Docking of protein/protein

Haddock : A. Bonvin's lab http://zdock.umassmed.edu/ Zdock : Z. Weng's lab http://haddock.science.uu.nl/services/HADDOCK2.2/haddock.php Grammx server : I. A. Vakser's lab http://vakser.compbio.ku.edu/resources/gramm/grammx/ Rosetta : D. Baker's lab http://rosie.rosettacommons.org/docking2/submit http://rosie.rosettacommons.org/

Docking

Docking is a method which predicts the preferred orientation of one molecule to a second when bound to each other to form a stable complex.

Knowledge of the preferred orientation in turn may be used to predict the strength of association or binding affinity between two molecules using (energy as scoring functions). Docking used to predict the binding orientation of small molecule drug candidates to their protein targets in order to in turn predict the affinity and activity of the small molecule.


Dr Alain Rapaport
email: rapaport@inra.supagro.fr

Pascale Cuevas
email: pascale.cuevas@usach.cl.

Introduction

In our environment, we can frequently identify phenomena that can be well studied under single input / single output representation (from now on SISO), for example in the fields of Biotechnology (case of the study of Landfills) or Geosciences (propagation of water through cracks), when researchers fill a tracer in an determined area. In the first case, many reactions take part in the area, but since a landfill is usually huge, it is difficult to know what happens in the inside of it. The only thing that we know is that the re-circulation leachate increases the bio-reaction rates since it improves the system mixing. So, we would like to study what happens if we put an inert substrate in the leachate to understand the behaviour of this fluid. In the second case, it could be interesting to study how the water or any source propagates in an area, in order to know for instance what could happen in case of a natural disaster as a big rain or a melting of glaciers and this way to know where to install an urban settlement. So, the idea here is as before, to put an inert substrate in a source and to measure the output response. The motivation for this work is to characterize these two phenomena exposed above, assuming that initially biological interaction does not happen or considering an inert chemical tracer. These phenomena can be well modelled as a SISO compartimental system with a large network of many tanks, to capture the spatial inhomogeneity and the complex routes of water through the media. It has been proved in the work of Alejandro Rojas and Alain Rapaport (not published yet but with two presentations made), that a large network of tanks in a SISO compartimental system, can be well approximated and studied as a smaller network, let us say of two or more tanks in Serial, Parallel or Mixed SISO. [START_REF] Andréa-Novel | Control Theory for Engineers[END_REF] Consider, as a first approximation, a network consisting of two tanks that can have a Serial, Parallel or Mixed configuration. Define the total volume V = V 1 + V 2 as the sum of the volumes of the two tanks (which will be a fixed parameter), and define a := V 1 /V the proportion of volume in the first tank. Let S 1 and S 2 be the concentration of the substrate in the first and second tanks, and Q be the input flow rate. The problem consist of, given certain data as a time series {tdata i , Soutdata i } N i=1 of the output response of the observed system and the input function u = S in = S in (t) for the substrate, to determine the 3-tuple of parameters (a, α, d) (involved in the respective ODE system for the Serial, Parallel or Mixed configuration) and the system configuration that best fits to the data. This will be done by the least squares method in a numerical way in Python and a graphic interface for the problem will be also developed.

The three possible configurations for the two tanks network with one input and one output are the following:

The serial configuration, where there is a linear order, a diffusion rate d, and also an advection rate Q. Notice that here S out = S 2 : The parallel configuration, which is a little more complex than the serial because it has more parameters. Here we have a diffusion rate d and input goes directly to the two tanks with a rate αQ and (1 -α)Q respectively. Notice that here S out = αS 1 + (1 -α)S 2 The mixed configuration, where the input goes directly to the two tanks with a rate αQ and (1 -α)Q respectively as in the parallel configuration, but with an advection term between the first and the second tank as in the series configuration. In this case S out = S 1 . Always under the assumption that the content in each tank is perfectly mixed, and the total volume V and the rate Q are constant; we have three models that represent the configuration Serial, Parallel and Mixed of the two tanks network. As a result of the mass balance equations [START_REF] Smith | The theory of the chemostat[END_REF], we have the following system of ODE with initial condition (S 1 (0), S 2 (0)) = (0, 0) that we consider to be null (absence of former tracer):

S 2 , (1-a)V S out S 1 , aV d Q, S in αQ (1-α)Q αQ (1-α)Q =αS 1 +(1-α)S 2
Serial Configuration      Ṡ1 = Q aV (S in (t) -S 1 ) + d aV (S 2 -S 1 ), Ṡ2 = Q (1 -a)V (S 1 -S 2 ) + d (1 -a)V (S 1 -S 2 ); Parallel Configuration      Ṡ1 = αQ aV (S in (t) -S 1 ) + d aV (S 2 -S 1 ), Ṡ2 = (1 -α)Q (1 -a)V (S in (t) -S 2 ) + d (1 -a)V (S 1 -S 2 ); Mixed Configuration      Ṡ1 = Q aV ((αS in (t) + (1 -α)S 2 ) -S 1 ) + d aV (S 2 -S 1 ), Ṡ2 = (1 -α)Q (1 -a)V (S in (t) -S 2 ) + d (1 -a)V (S 1 -S 2 );
where (S 1 , S 2 ) ∈ R + × R + and S in (•) is supposed to be a positive and bounded function of time (Heaviside or Periodic), where the parameters (a, α, d) ∈ (0, 1) × (0, 1) × R + .

Notice that any of the three configurations can be written in the form ẋ = f (x, u, p), with x 0 = 0, where x is the state variable with x = (S 1 , S 2 ), u represents the input control S in (t), and p represents the vector of parameters (a, α, d). It is also important to notice that for the three cases, we have that the dynamics f is linear with respect to the state variable x and with respect to the control variable u.

This fact becomes clearer if we write the equations in the SISO representation in the state space [START_REF] Antsaklis | A linear systems primer[END_REF] ẋ = Ax + Bu, y = Cx + Du, which is called controlled dynamical system and where A is the dynamics matrix, B is the control matrix, C is called the sensor matrix and D the direct term. Here y represents the output response. In this work, we will see that the term D does not appear in the equations, concluding that the input signal does not have a direct influence in the output response.

We are going to choose x = (S 1 , S 2 ) t and u = S in (t) for the three configurations. In each case we have that

• in Serial Network A = -(Q+d) aV d aV (Q+d) (1-a)V -(Q+d) (1-a)V B = Q aV 0 , C = 0 1 t • in Parallel Network A = -(αQ+d) aV d aV d (1-a)V -((1-α)Q+d) (1-a)V , B = αQ aV (1-α)Q (1-a)V , C = α (1 -α) t • in Mixed Network A = -(Q+d) aV (1-α)Q+d aV d (1-a)V -((1-α)Q+d) (1-a)V , B = αQ aV (1-α)Q (1-a)V , C = 1 0 t
It is easy to see that the linearity of f with respect to the state and control variables inmediately implies that the usual Cauchy-Lipschitz condition guarantees the uniqueness of the Cauchy problem. Furthermore, the solutions are defined for all time as the vector x(t) and can be bounded by an exponential function by Gronwall Lemma [START_REF] Trélat | Contrôle Optimal[END_REF]. Then, there exists a unique solution for each of this initial value problems, and to numerically solve them it is used the Runge Kutta 4 Scheme in all the scripts.

Runge Kutta 4 Scheme

The Runge Kutta method is used to solve numerically nonlinear ODE systems. It comes from the Euler Scheme, but it has order 4th and It use information of 4 points [START_REF] Burden | Numerical Analysis Prindle[END_REF].

Given a Cauchy Problem of the form ẋ = f (t, x), x(0) = x 0 , with the dynamics f ∈ C 1 we have that if t k+1 = t k + h, then the Runge Kutta 4 Scheme is given by

                       k 1 = hf (t n , x n ), k 2 = hf (t n + h 2 , x n + k 1 2 ), k 3 = hf (t n + h 2 , x n + k 2 2
),

k 4 = hf (t n + h, x n + k 3 ), x n+1 = x n + k 1 6 + k 2 3 + k 3 3 + k 4 6 .

Transfer Function and Equivalence

We introduce the concept of equivalence between two controlled dynamical systems and the concept of transfer function [START_REF] Trélat | Contrôle Optimal[END_REF]. Let us consider a linear system of the form ẋ = Ax(t) + Bu(t), y = Cx(t),

where x(t) ∈ R n , u(t) ∈ R m , y(t) ∈ R p , A ∈ M n (R), B ∈ M n,m (R) and C ∈ M p,n (R).
The following expression of the output y(t) is called input-output Relation or also Inner Representation

y(t) = Ce tA x(0) + Ce tA t 0 e -sA Bu(s)ds.
The Impulsional Response of a linear system is its Output signal with null initial conditions, when the Input signal is excited by a Dirac Impulsion. In this context, The Impulsional Response Matrix W is given by

W (t) = Ce tA B, if t ≤ 0, 0, if t < 0.
The Transfer Matrix H is the Laplace Transform of the Impulsional Response Matrix W

H(s) = L(W )(s) = +∞ 0 W (t)e -st dt
where if Y (s) = L(y)(s) and U (s) = L(u)(s), with y(t) = 0 and u(t) = 0 if t < 0.

We have that

Y (s) = H(s)U (s) with Y (s) = C(sI -A) -1 BU (s)
where

H(s) = C(sI -A) -1 B.
In this context, we have that two linear systems are said equivalent if they have the same transfer function of minimal realization, i.e. with irreducible numerator and denumerator polynomns in s. The matrices A, B and C depend on the coordinate system. Since the transfer function relates input to outputs the transfer function should also be invariant to coordinate changes in the state space.

The Least Squares Method

The least squares method for this problem can be expressed by

min p l 2 , l 2 (p) := || r[x(t 1 ), • • • , x(t N ), p] || 2 2 = N k=1 [r k (p)] 2 , with r(•) ∈ R N ,
where p is the vector of parameters (a, α, d) and N is the length of the vector of time and the length of the solution of the ODE system. In this case, each residual is given by the difference between r k (p) = Soutdata k -Sout k (p), where Sout k (p) is the solution of the ODE system for the serial, parallel or mixed network, and Soutdata k is the output response of the given time series.

The problem of the Least Squares has been well studied in Statistics, for different functions to fit to some observable data, such as the linear function, polynomial function and other kind of given functions. The important thing here is to notice, that for some of these cases we can assure the existence of a unique minimum if the dependancy on the parameters is linear.

In this problem, the existence of local extrema points is guaranteed if the objective function is coercive. We cannot guarantee uniqueness, but the existence of local minimum points and to characterize them by computing the gradient with respect to p and to see if it is near to 0 in these extreme points. We also know that the objective function is positive since it is a sum of squares or errors so it means that the function is bounded below by 0 [START_REF] Walter | Identification of Parametric Models[END_REF].

