, Angola, Libya, Gabon and Egypt) are among the top 20 countries in the world that use flaring, with Nigeria being the largest one in Africa and the second largest in the world [START_REF] Elvidge | A Fifteen Year Record of Global Natural Gas Flaring Derived from Satellite Data[END_REF], despite the fact that flaring has been legally banned there since 1984. Most flaring occurs in developing countries where there is a lack of market and infrastructure in place to recycle, transport and sell the associated gas.

The spatial distribution and evolution of flaring emissions are not well characterized and poorly quantified, if they exist at all, in many current global and regional inventories. Among current inventories, the amount of emission varies significantly. According to [START_REF] Stohl | Black carbon in the Arctic: the underestimated role of gas flaring and residential combustion emissions[END_REF], the amount of BC from gas flares was approximately 228 kiloton (kt) in 2010, representing about 3 % of the total global BC anthropogenic emissions (7109 kt) as given by the ECLIPSEv5a inventory [START_REF] Stohl | Evaluating the climate and air quality impacts of short-lived pollutants[END_REF]. At the other extreme, [START_REF] Weyant | Black Carbon Emissions from Associated Natural Gas Flaring[END_REF] reported a much lower estimate of total global BC flaring emission (20 ± 6 kt) than that of [START_REF] Stohl | Black carbon in the Arctic: the underestimated role of gas flaring and residential combustion emissions[END_REF]. The large uncertainty, or even absence in some cases, of flaring emissions that exists in current inventories can lead to large disparities when comparing models and satellite observations, as documented in studies over regions such as the Niger Delta which are heavily influenced by large flaring activities [START_REF] Liousse | Updated African biomass burning emission inventories in the framework of the AMMA-IDAF program, with an evaluation of combustion aerosols[END_REF][START_REF] Malavelle | Simulation of aerosol radiative effects over West Africa during DABEX and AMMA SOP-0[END_REF].

Uncertainties in flaring emissions in current inventories are mainly due to limited access to official flaring volume records and to the lack of field measurements of representative emission factors (EFs). Up until now, only a few limited studies based on satellite observations or modeling simulations have been performed in order to provide estimates of the amount and spatial distribution of flaring emissions. In this paper, we use nighttime lights as a proxy for the determination of the spatial distribution of flaring emissions in Africa and their evolution over time (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010). Nighttime light data, collected by the US Defense Meteorological Satellite Program (DMSP), have been used to measure the human footprint over the world since 1992. Data collection ceased in 2012 due to the natural degradation of the DMSP satellite sensors.

The goal of this study is to develop a detailed analysis of the quantity and spatial distribution of emissions of different atmospheric compounds resulting from flaring activities. The methodology described in Section 2 is first applied and validated over the Niger Delta where oil companies provide publicly available data. After presenting a review of the emission factors, in Section 3 we present the spatial distribution and trends of flaring emissions in Africa, followed by a comparison with other flaring emissions data provided from other sources, namely the ECLIPSE [START_REF] Stohl | Evaluating the climate and air quality impacts of short-lived pollutants[END_REF] and EDGAR [START_REF] Janssens-Maenhout | Global emission inventories in the Emission Database for Global Atmospheric Research (EDGAR): manual (I) -gridding: EDGAR emissions distribution on global gridmaps[END_REF] inventories. Finally, the contributions of flaring to the total anthropogenic emissions in Africa are discussed.

Methodology

Distribution of flaring volumes from DMSP satellites

The DMSP satellites provide global nighttime light coverage every 24 hours from 1992-2012 (http://ngdc.noaa.gov/eog/dmsp/). The images, captured through a sensor called Operational Linescan System (OLS), were inter-leaved to obtain yearly composites covering the whole world. Two satellites orbiting simultaneously, each with a lifespan of 6 to 8 years, provided 32 composites between 1992 and 2011. Each pixel of the composite images has a resolution of 30 arcseconds, corresponding to approximately 0.86 square kilometers at the equator. The DMSP satellites provide different types of data, including worldwide cloud cover, radiance calibrated data, stable lights and average lights multiplied by the percent of light detection (avg_x_pct), which are used to infer national flaring volumes [START_REF] Elvidge | A Fifteen Year Record of Global Natural Gas Flaring Derived from Satellite Data[END_REF]. This 1. Avg_x_pct images: The satellite composite images are the primary data used in this study.

First, if two composites are available for a single year, a calibration following the recommendations given by [START_REF] Elvidge | A Fifteen Year Record of Global Natural Gas Flaring Derived from Satellite Data[END_REF] is performed. Large changes can be observed between different years resulting from the aging of on-board electronics, particularly the sensors. An equation for inter-calibrating yearly nighttime light products determined by [START_REF] Elvidge | A Fifteen Year Record of Global Natural Gas Flaring Derived from Satellite Data[END_REF] is applied to the data to adjust the Digital Number (DN) values.

