Method for estimating the concentration of an analyte in the air

Abstract

Method for establishing a concentration map of an analyte in a geographical area comprising measurement stations (11n), the method comprising the following steps: a) spatial meshing of the geographical area into different cells (Mi); the method being characterized in that it comprises: b) association of measurement stations to each cell; c) assignment, in each spatial cell, of a weighting factor () defined as a function of a distance between the cell and each measurement station associated with the cell, the weighting factor being less than or equal to a maximum value ().d) at different times, and for different grid cells: di) consideration of a modeled concentration of the analyte ( ); d-ii) consideration of a measured concentration of the analyte ( ) by each measurement station (11n) associated with the grid cell, so as to obtain, by interpolation, an interpolated concentration ( ) of the analyte in the grid cell; d-iii) estimation of a concentration of the analyte ( ) in the grid cell, by combining the modeled and interpolated concentrations. Figure 1B.

Description

Title of the invention: Method for estimating a concentration of an analyte in air Technical field

[0001] The technical field of the invention is the estimation of a concentration of an analyte in the air. The invention is particularly suitable for obtaining a map in large areas, for example areas comprising several cities. PRIOR ART

[0002] Simulation tools exist that allow air pollution to be modeled on a large scale. In Europe, the CAMS (Copemicus Atmosphere Monitoring Service) system is a tool for modeling the atmospheric concentration of air pollutants, essentially based on observations made by satellites compared with ground measurements. The observations and measurements are combined to establish a numerical model, taking into account meteorological data or other types of data provided by the satellites. The concentrations resulting from the model are easily accessible to the public. They are intended to be used for public or commercial exploitation purposes. They make it possible to estimate, over a given geographical area, a spatial distribution of the concentration of an air pollutant.

[0003] This type of model makes it possible to obtain data with a broad geographical coverage, on the scale of a country, a continent, or even on a global scale. However, such a model does not take into account local variability.

[0004] Furthermore, there are measuring stations, operated by operators, in particular public or institutional operators, which provide regular measurements, known as reference measurements, of pollutant concentrations. Such measuring stations have been deployed on a large scale, in extensive geographical areas, on the scale of countries or continents.

[0005] The inventors propose a method for using modeled data resulting from a public database, such as the database from CAMS, in order to obtain a more precise map, taking into account local variability. An advantage of the method is that it does not require excessive computing power. It is then possible to update the map regularly, for example every hour. Statement of the invention

[0006] A first object of the invention is a method for establishing a mapping of concentration of an analyte, likely to be present in the air, in a geographical area comprising measuring stations, configured to measure the analyte, the measuring stations being distributed in the geographical area, the method comprising the following steps:

[0007] - a) spatial meshing of the geographical area in different meshes;

[0008] the method being characterized in that it comprises, at a measurement instant:

[0009] - b) association of measurement stations with each mesh; - c) allocation, to each mesh, of a weighting factor defined according to of a distance between the mesh and each measuring station associated with the mesh, the weighting factor being less than or equal to a maximum value; - d) at different times, and for at least one mesh: • (di) taking into account a modelled concentration of the analyte, the concentration resulting from the application of a numerical model modelling the concentration of the analyte in the geographical area; • d-ii) taking into account a measured concentration of the analyte by each measuring station associated with the mesh, so as to obtain, by interpolation, an interpolated concentration of the analyte in the mesh; • d-iii) estimation of a concentration of the analyte in the mesh, by combining the concentrations respectively modeled and interpolated, resulting respectively from sub-steps di) and d-ii), at least one of said concentrations being weighted using the weighting factor attributed to the mesh.

[0010] According to one embodiment, during step c), the weighting factor is higher the closer the mesh is to a measuring station (1 ln) with which it is associated. The concentration of the analyte in the mesh can then be estimated by a sum:

[0011] - a product of the interpolated concentration and the weighting factor assigned to the mesh; - a product of the modeled concentration and the complement to the maximum value of the weighting factor.

[0012] By complement is meant a difference between the maximum value and the weighting factor.

[0013] According to one possibility, each measuring station is located at a measuring point, in the geographical area. Step c) can then include:

[0014] - ci) assignment of a two-dimensional influence function to each measuring station, the influence function being centered on the measuring point corresponding to said measuring station, the influence function being de increasing as a function of distance from the measuring point; - c-ii) determination of the weighting factor as a function of the value, in each mesh, of a sum of the influence functions respectively assigned to each measuring station associated with the mesh.