As a first step, we need to generate different sets of data as a Parallel, Serial and Mixed time series and we do this in python using the modules numpy, scipy (even though the initial motivation has always been and will be to apply these results to real data). We generate the data {t i , S out (t i )} N i=1 with parameters (a , α , d ) by solving the associated dynamics and saving the results in a text file with the two columns of the time series, one of them corresponding to the time variable and the other one corresponding to the output response of the parallel, serial or mixed network configurations, considering this 3-tuple of parameters. We do this using a positive input signal which makes the solutions of the dynamics to remain positive [START_REF] Farina | Positive Linear Systems[END_REF]. The function that we use is a step function of the form

f (x) = a si 0 ≤ t ≤ 40, 0 si t ∈ (-∞, 0) ∪ (40, +∞),
where a > 0.

Then, we would like to find as we said before, which of the three solutions of the parallel, serial and mixed dynamics best fits to the time series. This is done by the Least Squares Method and we use a module developed at MIT that is called lmfit [START_REF] Newville | Non-Linear Least-Squares Minimization and Curve-Fitting for Python[END_REF], wich allows contraint problems as in this case where with (a, α, d) ∈ (0, 1) × (0, 1) × R + and uses the Levenberg-Marquardt algorithm.

Generation of a Parallel time series test

We generate the data in a parallel configuration {t i , S out (t i )} N i=1 with parameters (0.9, 0. We can notice in these results that, for the 5 random initial conditions, the serial configuration is not good for the parallel time series because the value of the residual is r ≥ 2 with partial derivatives close to 0 R 3 .

We can also notice that the mixed and the parallel configuration are good approximations of the parallel time series, and this is a non intuitive result. For each of the 5 random initial guesses, the value of the residual for each configuration is of the order of 10 -5 o 10 -6 , but the value of the partial derivatives aren't so close of the vector 0 R 3 . The candidates to local minimum found with more coincidences are (0.27, 0.72, 0.89), (0.72, 0.27, 0.89) for the parallel configuration and (0.35, 0.71, 0.89) for the mixed configuration. Even though, we know that a value near to the 3tuple of parameters chosen to generate the time series has to be found, but it seems that the parallel dynamics depends strongly on the initial guess. This situation is illustrated in the following figures, where it is possible to see 4 curves with different tuples of parameters. In black crosses we have the experimental data; in blue, green, and red, we have the solutions of the parallel, mixed, and serial ODE systems respectively, from which the mixed configuration seems to be the closest to the experimental data, using the 3-tuple (a, α, d) found in the search of a local minimum by the Least Squares method. It is not difficult to see that for the 5 initial guess, the two configuration that best fit to the experimental data are the serial and the mixed ones. In the case of the parallel configuration, we have that the residual value is r ≥ 1 with partial derivatives in the minimum point very close to 0. The candidates to be local minimum point are (a , d ) = (0.49, 0.09) for the serial configuration with residual value of the order of 10 -6 and partial derivatives are close to 0. For the mixed configuration we have the candidate (a , α , d ) = (0.59, 0.01, 0.01) with a residual value of the order of 10 -2 . In this case, the fact that the mixed configuration fits good to the serial data is more intuitive, because if we see the ODE system that models this configuration, we see that if α ≈ 0 the equations are the same that the equations for the serial configuration. In any case, the configuration that best fits the time series is the serial one.

Mixed Experimental Data

As before, we generate a time series using the Mixed configuration with parameters (0.7, 0.6, 0.1) and we to explore the results of the fitting with the three configurations for 5 random initial guesses. It is interesting to notice that in this case the three configurations are good approximation of the time series. For the 5 random initial guesses we found that the best candidates to be local minimum value, due to its residual value and partial derivatives, are those corresponding to the mixed configuration (a , α , d ) = (0.84, 0.71, 0.021) with residual value of the order of 10 -6 and partial derivatives near to 0, for the serial configuration (a , d ) = (0.11, 0.88) and (0.88, 0.85) with a residual value of the order of 10 -1 and partial derivatives close to 0, for the parallel configuration (a , α , d ) = (0.1, 0.1, 0.01) and (0.79, 0.79, 0.77) with residual value of the order of 10 -1 and partial derivatives in the local minimun candidates near to 0.

We illustrate this situation in the following figures:

The influence of the input signal

We consider now another time series given by an experiment with a signal of the type S in (t) = a(1 + sin(2πt)), with a > 0 and t ∈ [0, 40]. This signal is positive and continuous, so the solution of the ODE system remains positive [START_REF] Farina | Positive Linear Systems[END_REF].

In this case we can see that the residual value grows, but in all the cases the behaviour is similar. The interesting cases are those in which, given a time series, we can find more than one dynamics that best fits the time series, but the idea is to see what happens with a new input Signal, because this will show which dynamics achieves the best fit.

Such as we did before, we generate the data {t i , S out (t i )} N i=1 with parameters (a, α, d), i.e to save in a file the two vector columns, one of them the time and the other one the output response considering this 3-tuple of parameters. We apply the least squares method to the three configurations in serial, parallel and mixed, and we are going to use the module lmfit, the class Parameters and the function minimize which works with the algorithm Levenberg-Marquardt for constraint optimization problems, with (a, α, d) ∈ (0, 1) × (0, 1) × R + .

Parallel Experimental Data

We generate 5 random initial guesses and as we do before for the first input Signal, we will obtain a candidate to be a local minimum for the parameters in the dynamics.

If we consider the same parameters as before, i.e., (0.9, 0.6, 0. In the same way as we saw before, we can see that for the 5 random initial guesses we have that for the serial configuration, the residual value remains r ≥ 4 with partial derivatives near to 0 so this configuration remains actually far from the time series. The best configurations are the mixed and the parallel one with residual value of the order of 10 -6 and candidates to be local minimun with more concidences being (0.27, 0.72, 0.89) for the parallel configuration and for the mixed configuration we have (0.35, 0.71, 0.89). Notice that the 3-tuple of parameters has been found in the case of the first Input.

This situation can be seen in the following Figures:

Serial Data

If we generate the time series with the parameters (a, α) = (0.5, 0.1) as we did before for the first input Signal, we obtain the following set of results: Through the results of the previous sections, we have seen the behaviour of the results for the fitting process for data generated as time series by the three different configurations of two tanks, succesfully obtaining the original configuration. For this, we implemented in python a discretization of the corresponding ODE systems, and then used the lmfit package (as well as other mathematical and computational tools).

It is relevant to emphasize the importance of the Input Signal to be able to identify what kind of configuration is better than other to fit to the given data. In the case of the mixed time series this fact is clearer, because with the first input signal, the serial configuration could be a good approximation to the data, but with the second input signal we have seen that this is not the case, because the value of the residual for the 5 random initial guesses is large (r ≥ 1).

It is also relevant to emphasize that for the parameter d and for certain value of the parameters a and α, even though we supposed that d ∈ (0, +∞), we could see numerically that if d * is too large with respect to the parameter d taken to generate the time series, the solutions of the ODE systems goes far from the experimental data, which means that any tuple in the form (a, α, d) with d >> d * drives the solutions to diverge from the experimental data. This result, could be interesting to be explored in the future in order to improve the fitting method, specially concerning to the algorithms used to minimize the residuals.

The following images show the situation when d is larger than the value for which the time series is generated. In these cases, d = 0.1.

Figure 1 :

 1 Figure 1: Geosciences researchers filling a tracer near Montpellier, France.

Figure 2 :

 2 Figure 2: Serial configuration for the two tanks network

Figure 3 :

 3 Figure 3: Parallel configuration for the two tanks network

Figure 4 :

 4 Figure 4: Mixed configuration for the two tanks network

Figure 5 :

 5 Figure 5: Local Minimum at (0.89, 0.58, 0.11) Parallel Configuration

Figure 6 :

 6 Figure 6: Local Minimum at (0.27, 0.72, 0.89) Parallel Configuration

Figure 11 :

 11 Figure 10: Minimum value (0.59, 0.01, 0.01) Mixed Dynamics Zoom

Figure 12 :Figure 13 :Figure 14 :Figure 15 :Figure 17 :

 1213141517 Figure 12: Minimum Value Mixed Configuration (0.84, 0.71, 0.021)

  Figure 18: Minimum Value Parallel Configuration (0.27, 0.72, 0.89)

Figure 24 :Figure 25 :Figure 26 :

 242526 Figure 24: Values of the parameters for which the solutions of the ODE escape from Parallel Data

  We generate the data in a serial configuration {t i , S out (t i )} N i=1 with parameters (a, d) = (0.5, 0.1). If we consider 5 random initial guesses for the parameters we obtain the following results