Following this adjustment, when two satellites provided images for the same year, an average of these two images is performed. In order to minimize the background noise and reduce saturation effects, DN values lower than 9 and higher than 60 are removed from the avg_x_pct files [START_REF] Elvidge | A Fifteen Year Record of Global Natural Gas Flaring Derived from Satellite Data[END_REF].

2. Gas flare areas: Some issues remain with the avg_x_pct images because city lights are still present in the data which can be problematic in areas where there are oil/gas platforms located over land. To correct this problem, pixels with city lights in the avg_x_pct images are identified using maps featuring the location of gas flare areas and are excluded from the analysis. These maps are obtained from a group of shapefiles (one per country) downloaded from the NOAA-NCEI website (http://ngdc.noaa.gov/eog/interest/gas_flares_countries_shapefiles.html). The country-level maps are merged using ArcGIS tools to create a unique dataset of flaring locations over Africa that is used for all years. Unfortunately, for some countries the shapefiles are out-ofdate and do not cover all flaring areas, nevertheless they represent the best data available in the literature at the time of this study for the period of interest. The newly created shapefile is then used to mask pixels outside the flaring areas, which are assumed to be city lights and are thus excluded from the analysis.

3. World maritime boundaries: This step accounts for the volumes of flaring from onshore and offshore oil/gas platforms. Information on world maritime boundaries is used (http://www.marineregions.org/downloads.php) to attribute each offshore platform to a country by combining avg_x_pct over gas flare areas from step 2 and the maritime boundaries shapefile.

4. Weighted coefficients within each grid cell for each country: This is calculated as the ratio between the light intensity within a grid cell quantified in step 3 and the total DN within a country as determined in step 1.

5. National flaring volumes: [START_REF] Elvidge | A Fifteen Year Record of Global Natural Gas Flaring Derived from Satellite Data[END_REF] have estimated the yearly volume of gas flared from 1994 to 2010 for each country. The error associated with each national volume is also provided, generally ranging from 2 to 3 billion cubic meters (BCM) for African countries. These data are available from the NOAA-NCEI website previously indicated;

6. Gridded flaring volumes: We obtain gridded files by multiplying the volume of gas flared at the country-level from step 5 by the weighted coefficients calculated in step 4. A grid of polygons consisting of multiple grid cells of 0.1° x 0.1° resolution is defined. Then, the mean volume is calculated in each polygon;

The main uncertainties associated with this methodology are 1) the identification of flares from lights based on gas flaring shapefiles only, and 2) the use of national flaring volumes that are derived themselves from nighttime data. These data contain uncertainties regarding the quantities of flares that are identified and the effectiveness of the conversion from light brightness to flared volume. In addition, some small flares and flares that are too bright might be missed due to background noise and saturation effects removal, respectively. Figure 1: Schematic view of the methodology used to derive the spatial distribution of flaring volumes using DMSP satellite data.

Comparison with field company data: validation in the Niger Delta

In order to validate our methodology, a comparison between flaring volumes obtained from this work with those provided in the Nigerian National Petroleum Corporation (NNPC) 2011 report was performed. NNPC collects the quantities of oil/gas produced, used and flared as communicated by different oil companies such as Shell, Mobil, Chevron, Texaco, SNEPCO, NAOC, NAE, Esso, AENR, Pan-Ocean and Elf_Total, operating in the Niger Delta.

Statistical data are published on an annual basis as bulletins, which are available at: http://www.nnpcgroup.com. The geographic coordinates of oil/gas fields from the report are used to verify the accuracy of the location of flares by comparing them with the position of nighttime light intensities (avg_x_pct image) (Figure 2). We compare 2011, the most recent year with available and exploitable DMSP world nighttime light images and flaring volumes for Nigeria (Elvidge et al., 2015). A good consistency in the location of flares is found between the two datasets (Figure 2). Both the oil/gas companies and the DMSP data highlight three major oil/gas activity zones in the Niger Delta: southwest, southeast and north central.

As can be seen in Figure 2, the DMSP data provide a more extensive and accurate coverage of flaring areas than the data reported in the literature. Differences between the datasets can be explained by the fact that 1) NNPC does not represent all oil companies in the Niger Delta, 2) oil company data do not take into account the non-official (e.g. indigenous or black market, 2.

3-4.

5.

6.

etc.) oil/gas activities, which are very important in Nigeria, and 3) processing composite images using the method described in this study may result in the removal of potential flare lights. Moreover, nighttime city lights, which are present in the satellite images, could lead to misinterpretation of flare locations over land areas despite our attempts to minimize this source of error. estimated from satellite measurements. This 20 % difference is on the same order of magnitude as the largest error (3 billion m 3 ) of the estimated regional gas flaring volumes from DMSP satellites. When considering only offshore platforms, the amount of flaring from this study is on average 28 % higher than that reported in the field company data. The differences are considerably less for onshore fields where the reports are approximately 13 % higher the values found using our methodology. This supports the fact that possible flare points were removed during the processing of nighttime light images and data concerning offshore fields are likely missing from the NNPC reports. Overall, we find a reasonable agreement between the calculated amount of gas flared in the Niger Delta and what is reported, thus giving confidence to our methodology which we extended to the rest of Africa as presented in Section 3.