[0015] Each influence function can for example follow a parametric statistical law, for example a Gaussian law.

[0016] In sub-step c-ii), the weighting factor can be determined based on a sum of the influence functions respectively assigned to each measuring station associated with the mesh.

[0017] According to one embodiment, when a mesh comprises a measuring station, during step c), the value of the weighting factor is the maximum value. In this case, sub-step c-ii) is implemented for the meshes not comprising a measuring station.

[0018] According to one embodiment, a minimum threshold value min is assigned to the weighting factors whose value is lower than said threshold value.

[0019] Preferably, each measuring station is considered not to be impacted by road traffic in the mesh comprising the measuring station.

[0020] The analyte may be a particle, for example a fine particle, or a molecule. It is generally an analyte considered to be an atmospheric pollutant.

[0021] Steps a) to d) are implemented by a processing unit comprising a microprocessor. They use concentrations measured by different measuring stations distributed throughout the geographical area. The objective sought is to obtain a more precise map than a map which would be obtained solely from the digital model.

[0022] Another object of the invention is a processing unit, comprising a microprocessor, the processing unit receiving input data comprising:

[0023] - concentrations of an analyte, in the air, measured by measuring stations, distributed in a geographical area; - modeled concentrations of the analyte in the geographical area, resulting from a numerical model;

[0024] the processing unit being programmed to implement a method which is the subject of the first subject of the invention from the concentrations respectively measured and modeled.

[0025] The invention will be better understood upon reading the description of the exemplary embodiments presented in the remainder of the description, in conjunction with the figures listed below. FIGURES

[0026] [Fig.1A] Figure 1A shows the main entities for implementing a method according to the invention.

[0027] [Fig.lB] [Fig.lB] shows the main steps of a method according to the invention.

[0028] [Fig.lC] [Fig.lC] shows diagrammatically two influence functions respectively assigned to two measuring stations.

[0029] [Fig.2A] [Fig.2A] represents measurement points, distributed in a geographical area, with each measurement point corresponding to a measurement station.

[0030] [Fig.2B] [Fig.2B] shows an interpolation of concentrations of an analyte measured by different measuring stations in the geographical area represented in [Fig.2A].

[0031] [Fig.3A]

[0032] [Fig.3B]

[0033] [Fig.3C]

[0034] [Fig.3D] Figures 3A, 3B, 3C and 3D show respectively:

[0035] - a distribution of measuring stations in a geographical area; - a spatial distribution of weighting factors in the geographic area shown in [Fig.3A]; - a spatial distribution of interpolated concentrations of an analyte, the interpolations resulting from concentrations measured by different measuring stations, in the geographical area; - a mapping resulting from a combination of the data represented in figures 3C and 3D.

[0036] [Fig.4A]

[0037] [Fig.4B]

[0038] [Fig.4C] Figures 4A, 4B and 4C show respectively:

[0039] - a spatial distribution of so-called complementary weighting factors; - a spatial distribution of concentrations of an analyte modeled by a digital model; - a mapping resulting from a combination of the data represented in Figures 4A and 4B.

[0040] [Fig.5] [Fig.5] shows a combination of the maps shown in Figures 3D and 4C.

[0041] [Fig.6A]

[0042] [Fig.6B]

[0043] [Fig.6C]

[0044] [Fig.6D]

[0045] [Fig.6E] Figures 6A to 6E are curves respectively obtained in a mesh of five different geographical areas, in this case in the states of Montana, South Carolina, England, New York City and the South Dakota. These curves show a comparison, as a function of time:

[0046] - of a concentration estimated by a numerical model; - a concentration resulting from an interpolation of concentrations measured by measuring stations; - of an estimated concentration according to the invention; - a reference concentration, present in the mesh considered, and not used for the estimation of the concentration according to the invention.

[0047] In Figures 2A, 2B, 3A to 3D, 4A to 4C and 5, the abscissa and ordinate axes correspond to spatial coordinates. In Figures 6A to 6E, the abscissa axis corresponds to time and the ordinate axis corresponds to measured or estimated concentrations. PRESENTATION OF SPECIAL EMBODIMENTS

[0048] A basic idea of ​​the invention is to improve the spatial resolution and accuracy of data from large-scale public digital models by using data measured by measuring stations deployed over a geographical area covering one or more countries, or even on the scale of a continent.