	Evolution of the Dynamics with respect to the Parameters Sout Parallel Sout Mixed Sout Serial Experimental Data [[Variables]] Serial Config [[Partial Derivatives with respect to (a,alpha,d)]] [[Value of the residual]] C(a, alpha) = 1.000 a: 0.39655530 +/-0 (0.00%) (init= 0.6322445) 4 5 6 Evolution of the Dynamics with respect to the Parameters (0.15577115499028071, 0.15170667682713468, -1.1513665576501353e-07) 1.8647353184 C(alpha, d) = -0.999 Sout Parallel Sout Mixed Sout Serial alpha: 0.12466967 +/-0 (0.00%) (init= 0.1246697) [[Variables]] [[Partial Derivatives with respect to (a,alpha,d)]] C(a, d) = -0.999 Experimental Data d: 0.01011291 +/-0 (0.00%) (init= 0.2492205) a: 0.39743342 +/-0 (0.00%) (init= 0.8363037) Serial Config (0.12747220141038351, 0.12791559235907357, -3.3479885530596221e-10) [[Value of the residual]]
	2 3 [[Correlations]] (unreported correlations are < 0.100) alpha: 0.66255434 +/-0 (0.00%) (init= 0.6625543) 1.86489425509 Sout [kg/L] [[Value of the residual]] d: 0.01163249 +/-0 (0.00%) (init= 0.6589677) [[Variables]] Serial Config [[Partial Derivatives with respect to (a,alpha,d)]]
	1 [[Correlations]] (unreported correlations are < 0.100) 2.7863420143e-06 a: 0.49006838 +/-0 (0.00%) (init= 0.5760886) (0.24094935839573672, 0.047922052648186053, -0.000129227948120203)
	a alpha [[Partial Derivatives with respect (a,alpha,d)]] 0.72 [[Correlations]] (unreported correlations are < 0.100) a alpha alpha: 0.53559937 +/-0 (0.00%) (init= 0.5355994) 0.27 d 0.89 0 20 [[Partial Derivatives with respect (a,alpha,d)]] [[Value of the residual]] alpha: 0.90000000 +/-0 (0.00%) (init= 0.9) [[Variables]] 0 d (1.6795648030742876, 0.0, 1.0104043523445863) 2.7863451885e-06 d: 0.09917110 +/-0 (0.00%) (init= 0.3650976) a: 0.60350331 +/-0 (0.00%) (init= 0.4735397) Serial Config	40	time	60	80	0.35 0.71 0.89	100
	Mixed Config (1.6633220404641116, 0.0, 1.0096459581509412) [[Value of the residual]] d: 0.01001101 +/-0 (0.00%) (init= 0.8049689) [[Variables]]
	Figure 7: (0.72, 0.27, 0.89) Parallel Configu-Local Minimum at ration 2.78634188548e-06 [[Correlations]] (unreported correlations are < 0.100) Figure 8: a: 0.51026669 +/-0 (0.00%) (init= 0.9) [[Variables]] Mixed Config [[Partial Derivatives with respect (a,alpha,d)]] [[Value of the residual]] alpha: 0.77659502 +/-0 (0.00%) (init= 0.776595) (0.35, 0.71, 0.89) Mixed Configuration Local Minimum at a: 0.59566256 +/-1.327511 (222.86%) (init= 0.6322445) (0.080304389289425834, 0.0, 0.96772867859970091) 2.78634275689e-06 d: 0.79262414 +/-0 (0.00%) (init= 0.1586722)
	alpha: [[Variables]] [[Partial Derivatives with respect (a,alpha,d)]] 0.01000000 +/-0.019228 (192.29%) (init= 0.1246697) [[Correlations]] (unreported correlations are < 0.100)
	d: a: Mixed Config (1.8513078914105008, 0.0, 1.01045584178669) 0.01000009 +/-1.898074 (18980.57%) (init= 0.2492205) 0.59566262 +/-14.48835 (2432.31%) (init= 0.8363037) [[Value of the residual]]
	[[Correlations]] (unreported correlations are < 0.100) alpha: 0.01000000 +/-0.011746 (117.47%) (init= 0.6625543) 0.505689491318
	C(a, d) d: [[Variables]] 0.01000000 +/-12.62627 (126262.78%) (init= 0.6589677) = -1.000 Mixed Config [[Partial Derivatives with respect (a,alpha,d)]] 4.2 Serial Experimental Data C(alpha, d) = 0.999 [[Correlations]] (unreported correlations are < 0.100) a: 0.58977569 +/-673.5588 (114205.94%) (init= 0.5760886) (0.18593744763312214, 0.0, 0.54294360937714448)
	C(a, alpha) C(a, d) alpha: 0.01000565 +/-13.07552 (130681.37%) (init= 0.9) = -0.999 = -1.000 [[Variables]]
	[[Value of the residual]] C(alpha, d) d: 0.01867549 +/-934.2440 (5002514.16%) (init= 0.3650976) = 1.000 a: 0.59566262 +/-0.213973 (35.92%) (init= 0.4735397) Mixed Config
	0.0157716808366 C(a, alpha) [[Correlations]] (unreported correlations are < 0.100) = -1.000 alpha: 0.01000000 +/-0.003244 (32.44%) (init= 0.5355994)
	Initial Guess [[Partial Derivatives with respect to (a,alpha,d)]] [[Value of the residual]] C(a, d) = -1.000 d: 0.01000000 +/-0.020411 (204.11%) (init= 0.8049689) [[Variables]]
	(0.70290349709393074, 1.8982344039116974, 0.31405528320978432) 0.0157716791163 C(alpha, d) = 1.000 [[Correlations]] (unreported correlations are < 0.100) a: 0.26904375 +/-7.129365 (2649.89%) (init= 0.9)
	(0.6322444961620276, 0.12466967744882029, 0.24922045654726677) [[Partial Derivatives with respect to (a,alpha,d)]] C(a, alpha) = -1.000 C(a, d) = 1.000 alpha: 0.01068730 +/-0.830477 (7770.69%) (init= 0.776595)
	Initial Guess (0.70290499827721298, 1.8982343400912016, 0.31405574092486754) [[Value of the residual]] C(alpha, d) = -0.970 d: 0.73922213 +/-22.11993 (2992.33%) (init= 0.1586722)
	Parallel Config 0.0159397278534 C(a, alpha) [[Correlations]] (unreported correlations are < 0.100) = -0.969
	(0.83630373497318544, 0.66255434137164582, 0.6589677498628117) Initial Guess [[Partial Derivatives with respect to (a,alpha,d)]] [[Value of the residual]] C(a, d) = 1.000
	[[Variables]] (0.61952512228376744, 1.9292917843885624, 0.30873191422941676) 0.0157716791047 C(a, alpha) = 1.000
	a: Parallel Config 0.62586632 +/-5.25e+05 (83958685.96%) (init= 0.6322445) (0.57608858417469677, 0.90891311569352884, 0.36509756722516973) [[Partial Derivatives with respect to (a,alpha,d)]] C(alpha, d) = 1.000
	alpha: Initial Guess 0.62585570 +/-5.05e+05 (80689574.22%) (init= 0.1246697) (0.70290450674445437, 1.8982341219193775, 0.31405540962435202) [[Value of the residual]]
	d: [[Variables]] 0.66932790 +/-1.45e+07 (2171618843.16%) (init= 0.2492205) Parallel Config 0.311280258793
	[[Correlations]] (unreported correlations are < 0.100) a: 0.74946479 +/-1.30e+05 (17337137.04%) (init= 0.8363037) (0.47353965926462938, 0.53559937648661859, 0.80496894103776184) Initial Guess [[Partial Derivatives with respect to (a,alpha,d)]]
	C(a, alpha) alpha: 0.74945393 +/-1.24e+05 (16517951.46%) (init= 0.6625543) = 1.000 [[Variables]] (-2.8256922095596715, 3.3086492542728219, 0.42442871994985421)
	C(alpha, d) d: 0.27487412 +/-2.73e+06 (993239265.49%) (init= 0.6589677) = 0.248 a: 0.89964568 +/-1.16e+04 (1293305.05%) (init= 0.5760886) Parallel Config (0.94814012821816906, 0.77659502500081745, 0.15867223825873666)
	C(a, d) [[Correlations]] (unreported correlations are < 0.100) = 0.245 alpha: 0.89955888 +/-2.15e+04 (2392821.05%) (init= 0.9)
	[[Value of the residual]] C(a, alpha) d: 0.70415516 +/-7.44e+05 (105620924.48%) (init= 0.3650976) = -0.516 [[Variables]] Parallel Config
	1.86473531841 C(a, d) [[Correlations]] (unreported correlations are < 0.100) = 0.228 a: 0.50446171 +/-2.89e+04 (5733496.96%) (init= 0.4735397)
	[[Partial Derivatives with respect to (a,alpha,d)]] [[Value of the residual]] C(a, alpha) = 0.997 alpha: 0.50447180 +/-2.88e+04 (5707267.56%) (init= 0.5355994) [[Variables]]
	(0.10038847063060796, 0.099787253190974923, -5.8846261197231797e-10) 1.8647353184 C(alpha, d) = -0.496 d: 0.01322907 +/-2.71e+05 (2046213252.10%) (init= 0.8049689) a: 0.82754886 +/-955.1720 (115421.83%) (init= 0.9)
	[[Partial Derivatives with respect to (a,alpha,d)]] C(a, d) = -0.489 [[Correlations]] (unreported correlations are < 0.100) alpha: 0.82420778 +/-774.7447 (93998.72%) (init= 0.776595)
	Serial Config (0.1502850045426829, 0.14822747856717555, -1.106492675262416e-09) [[Value of the residual]] C(a, alpha) = -0.380 d: 0.56901149 +/-1.24e+03 (217957.01%) (init= 0.1586722)
	1.86473531917 C(a, d) [[Correlations]] (unreported correlations are < 0.100) = -0.281

We can notice that the parallel configuration is not the best again, because of the value of the residuals for the 5 random initial guesses are r ≥ 2 with partial derivatives very close to 0.

In this case the serial configuration fits the best to the serial time series with residual values of the order of 10 -6 , candidate to be local minimum being (a , d ) = (0.52, 0.09) and partial derivatives close to 0. After that, the mixed configuration is the second best fit, with residual values of the order of 10 -2 , candidate to be local minimum (a , α , d ) = (0.59, 0.01, 0.01) with partial derivatives near to 0. The values found are almost the same that the value found for the first input signal. We have to emphasize the fact that the candidate to be local minimum for the mixed configuration is such that the value of α ≈ 0, and as we said before when α = 0 in the equations for the mixed dynamics, we get the serial dynamics. This situation is illustrated in the following figures

Mixed Experimental Data

We generate data in this configuration with parameters (a, α, d) = (0.7, 0.6, 0.1). If we consider again 5 random initial guesses we obtain the following results In this case, we have that the configuration that best fits the time series is the mixed configuration with residual values of the order of 10 -6 and the candidate to be local minimum being (0.72, 0.61, 0.097) and then the parallel configuration with residual values of the order of 10 -1 and candidate to be local minimum (0.427, 0.427, 0.027) and partial derivatives near to 0. The serial configuration is not good to approximate the mixed configuration because for this 5 random initia guesses we have that r ≥ 1 with partial derivatives near to 0.

Initial

We show this results in the following pictures


Pamela Dominutti
email: pamela.dominutti@uca.fr

Thiago Nogueira

Adalgiza Fornaro

Agnès Borbon

One decade of VOCs measurements in São Paulo megacity: Composition, variability, and emission evaluation in a biofuel usage context

Keywords: VOCs, ethanol, emission ratios, megacities, emission inventory, South America

come     One decade of VOCs measurements in São Paulo megacity: Composition, variability, and emission evaluation in a biofuel usage context