Flaring emission estimates

Emissions from gas flaring are calculated using the following equation:

Xflaring = GFvolume * XEF * df
where Xflaring is the emission rate of a pollutant X (kiloton), GFvolume is the volume of gas flared in billion of cubic meter (bcm). The volume of gas flared at each grid cell is estimated from remote sensing data following the methodology described in section 2.1. XEF is the emission factor (EF) in g of species per kg of gas flared. The EF depends on many factors including the quantity/quality and the composition of the fuel burned, the combustion devices and the operation conditions [START_REF] Torres | Industrial Flare Performance at Low Flow Conditions. 1. Study Overview[END_REF] . Finally, df is the density of the fuel gas, typically varying between 0.75 and 1.2 kg/m 3 depending on the fraction of heavy hydrocarbons present in the fuel (US Standard Atmosphere, 1976). In this paper, we assume a gas density df of 0.8 kg/m 3 (E&P Forum, 1994). Due to the characterization of all these parameters, determining emission rates of chemical compounds emitted during flaring processes can be quite challenging, especially because very few field measurements exist that are publicly available.

Most of the EFs published in the literature concern industrial flares from petroleum refineries, chemical plants, natural gas processing industries, and oil and gas extraction. The EFs discussed within the framework of this study were taken from the literature, and were obtained using different techniques such as direct field and laboratory measurements, model estimates generally evaluated using data from laboratory experiments, and estimations by applying data from company's facilities. Direct measurements from field companies are difficult to obtain if they exist at all. This suggests that the EFs reported here have a great deal of uncertainty. For these reasons, low and high values are used in order to be representative of all flaring types.

Table 1 gives a review of EFs for various species (CH4, NMVOC, CO, CO2, NOx, SO2, OC and BC) published in the literature. For most areas, the composition of flared gas is not well known and most of the species cited were not directly analyzed. For example, SO2 is formed when fuel containing hydrogen sulfide compounds (such as H2S) are burned. The EF for SO2 is based on the assumption that sulfur content in the flared gas is known. the minimum EF is 2-5 times lower than the highest value. For OC, we consider the EF as a fraction of that of particulate matter (PM) (Statistics Norway, 2013). In their calculation, it is assumed that 1) PM2.5 is approximately equal to the sum of BC and organic matter (OM = 1.4*OC) and 2) the amount of BC is equal to the amount of OM. Therefore, using an EF of 1.07 g/kg for PM2.5 as taken from the Norwegian national inventory, and an EF of 0.85 g/kg for BC based on [START_REF] Mcewen | Black carbon particulate matter emission factors for buoyancy-driven associated gas flares[END_REF]. Statistics Norway, ( 2013), we derived an OC EF equal to 0.15 g/kg.

In order to assess the impact of the large uncertainties associated with the EFs, we provide a range of flaring emission estimates using both the lowest and highest EFs. The average emissions are calculated based on the mean EF given in Table 1 and will be used for the comparisons.

Results

Spatial distributions of flaring emissions in Africa

We have estimated the emissions for Africa from 1995 to 2010, the period for which the data are available, at a 0.1°x0.1° grid resolution.

Flaring emissions occur in two major parts of Africa; the north, which we refer to as Region I, includes Algeria, Tunisia, Libya and Egypt, and the southwest, referred to as Region II, which includes Nigeria, Equatorial Guinea, Gabon, Democratic Republic of Congo (DRC) and Angola (Figure 4). CO2 has been reported to be one of the largest atmospheric pollutants emitted during flaring activities. This is confirmed by its higher EF compared to other chemical compounds (Table 1). Figure 4 displays the spatial distribution of the average estimated CO2 flaring emissions for 1995, with the largest values occurring in Nigeria as well as a few hotspots in Algeria and Libya.

Trends in CO2 emissions vary spatially as indicated by the spatial distribution of the differences in CO2 flaring emission between 1995 and 2010 (Figure 5). A significant reduction is seen in many areas, reaching up to 4 Tg. However, we also note local increases in several locations of up to 2.5 Tg, namely along the coastal areas of the Niger Delta, Equatorial Guinea, Gabon, DRC and Angola, as well as on offshore platforms and onshore fields situated in region I (Figure 5). Several factors likely contribute to these local increases, including offshore concessions development to expand deepwater oil extraction and avoid security concerns, particularly in the Niger Delta. Also, it is more difficult for the governments to regulate offshore activities [START_REF] Mclennan | Deepwater Africa reaches turning point[END_REF]EIA, 2016).