[0049] The invention is intended to be implemented by a processing unit 10, for example a computer, from resulting data, cf. [Fig.lA]:

[0050] - of a digital model 12, the latter being able to be, in a non-limiting manner, the CAMS model described in connection with the prior art; - a set of 11 measuring stations IL, 112, 1 ln, 1 In distributed in a given geographical area. N is an integer designating the number of measuring stations taken into account. n is an integer corresponding to a rank assigned to each measuring station.

[0051] The processing unit 10 implements an assimilation method, according to steps described in connection with [Fig.lB]. The objective of the method is to obtain a spatial map of the concentration of an analyte in the air. The analyte may be a molecule, for example a molecule usually considered to be polluting (CO2, CH4, O3, NO2), or a fine particle, usually designated by the acronyms PM10 or PM2.5, PM meaning particulate matter, the associated number corresponding to a diameter.

[0052] Generally, two types of measuring stations are distinguished, depending on their location in relation to road axes or dense urban areas. Some measuring stations, called "Traffic stations" (traffic stations), are heavily impacted by road traffic, while other measuring stations are considered not to be impacted by road traffic. The latter are referred to as "Background stations". Their measurements are considered to be representative of background pollution affecting a given geographical area, independently of local and fluctuating sources of pollution, in particular road traffic. While data from models can be established according to a regular spatial grid, measuring stations are not distributed regularly across a geographical area.

[0053] The inventors consider that the use of background measuring stations is recommended to improve the accuracy of measurements resulting from public models, as described in the prior art. It is indeed preferable to avoid the use of measurements from “traffic” type measuring stations, located near road axes, the latter being subject to excessive local variability.

[0054] Thus, the method implemented by the processing unit 10 considers as input, physical data, which comprise concentrations of an analyte respectively modeled by a numerical model 12 and measured by measuring stations 1 ln. The objective is to carry out a correction of the data resulting from the numerical model, taking into account the measurements carried out by the different measuring stations considered.

[0055] [Fig.2A] shows values ​​of the NO2 concentration measured by different background type measuring stations distributed across European countries, the Maghreb and the Middle East. The gray level depends on the measured concentration, see gray level scale. As indicated in the prior art, these measurements are provided by fixed measuring stations in a geographical area considered. Each measuring station lin is located at a measuring point Pn.

[0056] In [Fig.2A], we observe that the spatial distribution of the measuring stations is not uniform across a country or continent. However, it is possible to obtain a continuous spatial distribution of the concentration of the analyte by interpolating the concentrations measured by the measuring stations. We can thus obtain interpolated concentrations, according to a regular spatial grid, from the concentrations measured punctually by the measuring stations. [Fig.2B] shows an example of a map obtained by such an interpolation. The interpolation can, for example, be linear or polynomial. [Fig.2B] was obtained by taking into account a regular spatial grid of the geographical area considered, in this case Europe, without carrying out extrapolations. The geographical area subject to the interpolation is then delimited by the measurement points.

[0057] The method, the main steps of which are described in connection with [Fig.lB], aims to take into account such interpolated measurements to correct the data from the digital model.

[0058] Step 100: Meshing

[0059] This involves spatially meshing the geographical area considered. Preferably, the mesh is regular and makes it possible to define meshes M;, the index i corresponding to the spatial coordinate of each cell. Typically, a cell can be a quadrilateral with sides of a few kilometers. The size of the cell determines the spatial resolution of the mapping.

[0060] Step 110: Taking into account Sn(t) measurements carried out by 1 ln measuring stations, at a measurement time '. Each Sn(t) measurement is a concentration of an analyte measured by a 1 ln measuring station.

[0061] Step 120: Taking into account concentrations of the analyte from the numerical model 12 at the time These are modeled concentrations available over the entire geographical area considered.

[0062] Step 130: Discretization of the model: from the measurements of the digital model 12 and the mesh resulting from step 110, a modeled concentration Ce(t) is established in each cell M;. The modeled concentration can be an average value of the model at the level of each cell M;.

[0063] Steps 140 to 160 aim to use the measurements from the measuring stations to correct the modeled concentration C^t).