Introduction

Volatile Organic Compounds (VOCs) are crucial pollutants present in urban environments, which affect air quality by producing secondary pollutants such as ozone and secondary organic aerosols (SOA) [START_REF] Seinfeld | Atmospheric Chemistry and Physics. From Air Pollution to Climate Change[END_REF] and causing harmful effects on human health (Laurent and Hauschild, 2014). Accurate VOCs field observations can provide relevant information for a better assessment of their sources and prediction of ozone and SOA formation towards the improvement of air quality policies. Likewise, VOCs speciation at emission is substantial for building up accurate emission inventories [START_REF] Coll | Evaluation of an urban NMHC emission inventory by measurements and impact on CTM results[END_REF][START_REF] Wang | A temporally and spatially resolved validation of emission inventories by measurements of ambient volatile organic compounds in Beijing, China[END_REF]Salameh et al., 2016), which strongly depends on the knowledge of their primary emissions. Nevertheless, speciation and quantification of VOCs emissions and their spatial distribution are still misestimated [START_REF] Huang | Speciation of anthropogenic emissions of non-methane volatile organic compounds: A global gridded data set for 1970-2012[END_REF]. In places like Africa and South America, where the anthropogenic pressure is high, there is still an urgent need of information for developing emission inventories [START_REF] Dominutti | Anthropogenic VOC in Abidjan, southern West Africa: from source quantification to atmospheric impacts[END_REF][START_REF] Huang | Speciation of anthropogenic emissions of non-methane volatile organic compounds: A global gridded data set for 1970-2012[END_REF]. The lack of speciated VOCs observations along with the uncertainties of emission sources in urban regions have an impact in the quality of global and regional emission inventories, which frequently use observations to estimate anthropogenic emissions [START_REF] Dominutti | Anthropogenic VOC in Abidjan, southern West Africa: from source quantification to atmospheric impacts[END_REF]Salameh et al., 2016b). Several studies in northern mid-latitude cities have estimated the urban enhancement emission ratios (ER) from VOCs ambient observations relative to an inert tracer of combustion, such as carbon monoxide (CO) and acetylene (C 2 H 2 ) [START_REF] Baker | Measurements of nonmethane hydrocarbons in 28 United States cities[END_REF][START_REF] Warneke | Determination of urban volatile organic compound emission ratios and comparison with an emissions database[END_REF][START_REF] Von Schneidemesser | Global comparison of VOC and CO observations in urban areas[END_REF][START_REF] Borbon | Emission ratios of anthropogenic volatile organic compounds in northern mid-latitude megacities: Observations versus emission inventories in Los Angeles and Paris[END_REF][START_REF] Boynard | Spatial and seasonal variability of measured anthropogenic non-methane hydrocarbons in urban atmospheres: Implication on emission ratios[END_REF][START_REF] Wang | A temporally and spatially resolved validation of emission inventories by measurements of ambient volatile organic compounds in Beijing, China[END_REF]. These calculated ER were successfully used as constraints to evaluate regional and global emission inventories. Large discrepancies were found in previous studies between the ER derived from inventory and the ones derived from observations. For instance, discrepancies were observed in Paris and Los Angeles up to a factor of 4 [START_REF] Borbon | Emission ratios of anthropogenic volatile organic compounds in northern mid-latitude megacities: Observations versus emission inventories in Los Angeles and Paris[END_REF]. Similarly, a quite large difference of 2 orders of magnitude was also revealed by comparing VOCs emissions derived from the ER to the ones from global downscaled inventories in Cote d'Ivoire (South Western Africa, [START_REF] Dominutti | Anthropogenic VOC in Abidjan, southern West Africa: from source quantification to atmospheric impacts[END_REF]. The oxygenated VOCs fraction (OVOCs) frequently presents the more substantial discrepancies in the emission comparison, not only because of the misunderstanding of their sources (Karl et al., 2018) but also of the lack of ambient observations of these compounds. Saturated and unsaturated alcohols are OVOCs commonly emitted into the atmosphere by biogenic sources [START_REF] Grosjean | Atmospheric chemistry of alcohols[END_REF]. However, in urban atmospheres their emissions are mainly ruled by anthropogenic sources [START_REF] Brito | Disentangling vehicular emission impact on urban air pollution using ethanol as a tracer[END_REF][START_REF] Colón | Survey of volatile organic compounds associated with automotive emissions in the urban airshed of São Paulo, Brazil[END_REF][START_REF] De Gouw | Increasing atmospheric burden of ethanol in the United States[END_REF][START_REF] Giubbina | A simple method for simultaneous determination of acetaldehyde, acetone, methanol, and ethanol in the atmosphere and natural waters[END_REF][START_REF] De Gouw | Chemistry of Volatile Organic Compounds in the Los Angeles Basin: Formation of Oxygenated Compounds and Determination of Emission Ratios[END_REF]. OVOCs have been pointed out as primary emissions of biofuels usage [START_REF] Niven | Ethanol in gasoline: environmental impacts and sustainability review article[END_REF]Poulopoulos et al., 2001a;Suarez-Bertoa et al., 2015b), which can be released either from combustion or evaporative processes [START_REF] Gentner | Diurnal and Seasonal Variability of Gasoline-Related Volatile Organic Compound Emissions in Riverside, California[END_REF]. Ethanol, introduced as a fuel or fuel additive in many countries, plays a crucial role in the tropospheric chemistry where its oxidation is a substantial source of aldehydes in the atmosphere [START_REF] Anderson | Ethanol fuel use in Brazil: air quality impacts[END_REF][START_REF] Corrêa | Five years of formaldehyde and acetaldehyde monitoring in the Rio de Janeiro downtown area -Brazil[END_REF]Martins et al., 2008;[START_REF] Miguel | Catalyst and noncatalyst exhaust aldehydes emission from brazilian ethanol-fueled vehicles[END_REF][START_REF] Nogueira | Formaldehyde and acetaldehyde measurements in urban atmosphere impacted by the use of ethanol biofuel: Metropolitan Area of Sao Paulo[END_REF][START_REF] Pinto | Comparison of Rural and Urban Atmospheric Aldehydes in Londrina, Brazil[END_REF].

Because of their high reactivity, the emissions of OVOCs impact the atmospheric chemistry, contributing to the radical's formation and photochemical processing in the atmosphere [START_REF] De Gouw | Chemistry of Volatile Organic Compounds in the Los Angeles Basin: Formation of Oxygenated Compounds and Determination of Emission Ratios[END_REF]Goldan et al., 2004).

Brazil is the only country worldwide where a large-scale alcohol program has been underway for more than 40 years. The Brazilian Ethanol Program (Proalcool) started in 1975 and enabled the increase of ethanol production together with the development of E100 vehicles. Since 2003, an increase in ethanol production and consumption has been observed due to the introduction of flex-fuel vehicles (Cortez et al., 2016), which led to Brazilian ethanol production reaching 27 billion litres in 2008 and, since then, has remained practically constant (UNICA, 2019). Flex-fuel vehicles can burn both 100% hydrous ethanol (7.5% of maximum water mass content) and a mixture called gasohol (73% gasoline + 27% anhydrous ethanol) (Cortez et al., 2016). The Metropolitan area of São Paulo (MASP, Figure 1) with more than 22 million inhabitants and more than 7 million vehicles is among the ten most populous regions worldwide and one of the main urban centres in South America. São Paulo Megacity (hereafter SPM, Figure 1), corresponds to half of the MASP population (~11 million inhabitants) and 4 million vehicles. In São Paulo, 50% of the fleet is composed of flex-fuel and ethanol vehicles and the annual ethanol consumption can overpass gasoline consumption depending on the price's fluctuation [START_REF] Nogueira | Seasonal Trends of Formaldehyde and Acetaldehyde in the Megacity of São Paulo[END_REF][START_REF] Salvo | Reduction in local ozone levels in urban São Paulo due to a shift from ethanol to gasoline use[END_REF]. A challenge in SPM, as in many other urban centres, is to control air pollution caused by tropospheric ozone. The Brazilian vehicle emissions control program (PROCONVE), the most important public policy implemented in Brazil to control air pollution caused by vehicle emissions, was created in the 1980s and it is currently on his 6 th phase.

Following the guidelines applied in California, US (California Environmental Protection Agency, 2015) and The California Low-Emission Vehicle Regulations (California Air Resources Board, 2019), the Brazilian government released the new PROCONVE phases (L7 and L8, (Diário Oficial da União, 2018). These new phases will start establishing limits for non-methane organic gases (NMOG) taking into account their ozone formation potential (OFP). However, up to now, there is a lack of official data for the OFP estimation based on the typical Brazilian gasoline composition and little is known about how the VOCs emissions could be affected considering the large biofuel content. Despite that scenario, limited ethanol ambient measurements were performed over the last years and the sources, burden and fate of this compound in the atmosphere remain unexplored [START_REF] Naik | Observational constraints on the global atmospheric budget of ethanol[END_REF]. Few short-term ethanol measurements were performed in SPM during the last two decades, which applied a wide range of measurement techniques at different sampling sites (traffic, road tunnels, urban background and background). Ambient ethanol concentrations observed at SPM were quite dissimilar, reaching between 18 to 460 ppb [START_REF] Pereira | Determination of methanol and ethanol by gas chromatrography following air sampling onto florisil cartridges and their concentrations at urban sites in the three largest cities in Brazil[END_REF][START_REF] Schilling | An enzymatic-fluorimetric method for monitoring of ethanol in ambient air[END_REF][START_REF] Colón | Survey of volatile organic compounds associated with automotive emissions in the urban airshed of São Paulo, Brazil[END_REF][START_REF] Nguyen | Atmospheric alcohols and aldehydes concentrations measured in Osaka, Japan and in Sao Paulo, Brazil[END_REF][START_REF] Alvim | Estudo dos Principais Precursores de Ozônio na Região Metropolitana de São Paulo[END_REF][START_REF] Brito | Disentangling vehicular emission impact on urban air pollution using ethanol as a tracer[END_REF][START_REF] Scaramboni | Aspectos do papel do peróxido de hidrogênio como oxidante na atmosfera no contexto das atuais políticas públicas de emissões veiculares[END_REF]. Hence, in view of the high uncertainties surrounding the global and regional emission estimations, specifically for VOCs, there is an urgent need for the assessment of their emissions. Particularly in specific ethanol contexts and in less covered areas such as South America, where that kind of evaluation has not been yet addressed.

This work aims to evaluate ethanol, aldehydes and non-methane hydrocarbons (NMHCs) ER by using field measurements collected during several campaigns in SPM, Brazil. In particular, this work relies on a four-year monitoring programme of more than 50 NMHCs at an urban background site. Urban enhancement emission ratios (ER) were established here by applying the linear regression fit (LRF) method. Afterwards, in order to investigate ER trends in the last decade our results were compared to previous near-source measurements at SPM, such as urban road-tunnel and traffic sites. In addition, an evaluation of the spatial variability was performed by comparing ER in SPM with those collected in contrasted urban environments worldwide, in order to assess commonalities and discrepancies in VOCs composition. Finally, speciated VOCs emissions were estimated and compared with a global inventory in order to investigate the distribution of VOCs species for the road transportation sector and their implications on atmospheric chemistry.

Materials and Methods

Ethanol measurements

Ethanol measurements were performed by a commercial gas monitor (INNOVA1412i Luma Scence), based on a photoacoustic infrared detection technique (more details can be found in the SM). A similar system has been used in previous studies to analyse the ethanol, CO and CO 2 concentrations from direct tailpipe vehicular emissions in Europe [START_REF] Suarez-Bertoa | Intercomparison of ethanol, formaldehyde and acetaldehyde measurements from a flex-fuel vehicle exhaust during the WLTC[END_REF]. However, to the best of our knowledge, this is the first time that a photoacoustic ethanol instrument has been used to measure ambient concentrations. This method enables the measurement of gases which absorb infrared light. In our study, the sampling strategy for ethanol integrates different intensive online field campaigns. One of them was developed inside a semi-confined residential parking garage to assess the contribution of evaporative emissions. This campaign was developed for 2 weeks and the ethanol measurements were performed every 10 minutes. The residential garage has a capacity of approximately 400 light-duty vehicles burning ethanol and gasohol, representative of the fleet running on SPM. More than 90% of vehicles go out in the morning and return in the evening. The sampling point inside the garage, chosen to minimize external influences, was located ~100 meters from the unique entrance of the garage.

Additionally, near-traffic measurements were achieved for six weeks in 2013, by measuring ethanol, CO and CO 2 concentrations next to the main University of São Paulo entrance enclosed by high traffic avenues. Furthermore, urban background measurements were also performed at the same point of NMHCs online measurements. These data were collected for several months in 2013 and 2014.

However, due to instrument detection limits, the number of missing values was significant, restricting the diurnal-basis analysis at the background site.