Consequently measures to reduce flaring emissions in these production areas are partially, or not all, implemented. The observed increase in inland areas may result from the lack of flaring reduction implementation policies, in addition to the aging infrastructures of oil and gas fields in several flaring countries in Africa. between 1995 and 2010 calculated in this study.

National flaring emissions and trends

In Figure 6 and Angola (~10 %). These country-level decreases are in-line with the local decreases mentioned above (and shown in Figure 5), and are largely driven by the fact that the impacts of flaring have received more attention recently and corrective actions have been taken. Local governments and international producers have taken necessary initiatives to limit the amount of gas flared, including, for example, creating markets for selling the gas and putting it to productive use. Furthermore, security issues in some countries during past years have led to a decline in oil extraction and have contributed to decreased flaring. However, this is not the case in all African countries. For example, CO2 flaring emissions in 2010 in South Africa, Sudan, Tunisia and Equatorial Guinea increased by more than 50 %, compared with 1995 levels. This is most certainly the result of increases in oil and gas production in these countries since the 2000s, as well as the lack of adequate infrastructure to commercialize the gas currently flared. Figure 6: National trends of estimated CO2 flaring emissions. The emissions were calculated using an average CO2 EF of 2793.6 g/kg (Table 1).

Figure 7 shows the national contribution (in %) to the total CO2 flaring emissions in Africa Figure 7: The contribution of each country to the estimated total CO2 flaring emissions in Africa. The emissions are calculated using an average CO2 EF of 2793.6 g/kg (Table 1).

Comparison with current inventories

Emissions estimated from this work are compared with the emissions from the ECLIPSE and EDGAR inventories, which are provided for different sectors including flaring. The main uncertainty in this comparison arises from differences in the exact definition of the emission sectors. ECLIPSE has been developed as part of the Evaluating the CLimate and air quality ImPacts of Short-livEd pollutants project [START_REF] Stohl | Evaluating the climate and air quality impacts of short-lived pollutants[END_REF]. Version 5a provides baselineflaring emissions from 1990 to 2030 in five-year intervals at a 0.5° x 0.5° grid resolution (no CO2 data are available) (Klimont et al., 2017, in preparation). ECLIPSE estimations are based on the location of flares from the World Bank's Global Gas Flaring Reduction initiative (GGFR) (http://www.worldbank.org/en/programs/gasflaringreduction) combined with flaring volumes from [START_REF] Elvidge | A Fifteen Year Record of Global Natural Gas Flaring Derived from Satellite Data[END_REF]. We also consider the EDGAR (Emissions Database for Global Atmospheric Research) which has been developed by the Joint Research Center and the PBL Netherlands Assessment Agency [START_REF] Janssens-Maenhout | Global emission inventories in the Emission Database for Global Atmospheric Research (EDGAR): manual (I) -gridding: EDGAR emissions distribution on global gridmaps[END_REF]. It provides emission of gases and particles at a 0.1° x 0.1° grid resolution. We consider the emissions

2010$

from version 4.2 (v4.2FT2010), which provides gridded emissions by sector including oil production and refineries (referenced as 1B2a) for greenhouse gases (GHG), while version 4.3.1 is used for emissions for non-greenhouse gases.

The analysis focuses on region II as defined in Figure 5. The calculation of regional emissions have been performed for the seven largest flaring countries together for the whole of Africa. Table 2 summarizes these emission estimates from different inventories and chemical compounds for 2005. In the table, the emissions estimated with the lowest and highest values of the emission factors from our work are shown. The total CO emissions in Africa as estimated using our method are in the range of 227-794 kt, with an average of 390 kt, and are in relatively good agreement with those of ECLIPSE and EDGAR4.3, 348 and 285 kt, respectively. ECLIPSE regional flaring emissions for CO (average values within the range of 11-108 kt) and NOx (2.2-21.6 kt) are within the same order of magnitude as the average estimations found in our study (11.9-187.7 kt for CO and 2.4-37.6 kt for NOx), except for Equatorial Guinea, in which the ECLIPSE emissions (34 kt for CO and 6.9 kt for NOx) are about 3 times higher than our average estimations (11.9 kt and 2.4 kt, respectively). EDGAR4.3 emissions are also comparable with both ECLIPSE and our estimations, with values ranging from 8.5 to 133.9 kt for CO and 1.6 to 24.4 kt for NOx.

However, in Equatorial Guinea ECLIPSE emissions are up to 4 times larger than the 8.0 kt of CO and 1.6 kt of NOx estimates provided by EDGAR4.3. These regional discrepancies reflect the differences observed in the spatial distribution of CH4 emissions in Equatorial Guinea.

Regarding average levels, the regional amount of emissions obtained in this study for BC (within the range of 1.7-27.4 kt) and SO2 (0.1-1.5 kt) are relatively consistent with those from ECLIPSE (2.6-25.1 kt and 0.02-1.4 kt, respectively). However, there are large differences in Equatorial Guinea where the ECLIPSE emissions are notably higher than our estimations.