[0064] Step 140: Determination of influence functions

[0065] The objective of this step is to assign, to each measuring station 1 ln, a spatial influence function Gtl. The influence function Gn is a two-dimensional spatial distribution centered on the measuring point Pn, corresponding to the measuring station 1 ln. The value of the influence function Gn is maximum at the measuring point Pn. The influence function is decreasing around the measuring station, that is to say it decreases as a function of a distance from the measuring station. The influence function Gn makes it possible to quantify a correlation between a concentration of an analyte in a mesh M; with the concentration Sn of the analyte measured by the measuring station 1 ln. It is assumed that the closer the mesh M; is to the measuring station 1 ln, the higher the value of the influence function Gn.

[0066] The influence function is defined in different meshes of the geographical area considered. The influence function Gn is defined at least in each mesh M; with which the measuring station 1 ln is associated. Preferably, each influence function is defined in each mesh of the geographical area considered.

[0067] The influence function G„ can be established based on a parametric statistical law, for example a Gaussian law. At each mesh M;, the influence of the measuring station 1 ln is given by the value, in this mesh, of the influence function G„{i)

[0068] Figure IC is a representation, along one dimension, of the influence of two neighboring measurement stations lln, 1 ln+b in meshes Mi located between these two measurement stations. The two measurement stations are respectively located at two points Pn, Pn+b located in two meshes Mi=n, Mi=n+b The abscissa axis corresponds to spatial coordinates along one dimension, each mesh being represented by a brace. The two influence functions Gn and Gn + ! respectively assigned to each measuring station are represented. The y-axis corresponds to the value of each influence function. The value of each influence function Gn is fixed at a maximum value max at the measuring point Pn corresponding to the location of the measuring station 1 ln. The maximum value max can be identical for each influence function G^ by being for example equal to 1.

[0069] Each mesh M; is associated with all or part of the measuring stations 1 ln present in the geographical area considered. When a mesh M; is associated with a measuring station 1 ln, the influence function Gn of the measuring station 1 ln is defined in the mesh. In the example described, each mesh M; is associated with all the measuring stations in the geographical area.

[0070] Step 145: Assigning a weighting factor to each mesh

[0071] Each influence function can be summed to obtain a cumulative influence function W. In each mesh M, the value Wi of the cumulative influence function W corresponds to the influence, in the mesh, of all the measuring stations associated with the mesh.

[0072] This step is shown in Figures 3A and 3B. Figure 3A represents a spatial distribution of measuring stations. At each position of a measuring station, the same maximum value ma is assigned, for example equal to 1. A zero value is assigned outside of the points not corresponding to a measuring station. Figure 3B was obtained by applying Gaussian smoothing to Figure 3A. Applying such smoothing makes it possible to assign a Gaussian influence function to each measuring station, and to obtain a cumulative influence function, as previously described. In Figure 3B, the cumulative influence function W has a value between 0 and 1. The cumulative influence function can be discretized, at the level of each mesh M;, so as to obtain a weighting factor H\(f) at the level of each mesh. Note that the maximum value max (1 in this example) is the same for each measuring station.

[0073] Preferably, following Gaussian smoothing, it can be imposed that each weighting factor is equal to the maximum value max (in this case 1) when the mesh Mi comprises a measuring station.

[0074] Generally speaking, steps 140 and 145 make it possible to determine a weighting factor W / G0 at the level of each mesh M;, the latter being all the higher as the associated mesh M; is close to measuring stations 1 ln. If we consider an average distance between a mesh and the measuring stations associated with it, the weighting factor of the mesh is all the higher as the average distance is high.

[0075] The value of the weighting factor h\(0 assigned to a mesh M; can be constant over time. It can also vary, for example following a modification of the reference stations associated with the mesh.

[0076] According to one possibility, a minimum threshold value min is defined, which is assigned to the weighting factors whose value is lower than said threshold. This allows for minimal consideration of the interpolated concentrations, as described below.

[0077] Step 150: interpolation

[0078] During this step, the concentrations Sn(t} measured by the measuring stations 1 ln are interpolated, so as to obtain interpolated concentrations at the level of each mesh M;. [Fig.3C] represents the result of such an interpolation. [Fig.3C] is similar to [Fig.lB].

[0079] Step 160: correction of the values ​​from the model.

[0080] During this step, the modeled concentrations C^t) resulting from the discretization of the numerical model at the level of each mesh are corrected in order to take into account the interpolated concentrations 5 / . The correction takes into account the weighting factors w,( / ) defined on each mesh during step 145.