VOCs measurements in São Paulo megacity

The non-methane hydrocarbons (NMHCs) dataset used in this study was obtained by long term realtime measurements deployed at an urban background site and by offline sampling at various urbantraffic sites. Long-term NMHCs measurements were performed between 2012 and 2015 inside the University of São Paulo Campus (USP), by using a gas chromatography flame ionization detection (GC-FID) instrument. More details about the instrument and the percentage of data available for each year are shown in the supplementary material (Table S1). The chemical families analysed targeted several species of alkanes, alkenes, aromatics and acetylene. To complete this unprecedented dataset, the data reported in previous studies performed in SPM at traffic (UTr), urban road tunnel (UT) and urban background (UB) sites [START_REF] Colón | Survey of volatile organic compounds associated with automotive emissions in the urban airshed of São Paulo, Brazil[END_REF]Martins & Andrade, 2008;[START_REF] Alvim | Estudos dos compostos orgânicos voláteis precursores de ozônio na cidade de São Paulo[END_REF][START_REF] Brito | Vehicular Emission Ratios of VOCs in a Megacity Impacted by Extensive Ethanol Use: Results of Ambient Measurements in São Paulo, Brazil[END_REF][START_REF] Alvim | Estudo dos Principais Precursores de Ozônio na Região Metropolitana de São Paulo[END_REF][START_REF] Alvim | Main ozone-forming VOCs in the city of Sao Paulo: observations, modelling and impacts[END_REF][START_REF] Dominutti | One-year of NMHCs hourly observations in São Paulo megacity: meteorological and traffic emissions effects in a large ethanol burning context[END_REF][START_REF] Nogueira | Seasonal Trends of Formaldehyde and Acetaldehyde in the Megacity of São Paulo[END_REF][START_REF] Nogueira | On-road emissions of carbonyls from vehicles powered by biofuel blends in traffic tunnels in the Metropolitan Area of Sao Paulo, Brazil[END_REF] were re-analysed. The sampling times and data availability from each compound are shown in Figure 2, and the details about the instrumentation and time resolution are disclosed in Table 1. Aldehydes measurements were performed by deploying the 2.4-DNPH technique during intense field campaigns at UB [START_REF] Nogueira | Formaldehyde and acetaldehyde measurements in urban atmosphere impacted by the use of ethanol biofuel: Metropolitan Area of Sao Paulo[END_REF], UTr [START_REF] Alvim | Main ozone-forming VOCs in the city of Sao Paulo: observations, modelling and impacts[END_REF][START_REF] Nogueira | Seasonal Trends of Formaldehyde and Acetaldehyde in the Megacity of São Paulo[END_REF] and inside UT [START_REF] Nogueira | On-road emissions of carbonyls from vehicles powered by biofuel blends in traffic tunnels in the Metropolitan Area of Sao Paulo, Brazil[END_REF]. Aldehydes concentrations were also measured in long-term campaigns developed by the São Paulo State Environmental Agency (CETESB) [START_REF] Nogueira | Seasonal Trends of Formaldehyde and Acetaldehyde in the Megacity of São Paulo[END_REF]. More details about the instrumentation and time resolution can be found in Table 1.

Ancillary data of CO and nitrogen oxides (NO, NO 2 and NO x ) concentrations were obtained from CETESB and were also considered in the data analysis of this study (CETESB, 2018b).

Determination of VOCs enhancement emission ratios

The VOC enhancement emission ratio refers to the ratio of a selected VOC to a vehicular tracer compound in fresh emissions without undergoing photochemical processing. The first step in the derivation of ER is the selection of a reference compound. Commonly, combustion tracers compounds, CO and C 2 H 2 [START_REF] Borbon | Emission ratios of anthropogenic volatile organic compounds in northern mid-latitude megacities: Observations versus emission inventories in Los Angeles and Paris[END_REF]Salameh et al., 2016b;[START_REF] Von Schneidemesser | Global comparison of VOC and CO observations in urban areas[END_REF][START_REF] Warneke | Determination of urban volatile organic compound emission ratios and comparison with an emissions database[END_REF], both have low reactivity in the atmosphere (k OH = 0.90 x 10 -12 cm 3 molecule -1 s -1 for C 2 H 2 and k OH =1.4×10 -13 cm 3 molecule -1 s -1 for CO) [START_REF] Atkinson | Atmospheric Degradation of Volatile Organic Compounds[END_REF]. A good linear correlation (R 2 =0.78-0.82) between CO and acetylene was obtained with similar slope and high correlation coefficients. Overall, better correlation coefficients were obtained in winter than in summer for both vehicular combustion tracers (CO and C 2 H 2 ). Therefore, considering global comparisons, ER were established relative to both compounds (CO and C 2 H 2 ) for all the VOCs under study to provide a complete analysis. A commonly applied method to determine these ratios is the LRF by estimating the slope of the scatter plot between a selected VOC and C 2 H 2 or CO as a tracer [START_REF] Borbon | Emission ratios of anthropogenic volatile organic compounds in northern mid-latitude megacities: Observations versus emission inventories in Los Angeles and Paris[END_REF][START_REF] Warneke | Determination of urban volatile organic compound emission ratios and comparison with an emissions database[END_REF] (Figure S1). The ER performed for the night-time data presented a very well mixed scatterplot, when compared with the daytime data, for most NMHCs (Figure S1). Consequently, we applied the LRF method to all the data obtained without any filtering to determine enhancement of NMHCs ER. As for aldehydes measured at the UB site, only the measurements obtained between 6-8 a.m. were considered to determine ER in order to avoid their secondary formation contribution during the daytime. However, the aldehydes ER established at the traffic site were collected by 24-hourpassive sampling and, consequently, the effect of secondary sources needs to be considered. In general, a reduced number of samples were obtained at urban traffic and road-tunnel sites, limiting the application of the LRF method. Since road-tunnel concentrations are mainly impacted by direct vehicular emissions, ERs were established from concentration ratios, after subtracting the VOC background concentrations obtained from measurements outside the tunnel.

Comparison with a global emission inventory

The emissions of fifty-three VOCs were estimated in annual basis for SPM (Figure 2). Our estimations were calculated by using the São Paulo State inventory which was developed by CETESB based on emission factors (EF) obtained for different vehicle categories, considering the fuel, age and vehicular technology used (CETESB, 2018c). Hence, the annual emissions of CO, NOx, PM, SO 2 and total NMHC were estimated for São Paulo State. We used here a top-down approach to estimate the total CO emissions of the vehicular fleet in SPM, based on the number of vehicles circulating in the SPM. Subsequently, our detailed ER (VOC/CO) database was scaled by the total annual CO emissions estimated by the local environmental agency to assess speciated VOCs emissions from road transportation sector at SPM. Afterwards, species were grouped into VOCs families following the GEIA groups provided by the global VOC inventory, EDGAR v4.3.2 (http://edgar.jrc.ec.europa.eu/).

Based on the species observed, sixteen VOCs emission families are here investigated from VOC1 to VOC21, including ethanol (VOC1), ethane (VOC2), propane (VOC3), alkenes (VOC7-8 and 12), butanes (VOC4), pentanes (VOC5), heavier alkanes (VOC6), acetylene (VOC9), isoprene (VOC10), benzene (VOC13), toluene (VOC14), C 8 -and C 9 -aromatics (VOC 15-16), formaldehyde (VOC21) and other aldehydes (VOC22). The VOCs emissions provided by the inventory were obtained by integrating the eight grids covering SPM, at a spatial resolution of 0.1° x 0.1° (EDGAR database, [START_REF] Huang | Speciation of anthropogenic emissions of non-methane volatile organic compounds: A global gridded data set for 1970-2012[END_REF]. Finally, our VOCs emission estimation is compared with the annual total VOCs emissions provided by the global inventory for the road transportation sector.

Results and discussion

VOCs concentration levels in SPM from 4-years measurements

Figure 3 displays the average and standard deviation for a selected number of VOCs mixing ratios obtained during the 4-year measurements at SPM including also ethanol and aldehydes (formaldehyde and acetaldehyde), at the UB site. Higher mixing ratios of all VOCs were observed in SPM during the period under study, when compared with those reported in other urban atmospheres, such as London, Los Angeles, Beijing and Paris. The VOCs values observed in SPM were higher by a factor of 2 to 9 for aromatics, 1.8 to 5 for alkanes and 1.5 to 10 for alkenes. In spite of the high levels of ethanol also observed in Los Angeles and London (average of 5 ppb and 9±5 ppb, respectively, de [START_REF] De Gouw | Increasing atmospheric burden of ethanol in the United States[END_REF][START_REF] Dunmore | Atmospheric ethanol in London and the potential impacts of future fuel formulations[END_REF], where ethanol is used as a fuel additive; acetaldehyde, formaldehyde and ethanol were greater in SPM by factors of 4 to 7.The increase of these compounds together with some alkenes in the emissions has been pointed out in previous studies as a result of ethanol combustion processes [START_REF] Niven | Ethanol in gasoline: environmental impacts and sustainability review article[END_REF]Suarez-Bertoa et al., 2015a). Nevertheless, and despite the large biofuel use in SPM, there is not a clear enrichment for those compounds in São Paulo when compared to other locations. Even though the higher levels observed, the distribution profile does not depict any difference in the VOCs distribution. First, our results suggest that the number of circulating vehicles compensate the effect of cleaner biofuel and vehicular technologies used in SPM when looking at the high concentrations observed. Second (1) vehicular emissions in general have a strong influence in the VOCs levels in SPM; (2) surprisingly, the large ethanol usage does not affect on average the distribution of OVOC.

Seasonal and inter-annual variations in VOCs emission ratios in SPM.

In this section we assess the VOC to C 2 H 2 and VOC to CO ER obtained from the measurements performed between 2013 and 2015 at the UB site. ERs were established individually for each VOC species and then grouped into VOC families, such as aromatics, alkanes, alkenes, CO and oxygenates.

The ER were also evaluated on seasonal basis (summer and winter, Figure S2) and inter-annual basis (summer and winter of each year, Figure S3). Globally, all the VOCs species showed a good correlation with C 2 H 2 and CO in summer and winter (Table 2). The calculated correlation coefficients (R 2 ) with C 2 H 2 ranged from 0.4 for weaker correlated species such as butenes to 0.9 for most of the species such as pentanes, butanes, aromatics and alkenes. Regarding aromatics, most of them showed a reasonably good correlation with coefficients ranging from 0.5-0.76. When related to CO, strong correlation values were also obtained for all alkanes, alkenes and aromatics with exception of o-xylene and 1,2,4-trimethylbenzene (R 2 =0.48 and 0.3, respectively). Since ethanol concentrations concomitantly with CO were only measured during short-term campaigns, the correlations were performed related to this tracer. The correlation coefficients were dissimilar about the sampling sites, ranging from 0.23 to 0.99 in UB and UTr site, respectively. Aldehydes ER derived from UTr observations presented a good correlation to CO for acetaldehyde (0.75-0.90) and moderate correlation for formaldehyde (0.40-0.70), but lower coefficients were obtained at the UB site (0.43).