This may explain the differences in their total BC (SO2) emissions for Africa, which is estimated at, on average 56.9 kt (3.1 kt) in our study, 40.5 kt (2.3 kt) by ECLIPSE. Both our estimates and that of ECLIPSE are up to 90 times (6 times) higher than the EDGAR4.3 BC (SO2) emissions for most countries. OC emissions for all regions are higher in ECLIPSE (0.4-4.9 kt) compared to EDGAR4.3 (less than 0.02 kt) and to lesser extent to our work (0.2-3.2 kt). For OC, only one value for the EF has been found in the literature, thus no emission range can be provided: the emissions of this chemical compound are very uncertain, because its EF is derived from particulate matter and is not yet verified by direct or experimental measurements.

CH4, which is known as the primarily component of natural gas, shows the largest differences between the three datasets. For example, ECLIPSE (EDGAR4.2) regional CH4 flared are 15-80 (5-40) times higher than our mean estimations in all regions, with a ratio up to 40 (10) for the whole of Africa. When considering the emissions determined using the highest value of the EFs, these ratios are within the range of 5-20 and 2-10, when compared with ECLIPSE and EDGAR4.2, respectively. The emissions of NMVOCs, which are also abundant in flared gas, are 5-10 times larger in EDGAR 4.3 (96-851 kt) and to a lesser extent in ECLIPSE (67-488 kt) than in our study (10-156 kt). When compared to our maximum estimations (20-319 kt), the differences become only 2-4 times larger. The regional CO2 emissions resulting from our lower estimations range from 3.7 to 42.1 Tg. The total amounts of flaring emissions in EDGAR4.2 within the range of 2.4-37.6 Tg are consistent with our lower estimations, while our average values ranging from 3.8 to 59.4 Tg are approximately 30 % higher.

This comparison highlights how differences in the methodologies and data used have a large impact on the quantification of flaring emissions. The large uncertainties in the EFs are limiting and further direct measurements are needed to improve the estimation of flaring emissions. 11,300-19,200 9,300-15,900 3,300-5,700 4,700-7,900 9,100-15,500 42,100-71,500 2,700-4,600 87,379-148

Contribution of flaring to African anthropogenic emissions

We have analyzed the contribution of flaring to the total anthropogenic emissions for different countries in Africa. Table 3 shows the inventories used in this section: in addition to ECLIPSE and EDGAR, we have also included the Liousse et al. (2014) and MACCity [START_REF] Granier | Evolution of anthropogenic and biomass burning emissions of air pollutants at global and regional scales during the 1980-2010 period[END_REF] inventories of anthropogenic emissions over Africa. Note that these latter two inventories do not include flaring emissions and were therefore not included in the previous analysis. The relative importance of flaring is determined as the ratio between the amount of flaring calculated in this work and the sum of the average of total anthropogenic emission from the different inventories (excluding flaring) and the amount of flaring derived in our study (from Table 2). Figure 9 shows the results for BC, CH4 and CO2 emissions in 2005. Based on our minimum and maximum estimations, we estimate that BC emitted from flaring accounted for between 1 to 15 % (with an average of 7 %) of the total African emission while the contribution of CH4 and CO2 ranged from 0.5 to 8 % (with an average of 2 %) and from 8 to 13 % (with an average of 11 %), respectively. The contribution of flaring to total African anthropogenic emission represent less than 1 % for NMVOCs, OC, CO, SO2 and NOx (not shown), illustrating their variability according to the species.

The importance of flaring also widely varies according to country. The minimum flaring amounts of BC released into the atmosphere represented about 4 % of the regional anthropogenic emissions for Algeria and Angola, 2 % for Nigeria, 8 % for Libya and Equatorial Guinea, 12 % for Gabon and less than 1 % for Egypt, South Africa, Sudan and Tunisia (Figure 9, top left). When considering the estimated maximum flaring levels, these percentages are multiplied by a factor ranging from 5 to 20. In regions with low population density such as Equatorial Guinea, Gabon and Libya, it can seen that BC are mainly emitted from flaring activities with an average contribution up to 40, 50 and 45 % of their regional BC anthropogenic emissions, respectively. The average contribution estimated for Nigeria and Angola are 1.5 to 3 times less. Our analyses indicate that BC flaring sources can not be neglected in most of these African flaring countries. Its absence or underestimation seem to support the large gap observed between the simulations and satellite observations of Aerosol Optical Depth (AOD) over the flaring regions of the Guinea Gulf [START_REF] Liousse | Updated African biomass burning emission inventories in the framework of the AMMA-IDAF program, with an evaluation of combustion aerosols[END_REF][START_REF] Malavelle | Simulation of aerosol radiative effects over West Africa during DABEX and AMMA SOP-0[END_REF]. The AOD, related to the amount of aerosol in the vertical column of the atmosphere over an observation location, represents a suitable indicator of BC. [START_REF] Liousse | Updated African biomass burning emission inventories in the framework of the AMMA-IDAF program, with an evaluation of combustion aerosols[END_REF] reported that the ORISAM model has not captured the AOD hot spots observed by the PARASOL satellite along the Guinean Gulf. They attribute this discrepancy to a possible missing source in the fossil fuel inventory used in the model. 8 (top right), the current estimates suggest larger contributions of CH4 emissions from oil and gas processes to the anthropogenic emissions at the regional scale. For example, CH4 flaring emissions in 2005 account for an average 10 % of the regional anthropogenic emissions in Nigeria, Algeria and Angola, 30 % in Libya, up to 35 % in Equatorial Guinea and Gabon, and less than 2 % in the other countries.