[0081] Step 160 makes it possible to obtain corrected concentrations such as:

[0082] [Math.l] C / z) = C £ -(r) ( max - w^t) ) + (t) (1)

[0083] In the example considered, max = 1, which gives

[0084] [Math.2] c / z) = c / r) ( 1 -

[0085] Obtaining the corrected values ​​c using expressions (1) or (2) reflects the fact that the weighting factors defined in each mesh M; quantify a level of confidence that is given to the concentrations S^t) interpolated on the basis of the measurements Sn( t) carried out by the measuring stations 1 ln. The higher the value of the weighting factor, the greater the confidence that is given to the interpolated concentrations, to the detriment of the importance attributed to the modeled values ​​C^t) resulting from the model 12.

[0086] Thus, in a mesh Mi far from measuring stations 1 ln, the weighting factor >^,(0 is low: the corrected value is close to the modeled value C^t). Conversely, in a mesh M; close to one or more measuring stations, the corrected value is strongly impacted by the interpolated measurement

[0087] Figure 3D shows a mapping obtained by performing a product, point by point, of the interpolated values ​​Sj(t\ represented in Figure 3B, with the factors of weightings shown in Figure 3C. Each point in Figure 3D corresponds to the second term of equation (2): w,(05,(0.

[0088] Figure 4A corresponds to concentrations of an analyte resulting from the CAMS model, discretized at the level of each mesh. Figure 4B shows a mapping of complementary weighting factors, i.e. of quantities 1 - H',(0. Figure 4C is a mapping obtained by performing a product, point by point, of the concentrations C,(0, represented in Figure 4A, with the complementary weighting factors 1-^,(0 represented in Figure 4B. Each point in Figure 4C corresponds to the first term of equation (2): ( 1 - w^t) ) .

[0089] Figure 5 represents a point-by-point sum of Figures 3D and 4C. This is a mapping of corrected values ​​q 0 as explained in expression (2).

[0090] Steps 110 to 160 can be repeated in several successive measurement moments.

[0091]

[0092]

[0093] Experimental tests The inventors implemented the method described in connection with steps 100 to 160 in different geographical areas, having different densities of measuring stations. In each geographical area, they selected a grid cell comprising a measuring station. The latter is used as a reference measurement. In each selected grid cell, they compared, for at least one analyte: - the discretized concentrations C^t) resulting from the application of the CAMS model; - interpolated concentrations 5,(0 resulting from an interpolation of the concentrations measured by measuring stations present in the geographical area, not taking into account the measuring station used as a reference; - the concentrations corrected according to the invention; - the reference concentrations measured by the measuring station used as a reference, and not taken into account during the interpolation. Figures 6A to 6E represent, in different geographical areas, the respective evolutions, as a function of time, of the concentrations C^t) (curves a), 5,(0 (curve b), c (curve c), and (curve d). On each of these curves, the ordinate axis, on the left, corresponds to the concentration (pg / m3), and the abscissa axis corresponds to the time course (dates in year-month-day format). Figures 6A to 6E also show the value of the weighting factor taken into account (dotted curve - ordinate axis on the right).

[0094] The weighting factor can vary over time, depending on the number of measuring stations taken into account in the geographical area examined. The closer the value of the weighting factor is to 1, the closer curve c (representing c) is to curve b (representing or even merged when the weighting factor is equal to 1 (see Figures 6C and 6D). The lower the value of the weighting factor, the closer curve c (representing Q(0) is to curve a (representing Q(0).

[0095] In each figure, the concentrations C^f) and c (t) were compared with the reference concentration. The mean square error was determined. (RMSE - Root-Mean-Square Error).

[0096] In Figure 6A, the geographical area considered was the US state of Montana, the analyte being PM2.5 particles with a diameter less than or equal to 2.5 pm. Comparisons of Cz(0 and c with 'cs reference concentrations result in RMSEs of 13.0 and 9.9 respectively.

[0097] In Figure 6B, the geographic area considered was the state of South Carolina, with the analyte being ozone. Comparisons of C^t) and with 'cs reference concentrations result in RMSEs of 25.3 and 14.2, respectively.

[0098] In Figure 6C, the geographical area considered was England, the analyte being ozone. Comparisons of Qf ?) and C-(t) with 'cs reference concentrations result in RMSEs of 50 and 35.6 respectively.

[0099] In Figure 6D, the geographic area considered was New York City, with the analyte being PM2.5 particles with a diameter less than or equal to 2.5 pm. Comparisons of C^t) and with the reference concentrations result in RMSEs of 10.6 and 7, respectively.