Figure 4 shows the seasonal averaged ERs of each VOC versus C 2 H 2 and versus CO for the whole period. In general, no significant differences were found within summer and winter for the UB site, in more than 90% of the evaluated species. These results contrast with the findings in other places. For instance, [START_REF] Wang | A temporally and spatially resolved validation of emission inventories by measurements of ambient volatile organic compounds in Beijing, China[END_REF] reported lower ERs in winter than in summer by a factor of 2 for most VOCs species measured in Beijing. Similar results were also found in French urban areas where a strong effect of seasonality was found for C 4 -C 5 alkanes and C 7 -C 9 aromatics [START_REF] Boynard | Spatial and seasonal variability of measured anthropogenic non-methane hydrocarbons in urban atmospheres: Implication on emission ratios[END_REF]. This difference usually affects specific VOCs species, such as pentane and isopentane due to seasonal adjustment in the fuel formulation among winter and summer to reduce the effect of summertime vapour pressure [START_REF] Boynard | Spatial and seasonal variability of measured anthropogenic non-methane hydrocarbons in urban atmospheres: Implication on emission ratios[END_REF][START_REF] Gentner | Diurnal and Seasonal Variability of Gasoline-Related Volatile Organic Compound Emissions in Riverside, California[END_REF]. In contrast, a study in Lebanon, showed a similar profile without a strong seasonal variation in the urban ERs obtained (Salameh et al., 2016a). These findings show a common non-seasonal behaviour between SPM and Lebanon, contrasting the results obtained in northern mid-latitude cities in Europe, United States and Asia [START_REF] Borbon | Emission ratios of anthropogenic volatile organic compounds in northern mid-latitude megacities: Observations versus emission inventories in Los Angeles and Paris[END_REF][START_REF] Boynard | Spatial and seasonal variability of measured anthropogenic non-methane hydrocarbons in urban atmospheres: Implication on emission ratios[END_REF][START_REF] Wang | A temporally and spatially resolved validation of emission inventories by measurements of ambient volatile organic compounds in Beijing, China[END_REF][START_REF] Warneke | Determination of urban volatile organic compound emission ratios and comparison with an emissions database[END_REF]. One reason could be an unchanged contribution of evaporative emissions in SPM between winter and summer and also to the absence of domestic heating due to the high temperatures in winter (13-23 °C).The non-seasonality observed in the averaged values for the whole period, was also observed between the years 2013, 2014 and 2015, agreeing within a factor of 2. These results show that ERs are not strongly affected by seasonality, suggesting that emission patterns and source composition are almost constant all through the year in SPM.

VOCs ERs variability in SPM: from urban background to traffic emissions

A few previous studies were developed in SPM, reporting a limited number of VOCs species by shortterm measurements at UTr, UB and UT sites. To analyse the VOCs spatial distribution in SPM, the average ERs obtained at the UB site were selected as reference and then compared with those obtained in previous studies. Figure 5 shows the comparison between the ERs estimated in the UB site with those derived from UTr, UT and UB measurements. As shown in the previous section, there is no significant seasonal and interannual variability in the calculated ERs. Therefore, the comparison is based on ERs averages integrating all seasons and years at the UB site. A very good consistency between UTr and UB sites is observed, with slightly higher ERs for heavy alkanes (nonane and decane) at the UTr site (Figure 5a). This would suggest that the urban VOCs composition is mostly affected by vehicular emissions. On the other hand, most compounds showed lower ERs inside the urban road-tunnel than at the UB site. The differences observed between these sites could be associated with the higher CO levels from direct combustion emissions inside road tunnel where the fleet mainly comprises light-duty vehicles. These also could be influenced by the combustion emission of buses and diesel vehicles, circulating near the UTr and UB sites, affecting the CO, NOx and VOCs emission profiles. These findings also suggest that, besides sources by transport-related ones there is the presence of other sources at the UB and UTr sites. Indeed, there were more discrepancies for alkanes (propane, i-butane and n-butane, in particular) which presented higher ERs at the UB than inside the road tunnel. The high ambient concentrations of these compounds at the UB site were already referred to the presence of sources associated with the use of both liquefied petroleum and natural gases (LPG and NG) in SPM [START_REF] Dominutti | One-year of NMHCs hourly observations in São Paulo megacity: meteorological and traffic emissions effects in a large ethanol burning context[END_REF]. Similar results were found in the ERs comparison in Los Angeles, where a considerable difference of light alkanes related to gas use and production was detected [START_REF] De Gouw | Increasing atmospheric burden of ethanol in the United States[END_REF]. Likewise, discrepancies were also observed for oxygenated compounds, alkene species (1-pentene, cis-pentene and cis-butene) and aromatics (ethylbenzene and m+p-xylene), all presenting higher ERs at the UB site. Additionally, a VOCs dataset obtained during an urban road-tunnel campaign performed in 2004 was also evaluated (not shown here) to elucidate possible ERs variations due to the changes in the Brazilian fleet between 2004 and 2011. Main differences are associated with aromatics, which were larger within factors of 1.5 to 6.6 in 2004 compared with those obtained in the road-tunnel in 2011. A decrease on the aromatic ERs is also observed when compared to those obtained in 2011 at UB site with our VOCs dataset.

Main discrepancies were detected for C8 to C10 aromatics, which could be related to the emission by other sources such as solvents and chemical products. This 7-year-change in aromatic contributions could be also associated to changes in SPM fleet, the increase of ethanol consumption and the improvements in vehicular technologies.

Sources of ethanol in SPM

Here we analysed the results obtained by online ethanol measurements in different short-term campaigns in SPM. Figure 6 shows the concentrations profile of ethanol and CO measured at an UTr site (Figure 6a); the scatterplot between both compounds obtained at the UTr site (Figure 6b) and inside a semi-confined residential garage (Figure 6c). A good agreement is observed in the time series of ethanol and CO obtained at the UTr site, suggesting the emission from a similar traffic source (Figure 6a). The average concentrations of ethanol and CO were 66.2±39.5 ppb and 0.88±0.55 ppm, respectively. These concentrations were higher than those observed at the urban background site, where average concentrations were 35.0±14.0 ppb and 1.35±0.40 ppm for ethanol and CO, respectively. In addition, the average concentrations observed during our campaigns were higher than those measured in other studies in MASP [START_REF] Brito | Disentangling vehicular emission impact on urban air pollution using ethanol as a tracer[END_REF][START_REF] Scaramboni | Aspectos do papel do peróxido de hidrogênio como oxidante na atmosfera no contexto das atuais políticas públicas de emissões veiculares[END_REF]. This fact could be related to the distance to the emission sources and other external factors such as ethanol consumption and usage, atmospheric and meteorological conditions, and differences on the measurement techniques used. Ethanol concentrations were even higher inside the semi-confined residential garage than at the UTr site, where online observations were performed for two weeks (average concentrations of 600.0 ppb and 3.23 ppm, for ethanol and CO, respectively). The correlations between both compounds at the UTr site and the residential garage site are shown in Figures 6b and6c, respectively. The scattered correlation at the traffic site suggests the additional contribution either of non-combustion sources or other processes affecting the concentrations observed. In contrast, a good correlation is depicted (R 2 =0.89) when analysing the daytime observations inside the residential garage (light-blue dots, Figure 6c). Interestingly, the highest ethanol concentrations inside the garage were reported at nighttime rather than during peak traffic times (early in the mornings and evenings, not shown here). The correlation of these night-time observations is reported in Figure 6c (dark-blue dots). The emission ratio obtained (0.16 ppm/ppm) could be related to evaporation losses since ethanol concentrations are higher than those observed for CO, and the correlation coefficient lower than the one from exhaust emissions (R 2 =0.45). On the opposite, when considering the daytime observations inside the garage (light-blue dots, Figure 6c), a lower ER is reported (0.12 ppm/ppm) with higher CO concentrations suggesting the contribution from exhaust emissions. However, it is not possible to separate both evaporation loss and exhaust emission contributions for all the observations obtained. Therefore, we consider the ER obtained as a mixture of evaporation and exhaust emissions.

Ethanol ERs were also established from the observations obtained at other sampling sites and compared with the ER at UTr and at the residential garage, previously discussed (Figure 6b). The ERs obtained at UTr and UB sites were 0.046 and 0.036, respectively. Considering the studies performed in MASP fifteen years ago, a decrease in ER (0.282 ppm/ppm) and ethanol concentrations (468 ppb, [START_REF] Colón | Survey of volatile organic compounds associated with automotive emissions in the urban airshed of São Paulo, Brazil[END_REF] in traffic sites is depicted, by factors of 6.5 and 5, respectively. A similar but less pronounced decrease pattern was observed in the UB site. Previous ethanol measurements in the UB site displayed average concentrations of 47.4 ppb in 2011 and ethanol/CO molar ratios of 0.060 ppm/ppm [START_REF] Alvim | Estudo dos Principais Precursores de Ozônio na Região Metropolitana de São Paulo[END_REF]. However, weak correlations were obtained between ethanol and CO in our UB observations, which could suggest the contribution from other sources rather than only traffic emissions.

Biofuel consumption and its implications in aldehydes emission ratios

Several studies have investigated the aldehydes concentrations in Brazil and then compared those levels with other places worldwide. Most of these studies suggested that major differences are related to fleet composition and regional practices in Brazil, increasing the levels of aldehydes in the atmosphere [START_REF] Correa | The impact of BTEX emissions from gas stations into the atmosphere[END_REF][START_REF] Grosjean | Speciated ambient carbonyls in Rio de Janeiro, Brazil[END_REF][START_REF] Martins | Atmospheric levels of aldehydes and BTEX and their relationship with vehicular fleet changes in Rio de Janeiro urban area[END_REF][START_REF] Nogueira | Formaldehyde and acetaldehyde measurements in urban atmosphere impacted by the use of ethanol biofuel: Metropolitan Area of Sao Paulo[END_REF]. A recent study discussed the seasonal variations in the ambient concentrations of formaldehyde and acetaldehyde over 5-yearmeasurements in SPM [START_REF] Nogueira | Seasonal Trends of Formaldehyde and Acetaldehyde in the Megacity of São Paulo[END_REF]. In that study, no evidence in the aldehydes trends was found, indicating that an increase in ethanol consumption could affect the aldehydes concentrations in the atmosphere. We evaluate here those observations by applying the LRF to obtain acetaldehyde and formaldehyde ERs related to CO. Figure 7a shows the formaldehyde and acetaldehyde ERs obtained for each year. An increase in the formaldehyde (1.35 to 2.80 ppb/ppm) and acetaldehyde (2.08 to 2.93 ppb/ppm) ERs was noticed in 2015. This shift was up to 60% and 40 %, respectively higher when compared with the ER obtained in previous years. The increase in the ER could be associated to the change in the fuel consumption observed, characterized by an increase in the ethanol and biodiesel sales and a decrease in the gasohol sales in 2015 (Figure 7b). Ethylene (ethene, C 2 H 4 ), a compound identified in ethanol combustion emissions [START_REF] Niven | Ethanol in gasoline: environmental impacts and sustainability review article[END_REF]Suarez-Bertoa et al., 2015a), also underwent a change in the ERs in the winter 2015. Ethylene to CO ER increased by 80 % and 56% in 2015, when compared with those in the winters 2014 and 2013, respectively. These results suggest that the analysis of ERs provide more sensitive information to assess the impact that a change in fuel consumption can imply in the primary combustion emissions and thus, in the atmospheric chemistry. Regarding atmospheric concentrations, higher formaldehyde and acetaldehyde levels were usually observed in winter in SPM [START_REF] Nogueira | Seasonal Trends of Formaldehyde and Acetaldehyde in the Megacity of São Paulo[END_REF]. However, the ERs display a dissimilar pattern when analysed on seasonal basis. Since aldehydes were passively sampled during these campaigns, the separation of secondary formation sources could not be achieved. Figure 7c shows the scatterplot of acetaldehyde and formaldehyde versus CO, colour-coded by the season under analysis (winter and summer). A higher acetaldehyde to CO ER is depicted in winter (2.11 ppb/ppm) when compared to that in the summer (1.70 ppb/ppm). Conversely, a lower ER is observed for formaldehyde in winter when compared with that in the summer 1.38 ppb/ppm and 1.68 ppb/ppm, respectively. The opposite trend between both compounds and the lower correlation coefficients between formaldehyde and CO could suggest the presence of secondary formation rather than traffic-related ones.