Finally, the values of CO2 flaring emissions in Africa derived from this study range from 87 to 148 Tg/yr, representing 0.3-0.5 % of the EDGAR total CO2 anthropogenic emissions of 29370 Tg/yr in 2005. Our estimation is in-line with that of EDGAR (0.3 %). This means CO2 from flaring has small impact to the global CO2 emissions. However, the analysis over Africa reveals that the relative contributions of flaring in 2005 reached 50 % of the regional anthropogenic emissions in Nigeria and Angola for all values of emission factors (Figure 9, bottom). In Gabon and Equatorial Guinea the contributions exceeded 50 %. Therefore, in these African countries gas flaring dominated over its regional CO2 anthropogenic emissions, especially along the Guinean Gulf.

Conclusions

Flaring is a major concern due to the large amount of gases and particulate matter emitted during flaring activities. Despite the fact that it may represent an important pollutant source in some regions, there are still only limited studies and inventories providing the spatial distribution of emissions from flaring due to lack of real field measurements and systematic field data publicly available. In this study, we have developed a method based on nighttime light intensities combined with total regional flaring volumes from the U.S Defense Meteorological Satellite Program (DMSP) data to provide spatial distributions over time (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010) of flaring emissions for several atmospheric chemical compounds. In this study, it is estimated that flaring in Africa released on average 150 Tg of CO2 emissions into the atmosphere in 1995, and about 100 Tg in 2010, indicating an overall downward trend (33 % decrease) over the considered period. The results indicate that emissions have increased the most at offshore platforms and, to a lesser extent, at some onshore oil fields, which we attribute to the lack of regulations and the aging infrastructure of oil and gas fields.

Comparisons between our estimations to the ECLIPSE and EDGAR inventories, which include flaring, show significant differences in the location of the major flaring areas, as well as in their magnitudes. Results suggest that flaring accounted for 2, 7 and 11 % of the total CH4, BC, and CO2 anthropogenic emissions over Africa, respectively, for the year 2005. The impact of flaring on the anthropogenic emissions at the country level may be much more important. For other chemical species, the estimated average contributions of flaring were too low compared to the anthropogenic emissions (less than 1 % for NMVOCs, OC, CO, NOx and SO2). We have shown that the relative importance of flaring varies from one country to another.

The quantification of emissions based on the amount of flared volumes and observations of the nighttime light intensities from space has the advantage of improving the consistency of time series and the representativeness of the local features in the emissions distributions.

Therefore, the methodology developed in this work can be extended to global data for the same period of interest. Even if uncertainties remain large, especially due to emission factors, this technique has the potential to provide more accurate emission data to improve the performance of climate models in regions where flaring is important.

  latter product represents the most extensive time series available for estimating national and global magnitudes of flared activity. The avg_x_pct images give a global distribution of the average visible band Digital Number (DN), with values ranging from 0 to 63, reflecting the brightness of light. Generally, because flares are very bright, large flares are more likely to be captured by the images. A Geographic Information System (ArcGIS software, ESRI 2014) is utilized to derive yearly spatial distributions of gas flare volumes. A schematic diagram of the methodology employed is presented in Figure 1 and detailed step-by-step in the following paragraphs:

Figure 2 :

 2 Figure 2: Geolocation of the oil/gas fields (in green) in the Niger Delta from the NNPC 2011 annual statistics bulletin superimposed on the avg_x_pct image for the same year from the DMSP satellites (in yellow-brown). The markers represent the different multinational oil companies.