[0100] [Fig.6D] is representative of a geographical area with a high density of measuring stations. In this type of geographical area, due to this density, the correction is particularly effective. Figures 6A to 6C are representative of a moderate density in the distribution of measuring stations. The implementation of the method makes it possible to significantly improve the accuracy of the concentration estimation.

[0101] Tests were carried out in geographical areas with a low density of measuring stations. In Figure 6E, the geographical area considered was the US state of South Dakota, the analyte being PM2.5 particles with a diameter less than or equal to 2.5 pm. Comparisons of C^t) and £ 0 with the reference concentrations C , result in RMSEs of 8.6 and 8.1 respectively. Also, even when a mesh is relatively isolated from measuring stations, the process allows a relevant correction of the modeled concentrations.

Claims

Claims

1. Method for establishing a concentration map of an analyte, likely to be present in the air, in a geographical area comprising measuring stations (lln), configured to measure the analyte, the measuring stations being distributed in the geographical area, the method comprising the following steps: - a) spatial meshing of the geographical area in different meshes (Mi); the process being such that it comprises, at a measurement time ('): - b) association of measuring stations with each mesh; - c) allocation, to each mesh, of a weighting factor ( w((z)) defined as a function of a distance between the mesh and each measuring station associated with the mesh, the weighting factor being less than or equal to a maximum value ( max^ - d) at different times, and for at least one mesh: • di) taking into account a modelled concentration of the analyte (Q( / )), the modelled concentration resulting from the application of a numerical model (12), modelling the concentration of the analyte in the geographical area; • d-ii) taking into account a measured concentration of the analyte (^(Z)) by each measuring station (lln) associated with the mesh, so as to obtain, by interpolation, an interpolated concentration of the analyte in the mesh; • d-iii) estimation of a concentration of the analyte (q in the mesh (Mi), by combining the concentrations respectively modeled (Q (f)), and interpolated (S) (?)), resulting respectively from sub-steps di) and d-ii), at least one of said concentrations being weighted using the weighting factor (wXO) attributed to the mesh; the method being characterized in that - the weighting factor (wz ( / )) is higher the closer the mesh (Mj) is to a measuring station ( 1 ln) with which it is associated; - during sub-step d-iii), the concentration of the analyte in the mesh (£.^) is estimated by a sum: • of a product of the interpolated concentration (S) (0) and the weighting factor (H'; (?)) attributed to the mesh; • of a product of the modeled concentration (Q (r)) and the complement to the maximum value (t)) of the weighting factor.

2. Method according to any one of the preceding claims, in which each measuring station (1 ln) is located at a measuring point (Pn), in the geographical area, and in which step c) comprises: - ci) assignment of a two-dimensional influence function (Gn) to each measuring station (1 ln), the influence function being centered on the measuring point corresponding to said measuring station, the influence function being decreasing as a function of a distance from the measuring point; - c-ii) determination of the weighting factor (H'XO) as a function of the value, in each mesh, of a sum of the influence functions (Gn), respectively assigned to each measuring station (1 ln) associated with the mesh.

3. Method according to claim 2, wherein in sub-step ci), each influence function (G^ follows a parametric statistical law, for example a Gaussian law.

4. Method according to any one of claims 2 or 3, wherein in sub-step c-ii), the weighting factor (w,(f)) is determined as a function of a sum of the influence functions respectively assigned to each measuring station associated with the mesh (M;).

5. A method according to any preceding claim, wherein, when a mesh comprises a measuring station, when

6.

7.

8.

9. step c), the value of the weighting factor (wf- (ï)) is the maximum value Method according to any one of the preceding claims in which each measuring station (1 ln) is considered not to be impacted by road traffic in the mesh comprising the measuring station. A method according to any preceding claim, wherein the analyte is a molecule or a particle. Method according to any one of the preceding claims, wherein steps a) to d) are implemented by a processing unit (10) comprising a microprocessor. Processing unit (10), comprising a microprocessor, the processing unit receiving input data comprising: concentrations of an analyte (Sn), in the air, measured by measuring stations (lln), distributed in a geographical area; modeled concentrations of the analyte (Q) in the geographic area, resulting from a numerical model; the processing unit being programmed to implement a method which is the subject of any one of claims 1 to 8 from the concentrations respectively measured and modeled.

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