Comparison of São Paulo megacity ER with other cities worldwide

In order to assess the spatial heterogeneity of our results, the average ERs obtained here were compared with those reported in previous studies in cities of North America [START_REF] Bon | Measurements of volatile organic compounds at a suburban ground site (T1) in Mexico City during the MILAGRO 2006 campaign: measurement comparison, emission ratios, and source attribution[END_REF][START_REF] De Gouw | Chemistry of Volatile Organic Compounds in the Los Angeles Basin: Formation of Oxygenated Compounds and Determination of Emission Ratios[END_REF][START_REF] De Gouw | Increasing atmospheric burden of ethanol in the United States[END_REF], Europe [START_REF] Borbon | Emission ratios of anthropogenic volatile organic compounds in northern mid-latitude megacities: Observations versus emission inventories in Los Angeles and Paris[END_REF][START_REF] Mcmeeking | Airborne measurements of trace gases and aerosols over the London metropolitan region[END_REF][START_REF] Von Schneidemesser | Global comparison of VOC and CO observations in urban areas[END_REF], Asia and Middle East (Salameh et al., 2016;[START_REF] Simpson | Air Quality in Mecca and Surrounding Holy Places in Saudi Arabia During Hajj: Initial Survey[END_REF][START_REF] Wang | A temporally and spatially resolved validation of emission inventories by measurements of ambient volatile organic compounds in Beijing, China[END_REF].

For each comparison, seasonal means were applied considering the same season in the studied city.

For those ERs relative to C 2 H 2 , discrepancies with aromatics were found, which were higher in Paris, Beirut (summer and winter) and Mecca, by factors of 3, 2.5 and 1.2, respectively (Figure S4). In SPM, alkenes ERs showed higher values when compared with those in London (by a factor of 2.4), Beirut (by a factor of 1.3) and slightly higher than those in Mecca and Beijing. Regarding alkanes, ERs in SPM presented higher values than those in Beijing (within a factor of 2.3) and Beirut (within a factor of 1.7). However, the CO versus C 2 H 2 ratio was lower in SPM when compared with that in the cities investigated. The VOCs versus CO ERs were also reported in some megacities previously discussed or estimated when CO data was provided. Additionally, ERs for oxygenated compounds (acetaldehyde, formaldehyde and ethanol) were included in the comparison when available. Figure 8 shows the global ΔVOC/ΔCO ERs comparison between SPM and other cities worldwide. In general, a high consistency with northern mid-latitude cities (Los Angeles and Paris) was found, especially for aromatics (benzene, C 8 -aromatics) and alkanes (butanes, pentanes and n-octane). ERs reported in Beijing and Mexico presented a moderate consistency when compared with those obtained in São Paulo for C 9 -aromatics, benzene, n-nonane and n-pentane. However, a few differences were found especially for alkenes, being higher in SPM by factors of 3 to 12. Mexico also presented higher ERs of light alkanes (by factors of 2 to 6), especially for those NG/LPG-related compounds, whose high ambient concentrations were already pointed out in a previous study [START_REF] Bon | Measurements of volatile organic compounds at a suburban ground site (T1) in Mexico City during the MILAGRO 2006 campaign: measurement comparison, emission ratios, and source attribution[END_REF]. Regarding the ERs comparison with Middle East cities, Beirut and Mecca, dispersed correlations were obtained. São Paulo presented higher aromatic ERs when compared to Beirut, by factors of 2 to 6. In general, the largest differences were usually observed in SPM for alkanes and alkenes ERs, especially for propane, butanes, ethylene, propylene and butenes. The larger ERs of these species in SPM could be related to the large biofuel usage in the megacity affecting the distribution and intensity of the VOCs emissions. Regarding oxygenated compounds, higher ERs within factors of 1.2 to 5.8 were observed in SPM. As already discussed in section 3.4, the dissimilar profile also observed for ERs could be associated with a difference in fuel consumption and acetaldehyde emissions by ethanol burning process. Interestingly, similar ethanol ERs were found between São Paulo and Los Angeles and in general a comparable emission profile between the megacities is observed (Figure 8). This good agreement suggests that ethanol emissions are mainly related to road transportation in São Paulo and despite the extended use of biofuels, the distribution of the VOCs emissions is analogous to the ones observed in other places where ethanol has been used as a fuel additive. Nevertheless, other sources of ethanol such as solvent and volatile chemical usage cannot be ignored, and they need to be further investigated.

VOCs emissions in SPM: a comparison with a global emission inventory

In South America, the observations of atmospheric pollutants are deficient, and few cities have implemented air quality monitoring programs. Likewise, the availability of VOCs data in terms of speciation, temporal and spatial resolution, remains limited. As a result, regional emission inventories are scarcely developed or missing in most of the Latin American countries. Most of them, only estimated CO, NOx and particulate matter emissions from the road transportation sector. Here we estimate the speciated VOCs emissions from the ERs established in SPM and then we compare to those provided by the global emission inventory, EDGAR V4.3.2. Since the vehicular emissions were pointed out as the main sources of air pollution in SPM, we evaluate the VOCs contribution for the road transport sector. The regional emission inventories developed by CETESB, provide information about CO emissions detailed by type of fuel and vehicular categories. This data was used to estimate total CO emissions in São Paulo and later applied to estimate the VOC emissions by using the ERs (ΔVOC/ΔCO) established in our study. Nevertheless, since CO emissions could have high uncertainties, our estimation should be considered as a lower limit, implying an underestimation of VOC emissions. Figure 9 shows the comparison between the VOCs emissions estimated by the global inventory and the ones calculated from our ERs on year basis. The total annual VOCs emissions related to the road transport sector in EDGAR inventory were estimated to be 22 Gg year -1 in SPM, which represents almost 30 percent lower than the annual emissions obtained via our ERs results (32Gg year -1 ).This difference is expected to be a lower limit regarding the fact that our study only considers 53 VOCs species for the road transport sector. In terms of VOCs speciation, main differences were obtained in the estimation of oxygenated emission, such as aldehydes (VOC21 and VOC22) and ethanol (VOC1). Our ERs estimation presented higher values by factors 6 and 7 respectively, when compared with EDGAR contributions. These results suggest that the extensive use of biofuels in Brazil has greater contribution on the road transport emissions than that estimated by the global inventory. Inconsistencies were also observed for the heavy alkanes (VOC6) which presented greater emissions in the global inventory by factors of 2.3. Similarly, higher contributions were observed for most of the aromatic species, which together with heavy alkanes dominate the global inventory profile. On one hand, this disparity could be associated to the restricted number of heavy alkanes measured in our study and the absence of VOCs of intermediate volatility, which are significantly emitted by vehicles burning diesel. On the other hand, this difference suggests that conventional gasoline and diesel emission profiles have been prevailing the road transportation VOCs profile estimated by the global inventory. Although the differences in VOCs distribution among the inventory and our estimation are not significant, they can have a substantial impact in terms of atmospheric reactivity. Even though some VOC families present low OH reactivity, they can have an important contribution in the formation of secondary organic aerosols, as is the case of heavy alkanes and aromatic compounds. Thus, it is necessary to well represent the contribution of each VOC family to better evaluate their effects on the urban atmosphere. Figure 9b shows our VOCs emissions contribution weighted by k OH and compared with those reported by the global inventory. Thus, averaged k OH rate constants were obtained for each VOCs family and then multiplied by an assumed emission of 100 tonnes. Despite that discrepancies in the mass profile of VOC6 were fairly large (Figure 9c), heavy alkanes have relative low reaction constants which do not produce a great difference in terms of OH reactivity. However, for other VOC families a small difference in mass can lead to a high increase in reactivity. For instance, despite the minor differences observed in the alkenes mass emissions (VOC12), these discrepancies are remarkable when weighted by the k OH constants, dominating all the VOCs reactivity profiles (Edgar and ERs estimation). It is important to note that we have only evaluated here the VOCs reactivity in OH-basis, nonetheless other alkenes reaction pathways should be considered, such as ozone and nitrate reactions which dominate the night-time removal processes of these species [START_REF] De Gouw | Chemistry of Volatile Organic Compounds in the Los Angeles basin: Nighttime Removal of Alkenes and Determination of Emission Ratios[END_REF]. On the other hand, the high ethanol levels observed by our estimation do not seem to have a substantial direct impact on the k OH contribution.

Nevertheless, ethanol oxidation is an important source of aldehydes in the atmosphere, thus its high concentrations could lead to an indirect increase of atmospheric reactivity. Indeed, despite the moderate contribution of aldehydes species (VOC21 and VOC22) on the total emission mass (6.3%), they represent a meaningful input on the k OH profile. Furthermore, our estimation only contemplates the emissions from two aldehydes species (formaldehyde and acetaldehyde) which should be considered as a lower limit. It should be emphasized that despite the good agreement between observed emissions and inventory total estimations, the VOCs speciation is still not well represented in global inventory. VOCs emission inventories are fundamental inputs of air quality models, playing a meaningful role in the estimation of air pollution and secondary pollutants formation. Consequently, to ameliorate the prospective VOCs emission estimations, more efforts are needed in the development of representative local and regional ERs, the collection of comprehensive activity data and the better speciation of emission sources. These findings are important for decision makers and public policy makers in Brazil who now intend to implement the control of hydrocarbon emissions considering the reactivity of these species.

Conclusions

In this work, we analysed an extensive dataset of VOCs obtained by several field campaigns in São Paulo megacity (SPM) over the last decade. Our long-term measurements of ethanol, aldehydes and NMHCs were complemented with previous short-term field campaigns performed in different sampling sites in SPM. Our study provides a comprehensive observational database for the assessment of local and regional VOCs levels in SPM, the evaluation of emission inventories considering the observations performed in the last decade and the implications of the large use of biofuels in one of the most important megacities of the world.