Figure 3 Atlan&c

 3 Figure 3 compares gas flaring volumes sampled/extracted at each flare location using latitude/longitude coordinates of oil/gas fields (Figure 3, left) with individual flare volumes provided by agency sources (Figure 3, right). Both DMSP satellite and field company data clearly confirm the three major flaring areas previously identified in the Niger Delta, with flaring volumes reaching more than 100 million cubic meters (MCM) in most areas. These data also illustrate large amounts of flaring volumes emitted along the coast of Nigeria, withthe highest volumes concentrated on offshore platforms. In comparing individual oil/gas stations, flaring volumes estimated in this work are consistent with values provided by field companies (only 6 % difference). However, the total gas flared in Nigeria reported by the NNPC for 2011 is 17.5 billion m 3 , about 20 % higher than the value of 14.6 billion m 3

Figure 3 :

 3 Figure 3: Comparison of flaring volumes in million cubic meters (mcm) in 2011 between reporting NNPC data (right) and estimated values from DMSP satellite observations over the Niger Delta (left).

Figure 4 :

 4 Figure 4: The spatial distribution of CO2 flaring emissions (in kiloton, kt) in 1995 as estimated in this study. There are two main flaring regions in Africa: region I located in the north (Algeria, Tunisia, Libya and Egypt) and region II in the southwest (Nigeria, Equatorial Guinea, Gabon, Democratic Republic of Congo and Angola).

Figure 5 :

 5 Figure 5: Spatial distribution of the difference in CO2 flaring emissions (in Teragram, Tg)

  we present the average CO2 flaring emission levels for1995, 2000, 2005 and 2010 for different countries in Africa, calculated using an average CO2 EF of 2793.6 g/kg. The total estimated CO2 flaring emission for Africa was approximately 150 Tg in 1995 and decreased to about 100 Tg in 2010, a reduction of about 30 %. This decline is linked to the significant reduction of emissions in Nigeria from about 75 Tg in 1995 to 42 Tg in 2010 (~44 % decrease), as well as in Algeria from about 26 to 15 Tg (~42 % decrease) and Libya from 18 to 10 Tg (~44 % decrease).[START_REF] Ismail | Modelling combustion reactions for gas flaring and its resulting emissions[END_REF] found flaring emission of 44 Tg of CO2 in the Niger Delta in 2006, which is in reasonable agreement with the average emission of 59 Tg of CO2 obtained in this work for 2005. Figure6indicates that less significant downward trends during this 15-years period were found in Egypt (~30 %), Gabon (~20 %)

  for 1995 and 2010. The CO2 emitted in Nigeria represents about 50 % of the total amount flared in Africa in 1995. This contribution fell to approximately 40 % in 2010, i.e. a 20 % reduction from 1995. Algeria is the second contributor with a percentage of 17 % in 1995 and 15 % in 2010. These two countries accounted for nearly 70 % of Africa's total CO2 flaring emission in 1995 and 60 % in 2010. The remaining 30 and 40 %, are mainly resulting from flaring activities in Libya and Angola (8-12 %), Gabon (4-5 %) and Egypt (3-4 %). The main Figure7is that the relative contribution of each country to the total flaring in Africa has not changed significantly from year-to-year since 1995 and their positions in the ranking of flaring regions remain unchanged.

  Figure8displays the spatial distribution in 2005 for CH4, the unique chemical species for which gridded emissions are provided in all inventories. CH4 EFs found in the literature vary between 2.5 and 45.0 g/kg, thus the average emissions estimated in our work are calculated using an average EF of 19.2 g/kg. Overall, results indicate a similar spatial pattern of distributions among the inventories.Our maximum emission estimate over Africa is up to 10 times much lower than that of ECLIPSE and about 3 times less than EDGAR (Figure8). The dominate flaring areas in Nigeria, Gabon, Democratic Republic of Congo and Angola are well represented in all three maps. However, the exact location of the highest emissions and their magnitudes are quite different in ECLIPSE, which is in part related to it's lower spatial resolution. Despite the good agreement in spatial distribution, there are some notable discrepancies in emission peaks between the three maps. For example, our estimates indicate peaks occurring at offshore platforms in southern Nigeria which are not reproduced in EDGAR, and likewise, flares noted at some onshore concessions in Nigeria, Cameroon and Angola are present only in the EDGAR map and not in the other two. Sources for these discrepancies could be linked to differences in the gas flaring shapefiles used in our analysis and ECLIPSE, and with the removal of potential flare points during processing nighttime light files in our analysis. Other inconsistences in hotspot emissions are observed in the ECLIPSE map (Figure8, middle) at Malabo Island in Equatorial Guinea where values are much higher than in Nigeria, which is identified as the dominant flaring region in Africa. Furthermore, the EDGAR emissions (Figure8, right) show emissions covering the entire country of Equatorial Guinea, which might be due to the presence of other sources different from flaring.As previously mentioned, emissions determined in this work (Figure5) increased or decreased from 1995 to 2010 according to oil field locations. Similarly, EDGAR exhibits both decreases in emissions in some areas between 2000 and 2010, as well as increases in some countries such as Equatorial Guinea, Cameroon and Angola where local increases are observed (figure not shown). In contrast, ECLIPSE indicates a decrease in all grid cells for the period under study(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010). Nevertheless, overall the temporal changes in EDGAR and ECLIPSE are in agreement with the general reduction in flaring emissions estimated in this work for most countries in Africa.