The VOCs urban enhancement emission ratios (ERs) related to CO and acetylene were successfully derived from ambient measurements in summer and winter for three years of measurements, by applying the linear regression fit method. Our results depict the high concentrations of ethanol and ethanol emission-related VOCs in the urban atmosphere. The ERs of ethanol relative to CO derived from the observations showed the different sources and processes being responsible for the emission of this compound into the atmosphere. Our results bring to light that evaporative emissions are a substantial source of ethanol that needs to be contemplated. Analysing the relation between fuel consumption and aldehydes ER, our results suggest a change in the emission profiles of acetaldehyde and formaldehyde when the ethanol sales over passed the gasoline ones. These compounds are one of the main limitations associated to "clean" biofuel combustion emissions and their high concentrations in Brazilian atmospheres were commonly associated with the large consumption of ethanol. However, our findings suggest that other sources than vehicular emissions could be responsible for the presence of oxygenated compounds in the atmosphere, such as secondary formation processing. In general, the ERs derived from the observations did not show significant seasonality regardless of the species, unlike the seasonality usually observed in other cities. We compared the composition of VOCs emissions with those from other traffic studies and generally a good agreement was found with a few notable exceptions. When compared with tunnel emissions, higher ERs were observed in the urban background site for 40% of the species evaluated. Those results suggest not only the strong contribution of vehicular sources but also the influence of other sources in the urban background.

When compared with other cities worldwide, a good consensus met the ERs obtained for Los Angeles.

These findings highlight that none changes are observed in the VOCs distribution by the extensive use of biofuels in SPM.

Finally, the establishment of ERs allowed the estimation of VOCs emissions by the road transportation sector. The comparison with the global emission inventory has shown an underestimation of oxygenated compounds (aldehydes and ethanol) by a factor of 6. Those discrepancies have consequences on the atmospheric reactivity and on the estimation of the effects that vehicular emissions can have on the regional air quality. At a local and regional level, long term measurements integrating different sampling sites and regional-specific tracers, are of great interest in order to provide more reliable information to improve the VOCs magnitude and speciation of emission estimations.

the data supported by the São Paulo State Environmental Agency (CETESB-www.cetesb.sp.gov.br) and EDGAR inventory (https://edgar.jrc.ec.europa.eu/). with those reported at Los Angeles [START_REF] De Gouw | Chemistry of Volatile Organic Compounds in the Los Angeles basin: Nighttime Removal of Alkenes and Determination of Emission Ratios[END_REF], Paris [START_REF] Borbon | Emission ratios of anthropogenic volatile organic compounds in northern mid-latitude megacities: Observations versus emission inventories in Los Angeles and Paris[END_REF]; Beijing [START_REF] Wang | A temporally and spatially resolved validation of emission inventories by measurements of ambient volatile organic compounds in Beijing, China[END_REF], Mecca [START_REF] Simpson | Air Quality in Mecca and Surrounding Holy Places in Saudi Arabia During Hajj: Initial Survey[END_REF]; Beirut (Salameh et al., 2016a) and Mexico [START_REF] Bon | Measurements of volatile organic compounds at a suburban ground site (T1) in Mexico City during the MILAGRO 2006 campaign: measurement comparison, emission ratios, and source attribution[END_REF]. Markers are colourcoded by VOC chemical group; solid line represents the 1:1 relationship between sampling sites compared and dashed lines represent the difference by a factor of 2.

Graphical abstract

Highlights Homogeneous VOCs distribution to other cities despite higher concentrations by factors of 2 to 10. No significant seasonality in emission ratios regardless of the species Ethanol measurements show a strong impact of fuel evaporation processes Multiyear acetaldehyde ER displayed the impact of a higher biofuel consumption in SPM Consistency with Edgar inventory up to 75%, however inconsistencies in the speciation profile

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Figure 3 .

 3 Figure 3. Mean and standard deviation for the VOCs concentrations observed by long-term measurements in Sao Paulo and compared with those levels in other cities worldwide. Green squares represent the average NMHC concentrations obtained for 4-years of online measurements and the error bars display their standard deviation. Ethanol and aldehydes average values (green squares) are those obtained at the urban background by the campaigns developed in 2013-2014 and 2012-2014, respectively. VOC data from other cities was obtained from previous studies in Los Angeles, Paris, London and Beijing.

Figure 4 .

 4 Figure 4. Seasonal average VOC relative to CO (above) and acetylene (below) emission ratios, obtained for 2013-2015 measurements. Solid line represents the 1:1 relationship between seasons and dashed lines represent the difference by a factor of 2.

Figure 5 .Figure 6 .

 56 Figure 5. Average emission ratios of VOC/CO derived from urban background (UB) observations and compared with those obtained at (a) an urban traffic (UTr) site and b) an urban road-tunnel (UT) in SPM. Color-coded markers represent VOC families, solid line represents the 1:1 relationship between sampling sites compared and dashed lines represent the difference by a factor of 2 Figure 6. Ethanol measurements and emission ratios obtained in different campaigns in MASP. a) time series of ethanol and CO concentrations observed at urban traffic site (UTr), b) scatterplot of ethanol versus CO measurements performed at UTr site, purple line represents the ER obtained at the UTr site, dark blue line the ER obtained for evaporative emissions at a residential garage and light blue line represents the ER obtained from total emission sources at a residential garage and c) scatterplot of ethanol and CO observations at a residential garage integrating daytime data in light blue (exhaust + evaporative emissions) and night-time data (evaporative emissions) in dark blue.

Figure 7 .

 7 Figure 7. Aldehydes ERs (a) and fuel sold (b) in SPM between 2012 and 2016. Figure a) represents the ERs of acetaldehyde and formaldehyde versus CO obtained by the LRF on annual basis, b) represents the total fuel sold in m3 of diesel, gasohol (25-27% anhydrous ethanol + 75-73% gasoline), total ethanol (hydrous and anhydrous) and biodiesel consumptions for SPM, and c) shows the correlation between acetaldehyde and formaldehyde versus CO for all the years under analysis, colour-coded by winter and summer measurements.

Figure 8 .

 8 Figure8. Comparison of VOC to CO (ppb/ppm) emission ratios derived at São Paulo urban background site (UB) with those reported at Los Angeles[START_REF] De Gouw | Chemistry of Volatile Organic Compounds in the Los Angeles basin: Nighttime Removal of Alkenes and Determination of Emission Ratios[END_REF], Paris[START_REF] Borbon | Emission ratios of anthropogenic volatile organic compounds in northern mid-latitude megacities: Observations versus emission inventories in Los Angeles and Paris[END_REF]; Beijing[START_REF] Wang | A temporally and spatially resolved validation of emission inventories by measurements of ambient volatile organic compounds in Beijing, China[END_REF], Mecca[START_REF] Simpson | Air Quality in Mecca and Surrounding Holy Places in Saudi Arabia During Hajj: Initial Survey[END_REF]; Beirut(Salameh et al., 2016a) and Mexico[START_REF] Bon | Measurements of volatile organic compounds at a suburban ground site (T1) in Mexico City during the MILAGRO 2006 campaign: measurement comparison, emission ratios, and source attribution[END_REF]. Markers are colourcoded by VOC chemical group; solid line represents the 1:1 relationship between sampling sites compared and dashed lines represent the difference by a factor of 2.

Figure 9 .

 9 Figure 9. Comparison of VOC road transport emission profiles for Sao Paulo Megacity (SPM) estimated from the measurements of this study (ER SPM) and the EDGAR v4.3.2 global inventory (Edgar SPM) (Huang et al., 2017). The profile analysis of EDGAR integrates the road transportation based on the sector activity for 2012. (a) Absolute emissions, in Gg yr-1, (b) relative mass weighted by kOH, (c) relative mass contribution calculated for each VOC family.

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8

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Figure 9

 9 Figure9

Table 1 .

 1 Instrumentation details and data used in this study

	Sampling	Instrument	Operating principle	Species	Time	Site	Reference
			/Technique	measured	resolution
	Online	Perkin Elmer	GC-FID	NMHCs	1 hour	urban	Dominutti et al.,
		Clarus 500 +		(55 species)		background	2016
		Turbo Matrix
		650 ATD
	Online	INNOVA	Photoacoustic infrared	Ethanol/	10 min	Traffic /	this study
		1421	detection	CO/CO 2		evaporative
						emissions /
						urban
						background
	Online	PTR-MS	Proton Transfer	Ethanol +	1 min	Traffic	Brito et al.,
			Reaction Mass	VOCs			2018
			Spectrometry; H3O+
			reagent ions
	Offline	Shimadzu LC-	HPLC -UV + 2,4 -	Aldehydes	2 hours	urban	Nogueira et al.,
	Sorbent	10AD	DNPH derivatization			background	2014
	tubes
	Offline	Shimadzu LC-	HPLC -UV + 2,4 -	Aldehydes	2 hours	Road tunnel	Nogueira et al.,
	Sorbent	10AD	DNPH derivatization				2015
	tubes
	Offline	Shimadzu LC-	HPLC -UV + 2,4 -	Aldehydes	24 hours	Traffic	Nogueira et al.,
	Sorbent	10AD	DNPH derivatization				2017
	tubes
	Offline	Varian 3800 +	GC-MS	NMHCs (69	2 hours	Traffic	Alvim, 2013;
	Canisters	Saturn 2000		species)			Alvim et al.,
							2016, 2011
	Offline	Varian 3800 +	GC-MS	NMHCs (69	2 hours	urban	Alvim, 2013;
	Canisters	Saturn 2000		species)		background	Alvim et al.,
							2016, 2011
	Offline	Varian 3800 +	GC-MS	NMHCs (69	2 hours	Road tunnel	Alvim, 2013;
	Canisters	Varian Saturn		species)			Martins et al.,
		2000 ion trap					2006
	Offline	Perkin	GC-MS	Ethanol +	1-2 hours	Road tunnel	Colón et al.,
	tubes and	Elmer ATD		NMHCs			2001
	canisters	400 + Varian
		Star 3400 CX
		+ Varian
		Saturn 2000
		ion trap CA)
	Online	Thermo 48i	Infrared Photometry	CO	hourly	traffic/ urban	(CETESB,
						background	2018)
	Online	Thermo 42i	Chemiluminescence	NOx	1 hour	traffic/ urban	(CETESB,
						background	2018)

Table 2 .

 2 Average and standard deviation of VOC emission ratios obtained in Sao Paulo megacity related to acetylene (VOC/C2H2) and related to CO (VOC/CO) in summer and winter for 3 years of data. Figure 1. Location and extent of São Paulo Megacity (SPM) and São Paulo Metropolitan area (MASP) in Sao Paulo State and Brazil.Figure2. Data availability and sampling times of the various VOCs measurements analysed in this study. Continuous lines represent online measurements, dashed lines represent the off-line continuous measurements and markers represent the data obtained by short term campaigns. More instrumentation details can be found in Table1.

Acknowledgments

The authors gratefully acknowledge the financial support from Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP, São Paulo Research Foundation; Grant nos. 15/50128-9,08/58104-8 and 11/18777-6) as well as from the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES, Office for the Advancement of Higher Education). The authors also thankfully acknowledge the PVE-CAPES program (Project number: 88881.068087/2014-01 for A. Borbon and P. Dominutti international exchanges). We thank Journal Pre-proof J o u r n a l P r e -p r o o f

Authors contributions

PD, TN and AF designed the project and field campaigns; PD and TN operated, calibrated and performed QC/QA of instrument measurements; all authors contributed to the interpretation of data; PD and AB led the manuscript preparation, with TN and AF contributing and critically reviewing the paper.

Summer