Figure 8 :

 8 Figure 8: Spatial distribution of CH4 flaring emissions (in kt) estimated in this work (DMSPderived method), ECLIPSEv5 and EDGARv4.2 (FT2010) for 2005.

Table 1 :

 1 Review of the literature emission factors (EF) (in g/kg) for industrial flares for different species.

	CAPP: Canadian Association of Petroleum Producers
	CORINAIR: CORe INventory AIR emissions
	CONCAWE: CONservation of Clean Air and Water in Europe
	EEMS: Environmental Emissions Monitoring System
	E&P Forum: oil/gas Exploration & Production, actual Association of Oil & Gas producers (OGP)
	US EPA: United States Environmental Protection Agency
	UK NAEI: Unite Kingdom National Atmospheric Emission Inventory
	OLF: Oliearbeidernes Fellessammensltning (Norwegian Oil Industry Association)
	SN: Statistic Norway

Table 2 :

 2 Comparison of flaring emissions of this work (DMSP-derived method), ECLIPSEv5a, EDGARv4.2 (FT2010) for GHG (CO2 and CH4) and EDGARv4.3.1 for the other species in 2005. For this work, we provide a range of emissions using lowest and highest EFs from Table1. The unit is in kiloton (kt).

			Algeria	Angola	Egypt	Gabon	Libya	Nigeria	Eq. Guinea	Africa
		This work	29-102	24-85	9-30	12-42	24-83	109-383	7-24	227-794
	CO	ECLIPSEv5a	45	33	11	15	23	108	34	348
		EDGAR4.3	39	30	11	15	29	134	8	285
	NOx	This work ECLIPSEv5a	6.0-21.1 9.1	5.0-17.5 6.8	1.8-6.2 2.2	2.5-8.7 2.9	4.8-17.0 4.7	22.3-78.6 21.6	1.4-5.0 6.9	46.3-163.3 69.7
		EDGAR4.3	7.0	5.4	1.9	2.7	5.3	24.4	1.6	51.9
		This work	0.85	0.71	0.25	0.35	0.69	3.2	0.20	6.6
	OC	ECLIPSEv5a	2.1	1.6	0.52	0.69	1.1	5.0	1.5	16.1
		EDGAR4.3	0.005	0.004	0.001	0.002	0.004	0.019	0.001	0.04
		This work	0.80-18.2	0.66-15.1	0.24-5.4	0.33-7.6	0.64-14.7	3.0-68.0	0.19-4.3	6.2-141.2
	BC	ECLIPSEv5a	10.3	7.8	2.6	3.4	5.3	25.1	8.0	80.6
		EDGAR4.3	0.061	0.047	0.017	0.023	0.046	0.212	0.013	0.45
	SO2	This work ECLIPSEv5a	0.07-0.74 0.60	0.06-0.61 0.45	0.02-0.22 0.02	0.03-0.31 0.20	0.06-0.6 0.31	0.28-2.8 1.4	0.02-0.18 0.46	0.57-5.7 4.5
		EDGAR4.3	0.06	0.05	0.02	0.02	0.05	0.28	0.01	0.48
	NMVOC	This work ECLIPSEv5a EDGAR4.3	17-85 354 598	14-71 153 398	5-25 99 143	7-35 67 88	14-69 183 502	64-319 488 851	4-20 156 96	132-662 2,005 3,019
	CH4	This work ECLIPSEv5a	14-256 5,645	12-213 1,292	4-76 789	6-106 564	11-207 2,922	53-956 4,122	3-61 1,313	110-1,986 23,696
		EDGAR4.2	1,698	392	993	163	674	1,722	109	6,365
	CO2	This work

  Malavelle et al. compared the satellites-derived AOD from MISR, MODIS and OMI with AOD simulated by regional climate model RegCM for different seasons averaged between 2001 and 2006. The model simulates considerably lower AOD compared to observations over flaring areas of the Gulf of

	Guinea. The authors reported that this underestimation of AOD by RegCM can be attributed
	to inaccurate model transport of aerosols together with an underestimation of both dust and
	biomass burning emissions.
	This work shows that maximum annual CH4 flaring emissions in Africa is about 2.0 Tg/yr for
	2005 (Table 2), which corresponds to about 0.6 % of the 324 Tg/yr global anthropogenic CH4
	emissions (Janssens-Maenhout et al., 2013). EDGAR CH4 emissions from oil and gas
	production account for about 2 % (6.4 Tg/yr), while ECLIPSE estimations indicate a
	contribution of about 7 % (23.7 Tg/yr). Nara et al., (2014) reported that CH4 from flaring
	contributed to approximately 20 % of worldwide anthropogenic emissions in 2010. These
	results reflect uncertainties inherent in the differences in approaches, as well as the emission
	factors considered. From Figure